ML20092M707
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| Issue date: | 07/31/1995 |
| From: | Additon S, Liu C, Theofanous T ENERGY, DEPT. OF |
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| DOE-ID-10460, NUDOCS 9510030239 | |
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{{#Wiki_filter:--- - - - - - - - - - - - - _ - - - - _ - _ _ - - - _ - - - - - - - _ - _ _ - - - - - _ - - _-_ _--__-_----- - [ [ [ DOE /ID-10460 IN-VESSEL COOLABILITY AND VOLUME 1 RETENTION OF A CORE MELT November 1994 July 1995 4 T.G. Theofanous, C. Liu, S. Additon, [ S. Angelini, O. Kymnininen, T. Salmassi [ 1 L E ] L [ [ Advanced l
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!g DOE /ID-10460 IN-VESSEL COOLABILITY AND VOLUME 1 ja RETENTION OF A CORE MELT
'I jl T.G. Theofanous, C. Liu, S. Additon, j S. Angelini, O. Kymslsinen, T. Salmassi ll l contributed appendices by: l F.J. Asfia and V.K. Dhir (UCLA), I il T.Y. Chu et al. (SNL), J. Rashid (ANATECH) L. Baker, Jr., C.C. Chu & J. Sienicki (ANL)
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! First Dmft: September 1993 il Final Draft: November 1993 PeerReview Version: November 1994 ll l PeerRe-Review Version: July 1995 Center for Risk Studies and Safety Department of Chemical and Nuclear Engineering l l University of California, Santa Barbara SantaBarbara,CA 93106 l Pmpared for the l , U. S. Department of Energy Idaho Operations Office CRE5 Under ANL Subcontract No. 23572401 I
PREFACE This is intended as the final version of DOF/ID-10460, addressing in-vessel retention as an accident management strategy for an AP600-like reactor design. The first volume is a revision of the peer review version first issued in November 1994. The second volume consists primarily of the peer review comments and our responses. Both volumes contain new technical material in the form of addenda (in the first volume) and new appendices (in the second). Some explanations are offered as follows: e To maintain scrutability with reference to the reviewer's comments, the original material in DOFJID-10460, including page numbering, was left untouched, except for a few typos. e Revisions were made either by means of minor addenda incorporated into the text without affecting page numbering, or by major addenda provided at the end of preexisting chapters or appendices in Volume I. All such addenda are clearly marked by being enclosed in double brackets, i.e., ((. . . )). A listing of the major addenda is provided at the end of this Preface. e Further additions were made in the form of new appendices in Volume II. They are marked by the double bracket notation, also, and a listing is provided at the end of this Preface. e The as-received review comments are collected in Appendix S. Point-by-point responses are provided in Appendix T. For convenience, this material is also presented in a topic-by-topic form collated in Appendix U. Both appendices (T and U) also contain overview statements (General Comment and Highlights) on each reviewer's comments. e The new round of review comments received, and any responses, if warranted, will make up Appendix V in the final document. LISTING OF MAJOR ADDENDA AND NEW APPENDICES Chapter 3. Summary of New ULPU Runs ) Chapter 4. Investigation of the Tearing Model of Failure l Chapter 5. Locally Enhanced Heat Transfer Due to the Laminar Boundary Layer Chapter 7. Summary of New System Effects Results and Parametric Studies Chapter 9. Final Conclusions Appendix E.3. New ULPU Results on Flux Shape and Flow Rate Effects Appendix E.4. ULPU Configuration III Results Appendix J. Further Results on Long Term Eutectic Interactions Appendix K. The AP600 Insulation Design Appendix M. Cavity Flooding System (Modified) and Its Reliability Appendix O. Consideration of Meltdown Scenarios l Appendix P. Further Parametric and Sensitivity Studies Appendix Q. Detailed Results from Selected Cases Appendix R. Decay Heat Generation In the Metallic Layer iii
I I ABSTRACT l De efficacy of external flooding of a reactor vessel as a severe accident management strategy is assessed for an AP600-like mactor design. The overall approach is based on the Risk Oriented Accident Analysis Methodology, and the assessment includes consideration of bounding scenarios and sensitivity studies, as well as arbitrary parametric evaluations that allow l the delineation of the failure boundaries. The technical treatment in this assessment includes: I j (a) new data on energy flow from either volumetrically heated pools or non-heated layers on top, boiling and critical heat flux in inverted, curved geometries, emissivity of molten (superheated) samples of steel, and chemical reactivity proof tests, L (b) a simple but accurate mathematical formulation that allows prediction of thermal loads by means of convenient hand calculations, and (c) a detailed model programmed on the computer to sample input parameters over the un-certainty ranges, and to produce probability distributions of thermal loads and margins for departure from nucleate boiling at each angular position on the lower head. p Quantification of the input parameters is carried out for an AP600-like design, and the results of the assessment demonstrate that lower head failum is " physically unreasonable." Use of this conclusion for any specific application is subject to verifying the required reliability of the L depressurization and cavity-flooding systems, and to showing the appropriateness (in relation to the database presented hem, or by further testing as necessary) of the thermal insulation design ! and of the external surface properties of the lower head, including any applicable coatings. De AP600 is particularly favorable to "in-vessel retention"-some ideas to enhance the assessment basis as well as performance in this respect, for applications to larger and/or higher power density reactors are also provided. L l
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CONTENTS PREFACE ........................................111
- ABSTRACT ........................................v:
NOMENCLATURE .....................................ix LIST OF ACRONYMS ....................,..............xi. ACKNOWLEDGEMENTS ................................. xiii
- 1. INTRODUCDON . . . . . . . . . ......................... 11
- 2. PROBLEM DEFINITION AND OVERALL APPROACH ,................. 21
- 3. THERMAL FAILURE CRUERIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
. 4. STRUCIURAL FAILURE CRITERIA .......................... 41
- 5. PARTrnON OF THERMAL ENERGY PLOW BY NATURAL CONVECTION ......... 5-1
- 6. PORMULATION OF THERMAL LOADS UNDER NA'IURAL CONVECTION . . . . . . . . . 6-1
- 7. QUANTIFICATION AND ASSESSMENT OF THERMAL LOADS UNDER NATURAL CONVECHON ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
- 8. QUANTIFICATION AND ASSESSMENT OF THERMAL LOADS UNDER JET IMPINGEMENT ................................. 8-1
- 9. CONCLUSIONS AND RECOMMENDATIONS ...................... 9-1
- 10. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10- 1 APPENDIX A. THE ROAAM AND PROCEDURES . . . . . . . . . . . . . . . . . . . . . . . A 1 I APPENDIX B. THE COPO EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . B-1 APPENDIX C. THE UCLA EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . C-1 APPENDIX D. THE MINI-ACOPO EXPERIMENTS ......................D-1 APPENDIX E. THE ULPU EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . E-1 APPENDIX F. THE CYBL EXPERIMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . F-1 APPENDIX O. CREEP CONSIDERATIONS FOR THE IDWER HEAD ..............G1 APPENDIX H. INDEPENDENT ANALYSIS OF MELT IMPINGEMENT . . . . . . . . . . . . . . H-1 APPENDIX !. THE EMISSIVITY OF THE STEEL LAYER , . . . . . . . . . . . . . . . . . . . I.1 APPENDIX J. CHEMICAL REACTIVITY TESTS ....................... J.1 APPENDIX K. THERMAL INSULATION DESIGN OPHONS ..................K-1 APPENDIX L. THERMAL-PHYSICAL PROPERTIES AND UNCERTAINTIES . . . . . . . . . . . L-1 APPENDIX M. CAVITY FLOODING AND RELATED FLOW PATHS . . . . . . . . . . . . . . . M 1 APPENDIX N. THE MELAD EXPERIMENT .........................N-1 APPENDIX O. CONSIDERATION OF "OTHER" PROPOSED SCENARIOS ............ 0-1 APPENDIX P. ADDIDONAL PARAMETRIC AND SENSITIVITY STUDIES . . . . . . . . . . . . P1 APPENDIX Q. DETAILED RESULTS FROM SELECTED CASES . . . . . . . . . . . . . . . . . Q-1 APPENDIX R. DECAY HEAT GENERATION IN THE METALLIC LAYER . . . . . . . . . . . . . R-1 APPENDIX S. REVIEWER LETTERS IN THE ORIGINAL ................... S-1 APPENDIX T. EXPERT COMMENTS AND AUTHORS' RESPONSES - POINT-BY POINT ..... T-1 APPENDIX U. EXPERT COMMENTS AND AUTHORS' RESPONSES - BY TOPIC . . . . . . . . U- l vii
f NOMENCLATURE A property group evaluated at " film" temperature, s 0.15k {(g#)/(av)}'/8 c, . heat capacity
- D. diameter Da ~ Dammk6hler number, s 4H2/k(T .,- Tg)
E. ' Young's modulus of elasticity Gr Grashof number, 's g#(Tm., - T )H8/v 2 4 y acceleration of gravity
'N depth of oxidic pool h' heat transfer coefficient I Impulse k thermal conductivity Nu . Nusselt number, = (gH)/k(Tm., - T 4)
P; pressure Pr Prandtl number, s v/a 4 volumetric heat generation rate g average heat flux at pool boundaries
- i. characteristic heat flux, = caf4 q' dimensionless heat flux, = g/(
fcur critical heat flux q.,(6) local heat flux across the vessel wall, at angular position 6 R reactor vessel, hemisphere radius Ra Rayleigh number, = {p#(T .,- Tg)H8}/(av) Ra' Rayleigh number (internal), s (g#4H5)/(kva) Re Reynolds number, s (UD)/(v) r radial coottlinate
'S surface area . ;
T temperatum T* dimensionless temperature, a T/f ; T" water saturation temperature !
'l' characteristic temperature, s (A/ca)s/s T. oxidic poolliquidus T ., maximum (or " bulk," if uniform) pool temperature U velocity V volume of oxidic pool )
Zr total thickness of ablated wall following a miocation event Z wall ablation rate ix
1 I-Greek a thermal diffusivity
# thermal expansion coefficient linear thermal expansion coefficient 6 thickness e emmisivity 6 polar angle on the lower head (see Fig. 2.1) 64 6,
polar angle of metal layer top polar angle of oxidic layer top l A latent head of fusion v kinematic viscosity v' Poisson Ratio p density a stress or Stefan-Boltzman constant 7 duration of main relocation event Subscripts I b bulk value i CHF critical heat flux cr crust value dn downward (over the hemispherical boundary) F failure condition i boundary value j based on jet properties t metal layer t, i inner metal layer boundary value t, m liquidus of the vessel wall in contact with metal layer t, o outer metal layer boundary value I, w at vessel wall in contact with metal layer m liquidus r core relocation quantity, or radial coordinate a radiative sink value s,i inner radiative sink surface value s, o outer radiative sink surface value up upward (over the flat boundary of the oxidic pool) v inner vessel wall (upper vessel only) w vessel wall value z axial coordinate 0 initial value 6 azimuthal coordinate X I i
I I LIST OF ACRONYMS ANATECH ANATECH Research Corporation ANL Argonne National Laboratory BC boiling crisis CEN Centre d' Etudes Nucleaires de Grenoble CHF critical heat flux CRSS Center for Risk Studies and Safety (at UCSB) CSNI Committee on the Safety of Nuclear Installations (under OECD) DOE Department of Energy EPRI Electric Power Research Institute FAI Fauske & Associates,Inc. FCI fuel-coolant interaction KfK Kernforschungszentrum Karlsruhe GmbH NRC Nuclear Regulatory Commission OECD Organization for Economic Cooperation and Development PWR Pressurized Water Reactor ROAAM Risk Oriented Accident Assessement Methodology SNL Sandia National Laboratories TMI-2 Three Mile Island, Unit II UCLA University of Califomia, Los Angeles UCSB University of California, Santa Barbara I I I I I b I . XI I
} ,)- ACKNOWLEDGEMENTS This work was supported under the ROAAM program carried out for the US DOE's Ad-i vanced Reactor Severe Accident Program (ARSAP), under ANL subcontract No. 23572401 to . UCSB. The program was initiated in 1991 and managed by Mr. W. Pasedag (DOE, Headquar-J ters) and Mr. S. Sorrell (DOE, Idaho Operations Office). The authors are grateful for the support, cooperation, and advice received from these individuals throughout the performance of this work, including the preparation of this document. For ANL the contract was managed by Dr. L. Baker, { and his cooperation significantly facilitated the authors' focusing on the technical aspects of the work. { This has been a multifaceted technical effort that was enriched significantly by interactions with several individuals in other organizations outside UCSB. These include: J. Scobel (Westing-house), J. Sienicki (ANL), J. Rashid (ANATECH), V.K. Dhir (UCLA), T.Y. Chu (SNL), C. Chu (ANL), and R. Hammersley (FAI). Thanks are also due to the following individuals affiliated ( with UCSB: M. Frye, J. Smith and G. Wang. Last but not least we wish to acknowledge Ms. Eileen Horton, Administrative Assistant of CRSS, for her unhesitating devotion to this project, from contractual matters to budgeting and I accounting to the preparation of this report, often under very tight schedules. f XIij
L ! 1 INTRODUCTION This document addresses a severe accident management concept known as "in-vessel re-tention," and it has been put together with two purposes in mind: one, to demonstrate the effectiveness of the concept for an AP600-like design; and two, to provide a readily adsptable path for its consideration for other designs. The accident management strategy is to flood the reactor cavity, submerging the reactor vessel. The concept is based on the idea that the lower head, cooled externally, will be able to arrest the downward relocation of a degraded (melting) core. The related issue before us, then, is whether lower head integrity can be maintained subject to the thermo-mechanical loads 1 i created during such a situation. hese loads are created because of the presence of the high temperature melt (~3000 K I for the oxidic, ~1800 K for the metallic) on the inside. De mechanisms leading to such melts can span a wide range of behavior, from that associated with the initial portion of the relocation, thmugh a series of intermediate states, to a final quasi-steady state, where essentially all the core materials have been relocated and are found on the lower head. Correspondingly, the process is , initially dominated by forced convection, eventually reverting through a series of mixed regimes, to a purely natural convection one. Lower head integrity can be compromised by meltthrough, or by a combination of wall thinning and mechanical loading (including any internal pressure
- and/or thermal stresses developed as a result of the heating on the inside and cooling on the outside) that can cause structural failure.
In addition, mechanical loads can be created due to thermal interactions of the melt with any coolant present in the lower head. Such contact can arise either during the core relocation I process, or later on if, upon regaining injection capability, water was to be supplied on top of the l molten pool in the lower head. Of particular concern in this respect are energetic interactions, j l also known as steam explosions, especially in the relocation regime as it is capable of setting 4 up conditions for " premixed" explosions. l Re overall problem, as described above, is depicted in Figure 1.1. This figure also in- ! troduces the terminology to be used for the various loads, failure criteria, and corresponding loading " regimes." There are three such regimes. The " thermal regime" constitutes the subject ! l
- of this report, and this portion of Figure 1.1 will be taken up again in the next chapter. For now, suffice it to say that: (a) 9.(6) and 6.(6) denote the heat flux through, and wall thickness of, the lower head at any angular position 6 (see Figure 1.2); and (b) integrity is to be assessed by
, comparing these " load" values with corresponding failure criteria; that is, the critical heat flux, i ge,,(6), and the minimum wall thickness,6e needed to ensure structural integrity. The other l l 1-1 I
I I I I Thermal Leading Thermal Failure Criteria (Long Term) W u u o Geometry Weights (Net) Power Level Melt Quantity Flow Paths Thermal Stresses Mel t Composition I Geometry, Properties Integrity under gg).................. q g) un ,, ,,,
" Thermal Regime" g ,gy .................................. gr Mechanical (FCI) Loads Structural Failure Criteria under Late Reflood of RPV Dynamic / Quasi-Static 6,(0)
Inte ty in P p the *Oy Re ion: e M FCis in the g erm 7_ P 6)dt ~ ~ - ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ frv u "FCI Regime" p ....................................p, Dynamic SE Loads (Earty) Dynamic Structural Failure Criteria Based on 8,, u Melt Pour Rate h Geometry, Properties l Geometry, Properties l 4 Integrity under Dynamic Steam o o + Er
" steam gosion Pl osionLoads Regime"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I= 'P 6)dt h Figure 1.1. An overall view of the in vessel retention issue. 1-2 I
two regimes in Figure 1.1 refer to the consequences of melt-coolant interactions, and they are to be addressed in a separate report (neofanous et al.,1995). [ I t 01 OP xm J) i Metallic Layer [ Oxidic Crust Sw(0) Oxidic qw(0) Pool [ ( Figure 1.2. The basic geometry and nomenclature of in-vessel retention in the long-term, natural convection-dominated, thermal regime, r L Briefly however, a key distinction (that gives rise to the subdivision of melt-coolant inter- [ actions into two regimes) with some bearing on the present effort needs to be made at this time. Namely, that energetic interactions can be of concern mainly in premixed explosions, (melt and water intermixed at coarse scales) as they might adse, for example, during the early stages of L the core relocation, while interactions in a stratified configuration, concerning late water injec-tion, are relatively benign. De key implication then is that integrity in the potentially energetic ( " Steam Explosion Regime" can be assessed against the full lower head capability (normal wall thickness), while in the benign "FCI Regime" any wall thinning, as a result of the thermal loads considered in the present report, must be taken into account. De other point made in Figure l f l 1.1 is that due to the reduced wall stmetural capability in the FCI Regime, the static (or quasi-static) primary system pressure rise (to a peak pressure Pou) as a result of the steam produced, [ but not immediately vented, in the melt-coolant interaction might also have to be considered against a failure level, Pr, consistent with wall thickness,6 (6), and prevalent thermal stresses.
)
L Finally, in both melt-coolant interaction regimes, the main structural consideration is indicated 1-3 [ o ( _- _ _-_____ - _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
in Figure 1.1 in terms of the delivered impulse, I, against the failure criteria If and I F,. This is illustrative only of the key global consideration; the actual assessment is likely to require additional details, such as the space-time distribution character of the loads. So far, the subject has been approached only from the standpoint of the Thermal Regime in the long term, and all this work is relatively recent. The technical feasibility of the idea was first demonstrated for the Loviisa nuclear power plant, a Russian VVER-440 in Fmland (Theofanous, 1989). This reactor is equipped with a Westinghouse ice condenser containment, and the cavity design happens to be, both in size and location, subject to flooding by the ice melting during the course of any severe accident. hus, in-vessel retention formed the comerstone of severe accident g management in Loviisa (homisto and Theofanous,1994), and a related research program has 5 been going on for the past several years (Kymullinen et al.,1992; KymHIEinen et al.,1993). He complete assessment, representing the culmination of these efforts, has been submitted recently to the Finnish regulatory authority, STUK, (Kymnluinen,1994). The present effort for an AP600-like design evolved in close relation to this Finnish work, including the sharing of some facilities and personnel (Theofanous et al.,1994a; neofanous et al.,1994b). More recently this informal l bilateral effort has been expanded to a formal agreement to include the Italian utility ENEL and the Electric Power Research Institute (EPRI) for the purpose of furthering the confirmatory basis ! of the current assessments and extending the application to larger reactor designs. Independently, the idea ofin-vessel retention has been pursued also by Henry and co-workers (Henry et al.,1991; Henry and Fa uske,1993), by Hodge (1991), and it has been critically examined by Park and Dhir (1991), Park et al. (1992), and Hawkes and O'Brien (1991). Interest l around the world developed rapidly; a number of new research programs are in place; and a l CSNI-sponsored specialists meeting on the subject took place recently in Grenoble, France. The summary of this meeting, prepared for the CSNI by the participating experts, pmvides the most recent and comprehensive status report on the subject (CSNI,1994). More detailed reviews of the technical issues involved, and of the various experimental programs worldwide, also have l been prepared by groups of experts for the CSNI (Okkonen,1993; Roug6 and Seiler,1994). g By virtue of this large, intemational activity the problem can now be considered to be ripe for j decisive steps, such as those needed in the regulatory context, towani resolution. This is the intent of the present document. It is instructive to emphasize, however, that such a task must be approached on a reactor-specific basis-the design of interest here is that of the Westinghouse advanced passive design: the AP600. This report consists of five main technical chapters and a large number of supporting g appendices. Two chapters (3 and 4) address the failure criteria: the qc,,, and 6 F , as identified 5 in Figure 1.1 aheady, while the remaining four contain the development of the thermal loads. 1-4 I
E Chapters 5,6, and 7 address the long-term natural-convection 4cminated regime, while Chapter 8 is devoted to the consideration of forced convection effects. The overall aim of these chapters and their intenelations are explained as a part of the overall approach and methodology in Chapter 2. The report comes to an end with the conclusions and recommendations presented in Chapter 9. E E E L ~ I b c I' I u u . E E 1-5 { c
2 PROBLEM DEFINITION AND OVERALL APPROACH We begin with the basic assumptions that if core degradation takes place, the primary system i will be depressurized and the lower head will be fully submerged in cavity water prior to the arrival of core debris on the lower head. Further, we assume that the water level in the cavity would be maintained indefinitely. Detailed consideration of these inherent aspects of the AP600 design are beyond the scope of this report, but the design attention given to the assurai ce of their validity is summarized in Appendix M. Their consequences can be listed as follows: (a) Prior to being exposed to the melt the lower head is quenched down to the saturation temperature of water at ~1 bar: ~100 'C. (b) In the absence of significant primary pressures, only a very small fraction of the lower head thickness is needed to support the dead-weight loads-thermal stresses and creep are the primary failure mechanisms to be considered instead. (c) With the lower head fully submerged, the outside surface will remain in nucleate boiling (at
~100 'C) provided the critical heat flux is not exceeded at any point on it-a dgnificant aspect of this requirement is that the thermal insulation allows sufficient flow paths for water to flow in and vapor to escape. The design of the thermal insulation for the AP600 has not been finalized yet, but as discussed in Appendix K, no difficulties in principle are anticipated.
Additional attractive features of the AP600, relative to this accident management strategy, are that its lower head is free of any penetrations, and its core power density is rather low. To predict the thermal loadings on the lower head in all their detail, one would need the l complete sequence of thermal states of the core and other internal structures throughout the core degradation and melt relocation processes. Rather than getting immersed, and perhaps lost, in such details, our approach is based on the identification of certain dominant features of these complex scenarios, and the detailed study of the loads in certain well-defined material and thermal state configurations. Our aim is to thus envelop the behavior, with regard to loads, and we will argue that this indeed has been achieved. Quantification of uncertainties will be emphasized in the detailed analysis carried out for each of these representative, enveloping configurations. The overall philosophical / methodological approach follows the risk oriented accident analysis methodology (ROAAM), which is described in Appendix A. The scenario-independence stated above, and explained below, will be recognized as a Grade B approach, which is desirable in realizing the high confidence assessment sought here. This approach is conservative, but not unduly so, and it is consistent with the existence of a wide range of bifurcating behavior possible in such phenomenologically complex situations. 2-1
In the same vein we restrict our attention to scenarios in which failure to supply coolant into the reactor vessel persists indefinitely." This is clearly a limiting case, especially in light of the recovery that took place in Three Mile Island, Unit II (TMI-2). The unexpected arrest of lower head heatup and eventual quenching was key to the survival of the vessel (Strickler et al., 1994; Turland et al.,1993), and it is currently pursued mechanistically as yet another potentially j important approach to arresting a severe accident in-vessel (Henry and Dube,1994). l The basic geometry can be repmsented in rather general terms in the manner shown in Figure 2.1. It consists of the lower head with some of the core debris on it, the rest of the reactor pressure vessel not in direct contact with core debris, and the core barrel, the reflector, and the core support plate, with any remaining core debris on it, as the key internal components. This figure also indicates the various pathways for the flow of thermal energy generated by radioactive decay processes within the core debris. These energy flows occur in accordance with the driving potential (temperature differences) and corresponding resistances. We have a strongly coupled problem here in that any imbalance between production and dissipation (( heat input and heat loss)) is accommodated by an increase in the driving potential which, in turn, gives rise to phase change (heat sinks) and convective losses either by relocation or by enhanced natural convection. Considering the natural convection process, in this context, first, the thermal load to the lower head is maximized when: (a) The debris pool has reached a steady thermal state, (b) The heat generating (fuel) debris volume has been maximized, and I (c) The thermal resistance along the upward thermal radiation path has been maximized. Indeed, for any given volumetric heat source, steady state implies that all internal heat sinks have been eliminated (melt-out of steel structures in the lower plenum), and that the pool temperature reached the highest value, as needed to exactly balance production by natural convection to the boundaries (see also Chapter 6). What occasionally has been mentioned as a slow approach to steady state is really attributable to the thermal capacitance of the pool rather than to unsteadiness l in the natural convection process. In particular, in Appendix D we demonstrate that boundary layer effects dominate, so that the behavior of such pools is readily predictable even under non-stationary conditions. What this means is that thermal loads to the pool boundaries throughout the time period of a heat-up transient are bounded by the thermal loads in the final steady state. The effect of debris volume (item (b) above) is due primarily to the reduction in surface-to-volume
- However, the structural loading implications of coolant supply, late in the retention scenario, is considered in the "FCI Regime," as noted above (Figure 1.1).
2-2 I
F "
~
Upper InternalPackage RPV + 4 - Core Barrel Radiation Upward and Melting Adjacent ,
- w. L .
Reflector k::
~
Structure N : Convection to Boundaries and Melting Adjacent _ Crucible Conduction Downward and : . . - Melting Adjacent Structure fff
. . . .. b..
., .; f f[
- Bottom Blockage f :::;: .E Lower Suppons gjy,ppy,yyppy,g Melting of Lower Supports N Lower Support Debris Plate
,r Water Boiling or Sw Radiation Upward Convection to Boundaries i
Figure 2.1. Material configuration and heat transfer processes at an intermediate state of the melt progression-after the initial, major relocation event, and befom the attainment of a final steady state, ratio as the pool level rises in a hemispherical geometry. Finally, the effect of the thermal resistance along the radiation path is straightforward-as the resistance incmases the pool must reach a higher temperature to reject the same amount of heat, which causes an increase in the downward heat transfer and hence in the downward-to-upward thermal energy split.
'Ihus we arrive at the first configuration appropriate for detailed examination and quan-tification. It is schematically illustrated in Figure 2.2, and its key elements can be listed as follows:
(a) All the core debris, as either a solid oxidic crust or a molten oxidic pool, at steady state in the lower head. 23
l l js rs e s ., 4 e Metallic ! layer q' l
\ !/
100% of y y Oxidic Core 9, Figure 2.2. Materials configuration in the natural convection, steady state, extreme. (b) A molten steel layer on top of the oxidic crust / pool, made up of all the " light" components of the core region, the reflector and core support plate, at least a portion of the core barrel, as well as all lower (plenum) internal structures. l In Chapter 7 we will demonstrate that the incorporation of the structural elements listed under item (b) above into the molten steellayer is a necessary consequence of the existence of a molten pool of significant size in the lower plenum.
~
'Ihis configuration is of fundamental significance in assessing the problem at hand, not only because it bounds all intermediate states, but also because it represents the final state that would actually be realized in any in-vessel retention scenario.
The bounding nat the configuration described above could be violated only in the presence of significant forced convection effects. Such effects can arise as core debris relocates 2-4 I
[:
'into the lower plenum, throughout the com degradation sequence, and most notably so during
[. the major, initial discharge. This discharge would be expected to occur upon failure of a core-internal crucible that forms as a consequence of the melting-fmezing phenomena-melting in { the inner, higher power density region, and freezing as the melt relocates in the outer, colder boundaries. - As it happened in TMI-2, the tight PWR bundle geometry favors the formation of such internal crucibles and the accumulation of significant melt quantities ir. them prior to {' their failure. ((The explanation for this TMI-2 behavior was first given by Epstein and Fauske (1989).)) In the AP600 such behavior is further favored by the bundle inlet geometry and b the solid zirconium slug in each pin in the entrance region-an additional heat sink-and by the substantial steel reflector component that surrounds the core inside the core barrel. These, [ together with the thermal load distribution at the boundaries of a volumetrically heated pool, as discussed in Chapter 5, guarantee that in the AP600 failure will occur at the core side and that the initial discharge will involve a sizeable fraction of the core ((something like 30%)) (Sienicki { et al.,1995). E Clearly, then, this is the second configuration of major interest for thermally loading the u lower head. It is illustrated in Figure 2.3, and involves a " wall jet" released from near the top r of the molten core pool, throngn the downcomer, and into the lower plenum. Subsequent to this . L ! initial release, melting and relocation occur in a much more gradual fashion, and melt and crusts already on the lower head further reduce the impact of these forced convective effects. Thus we , F u can see that this second configuration provides an appropriate bound for all convective effects as they are found in the intermediate core degradation states. I To summarize, we have identified two specific configurations (as described by debris mass and thermal state), one dominated by natural convection and the other by forced convection and L impingement effects. We take the position that these configurations bound the thermal loads on the lower head with respect to any other intermediate state that can reasonably be expected [ in the time interval between, and including, the initial major relocation event and the final steady state where all debris is contained in the lower head. The terms " natural convection" and l
" impingement" will be used to describe these two extreme thermal loading configurations. They
{ are covered in Chapters 5 through 7 and Chapter 8, respectively, b E E l 2-5 ' {
1 1 1
- m g
#ge- >
I: 1
=
1 ..
-- 3
- r i,
J
'E Queible 4
Jet --> -- -- e - Bottom Blockage i --
.g i
- Lower Suppons yp,yp,,pp,,,,,,,,
4 Lower Suppon i Water n Plate
./
, y, '
qW Water Boiling Figure 2.3. Materials configuration, in the fomed convection, jet impingement extreme, associ-ated with the major core relocation event. i 4 I d 3-2-6
3 THERMAL FAILURE CRITERIA The principal and, as we will show in the next chapter, most limiting failure mechanism of the lower head is the boiling crisis (BC). It occurs when the heat flux through it exceeds the critical heat flux (CHF) at the same location, and it results in a sudden transition of the flow regime from nucleate to film boiling. Film boiling is characterized by considerably lower heat transfer coefficients, and as a consequence the surface temperature rises to considerably higher values in order to accommodate the imposed thermal load from the inside. For example, for a heat flux of 400 kW/m 2the surface temperature must rise to ~1200 'C in saturated water, while subcooling can only modestly moderate this rise (i.e., ~1100 *C for 20 *C subcooling). At such temperatures the steel loses essentially all of its strength, and it becomes susceptible to creep, and structural instability, even under the modest mechanical loads of interest to this problem. Moreover, the thermal gradient in the wall at the same flux level is 160 *C/cm which, considering a wall liquidus of 1300 *C (see Chapter 7) indicates a wall thickness of only 6.0 mm. As we will see in Chapter 6, heat fluxes on the lower head can considerably exceed the 400 kW/m2 geyei considered in the above example. By contrast, nucleate boiling heat transfer coefficients are so high that any flux level, up to the CHF (but prior to BC), can be accommodated with only a few " tens" of degrees in wall superheat (temperature above the coolant saturation temperature). Nominally, therefore, in nucleate boiling the outer surface of the lower head is at ~100 *C. This is very significant for the structural stability of the lower head, and it is taken up again in the next chapter. In the remainder of the present chapter our task is to discuss the boiling crisis and come up with reliable estimates of the heat fluxes necessary to cause its occurrence. l The key features of the problem can be seen with the help of Figure 3.1. Considering l l first the " local" aspects, we will note that the downward-facing geometry lends itself to the formation of a two'-phase boundary layer that is " squeezed" upon the heating surface by grav-ity forces. This " squeeze" is moderated by turbulent mixing (including interfacial instabilities and entrainment) as buoyancy drives the steam past the heating surface and the surrounding water. The balance between these two mechanisms is quite different in the various regions around the lower head. This gives rise to widely different two-phase flow regimes, and as a consequence, we can expect significant variations of the critical heat flux and perhaps even of the underlying mechanism (s) for it. For example, in the vicinity of the stagnation point (6 ~ O') the vapor velocities are very low and the surface orientation, relative to the gravity vector, drives the maximum phase separation with the vapor " squeezed" up against the wall. We expect periodic formation of relatively large bubbles, growth, and escape. Under such flow conditions we can expect that boiling crisis will occur if the underlying thin liquid film dries out, within one such period, and if the surface temperature rises to high enough levels to prevent 3-1
1 L I
#,..-- ,,h
~ t E $f$ 2;b fy-- E anse fs evs^. I m I . 6 ! N,%' M
" W/"w Total Clearance l
j a t
'$I 2.8 m2 k t '
*h Downcomer l h .
\ Total Clearance qr 1.7 m 2
, 4 I!N k f' t Riser g -.e s l .
EEP W L G S M X:XE ZGG.G l W$22%%$$%$$fy' i
~
z, "Q S%$%%2l ? .-
. ed q # 'W# fi '.3
^
I h@h$$$ii$$$l: a_ I Figure 3.1. Key geometric features of cavity flooding and venting paths. Illustration of the two-phase boundary layer on the lower heaJ. Thermal insulation not shown. rewetting when the liquid rushes back-in following bubble escape. As a consequence, surface wettability (controlling the behavior of the thin film) and wall thickness (controlling the rate of heatup following the dryout of this film) should be important. Aspects that could affect the behavior of these bubbles, including any convection in the free-stream water (see global 3-2
behavior discussed below) and its subcooling, should also be important. On the other hand, near the equator of the lower head hemisphere (6 ~ 90'), we expect that cumulative vapor generation from all the upstream positions will give rise to high vapor, and entrained liquid, flow velocities, and in addition, the vapor " squeeze" effect described above would be minimal in the near-parallel orientation of the surface to the gravity vector. As a consequence, we expect a highly turbulent two-phase flow within a relatively " diffuse" boundary layer. Correspondingly, the BC mechanism would be convection-dominated. However, phase separation and perhaps even capillarity may continue to have some bearing on the mechanism in this regime, as well. Evidently, intennediate (or mixed) mechanisms can be envisioned as we go from the stagnation { region to the equator with the details of this transition region being strongly dependent upon the power (input) shape. Let us turn next to the global aspects. In a fully-flooded cavity, as indicated in Figure 3.1, the gravity head would be ~7 meters, which corresponds to ~14 *C subcooling with saturated water at the top. The supply of this subcooled water to the cavity depends on any flow restrictions on the flow path, and on the gravity head developed due to the two-phase flow in the riser. Moreover, the availability of any subcooled water in the immediate vicinity of the heating surface would l depend on the local mixing and flow pattems as described above. His coupling of the local to l the global behavior is quite important in that it indicates a truly conjugate behavior. The situation l is less so at a flooding level low enough to interrupt the natural cimulation flow path; still, level swell is important in determining the extent of the cooled portion of the reactor vessel. Such l partially flooded conditions are of limited interest only, as discussed in Appendix M; however, I as demonstrated later on, the resulting " pool boiling" pmvides a low (conservative) estimate of the critical heat flux under fully flooded conditions. Back to a fully flooded condition, the key l mechanism is void drift in the riser, and the void fraction distribution depends on the power input (including shape), the subcooling, and on the flow losses along the natural circulation path-especially on any inlet or outlet restrictions. The following clarificaticns need to be made: (a) power is also supplied along the riser section, it being the radiative heat .' ow conducted through the side wall of the reactor vessel; (b) in the AP600, as indicated in Figme 3.1, the flow path into the reactor cavity is wide open; and (c) key aspects of the flow geometry would be dictated by the thermal insulation design (and response in a severe accident) as discussed in Appendix K. In addition, the dynamics of the natural circulation loop, such as flow and pressure oscillations may be important (i.e., loop elasticity), especially on the bubble regime discussed above. ! Mechanistically, these are behaviors unlike any CHF situations considered previously. Con-I sidering also the status of fundamental understanding in the extensively investigated problem of BC on a horizontal, upwards facing plate (Lienhard,1994), we chose to pursue an experi-3-3
I: mental approach that faithfully simulates the reactor in all the key aspects of the I phenomena involved. Based on the above discussion, these key aspects include:
- 1. Heater length scale and shape. To properly represent the two-phase boundary layer behavior, especially in the intermediate region, we need a full-length geometry, including the l correct curvature. l
- 2. Heating surface thermal inertia. In the reactor, the lower head thickness could vary E fmm its initial value of 15 cm (for most of the region), to a low value of a few centimeters due E' to thinning by melt attack near the equator (see Chapter 7). Therefore, a minimum of a few centimeters in heated thickness is needed to properly represent the thermal inertia.
- 3. Power shape. In conjunction with the above item 1, a correct power history in the upstream region is necessary to represent the two-phase boundary layer conditions in the reactor.
In addition, the total power shape, including that in the riser, must be represented to simulate void distribution and flow behavior. l
- 4. Heating surface wetability. The reactor lower head is designed to be made of forged carbon steel (SA 508), machined to 200 r.m.s. mean roughness. Even though it is to be painted in situ, the paint is expected to flake off in boiling water, and the exposed steel surface to be well-wetted. This surface condition must be confirmed and matched experimentally.
l
- 5. Loop length scale and hydraulic diameter. To properly represent subcooling due to gravity head we need a full-length loop (~7 m). The annular gap in the reactor is ~20 cm, and a similarly large cross sectional length scale (diameter) is needed in a one-dimensional geometry to allow proper simulation of the vapor drift. l He ULPU facility was built to embody all of the above key characteristics, allowing, g therefore, a full-scale simulation capability. The facility, experimental program, and results u obtained are described in detail in Appendix E. One key aspect discussed but not listed above concerns the detailed representation of the thermal insulation geometry, especially the inflow and outflow paths and hence of the loop flow and dynamic response. As discussed in Appendix K, this is because the design has not actually focused yet on this aspect of the thermal insulation performance under severe accidents. Our approach in this respect, therefore, has been to study a rather broad range of conditions (Configurations I, II, and III, as described in Appendix E).
Clearly, however, this is one restriction imposed on the conclusions of the report that will have to be revisited once the design is finalized. The other g qualification on the results available to date fmm the ULPU facility is that they were obtained 5 in the well-wetting condition of an aged copper surface. We expect to confirm these results 3-4 l
with a test section made to order, according to AP600 specifications, from one of the potential suppliers of the reactor pressure vessel-He Japan Steel Works plant in Hokkaido, Japan. This piece of steel is expected to be delivered for installation in the ULPU facility by November 15, l 1994. It will be shipped and handled in a manner very similar to that normally used for reactor vessels, and we expect to have test results from it prior to the completion of the peer review of g this report. l Re ULPU experiments confirmed the flow regimes and the general point of view taken in our experimental approach as expressed above. Details can be found in Appendix E. Here, I we present the main results as summarized in Figures 3.2 and 3.3. The results in Figure 3.2 were obtained in experiments carried out with a limited submergence and absence of natural circulation (pool boiling). As noted above, these conditions are of limited, if any, significance to the problem at hand, but the results provide interesting perspectives in comparison to those of l I Figure 3.3 obtained under almost full submergence (~6 m) and natural circulation. This Figure 3.3 is the result appropriate for quantifying the thermal failure criteria. From an evaluation of uncertainties, as discussed in Appendix E, we expect this result to be good within a few percent, so that CHF can be excluded outside a rather narrow range around it. In Chapter 7 we will see that the margins to failure are so significant that they totally dwarf this uncertainty in this failure l criterion. 1500 , , , , , , , , p - l E . I N k 5 1000 X . 500 - g . D / l
'C o -
' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' 'I
-0 I -0 20 40 Angle (degrees) 60 80 I Figre 3.2. Critical heat flux as function of position on the lower head; from ULPU, in pool boiling.
I 3-5 1-
I 2000 , , , ,
=
^
- E E .
E
)x1500 -
v . g .
~
f1000 g .
.9 000 2 -
y . _o
, , , , ! , , . . I . , , , I , , , . I , .
- I
-0 20 40 60 60 Angle (degrees)
Figure 3.3. Critical heat flux as function of position on the lower head; from ULPU under full 3 submergence and natural convection. E In concluding this chapter we would like to mention certain others' past and on-going efforts addressing CHF in mlation to lower head integrity.
- 1. The CYBL experiment (SNL). A full-sized, stainless steel vessel with torospherical lower head of I cm thickness. Radiant heating applied internally (to the lower head) with peak flux capability of about 200 kW/m'. Experiments showed persistent nucleate boiling up to this level of heat flux. This work was carried out for the DOE's Advanced Reactor Sevem Accident l
Program as a complement to that in ULPU. For more details'see Appendix F. It is interesting to note that the periodic bubble formation and departure observed in CYBL was found also in ULPU-about 2 Hz at 200 kW/m2 .
- 2. The FAI experiments (Henry et al.,1991; Henry and Fauske,1993). These were carried out in a 32 cm diameter (outer) pipe cap, with thermite as the heat source, in a transient mode. Peak fluxes of ~1 MW/m wem 2 measured. The effect of reflective thermal insulation was assessed, both experimentally and analytically, and it was found to introduce no important limitation to coolability.
- 3. The SULTAN experiments (CEN, Grenoble). The test section consists of a long, straight g channel in an adjustable orientation relative to the gravity vector. Experiments are in progress 5 (Bonnet et al.,1994).
3-6 I I
-4. De Penn State experiments. These NRC-sponsored experiments involve steel hemispheres up to 30 cm in diameter (1/24- to 1/10-scale) and are on-going.
- 5. Other small scale work. This involves quite a few experiments with centimeter-scale heating
]
surfaces, or very narrow channels, carried out primarily in connection with cooling of electronic components. His work is not relevant to the present problem and thus is not mentioned explicitly. (( ADDENDUM TO CHAPTER 3)) De experimental basis for the main result of this chapter - Figure 3.3 and Eq. (3.1), below, shown in it - is now supplemented by two addenda to Appendix E, prepared simul-taneously, and as a part of, the responses to the first round of the reviewers' comments. The first addendum is provided as Appendix E.3. It covers the results of an extended experimental matrix in Configuration II with flux shapes that include those found in the sensitivity / parametric studies as well as variations thereof, and arbitrary variations of recirculation flow rates, obtained by throttling the inlet, to 50% of the normal (~130 gpm) flow rate, and to full stagnation. The results indicate that Eq. (3.1) is a robust conservative estimate appropriate for the evaluations performed in this report. 'Ihe second addendum is provided as Appendix E.4. It covers Con-figuration III ULPU experiments, built in accordance with the thermal insulation design just completed by Westinghouse (see Appendix K). In addition, this set of experiments included the effect of a prototypic heating surface, i.e., reactor vessel grade steel with and without the normally employed paint. The results once more demonstrate the robustness of Eq. (3.1) and its applicatility for our purposes. q,r(6) = 490 + 30.2 6 - S.88 10-162 + 1.35 10-8 63 - 6.65 10-86 4 kW/m 2 (3,3) 3-7
E 4 STRUCTURAL FAILURE CRITERIA In this chapter we examine the behavior of the lower head under thermal loads severe enough to cause extensive wall thinning, and we show that structural failure cannot occur unless there is boiling crisis. In other words, we will endeavor to demonstrate that the thermal failure criteria discussed in the previous chapter are both necessary and sufficient for assessing lower head integrity. Under the low pressure conditions of interest here there are sufficient margins in the consideration to allow a basic-principles approach while avoiding the actual determination of structural failure. Other situations involving higher pressures may require detailed numerical simulations of the type illustrated in Appendix G, and for them, the so-derived structural failure criteria may become more limiting (than CHF). He purpose of including Appendix G is, in { addition to this illustration, to provide further perspectives confirmative of the basic-principles approach pursued in this chapter. We have already shown in the previous chapter that boiling crisis is a sufficient condition for lower head failure. Now, we wish to demonstrate that this is also the necessary condition; that is, unless BC occurs, there can be no failure. For this purpose it is adequate to demonstrate that a CHF-limited wall thickness is sufficient to support the lower head and its contents. He CHF-limited wall thickness can be readily obtained from Figure 3.3, using the steel thermal conductivity referenced together with other useful properties in' Appendix L, and a steel liquidus temperature (see Chapter 7) of 1300 *C (1573 K). The zesult is shown in Figure 4.1. De critical region is around 8 ~ 90', and the integrity of this region must now be examined in [ detail. Interestingly enough, this is the region revealed to be the most limiting from the thennal margins point of view as well (see Chapter 7). [ ne physical situation is illustrated in Figure 4.2, and the following key points can be made reganiing the state of stress in the segment shown.
- 1. Deadweight and Buoyancy. Dese two forces nearly cancel each other out. Take, for example, a melt layer 2 m deep, in the lower head, and a vessel submerged up to the hot leg nozzle elevation (~7 m from the bottom of the lower head). With a melt density of 8000 kg/m8
( ) we have a melt weight of 134 tons, a lower head weight of 29 tons, and a buoyancy force of ) 92 tons due to the effective hydrostatic head of 6.33 m on the lower head outer surface. De { 5 l net force of 71 tons (7 10 N) would require a wall thickness of 0.15 mm to reach the yield stress of this steel at full strength (355 MPa). In Figure 4.2 we can see that this region of full strength (i.e., below 900 K), under the heat flux condition of interest is 1.1 cm, and thus able to comfortably carry the applied stress. 4-1 l
I 10 , , , ,
,,.j,,,
E - . E 3 0 - - E m : : 5 t
" : z l
E b
* : T
! l
.2 l
15 : :
- -: 2 -
e . . 5 . o
. . . . I . . . . I . , . . I . . .l . .-
0 20 40 60 80 Angle (degrees) Figure 4.1. Maximum wall thicknesses allowed to accommodate the critical heat fluxes at various 3 angular positions around the lower head, subject to 400 K and 1573 K temperature boundary 5 conditions at the outside and inside boundaries respectively. l l
\l 1.1cm l
1 Melt gl t Water i l 1 3l ' ' 1573 K U 900 K *-- q = 1.5 MW/m - E 400 K - i g l l e ' = l ' 2.5 cm g I l I{ Figure 4.2. Illustration of conduction-limited wall thickness, and of the full-strength outer region i (T < 900 K), under an imposed heat flux of 1.5 MW/m2, l I l ' 4-2 Il
L E
- 2. Thermal Stress. As a result of the steep temperature gradient, the inner region is in
[ compression, and the outer region is subject to tension at levels that, on an elastic basis, would significantly exceed the yield stress. A basic characteristic of thermal stresses is that they are self-equilibrating, i.e., in the absence of other stresses, thermal stresses must integrate to a net zero [ force on any freebody section of the structure. Material inelasticity would cause the temperature stresses to relax and redistribute to a profile that is bounded by the temperature-dependent tensile strength of the materials. In order to satisfy the self-equilibrating property, the thermal stress must redistribute to a profile that exhibits high tensile stress over a relatively narrow external l (colder) portion of the vessel wall and a low compressive stress on the remainder of the wall. This thermal stress redistribution, when superimposed on stresses from other sources such as [ the differential internal pressure discussed under item 1 above, would result in the enhancement of the tensile stresses with the final stress distribution remaining at or below the temperature { dependent flow stress of the material. Thus, the load carrying capacity of the vessel will be governed by the outer thickness of the wall that is under tension. Below, we will show that for the conditions of this problem, this outer region has a thickness of about one-fifth the wall thickness; that is, it is ~5 mm thick for the limiting case considered in Figure 4.2. It is easy to see that this clastically stressed portion of the wall is more than sufficient to carry the stress L levels due to the externally imposed forces (as discussed under item 1). ~ In carrying out the quantitative demonstrations indicated above, we take a three-step ap-L proach. The first is idealized enough to allow an analytical result showing the basic features and extent of the tensile-stress region. We assume a linear dependence of the yield stress on [ temperature and a perfectly plastic behavior. The second step makes use of a simple numerical model to show the relief mechanism described above anri the load carrying capability of the outer F tensile region. In Appendix G-finally, the third step-we can find that incorporation of creep confirms these results and that stmetural integrity is assured even under relatively significant primary system pressure. To illustrate the first step let us consider the thermal stresses in a cylindrical wall subject to a linear temperature distribution with a total temperature difference across it of magnitude k AT. For a wall thickness,6 ,, small compared to the vessel radius, the analytical solution for the stress distribution (the azimuthal, ae, axial, o,, and radial, o r, stresses) in the elastic region can be simplified to: F D' eat r o, = o, ~ 2(1 - v') 1 - 2 6., or~0 (4.1) E 1 where #', E, and v' are the linear thermal expansion coefficient, Young's modulus of elasticity, j and the Poisson t. tio, respectively, and r is the distance from the outer boundary. The resulting 4-3
I . equivalent (von Mises) stress is shown in Figure 4.3. Note that because the response is still clastic the midpoint is at zero stress and a region around it is subject to a low stress level. As T and AT increase the stresses in the extreme outer and inner regions reach yield, and assuming a perfectly plastic behavior, the situations obtained would be as illustrated in Figure 4.4. Clearly, l the size of the elastic core decreases as the applied T and AT increase, and the clastic stress gradient increases with it. I
~~
Yield Stress g I I Radial Position Figure 4.3. Equivalent (von Mises) stress distribution due to temperature gradient across the I thickness of a vessel wall. Note that the yield stress is assumed to be linear with temperature. For the second step, we make use of a finite element model of the whole reactor vessel (see Figure 4.5) Calculations were carried out with the code ABAQUS (version 5.2) and material properties accounting for the variation of the yield stress with temperature accortling to the l recent data of Chavez et al. (1994). These data (for steel SA 106B, which is quite similar to g that specified for the AP600) extend to 1150 K, and they were extrapolated linearly to zero at the steel liquidus (~1500 K). A wall thickness of 5 cm was taken in the calculation. The result is shown in Figure 4.6. Again, the tensile zone, which consists of an clastic core and a plastic outer region add up to about one-fifth of the wall thickness. The effect of yield variation with E temperature is to shift this tensile zone toward the outside while much of the inside is seen to E have relaxed to a near stress-free level. In concluding this chapter we emphasize again that boiling crisis is the limiting failure criterion only at primary systems pressures near ambient (containment atmosphere). In fact, at 4-4 I I
( non-yielding region f 7 elastic /
' (-
N{ s Yield Stress - N /- A I plastic I L Radial Position ( Figure 4.4. Equivalent stress distribution due to temperatum gradient across the tidekness of a e vessel wall. The continuous line represents the stmss distribution for clastic plastic behavior. ( r
>C i
L ) 1 l
~v~
Figure 4.5. 'Ihe finite element model utilized in the computations. 4-5 L
l E 350 i i i i I L 2 I a 300 : : m 4 250 h 1 k
- l E 200 i
=
y 150 . I
}a 100 h l
- 50 -
? -
0
~
' ' ' )' ~
0 1 2 3 4 5 E radial position (cm) u Figure 4.6. Equivalent stress distribution in the most critical section of the vessel from an ABAQUS calculation. Dashed line represents yield data at the temperatures corresponding to the various positions along the wall (fmm Chavez et al.,1994). some higher pressure level we would expect that control passes over to structural failure criteria, for which the computational approach of Appendix G is appropriate and should be applied (with gl due consideration of uncertainties). Note that in this respect (of uncertainties) the present case 5 is rather straightforward: boiling crisis is a conservatively limiting structural failure criterion. That is, structural failure margins are larger than margins to boiling crisis, which in turn are very large compared to uncertainties in this criterion (see Chapters 3 and 7). I (( ADDENDUM TO CHAPTER 4)) l CONSIDERATION OF DUCTILE TEARING The purpose of this addendum is to address a question brought up by one of the reviewers (Nickell) about " ductile tearing" as a failure mode. The concern is about large, local defor-mations, and strains sufficient to cause tearing, brought about by the combination of the highly non-uniform loads (hydrostatically induced both internally and externally), wall thicknesses, and temperature distributions. As correctly noted by the reviewer, much more detailed nodalization 4-6 I I ;
I (than that utilized previously) would be needed to properly consider such local behavior. This l was done here for the most extreme parametric case considered in Chapter 7 (the one illustrated in Figure 7.16). This does push the problem to the limit of thermal failum, and as we will see below, in terms of mechanisms, it has the greatest potential for the local deformations that are ; I of concern here. The results show that a core of strong (below yield) material remains in the manner described previously in the report, leading to the conclusion that ductile tearing is not a feasible failure mode, in our case. Also the local maximum strains in the direction along the I wall meridian (longitudinal bending) are below 7%, indicating margins to tearing everywhere. l I Rather than the shell elements used previously, we now use " bricks" (which give more flexibility in the specification of the geometry) and rather than a full-vessel 3D model, we use an axisymmetric model of the lower portion (extending by 0.35 m into the cylindrical segment). Because the main part of this cylindrical segment remains cool and strong,it provides an effective isolation from the remainder of the vessel that is not modelled (this was tested by calculations). l Also, this time we use the actual hydrostatic load distributions (of the melt pool on the inside and of the water pool on the outside), but numerical experiments demonstrated that their effect, compand to the thermal stresses, is negligible. The intemal temperature and wall thickness profiles, as functions of the angular position, are shown in Figure 4.7. The temperature at the ! I outside boundary was specified as 130 *C (nucleate boiling). The finite element model is shown in Figure 4.8. The grid is made of 31 nodes acmss the wall thickness at all angular positions. In the meridian plane, nodes are 0.1 apart in the region of major intenst (that of varying thickness plus segments of the thick parts connecting to it) and 2* elsewhere. This corresponds to bricks that are 3.5 mm long and 1 mm thick in the highly-croded portion of the wall, and 7 cm long, 5 mm thick in the intact portion. In the straight cylinder section, nodes am 5 cm apart in the vertical direction and the wall thickness is again divided into 30 elements. Change in elastic properties of the material with temperature is included, but perfect plasticity is assumed (strain hardening present in the actual material makes this a conservative assumption). The results are depicted in Figures 4.9 through 4.14, focusing on the region of interest. The predicted deformation pattern, alongside with the undeformed grid, is shown in Figure 4.9, and ; it is as expected, forcing a longitudinal bending in the narrow region driven by the cumulative j expansion of the lower part, while confined by the upper cylindrical portion. This bending subjects the outer wall material, at the " junction" between hot and thin segment to the upper l cold and thick segment, to compression (see Figure 4.10), which in part compensates for the tension driven by the local thermal stresses. The axial stress component is thus strongly reduced, in turn lowering the equivalent (Von Mises) stress. Consequently, the non-yielding region which l under unconstrained thermal loading is within the wall, is now located on the outside. This l I 4-7 l _ _ _ _ _ _ _ _ _ _ _
0.16_ , , , 1400 I l 0.14p j d 1200 m E 0.12 F
- I H i
E 0.1 F *
,' -i 1000g t
l
~~~~.... -
800 $" l .E 0 .08 . l! l
$ i -
600 .E , ~ 0.06 _-
= - ~
400 j 0.04 ) ----- temperature ; S 0.02 ? thickness 200 l 0 18 36 54 70 g Angle [ degrees] Figure 4.7. Inner temperature and wall thickness profiles used in the ABAQUS calculation. I I I I I I I Figure 4.8. Finite element model used in the ABAQUS simulation. 4-8 I I
L r L I f L f. r UNDEFORMED DEFORMED L Figure 4.9. Undeformed grid (left) and deformation pattern after loading (right) in the region of r Interest L F Compression of element L (" squeezing") d Bending effect due to expansion of f lower secdon L Figure 4.10. Axial stress relaxation due to longitudinal bending. L 4-9 (
I can be identified in Figure 4.11, depicting the map of the Von Mises stress. In this figure, we can see that a relatively low stress zone (the green region) exists throughout. Strains are below 1% cverywhere, aside around the lower junction between the thin and the thick part. Here the maximum principal strain reaches values of about 7% and 18% at the outer and inner layers respectively, as illustrated in the map of Figum 4.12. Figure 4.13 shows the distribution of the principal strains at these inner and outer layers in the region of interest. On the inside, the maximum principal strain (ep3) is in the local radial direction, while the minimum principal strain (epi) is in the local meridian direction; that is, the elements in that area am very compressed and of no concern for tearing. On the outside, the maximum principal strain is in the local meridian g direction while the minimum principal strain is in the local radial direction: the elements in this E area are stmtching, although far from what is needed to cause tearing. Finally, in both inside and outside layers the intermediate principal strain (e p 2, in the azimuthal -hoop- direction) is not affected strongly by the displacements and remains always at values below 1%. The existence of the unstretched " core" material mentioned before is illustrated in Figure 4.14, showing the profiles of the two principal strains discussed above over the local radial direction. The localized strains are due to the fact that the thin section represents the " weak" transition between the cold, strong and not-displacing part at the top and the expanding lower shell. ' Die latter wants to "open up" to accommodate the thermal loading. These " external" forcings subject the " weaker" thinner region to a reverse bending (as aheady shown in Figure 4.9), which nevertheless is able to accommodate the situation with longitudinal strains far lower than needed I to cause tearing (on the outside of the lowerjunction), and a strong core of non-yielding material E throughout. In fact we found this " accommodating" quality of the thin region to prevent failure in trial calculations even under much higher temperature gradients. A concluding note about this calculation: a linear temperature gradient through the wall g has been assumed. The wall actually must go through a transient, during which the gradient is 3 steeper on the inside than on the outside. However, the transient heat transfer analysis presented in the addendum to Chapter 5 shows that for the imposed heat fluxes, the gradient becomes almost linear before the inside temperature reaches 1000 C, which takes place within about 4 minutes. To investigate the effect of this non-linear temperature distribution through the wall thickness, we have canied out computations in which we forced a very steep gradient in the first quarter of the section and relaxing slowly to the outside temperature over the remainder of it. This calculation has shown additional margins, due to a greater portion of the wall that remains cold and thus can better lesist to the imposed loads. This, together with the assumption of perfect plasticity, adds to the conservatism of our analysis. 4-10 I
1 i
)
i i i i i y / r d /
/,
Of / /, O /
/
/ / r / / y j./ ? / l l ! Figure 4.11. Map of equivalent (Von Mises) stress distribution. f i i ! 4-11 l i
- u. . .me -d K *e.am esew Ma.%_.Aa-*aem-*.ma_. .-. -4me4, ashe. sa m-a-.ha I
I I I
//
p:
/.
/-
49 / i 1;
/
p:
/
/
/
/
T/4 hp Of 'bly be, #4kf ong
/
I-
#Vp /
I
[ [ E Inside 0.2.... ... ... .. . E ,f radial 0.15F e 5 - " " E **, azimuthal -
.E 0.1 r 2 _ E ,,, meridian
~
a 0.05- v - 2 - --. ~~~ ~__
- J '
S 0 - o ' 2 {5 -0.05h
-0.1 h h -
1 ~ P -0.1 68 70 72 ! 2 64 66 Angle L Outside 0.08 i i . . _ F - E pr meridian - L 0.06? Eg. azimuthal r c - l g : E '3, radial H um 0.02: -
' h-- -
F g 0 1-- q g -0.02 -
~
2 E -0.04 -
~
-0.06- - -
t L -0.08'2 0 64 66 68 70 72 Angle I L r Figure 4.13. Maximum and minimum principal strain distributions along the inside (top) and outside (bottom) walls. 4-13 _ _ _ _ _ _ _ _ . _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ . _ _ _ _ . _ . _ _ _ _ _ _ . _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ ___ a-
0.15 . . . E - i i
- p1 -
0.1 -
~
m - E P3 - c -
'iii : _
I!
- 5 0.05E g _
- g
._2, _-
, 0 o _ ! .E m
- a
- n. ~
5
- 0. 0 5 h N '
-0.1 ' '
3 i inside outside l Radial position I Figure 4.14. Maximum and minimum principal strain distribution across the wall thickness at the element with the largest positive strain on the outside. I I I I 4-14 I
5 PARTITION OF THERMAL ENERGY FLOW BY NATURAL CONVECTION { [ In this chapter we consider the configuration dominated by natural convection phenomena and seek to determine the heat flow distribution at the boundaries of the volumetrically heated pool and of the steel layer. This is the key aspect of the overall model described in the next chapter, and therefore it is treated here separately. The physical situation is depicted in Figure 5.1, and its main characteristics can be listed as follows: [ 1 r s susssssssgsmssssssssss) [ l Ss - - o-;e - l T" Tv S8 g Tse Ts.i * < { So -{
; s m sia ' -
[ Tio s -] n Sup gg ; -
' ^
-n_ cc__E'- ,.
' Ti.m - A s P <owSMC RA , AWM0 m i" Ti.i *lflCl8QHg g Op).
. Oli % -
[ r> - '- 1khbhhfhkhN?h j si.w c em- ~ ag$] R ~wket me me g@ ' L Tw(0) l-{ n,. T" h F g qw(0) Sw(0) &de) Figure 5.1. Schematic of the physical model used to quantify energy partition, and thermal loads l in the long-term, natural convection thermal regime. Also shown is the nomenclature used in the formulation of the mathematical model. I
- 1. 'Ihe hemisphere is almost full (6, ~75') with the oxide pool and the metal layer on top y (64 ~90*). This means that the effect of the " fill level" can be considered negligible for our purposes.
5-1 L - _ ---_ - ---_- _ - _ - - _ _ - - _ - _ _ - _ - - - - _ _ - - - - _ _ _ - - - - _ _ - _ - - - _
I
- 2. De oxide pool contains the oxidic components of the core melt (mainly UO2 and ZrO2),
with a liquidus of ~2973 K. Because of this very high liquidus relative to the cooling capability at all boundaries (see Chapter 6) this pool is surrounded completely by cmsts. l
- 3. The crusts are thin enough not to appreciably alter the shape of the enclosure, and they :
impose a uniform temperature boundary condition-the melt liquidus. As a consequence, the pool-internal heat transfer problem is uncoupled from what goes on outside, (as long as the crusts do not vanish from any part of the boundary). This means that the internally imposed heat flux, together with thermal resistances and sink temperatures, determine the crust thickness distribution all around the pool boundary.
- 4. The metallic layer is of a large aspect ratio (thin compared to its diameter) and with its sidewalls almost vertical. It is heated from below and cooled from above and its sides. g Again, natural convection drives the heat flow distribution, but now only the side boundary temperature is fixed-at the liquidus of the metal layer of ~1300 *C (see Chapter 6).
The nomenclature to be employed is as follows: From the oxide pool we have an "up" to "down" energy flow split. These two heat flows will be characterized by the average heat fluxes over the horizontal and hemispherical boundaries of the pool (q., and gan) respectively. Local values , on the hemisphere will be defined by the angular position as indicated in Figure 5.1. Note that q.(6) contains gan(6) plus the contribution of the heat generated in the crust at angular position G. The heat flows "into" and "out" of the horizontal boundaries of the steel layer will be characterized by the average fluxes qt,g and gt,,, respectively. The average heat flux through the side boundary of the steel layer will be denoted by qt,.. The quantities of primary interest to the task of this chapter are those that directly affect lower head integrity; that is, q.(6) and qi,.. However, these quantities can only be obtained from an integral analysis (presented in the l next chapter) which makes use of all the heat fluxes defined above. The formulation necessary for this purpose is provided below. Natural convection phenomena can be scaled in terms of the Grashof, Gr, and Prandtl, Pr, numbers, end in the presence of volumetric heating the Dammk6hler, Da, number is also needed. l These numbers are expressed as (Mayinger et al.,1975) Gr = gf(Tm., - Ts)H QH3 Pr = v Da = k(Tma, - T i ) (5.1) v2 a where 4 is the volumetric heat generation rate, H is a charicteristic dimension of the region in the vertical direction (i.e., pool depth), and #, k, v, and a are the fluid thermal expansion coefficient, thermal conductivity, kinematic viscosity, and thermal diffusivity, respectively. The 5-2 I I
L overall heat transfer phenomenon is characterized by the Nusselt number, Nu, defined by r qH Nu = k(Tm., - T i) (5.2) [ where 9 is the average heat flux over a boundary of interest kept at uniform temperatum T,4 and Tm., is the maximum temperature in the pool. [In the absence of volumetric heating the [ " bulk" temperature (Ta) is used in place of Tm.,.] 'Diat is, the behavior can be characterized by correlations in the form ( Nu = 7 (Gr, Pr) no volumetric heating (5.3) Nu = G (Gr, Pr, Da) with volumetric heating (5.4) L which can be obtained from model experiments or numerical simulations. Experience indicates , that most, if not all of the effect of the Prandtl number is to be found in combination with the l other dimensionless groups in the form of the Rayleigh, Ra, or " internal" Rayleigh, Ra', numbers given by l Ra = Gr Pr Ra' = Gr Pr Da (5.5) such that Nu = 7 (Ra, Pr") (5.6) Nu = G (Ra', Pr") (5.7) where rn and n indicate a small (or zero) dependance. Our task, then, is to determine the functions G and 7 (and the exponents rn and n) for the oxidic pool and metal layer, respectively. A key l point, of course, is " similarity"-that is, these functions should be appropriate for the Ra, Ra', and Pr number ranges of interest in the reactor. For the present application these ranges are: Oxidic Pr .,1 : 1028 < Ra' < 6 1016 Pr ~ 0.6 (5.8) Metallic Layer : 5 10' < Ra < 2 103 Pr ~ 0.1 (5.9) f Another key point regartling similarity is the relationship of the final, truly steady state, to the sequence of transient states leading up to it. Finally, any correlation scheme has to be explicit on the " effective" temperature at which the various thermophysical propenies are to be evaluated-normally the " film" temperature, i.e., the average value between the bulk and wall, is used, but because experiments so far related to Eq. (5.7), have been carried out with relatively small (Tm., - Tg), this is still an open question. (( Molecular diffusion considerations indicate that multicomponent effects on density and resulting natural convection cannot provide any sustain-able influence, especially at high Rayleigh numbers. This was demonstrated experimentally by Schneider and Turland (1994).)) 5-3 l
I 5.1 The Oxidic Pool The basic features of the flow regime in the oxidic pool are indicated in Figure 5.2. They consist of steep boundary layer regions adjacent to the isothermal boundary, a well-mixed upper pool volume, and a broadly stratified lower pool portion. These regions can be expected from E consideration of basic principles of natural convection and have been demonstrated by the in- E terferograms of Jahn and Reineke (1974) in a slice (semicircular) geometry. The upper mixed region is created by the cold " plumes" detaching continuously from the upper boundary layer, and the lower stratified region is the result of the downflowing boundary layers along the curved l boundary and the induced bulk motion; that is, a combination of entrainment all along the outer edge of the boundary layer, and a turnover process in the bulk (due to the wall-plume penetra-tion). The transition from the well-mixed to the stratified region is controlled by the interplay between the mixing process from above and the bulk-convection (turnover) from below. The Ra' numbers of interest are high enough to ensure turbulent motions for which we generally expect little or no effect of the length scale. This means correlations of the form Nu ~ Ra' ' (5.10) from which the length scale just cancels out. As a consequence, irgarding the behavior at the upper (flat) boundary we can also bring to bear results from fluid geometries enclosed between two horizontal boundaries, with at least the upper one held isothermal (i.e., the lower boundary l can be isothermal or adiabatic). This is fortunate because this geometry has received wider attention than the hemispherical one, and available data for it extend to higher values of the Ra' number. The following material in this section is arranged in three segments. In the first two g we consider the upper (flat) and lower (curved) boundaries, respectively, while in the third we B pursue certain interesting deductions from their interrelationship.
'Ihe best known correlations for the upper boundary have derived from the experiments of Kulacki and Emara (1975) and Steinberner and Reineke (1978). The correlations and respective ranges of the experimental variables can be summarized as follows:
Kulacki-Emara6 Nu,, = 0.34 Ra' '"' (5.11) 4 2 10 < Ra' < 4.4 1012 Pr ~7 Steinberner-Reineke Nu,, = 0.345 Ra' '" (5.12) 7 10 < Ra' < 3 1038 Pr ~7 6 (( Recast to the present definition of Ra' number)) 5-4 I
I
- I 4
ll ^ qpnpn - a V n Vj" 1 "/ I lI i g - - i5 s _/ w ./
- s Figum 5.2. Illustration of the natural convection flow and stratikation patterns in the oxidic lI pool.
The experiments were carried out in rectangular geometries, under relatively small temperature differences. Kulacki and Emara also attempted to identify an independent Prandtl number effect j (the n in Eq. 5.7) and wrote: 5 Nuo, = 0.2 Pr .239 Ra' '"* (5.13) which, interestingly enough, gives the same Ra' number dependance as Eq. (5.12). However, it has been recognized that the data base was inadequate to support the Pr number dependance. Using a Pr number of 7 in Eq. (5.13), we obtain i Nu , = 0.32 Ra'"" (5.14) which can only be seen as an independent confirmation of the correlation by Steinberner and Reineke (1978). More recently, the COPO experiments (see Appendix B) extended the Rayleigh number range to 1.5 10 18 . The COPO data were obtained with hot water (Pr ~2.5), in a large-scale facility (H = 0.8 m), and were found to be in excellent agreement with Eq. (5.12) up to a Ra' of 6 10". However, an apparent rapid transition occurred at this value of Ra' number that produced I a relatively consistent ~30% underprediction at the upper end of the range investigated. The authors of Appendix B express some caution that such a transition is not understood and that its I 55 4
I existence needs further investigation. The UCLA data (Appendix C) were obtained with Freon (Pr ~8) in a medium-sized hemispherical test section (R = 0.4 m). Both data points am below Eq. (5.12), one by 37% and the other, at Ra' = 9 1028, by 17%. It should be noted, however, that due to the experimental arrangement the values reported pertain only to the outer position l of the upper boundary. Finally, the subject has been approached thcomtically by Cheung (1980), who concluded that the asymptotic dependance for large Ra' numbers is to the 1/4 power, and that at low Pr numbers there is a separate dependance (on Pr) to the 1/4 power as well. For the intermediate Pr number range (which is of interest here) he found that Nu = (5.15) B A - B 2Pr-2/8 Ra'* " where B 3, B ,2 and A are all functions of the Pr number. He then used the data of Kulacki and Emara to show that the above formulation is consistent with " fitting" correlations of the form of Eq. (5.12) to data over lirrdted ranges of the Rayleigh number, and that the exponent would be expected to increase asymptotically to the 0.25 value. In particular, he proposed that Nu,, ~ Ra'""' for Ra' < 1022 (5.16) Nu,, ~ Ra'~ for 1028 < Ra' < 1022 (5.17) Note that this is consistent with Eq. (5.12), and its potential applicability up to the range of I our interest (Ra' ~ 10 28 ). However, he did not consider the Kulacki-Emara data adequate for g extracting the Pr number dependance. 5 In light of the above, the basic issues regarding our present needs can be summarized as follows:
- 1. Validity of Eq. (5.12) to a Ra' numbers range extended by 3 orders of magnitude. Besides the basic requirement for data support, we have the doubt cast on it by the COPO data and even (to a much lesser extent, however) by the UCLA data. It should be noted hem that due to the importance of q , on the behavior of the steel layer (see the next section), even a 30% discrepancy could be potentially rather significant to our conclusions.
- 2. Independent Prandtl number effect. Since our case requires an extrapolation (of the main data base) by a'oout one order of magnitude (fmm ~7 to ~0.6) even a small dependance g could produce a significant effect. For example, the dependance in Eq. (5.13) would produce W a reduction by almost a factor of 21 Now, the COPO data indicate that such a strong effect 5-6 I
is unlikely, since a Pr ~3 could have produced a 20% effect, rather than the excellent agreement found for Ra' < 0 1014 However, the discrepancy found for Ra' > 6 10" l prevents this issue from being considered closed. The mini-ACOPO experiments, described in Appendix D, have been carried out for the purpose of addressing these issues. They were carried out in a medium-scale (R ~0.4 m) hemispherical geometry, using water or freon as the working fluids. The experimental ranges covered were 1012 < Ra' < 7 10" 2.6 < Pr < 10.8 (5.18) and pool-to-wall temperature differences ranged up to 70 K. The main results for the upper boundary are summarized in Figures 5.3 and 5.4. Figure 5.3 shows the comparison with the Steinberner-Reineke correlation. The agreement in the region of overlap with their data (1012 < I Ra' < 3 1013) is excellent, which confirms the experimental approach in the mini-ACOPO. The agreement of the extended correlation with the data for Ra' numbers that reach up toward prototypic values is also excellent. In Figure 5.4 we show the same data in a form suitable for detecting any Prandtl number effect. None can be seen, and we can thus see no problem for I using this correlation under a small extrapolation down to Pr ~0.6. r.,,g , , , , , , , ,
,,,,,,g
,,,,,,g i
1000 - [500 - f Z _ l 200
- l 1
. i ,1 , , ,,,,,,I , ,
,,,,.I , ,
,,,,,,I 13 15 10 '
1 10 10 " 10 Ra' ; E Figure 5.3. The mini-ACOPO results for upward heat transfer against the Steinberner and Reineke (1978) correlation. Data in the range 3 1013 < Ra' < 7 10" are from run A16, the last Freon run, and the rest of the data are from runs B1, B2 and B3, carried out with water at various temperature ranges. Properties evaluated at " film" temperature I 5-7
i 1.4 - gI g g _ y 1.2 - 8 5....- _
$ 19
~
d AM d. . S i....... z
- ? 0 6 h T
l 06 .
,.,,I , , , , I , , , .l . , , . l . . . .-
2 4 6 8 10 12 g Pr 5 Figure 5.4. Mini-ACOPO data normalized according to the correlation in Figure 5.3, shown against the applicable Prandtl numbers. Finally, it is worth mentioning the numerical simulations of Mayinger et al. (1975) and of Kelkar et al. (1993), mainly because they appear to have actually produced correct predictions for the downward heat flux (see below). Both calculations were carried out for a hemisphere. E Mayinger et al. covered the range 7 10 8
< Ra' < 5 10", using a Prandtl number of 0.5 and 5 fitted the results (for the upward heat flux) by Nu,p = 0.4 Ra' .2 (5.19)
I It can be readily seen that this result at a Ra' of 10 18 would under-predict Eq. (5.12) by a factor of 3. The numerical simulations of Kelkar et al., were run with the low Reynolds number turbulence model of Jones and Laurder and included a " wall correction" due to Yap. Results were given for 10 8
< Ra' < 10 18 and a Prandtl number 1. They can be well fit by Nu,p = 0.18 Ra'""* (5.20) which can be seen to be essentially parallel to Eq. (5.12), but to provide a consistent under-prediction by almost a factor of 2.
Experiments for the hemispherical boundary ((downwards heat transfer}} have been prob-lematic because of the difficulty in producing uniform heating. Thus, a slice (semicircular) 5-8
E geometry has been favored, even though it cannot reproduce the converging effect of the bound- [ ary layers pmsent in the full geometry. The experiments of Jahn and Reineke (1974) were run with water (Pr ~7), covered the range 10 7
< Ra' < 5 10 10
, and produced H 3 2s Nuan = 0.54 Ra'o'i. l (5.21)
-R) l The measuament also provided local heat fluxes and an indication of the peaking at higher polar angles. Equation (5.21) was confirmed by the COPO experiments and thus extended to I 4 1012 < Ra' < 1.8 1018 and Pr ~3. Data wem also provided for the local heat fluxes on the vertical and lower boundaries. Mayinger et al. (1975) were able to reproduce Eq. (5.21) using the Navier-Stokes equations with an eddy diffusivity model, which was then applied to an axisymmetric geometry to produce Nuan = 0.55 Ra'" (5.22) for 7 108 < Ra' < 5 1014 and Pr = 0.5. These as well as the COPO data were also interpreted
[ by means of a turbulence model, incorporating an empirical modification of the eddy diffusivity F via the Richardson number (Dinh and Nourgaliev,1994). Kelkar et al., (1993) in the calculations mentioned above provided predictions for Pr = 1 and Ra' numbers up to 1018 which can be fit L Nuan = 0.1 Ra'0,25 (5.23) 7 This is a quite different trend than that in Eq. (5.22), but interestingly enough, at a Ra' number ' of 1015 a discrepancy between these two equations is only ~2%! p The UCLA experiments mentioned above, and descdbed in Appendix C, also provided data ' for the lower boundary of the hemisphere. Two data points on the average fluxes obtained at 8 y Ra' numbers of 3 10 8 and 9 10 are in good agreement (15% higher) with Eq. (5.22), and L the local fluxes were cormlated by c h(6) L = ci sin 0 - c2 cos O for 0.75 < 6 < 1 (5.24) where c1 = -1.25 cos p + 2.6 [ c2 = -2.65 cos 4 + 3.6 and h(6) 6 l = 1.17 sini O + 0.23 (5.25) h for 0 < 4 < 0.75 5-9 i
I where d is the polar angle at the pool surface, and O = jj. These experiments are encouraging in tying in with Eqs. (5.22) and (5.23); however, there are several aspects in relation to the present application that iequire further clarification. They can be summarized as follows:
- 1. Based on the highest UCLA data point, the present use would require an extrapolation on the Ra' number by nearly two orders of magnitude. The higher trend in Eq. (5.23) than from Eq. (5.22) (with Ra' number) then becomes of concern, especially as Kelkar et al. noted l
that (due to this trend) the downward heat flux approaches the upward flux at the high Ra' , number range of interest here. As noted previously, their upward fluxes are underestimated by a factor of 2, which weakens this conclusion but does not eliminate the concern.
- 2. Although there is adequate experimental basis now (as explained above) that any inde-pendent Pr nuaber effect is slight enough to be negligible at the upper (flat) boundary, g indicating a high likelihood that the same is true for the curved boundary, this is still tenta- E tive and subject to experimental verification. [Both UCLA data points were obtained at Pr
= 8.2.]
- 3. The microwave radiation heating technique employed in the UCLA experiments requires a slightly coupling medium (freon) in order to obtain uniformity over the scale of the experiment. This low heating rate forced operation at mther low tempemture differences (Tm., - T4), while conduction resistance through the glass wall produced a non-uniformity in Tg of similar magnitude as the (Tm.,- Tg) itself. For example, the run at Ra' ~ 0 1023 l
involved a (Tm., - Tg) of 1.9 K at the top and a (Tm., - Tg) of 5.8 K at the bottom of the pool, while the Tg varied by 4.5 K from the equator to the bottom of the hemisphere (Asfia,1994). This could raise concerns about the appropriateness of the comparison with Eq. (5.22), or the validity of Eq. (5.24) to an isothermal boundary situation. [However, current efforts at UCLA are directed at obtaining freezing at the boundaries which would ensure an isothermal boundary-in this case the flux distribution can be obtained from the variation of crust thickness.]
- 4. Transient effects. While heat transfer at steady state occurs with a stable stratification pattern as indicated in Figure 5.2, consideration of transient behavior, besides pool thermal inertia effects, also needs to be concerned with timewise variation of this stratification pattern.
In particular, starting from a uniform pool, this final pattern would be approached from a sequence of more uniform (than the final) states, and one might ask how this would affect the up-to-down energy flow split and the flux distribution over the curved boundary. Clearly, there is a potential here for significantly higher (than at steady state) thermal loads E at lower positions on the lower head. Given the shape of the critical heat flux (Figure 3.3), E it is immediately obvious that this topic constitutes a major open issue. 5-10 I
[ 1000 ,,; , , , , , , , , , , , , , , 500 {
~
( 6 . . , -
- $ 200 -
100 - [
~
50 l ' ' ' l - 'l - - - 'l 10 10 28 lo u tois Ra' Figure 5.5. The mini ACOPO results for downward heat transfer against Eqs. (5.27) and (5.28). Shown are: run A16, the last Freon run, and runs B1, B2 and B3 carried out with water at [ various temperature ranges. Properties evaluated at " film" temperature. The mini-ACOPO experiment mentioned above (and described in detail in Appendix D) L was built and operated to address this different set of issues as well. Again, the experimental ranges covered were 1012 < Ra' < 7 10" 2.6 < Pr < 10.8 (5.26) y and the pool-to-wall temperature differences ranged up to 70 K. The main results for the down-L ward heat transfer are summarized in Figures 5.5 and 5.6. As seen in Figure 5.5, the data are ~ tightly correlated by
-Nugo = 0.048 Ra' '" 1028 < Ra' < 3 1028 (5.27)
Nugo = 0.0038 Ra' '" 3 1028 < Ra' < 7 10" (5.28) [ Even though an overall correlation c L Nugo = 0.02 Ra'" 1012 < Ra' < 7 10" (5.29) would still fit quite well, the use of the upper branch (Eq. (5.28)) is deemed preferable for this application. In Figure 5.6 we show the data in a form suitable for detecting any independent Pr number effect. None can be seen, and we can thus conclude that Eq. (5.28) is applicable under L the modest extrapolation to a Pr number of 0.6. r 5-11 i L ! m_-._____ _ _ ___-____._ m_.___m________._..__.__________--m_.-_ _ _ _ _ _ _ - _ _ _ - _ _ _ _ _ - _ _ -__-____-.___________._:___._______._________ _ _ _
a h _ , , , ,
~
1.4 - - g - 3 : :
< 1.2 - -
l 4 - - I t t , ., l\ lANI l1' . , ,
] ' l/ 7 h;f4 ,A~" S y i O - -
08 h b g _ _ 9 . : a
%y 0.0 -
B j - , , ,,J . . ..l . , ,,I . ..,! , . , ,- 2 4 6 8 10 12 Pr , Figure 5.6. Mini-ACOPO data normalized acconting to the correlations in Figure 5.5, shown against the applicable Prandtl numbers. l Another interesting perspective can be obtained from Figure 5.7, containing the present data and correlations, Mayinger's correlation (Eq. 5.22), the numerical results of Kelkar et al., and l the UCLA data. We can see that all of these results are mutually reinforcing. While in the range expected to dominate the thermal loads in this application (1018 < Ra' < 5 1018), the Mayinger correlation provides a lower bound, the present correlation provides an upper one (the g trends of the UCLA data and Kelkar et al. simulations indicating an intermediate behavior). The E effect of using the lower bound in the analysis is examined in a sensitivity study in Chapter 7. Now, revisiting the four issues being addressed here, the mini-ACOPO data show that even under the most extreme transient conditions (as in run A16), the boundary layers and overall stratification patterns develop quickly enough to exhibit an average behavior quite consistent with steady state behavior. However, these data also show a finer structure of stratification pattern adjustment, as a result of the transient, that produces some variation of the heat flux distribution. This is illustrated in Figure 5.8, containing all the mini-ACOPO data, and including l for comparison the UCLA correlation and the shape found by Jahn (Mayinger et al.,1975) in a slice geometry at an Ra' number of 1.2 1010. This figure also shows that g 2 a Nugo(6) Nuan 6
= 0.1 + 1.086,- - 4.51ge,)l
/63
+ 8.6 -
g
- g< 0.6 0.1 < 6, (5.30a) 6, 5-12
I , 1000 i
~
o 500 ''h* l l
,,..-v,,-
i D
.g
***~,,, . **'
]
E a .... 200 0.0038 I - 3 -
--- 0.55 Ra'g'"5 Run A16 O Asfia and Dhir o Kelkar et al.
100 ' ' ' I - ' > iil i i i 10 10 10 Ra' I Figure 5.7. The mini-ACOPO data (downward heat transfer) and correlation obtained from them (Eq. (5.28)), shown against the Mayinger et al. (1975) correlation, the UCLA data, and the results of the numerical simulations by Kelkar et al. (1993). 2 Nua"(6) 6 6
= 0.41 + 0.35 - + - ,
0.6 < 6p 6<1 (5.30b) I Nuan 6p 6p reasonably represents the mini-ACOPO data. Although this correlation wat derived with full hemisphere, it remains adequately normalized, and we expect it to be reasonably valid for I 60 < 6, < 00'. The UCLA correlation exhibits a somewhat more peaked distribution, and it will be used in a sensitivity study in Chapter 7. Also shown in Figure 5.8 is the result of the numerical simulations (Ra' = 10" and 10") of Kelkar et al. (1993). It exhibits a trend more uniform than any of the experiments and, in fact, in the important upper regions it provides a lower bound. Further confirmation of the treatment proposed here will be obtained with the ACOPO experiment which is presently under constmetion. Operating at a 4 times larger scale than the mini-ACOPO it will afford a much longer " internal time scale" and hence full exploration of the stratification adjustment effects discussed above. The key characteristics of this experiment have been summarized in Table 5.1, and put into perspective with the mini-ACOPO, and the other ongoing experiments at UCLA (currently efforts to obtain freezing at the boundaries), and at IVO (currently directed to a semicircular slice geometry, with freezing at the boundaries). In addition, the BALI experimei.. . CEN, Grenoble (similar in concept and scale to the COPO, 5-13
) ) ,
o Mini-ACOPO
/-
Eqs. (23)-(25)
/ '
2 -
/
Mayinger et al 1985) / -
--------- UCLA Eqs.(2
" 21) /
Kelkar et al 1993) ,/ p
$ / {f '
g' ' l. ...!
.) 1 -
5,
% ~,-
... s -
~*
. .. ... . g ' c- *** '
o '
'l I - . . . l . , , , ! , , , ,l , , ,
0 20 40 00 00 Angle (degrees) g Figure 5.8. The mini-ACOPO data and the correlation obtained from them (Eq. (5.30)), for heat flux distribution as function of the angular position, shown against the UCLA correlation. Also shown is a line through the data obtained by Jahn (Mayinger et al.,1975), for Ra' ~ 2 1038, renormalized (by area averaging) to an axisymmetric geometry, and the result of numerical simulations by Kelkar et al. (1993), for 1034 < Ra' < 1038 . but including additional capabilities, such as gas or liquid injection at 6e boundaries), expected to be operational in the near future, should be mentioned (Bonnet et al.,1994). Table 5.1. An Overall View of Recent Work with %lumetrically Heated Pools Experiment working scale / Shape T .. - T4 Pr Ra' 4 Concept Dimensionality Fluid (K) COPO 1/2 L ,Mu Water 10 2 < Pr < 3 1
- 10" < Ra' < 8 10" Joule IIcating 2-D slice UC1.A t/8 semisptwrical Fnon-ll3 2 to 8 8.2 < Pr < 0.5 4 1088 < Ra' < 1 10" Macrowave Heating Axisymmetric Mmi-ACOPO 1/8 Semlaphenical Freon-ll3 40 7 < Pr < 11 2 lois < Ra' < 7 10" Cooldown Axisymmetric 9'ater 100 2 < Pr < 10 1 10u < Ra' < 3 10 8 ACOIC I/2 Semispherical Fream-Il3 40 Cooldown 7 < Pr < 11 1 10" < Ra' < 2 10" Aalsymmetric Water 100 2 < Pr < 10 4 10" < Ra' < 2 1088 um 5-14
E Finally, it is instructive to consider what can be learned from Eqs. (5.12), (5.28), and (5.30), regarding energy partition from the oxidic pool, and resulting local thermal loads at the curved boundary. First, the ratio of the up-to-down heat fluxes can be obtained from: R' s "" = 90 Ra'~ " (5.31) Nua, which for Ra' ~ 5 1018 gives a ratio of 1.31. Using Eq. (5.22) in place of Eq. (5.28), on the other hand, we obtain l R' s """ = 0.63 Ra'"" Nuan (5.32) which for the same Ra' yields a ratio of 2.1. Now, from an overall energy balance on the oxidic pool (of volume V) we have 4V = S.pg., + Sanga, (5.33) which for an hemisphere can be written as gan = QV {2rR2 (1 + 0.5R')}-* (((5.33'))) where R' is the ratio defined above (Eq. (5.31) or (5.32)). This allows a simple estimate of gao, for Ra' numbers around the 5 10 52 value utilized in the derivation, and using it to estimate the flux shape (from Eq. (5.30)), and q., (from the value of the Ra'). In the next section we will l show how the complete solution for the steel layer can be obtained after q., is known. [For , cases where the Ra' is significantly different than 5 10 15 , the same procedure can be utilized, after solving Eq. (5.33) for the Ra' number, as discussed in Chapter 6.] For example, supposing 8 that @ = 1.3 Mw/m3 and V = 10 m (typical values for the AP600), and with R = 2 m, we obtain gao as 313 kW/m2 or 252 kW/m 2depending on whether the R' is obtained from Eq. l (5.31) or (5.32), respectively. We can see that the sensitivity is only ~25%. We can also see that even with a bounding peak-to-average value of 2 (see Figure 5.8) we cannot expect local 2 f values much in excess of 626 kW/m at 6 ~ 90", which shows a margin of safety by over a factor of 2 (see Figure 3.3). ((The 10 m 8do not quite fill the hemisphere and use of Eq. (5.33') j is only approximate. Using Eq. (5.33), we obtain gao = 391 kW/m2 . On the other hand, using , the complete numerical solution according to Chapter 6, we have gao = 357 kW/m2 ,jj l 5.2 The Metallic Layer l Available work in this area has considered only situations without side wall cooling; that is, liquid layers heated from below and cooled on the top. Our approach is to make use of this work in conjunction with heat transfer to a vertical wall, in a manner that conservatively represents this most important, for our purposes, component. The discussion proceeds in three steps. In the first we summarize available results for natural convection through liquid layers. In the second we consider natural convection to a venical, cooled wall from an ambient fluid. l i 5-15 l i
Finally, in the third step, we explain how the previous two components can be put together to treat conservatively the role of the metal layer in the model that integrates the heat transfer behavior. This third step is also supported by a simple simulant experiment, run specifically for this purpose. On the first step, let us begin with the widely used Globe and Dropkin (1959) correlation, 7' Nu = 0.069 Ra2 /8 Pr (5.34) incorporating data with various fluids (0.02 < Pr < 8750) at Rayleigh numbers in the range 5 8 3 10 < Ra < 7 10 . For the relevant Prandtl number (~0.13) the above correlation reduces to: Nu = 0.059 Ra2 /8 (5.35) On the other hand, there is considerable evidence in the literature that for turbulent flow (high l Ra) the Rayleigh number exponent should be less than 1/3. In fact, works by Silveston (1958) and O'Toole and Silveston (1961) recommend, respecdvely, Nu = 0.1 Ra' 82 Pr 8 and Nu = 0.104 Ra 8 8 Pr 84 (5.36) while Goldstein and Chu (1969) determined an exponent of 0.294 for air (Pr~1). For Pr = 0.13 Eqs. (5.36) reduce to i Nu = 0.09 Ra .31 and Nu = 0.088 Ra' 8'8 (5.37) which are in apparent difference with Eq. (5.35). In fact, at the range of Rayleigh numbers of interest here, Ra ~10 , these results are quite close, as can be seen by forcing Eq. (5.35) to a l 0.31-type dependence on the Rayleigh number, that is, Nu = 0.1 Ra882 (5.38) Based on these considerations we can be quite confident in using Eq. (5.35), which is therefore I selected for the analysis carried out in the next chapter. For the second step, the situation is one of heat transfer to an isothermal vertical plate, and the appropriate driving force is the bulk liquid temperature rninus the plate temperature. The heat transfer coefficient can be obtained according to Churchill and Chu (1975) from t 0.387 Ral /8 Nu /2 = 0.825 + (5.39) {1 + (0.492/Pr)8/18 }"/8' 5-16 Il I
which is valid for any Prandtl number and Ra < 1012. Again, the properties are to be evaluated at the " film" temperature. For Pr = 0.13, the reduced form of the above equation is Nu = 0.076 Ra3 /8 (5.40) Note the similarity of this to Eq. (5.35) above; however, also note that Eq. (5.35) is based on a AT that invclves two, rather than one, boundary layers. As we proceed now onto the third step it is appropriate to first consider the role of the metal layer qualitatively. For a given thermal load at the lower boundary of this layer (note that this is determined solely from the natural convection processes within the oxidic pool) the behavior is controlled by the thickness of this layer and the radiative emission properties of the upper boundary. De basic trend is easy to see: as the thickness and/or the emissivity decrease, the layer temperatures must reach higher and higher levels, and since the thermal boundary conditions at the vessel wall must remain fixed (at the melt liquidus), the heat fluxes into it must increase correspondingly. This " focusing" effect can be counteracted only by one mechanism, owing to the rather large aspect ratio (layer diameter to height) at which this focusing effect begins to become important. That is, eddy diffusion limitations in the bulk, and the development as a consequence of a significant lateral temperature gradient. This rnechanism has been confirmed in the experiment discussed at the end of this chapter and in Appendix N, and we expect to quantify it in the large ACOPO experiment in the near future. For now, we will make the conservative assumption that the layer is well mixed in the bulk. l In addition, recognizing that the situation described by the Globe-Dropkin correlation is symmetrical (two boundary layers of equal magnitude in temperature drop), we can " specialize" Eq. (5.35) to either of the two boundaries as h = 0.15 k I av AT'}1/3 (5.41) where AT' = Tr,4 - Te or AT' = Ta - Tr,,, and T is5 the " bulk" temperature, and where properties are evaluated at the " film" temperature of the respective boundary layers. In Chapter 6 this equation is used in conjunction with Eq. (5.40) to describe the metal layer. That this formulation is appropriate and conservative has been demonstrated experimentally, as discussed l in Appendix N. , To gain some general perspectives here on the role of this metallic layer, we make use of these equations together with the following simplifying assumptions (to eliminate second order effects): 5-17
- 1. He property group in Eqs. (5.40) and (5.41) has the same value at all three boundaries.
- 2. He upper and lower boundaries of the layer have the same area (thin, at ~90*).
- 3. He crust between the oxidic pool and metallic layer is thin.
- 4. He energy radiated from the surrounding cavity to the layer is negligible.
From energy balance considerations we then have (see Figure 5.1 for nomenclature): (Ts,4 - T6 )4/s = (Ts - T,,,)'/8 + (Ts' - Ts,m)'/8 (5.42) 0.15k (T6 - Ts,,)'/8 = cat,4,, (5.43) au) q,, = 0.15k f b (T,,4 - T 6)</a (5.44) (av) that is, three equations in the three unknowns Ts, Ts,4, and Ti,.. The Ts,4 can be eliminated by { substitution from Eq. (5.44), and the T5 can be solved explicitly in terms of Tr,, from Eq. (5.43) to obtain: l
- T6 = Tt,, + ( Tf,, (5.45) and q., = (ea)T,',, + A I (Te,, - T,,m) + ( T/,, (5.46) where 3
( ggt 2/8 . g A = 0.15k 1 l (5.47)
@v)
This system of equations reveals a characteristic temperature for this problem given by l' = ( A )l3/8 to) (5.48) from which we can also define a characteristic heat flux, i = cal'4 (5.49) l Based on these quantities we can define the dimensionless variables: Ti = .Tb T/,, = T'J* T/,,= b* T q,,= M q (5.50) l 5-18
~
I
l i and the above system becomes: ( Ti = T/,, + T/,*, (5.51) 9., = Tj,.,+ /H,}S f/,, + Tj,, -. Tj,,}4/8 (5.52) and the heat flux to the sidewall can then be written as: 97,, = (Ti - Tj, )*/8 (5.53) [ where the independent parameters of the problem, A, e, Te,,, and g.,, have been recast in terms of q;, and T/,,,, only. 'Ihe other 3 xlependent parameter, Hs/R, remains the same. The solution of the above system of equations can be obtained numerically, once and for all, and it is shown in Figures 5.9 and 5.10. Fmm these, the sidewall heat flux can be obtained using Eq. (5.53), and the result is shown in Figure 5.11 When q., is less than the value at which Tj,, = Tj,, freezing of the upper boundary is predicted, and a closed form solution for the sidewall heat flux can then be simply obtained as: 1
-3 1 Hi gt, = 39., 1+7 .
(5.54) As an example of using these solutions, consider the following typical values of the pa-rameters: A = 2764 W/m2 . K4/8, c = 0.45, T4,, = 1600 K, g., = 600 kW/m , 2and suppose that Hr/R = 0.4. From Eqs. (5.48) and (5.49) we obtain l' = 1.37 104 K, and i = 9.1 10 8 2 l kW/m , from Eq. (5.50) we obtain Tj,, = 0.116 and q , = 0.66 10-8, and from Figures 5.9 and 5.10 we read Ti = 0.12254 and Tj,, = 0.12078. Then, from Eq. (5.53) we calculate 2 97,, = 5.58 10-4, which finally gives gt, = 508 kW/m (this can also be read directly off Figure 5.11). Moreover, from Figure 5.10 we find that freezing of the upper boundary will occur for an Hi/R value of 0.3, if q., = 220 kW/m2(q:, = 0.24 10-8); in this case the sidewall heat flux would be (from Eq. (5.54)) 85 kW/m2, and for any larger value of Hr/R the side heat flux could be obtained from 2 gt,,= 110 1+ kW/m for > 0.3 (5.55) Finally, the above results can be used to determine in a rather general way the metal layer
- thickness below which the sidewall heat flux will exceed the peak heat flux from the oxidic pool boundary (at the upprmost end of it). Again, the above typical values of A, e, and Ts,, can be used, so that we have only one " free" parameter-the q p. A given value of q., implies a pool
{ 1 5-19
0.15 ' - , , ' - . , ' ' ' ' - , I l g . Us/R. O'.g UdR= 0 ~
...-~~.
Hs/R= 0.0 g Ra 0.14 H /R= 0',4 05
'~~~~ -
~
' ' ' . . . . .. .- .. .. .. . . ~ . .
fD _
]......**,,,,,,,,....
- ;.!. !!".'.'2,_ ____
___"._. _ _ - _ _ ___ - _____ _ __ __~ 0.13
~ . . ..z-;2.0.0._3___:_:_:_:_ __. ...
.......-. ~~~~~~~~~ ~~~~~~~~~~~~
_ . . . . . . . . . .~.~.~. .~ O'IU
'. ...=,.... . _.__. _ _ . .' . _ . _ . . _ . . . _ . . . _ . . _ _ _ _ _ _ _ _
_ ~
; ' ,,l - . . .
0.2 0.4 9 up* 0.6 X 10 3 O~8 1.o I O.16 , '
.,,l ' ' , , ' ' . . ' . ,
l I l U,/R, o,3 H /R= 0.2
~
3 Un/Ra 0'3 -
.. ""' H,/R a o'4 H /R= 0,5 '
~~-
0.15 -
~
~._.~
.4
....._ . ._ . .,,_._ ,_ ,_ , ,_ , ,_ , ,_ , ,_ , , _, ,_. ._~ _
-~ _
~ '_
E~ I
~ ..
" ~ " ~ " '.... -
0.14 ...
'""((...........~....~~"......_ _ __ __ __.__ ___
.~'[__
; / , , B ' , ,
0.4 0.6 9up' X 10 0.8 3
'O 1.2 I
Figure 5.9. Solution to the system of Eqs. (5.51) and (5.52) for Ti, with He/R and T/,, as the parameters. Each group of Hr/R lines is for one value of Tj,,,,. Before using these figures first l identify the T,*m values for each for the four groups of lines in Figure 5.10, and then proceed to Figure 5.9, recognizing that the four groups are similarly placed. Also note that corresponding lines (same Tj,,,,) start at the same value of the coordinate (qlp). 5-20 f
l I I 0.14 . , , , , , , , , , , , , , , , g
~ Hs/R. o'; ~~~
Hs/Ru o,g Hs/R. o# . .. .. -
....'~ U/Rm o_ ...
s 0.13 , Hs/R. .5 - g o
~ " " _....... ...
~ ~ ~ ~- . - . - - . " . - _ _ _ _ _ ..
-: -:~~.!~~ ..... .. -- - - - _
0 12 ~
....- . . ~ -
... : ..22..
. 222... .__. -
' ' I ' I ' ' I '
0.11 O.2 0.4 0.6 0.8 1.0 3 qup X 10 l l l l _ M U o . 0.15 l!$s/Ra " gj R: U /g, 0'4 Ha,/R. 0,o
~
O
-= .______. ...__ _____, . . . . . . . . . . . ,. . , . . .
*4 .
p ' 0.14 ~e
......... ___ _... ~_ ....
_________ "_~___ _________.. f
. ...;.;; _;; _. _. _. .__~ ._ _ _ _ ____ _ ___
' I - - - - I I I o.13 - - - - - - - - - . . -
0.4 0.6 0.8 1.0 1.2 8 qup' x 10 Figure 5.10. Solution to the system of Eqs. (5.51) and (5.52) for Tj,,, with He/R and Tj,, as the parameters. Each group of H t /R lines is for one value of Tj,m-it can be read from the position at which the lines stop. As noted in the text, the lines stop when there is freezing at the upper boundary, that is, when Tj,, = Tj,m. There are four such groups. 5 21
I 3 ' . , , ' ' . , ' ' , ' ' ' ' I I / I g Ilj/R. og /
- .-....lpg/Ull: i-y=
11 3 o',S . af 2 ~ - a. a ~ N . . . . . . . .. .. ... .. .. .~. .~. .. . - . . - . . - - - c ,,,,,.......- w .
- -- ---- -~~------- --..
1- ...... . ..-..
.r s= ,,a:.......................................=
...... ~~~~~~~:::.~.~.~.'
A,"**~C,~..,,.====-----
- , . . ,$ . :.j'~-l-
, ,- ' ' ' . l , , ' - I , , ' '
0.2 0.4 0.6 0.8 1.0 3 9ap. X 10 I l 3, - . , , - . , , ' ' - , I '...I I I
' il>/R. o,3 Ils/R= 0.2 --
!!h":y
^
ll,/R. 0,5 2 ~ ~ n. D w - N ........--...- W .... . 1
- - - - . . . . . . .- .. .. .. -. ... .. .. .. .. ~
. ,..,- w - -- ---- - - - -- - ---- _-_-- -__- -.. ..-
- - w.: . - = -
... a:.:
~
,,t
-o ' I . , . , ' ' f . . . , f ' ' - i 0.4 0.6 0.8 1.0 1.2 8
qup X 10 Figum 5.11. The heat flux to the sidewall, in contact with the metallic layer, obtained from the I solutions in Figure 5.10 and Eq. (5.53). Again, each group of H,/R lines corret ponds to one value of Tj, . Note that the Tj,, can be found in each case with the help of Figure 5.10 (by locating the cormsponding minimum value of q',) l 5-22 I
1000 , ,
^
g,, , u s . E- c = 0.4 0 - N c = 0.50 - 5 000 -
.-- - ... . . c = 0. 6 0 -
c = 0.70 : 4 - k 600 4 '
, - ' . , ~. -
~2 '.'. :
v2 .. . 400 -
- o
- a .......a ..
) .. . , ,
200 - a --..--..._.,,,----.---.. c . , , , , , o . .. _o . . . . l . . . . 1 . . . . l . .. . l . . . . 0.1 0.2 0.3 0.4 0.5 0.6 Hi /R Figure 5.12. Solution to the system of Eqs. (5.51) and (5.52) in physical variables, with the emissivity as the parameter. g., = 400 kW/m 2, and A = 2764 W/m .2 K4/s. For the chosen value of q.,, the peak heat flux at the edge of the oxidic pool is 350 kW/m2, and the intersections j shown represent the threshold values of He/R for the various emissivities. 2000 , , , , g, , , , g g, ,,. g N g q,,= 300.k W 8 ' N q,,= 4 00.k W k , o,,=500.kW m, - d 1500 's, q,,=600.kW m' - 4 -
~
k -, ',. , g 1000 - v> ., ., O '. x
.3 ' '
500 -'-
- k. -'-o-...'.," _ , ,
a _ e .. ,, ---~~-.......,,_, d ...... *--*--_ U m _ t
* ' ' ' I ' ' ' ' I ' ' ' ' I I
-0 ' ' ' ' '
O.1 0.2 0.3 0.4 0.5 0.6 l Hi /R Figure 5.13. Solution to the system of Eqs. (5.51) and (5.52) in physical variables, with the imposed upward heat flux as the parameter. e = 0.45, A = 2764 W/m 2 K4/8 The threshold values of Hi/R, obtained as in Figum 5.12, are shown by the +'s. 5-23
1 Il Rayleigh number (from Eq. 5.12), which in turn gives ga,, (from Eq. 5.28), and the peak flux at 6 ~ 90', from Eq. (5.30). This value is then set equal to gt,, and making use of the procedure in the previous paragraph,in reverse, we can determine the cormsponding value of He/R. That 1s, calculate T, T,*,, and q, use q., and gt,. to get q', and q;,,, use Eq. (5.53) to get Ti, and l from Figum 5.10 read (or interpolate) the He/R value that satisfies this solution. A graphical depiction of the solution in dimensional variables, and including the just-discussed " threshold" values of He/R (the " threshold" marks the transition from oxidic pool to melt layer heat flux g dominance) is provided in Figures 5.12 and 5.13. E I (( ADDENDUM TO CHAPTER 5)) FLUX SHAPE EFFECTS OVER THE METAL LAYER It is well established that in natural convection from a vertical, flat plate, under turbulent flow conditions, the Nu number is proportional to the one-third power of the Ra number, which leads to a length-scale independence of the heat transfer coefficient. In particular, this is true for Eq. (5.39) utilized in the present work. Now, transition to turbulence occurs at a local Gr, number (based on the length from the initiation of the boundary layer) of ~108, which for a Pr number fluid of 0.13 translates to a local Ra, of ~10 . 7For our base case the Ra based on the whole metal layer thickness is ~ 1020, and noting that
=
(5.56) we find that transition occurs at an z/Hi value of 0.1. For the 80 cm pool, therefore, we can expect a uniform heat transfer coefficient for the lower 90% of the height (or 72 cm) and a short, 8-cm long, region at the top, where the flow may be laminar and/or transitional. For the l extzme parametric case (Figure 7.16) the P.a number is ~ 5 10s, and transition is obtained at an z/He value of 0.27, or 6 cm. These represent the two extremes for the problem at hand, and the insensitivity in the physical dimension of the laminar mgion is due to the cubic dependence g in Eq. (5.56). 5 In the laminar region the heat flux varies with position in the manner derived by Squire g (1938): E Nu, = 0.508 Pr /4(1 + Pr)-3/4 Ra /4 l i (5.57) 5-24 I I
For Pr = 0.13, this becomes Nu, = 0.30 Ra i /4 (5.58) and the flux (heat transfer coefficient) shape relative to that in the turbulent region can be obtained by dividing through Eq. (5.40), as h, Nu, /Hi Hi
-= -
= 3.95 Ra'2/4 -
Ra, < 10 7 (5.59) h Nu l( x Ra /3 z
'Ihe result for the two extreme cases considered above is shown in graphical form in Figure 5.14.
Note that the high fluxes are confined to such a small region that we can expect 2D conduction effects to more than compensate for them. This is demonstrated below for the more limiting, the extreme parametric case. The heat transfer model is illustrated in Figure 5.15. The convective heat fluxes over the segment of the wall in contact with the oxidic pool was obtained from the analysis that led to Figure 7.16. The radiative flux at the upper exposed segment was obtained from the radiation f t emitted from the top of the metallic pool, again according to the integral analysis. The wall shape was adjusted so as to obtain an intemal isothermal boundary at the specified melting point of 1600 K. The results of the calculation are shown in Figure 5.16. The wall shape can be seen more precisely in Figure 5.15. In the upper portion we find that 2D conduction is able to just about compensate for the enhanced heat transfer in the entrance region. In the lower portion we find [ that 2D conduction can provide some relief of heat flow and hence allow a locally smoother transition in the wall thickness. These are generic, bounding results. L : 5-25
I 15 y , , , , I k Hi = 22cm - 13-1 ----- K - 80cm _ 7
~ -,
5, I
~E 11 ..',
l 3 . . d 9
/ f \.,'.* -
l 7 -
- ...,... . = . . . . a,c.......... -
ll i , , , 0 0.02 0.04 0.06 0.08 0.1 x [m] l Figum 5.14. Heat flux shape in the entrance, laminar boundary layer, region for the two extreme g cases considered in Chapter 7. The H = 80 cm is for the Base Case, and the H = 22 cm is for a the Extreme Parametric (see Figure 7.16 in Chapter 7). p adiabatic
\\\NNNNN y a: radiative flux 0.08 MW/m2 l u
> b: radiative flux 0.165 MW/r$
2.1 W/E , ,,p og g metallayer 3 b 1.21 MW/m2 s,,j l E E x die pool 0.s1 Mw/m2 g
+
e fixed temperature <i20oc)
+
- m I
adiabatic Figure 5.15. The heat transfer model employed to evaluate entrance region effects in conjunction with 2D conduction. Wall dimensions are to scale, the upper portion being the full wall thickness of 15 cm. 5-26 I
7-4 4
*.. 97
~
- l
- 4. JOR +GJ 1600 1400 1300 l1500 1200 1100 1000 900 800 Figure 5.16. Calculated temperatum (left; in degmes Celsius), and normal (to the wall outer boundary) heat fluxes (right, only the region at the metallic layer is shown; in kW/m2 ) for the model of Figum 5.15.
I f l 5-27 l
6 FORMULATION OF THERMAL LOADS UNDER NATURAL CONVECTION The purpose of this chapter is to explain how the key transport processes discussed in the previous chapter are integrated into an overall computational scheme. In addition to these processes, the thermal radiation / conduction path to and through the core barrel and vessel wall to the water outside is considered explicitly. Since the model and the computer programming work are straightforward, we took a special purpose approach; that is, emphasizing simplicity of presentation through approxi.aations quite acceptable in this application, rather than generality. Checks in the calculations, as described below, ensured that the error due to these approximations is less than a few percent and always on the conservative side. We are given the volumes V and V, of the oxidic pool and the metallic layer respectively, their compositions, and the volumetric heat generation rate, Q, and we seek to find qu,(B) all around the lower head. From the volumes we can calculate the heights, H and Hi , and polar angles,6, and 6,t using: 1 2 2 (6.1) V=3xH (3R- H) for V $ '3wR' 1 2 V + V, = gx(H + H,)2(3R - H - Hz) for V + V, 5 grR (6.2) and cos yB = R - H , cos Og = R - H - He The above apply for volumes less than that of the hemisphere (jrR3), which is always true for V. When this is violated for V + V all that is needed is He, which can be obtained by adding ( i the height in the cylindrical portion of the vessel to the metal height in the hemisphere (i.e., R - H).Using the compositions we can obtain the thermophysical properties from Appendix [ L and the liquidi from the phase diagrams in Figures 6.1 and 6.2. The heat generation rate is assumed to be uniformly distributed throughout the oxidic pool (including crusts). In reality, ' some of this decay energy will escape the pool as gammas, to be deposited in the vessel wall or the metallic layer, while some will escape the system altogether. Scoping and sensitivity calculations have indicated that such effects are quite negligible. We now proceed to solve for the pool, the metal layer, and the radiative / conduction path, in that order. The oxidic pool maximum temperature (Tm.,) is obtained from an energy balance, which, ignoring the crusts, can be written as: [ QV = q,pS., + qanSan (6.4) where S , and San are the flat and curved areas respectively of the surface of the hemispherical l segment. 6-1 s
/
I 1900 - ,,... ',,3
.,. 3 .,. .,. .,. .,. 3 0 g
, O 1750 -
1675 0
- p d ,
1500 o' 8.:.8 t!. o.ats
<-0.333 LIOUID
- / I 02 ns4* e l
u 1335 o th N I
\ 0.000 *
- 1250 -
0 l h 1175 1 , E E 1000 - 995 0 N g, O y 909 0 0.644 % 9280 0.94 ## o.76 eosa \ Jo,j l g 0 l t a 796 h/ l 750 -
% 0.973 -
u. O O ( 554 y 500 - - , 400' " "'- - 'I- - l 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Mole fraction 2r Figure 6.1. The iron-zirconium phase diagram (Pelton et al.1994). 3000 I E g w g, ,-::; ':ll". ~#~ Fa e tered / \ Tetrahedral p 2M0 - 7
/ \
/ \
/
/ \
1MO - f fec + Tetrahedral
~
[ I
/
I \L l
- t. _ _ _ _ _ ._ _ er i fcc + Monohedral i5 l g 8 I ' ' ' ' I 0
100 80 60 40 20 0 UO, mot % Zro a (a) U-Zr-O Figure 6.2. The UO2 -ZrO 2 Phase diagram (Butterman and Foster,1967). 6-2 I
The q.,and qan are obtained from: q,p = hup (Tma, - Tm) and qan = han(Tmas - Tm) (6.5) with hop and han given by Eqs. (5.12) and (5.28) respectively. As we will see in the next chapter, the H/R is greater than 0.8, which makes the factor (H/R) .2s grcater than 0.95, which indicates that it can be ignored. Tm is the oxidic material liquidus temperature. Once Tm., is found the fluxes are also known from Eqs. (6.5). The q,p will be used (further below) as an input to the treatment of the metallic layer, while gan is now used to obtain the crust thickness,6cr(6), and the heat flux into the vessel wall, qw(6), as functions of 6. This can be done by means of a local energy balance as: qw(6) s gan(6) + 46er(6) = kw Tw(6) - T" (6.6) 6,(6) ((kw is the effective thermal conductivity of the steel wall, accounting for the temperature dependence as given in Appendix L)), and consideration of conduction within the crust ((we mean here an " effective" crust that includes the slush layer that allows the transition from the liquidus to the solidus temperature-see also responses to Henry (item #2) and Tuomisto (item
#2))):
Tm - Tw(6) = d62 ' (6) + 6cr(6)qan(6) (6.7)
,kcr
. ker
( ( where gan(6) is obtained from gan and the shape function given by Eq. (5.30) as discussed in Chapter 5. In the above, Tw(6) is set equal to the wall liquidus temperature, Tw,m, if it is found to be above it. Thus, Eqs. (6.6) and (6.7) constitute a system of two equations in two unknowns, { 6cr(6) and Tw(6) or 6w(6), depending on whether there is wall melting. At the conclusion of this calculation we compute e (6.8) lO6cr(6')2rR coa 6d6 and have thus ensured that it is always less than a few percent of F (the oxidic pool volume) in this application. Now, having q p, the metallic layer is treated in the manner described by Eqs. (5.42) to (5.44) except for three additions: (a) accounting for the area difference between the upper and lower boundaries, (b) accounting for variations of thermophysical properties with temperature, and (c) representing the radiation / conduction path. Thus, we have: 2 2 cos2 6pAr, (Te,g - T6)4/8 = cos 6f Ar,,(T6 - T ,o)4/3 i 4 ' Ar,m(T6 - T ,m)4/ i (6.9) R
-1 Ar,o(T6 - T ,o)4/ = a(Tg,,4
- Tl) 1 + ~ ' ' (0.10)
S,' i e e, 6-3 e
1 9ap = Al,i(I ,i - I ) I 6 (0.11) I where A ,j = 7(Prt,j)k t j = i, o, or m al' t,j the index indicating the boundary layer at who3e " film" temperature the properties are to be evaluated, and a(T/,o - Tl,4) *+ *
= k , 6
= co(Tl,,- Tl) = kw (6.12)
This system of equations is solved by using T, as an iteration parameter. That is, with a value of T, assumed, Eqs. (6.9) to (6.11) are solved; with the T i,o thus found, T,,, and T,,o are computed from the first two equations in Eq. (6.12); with these values the third equation is checked to determine whether it is satisfied, and the procedure is repeated until this is so. Once g the temperatures are known the heat flux to the sidewall, qt,w, can be computed by 4t,w = A t,m(T6 - T t,m)#8 (6.13) and the existence of an oxidic crust between the pool and the metallic layer is verified by the conditions that the quadratic Q6"2 Tm - Te,i = 9.kcr + her6" qu p (6.14) has one positive root as long as (Tm - T,5) I > 0. That this crust is thin is verified by the condition: 0< < 0.03 (6.15) Qup Finally, at the conclusion of a computation the Rayleigh numbers are computed at the appro- E priate film temperature properties to ensure that the correlations have been applied within their designated ranges. Before carrying out the detailed quantification with this model it is interesting to determine the effect of the additional effects included in the treatment of the metallic layer, in relation to the model described at the end of Chapter 5. For this purpose, we have carried out a series of calculations, spanning relevant ranges of the parameters for this application, and plotted the results in the manner of Figures 5.12 and 5.13. As seen in Figures 6.3 and 6.4, the results are essentially indistinguishable for 0.4 < e < 0.5, which constitutes the main range of interest to this study. Some difference appears for higher values of the emissivity, but it remains less than 12% even for the extreme case of e = 0.7, He = 0.1. Note that on this basis the whole problem 6-4 I I
-- l.
can be reduced to a hand calculation. Specifically, once Eq. (6.4) is solved for (Tm., - Tm), the go, and gen can be found via Eqs. (6.5), and then the solution for the metal layer can be simply read off Figuies 5.9 through 5.11. This may be convenient for the reader, in exploring thermal loads under any specific conditions of interest. Our calculations in the next chapter are carried out with the full model put into a relatively straightforward computer program. t000 , , , , , , , , ,, , , , , , , , , , , N - 6 T c = 0.4 - N \ c = 0.5 - k 800 . c=0.6 - y v _t , e = 0.7 :
=d - '., \
.\ , .
k 600 '.', _
- * ,N '
g . -
] [ ',',
w - .,', : o 400 - -
~, ._.
# c-
' 'm.h hug.... ... -
x -
- . " .,.., l -. .:.:; -
.2 N 200 -
~
' 77 - --..:. .: ::::--- - : : . .-._. -
g - y - y -
~
' ' ' - I - - - - I I I
-0 - - - - - - - - - - - -
0.1 0.2 0.3 0.4 0.5 0.6 Hi /R l I Figure 6.3. Solution to the system of Eqs. (6.9) through (6.13), with the emissivity as the - parameter. g , = 400 kW/m 2, and A ~ 2764 W/m 2. Ki/s (property variations with temperature properly accounted for). For the chosen value of g p, the peak heat flux at the edge of the oxidic pool is 350 kW/m 2, and the intersections shown represent the threshold values of He/R for the various emissivities. 1 i V 6-5
l I I 2000 , , , , g p - - a -
$ q,,= 300.kW/m a N ', .
q,p=400.kW/m E k -- - g
$ 1500 \., .......... q[=500.kW/m q = 600.kW/m a _
m + e . . s, s, 3 1000 - ', - '.- m _s. O . a . y - 500 - - - C -
.~...".....,...o-.---~~~~.....................-
a, _ Z . _ _o . . . . l . . . . l . . . . l . . . . l . . . . 3 0.1 0.2 0.3 0.4 0.6 0.6 Hi /R Figure 6.4. Solution to the system of Eqs. (6.9) through (6.13), with the imposed upward heat flux on the parameter. e = 0.45, A ~ 2764 W/m2 . K4/8 The threshold values of Hi/R, obtained as in Figure 6.3, are shown by the *'s. I I I I I I I 6-6 I
E 7 QUANTIFICATION AND ASSESSMENT OF THERMAL LOADS UNDER NATURAL CONVECTION I 7.1 Quantification ofInput Parameters In this chapter we take on the numerical implementation of the formulation provided in Chapter 6. But first it is appropriate to briefly discuss some methodological aspects, and this is done with reference to Appendix A. We recognize that we have a deterministic model, fully supported by experiments and scaling considerations, and therefore modelling uncertainty can be considered negligible in relation to the margins inherent in the definition of this one bounding , configuration. Also, we have seen that there is no scenario dependence. Thus, the model is appropriate for a Grade B assessmem (as defined in Appendix A). The parameters are basically deterministic, except for the decay power, the quantity of l zirconium oxidized (this affects the volumes and compositions in the metallic layer and oxidic pools), and the quantity of steel in the metallic layer (this affects the depth). All three quantities are to some (minor) degree intangible and, therefore, their values and uncertainties will be considered very carefully. Our approach is to provide reasonably bounding distributions in the ROAAM sense using Table A.1 as a guide. More of an intangible is the possibility of an oxidic " film" on top of the metallic layer, a film that is thick enough to make the conduction resistance overtake the improved radiation emissivity due to it. This is approached by means of a sensitivity study. Also approached by sensitivity studies is the use of Mayinger's correlation instead of Eq. (5.28), and of the UCLA flux shape correlation instead of Eq. (5.30). Finally, we have uncertainties on thermophysical properties, as described in Appendix L; they are of minor significance, but included anyway by means of Gaussian distributions with two standard deviations at the uncertainty intervals quoted in Appendix L These parameters, their mean values, and their 2a values, are summarized in Table 7.1. In this table is included also the emissivity value used for the steel layer, as measured in the laboratory (see Appendix I). While any small , amount of oxides and/or impurities would tend to produce higher values, such effects are difficult to judge, and the conservatively bounding value for a perfectly clear surface is preferred for these i calculations. The emissivity of the " sink" surface (upper reactor inner boundaries), e,, is taken as 0.8, as is appropriate for high temperature (oxidized) solid stainless steel. Because of the very l large areas involved, the effect of any reasonable variation in this parameter is negligible. l The decrease of the radioactive decay power with time is shown in Figure 7.1. From this we have to subtract the volatile component; however, this cannot be done as a constant fraction
- because the volatiles are decaying faster. Thus, in Figure 7.2 we show how the volatile compo-nent fraction changes with time (Schnitzler,1981), and in combination with Figure 7.1, we obtain l
7-1
I I Table 7.1. Property Values and Uncertainty Intervals Used in the Computations Property Oxide Phase Metallic Phase Melting Point (K) 2973 1600 Volume Averaged Volume Averaged Density (kg/m8 ) puo, = 8740 pp, = 7020 pzro, = 5990 pzr = 6130 I Thermal Conductivity 5.3 1.6 ( 30%) 25 6.3 ( 25%) l l (W/k m) Viscosity l3 erp(lya) 8 2.5 l['o exp(y) 1.1 (Pa s) x10-3 l I l Mass Averaged Mass Averaged Specific Heat (J/kg K) cp,Uo, = 485 cp ,r, = 835 cy ,zro, = 815 cy,zr = 458 Volume Thermal Expansion 1.05 0.12 ( 11 %) 1.1 0.18 ( 16 % ) Coefficient (1/K) x10-4 I l Effective Thermal 2.8 0.4 ( 14%) 32.0 g Conductivity (W/k m) Crust Vessel Wall 3 Emissivity Crust 0.8 Molten State 0.45 I I 1 7-2 I I l
I 1 60.0 I , , ,,,e . . .. , . . . . - a,v. r.-p..+.---~ . m 9, Deea Power 33..g. - ~, . i .%.44.L - Decay Power in the Pool { 50.0 r, ,- r ,,w ,, .,; n st. v, r:.- ,, I - ir m
~~
mi
-t M
i.
; tr.
$a 40.0
+
4e i 4 .,, i
; .. i.
, ub x ! '
i 4 t.4.UJ \' i' 6 o isi A -;!. ! i .' - ! ' c 30.0 r
, M i n, s lX I : p.,l
. v rr i
i re+
.. 4 b j,jj, ,j
!I i i , , , 1' j f,i ! e Iv 20.0 4: 4; II! n N r- w!7h M
,c I g i
>i 4 y r+._g.
10.0
-i i
. . g, i i. i , , 8 4
I O.0 l lll % t- ', l l f lo I 2 3 4 5 10 10 10 10 I l Time (s) N Figure 7.1. The decay power as a function of time after shutdown (AP600,1994). The "in pool" g curve accounts for loss of volatiles, their contribution being as in Figure 7.2. The rated power l of the AP600 is 1933 Mw. I 1.0 .
,. .i..n.. .
n..n - i . inni i ;;;nn i , i nnn i ;mn
!!!I ! . t i!III i ! !!!!!
! ! l ! !! ! '!!! l ! l i!!!!
! i ';i! l i l i!!!!!
I f l!iH i i i!! !!i i gll ! i .- til i i i iI!!O I I li!!! l ! iii P..
- . I i !!!!
.C ii l !!! I i !iliti I l l!III i 1' 4 fit I !!!il i .t. 1
. ..lll l 1 l lIII! I i lilli . lliii i !Il!!
i IIIli! 3 iji !i i ! !!IIi! I i I! I i !ll H 6 i +*- * : it*** .. ..
! I.-l l ill !
! I iill I ! 1 I i ,
I.!.!.
/Iillil t
I
!!! I l ilil i l ! l I Iillli
@ l ! ! ..i i. ..I I ! .l i I.I.ll / *I !"llill l l 1 i i ! lI!!!
% 0*8
! !ll l l
I I !ll1
- - / l I '!!! I iiI il il!llll l a O
m l l. ' li l l ill i 11! I Ii 'l' ll ! i lllll
.l!!Iii( -
I h g g I .! i l iI ll1 01 \! l l i- i iil l I I ij/. I
. lil I
Ii li li I iI l i l i i il
!i i
i i i!iI
.i i !
I+ l i 0.7
@ ri iin , i i i i ! .
I l!! ! ! ! !! I I
! ii!Ni ! !! l !i i iii i il I 11!! W4*+
I' il I il i' I i' l i llll! lil I I !! I 11 il I ill i 0'6 2 I 3 4 5 8 7 10 10 10 10 10 10 Decay Time (s) Figure 7.2. Fractional contribution of the non-volatile components to the decay power, as function of time after siiutdown. 7-3
I the decay power for the non-volatile components as a function of time (aL;o shown in this figure). We now proceed to quantify the fraction of the zirconium oxidized and, with this plus all the above information, to arrive at probability distributions that characterize the volumes (and heights) of the oxidic pool and metallic layer, and the velumetric heat generation rate. The various materials inventories within the reactor vessel are listed in Table 7.2. Table 7.2. Material Inventories in the Reactor Vessel 3 Component Material Mass (kg) x10~3 Volume' (m ) Fuel UO2 75.9 8.68 Core Cladding Zircalloy 15.8 2.58 Peripheral Cladding 2 Zircalloy 3.4 0.56 Control Rods Silver / Indium / Cadmium 2.9 0.43 Lower Internals Package (LIP) - Estimated Core Barrel Swinless 40 5.70 Lower Suppon Plate t Stainless 25 3.56 Lower Supports Stainless 2 0.29 Reflector Stainless 40 5.70 g Upper Internals Package (UIP)- Estimated W Upper Support Plate Stainless 23 3.38 Support Columas Stainless 4 0.57 g Rod Guides Stainless 8 1.14 EB Lower Guide Tubes Stainless 8 1.14 Upper Core Plate 3 2 In liquid state Stainless 3.5 0.5 l Mostly at the core entrance, as 7.5 cm-long pellets. at the lower end of the fuel rods 3 Including inlet nozzles Available information on zirconium oxidation in a severe accident includes: the TMI-II accident, a large number of out-of-pile experiments such as those in the CORA facility in KfK, l and a large number of special purpose models and code calculations. All this evidence points strongly to a heavy zirconium oxidation, and this is easy to see especially because of the open core geometry in a PWR. Thus, we assign a most likely expected value, for the fraction oxidized, in the range 40 to 60%, one unlikely range (the 10-1 level) in the 10% interval immediately E 3 above this range, and one highly unlikely (10-2) in the 20% interval beyond. Higher values may be appropriate with recovery, but our interest here, obviously, is for unrecovered cases. [Also, higher values would reduce the decay power density, and hence the thermal loads.] This quantification is shown in Figure 7.3 in the form of a probability density function. 7-4 i I, l l
5 e 0 M : 34 7 E : : r X 3 - - d - 8 : k - i 5 - t : : 2 1 s - _o
~, , ! ,,,,I , ,
-- . I -
a 0.4 0.6 0.8 Zr oxidation Fraction Figure 7.3. Specification of the fraction of zirconium oxidized, as a probability density function. Using these fractions and the total quantity of zirconium present we can obtain the quantities of ZrO 2to be mixed with UO in 2 the oxidic pool, and the quantity of Zr metal to be mixed with steel in the metallic layer. For the UO2we use the whole inventory which leads directly to the probability distribution of the oxidic pool height, shown in Figure 7.4. Since the radius of the vessel is 2 m, these heights correspond to polar angles in the range 75' < 6 < 81*; that is, a nearly full hemisphere, as mentioned aheady. For the metallic layer, we note that the lower (or core) support plate is positioned at a height of 1.5 m (its bottom face), and according to the above, it would be in contact with the oxidic pool. His implies that the metallic layer cannot form until this plate (25 tons) melts in, which would also release any remaining (not yet melted) portions of the reflector (40 tons), and the lowest portions of the core barrel (a total of 40 tons). He metallic layer should also have to include all the lower internal structures (2 tons). Hus, the only intangible aspect is the extent of involvement of the upper internal structures, and the probability assignments are made as follows: a likely range (~10') for 67 to 72 tons (to include 1 m of core barrel), an unlikely range (~ 10-1) for 72 to 77 tons (to include 2 m of core barrel), and a very unlikely range (~ 10-2) for 77 to 87 tons (to include a small portion of the upper internals). He probability density function corresponding to this specification is shown in Figure 7.5. With these values added to the amounts of unoxidized zirconium, we can obtain the probability distribution of the 7-5
15 , , , , E
~
~
h b., 10 - - y -
-[;; _
Q 5 - - f t g l
. , I . I . _.
~
_o , , , , , 1.4 1.5 1.6 1.7 l Height of Oxide Pool (m) 2 Fip 7.4. The oxide pool height probability distribution resulting from a UO volume of 8.68 I m , a hemisphere radius of 2 m, and the specification of Figure 7.3. metallic volume, and hence the layer height, se shown in Figure 7.6. Note that in constructing this figure we had to combine also Figure 7.4, to account for the actual position of the layer's l q lower boundary. Finally, for the volumetric heat generation rate, besides the volume of the oxidic pool (Figure 7.4), we must consider the timing for the formation of the configuration under investigation. We ' wish to do so in a manner that is generally conservative (i.e., minimizing this timing), and not g relying on detailed aspects of code calculations (to maintain the Grade B rating). Rather, we proceed from a general perspective of severe accident initiators, as provided by the level 1 PRA , for AP600, to a selection of bounding, from the point of view of timing, scenarios of interest here, and finally to an understanding of what controls this timing. All non-negligible contributors to severe core damage, found in the AP600 PRA (submitted to the NRC) are listed in Table 7.3. This table also lists the time for the first relocation event into the lower head (es calculated with the MAAP code) and includes comments on each case relevant to the present usage. The term l
"Not Relevant to IVR" was applied to cases l A, I AP,3BR and 3C on the following basis:
e Case 3BR. This variant of a large break LOCA accident leads to recovery and arrrest prior to any debris relocation.
- Case 3C. 'Ihis is clearly outside the scope of IVR, and subject to meeting a screening frequency criterion.
I 74 I.
E ) 0.20 , , , , E c O
~
~
W ~ ! D - - y 0.15 - -
~
3 2 : s . . E 0.10 - - I y . . E j 0.05 - ! t : E - E l -0.00
, ' M , ' '
60 70 80 90 E Steel Mass (kg) X 10-l Figure 7.5. Specification of the steel mass in the metallic layer, as a probtbility density function. i 10 , , , , , , , , , , , , ] g . . r . ^ d 10 - - a bg -
$6 - -
- i
$ ~
t _ . g , , I , , , , I ,
._ o 0.8 0.9 1.0 1.1 Height of Metallic Pool (m) l Figure 7.6. The metallic layer height probability distribution resulting from the specifications in Figures 7.3 and 7.5.
L F I 7-7 i
l Table 7.3.* Accidents Contributing to the Core Damage Frequency (CDF) I of the AP600 as Developed in the Level 1 PRA (AP600,1994) Case I.D. % of CDF2 'Ilming of First Accident Description and Comments Relocation (hr) 1AC 18 ~5.5 e Transient or Enall LOCA2 at high I pressum; manual ADS8 failure, e Not Relevant to IVR. l 1APC 0.5 ~10.5 e Like 1A, but PRHR operating. e Not Relevant to IVR.4 3BE 30 ~4+ e Large or medium LOCA with full g depressurization. Injection failure. E e Of Main Interest to IVR. 3BRC 22 N/A e Early accumulator and CMT5 failures but manual depressurization leads to IRWST8 availability and reflood. Recovered accident. e Not Relevant to IVR 3C 23 N/A e Vessel rupture. I
- Not Relevant to IVR.
3DC 2.7 ~22+ e Non large LOCA with partial depressurization. e Of some Interest to IVR 6E 3.3 ~22+ e Core damage after SG7 tuk rupture g e Of Some Interest to IVR E 2 CDF = Core Damage Frequency 2 LOCA = Loss of Coolant Accident 8 ADS = Automatic Depressurization System l 4 IVR = In-Vessel Retention 8 CMT = Core Makeup Tank 8 IRWST = In-Containment Refueling Water Storage Tank 7 SG = Steam Generator
*((This table has been revised on the basis of design updates and a revised PRA. For the revision and a discussion on IVR scenarios see addendum at the end of this chapter.))
I 7-8 I I
[ e Case 1AC. Such high pressure accidents are expected to fail the hot leg nozzle and de-pressurize in any case. For the passive AP600 it is expected that failure to depressurize will meet the semening fmquency criteria, such as to be negligible. It is inherent in these accidents to proceed at a slower rate (due to lower rate of coolant loss) as compared to large LOCAs-see Table 7.3--thus a depressurization too late to recover the accident still can be covered, conservatively, under case 3D. [As one can see in Figure 7.1, the decay power at 10 hrs is only 80% of that at 4 hrs.] he term "of Some Interest to IVR" was applied to cases 3DC and 6E in recognition thrt even { though small contributors to CDF, these cases could be readily accommodateable in the IVR. De long term evolution is inherent of coolant availability and passive cooling design feature in these accidents; at 22 hrs the decay heat is only 67% of that at 4 hrs, and the so-reduced thermal loads are expected to accommodate structurally at least part (if not all) of such higher L pressure scenarios-with a fourth stage ADS failure the pressure would be under 100 psi-(see
. Appendix G). Finally, and in light of the above, we are left primarily with case 3BE, which
( therefore has been termed "of Main Interest to IVR." It is the simplest, and fastest, scenario, thus it is of good bounding quality for timing the decay power. Both the core makeup tanks r t and the accumulator will passively inject to quench the core down to ~400 K and leave the primary system essentially full of water. A severe accident from this condition requires failure g of the gravity-driven injection system, depletion of the in-vessel coolant inventory, and core k heatup. Material relocation to the lower head in addition requires core melting with significant , melt accumulation to cause side failure (s) through the mflector (minimum thickness 13 cm) and L core barrel (minimum thickness 5 cm). An independent assessment of the timing of all these phenomena (Sienicki, et al.,1995) are in general agreement with the MAAP result, in Table 7.3, ( of 4+ hours. Thus, we assign the main probability interval (~10') between 4 and 5 hours, an unlikely range (~ 10-2) between 5 and 6 hours, and a very unlikely range (10-2) between 6 [ and 7 hours. As a perspective on the insensitive nature of this quantification, note, from Figure 7.1, that from 3 to 5 hours' shutdown time the decay power changes from 15 to 14 MW, that is, by less than 7%. The resulting probability density function from such a specification of the L shutdown time is shown in Figure 7.7. The probability density function for the decay power density is then obtained by combining Figures 7.1,7.3 and 7.7. The result is shown in Figure ( 7.8. - Note that the primary quantification carried out above is contained in Figures 7.3,7.5, and L 7.7, and they are independent of each other, as will be explained in the next paragraph. %e quantities H, He, and 4 (Figures 7.4,7.6, and 7.8) were derived using a Monte Carlo sampling (. program from these primary quantifications. Dese are not independent of each other, thus they r 7-9 ' L
I 1.0 , , , , , , , , d o - M - 3 0.6 - - u - . d . . 2 : : h 0.6 - -
.t n . .
~
'3 0.4 - -
g _- t : : 4 0.2 - - o . . _ o,o . . . . I ,,,.I __ -, 3 4 5 6 7 Time (hr) Figure 7.7. Specification of the shutdown time (for use in estimating decay power), as probability E density function. W 8 , , . , , , , , , , , , e o - r . y 6 - u - N . b y ' d 4 - v . c2 _ b O - S 2 -
.O -
8 - _o '. . l . . . l . . . , , , 1.0 1.2 1.4 Decay Power Densit.y (MW/m") Figure 7.8. The decay power density probability distribution resulting from combination of E Figures 7.1,7.3, and 7.7. g 7-10 I
l are not convenient as inputs to the main calculation; rather, they were derived to provide some ( transparency of the quantification since any vdues from these figures can be used to directly read off the answers (heat fluxes) as described aheady in Chapter 5. In carrying out the calculations j with the model we use the primary quantifications as above, but each sample is carried through the model to calculations of the heat flux distribution at the outer boundary of the lower head. Thus, the result is the probability distributions of the thermal loads at all angular positions in f contact with the oxidic pool and the steel layer. As noted already, the distributions of property I values are also sampled simultaneously. f Before displaying the results of these calculations, let us address the question of indepen-I dence between quantities shown in Figures 7.3, 7.5 and 7.7. The basic reason is that each l quantity is governed by completely different aspects of the melt progression sequence. Starting with the timing r, the primary consideration is in the early i>ortion of the sequences (as dis- ! cussed above), prior to core uncovery, and the starting of degradation, which draws heavily on the likelihoods of various accidents leading to core melt, and thermal-hydraulic assessments l j (and systems codes) that operate in relatively "well-charted' space. The zirconium oxidation is related primarily to the early portion of severe accident sequences-during core uncovery-and it is clearly quite independent of r. Finally, the quantities of upper internals melted, at low ; pressure as in the case here, primarily depends on the phenomenology of the late phases of the I core melt scenario, timing of core relocation, and heat transfer processes (radiation / conduction, primarily) between the upper core and the upper intemal structures. i 7.2 The Main Results The results of the calculations are summarized in Figures 7.9 and 7.10. Figure 7.9 shows the cumulative probability distributions of the heat fluxes at various angular positions around the lower head, [if it is of interest, corresponding wall thicknesses can be read directly off Figure 4.1] while in Figure 7.10, the same results are presented as probability density functions of the heat fluxes at selected positions, divided by the cortesponding critical heat flux value at the same I position. This second manner of presentations makes the margins to failure immediately evident, I and it is interesting to note that contrary to popular opinion these margins are greatest at the lower positions (6 ~ 0*) of the lower head. However, even at the high positions the margins-to-failure are sufficiently comfortable to lead to the conclusion that failure is " physically unreasonable."
)
This conclusion is further buttressed by the numerous sensitivity aryl parametric calculations l presented immediately below. I I i = 7-11 ! 1 I
I l I' c 1 , F, , , , g
~- .
3
,P), ,
I - 5 : g 0= 5.0 : E
.o _
g i 0 = 20.0 4
'E ~
i ; 0 = 30.0 '
% \ \ 0 = 40.0 y 0.1 -- \, \ 0=50.0 0 = 55.0 b
\ '\ 0 = 60.0
~
) 0-65.0 -
j . { 0=70.0
.o k 0 = 75.0 o -
1 0=00.0 - g j .... ..... g> 80,0 0.01 _-- g 3 -
~
~
N -. .. I y ...... o 0.001 ' ' ' I ' '! ' '
-0 500 1000 8
Heat Flux (kW/rn ) Figure 7.9. Probability distributions of the heat fluxes at various angular positions around the E, lower head. Over the region of the oxidic pool, fluxes increase monotonically with angle (all a solid lines). The lines cormsponding to the metallic layer are identified separately. The stepwise behavior at positions 6 = 75* and 80* arises because of " sharing" the oxidic pool and metallic layer contact. 60 , ,
, , q:
d
!! 0= 0 qCur= 500 kW/ 8 l
W 8
.O !; --- --
0=30 qcur= 900 kW e 5 ji 0-50 qcur=1050 kW s C : 0=75 qcar=1350 kW ' 5 40 - cur *1M W _ m x :: , e
~
!i A
E 0 x i!
- : *\
l,i l ii \, g 20 -
; ;: ,f g o . , .
e : . t j g -
.1 i t. -l / i i
_o . . . . . . . 0.1 0.2 0.3 0.4 0.5 0.6 9.(o)/9 cur (e) Figure 7.10. Probability distribution of the heat fluxes normalized by the local critical heat g fluxes, for selected positions around the lower head. The position 6 = 85* corresponds to time g metallic layer. The double-hump behavior at position 6 = 75*, arises because of " sharing" the oxidic pool and metallic layer contact. 7-12
7.3 Sensitivity and Parametric Studies One group of sensitivity and two groups of parametric studies have been performed to make
.I apparent:
1 (a) He effect of shifts in the input distributions, namely: l e Fraction of Zr oxidized: Shift the distribution of Figure 7.3 to the right by 0.1 o Time: Shift the distribution in Figure 7.7 to the left by 1 hr.
. (b) he effect of using different correlations for:
e Downward heat transfer: Eq. (5.12) instead of Eq. (5.28) J j e Flux shape: Eqs. (5.24) and (5.25) instead of Eq. (5.'30). I both done in conjunction with assuming a 1 cm-thick oxide crust on top of the metal layer, or an adiabatic upper boundary. (c) De extreme specification necessary to approach failure: e Assuming that the lower support plate is intact, j Each group is presented and discussed, in turn, in the following. He distribution shifts are straightforward, and the results are displayed in Figures 7.11 and 7.12. We see no significant effect on the margins understood from the base case results. Note i that the double-hump is not present in Figure 7.11 because, with the oxide volume increase (due to added ZrO2 ), the metal layer shifted higher, while the slight shift to higher g/qcur values is due to the correspondingly thinner metallic layer. As additional sensitivity on the base case, we also considered the effect of dividing the coefficient in the Globe-Dropkin correlation by a factor of 2, and of reducing the wall melt temperature by 100 K (i.e.,1500 K instead of 1600 K). He effect of both of these variations was slight.
- I ne calculations using the various correlation options were carried out with H = 1.6 m,
~g He = 0.8 m, and Q = 1.4 MW/m .8He results are displayed in Figures 7.13 through 7.15. ) 5 In Figure 7.13 we see that even with an adiabatic upper boundary the metallic layer is quite sufficient to dissipate the heat load over its side boundary, still leaving significant margins to failure. In Figure 7.14 we see that use of the UCLA flux shape produces a 20% more peaking at 6 ~ 80', but still a significant margin to failure remains. Finally, in Figure 7.15 we see that the j use of Mayinger's correlation biascr> dre flux upward over the steel layer portion of the boundary by ~15% only. His rather low sensitivity was predicted aheady in Chapter 5. 7-13 1 l l
I I 60 , , ,
,g , , , , , ,,, , ,
a d _ f! 6= 0 qcur= 500 kW/ a
.3 :: 6=30 qcur= 900 kW o
~
jj p 6=50 qcur=1050 kW m' - c . :: 1 6=75 qcur=1350 kW s
=85 qcur=1@0 W k 40 -
ll - 5 ~ h
'E _
c : I* o - Q ! ii [\ ~ ij \;
~
h
= 20 -
- : j! \. ;
o : : i , , - d
- : i t
- ; [ ' \
D . I \ . o u . (
\. l \, -
w
~
- : i 1 I \
-0 ' ' ' ' I #' 'I\4- ' ' I
l ' ' ' '
O.1 0.2 0.3 0.4 0.5 0.6 9.(o)/9ca7(o) g Figure 7.11 He results of a sensitivity study, specified by shifting the distribution for the zirco-nium fraction oxidized to higher values by 10%. All other inputs as in base case. l 60 , , , , ,,,, , ,,, , , ,, , , , , d Wu
- g 6= 0 qCur= 500 kW/m'8 _
.3 ::
6=30 qcur= 900 kW/ , 6=50 qcur=1050 kW
'o l: ,
c -
- i 6=75 qcur=1350 kW/ , .
6=85 qcur=1450 kW/ 5 40 - ll [! _ x :i f l Ne f!
- 1 -
Q x : i , .
& 30 -
l\ j\ j-'\ - 4
- a l!: /
i l
't i !
/ \.\ -
0 I ; l \ ! \ w ;
\. \.. .,/ \.
. i
-0 ' ' ' I A
- " A I ' ' 'I ' ' '
O.1 0.2 0.3 0.4 0.5 0.6 9.(8)/9 car (o) Figure 7.12. The results of a sensitivity study, specified by shifting the distribution of the shutdown time to lower values by 1 hr. All other inputs as in base case. 7-14 l 1
F L i . i .
. . 1.0 Adlahatic: q q/qor 800 - -
. Crust (Icm): - - - - q - - - - - q /qa, ,
0.8
- c. _
k - 0.6 yb 4 D M m 400 - l~~' - E _ 0.4 y - e - [- % 200 -Y 0.2 l b 0 O.0 0 20 40 60 80 100 Angle (degrees) Figure 7.13. Results of a parametric study using an " adiabatic" boundary or a 1-cm-thick oxidic L crust on top of the metallic layer. Values for H, He, and Q were fixed at 1.6 m,0.8 m, and 1.4 MW/m 8, respectively. ~ \ 1200 ' i ' ' ' i ' i
, 1.0 Adlahatic q q/qor _
! Crust ficm): - - - - - q ----- q/qo, 1000 L
- 0.8 p _
- E - l s 800 - y . 0.6 h r x 600
. ,m sc
! m ' & g - ...
- 0.4
% 400 _
$ ~
0.2 200
~
l L 0 ' - ' - ' - ' - 0.0 0 20 40 60 80 100 I F L Angle (degrees) ) Figure 7.14. Results of a parametric study specified as in Figure 7.13 but using the UCLA flux ; sl. ape (Eq. 5.24) in place of Eq. (5.30). m 7-15 i
I 1000 - i t
. 1.0 g Adlabatic 9 9 /9ar _
E Crust (Icm):- - - - - q =----q/qa,
,800 - '----- - 0.8 "E
~
~
3600 0.6 $ cr , Cf 5 E 400 0.4 5 g
%a .
- 200 -
0.2 0 O.0 0 20 40 60 80 100 Angle (degrees) Figure 7.15. Results of a parametric study specified as in Figure 7.13 but using the Mayinger et al. (1975) correlation (Eq. 5.22) in place of Eq. (5.28). From all the above we can conclude that there is no way to cause failure over the oxidic I pool boundary. Thus, as we are left to seek "the limits to failure," in an arbitrary parametric study using the " focusing" mechanism due to the steel layer, described in Chapter 5. For this to occur, the top of the metal layer must be below the lower support plate. The metallic layer will then consist of only the lower support structures and the molten metals that relocated together with the fuel. To create a significant thermal load this fuel must be in excess of 70% of the core, which implies a rather extensive melt attack on the reflector and the core barrel. [ Note that failure of both of these boundaries (see Figure 2.2) is required for the relocation of molten core materials to the lower plenum.] The reflector will mpply ~10 tons of steel per axial meter melted, and the core barrel similarly ~5 tons per meter. One, axial meter corresponds to 25% of the core height, and it can be considered (together with the 2 tons from the lower support structures) as a reasonable lower bound of the metallies available to form a layer on top of the oxidic pool. That is, a total of 17 tons, which if made to just touch the bottom face of the lower support plate (1.4 m from the bottom of the lower plenum) would produce a depth of 22 cm, and would allow a maximum oxidic pool depth of 1.18 m. [ Note that these are conservative limits in that no account was taken of the metallic zirconium that participated in the relocation, nor of the thermal expansica and creep in the core barrel.] Using these depths together with the 7-16 i
upper bound in the decay power, which from Figure 7.8 is seen to be 1.4 MW/m8 , we obtain the results shown in Figure 7.16. Marginal failure is indicated; however, it is doubtful that even this extzme specification could in reality produce failure. This is because in addition to ignoring zirconium in the metal layer and elongation (and possible failure) of the com barml, as just mentioned, this calculation has ignored 2-D effects due to (a) eddy diffusion in the bulk of the metal layer, and (b) conduction in the vessel wall. In addition, the effect of the highly localized l thermal loads on the critical heat flux, also expected to be mitigative, has beer. ignored. I 1400 . i i - i . i . i . 1 Emissivity 015: q qfqm, t 1200- Emissivity 0.65:- - q - - q/qmp g m ls 0.8 E "E 10 0 0 l ' } - 0.6 6 800 - g r y
~
~
E L 600 - 0.4 3 - E 400 - N - 0.2 200 - 0 0 0 10 20 30 40 50 60 70 80 Angle (degrees) i c Figure 7.16. Results of an extreme parametric study carried out to " test the failure boundaries." E H = 1.18 m, He = 0.22 m, and Q = 1.4 MW/m 3
. See text for explanation.
[ 7.4 Discussion As stated in Chapter 6, all these calculations were checked to verify that the conditions ! expressed by Eqs. (6.8) and (6.15) are satisfied. In addition, to check the applicability of the heat transfer correlations we computed the Ra and Ra' numbers in the metal layer and oxidic pool respectively. The results from the base case calculation, shown in Figure 7.17 and 7.18, respectively, indicate that for the AP600 the relevant ranges am [ 5 10' < Ra < 2 102 1028 < Ra' .< 6 1028 These also encompass the cases considered in the sensitivity and parametric studies: Ra = 1.1 10 2 Ra' = 4 1028, Ra = 2 10 8 Ra' = 1088 7-17 I _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ . _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
I and am to be compand to the experimental ranges, which for convenience are repeated here again: Globe-Dropkin: 3 105< Ra < 7 10 8 Ill 12 Chu-Churchill: Ra < 10 i Present (mini ACOPO): 1012 < Ra' < 7 10" We can see that in all three cases we are essentially there. There is a less than one order of magnitude extrapolation of the Globe-Dropkin correlation which besides being modest, it pertains to the thickest range of metal layers, which is uninteresting from a thermal loads point of view. On the simulation of the oxidic pools the mini-ACOPO revealed no significant surprises, and hence the extrapolation by about one order of magnitude can be considered modest also. This conclusion is to be confirmed by the main ACOPO experiment, scheduled for operation 27 in the next few months, which will afford Ra' numbers up to 1018 and 10 . Moreover, we l expect that with its widely different transient response, the ACOPO will further demonstrate the g adequacy of our present approach in bounding the behavior due to adjustments in the internal stratification pattems. g 1.5 , , , , y 3 E y _ g h - 3 - g 1.0 - g
# : I E -
$ 0.5 - -
p . O _
~
.D 4 ' ! ' - ' '
-0,0 ' ' '
5x10' 10 '" 2x10'8 l
=
Ra Figure 7.17. The Ra number distribution found in the calculations of the base case. 7-18
g 0.4 , ,
,,l . . . . . > . .
l , O - w , I
~
X l N 0.3 - z -
~
1 2 : ; y 0.2 -
- I
.g h . ,
A - I
~~
j $ 1 j _ 1 -
$ -0.0 5x 10" 10 88 2x10 88 5x10 18 10 '
8 2x10 28 ) Ra' Figure 7.18. The Ra' number distribution found in the calculations of the base case. 1 I I (( ADDENDUM TO CHAPTER 7)) 1 The purpose of this addendum is to summarize and refer the reader to certain new material l presented in addenda to Appendices K and M and in the new Appendices O and P. As separate items, we summarize hem also certain systems effects, including an update to Table 7.3 according l I to the revised PRA 1.evel 1 for the AP600, and the position of the designer regarding thermal shock. The addendum to Appendix K describes the thermal insulation design recently completed by Westinghouse, and with specific reference to the present work. The key features include a passively made available (upon flooding) large opening for water inflow opposite to the pole of the lower head, a minimum clearance of 23 cm at an angular position of ~30*, an annular gap between the vessel and insulation of 15 cm, and exit flow paths at the top with two successive I 2 2 restrictions (from the 1.88 m available in the annulus) of a total flow area of 0.7 m . On this basis, Configuration III of ULPU is presently being assembled, and the results will be made i 7-19 , l
I available in a new Appendix E.4 in the near future. This appendix will also contain the results on the influence of paint, data obtained with a heater block made of prototypic steel, and certain considerations on flow regimes and the CHF mechanism. The addendum to Appendix M contains the newly revised design of the cavity flooding system (now consisting of two 6" lines), and reliability considerations (including human factors) for it. Procedures call for the operators to start cavity flooding upon reaching core exit tem-peratures of ~2000 'F (just prior to the rapid oxidation phase). The lower head is immersed in less than 10 to 20 minutes for 2 or 1 drain line(s) operating respectively, and the vessel is effectively submerged (2 phase level with average void fraction of 50%) by 40 to 70 minutes g respectively. As explained in Appendix O, these times are well within the timing of the first relocation to the lower head. The unreliability of the cavity flooding system, conditional on de-g4 mand, is estimated at less than 10-2. This includes as a major contributor, human unreliability W conservatively estimated at 3.4 10-3 for each flow path. We believe that with the importance attached to this accident management scheme, operator training, and comfortable time intervals available for action (hours), the actual unreliability would be low enough that, together with the very low frequency of any core melt sequence relevant to IVR, it renders an unflooded situation below screening frequency levels of ~10-7 per year. l The new Appendix P provides a whole new set of parametric calculations, many requested by the reviewers, others taken up at the authors' initiative. These have to be examined in their entirety in Appendix P, but perhaps the most instructive result is about how quickly the margin to failure increases as the oxidic pool height decreases from its maximum value used in the l Extreme Parametric case examined previously. The new Appendix 0 is an attempt to get somewhat deeper into the potential intermediate states described in Chapter 2. This is done through some key timing considerations in the melt-downhelocation sequence, and it provides a perspective against which the scenarios proposed by l several reviewers can be considered. This consideration is also made in Appendix O. Additional perspectives on what might be required to cause failure are provided by a parametric study on the H, x H combination, where we see that shallower oxidic pools can accommodate thinner l g l metal layers without danger of failure. 5 In 1995, a revised Level 2 PRA for the AP600 was submitted to the NRC that also included ' l an update to the Level 1 quantification. On this basis our Table 7.3 was revised as shown in l l Table 7.4. The new core damage frequency estimate is 2.5 10-7 per year. The most important differences are in sequences 3C (vessel rupture), which decreased from 23% to 4.1%, 3BRC (in-vessel recovery, no interest to IVR),3BE (LOCAs of main interest to IVR) which increased 7-20 l
1 l l Table 7.4 Accidents Contributing to Core Damage Frequency (CDF) of the AP600 as I Developed in the Level 2 PRA with Update Level 1 Quantification (AP600,1995) Case % of Timing of First Accident Description and Comments ) I.D. CDF' Debris l Relocation (hr) )
~
e Core damage following trans ent or small LOCA2 at high pressuce; manual 1AC 1.9 ~5.5 hr ADS 8 failure.
. Some relevance to IVR4 if hot leg nozzle ruptures and depressurizes system.
e Like l AC, except PRHR operating. IAPC 0.4 ~10.5 hr e Some relevance to IVR; less decay heat , than 3BE; partially pressurized (<5 a.). I e Core damage following large LOCA or l I 3BE 50 ~4+ hr other event with full depressurization (injection failure); may reflood through break as cavity floods. l I e Of main interest to IVR. e Core damage following LOCA with early accumulator and CMT8 failures or 3BRC ~29 N/A any other sequences where manual depressunzation leads to reflood fmm IRWST8 and recovery in-vessel. I 3C 4.1 N/A e Typically, not relevant to IVR e Vessel rupture. e Not relevant to IVR. ' I 3DC 13 ~22+ hr e Non-large LOCA with partial depressurization. e Of interest to IVR, but less decay heat I than 3BE. e Core damage after steam generator tube 6E 2.3 ~22+ hr rupture. e Of interest to IVR, but less decay heat I than 3BE e Sensitivity case for 3BE without cavity 3BE.cc0 N/A ~3 hr flooding.
. Bounds IVR timing uncertainty ' CDF = Core Damage Frequency 2 LOCA = less of Coola At Accident 8 ADS = Automatic Depressurization System 4 IVR = In-Vessel Retentioa I 8 CMT = Core Makeup Tani:
- IRWST = In-Containment Refueling Water Storage Tank 7-21 I
I by 7% and 20% respectively, and 3DC (low decay heat) which inemased by ~10%. Also, sequence l AC (transient or small LOCA with core damage at high pressure) decreased from 18% down to ~2%; the designation of this sequence as "of no interest to IVR" was changed to "of some interest to IVR" because at least a fraction of them would lead to hot leg nozzle failure and depmssurization. These changes are all favorable to the IVR management concept. It is also important to note that the two potentially damaging sequences (l AC and 3C) have been reduced to only "a few percent" placing them at the margins, if not outside, the sevem accident management window of interest. Note, however, that even accounting for potential uncertainties in these values as well as in the total CDF estimate, their likelihood is so low as to be considered below a reasonable choice (~10-7) of a screening frequency criterion (see Appendix A). Finally, since several reviewers asked questions related to thermal shock performance of g the reactor vessel material, hereby we summarize some key aspects. Regarding the pressurized E condition, Westinghouse has a design requirement that the vessel accommodate one inadvertent flooding during normal operation. The analysis to demonstrate that this requirement can be met will include the effect of fluence on the lower head as a possible embrittlement mechanism, and will be ready later this summer. Regarding general low pmssure performance as during IVR, it is noted that the reactor vessel manufacturer can meet an initial RTvor of -10 *F with an inemase of 30 *F over the lifetime of the plant. The temperature range in the containment is specified as 50 to 120 *F, and 50 *F is, therefore, the lowest possible temperature for IRWST 1 water. This being significantly higher than the end-of-life RTuor (20F) value, is sufficient to g I establish absence of brittle behavior during IVR. 54 I l 7-22
[ 8 QUANTIFICATION AND ASSESSMENT OF { . THERMAL LOADS UNDER JET IMPINGEMENT In this chapter we examine the potential extent of local thermal attack on the lower head b during the initial core relocation event. His is the second bounding configuration discussed in Chapter 2. In this consideration we ignore the cooling and dispersive effect of water on the relocating melt-ignoring both effects is clearly conservative and useful in obtaining the simple, yet bounding argument sought here. Further, we assume jet impingement occurs even though TMI vessel inspection found no evidence of such impingement (i.e., no wall attack). A complementary perspective on this problem, including consideration of these effects, is provided in Appendix H. E The situation then can be described as one involving a superheated oxidic melt of diameter Dj impinging on the lower head with the velocity Uj. The fundamental consideration is that molten oxide cannot exist next to a steel boundary even under strongly convective conditions; accordingly, the potential driving steel melting is the jet superheat. This idea was originally L established by Epstein and co-workers (Epstein et al.,1980). More recently it was further validated and refined by Saito et al. (1990). In particular, they demonstrated experimentally [ the important effect of turbulence (in high Reynolds number jets) in enhancing the ablation rate significantly above that obtained in the laminar regime considered by Epstein et al. The p experiments were carried out with molten salt (Nacl) at temperatures up to 1140 'C (Pr ~1) impinging on tin plates; the condition covered jet velocities up to 5 m/s, diameters up to 3 cm 5 and Reynolds numbers up to ~ 3 x 10 . Two runs were also carried out with At 2 O3 at 2200 *C ' impinging on a steel plate at room temperature. In this case the Prandtl number is 5.46 and the Reynolds numbers were around 2 x 108 . The data yielded a heat transfer correlation indicative L of turbulent convection Nuj = 0.0033 Rej Prj (8.1) and from it an ablation rate
$ = 0.0033 ## # i~"
[ p(A+cpw(T.,m - T,,)] U>- (8.2) agreeing well with all the data that could be obtained. According to Eq. (8.1) the minimum [ required UO2 temperature to prevent crust formation on steel is ~4400 K (Saito et al.,1990). His is significantly lower than the 6400 K obtained for laminar flow, but still well above any p temperature of interest in the present application. We make use of Eq. (8.2), therefore, directly. I Using the material properties and a melt superheat of 200 K, Eq. (8.2) can be written as: 'L $ = 4 x 10"Uj (8.3) - 8-1 L
1 i which can be integrated, assuming Uj is constant, over the duration of the relocation, r, to yield the total ablation depth , Zr = 4 x 10-4Ujr (8.4) The Uj and r quantities am related by the total volume of relocated material and an effective jet diameter by V, = {DjUjr (8.5) : and if the principal variables are Vr and Dj Eq. (8.4) becomes Zr = 5.1 x 10-4 (8.6) i This result, for a relocated volume of 2.5 m' (~ 1/3 of the fuel volume), as a function of Dj is l shown in Figure 8.1. 15 , , , , E _ O 10 -
.g _
. a - I v l C _ c - o -
@ 6 -
3 4
~
, , , I , , , , I , , , , l , , , ,
_o , 10 15 20 25 30 Jet Diameter (cm) 8 Figure 8.1. Wall ablation depth as function of jet diameter, for a melt pour of 2.5 m (~1/3 of the fuel volume). l l 8-2 I
i l An equivalent pour (jet) diameter of 10 cm is considered to be an extreme lower bound for , such massive pours; still, it is scen to be unable to produce lower head penetration. Actually, ) j we would expect the pour rate to increase with time as the breech on the core side boundary is enlarged by ablation (i.e., Sienicki et al.,1995). These numbers are indicative of the rather intense and prolonged thermal loading required to produce local failures, and provide important perspectives on the even greater margins present in considering other transient phenomena, such as subsequent relocations into an existing corium pool. Such relocations would be expected to create " sinking"(cold) plumes, and in fact, Mayinger et al. (1980) measured the heat transfer rates in the impinging region of such plumes. Clearly, however, even ignoring the effects of crusts, momentum interactions in the corium pool, and turbulence would produce cooling and deceleration effects, thus making the wall interactions much more benign than those considered above. Based on the above, we can conclude that under no cizeumstance of a physically meaningful relocation scenario can we see local wall failures due to jet impingement. Under some extremely prolonged pours there may be some local attack and perhaps even a temporary CHF,if the ablation exceeds ~3 cm at 6 ~ 0*, or ~9 cm at 6 ~30'. However, due to the local nature of the thermal load, the dried out region would be expected to quench quickly after the temporary thermal load terminates.
'Ibriand (1994) also concluded that jet attack does not provide a viable mechanism for lower head penetration, even for pours as large as 1/2 the core inventory.
1 I I I I I 8-3
L 9 CONCLUSIONS AND RECOMMENDATIONS I The major conclusion of this study is that thermally-induced failum of an externally flooded, , AP600-like reactor vessel is " physically unreasonable." Methodologically (see Appendix L A for definitions), the assessment approach is of Grade B type (involving a single but complex physical process, slight scenario dependence, fully supported by scaled experiments, minimal intangibles treated in a reasonably bounding manner) which affords a high confidence level on [ this conclusion. Upon completion of the peer review of this report, the Phase of Development of this problem will reach the maturation status (Phase IV) which is appropriate for use in licensing (- activities. Phase V (extension) will follow shortly as various on-going programs internationally pmduce their own assessments. The breadth to be achieved by these efforts, oriented to the ( mose challenging task of larger reactors, is expected to further enhance the depth of the present
. assessment in a confirmatory sense.
[ In making use of these results for a specific AP600-like reactor, it is important to ascertain, or verify if appmpriate, the following key system's features: L e Reliability of the depressurization and cavity flooding systems (valves) to ensure that failures l can be classified in the "below-screening-frequency" category, t e Thermal insulation design that allows sufficient access of water to the bottom of the lower head ((and not subject to clogging)), and venting of a steam / water mixture on the top. Further, based on this geometry (and available clearances) the dynamic behavior of the [ two-phase natural circulation flow should be assessed, and experimentally tested if necessary (i.e., if significantly different than the cases considered already in this study).
- e lower head external surface characteristics (finish, coatings, oxidation) that do not impair critical heat flux performance. [This is currently being explored in ULPU with a prototypic piece of steel and various coatings.]
We believe that with appropriate attention in the design, none of these key features present serious difficulty in malizing this "in-vessel retention" concept. The key mechanistic features for this favorable conclusion in AP600-like reactor designs can be listed as follows: e A low power density core. In fact it is easy to see from the results of this study that at the decay power levels appropriate to this reactor it is virtually impossible for the oxidic pool to impose threatening thermal loads on the lower head, under any circumstances. I e A periodic bubble formation and detachment mechanism at the position of horizontal tan-gency (6 ~ 0*) on the lower head, that, in combination with the large thermal inertia of it, allows very significant margins to critical heat flax. At higher positions, the thermal loads increase faster than the critical heat flux and, depending on the thickness of the metal layer, 9-1
I there may be locally even an essentially discontinuous further increase in the thermal load. That is, the margins to CHF decrease monotonically as we move from the center to the equator; however, they remain comfortable under all practically conceivable circumstances. e Reactor vessel internals design that vinually prohibits the formation of superheated, thin, metallic layers on top of the oxidic pool. [Such layers would provide the only mechanism-a" focusing" in energy flow-that could conceivably compromise lower heat integrity). This design includes: (a) a core inlet geometry (with large heat sinks) that would arrest downward relocation, al-lowing the formation of a core-wide crucible, and sideward failum through the reflector and com barrel, (b) massive reflector and com barrel components, extensively ablated and incorporated in the melt prior to failure-that is, a significant metallic constituent with the relocating g melt and a (c) a massive lower (or core) support plate positioned such as to be subsummed in a large g molten pool contained in the lower head. 3 Pmsently, this " focusing" mechanism has been conservatively treated by ignoring internal trans-pon limitations (2D effects) due to the exceedingly large aspect ratio (~20) in such thin layers ((i.e., less than 20 cm)). Eliminating the conservatism may provide important (needed) mlief in assessing larger, and/or higher power density reactors. Other ideas to improve the assessment basis, or the in-vessel retention performance for large and/or higher power density reactors can be listed as follows: e Extend the database for heat transfer in volumetrically heated pools up to Rayleigh numbers of ~ 1017 This is presently underway in the COPO (IVO) and the ACOPO (UCSB) experiments, which will also investigate thin metallic layers. e Extend the CHF database to include reactor-specific thermal insulation, and relief path designs. This is ongoing in the ULPU experiment. Also under investigation (in ULPU) are surface treatment and structural modification to enhance CHF performance. The tmatment is more germaine to the region 6 ~ 0*, and the structural modification (such as " fins") are oriented more to the upper region (50 < 6 < 90* and including the vertical wall). e Design reactor internals that effectively prohibit the formation of thin, superheated metallic layers on the top of a molten oxidic pool of significant size. The desired trend refers to availability of steel around the core and position of the lower support plate in the lower l plenum, as discussed above, e (( Examine the potential for fouling effects in ULPU.)) Needless to say, slow accident progression to allow decmasing of the decay power to very low levels, comfortable times for primary system depressurization and cavity flooding, and a water return flow path would continue to be important. 9-2
10 REFERENCES
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{
- 2. Asfia, J. (1994) Personal Communication.
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1 15, Henry, R.E., J.P. Bureiback, R.J. Hammersley, C.E. Henry, and G.T. Klopp (1991) " Cooling of Core Debris Within the Reactor Pressure Vessel Lower Head," ANS Summer Meeting, Orlando, Florida.
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Sources," Proceedings of the Fifth International Heat Transfer Conference, Vol. 3, p.74.
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- 21. Kulacki, EA., and A.A. Emara (1975) "High Rayleigh Number Convection in Enclosed Fluid Layers with Internal Heat Sources," U.S. Nuclear Regulatory Commission Report NUREG-75/065.
- 22. KymElKinen, O., H. Tuomisto and T.G. Theofanous (1992) " Critical Heat Flux on Thick Walls of Large, Naturally Convecting Loops," ANS Proceedings 1992 National Heat Transfer Conference, San Diego, CA, Aug. 9-12,1992, Vol. 6,44-50.
- 23. KymalEinen, O., H. Tuomisto, O. Hongisto and T.G. Theofanous (1993) " Heat Flux Dis-tribution from a Volumetrically Heated Pool with High Rayleigh Number," Proceedings l
NURETH-6, Grenoble, October 5-8. [or Nuclear Engineering & Design 149, 401-408, 1994.]
- 24. Kymnininen, O. (1994) "Loviisa 1 & 2, In-Vessel Retention of Corium During a Severe Accident," IVO Int'l, Ltd. Report L01-GT1-64.
l
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l l l Technical University, Hannover, W. Germany. As myiewed by EA. Kulacki, Ohio State University, for the US NRC, march 31,1976.
- 27. Mayinger, F., et al. (1980)"Theretische und Experimentelle Untersuchung des Verhalten-1 seines Geschmolzenen Kerns im Reaktorbehulter und auf dem Betonfundament," BMFT l RS 166 79-05, Band V.
- 28. Okkonen, T. (1993) "In-Vessel Core Debris Cooling Through External Flooding of Reactor Pressum Vessel," Report by Group of Experts, Final Draft. To be published by CSNI.
l
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- 30. Park, H. and V.K. Dhir (1991) " Steady State Thermal Analysis of Extemal Cooling of a PWR Vessel Lower Head," AIChE Symp. Series, No. 283, Vol. 87, p.1.
- 31. Park, H., J. Ize, V.K. Dhir and A.K. Mal (1992) " Thermal Stresses and Creep Rupture Analysis for a PWR Vessel Lower Head During External Flooding," Proceedings 1992
- National Heat Transfemnce Conference, San Diego, CA, Aug. 9-12.
- 32. Pelton, A.D., L Leibowitz and R.A. Blomquist (19?4) J. Nuc1. Matter (in press). ,
1 l 33. Roug6, S. and J.M. Seiler (1994) "Com Debris Cooling with Flooded Vessel or Core-
- Catcher: Heat Exchange Coefficient under Natural Convection," OECD/CSNI/PWG4, Oc-i tober 1994.
- 34. Saito, M., et al. (1990)" Melting Attack on Solid Plates by a High Temperature Liquid Jet
- Effect of Crust Formation," Nuclear Engineering and Design 121, 11-23.
- 35. Schneider, S.B. and B.D. Turland (1994) '1' Experiments on Convection and Solidification in a Binary System," Proceedings, OECD/CSNI/NEA Workshop on Large Molten Pool Heat Transfer, Nuclear Research Centre, Grenoble, France, March, 9-11.
I 36. Schnitzler, B.G. (1981)" Fission Product Decay Heat Modelling for Disrupted Fuel Regions (FRECAY)," EG& G Report EGG-PHYS-5698, Dec.1981.
- 37. Sienicki et al. (1995) Appendix in Theofanous et al., (1995) l 38. Silveston, P.L. (1958) Forsch. Ingenieurwes 24,29,59.
- 39. Squire, H.B. (1938) in Modern Developments in Fluid Dynamics, S. Goldstein, Ed., Oxfoni University Press, London, Vol. II, p. 641.
, 40. Steinberner, U. and H.-H. Reineke (1978)" Turbulent buoyancy convection heat tansfer with ! internal heat sources," Proc. Sixth Intemational Heat Transfer Conf., Toronto, Canada, Aug 1978.
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1
- 41. Stickler, L.A., et al. (1"94) " Calculations to Estimate the Margin of Failure in the TMI-2 Vessel," NUREG/CR-6196, U.S. Nuclear Regulatory Commission.
~
- 42. Theofanous (1989)"Some Considerations on Severe Accidents at Loviisa," Theofanous &
Co., Inc. January 1989, IVO Proprietary Report.
- 43. Theofanous, T.G., S. Syri, T. Salmassi, O. KymnlEinen and H. Tuomisto (1994a) " Critical Heat Flux Through Curved, Downward Facing, Thick Walls," OECD/CSNI/NEA Workshop on Large Molten Pool Heat Transfer, Nuclear Research Centre, Grenoble, France, March, 9-11 [or Nuclear Enginecting and Design 151 No. 3).
- 44. Theofanous, T.G., C. Liu, S. Angelini, O. KymKlKinen, H. Tuomisto and S. Additon (1994b)
" Experience From the First Two Integrated Approaches to In-Vessel Retention Through Ex-ternal Cooling," OECD/CSNI/NEA Workshop on Large Molten Pool Heat Transfer, Nuclear Research Centre, Grenoble, France, March, 9-11.
- 45. Theofanous, T.G., et al. (1995) "The Probability of a Reactor Pressure Vessel Failure by Steam Explosions in an AP600-Like Design," to be published as an ARSAP Report.
- 46. Erland, B.D., N.A. Johns and M.P. Owens (1993) "The Implications of the TMI-2 Vessel Investigation Project for Lower Head / Melt Interactions," AEA Technology Final Report AEA RS 7771, October 1993.
- 47. Wrland, B.D. (1994)"In-Vessel Phenomena Relevant to the Achievement of Debris Coola-bility by Ex-Vessel Flooding for a PWR," Proceedings, OECD/CSNI/NEA Workshop on Large Molten Pool Heat Transfer, Nuclear Research Centre, Grenoble, France, March,9-11.
- 48. homisto, H. and T.G. Theofanous (1994)"A Consistent Approach to Severe Accident Man-l agement," Nuclear Engineering and Design, 148171-183 (1994). [see also Proceedings Specialist Meeting of Severe Accident Management Programme Development, ENEA/ DISP, Rome, Italy, Sept. 23-25, 1991, 133-151.]
. E l l I 10-4 l
I ! I l l ,i l
- )
l l i l l
.i APPENDIX A
- THE ROAAM AND PROCEDURES l
I Dealing with Phenomenological Uncertainty in Risk Analysis l Plenary Lecture in Workshop I in Advanced Topics in Reliability and Risk Analysis Annapolis, MD, October 20-22,1993 ' .I l I I I I A-1
APPENDIX A
- I DEALING WITH PHENOMENOLOGICAL UNCERTAINTY IN RISK ANALYSIS T.G. Theofanous l Department of Chemical and Nuclear Engineering Center for Risk Studies and Safety
- University of Califomia, Santa Barbara, CA 93106 ABSTRACT Tne Risk-Oriented Accident Analysis Methodology (ROAAM) is summarized and de-veloped further towards a formal defmition. 'Ihe key ideas behind the methodology and these more formal aspects are also presented and discussed.
A.1 INTRODUCTION The assessment of risks in very low probability, high consequence situations entails an 4 intellectual challenge of unparalleled dimensions in science and technology. The principal reason for this is that "by definition" these assessments must be made on the basis of more-or-less incomplete information. By this, we mean a lack of firsthand information on the behavior of the system under the postulated extreme (another way of saying, rare) conditions involving the manifestation of hazard! We need, of course, reliable estimates; normally there is a tendency to aim for reliably conservative estimates, while at the same time consideration of competing risks do not afford us the bxury of the more handily obtainable highly conservative, or " bounding estimates." We believe much of what is required to address this challenge is methodological and g
- u much of the thrust in this methodology is in communications and synergism among independent workers. We have developed the Risk-Oriented Accident Analysis Methodology (ROAAM) for this purpose. The germinal stages of it can be found in Theofanous and Bell (1986) and Theofanous et al. (1987); a full demonstration is given in Theofanous et al. (1991) and brought to completion in Theofanous et al. (1993); another application is currently underway in Pilch j et al. (1993); and a couple of new applications are presently in the offing (Theofanous et al.,
1994; Additon et al.,1994). We take the opportunity of this invitation to translate this experience into a somewhat more formal definition of ROAAM, especially including important classification aspects. Still, the best way to appreciate ROAAM is through its application to specific problems,
- such as those mentioned above, and this paper is written as a complement rather than a substitute A-3 i
1 of them in this respect. In particular, aiming for an efficient presentation of the main idcas here, we do not get into elaborations with particular examples. These can best be deduced from the applications already available. A.2 PROBABILISTIC FRAMEWORK l Given a " system" and " operating conditions" we seek to quantify " likelihood" of a certain g set of" damage" outcomes due to a set of externally imposed or internal perturbations. For each E damage component Dg we have: L(Dg) = 7(pi, p2, . .Pn) (A 1) I where the p's are parameters needed to completely characterize the response of the system. The fuac8on 7 is a "model" that is, in general, very complex and with many degrees of freedom. The medel can be deterministic, or ste::hastic, or some combination thereof. Definition. A "probabilistic framework" represents a decomposition ot the model into one or more "cause-effect" relationships and the assignment of p's into one of the following three categories: d , d 2, . . . d. i a set of deterministic parameters ri , r2, . . . rt a set of random parameters ii,i2 ,...im a set of intangible parameters subject to the following requirements: Requirement 1. The decomposition should be such that each "cause-effect" relationship represents a well-defined physical problem. A key aspect of "well-posedness" is absence of unquantifiable bifurcation or other sudden transitions in behavior - that is, continuity on ini-tial data. In this case, we have a deterministic model which, however, may admit, beyond deterministic parameters, random or intangible ones also. Requirernent 2. The random parameters should be supported by statistical bases, or at least be amenable to statistical inference - this means that developing an appropriate data base should be a practical task. In this case we have a stochastic model. Requirement 3. The set of intangible parameters is to include those that do not fall into either of the above two categories - that is, they cannot be related to other, known, parameters through either deterministic or stochastic models. A-4 l
, - _.. _ . - - . _ _ - -- . ..- - = .. - _- - . . _ - -
1 I By way of explanation, the following additional remarks can be made on the above:
- 1. De specific construction of a probabilistic framework cannot be prescribed (or automated).
As a key element, it involves the identification of the controlling physics / mechanism), I which often involved ad hoc creative elements. Rus, the central element of a probabilistic framework is one or more causal relationships (CRs). l
- 2. A similarly important decision is involved in allocating the key parameters in the three caagories. To some extent this depends on the state-of-the-art, but it must also anticipate, I or guide, the future developments. In any case, the identification of intangible parameters must be explicit, and thorough enough that it can be considered complete.
I 3. Both random and intangible parameters are quantified by means of probability density functions (pdf's)-in the former case by means of stochastic models (SMs) and in the latter case by means of engineering judgments (EJs) guided by whatever evidence is available. l
- 4. All three quantifications, CRs, SMs and EJs, are subject to errors which, however, are of qualitatively different natures and which become progressively, in the above order, more I and more ill-defined. His can be understood by the conditions of " applicability"; in the CR case it is based on relatively well-established scientific / engineering tools of scaling and experimentation; in the case of the SM it depends on the " similarity" of the circumstances l prevalent in the data base; and in the case of EJs it can only be judged on a case-by-case basis. On the other hand, the assessment of errors in all thwe cases involves judgment, and as such, an irreducible component that can be approached only qualitatively. The key aim of the methodology is to provide the necessary procedures and safeguards so as to recover imm this subjective element suBiciently to assum mbustness of the results. [That is, to counterbalance the " loss" due to the subjective element by rigor in the I assessment process.] This is the unique intellectual challenge mentioned in the introduction.
I 5. To this end, beyond what has been described above, we have introduced the idea of envelop-ing the behavior by means of " splinter scenarios" and conservatively-biased quantifications of the intangible uncertainties (as noted above, these include ermrs in the intangible param-eters as well as model errors in the CRs and SMs). Splinter scenarios give rise to multiple quantifications and, therefore, multiple results which by definition are indistinguishable (in l terms of likelihood) from each other. Dese results thus provide a conservative envelope of the behavior that could actually be obtained. As new knowledge becomes available, some of those splinter scenarios become inelevant and the envelope of results narrows correspondingly. I A-5
- 6. He other key idea is that the quantification is considered to be "a process," involving a wide range of experts, aiming for" refinement" and " enrichment" of the quantification bases, while explicitly recognizing " position on the learning curve" for the CRs and the SMs, and
" quality of quantification" for the probabilistic framework (and the intangibles). These are described further below. !
A.3 QUANTIFICATION By "quantification," we mean assigning probability distributions to the various components of the probabilistic framework. To deal with the irmducible, qualitative, component discussed above, we introduce a probability scale, as indicated in Table A.I. The scale itself is arbitrary, except for requiring that the thirti level is equal to the product of the first two which, in fact, gives our definition of " physically unreasonable" (that is, a consequence of two independent steps, events, or processes of likelihood equal to the first two levels, mspectively). The scale is used temporarily only, as a device of synthesizing through the framework an overall msult, which is to be converted using the same scale to the corn sponding qualitative meaning. An important consequence of this line of thinking is that in the presence ofintangibles we can have no l numerically expressed safety goals. Or conversely, such numerical goals are quite meaningless unless they am accompanied by an explicit definition of how they are to be computed. Table A.1. Definition of Probability Levels Process Likelihood Process Characteristics 1/10 Behavior is within known trends but obtainable only at the edge-of spect;um parameters. 1/100 Behavior cannot be positively excluded, but it is outside I the spectrum of reason. 1/1000 Behavior is physically unreasonable and violates well-I known reality. Its occurrence can be argued against positively. A-6
E { Another key questions is: What scenarios are to be quantified? This depends, to a large extent, on the reliability of the various active components of the system (including the human component), and is appropriate, and convenient, to consider it again in an enveloping manner by means of a " cut-off" frequency in admissible system damage states. His requies a safety goal, which must also be explicit in the consideration of" uncertainties" satisfying it. Thtv , a l concept of scenario, under which Eq. (A.1) is to be evaluated, is seen to consist of two sepkt.- aspects: the culling of potential scenarios to select those worhy of detailed examination and the { identification of physical laws which govern the ones to be studied. The first entails the " cut-off" frequency intending to establish an envelope of system behavior, while the second involves the progression of physical events being enveloped by means of a set of splinter scenarios and the quantification of a probabilistic framework. l The quantification is initiated by an integrated document that contains the framework, de-tailed explanations of all quantifications and their bases, synthesis of results, and a set of arbi-trary sensitivity studies - the latter have been found handy in anticipating "what if" questions that invariably arise during the review. For the process to work, this must be a highly cohesive l document and a largely valid first step in the quantification, containing a clear point of view, l that the authors have thought enough about to be willing and able to defend. Although we have l not tried it, our own experience indicates that the initiating document could not be successfully
]
! developed in a " committee" setting. Rather, most effective in this regard is a closely-knit group of individuals who can interact freely and with reasonable flexibility in carrying out support ^ activities or seeking outside help as necessary. There has been a enticism that this may bias the process to " converge" to a wrong solution. To this, we respond as follows: (a) once convergence has been achieved, in the manner described below, the solution cannot be wrong; (b) quite clearly, 7 ' such complex problems are amenable to a variety of quantifications yielding correspondingly a variety of conclusions, thus it is only reasonable that one aims at an effective solution; and (c) F l the effectiveness of a solution can be judged only after it is actually obtained - this depends l very much on the inherent merits of the probabilistic framework and the validity of the quan-tifications rather than on whether these, in the initial step, are a product of diverse committee L or the closely knit group which we advocate. Experience shows that diverse committees tend to diverge, and so far, we have no example of an issue resolved by such committee work. { He ROAAM peer-review process is to involve, to the extent possible, all key experts with L established credentials (i.e., having worked) in the various aspects addressed in the quantification. This allows experts at the generic level which is beneficial in both broadening the cadre of indi-viduals involved, but more impo:tantly in allowing the review to take on a strongly fundamental component. The review comments are to be published (signed) together with point-by-point 1 A-7 L ----- A
l I responses by the authors, together with the originating, called " peer-review version," document. The reviewers are encouraged to provide alternative quantifications together, of course, with the bases for them, and the authors' responses may make use of these inputs in synthesizing updated results as appropriate. Alternatively, the authors may elect to ignore any of these inputs by providing appropriate rebuttals. In any case, decomposition affords a focusing on narrow l technical issues that can be resolved sooner or later by means of either subgroup workshops, independent researth or audit activities or more likely by appropriate combinations. Experience j has demonstrated that very often initial disagreements are because of communications and/or difficulty to appreciate another way of thinking on a particular problem. Interactions are useful in overcoming these difficulties, but more importantly, these activities can add to the substantive aspects of the quantification by including consideration of alternative scenarios and enriching the quantification bases of the more controversial components. The aim is to achieve sufficient enrichment and eventually convergence on each of the components of the probabilistic framework. Such by-parts convergence assures agreement on the results of the synthesis, and this is defined as " resolution." A.4 SOME QUALITY ATTRIBUTES I!' Even before final resolution is achieved, during the ROAAM peer-review process, the results can be useful as the basis for tentative decisions and for allocating research resources. Following resolution, and depending on the problem, it may still be prudent that aspects of it continue to be pursued in what might be called " defense in depth in assessment." To aid , 1 , those responsible for making these decisions, we believe it is appropriate that the results of such ' analyses be transmitted with certain " higher level" quality indicators explicitly discussed. They are a " Quality Grade" on the framework, especially with regards to handling the intangibles, and a " Development Phase" on the various key models (the CRs and the SMs). Each is discussed in turn below. We define three quality grades. The highest, Grade A,is assigned to an assessment (frame-l work) carried out by means of a single, limiting process, evaluated on basic physical laws, with appropriately bounding inputs. Here there is no scenario dependence, any intangible parameters are bounded, there is no need for experimental verification, and the assessment can be consid-ered of extremely high reliability. The next, Grade B, is for an assessment involving a single but complex physical process evaluated at a high confidence level. Here there may be slight , scenario dependence (within each splinter scenario), there is need for solid experimental support and scaling, and any significant intangibles are treated in a reasonably bounding sense. Finally, we have Grade C, reserved for strongly, and clearly, coupled sequences of processes, each one A-8
h 1 quantified with suppon from scaled / applicable experiments. Here there may be some scenario dependence (and system's effects), counter balanced by appropriately conservative quantification of the intangibles. In all of these cases the emphasis is on controlling physics. Also note that we do not assign a grade, nor do we consider acceptable, in the present frame, an approach that relies heavily on the use of system's codes as the primary means of quantification. I De phases of development are introduced to explicitly denote a position on a learning curve, thus safeguarding against premature abandonment of the assessment process, and hence against inadequately verified results. We define six development phases, as indicated in Table A.2. As noted already, the examination of any problem normally begins with a scoping phase. It involves simple, and usually parametric models to check out the magnitude of the various effects. As the issues are mxlerstood better, we can expect the development of detaile( models, while at the same time we see various attempts at experimentation. By and lag:, however, this is still a pre-experimental phase. The quantitative phase is obtained when analyses and experiments converge ( sufficiently to obtain a mutually beneficial feedback, especially in identifying the important phenomenological regimes and especially in addressing scaling and applicability. This phase is consummated with the first arguably valid model comparison with scaled experiments. Further i refinement and enrichment of both analytical and experiment tools is obtained in the next phase, as results are verifi.ed, refined, or even corrected as further results arrive from multiple origins. l Hence this is called the " maturation" phase. Invariably, the maturation phase will be " driven" g by related applications, and depending on the variability involved (from the initiating study), I there may be a significant extension aspect and hence the " extension" phase. Finally, and depending on the problem, we may need a long-term activity to provide what we have described as " defense-in-depth in assessment." It is to further explore the intangibles. It will be recognized that the initiating ROAAM document will normally span phases II and III, while the ROAAM peer-review process can take on a significant portion of phase IV. It is understood that the actual completion of phase IV would take place outside and after resolution has been achieved, while j at the same time being reinforced by other related applications in phase V. Finally, the need for phase VI can only be judged on a case-by-case basis, and in a broader pmgrammatic context as vell. In the above, the phases of development have been discussed from the point of view of l CRs, as physical models are central to the ROAAM. These same phases, however, can also be defined for stochastic modelling, the emphasis here being on any physics with potential bearing I on the applicabilit of the data base, and on the necessary statistical tests to verify the model. Phase VI in this context would be concemed with any unaccounted for or unforeseen factors that could affect the results. A-9 I
I I Table A.2. Definition of" Phases of Development" for Causal Relations l Phase I Scoping Simple Models, Parametric Results Phase II Analytical Detailed Models, Pre-experimental Phase III Quantitative Experiments, Scaling, Model Comparisons gj Phase IV Maturation Verified Results from Multiple Origins E' Phase V Extension Other Related Applications 4 Phase VI Defense-in-Depth Further Exploration of Intangibles In both cases the long-term activity of phase VI is aimed at addressing the open-ended issue of " completeness." However, this is only in a defense-in-depth sense, since for the most part this has been addressed by the ROAAM peer-review process and the followup portion of phases IV and V. A.5 CONCLUDING REMARKS Parametric propagations of uncertainty can only explore a subregion of the true uncertainty space. The magnitude of the fraction thus explored is a strong function of the validity of the model, thus model uncertainty is related to this limitation. There is no way to a priori predict this limitauon, smce a given model either captures the basic physics or not. Thus, rather than l seeking a " theory" approaching this prediction task generally. there is much to be gained in focusing efforts on specific issues of great ance. We have outlined a methodology for such an applications-oriented, or product-o. approach, and we now have a significant amount of experience with it in real-life applications. We found in all cases that the answers lie in the depth afforded by this specificity, and that once an adequate understanding has been found and communicated that synergism and convergence among the experts is possible. This is fundamental since agreement among experts is a necessary condition for a rational approach
^
to decision making. The ROAAM avoids the arbitrariness of the so-called deterministic approaches (a true Grade A approach, which is, in effect, commonly found to be impractical), and the divergence of the so-called expert elicitation process (as well as other pitfalls) in level II PRAs. It is neither of l these two, and in applications it must be followed in its entirety. It can be applied equally well to assessing risk (likelihood-damage pairs) in existing facilities, as well as to guide the design and/or accident management options when improvements are deemed worthwhile. A-10
I I , A.6 ACKNOWLEDGEMENT ne development of the ideas that led to ROAAM took place over many years of work in various NRC programs, and more recently under the DOE's ARSAP program. The author is grateful to Mr. S. Additon (TENERA) for incisive comments during the preparation of this presentation and also on an early draft of the manuscript. A.7 REFERENCES
- 1. Additon, S.L., W.L. Pasedag and T.G. Deofanous (1994) "He Risk Oriented Accident Analysis Methodology (ROAAM) Applied to Passive ALWRS," ARS International Topical Meeting, Advanced Reactors Safety, Pittsburgh, PA, April 17-21,1994.
- 2. Pilch, M.M., H. Yan and T.G. Theofanous, "The Probability of Containment Failure by Direct Containment Heating in Zion," Draft NUREG/CR-6075, SAND 93-1535, June 1993.
- 3. Theofanous,T.G., W.H. Amarasooriya, H. Yan and U. Ratnam (1991) "The Probability of Liner Failure in a Mark-I Containment, NUREG/CR-5423, August 1991.
- 4. Theofanous, T.G. and C.R. Bell (1986) "An Assessment of Clinch River Breeder Reactor Core Disruptive Accident Energetics," Nuclear Science and Engineering 93,215-228.
- 5. Theofanous, T.G., C. Liu, S. Angelini, O. KymKlKinen, H. Tuomisto and S. Additon (1994)
" Experience From the First Two Integrated Approaches to In-Vessel Retention Through External Cooling," OECD/CSNI/NEA Workshop on Large Molten Pool Heat Transfer, i
- Grenoble, France, March 9-11. i
- 6. Theofanous, T.G., B. Najafi and E. Rumble (1987) "An Assessment of Steam-Explosion-
- Ir.duced Containment Failure. Part I
- Probabilistic Aspects," Nuclear Science and Engi- l neering, 97, 259-281.
.g , W 7. Theofanous, T.G., H. Yan/UCSB; M.Z. Podowski, C.S. Cho/RPI; D.A. Powers, T.J. Heames/ SNL; J.J. Sienicki, C.C. Chu, B.W. Spencer /ANL; J.C. Castro, Y.R. Rashid, R.A. Dameron, J.S. Maxwell, D.A. Powers /ANATECH (1993) "The Probability of Mark-I Containment Faihtre by Melt-Attack of the Liner," NUREG/CR-6025, November 1993. I
'I I l
A-11
l l l 1 I I APPENDIX B J I- THE COPO EXPERIMENTS I [ Heat Flux Distribution from a Volumetrically Heated Pool with High Rayleigh Number g Proceedings, NURETH-6, Grenoble, October 5-8,1993 or l Nuclear Engineering and Design 149,401-408,1994 l - I B-1 1
APPENDIX B HEAT FLUX DISTRIBUTION FROM A VOLUMETRICALLY HEATED POOL WITH HIGH RAYLEIGH NUMBER O. KymElsinen,* H. Tuomisto,* O. Hongisto,' T.G. Theofanous'
~
- Nuclear Power Engineering
' Process Laboratory IVO International Ltd, SF-01019 IVO, Finland E
- Department of Chemical and Nuclear Engineering University of California, Santa Barbara, CA 931%
ABSTRACT Experimental results are presented on the heat flux distribution at the boundaries of u volumetrically heated pools at high enough Rayleigh numbers to be directly relevant to the problem of retention of a molten corium pool inside the lower head of a reactor [ pressure vessel. The experimental facility, named COPO, is 2-dimensional (" slice"), Joule-heated and geometrically similar in shape (torospherical at 1/2-scale) to the lower { head of a VVER-440 reactor. The results show that e the heat flux on the side wall (vertical portion) is essentially uniform, f~ L e the downward heat flux strongly depends on position along the curved wall, and e average fluxes on the side and downward direction are in agreement with existing correlations, but somewhat underestimated in the upward direction. For the shape considered, the heat flux along the lower curved wall seems to be [ independent of the presence and extent of the liquid pool (contained by the vertical p sidewalls) portion above it. u B.1 INTRODUCTION
'Ihis study is motivated by an interest in arresting the progression of a hypothetical severe l l
[ accident in the reactor pressure vessel by submerging it in a pool of water (i.e., flooding the j reactor cavity). This is expected to occur in all risk-significant severe accident scenarios in the { Loviisa plant, because it is equipped with an ice condenser containment; thus, it has formed the cornerstone of the severe accident management approach for it (Tuomisto and Theofanous [1]). [ B-3
1 I The basic requirement in this accident management concept is that the thermal loads from the volumetrically heated, naturally convecting corium pool are dissipated through the lower head of the teactor vessel without jeopardizing its integrity. For this, it is sufficient to show that nowhere is the heat flux high enough to cause significant local wall thinning (by melting and/or chemical attack), and that everywhere the local fluxes am below the local critical heat flux limits on the outside. The first condition is interesting because existing data and numerical simulations ) indicate the possibility of strong heat flux peaking near the top of the vertical boundaries of such pools (e.g., Steinberner and Reineke [2]). The second condition arises because of the " inverted" boiling regime, expected to promote critical heat flux by forcing the two-phase layer to flow (while vapor accumulates) along the surface. Clearly, both processes (buoyancy driven) depend on the shape of the boundary and the radial position along it and knowledge of respective g distributions are a crucial part of the argument. In addition, total heat flows (or average fluxes) E in the upward, sideways, and downward dimetions am imponant because through them one can conveniently estimate the maximum pool temperatures required to dissipate the volumetric heat source (decay power). This, then, establishes the maximum driving force for the local evaluations. In the original assessment (Theofanous [3]) existing correlations were used in conjunction l with parametrics on local peaking to broadly scope out the problem. For a decay power level of 1 9 MW and a maximum pool height of 1.2 m, a Rayleigh number of ~ 3 10" and a maximum l pool superheat (relative to the boundaries) of ~100 K were estimated. By comparison, existing I data were limited to Rayleigh numbers smaller by at lease one order of magnitude, than the 10" order deemed relevant. Moreover, the Loviisa lowerhead is " dished" (torispherical) and the pool extends significantly into the cylindrical portion of the vessel, while previous studies were limited to rectangular, hemispherical, or semicircular shapes only. Thence was initiated the present experimental program. A parallel experimental program on the critical heat flux aspects of this problem is also in progress (KymalKinen et al. [4]). Similar calculations and limitations of the existing data base wem also noted recently by O'Brien and Hawkes [5] and Frantz and Dhir [6]. For power reactors of the 1000 MWe class employing hemispherical lower heads, the pool depth is 67% of the lower head radius and the Rayleigh numbers am of the order 1017. Frantz and Dhir [6] presented three data points obtained 18 with hemispherical pools (adiabatic top boundary) at Ra ~ 510 and " fill ratios," H/R,, of 0.4, 0.6 and 1.0, where H is the maximum pool height and R, is the equivalent radius corresponding to the pool volume. These data were only slightly lower than a numerically predicted result due to Mayinger et al. [7] Nua. = 0.55 Ra" (B.1) B-4
who used the data of Jahn and Reineke [8], obtained with semicircular pools, to benchmark the analysis. A related experimental correlation for cimular segments by Mayinger et al. [7] is
~
Nug,, = 0.54 Ra' 28 (7 (B.2) where H is the pool depth and R is the radius of curvature of the segment. The experimental conditions for this correlation cover the ranges 0.3 < H/R < 1.0 and 107 < Ra < 5 10 0 1 Note that in Eq. (B.1) the length scale cancels. This is also approximately true in Eq. (B.2) I when H/R = 1, and in any case the length scale dependency is rather small. i For the upward and sideways heat fluxes the most peninent are correlations obtained in a rectangular (slice) geometry by Steinberner and Reineke [2], o Nu,, = 0.345 Ra .233 (B.3) I Nus,. = 0.85 Ra* '* (B.4) The data range for these correlations was 8 1012 < Ra < 4 1028. Note, again, that the length 1 scale very nearly cancels from both correlations, so the application of them is not sensitive to the exact definition of pool height in cases of a curved lower boundary, as is the case here. I i Regarding the flux shapes, the data, and the theoretical interpretations of them, are even l more limited. On the vertical wall of a rectangular pool with aspect ratio of ~1, Steinberner l and Reineke [2] found a peak-to-average value of ~2. On a hemispherical boundary, Frantz and . Dhir [6] measured peak-to-average values of ~2 also, with a strong bias of strongly increasing flux with radial positions (away from the centerline). On the other hand, O'Brien and Hawkes l [5] from a numerical study (k-e model) noted the possibility, at high Rayleigh numbers, of a more uniform behavior, i.e., higher fluxes to the more downward facing parts of the lower head. l No data exist for torispherical shapes. l In this work we present data for the particular range of Rayleigh numbers, O (1015) and pool shapes (torispherical) of interest to the Loviisa case. However, comparisons with existing correlations (obtained at lower Rayleigh numbers) provide interesting insights of a more general nature, and the local flux distributions on the lower torispherical shape in conjunction with data from hemispherical shapes (obtained elsewhere) can be of value for a more fundamental understanding in numerical modelling efforts. B-5 'I
7 l l 3.2 EXPERIMENTAL FACILITY The experimental approach is based on using a two-dimensional" slice" of the Loviisa lower head, including a portion of the cylindrical vessel wall. This allows well-controlled, uniform ; heating (using the flats as the electrodes) and is convenient for achieving large characteristic length scale and thus large Rayleigh numbers. The test section of the facility (called COPO) is illustrated in Figum B.1, and the shape is shown in more detail in Figure B.2. It is at half-scale, l, geometrically similar to Loviisa, it measures a span of 1.77 m and allows a maximum pool depth of 0.8 m. The thickness of the slice is 0.1 m. 10 00 A#_1 58 59
, w -
,,f
$ ! u
. . ? wf .'
.e gg
- q g 9
. ':p* **
i - , s
-y ' 4 s.3Ni y g ,,,,ist * ,
Figure B.2. The shape of the COPO test I Figum B.I. Schematic of the COPO facility. section and identification of the cooling units on it. The flats of the test section am built from polycarbonate plates and are heavily insulated as shown. On the inside the plates are lined by seven pairs of electrode strips. At selected locations both electrodes and insulation have 20 mm holes to gain visual access to the fluid. The pool is g a conducting ZnSO4 -H O 2 solution and the current through each electrode can be individually 5 adjusted, if necessary, in order to produce uniform volumetric heating. De side and bottom walls consist of 57 separate cooling units, as illustrated in Figure B.2. Each cooling unit consists of a 50 mm thick brass wall electrically insulated from the pool by a 0.1 mm thick teflon tape. Coolant water is circulated on the back side of the brass walls. He units are grouped into three groups (Group 1: 1-8 and 50-57 units; Group 2: 9-18 and 40-49 units; and Group 3: 19-28 and 30-39 units) and the flow is adjusted evenly among the units of each group to obtain a nearly isothermal boundary. The top surface cooling is provided by two units (58 and 59). They are constructed out of aluminum sheet and are electrically insulated from the pool by a thin aluminum-oxide coating. The cooling water passes through heat exchangers and its flow rate is measumd by an electromagnetic flow meter. B-6
i ne fluid and pool boundary temperatures are comprehensively mapped by 140 thermocou-ples. Power input is deduced from electric curmnt and voltage measurements. The local heat fluxes are obtained from energy balances on the coolant circulating through each cooling unit. He overall energy balance was found accurate within 10%. B.3 EXPERIMENTAL RESULTS The conditions for all experimental runs performed are summarized in 'Thble B.I. The two pool heights employed were chosen to provide a significant variation in the H/He ratio (see Figure B.2), that is, in the " curved" portion to the total pool volume. De table also gives the l maximum pool temperature, T,..,, and Rayleigh numbers achieved in each experiment. The average temperatures at the top (cooling units 58 and 59), vertical (cooling units 1 to 10 and 48 l to 57), and lower (cooling units 11 to 28 and 30 to 47) pool boundaries, T.,,7,a, and Tan, respectively, are also reported as an indication of the degree of isothermality achieved. This degree can also be expressed by the parameter r defined by L T"' ~ T*d r- (B.5) T,..,- T,a L such that as r increases fmm 0 to 1 the upper surface condition changes from isothermal to adiabatic. In certain runs the conditions were purposely selected to yield r's in the 0.1 to 0.3 range, to test the effect of the degree of partial cooling of the upper surface on the heat transfer {' phenomena studied. This may be of interest to some special conditions in reactor applications. 7 For runs in which r<<1, any deviations from zero are due to limitations in controlling the L surface temperatures by handling the cooling units in three groups as discussed in section B.2. A more complete v'iew of this contml limitation in the present experiment can be obtained fmm Table 1 by comparing the differences in all pool boundary temperatures to the overall difference from the maximum pool temperature. In some cases the deviations seem to be excessive; [ however, no distinction could be made on the data trends of these (including runs in which the r was set as high as 0.3) as compared to runs in which the condition of isothermality was more { adequately observed. In all present runs, even those with r's up to 0.2 or 0.3, the pools appeared to be well mixed and all temperature non-uniformities were confined within narrow layers near the boundaries. This is not at all the case for pools with adiabatic boundaries (as in the case considered by Frantz and Didr [6]), in which the bulk is strongly stratified. B.3.1 Average Heat Fluxes I The experimentally measured local heat fluxes were grouped and averaged over the pool top boundary (cooling units 58 and 59), the vertical pool boundary (cooling units I to 10 { [ . B-7
l l l Table B.1. Main Parameters of the COPO Tests I Run H (m) Tmn y T., T,a Tan r Ra No. ('C) ('C) (*C) (*C) 29a 0.8 79.3 66.7 65.3 60.8 0.10 1.01 10 " 29b 0.8 81.0 68.4 66.1 61.4 0.15 1.53 1025 1 30a 0.8 64.4 55.5 55.4 53.2 0.01 6.79 1014 30b 0.8 64.5 56.1 53.0 48.6 0.27 7.24 1014 30c 0.8 65.6 57.7 53.5 48.8 0.35 6.79 104 2 30d 0.8 75.6 62.8 61.6 57.6 0.09 1.52 1025 30e 0.8 75.8 63.1 61.3 56.6 0.12 1.54 1015 l 32a 0.8 74.8 61.6 62.7 60.3 -0.09 1.43 1015 32b 0.8 77.9 66.3 64.2 59.7 0.15 1.59 1015 32c 0.8 79.9 68.3 65.5 60.1 0.19 1.66 1015 32e 0.8 80.4 68.1 65.7 56.8 0.16 1.62 1025 32f 0.8 70.5 59.7 59.1 56.5 0.05 8.76 1014 j 33a 0.8 70.8 60.4 59.5 56.8 0.08 9.89 104 1 33b 0.8 69.9 60.0 57.5 53.3 0.20 9.87 1024 33c 0.8 70.9 62.2 58.1 53.6 0.32 9.60 104 2 1 40a 0.6 82.8 67.6 66.6 58.4 0.06 5.23 1024 40b 0.6 83.7 68.4 66.5 58.5 0.11 5.70 104 2 40c 0.6 82.5 67.9 64.9 55.5 0.17 5.57 104 1 40d 0.6 81.8 66.9 63.8 55.8 0.17 5.34 104 1 41a 0.6 71.4 60.2 60.2 56.7 0.00 2.65 1042 41b 0.6 72.3 61.9 60.2 55.6 0.14 2.70 1024 41c 0.6 72.7 62.4 61.2 56.3 0.10 2.70 1041 41d 0.6 72.8 61.9 61.1 56.4 0.07 2.70 1014 42a 0.6 61.3 52.7 54.6 54.7 -0.28 1.38 1014 42b 42c 0.6 0.6 61.4 62.9 53.8 55.4 54.2 55.5 53.7 54.1
-0.06
-0.01 1.26 1024 1.24 1014 l
42d 0.6 63.1 55.5 54.8 $2.5 0.08 1.34 1042 and 48 to 57), and the lower, curved pool boundary (cooling units 11 to 47). Thus we have the " upwards," " horizontal" and "downwanis" heat transfer coefficients and Nusselt numbers, respectively, denoted by Nu.p, Nua,. and Nuan. Hey are considered in turn, below, in relation to the correlations quoted in the introduction. We plots are given in linear coordinates to make more evident the quantitative comparisons. B-8
For the upwards heat flux the data are shown in Figure B.3, together with Eq. (B.3) for comparison. While Eq. (B.3) is seen to be in reasonable agreement at the low end of the Rayleigh number range studied, we observe increasing deviations at the higher end. At Ra = 1.6 10 15 the maximum deviation of the prediction from the data is ~30% As mentioned already, Eq. (3) is very nearly independent of the length scale; in plotting the data the maximum pool depth was utilized; if one could visualize a somewhat smaller equivalent pool depth (because of the curved lower boundary), the deviation from the correlation would be somewhat larger. It is noted that for reactor assessments this trend is conservative since the upwards flux radiates to the vessel I side walls from which it is easily dissipated-a lower upwards flux means higher thermal loads on the lower head. For the horizontal heet flux the data are shown in Figure B.4 along with predictions from Eq. (B.4). We see that the use of the maximum pool depth works well considering the wide variation between the R/Hc covered by the two pool depths utilized in the experiments. upper surface side boundary 20 , , , 8 . , , 16 - a scP g 7 "
-D@c 6 '
Q. ; o 12 - a,,.- - o 5 F ,' 2
~~ , g ;
x x 4 F,g l 9 8 g ,b 'fL. - [3 F i
--- eg. (3) 2 ~
- -- e9- (4) 4 . -
O exper. 0 exper. ; 1 p O o 0 5 10 d, 15 20 0 5 10 15 20 , Ra x 10 Ra x 10"" I Figure B.3. Variation of upwards heat fluxes Figure B.4. Variation of the heat fluxes on the vertical boundary of the pool with the with Rayleigh number. Rayleigh number. 1 For the downwards heat flux the data are shown in Figure B.5, in comparison with Eq. (B.2). In this case Eq. (B.2) was evaluated in terms of the height of the curved position of the pool, He, l and the agreement is seen to be rather good. The radius of curvature, R, was taken as that of the major portion of the lower boundary, i.e., excluding the more highly curved two ends. Including these ends, in some, fashion, would produce a somewhat smaller " equivalent" radius of curvature and probably an even better agreement with Eq. (B.2). However, it is more straightforward for our present purposes (i.e., the Loviisa shape and Ra number ranges) to account for slightly higher data trends by increasing the Rayleigh number exponent slightly to 0.182. Figure B.5 B-9
i I also shows that for H > Rc the downwards heat flux is independent of the total pool height. This is an interesting and not unexpected result. On the other hand, recognizing that besides the significantly different shape the present data are at Rayleigh numbers (based on Hc) 3 orders of magnitude greater than the upper end of the data base used in deriving Eq. (B.2), the agreement is remarkable. B.3.2 Heat Flux Distributions For horizontal heat fluxes, measured local values from six typical runs (3 for each pool depth) are shown in Figures B.6a and B.6b. It is clear that there is no systematic tendency for peaking in the upper portion of the pool boundary. This is in contrast to the significant peaking reported by Steinbemer and Reineke [2], but it could well be expected by almost two orders g of magnitude spread in Rayleigh numbers between the two experiments, and, perhaps more B importantly, by the wide difference in aspect ratio (width to depth) i.e.,1 vs 3.4 or 5.6 for the 0.8 and 0.6 m pools, respectively (pool depth based on the rectangular portion of the pool only, i.e., H -Hc) in the present experiment. Both these aspects would tend to produce unsteady and
" broken" recirculation flow pattems favoring uniformity of heat flux on the vertical boundary.
The data for the lower, curved boundary for the same six runs are summarized in Figums i B.7a and B.7b. The decrease as the test section centerline is approached is much more gradual ; (essentially linear) than observed on a hemispherical shape (Frantz and Dhir [6]), and this could be indicative of the strong flow convergence not present in the slice geometry. However, this could also be the consequence of the strong thermal stratification present in the Frantz-Dhir experiments because of the adiabatic upper boundary in them. It is also remarkable that the flux j shape seems to be largely independent of pool depth and Rayleigh number variations within the ) 4 range covered in Table B.1. 1 B.4 DISCUSSION Having achieved the proper range in Rayleigh number, applicability of the results of these experiments depends primarily on the relation of the slice geometry to the " full" reactor geometry. This is the question addressed here. l As noted in the previous section, at these high Rayleigh numbers the pool is highly turbulent in the bulk and basically at uniform temperature. This certainly would be in the case of full geometry also. Now, the thermal transport processes at the upper and vertical boundaries would i be controlled by thin, turbulent boundary layers and the 10 cm gap in the experiment is certainly large enough to have no effect whatsoever. This is supported further by the agreement of the present results with the results of Steinberner and Reineke [2] obtained with a 3.5 cm gap. B-10
l
. Lower bounday 120 , , ,
E 100 Q3d' - a
~~~~~~
80 - 0 - [ E ad - E 8 80 t - l E 40 - -
~~' )
20 - g , 0 10 15 20 I O 5 Rae x 10'12 Figure B.S. Variation of the downwards heat fluxes with the Rayleigh number. 1 ~ 1 80 cm deep pool 80 cm deep pool 1.4 , , , , , , , , , 3 - ..- ,- - [ 1.2 d a mn 2:a
..x.
u x a 2.5 - x ,, 3o, .-
- .5 Y-
* *~"
*"5 6 *S !Ex D-9 1
g g
- 6 !2 E* 3 **x 8
- 6 ~ a x x *# g a2l -
[ ~ 20.6 - 23.5 y p**a$ E *" * - - 0.4 - x mn 30s 0.5 fU 0.2 - e un aan -
' ' ' ' ' ' ' ' ' h-0 o 0 4 8 50 54 58 10 15 20 25 30 35 40 45 50 b NUMBEROF COOUNG UNIT NUMBER OF COOLING UNIT 60 cm deep pool 60 cm deep pool 1.4 , , , , , , , , , 3 ... ... ,. ,. .. ... .,.
' U U ma doa
- 1.2 - - 2.5
. o x mndie
- mn 42b
(. Eo ,g3ax y
.1 k[
p a E 0.8 - g, e - s' g2 ' O [
~ E 1.5 -
5
~
" ~ y g 3 _ m , 0.4 - g ,,
- e l *" $
0.2 - - 0.5 - f 0 O .- - 0 4 8 50 ~54 58 10 15 20 25 30 35 40 45 50 [ Nt.MBER OF COOUNG UNIT NUMBER OF COOUNG UNIT Figure B.6a,b. Distribution of heat flux on Figure B.7a,b. Distribution of heat flux on the vertical pool boundary for three typical the lower, curved pool boundary for three typical runs. ~ runs. r j B-11 1 L______-_____--_-_-________-___-__--__________________ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ ______-_ -
For the downward heat transfer controlled by descending boundary layers we do expect some difference because of the converging flow found in the full geometry, which is absent in the slice geometry. We would expect that this would produce more progressive " thickening"
; of the thermal boundary layer as the vessel centerline is approached and, thus, correspondingly lower heat transfer coefficients, as compared to the slice geometry. If this is correct, the flux i shape obtained from the present experiments can be used to conservatively bound the behavior. i We plan to further investigate this issue by a numerical modelling approach, benchmarked for the turbulence treatment to the present data. On the other hand, it is probably intemsting to note that the agreement of the present data to Eq. (B.2), which is closely related to Eq. (B.1) obtained for a full hemispherical geometry, offer two other possibilities: (a) the flux shape from the slice geometry may turn out to be reasonably applicable, or (b) the average downwards flux, as obtained from the slice geometry and predicted by Eq. (B.2), is realistic for the full geometry. j 2
- In case (b) the calculated fluxes for Loviisa are low enough (~200 kw/m ) to expect that absence of CHF could be demonstrated for a uniform heat flux of this magnitude. Recognizing that the flatest portion of the lower head is controlling, this approach would be conservative.
l B.5 CONCLUSIONS Experimental results are presented on the heat flux distribution at the (isothermal) boundaries of volumetrically heated pools at high enough Rayleigh numbers to be directly relevant to the problem of retention of a molten corium pool inside the lower head of a reactor pressure vessel. l The results show that
- 1. The heat flux on the side wall (vertical portion) is essentially uniform and predicted well by Eq. (B.4),
- 2. The downward heat flux strongly depends on position along the curved wall, and for the shape considered it seems to be independent of the presence and extent of the liquid pool (contained by the vertical sidewalls) portion above it, and
- 3. The heat flux to the top boundary is somewhat underestimated by Eq. (B.3), but the deviation makes use of Eq. (B.3) conservative.
l The use of the heat flux distribution along the lower curved boundary requires some further i consideration along the lines mentioned in the discussion. j B-12
E { B.6 ACKNOWLEDGEMENTS The experiments were carried out in the Hydraulic Laboratory of IVO. Thanks are due b to the staff of the laboratory for their contribution and help. He efforts by Mr. E. Pessa in designing the instrumentation are gratefully acknowledged. E B.7 NOMENCLATURE
= gravitational saeleration (m/s2 )
{ g H = height of the pool (m) He = height of the curved part of the pool (m) Nun =& Nuc = k'Vx 2 q = heat flux (W/m ) [ Q = volumetric heat generation (W/m2 ) m R = radius of curvature of a semicircular cavity (m) N Rau =*]#j Rac = R#f , I T = temperature T = average temperature L Greek a = thermal diffusivity (m2/s) E # = thermal expansion coefficient (a/K) AT = difference between the maximum temperature of the pool and the wall 7 surface temperature (K) L A = thermal conductivity (W/m K) v = kinematic viscosity (m2/s) l I r = relative difference between upper surface temperature and the side wall temperature l l subscripts l L ou = average c = curved part of the pool { an u
= downward or bottom boundary
= height of the pool ar = horizontal, sideward direction E = local loc
,m., = maximum in the pool
,a = side wall, vertical portion of the boundary up = upward or upper boundary B-13
~
)
l B.8 REFERENCES [1] H. Tuomisto and T.G. Theofanous, A consistent approach to severe accident management. Proc. Specialist Meeting on Severe Accident Management Programme Development. OECD/ g CSNT/SESAM. Rome, Italy, September 23-25,1991. E l [2] U. Steinberner and H.-H. Reineke, Turbulent buoyancy convection heat tansfer with internal g heat sources. Proc. Sixth International Heat Transfer Conf. Toronto, Canada. Aug 1978. E 1 [3] T.G. Theofanous, Some considerations on severe accidents at Loviisa, TcI-891, Theofanous
& Co., Inc., January 1989.
[4] O. Kym111inen, H. Tuomisto and T.G. Theofanous, Critical heat flux on thick walls of large naturally convecting loops. ANS Proc.1992 National Heat Transfer Conf. San Diego, CA, August 9-12,1992. ANS HTC, Vol 6, pp 44-50. ; l [5] J.E. O'Brien and G.L. Hawkes, Thermal analysis of a reactor lower head with core reloca- I tion and external boiling heat transfer, AIChE Symposium Series, Heat Transfer-Minneapolis, MN,1991,159-168. I [6] B. Frantz and V.K. Dhir, Experimental investigation of natural convection in spherical seg- - ments of volumetrically heated pools. ASME Proc.1992 National Heat Transfer Confer-ence. San Diego, CA, August 9-12,1992. HTD Vol 192, pp 69-76. [7] F. Mayinger, M. Jahn, H.H. Reineke and U. Steinbrenner, Examination of thermalhydraulic processes and heat transfer in a core melt, BMFT R8 48/1,1976. Institut fur Verfahren-stechnik der T.U. Hannover. [8] M. Jahn and H.H. Reineke, Free convection heat transfer with internal heat sources, calcu-lations and measurements, Proc. Fifth In. Heat Trans. Conf., Tokyo, September 1974, Paper NC2.8. I B-14 I
[ r L b [ F L r APPENDIX C L THE UCLA EXPERIMENTS ' An Experirnental Study of Natural Convection in a Volurnetrically Heated Spherical Pool Bounded on Top with a Rigid Wall r Proceedings of the Workshop on Large Molten Pool Heat Transfer L Grenoble, France,9-11 March,1994 r L F L F L I L I L C-1
APPENDIX C l AN EXPERIMENTAL STUDY OF NATURAL CONVECTION IN A VOLUMETRICALLY HEATED SPHERICAL POOL BOUNDED ON TOP WITH A RIGID WALL
- F.J. Asfla and V.K. Dhir Mechanical, Aerospace and Nuclear Engineering Department School of Engineering and Applied Science University of California, Los Angeles Los Angeles, CA 90024 ABSTRACT Flooding of the reactor cavity is being considered as a cooling strategy to prevent vessel thermal failure in the case of severe core damage accidents in which telocation of core material into lower vessel head occurs. A recent study carried out at UCLA showed that the flooding of cavity could indeed be a viable option. However, one important factor contributing to uncertainty in that study was internal natural convection heat transfer coefficient. In the present work,
, experiments were conducted to examine natural convection heat transfer in internally heated hemispherical pools with external cooling. In the experiments, Freon-ll3 contained in a Pyrex bell jar, was used as a test liquid and the vessel was cooled from the outside with water. The ) pool was bounded with a rigid wall at the top, and was heated with a 750 Watt magnetron taken from a convendonal microwave. A series of chromel alumel thermocouples was used to measure the pool and wall temperatures at different locations. Experiments were performed for pools with both nearly insulated and cold rigid walls at the top. The depth of the pool was varied parametrically. Both local and average heat transfer coefficients based on maximum pool temperature were obtained. The results have been compared with the correlations obtained for pools with free surface. C.1 INTRODUCTION De study of natural convection in volumetrically heated pools is of interest in many engi-neering applicatioris, especially in nuclear reactor safety analysis. In the case of a severe core damage accident, it is possible that molten fuel and structures relocate into the reactor vessel
- nis work received support from EPRI and DOE.
C-3
I lower head. After the core relocation in the vessel, a pool of molten core material which is internally heated by fission product decay heat is formed. If the pool is not successfully cooled, it could lead to reactor vessel failure. One strategy for preventing vessel wall from melting is to B' a flood the cavity of a Pressurized Water Reactor (PWR) or drywell of a Boiling Water Reactor (BWR). Since the temperature of vessel inner wallis below the freezing temperature of the relocated core material, a crust of core material forms on the inner wall of the vessel and possibly on the free surface of the pool However, interior of the pool remains molten and decay heat induces natural convection in the pool. A recent study carried out by Park and Dhir (1991), showed that significant deviations in the predicted temperatures of the vessel head containing molten material l can occur because of uncertainties in the reported natural convection correlations. He earliest study on natural convection in volumetrically heated horizontal layers is that , of Kulacki and Goldstein (1971). In their experiments, an interferometer was used to measure ! the temperature distribution within a layer of dilute aqueous silver nitrate solution which was i bounded with two isothermal upper and lower plates. Rayleigh numbers covered a range of 200 $ Ra $ 1.27 x 10e which included laminar and turbulent regimes of natural convection. Upon ; examination of the temperature field data, they discovered the existence of cellular structures in the upper region of the laminar regime (Ra $ 10 4). He area occupied by the cells decreased with increasing Rayleigh numbers until the cells were nonexistent in the turbulent regime. In this regime, the temperature field consisted of an isothermal central region bounded by a thin, unstable upper boundary layer and a wider, more stable lower boundary layer. The energy transport at the upper bounding surface was found to be much higher than that on the lower surface. Later, Jahn and Reineke (1974) performed an experimental and numerical study of natural convection in internally heated pools contained in rectangular and semicircular cavities. In the experiments, holographic interferometry was used to measure the temperature field. He Rayleigh number range examined was 5 x 105 $ Ra 5 5 x 10s. Similar to Kulacki and Goldstein experiments, for rectangular cavity the fluid layer was bounded by two isothermal upper and lower flat plates. Jahn and Reineke found the existence of a series of non-uniform fluctuations in the temperature field in the upper region of the pool with a stable and calm liquid layer in the lower region. They concluded that for rectangular cavity, heat was transferred more effectively ir the upper region as opposed to the bottom. For the semicircular cavity, the fluid l ! layer was bounded by an isothermal spherical segment at the bottom and an isothermal flat plate at the top. He results were similar to those for the rectangular container in that the temperature field in the upper and lower regions exhibited the same type of behavior. The isotherm patterns C-4 I
[ for this emved region resembled those characteristic of a cooled vertical wall. This pattern led to b the conclusion that the Nusselt number varies greatly along the cooled surface. Nusselt number was highest at the equator and lowest at the bottom. Numerical results were found to be in a good agreement with the experimental data. Subsequently, a series of natural convection experiments in a horizontal fluid layer bounded from above with a plate maintained at constant temperature and from below by an insulated plate was conducted by Kulacki and Emara (1975). For this set of boundary conditions, average heat transfer coefficient were obtained for Rayleigh numbers up to about 2.17 x 10 12 . For Prandtl numbers varying from 2.75 to 6.85 a conelation for Nusselt number dependence on Rayleigh number for the upper surface was developed. His correlation was expressed as Nu.,,,,,,,f.,, = 0.403 Ra o.22e (g,3) L However, when explicit dependence of Nusselt number on Prandtl number was considered, the data were correlated as o Nu.,,,,,.rf.c. = 0.233 Ra 283 Pr.aso (C.2) g In these equations Nusselt and Rayleigh numbers were defined based on the thickness of the layer, H, as Nu = h.,H (C.3) r Ra = # (C.4) 2k,v,a, r l Suo-Anttila and Catton (1976) conducted an experimental study of a horizontal fluid layer with volumetric heating. The layer was bounded by two flat plates maintained at different 12 tempentures. Data were obtained for Rayleigh numbers up to 10 . Similar to the previous studies, they showed that the flow was unstable and turbulent in the upper portions and stable and calm in the lower portions of the layer. They also concluded that the heat transfer would be affected by a stabilizing or destabilizing temperature gradient. By imposing a stabilizing temperature difference, downward heat transfer could be increased. Later, Min and Kulacki (1978) performed the same type of experiment, with the exception ( that the fluid layer was bounded from below by a spherical segment with a polar angle of 60 L
' degrees rather than by a horizontal plate. They showed that aspect ratio, defined as I/D, where L is the depth of the fluid layer and D is the sphere diameter, has an important role in determining I
the relationship between Nusselt number and Rayleigh numbers for the upper surface. At low C-5
aspect ratios, the plot of Nusselt versus Rayleigh numbers is much flatter, which corresponds to the theory that conduction is the primary mode of heat transfer. However, when they increased g the aspect ratio, the Nusselt versus Rayleigh number results approached those for a horizontal a fluid layer. This is due to the fact that as the volume of fluid increases, the effects of the spherical boundary diminish. Mayinger et al. (1976) numerically and experimentally obtained the average heat transfer coefficient on the wall of a rectangular and a semicircular cavity. They also used numerical analysis to determine the average heat transfer coefficient on the wall of a hemispherical and a vertical cylinder cavity. In their calculations, the wall temperatures were kept constant. Ac-cording to their work, the average heat transfer coefficients on the upper surface and the lower curved surface for a filled hemisphere were found to be Nu.pper, rf.c, = 0.4 Ra o.2 (C.5) Nui...r,.rf.e. = 0.55 Ra o.2 (C.6) I Very recently, Sonnenkalb (1994) has presented a report on previous German research activities on natural convection in volumetrically heated fluids. According to this report, Reineke g (1979) used numerical analysis to determine the average heat transfer coefficient on the wall of a E partially filled hemispherical cavity with constant wall temperatures and he found the following correlations. Nuro ,r,.rf.c. = 0.49 Ra 28(H/R) .2s H/R > 0.2 (C.7) Nur...r,.rf.c = 0.64 Ra 28(H/R) H/R < 0.0 (C.8) where 107 5 Ra $ 10 .1 Both Nusselt and Rayleigh numbers were defined in terms of maximum fluid level. It should be noted that when for H/R = 1.0 Eq. (C.7) is extrapolated to Ra = 10 17 (Rayleigh number of interest in nuclear reactor applications), Nusselt numbers calculated from l Eq. (C.6) are about two times higher than those obtained from Eq, (C 7). Gabor et al. (1980) experimentally studied natural convection in intemally heated hemi-spherical pools with free surface. The surface of the hemispherical containers was cooled and the surface served both as a heat transfer surface and as one of the electrodes. A copper disc in the center, placed near the pool free surface, served as a second electrode. This arrangement l of electrodes led to non-uniformity in the heating process. In the experiments, ZnSO4 - H2O pools were formed in three sizes of hemispherical copper containers and pool depth was varied parametrically. No attempt was made in the experiments to calculate the variation of heat transfer C-6
coefficient along the curved surface. The average heat transfer coefficient data for 2 x 101 $ Ra $ 2 x 10" and 0.5 $ H/R $ 1.0 were correlated as 0 Nu = 0.55 Ra 18(H/R)* 1 (C.9) The Nusselt and Rayleigh numbers were defined based on the radius of the curvature. It was noted that the maximum temperature occuned in the middle of the upper pool surface, which was open to the atmosphere. A comparison of Eq. (C.9) of Gabor et al. for H/R = 1.0 and Eq. (C.6) of Mayinger et al. shows that heat transfer coefficients predicted from the conelation of Mayinger et al. at high Rayleigh numbers are much higher. The difference between the two increases as the Rayleigh number becomes large. For nuclear reactor applications Rayleigh numbers of interest are on the order of 1017. If the results of Mayinger et al. and Gabor et al. are extended for Rayleigh number of 10 17, the average heat transfer coefficient predicted from Mayinger is about ten times higher than that obtained from the correlation of Gabor . Frantz and Dhir (1992) have reported results of natural convection heat transfer in volu-metrically heated spherical cavities cooled fmm outside. Micro-wave heating was used in the experiments and it was concluded that a large variation in heat transfer coefficients existed along i the vessel wall. More recently Kymnininen et al. (1993) have performed large scale natural convection experiments in a two dimensional slice of torospherical lower head of VVER 440 reactor. Joule heating was used to pmduce thermal energy in the liquid and Rayleigh numbers (based on the height of the curved portion of the pool) of the order of 1.8 x 1013 were obtained. It was concluded that the data compared well with the correlation of Mayinger et al. (1976) for circular segments. Local heat transfer coefficient data showed a linear dependence on angular position as opposed to a very rapid increase in heat transfer coefficient near the equator found in the experiments of Frantz and Dhir (1992). As an extension of the work of Frantz and Dhir (1992), Asfia, Frantz and Dhir (1994) conducted natural convection experiments in volumetrically heated spherical pools with free surface. Similar to the Frantz and Dhir experiments, the pool was heated with Micro-wave and was cooled from the outside with water. The range of Rayleigh numbers for the data was 2 x 1010 $ Ra $ 1.1 x 10". They also found the existence of a large variation in heat transfer coefficients along the vessel wall. 'Ihe local heat transfer coefficients along the hemispherical wall were correlated as h(8)
= C 3sine - C2cose (C.10)
C-7
I 6 Cr = -1.25cos4 + 2.6 for 0.75 < 4 $1 and C2 = -2.65cosp + 3.6 l
= 1.17 sind e + 0.23 for 0< $ 0.75 Nusselt number based on average heat transfer coefficient for 2 x 10 10 $ Ra $ 1.1 x 10 24 was obtained as Nu = 0.54(Ra) '(H/R,)' 28 (C.11) l Re Nusselt and Rayleigh numbers were defined as Nu = (C.12) k, Ra = k yp ni a, (C.13)
For H/R, = 1.0 the average heat transfer coefficients predicted from Eq. (C.8) are compa-rable to those obtained from Eq. (C.6). The present work is a continuation of the work of Asfia, Frantz and Dhir and the objective the work is to experimentally study the role played by the following boundary conditions on local and average natural convection heat transfer coefficients in volumetrically heated pools: (i) insulated rigid wall boundary condition on the pool surface (ii) cooled rigid wall boundary condition on the pool surface. C.2 EXPERIMENTS I The apparatus used in this work consists of a rigid box which serves as a tank for subcooled water as well as a support for a glass bell jar containing the test fluid. Figure C.1 shows the test setup. The box is a 3-layer water-tight container made of plywood and polyurethane foam. The outer and inner layers are made of 0.635 cm thick plywood. He middle is a 7.62 cm thick layer of Hathane 1680-11 (11 lb/ft3 density) polyurethane foam. De outer and inner dimensions of the box are 0.927mx0.927mx0.762m and 0.762mx0.762mx0.686m, respectively. Two different sizes of Pyrex were used in the experiments. Bell jar 1 is 59.44 cm in length (from the top edge down to the center of the spherical bottom),43.65 cm in diameter (inner) and has a thickness of 1.1 cm in the cylindrical portion. Belljar 2 is 59.55 cm in length,60.1 cm in diameter and has a C-8 I I
L To Microwave Unit ( r: :1 Microwave Guide i ( Foam y
'1 ll %__m
) ll 7.8 eM l s 92.
en] I ll - Il I
' 76.2 cm l Bell Jar y[ ll x l l .
-___j l l < // l r
l // j d__.f- u Windo / I - l s' L _ _ _ _ _g_ _ _ _ _ _ _ _ f Figure C.I. Experimental apparatus. wall thickness of 1.17 cm. Two double-paned 0.25mx0.18m wooden picture windows are built into the opposite sides of the box to allow viewing of the lower portion of the vessel. The fluid i inside the vessel is heated uniformly with a 750 Watt magnetron, the power to which is controlled with a conventional microwave oven. The magnetron is attached to a 10.2 cm diameter copper j tube serving as a waveguide for the microwaves. His device is suspended by steel rods and ! aluminum clamps above the vessel. To control radiation from the microwave, bronze screens are placed along each inner wall of the large plywood box prior to pouring of the polyurethane foam. The screen is connected to ground in order to short out the electromagnetic charge. A lucite lid was made to cover the opening of the vessel. A square opening with dimensions 11.4cm x 11.4cm is cut in the center of the lid to allow the waveguide to be lowered into the belljar. To impose rigid wall condition on the pool surface, a second lid was fabricated from plexiglass sheets. The lid is made of two 0.31 cm thick discs separated by 0.95 cm air gap. The diameter of these plates are 42.7 cm for bell jar 1 and 59.3 cm for belljar 2. A rubber strip is used to hold these two plates. Thirty-four 4 mm diameter holes are drilled through the plates. Through these holes, C-9
I 4 mm diameter Pyrex tubes each containing chromel-alumel thermocouple wires in the lid are inserted. Thermocouples are located in two perpendicular plates. He location of thermocouples g in each plate (1/2 a plate) is shown in Figure C.2. Three more thermocouples are placed on the 5 face of the lid touching the pool surface. The diameter of this lid is changed for smaller pool depths. To impose the cooled rigid wall condition on the pool surface, a third lid was made. Similar to the second lid, a rubber strip is used to hold the two discs 0.95 cm apart. The lid is cooled by passing cold air in the passage. The passage is divided in six sections so that air is distributed uniformly. Two 1.9 cm diameter holes are drilled into the upper plate and fitted with two 1.9 cm diameter (outer) and 58 cm length plexiglas tubes for inflow and outflow of cold air. Thirty-four chromel-alumel thermocouples each located in a 4 mm diameter Pyrex tube are used to measure the pool temperature at different locations. On the two sides of the lower plexiglass plate which touches the pool surface, three sets of thermocouples are attached. To cool the air, compressed air is allowed to pass through a copper coil placed in an ice bath. Air flowrate is measured with a float type flowmeter, and the inlet and outlet air temperatures are measured with two chromel alumel thermocouples. Figure C.3 shows the sketch of the lid used for imposing a l cooled rigid wall boundary condition. Seven additional thermocouples are attached to the inner wall and seven more are added to the outer wall of the vessel using Omegabond 101 epoxy. Readings from the thermocouples are taken with an Acro 900 Data Acquisition System. The data am stored and later plotted using computer graphics. j=7 . g
. j="6 -
,. =o.
. . l j=l4 ----- g j=T3 T wi
~/
j T
~ ]2 y/- wo l~ M ~_ s Figure C.2. Location of thermocouples in the pool and on the wall, H/R, = 1.0.
C-10 I
I ) L cold air out in o
<F a) Side View TrL ai , _T g,i, a j i , ii t i II i im i= 1 m !
mg Thermocouples
,, n ,, -
Thermocouple Passages \ - i i b) Top View o
- O e
\ e 9 Figure C.3. Schematic diagram of the lid used to impose cold rigid wall boundary conditions. i C-11
I A water cooling system is used to mainatin the temperature of water surrounding the vessel nearly constant with time. A 2.5 cm hole is drilled into the bottom of the box and fitted with a g copper pipe and flange to serve as both a water inlet and a drain when a particular experiment 5 is completed. Water is removed from the upper surface of the pool. It is then passed thmugh a copper coil, around which there is a continuous flow of cold water. Water exiting the heat exchanger is retumed back to the bottom of the pool In the experiments, the free surface of the water was generally kept 6-9 cm above the free surface of R-113 in the test vessel. C.2.1 Procedure Before the actual experiment was run, each thermocouple was calibrated. All thermocouples were individually submerged sequentially in an icebath, a pool of boiling Freon-113, rad a pool of boiling water. The thermocouple outputs were compared with the temperature reading from a separate thermometer. Using these data, calibration curves were drawn for each thermocouple. g From these curves, relative error in reading from a particular thermocouple could be determined. 5 Once every thermocouple was properly calibrated, all of the thermocouples were placed in their designated spots. Prior to every test run, the test liquid was pumped into the vessel to the desired pool volume. With lids in place and all of the thermocouples checked, the waveguide was lowered and fastened in place. Before adding water to the tank, a calibrati on run for heat generation rate in ' e fluid (lasting approx. 25-30 min.) was made. This was done in order to calculate the power output from the micmwave and to determine the uniformity of heat generation rate in the test liquid. The data from these runs were plotted and the slopes of the temperature vs. time plots were used to calculate the heat input into the pool. Figure C.4 shows a typical rate of rise of fluid temperature at three locations in the pool when R-113 was used as the test liquid. The g heat generation rate at different locations in the pool for all experiments was found to be within E 7%. l After the calibration for heat input to the test liquid was performed, the tank was filled with l water and the cooling system was activated. For cold rigid wall boundary condition experiments, the air cooling system was also started. After assuring that everything was properly running, the microwave was turned on again, and the pool was allowed to heat up. After approximately one hour, the pool acquired a nearly steady state temperature. De entire test run was carried out for l about six hours. He Acro Data Acquisition System was adjusted to record the temperature every 15 seconds. It took almost 50 ms for the system to read the input of each thermocouple. Because of the inevitable interference from the microwave, proper thermocouple readings could not be obtained unless power was shut off. To avoid this problem, thermocouple readings were taken j C-12 I
L 30 . . . . 29
- Average Slope = 0.26 *C/mm. "
DeviaUon = + 0.012 'C/ min.
} _
o z/H = 0.2. r/R, m 0.9 ,
j 3'7 . O: t /H = 0. 05, r/ R, m 0.7 ,.** .
A: t/H = 0. 4. r/R, = 0.3 ' g .'* g 26 - - r ' ...',, . - t 25 ; - t
# 24 -
23 : 22 -
,s -
21 [' - 20 0 5 10 15 20 25
'nme (min. )
Figure C.4. Heat generation rate at different locations in the pool. at 10 minute intervals. Thus, after every 575 seconds, power was cut off for twenty five seconds [ and two sets of thermocouple readings were taken (at 585 seconds and at 600 seconds) . After reconting the second set, power was immediately restored. These short power interruptions [ appeared to have no effect on the temperature behavior of the pool over the duration of the experiment. C.3 RESULTS AND DISCUSSION One of the important considerations in the experiments conducted with internally heated pools is uniformity of the heat generation rate. Heating rates in various liquids, such as water, ethanol, olive oil, silicone oil, and R-113, using the microwave guide arrangement as shown in Figure C.1 were determined. A large difference in the heating rates near the pool free surface and at the bottom of the pool were found to exist in all liquids except R-113. As noted earlier L with R-113, the rate of temperature rise at any location in the pool did not differ by more than 7% from the mean value. Our lack of success in finding other liquids which could be heated [ uniformly with microwaves limited the number of data points that could be obtained. ( C-13 [ --
m-. I Prior to conducting the experiments, the equivalent radii, R., of the vessel were obtained by noting the volume of liquid needed to fill the jar to a certain height. Table C.1 gives the g equivalent radii along with other data. E Table C.I. Heat Transfer Rate for Each Experiment l Pool Surface R. II/A Ra dT/dt Q;. Q, Qu Condition cm deg C/sec W W W Insulated 21.83 1.0 3.23 x 10 13 4.31 x 10-3 4.5% 134.2 1.5 117.7 Rigid 23.5 0.57 2.9 x 1012 4.05 x 10-3i6% 66.7 1.2 65.2 21 36.1 Surface 22.7 0.43 4.7 x 10 4 x 10-3 5.5% 36.6 0.8 30.8 - 1.0 ' 7.8 x 10 28 2.03 x 10-3 7% 176.4 2.33 168.5 Cooled 21.83 1.0 3.03 x 1013 4.07 x 10-3 4% 134.3 21.2 103.6 Rigid Surface 22.7 0.43 5 x 10 11 3.53 x 10- 4.5% 32.3 7.3 25.8 30.8 1.0 8x10 ta 2.00 x 10-3 3% 177.4 30.7 126.8 Because of the spherical geometry of the pool, the heat transfer area changes significantly with the angular position measured from the lower stagnation point. To determine the area supported by each of the thermocouples located discretely on the bell jar surface, the angle between any two neighboring thermocouples was determined. Half of this angle on either side l of a given thermocouple was assigned to that thermocouple. By knowing the total subtended angle and the equivalent radius, the surface area and pool volume assigned to a given surface thermocouple could be determined. Figure C.2 shows how the strips are defined in the pool. From the thickness,6, and thermal l conductivity, k, of the bell jar, .neasured time averaged maximum temperature, T, .,, in the pool and the time averaged inside, Tw;, and outside, T. , wall temperatures, local time averaged l heat transfer coefficient could be determined as I k(Tw; - Two) h' = 6(T,ma, - Tw;) (C.14) Average heat transfer coefficient for the spherical segment is obtained as h ,, = EN.? ih bA i (C.15) Ej:EAAi g C-14
I he uncertainty in local heat transfer coefficient is found to range from 9% to 2SE The highest uncertainty in the heat transfer coefficient occurred at the lower portions of the bell jar where the difference between the inside and outside wall temperatures was found to have the smallest value. Heat transfer rate for each section was determined by knowing the surface area for each strip as: i AQj = (AAj)k/6(T.4 - T. ). (C.16) ne above equation is written under the assumption that heat transfer isross the vessel wall is one dimensional. He assumption is realistic everywhere except for two locations, near the pool surface and the lower stagnation point. Two dimensional conduction analysis were performed to calculate the heat losses through the vessel wall at the top and bottom strips. The total heat transfer rate to the water is the sum of heat transfer rate for each section, E AQj. Aside from the heat transfer across the vessel wall, the other contributor to the heat loss is condective heat transfer through the rigid wall bounding the pool surface. Due to the air gap, the heat conducted through rigid walls in the absence of air flow is relatively small. By knowing the inner surface and ambient temperatures, this heat loss can be determined from Ar...(T,. .. - T m s.) q, = 26 /km + 6 (C.17) 3 2 /k 2 + 1/h, Where kiand 6 are 3 the thermal conductivity and thickness of the two plexiglass plates ,k2 and 62are the thermal conductivity and thickness of the air gap, and h, is the natural convection heat transfer coefficient for air. The heat loss for the cold rigid surface was determined by knowing the air flowrate,m. and inlet and outlet temperatures of air passing through the air passage as Qi = m.C,.(T. - T.) 4 (C.18) Table C.1 gives the heat generation rate, Qgo, heat loss through the rigid wall on the pool surface, and heat transferred, Q, ,, across the curved surface. C.3.1 Rigid Nearly Insulated Pool Surface Figure C.5 shows the ratio of the local to average heat transfer coefficient as a function of angular position measured from the lower stagnation point. He plotted data are for H/R, = 1.0 and 0.43 for bell jar 1. Heat transfer coefficient is lowest at the stagnation point and increases along the periphery of the spherical segment except at the location very close to the rigid surface. At the location near the rigid surface the ratio decreases rapidly. Similar behavior in the ratio C-15
I of local to average heat transfer coefficient has been observed for other pool heights. Except at the location near the pool surface, the obtained data for local heat transfer coefficient could I 5 be correlated within 20% with the correlation developed for free surface pools, Eq. (C.10). Figure C.6 shows the isotherms obtained by linear interpolation of temperatures obtained from thermocouples placed at different locations in the pool. Isotherms are not exactly symmetrical in the azimuthal direction. Stratification in the lower part of the middle section of the pool is much stronger than in the upper part. A comparison of these isotherms with the free pool surface case reported by Asfia, Frantz and Dhir reveals that presence of a rigid wall tends to limit the circulatory motion in the upper region leading to a relatively larger stratification in the upper region. 2.5 . . . . . . . . O H/R, = 1.0 0 H/R, = 0. 43 0 o l'\
/
1.5 I I 1
- 1 w /
t2 /
/
1.0 - -
/
/
/c
.5 -
#_ o o
I
.0 E O 10 20 30 40 50 60 70 80 90 g 6(deg)
Figure C.S. Ratio of local to average heat transfer coefficient with respect to angle for insulated rigid wall for belljar 1. After initial heating of the pool, liquid and wall temperatures were observed to oscillate with I time. For H/R, = 1.0, Figure C.7 shows as a function of time the temperature output of one of the thermocouples located near the surface of the pool but closer to the cooled curved surface of the bell jar. The period, amplitude and time for onset of oscillations are given in Table C.2. It C-16 I
l 32.2- ~~
~, _ f32.2~ -
\ l _ / -
- ~~
3I _- \ j - -
~ ~~
^
~ \\ '
~~
,~ s 30 -30
~ ~ . . .
~ , _
~ .
^
~
_ ~ 29_ s 29 ~. s. ~ __ ~ .~ s T.cter=25.4 l y -.
%2 ~ ' - ~- -
'~ ~
~
~
27 ~ _~.~ ( ~, .
~n ~
~ ~
~
~ -
~ . ~.
s ~ _
~ ,, ,
~~ ~ ~ ,~ ~ ~
m
~
~~ ~
~
~
~ r ~ .
~ -.
~ . -
.. ~
~ ^ '~ g y -
' ~ ,- r~ e ~ H g & g 8 ,.) ,~ - , . .
NN *' r~ e c. n c' , > ei e f ~ e " ~ N
~
~ .,
/
Figure C.6. Isotherm patterns for bell jar i for insulated rigid surface, H/R, = 1.0. (All , temperatures are in Celsius.) l 30.0 . . . . . 29.4 ooo o ooo oooo 0aoo o 28.8 o - o l 28.2 o '
^
; o P*
27.6 - o - 27.0 l % H/R, = 1.0, r/R, = 0. 85. z/H = 0.2 ; h 6 26.4 ; Period of Oscillation = 30-40 min. >
'0 Anplitude of Oscillation = 0.01-0.07 'C o
l 25.2 - b - b ., = a.7a 'c i 24.6 io 24.0 0 50 100 150 200 250 300
'Ilme (min. )
Figure C.7. Variation of temperature respect to time for one of the thermocouples located in the pool with insulated rigid wall. ! C-17
I E Table C.2. Temperature Oscillations for Insulated Rigid Surface H/% Position g,(W/m3), Start Period Amplitude Tmu p Tw('C) min min *C 1.0 r/R=0.85, z/H=0.20 0443, 150 30-40 0.01-0.07 r/%=0.75,z/H=0.05 1.0 8.78 170 30-40 0.04-0.1 1.0 r/4 =0.95,z/H=0.2 130 2450 0.01-0.07 1.0 Tw,z/H=0.07 180 20-40 0.05-0.11 1.0 Tw,z/H=0.2 180 30-50 0.025-0.045 Belljar 0.57 r/N=0.85,z/H=0.32 6100, 160 20-40 0.05-0.14 1 0.57 r/%=0.67,z/H=0.08 8.51 160 20-40 0.1-0.18 0.57 r/R,=0.75,s/H=0.32 160 30-50 0.025-0.14 0.57 Tw,z/H=0.1 190 50 0.2 0.57 Tu,z/H=0.32 190 40 0.1-0.13 0.43 r/N =0.0,z/H=0.1 6000, 120 30-60 0.02-0.15 0.43 r/R=0.2,z/H=0.68 7.9 120 20-60 0.06-0.1 0.43 r/N =0.7,z/H=0.1 140 30 50 0.035-0.17 0.43 T.g,z/H = 0.1 120 30-50 0.02-0.2 0.43 Tw,z/H =0.8 120 50 0.02-0.2 1.0 r/%=0.9, z/H=0.03 3031.2, 230 20-40 0.1 Bell jar 1.0 r/R=0.65,z/H=0.55 7.65 210 20 40 0.05-0.1 2 1.0 r/R =0.5,z/H=0.80 150 20 40 0.05-0.1 1.0 T 4,z/H=0.03 230 20-30 0.04-0.15 1.0 Tw,z/H=0.48 210 20-40 0.08-0.12 generally took longer for pool temperature oscillations to develop near the cooled bell jar wall. In the lower portion, the temperature began to oscillate somewhat earlier. The largest values for the frequency and amplitude of oscillations also occur near the cooled walls. In comparison with the free surface pool case (Asfia, Frantz and Dhir (1994)), it took longer for the temperature oscillations to develop for pools with a rigid top surface. It was observed that the temperature oscillations for symmetrical locations across the pool are not symmetrical, even though the values for their time period and their amplitude are almost similar. The difference between the C-18 I
1 b maximum pool temperature and the water temperature is also given in Table C.2.The amplitude of oscillations is generally about 1% of the temperature difference. Generally, oscillation time periods varying from 2040 minutes were found. No cler effect of change in pool height on ( the above observations was noted. C.3.2 Rigid Cooled Pool Surface Figure C8 shows the variation of local heat transfer coefficient along the curved and flat walls bounding the pool for N/R, = 1.0. De heat transfer coefficient has been normalized with { the average heat transfer coefficients on the curved surface. The data beyond the angle of 90' are for the locations on the rigid wall. In plotting the rigid wall data, X is defined as the distance of each thermocouple from the bell jar wall. Except for the location near the pool surface, the obtained data for local heat transfer coefficients for the curved wall are again conelated ( within 20% with correlation developed for free surface pools, Eq. (C10). The maximum heat transfer coefficient occurs below the pool upper surface. From this location the heat transfer coefficient decreases both on the curved wall as well as on the rigid wall. Isotherms in the pool with cold rigid wall on the top are shown in Figure C9. A layer of fluid adjacent to the rigid j wall has a temperature slightly less than the maximum temperswe. Some circulatory motion in the upper region appears to have re-emerged and the propensity of stratification is weakened in r comparison to a pool with the rigid insulated wall. Again, stratification in the lower part of the middle section of the pool is much stronger than in the upper part. [ Similar to the insulated rigid wall case, after the initial heating of the pool, temperatures oscillated with time for the cold rigid wall. For H/R, = 1.0, Figure C10 shows as a function of time the temperature output of one of the thermocouples located near the surface of the pool but closer to the cooled surface of the bell jar. The period, amplitude and time for onset of oscillation are given in Table C3. The behavior of the temperature oscillations for cold rigid wall pools is similar to that for the insulated rigid wall. He data for the Nusselt number based on heat transfer coefficient averaged over the curved surface of the pool are plotted in Figure C.11 as a function of Rayleigh number. He plotted data are for H/R, = 0.43,0.57, and 1.0 for the insulated rigid wall and 0.43, and 1.0 for the cooled rigid wall when belljar 1 was used. In this figure, H/R, = 1.0 for both cases insulated rigid wall and cooled rigid wall for bell jar 2 are also plotted, Nusselt and Rayleigh number are defined by Eqs. (C12) and (C13). He heat transfer data have been correlated within 15 % with the correlation developed by Asfia, Frantz and Dhir (1994) for free surface pools, Eq. (C11). This correlation, Eq. (C11), for two different pool heights, H/R, = 1.0 and 0.2, has also been shown in Figure Cll. C-19 l l l
1 I I 2.5 . . , , , , ,
. y , , .
I I H'" = '0 1.- p ..rr... I 2.0 - 8 = 22 cm j - AI O. 4: T=. Sepe rot. Espe riment. I
^
1.5 - -
- I
~
o o 1.0 - g l l I I
.5 -
l a l l e .15 0.3
.0" ' ' ' '
10 20 30 40 50 60 70 80 90 O Pool ongle Figure C.8. Ratio of local to average heat transfer coefficient with respect to angle for cooled ngid wall for bell jar 1. u.. _ e *',
~
- - g l
~
nu
& '- ^'
l .~ , l
~
.~
~
- i... - -
^
_', ~ $~ ~ , .. ,~ 7, . ib ' ~
~. _ _
~
, ,- , - - l Figure C.9. Isotherm patterns for bell jar 1 for cold rigid surface, H/R, = 1.0. (All temperatures l are in Celsius.)
l C-20 I I I
E 24.0 , , , , , 23.5 - 0 00 23.0 - o gooo o00oo 0 o 00 oo o _ o o 22.5 - " oo G 22.0
~
s,a, , i , o , ,,R, - o. s2. r es - o. 2 . g 21.5 U
# 21.0 - p r,oo o, o ,cination . 3o_40 rnin. _
20.5
- 0 Arnpiitude of cecisiotion - o.o2-o.cs ac .
20.0 - r,,,, , - T. . . . , - 7. e s 'c ; 19.5 0 . 19.0 O 50 100 150 200 250 300 Time (min. ) L Figure C.10. Variation of temperature respect to time for one of the thermocouples located in r- the pool with cooled rigid wall. L 1b ., , ,, ,, , ,, , , ,, , . . , Insulated . Cold rigid wall ! 0 H/R, a o.43 g H/R, = 0.43 18 - g H/R, . o.37 y H, R, . i . o . A H/R, = 1.o .
~
l 5 Nu = 0.54 Rao .2 (H/Re )0.25, H/Re = 1.0 H/R e= 0. lz 1f , j 10 - - N . . Id ' -' ' ' ' ' ' ' ' ~ ' - Id idi 1f2 1f3 1f4 1f5 1fs 137 lfa Ra Figure 11. Comparison of the present data with the conelation developed for the pool with free surface. [ C-21
I Table C.3. Temperature Oscillations for Cold Rigid Surface H/N Position qu(W/m3 ), Start Pr ed Amplitude T,,mo Tw('C) mia ..nin
. 'C 1.0 r/N=0.82, z/H=0.20 6103, 140 30-40 0.02-0.06 1.0 r/N=0.75,z/H=v.05 7.86 140 40-50 0.06-0.12 1.0 r/ N =0.9,z/H=0.20 120 20-40 0.025-0.06 1.0 r/N =0.65,z/H=0.4 120 40-50 0.06 Belljar 1.0 Tw,z/H=0.07 120 20-30 0.05-0.11 1 1.0 Tw,z/H =0.2 140 50 0.025-0.045 0.43 r/N =0.25,z/H =0.78 5293.2, 70 50 0.02-0.15 0.43 r/N =0.9,z/H=0.1 6.16 90 30-60 0.05-0.09 0.43 r/N =0.7,z/H=0.1 90 30-60 0.05-0.06 0.43 Tw,r/H=0.1 110 20-50 0.06-0.12 0.43 Tw,z/H =0.8 110 20-30 0.04-0.1 1.0 r/N=0.8, z/H=0.07 3070, 160 20-40 0.02-0.08 Bell jar 1.0 r/N=0.65,z/Z=0.58 5.27 140 20-50 0.01-0.06 2 1.0 r/N=0.5,z/H=0.78 130 20-50 0.01-0.06 1.0 Tw,z/H =0.06 150 30-40 0.06 1.0 Tw,z/H=0.48 150 30-40 0.06-0.08 By knowing the inside and outside temperatures for the lower plexiglas plate which touches g the pool surface, local heat transfer coefficient on the cooled rigid wall could be determined. E he measured heat transfer coefficients were averaged over the area where thermocouples were attached to the plexiglas plate. This ama was about 50% of the total surface area for H/R, = 1.0 and 33% for H/R, = 0.43. The data for Nusselt number based on average heat transfer coefficient for the upper cooled rigid wall are plotted in Figure C.12 as a function of Rayleigh number. He Nusselt number and Rayleigh numbers for the cooled rigid wall are defined based l
on the depth of the pool, H. De prediction from the correlation developed by Kulacki and Emara for the upper surface is also shown in Figure C.12. It is seen that the present data compare favorably with predictions from the correlation of Kulacki and Emara (Eq. C.2). C-22
10 . , - - , ,, ., ,, ,, ,, . . . , , Cold rigid wall - e H/R,= 0.43 3 A H/R,= 1.0 10 - x - . Nu = 0.233 Ra .233 0 p,0.239, Pr = 8.2 A
, (Kulacki and Emara)
{ il 10 - - II - - l5 10' -
~
L U " ' " ' ' " " " ' ' " ^ ' ' ' ' ' " ' ' " ~ ' ' " " " ' ' " ' ' ' 1O - 12 10 10 10 10 10' 10' 10 10 10' # Ra = (g40,H5)/(2kva) Figure C.12. Comparison of the present data for cooled rigid wall bounding the pool surface with the correlation developed by Kulacki and Emara (1975). L C.4 CONCLUSIONS F t
- 1. Using R-ll3 as the test liquid, natural convection heat transfer in internally heated pools y contained in spherical segments cooled from outside have been obtained. Both insulated L rigid wall and cooled rigid wall at the pool surface have been studied.
P
- 2. Nusselt numbers data obtained in this work compare favorably with the prediction from the correlation of Asfia, Frantz and Dhir (1994).
L 3. Heat transfer coefficient is lowest at the stagnation point and increases along the spherical segment except at the location near the pool surface. Maximum heat transfer coefficient { occurs slightly below the pool surface. '
- 4. Diffemnt boundary conditions in the pool surface (free surface, insulated rigid surface or L cooled rigid surface) make only a slight difference in the average heat transfer coefficients.
e 5. Average heat transfer coefficients on the cold rigid wall bounding the pool surface appears to compam favorably with the cormlation of Kulacki and Emara (1975). C-23
~
l _ ----__ _ _ -_ __ __-_ _- - _A
I C.5 NOMENCLATURE A = wetted surface area (m ) 2 cp = specific heat (kJ/kgK)
- g = gravitational acceleration (m/s2 )
H = dool depth (m) ' 2 h(6) = local heat transfer coefficient (W/m K) h = time averaged heat transfer coefficient (TV/ms g) h., = time and area averaged heat coefficient (TV/ms g) k = thermal conductivity (TV/mK) Nu = Nusselt number (Q,,nR)/ (AkAT) Pr = Prandtl Number g Q = rate of heat transfer (W) Q,,o = heat generation rate (W) 4, = volumetric heat generation (TF/m8 )
- Qin = input heat (W)
Q,,, = heat transfer rate across the curved surface (W) Qi = heat transfer rate across the rigid surface (W) 2 q = heat flux (TV/m ) Ra = Rayleigh number (Ra = ppQ,R5/kva) R = inner radius of vessel lower head (m) R. = equivalent radius corresponding to pool volume (m) r = radial distance (m) T = temperature (K) t = time (sec) V = volume ' z = axial distance from the surface X = radial distance from the edge on the surface m = flowrate l Greek Letters 4 = pool angle (deg) 6 0
= angle along the vessel wall (deg)
= (6/4)(w/2) l p = density g
a = thermal diffusivity
# = coefficient of thermal expansion (1/K)
C-24
I l v = kinematic viscosity 6 = thickness Superscripts l -
= time average Subscripts I
l av j
= average
= indices max = maximum P = Pool l wi = inside wall l
I wo W
= outside wall
= water a = air r.w. = Rigid wall L cmb. = ambient I C.6 REFERENCES
- 1. Asfia, F.J., B. Frantz, and V.K. Dhir,1994,"ExperimentalInvestigation of Natural Convec-k tion in Volumetrically Heated Spherical Segments," Submitted to Journal of Heat '1Fansfer.
e 2. Frantz, B., and V.K. Dhir,1992, " Experimental Investigation of Natural Convection in Spherical Segments of Volumetrically Heated Pools," Proc.1992 National Heat Transfer Conference, San Diego HTD Vol.192, pp. 69-76.
- 3. Gabor, J.D., P.G. Ellison, and J.C. Cassulo,1980, " Heat Transfer from Intemally Heated Hemispherical Pools," Presented at the 19th National Heat Transfer Conference, Orlando, FL.
- 4. Jahn, M. and H.H. Reineke,1974, " Free Convection Heat Transfer with Intemal Heat i Sources," Proceedings of the Fifth Intemational Heat Transfer Conference, Vol. 3, p.74.
F 5. Kulacki, F.A., and A.A. Emara,1975, "High Rayleigh Number Convection in Enclosed Fluid Layers with Intemal Heat Sources," U.S. Nuclear Regulatory Commission Report NUREG-75/065. l
- 6. Kulacki, F.A., and R.J. Goldstein,1972, " Thermal Convection in a Horizontal Fluid Layer with Uniform Volumetric Energy Sources," Journal of Fluid Mechanics, Vol. 55, Part 2, pp.
L 271-287. [ C-M
I
- 7. Kymnininen, O., H. Womisto, O. Hongisto, and T.G. Theofanous,1993, " Heat Flux Dis-tribution From a Volumetrically Heated Pool With High Rayleigh Number," Proceedings of Sixth International Topical Meeting on Nuclear Reactor Thermal Hydraulic Grenoble 1993 I Vol.1, pp. 47-53.
- 8. Mayinger, F., M. Jahn, H. Reineke, and V. Steinbmnner,1976, " Examination of Hermo-I hydraulic Processes and Heat Transfer in a Com Melt," BMFr RS 48/1. Institute fur g Verfanhrenstechnic der T.U., Hanover, Germany. 5
- 9. Min, J.H., and F.A. Kulacki,1978, "An Experimental Study of Thermal Convection with g Volumetric Energy Sources in a Fluid Layer Bounded from Below by a Segment of a W Sphere," Pmsented at the 6th International Heat Transfer Conference, Toronto, Canada.
- 10. Park, H., and V.K. Dhir,1991," Steady State Analysis of External Cooling of a PWR Vessel Lower Head," AIChE Symposium Series, No. 283, Vol. 87, pp.1-12.
- 11. Reineke, H. H.,1979, "Numerische Untersuchung der thermohydraulischen Vorgange und I-des Warmeuberganges in einer Kernschmelze bei kugelsegmentf6rmiger Geometrie und bei g zuflie $cndem Material von oben," BMFT RS 166-79-05, Band II A1. W
- 12. Sonnenkalb, M,1994, " Summary of Previous German Research Activities and Status of GRS Program on In-Vessel Molten Pool Behaviour and Ex-Vessel Coolability," Presented at the OECD Conference on Large Molten Pool Heat Transfer, Grenoble, France.
- 13. Suo-Antilla, F.A. and I. Catton,1976, "An Experimental Study of a Horizontal Layer of I
Fluid with Volumetric Heating and Unequal Surface Temperatures," 10th National Heat g Transfer Conference, St. Louis. E I' I I I I C-26 I
I l I I ! I 1 'g APPENDIX D l j I THE MINI-ACOPO EXPERIMENTS \ I l 1 l I e i I I I I i i I I D-1 8
[ APPENDIX D NATURAL CONVECTION IN HEMISPHERICAL ENCLOSURES AT INTERNAL RAYLEIGH NUMBERS UP TO 7 x 10" ( T.G. Theofanous, C. Liu, J. Scott, D. Williams, and T. Salmassi Center for Risk Studies and Safety University of California, Santa Barbara, CA 93106 D.1. INTRODUCTION This appendix has been prepared under the assumption that it will be mad in ccnjunction with Chapter 5. [Figum 5.1 containing the basic nomenclature is reproduced here as Figure [ D.1 for convenience.) Themin one can find the background on this subject, and the specific motivation for this experimental work. The experiment is called ACOPO (for Axisymmetric p COPO), and mini-ACOPO is a small version of it, built to demonstrate the concept while at L the same time allowing to fill in most of the data needs in a time frame consistent with the overall schedule for completing this report. The ACOPO is a 1/2-scale model of the AP600 L lower head, it is presently under construction, and the data generated from it are expected to be confirmatory of the conclusions reached here. The mini-ACOPO is an 1/8-scale model, and 7 it constitutes the subject of this appendix. Although construction details are diffemnt between the two experiments, the design, operation, and instrumentation are precisely parallel, so the large experiment needs no further discussion here. The capabilities of these two experiments in L relation to other existing experiments can be found in Table 5.1 (Chapter 5). c > mu M s uss ss
- 6. -o-A -
T" T' Tad Tsa *---
^
Tu 9a "A;
- Tb S"P -
M- - L _g a"
% _ %@aEjnsP M p R f
"' ~~
T" '/ -
~ ' '
- q. (0)
[ 648) age e Figure D.1. Schematic of the in-vessel retention phenomenology and basic nomenclature used L to describe it. r D-3 L t
ne basic concept is to sidestep the heating " problem" (discussed in Chapter 5) by not insisting in a true steady-state operation. Rather, the idea is to use detailed data from a transient cooldown, which for a large enough volume should be slow enough to allow the process to pass through a sequence of quasi-steady states that approximate corresponding steady-states with l heating rates equal to the instantaneous cooling rates in the experiment. In other words, we use the heat capacity of the fluid as the " source" of heat that is being extracted at the boundaries. Some additional background on the genesis of the ACOPO concept, and the description of the mini-ACOPO experiment are given in section D.2. He measurements, related instrumen-tation and experimental error a e discussed in Section D.3. An overview of the experimental pmgram is provided in Section D.4. The results are presented and discussed in Section D.5 and the appendix concludes with a summary of the findings in Section D.6. D. 2 THE ACOPO CONCEPT AND THE MINI-ACOPO EXPERIMENT I As clearly illustrated by the interferograms of Jahn (Mayinger, et al.,1975) the key aspects of the natural convection process include:
- 1. Inverted plumes (thermals) descending from the upper boundary, creating a relatively uni-form and turbulent upper pool region,
- 2. A thin / steep boundary layer descending down, and all around, along the curved walls, and
- 3. A stratified lower pool portion, the size and structum of which would seem to be affected by the magnitude of the Ra' number. ,
For the very high Ra' numbers and isothermal pool boundaries of interest here, we expect that the uniform upper region will occupy a significant fraction of the pool volume and that the remaining stratified portion will reach a largely self-similar behavior as found, for example, in g enclosures with buoyant plumes. In the present case the wall-plume will decelerate as it enters a the stratified region not only because of a continuously diminishing body force, but also because of the increasingly more inclined (to the vertical) boundary, and the cylindrical convergence (creating a buildup). The self-similarity is created by the entrainment processes in these wall-plumes, which, therefore, also dominate the global circulation patterns (the turnover)-see Figure D.2. Our conjecture then is that instantaneous heat transfer rates at any of the quasi-steady states traversed during a cooldown transient are adequately close to the steady state, obtainable (in principle) from it if the cooldown was to be interrupted and volumetric heat was supplied to exactly balance these instantaneous losses. He mini-ACOPO has demonstrated that this is g the case, and for the ACOPO with its much larger time constant, this will be even w so. 5 ( Moreover, as we will see below, the ACOPO concept provides the experimental fb to l l D-4
[ address transient effects, especially effects due to adjustment of the internal stratification patterns, [ as well as other complicating aspects (i.e., non-uniform wall temperatures) that add important depth in understanding the behavior in the reactor. b n ~ oOnp h h h h w J w d
- 3
( L " [ Figure D.2. Conceptual model of natural convection processes in a hemispherical enclosure at high Rayleigh numbers. l A schematic of the mini-ACOPO test apparatus is shown in Figure D.3. It has been constructed from 1/4-inch copper tubing coiled, brazed into shape, and filled in on the inside ( crevices with low-melting solder to create smooth internal boundaries of a complete hemisphere L (0.44 m in diameter). The tubing was separated into nine separate circuits, each having its own inlet and outlet. As shown in the detail, the circuits were insulated from each other along all L their interfacing areas. Each wall region corresponding to each circuit can be heated or cooled to any desired temperature by simply connecting the circuit to an appropriate coolant bath (water I is used as the heating / cooling medium). In this way, either isothermal conditions or any desired degree of initial stratification can be created prior to starting a cooldown transient. The enclosure is filled / drained from the bottom, and the expansion volume is provided to accommodate specific volume changes of the fluid in the enclosure during operation.
'Ihe expansion volume provides the means also for ensuring removal of all gas / vapor bubbles after filling the enclosure and prior to commencing an experiment. After filling the enclosure, c hot water is circulated in all the coils until the fluid in the hemisphere is brought slowly to l
within a few degrees of the boiling point, and this is continued for a sufficient time to ensure removal of any gases initially present within by the escaping vapor. The vapors are brought to f a condenser for recovery. Just prior to the experiment the expansion volume is switched to another one that contains L the appropriate quantities and temperature of liquids that will be sucked back into the enclosure during the cooldown test period. This inflow is gradual and of a small quantity, so that its ( effects can be made negligible by choosing for it a temperatdre within the range of the upper r D-5 L
Freon 113 :: Expansion Volume E or Water B
, 9 ,
8 4 2e 7 3cm R - 22 cm
- 4 6 E Freon 113 3cm 3 l 4 or Water ,_ 5
*" 4 ,
i sem
/A sem
- Propoxy-20 j Insulator Cooling #2 Venturi C
Lead Solder - RTD Coolant 2mm L RTD 1/4" Copper Tubing
- Thermocuple Positions Figure D.3. Schematic of the mini-ACOPO experiment including the key construction details and instrumentation.
l pool temperatures during a run. By choosing it to be at a much lower temperatu ; the effect of such drain-flow can be determined. By choosing the fluid to be part water and part freon, a predetermined thickness of water layer can be deposited, very smoothly, on top of the freon pool within the enclosure. These special options have not been exercised in the experimental program reported herein. An actual experimental run commences when, after some settling time, the coolant circuits are switched to take suction from a cold water pool, usually maintained at ~ 0 *C (with ice) E W for runs with an isothermal boundary. Sep- te baths for each cooling unit circuit are used if a non-isothermal boundary is required. The above-described apparatus was designed primarily for use with Freon-113, i.e., max-imum pool temperature of ~ 40' C, and it is called mini-ACOPO A. An essentially duplicate apparatus, the mini-ACOPO B, was built for operation with water at temperatures up to 100* C (or even higher using other fluids) to pursue a special investigation on Prandtl number effects. D-6 I
In this second apparatus, not being interested in local behavior, we simplified the design, and improved the structural stability for the considerably larger temperatures necessary, by employ-ing a shell-within-a-shell concept. The two shells were made of copper such as to fit, one inside the other, with a spacer coil in between, to create the flow channel necessary for cooling to a
; uniform temperature. De top was built from two copper plates built in a similar fashion. The hemisphere was closed with a flanged connection and adequate insulation in between to ensure that the two cooling circuits could operate completely isolated from each other.
After carrying out most runs in mini-ACOPO A, it became apparent that the useful data range could be extended by minimizing the duration of the initial transient by rapidly cooling down the boundary to the desired temperature. This was accomplished by incorporating high flow circuits g to each cooling unit. These are called bypass flows, because they bypass the instrumentation, is as at such high flows the temperature change is insufficient for accurate measurement of the heat transfer rates. We procedure then was to first apply the bypass flow for 1 to 2 minutes, until the boundary structural material could cool to the desired temperature, and switch to the normal cooling circuits, for data acquisition, during the remaining of the transient. All runs with the mini-ACOPO B (B1 to B3) were performed in this fashion. Also, run A16 was performed ~ similarly, and more specifically in this run, having established the accuracy of our measurement systems and observance of the energy balance [between loss infered from pool thermocouples i and energy convected out by the cooling circuits), the high bypass flow was left on for the duration of the run. - D.3. MEASUREMENTS AND INSTRUMENTATION The basic measurements in this experiment are for temperature and flow. Temperatures are measured with K-type thermocouples which, calibrated and operated with a high resolution data acquisition board, are good to within 0.5 *C. This is quite adequate for all pool and wall temperature measurements (see Figure D.3). For the coolant stirams the requirement is ! more stringent because we cannot allow a temperature rise of more than ~1 *C (to maintain an isothermal boundary), while at the same time this rise must be measured accurately enough for the intended energy balance (that gives the local heat flux). Thus we use RTDs which allow an accuracy of 0.01 'C. Similarly, the flows must be measured very accurately. We use venturi j meters and orifices carefully and repeatedly calibrated, such that these measurements are good to within tS%. All data are recorded during a run at 1 Hz and analyzed immediately after. He apparatus and all lines were meticulously insulated and several key tests of accuracy have been and continued to be periodically performed during the experimental program. D-7 5
I : 1 (a) Total Heat Gain from the Environment. With the enclosure empty (filled with air) and isolated from the atmosphere, ice water at 2 'C was circulated through all cooling units at the highest and lowest rates typical during an experiment. We found an average rise of 0.04 *C at the highest rate, and of 0.08 'C at a flow of one-half this value. This translated to a total heat gain, which is only 2 to 3% of the thermal load in the high Rayleigh number range (at the beginning of a run, employing the maximum attainable temperature difference between the pool and the wall). Near the end of a run, the heat fluxes from the pool become low enough for this correction to be significant. In any case, it is accounted for in the data analysis by using the circuit-specific values measured. (b) Circuit-to-Circuit Heat Transfer. Such a heat transfer can affect the local shape of the thermal load, rather than values averaged over the upper and lower boundaries. Tests were carried out in an empty vessel as above, but with a lower grouping of the cooling circuits run about 5 *C lower temperature ths.n the rest of them. By repeating this process with different groupings of the cooling circuits, all interfaces were examined. The heat transfer thus measured could be reduced to a limiting conduction resistance between the circuits that corresponds well with the characteristics of the insulation material (k ~ 1 W/m K) and the thickness (2 mm) used in the construction of the facility. Under a circuit-to-circuit temperature difference of less than 2 C, this mechanism was estimated to cause an error of less than 3% in the measured heat loads, in the local sense. Again, this is negligible, but the correction was used in the data analysis. (c) Total Energy Balance. The data are reduced by a 50-second, sliding time-average during which heat loss from the pool and total heat picked up by the cooling circuits at the boundaries are calculated. Accounting also for the small corrections due to heat transfer from the environment [ item (a) above] and the makeup fluid from the expansion volume, the overall energy balance was found to be satisfied to a remarkable degree (see details in Section D.5). This is consistent with the individual measurement error described above and the interpretation of pool energy in terms of the temperature measurements at nine positions. D.4. EXPERIMENTAL PROGRAM ne experimental program carried out so far is summarized in Table D.1. Each experimental run involves a transient cooldown from some initial state, until the pool-to-wall temperature difference and corresponding heat fluxes are too low for reliable measurements. Using Freon-113, the maximum pool temperature was ~40 *C, and with ice water for cooling, the minimum wall temperature was ~3*C. With this maximum AT, cooldowns of up to 25 minutes could be 8 carried out, to cover a Rayleigh number range of 2 10 to 7 10". He data are recorded at I t D-8 I
E Table D.I. Overview of the Bapal Program in the mini-ACOPO Pacility E A Runs with Preco-113, B Runs with water Run# laitial Wall Purpose ; Pool Temperature Temperature l ('Q (*Q I A2 37 ~3 Test concept and Uniform Uniform instnnnansation A3 37 ~3 Check Reproducibility Uniform Uniform A4 40-19 ~3 Imn= hat, approach to Self-similar Uniform self-aimilar strata 8 cation [~ shape L A5 40-19 ~3 Check reproducibility - Self-similar Uniform l L-. W A7 30-5 ~3 Check data trend in early
- Self-similar Uniform portaon of the transient shape
- A10 40 8 to 3 Check effect of wall Uniform Linear temperature non-uniformity [ A6 40 ~3 Check eNect on flux shape F Uniform Upper boundary L not cooied A16 40 ~3 To extend the Ra' number Uniform Uniform range by mairing use of the earliest portaon of the transient r B1 95 ~26 Check Pr number efects L Uniform Uniform B2 100 ~66 Check Pr number eNects i ( Uniform Uniform l B3 100 ~3 Check Pr number eNects Uniform Uniform E D-9
l l Hz and analyzed using a 50-second-wide sliding time average, at the same rate of I Hz. Thus, ! up to 1500 data points covering the Rayleigh number quoted above am generated fmm each run; ) because of their proximity, the data actually look as continuous lines traversing the Ra' number space. De first two runs (A2 and A3) wem carried out with a unifomi pool initial temperature , and an imposed isothermal boundary. The purpose was to test the experimental concept and I especially the approach to self-similar stratification and the performance of the measumment and data analysis approach. With these established, the next two runs (A4 and A5) were aimed at l further exploring the evolution of stratification by imposing the self-similar stratification pat-tern. at determined in the previous two runs, right from the start. As expected, no significant changes in the pool stratification shape during the run wem observed. These mns established that g 1 the pool suffers no major internal adjustments during the cooldown, such that the quasi-static 5 ! approximation is valid throughout the cooldown transient, to a high degme of accuracy. The fifth run (A7) was carried out with a lower pool initial temperature, such that the initial I Rayleigh number was only 2 1014. De purpose was to check the behavior in the initial period of the transient by direct comparison to all four previous runs in which this Rayleigh number was reached after ~5 minutes. l he next two runs (A10 and A6) were oriented to non-isothermal boundary effects. Specifi-cally, run A6 was carried out without top cooling and an isothermal, cooled lower boundary; and run A10, with an imposed linearly increasing wall temperature.' These runs introduced imporwit insights about the heat flux distribution. He final run with mini-ACOPO A was A16, and it was carried out with the bypass flow l explained in the previous section. It allowed the collection of data for Ra' numbers up to I
~ 7 10 14.
l Finally three runs (B1, B2, and B3) were carried out in mini-ACOPO B with water as the working fluid to explore separate Prandtl number effects. With initial water temperatures at
~100 *C and cooling circuits operated to maintain wall temperatures at 3,26, or 66 *C, these ;
28 experiments could cover the ranges 2.5 < Pr < 11.0 and 1012 < Ra ' < 3 10 . ; 1 l D.5. EXPERIMENTAL RESULTS AND DISCUSSION l ne key point about the validity of the experimental concept is the establishment of a self- l similar stratification pattern in the pooi 'aring the cooldown. This was demonstrated by defining D-10 i l l
i a local dimensionless temperature
~'
(D.1) O = Tmax - Ts where Ts is the " bulk" (volume-averaged) pool tempenture, and plotting it against vertical position in the pool. The thermocouples in Figure D.3 show that lateral temperature gradients in the pool are always negligible ((less than 5% of the overall AT, oT = Tmu - Tg)), so the bulk temperature could be quite accurately estimated by volume averaging the temperatures from the central thermocouple tree, each corresponding to the corresponding horizontal slice of the hemisphere. [ Data in the first 3-4 minutes are not shown in these figures, as this time was required to eliminate the effects of the initial transient, as described in the next two paragraphs.] The results from run A2, and from all A runs (with isothermal boundaries) put together, are shown in Figmes D.4 and D.5 respectively. The choice of the ordinate is such that it reflects the , volume of fluid associated with each portion of the pool stratification pattern. From these figmes we see that only the very bottom (less than 10%) of the pool volume undergoes any significant change or departure from self-similarity during an experimental run. These figures also show that about one-half (the upper) of the pool volume is essentially at a uniform temperature (Tmax), , and that a well-defined, self-similar temperature gradient exists in the intermediate 10% to 50% of the pool volume. It is clear that the large, uniform temperature layer on top is reflective of the agitation created due to the strong cooling on the top boundary (and the associated descending plumes). l The other key point, as in any experiment, is the accuracy of the experimental measurements I and data reduction techniques. Aside from the individual instrument accuracy, and quantification of corrections due to non-perfect insulation effects, as discussed in Section D.3, an overall energy balance provides an important means for verification. This was affected by comparing the energy loss from computing the energy change in the pool (as deduced from thermocouple measurements), to the energy loss obtained by summing up the measured energy losses at the 4 I pool boundaries (to the nine cooling circuits). Because of the importance of this verification measure, the results from all runs are shown in Figures D.6(a) through D.6(j). In all but the 4 last three of these figures, the times at which some flow rate was changed in any of the cooling circuits is also marked - such changes were necessary to make during the course of a run, in order to maintain the measurement accuracy as the heat fluxes continually decrease as a result of the pool cooling down. We can see that, not unexpectedly, such changes cause short-duration, and marked departures from the energy balance, while for all the rest of the time the balance is observed to be within 10% (much less most of the time). The data during these short time periods of departure have been discarded from further use.
- g In the same light, the first 3-4 minutes in each run were discarded. It is interesting to note
!E that within the same time frame the internal stratification pattern stabilized to the self-similar long D-11 I
- ~. . - _
I 2 ,,,, , , , , , , , , , , , , , , , ,
~
l
; i .
0 - o _ u o i l - E H
. g 5^
s
.o -
I - E
-2 g g 4
- _g + 5 min 8fo 3
3 X o 6 7 min min o > 7 min
-42 3$,,,! , , , , I , , , , I , , , , I , , , ,
- 0.0 O.2 0.4 0.6 0.8 1.0 2 V,/V Figure D.4. Dimensionless pool stratification pattern obtained in run A2. Vg/V is the fractional pool volume below the pool elevation in question.
I 2 , ,,,,;,,,,i,,,,;,,,,,,,,, _
... o ..
l - U - T o - i g - . # I -2 l - l l l L ,8 o, , ,! , , , , i , , , , I , , , , I , , , , i _4
-0.0 0.2 0.4 0.6 0.8 1.0 Vi /V Figure D.5. Dimensionless pool stratification data from all runs with isothennal pool boundaries (A2, A3, A4, A5, and A7). Vg/V is the fractional pool volume below the pool elevation in question.
D-12 l-I
lI I 1 _ 1A - - 1.2 - I\ i cy - . N 1.0 - g c"r : . U 08 -
+ - - un. m .o no.
I 4 0.6 - -
. . . . l . . . . l . .-
-o 10 20 Time (min)
Figure D.6(a). The energy balance obtained in run A2. In this and all subsequent D.6 figures, "unstabilized flow" means a period of initial adjustments in cooling unit flow rates, as well
- as a transient associated with the thermal inertia masses associated with the cooling circuits j themselves.
f l ; .. 1.4 - _~ i _ 1.2 - cr - N 1.0 fn -
~
\ ,,
0.6 -- +- un. m .o now _ Flow Flow now Decr.e.e in Ice [ 0.0 - cw en.ne.o en.n,.o som T.a,.rnur. _ , i l _ l ( o y t .
. . . . . . . . l ,.
-0 10 20 Time (min)
Figure D.6(b). The energy balance obtained in run A3. D-13
l 1.4 - 1.2 - N 1.0 - en - a - . - e Tumed - 0.8 - ca
% Unstatszed Flow Flow Decreened 0.6 -
- , , , I ", , , , l , .
-0 10 20 Time (min)
Figure D.6(c). The energy balance obtained in run A4. I 1.4 - 1.2 - a -
)w 1.0 -
W _~ 00 _ ~ un. waxed rw -
,. ~
Decrossed Decrossed
}
0.6 -
,, e -
t g g g g .
-0 10 20 Time (min)
Figure D.6(d). The energy balance obtained in run AS. I I D-14
l l l i g. ; . 1.4 - - 1.2 -- --
~
3 [ N 1.0 - e. m - . cv . f . l . 08 . un.mw rw k
- urw :
. Ch8V J Many riow .
change. 0.6 - _ l -0
,_. 2 . . . "l 10 20 l . .
Time (min) I Figure D.6(e). The energy balance obtained in run A7. I
. J. l 1.4 -
nro .' I 1.2 I
-* - Turnw
~
}
~ ...k .. :
Of - N 1.0 - g,g
- .--- un.mw rw r w sersects incr.a d .
~ riow for S.ct : Ice Add.d .
0.6 U" It
~
- . F. . l . . l
-0 10 20 30 40 Time (min)
Figure D.6(f). The energy balance obtained in run A6. I D-15 l j
I I 1.4 - 1.2 - -
~
_- . . . ) . cy - - N 1.0 - M - U - h . 9 . e-- Unstaber.d now . 0.8 - _
~
FM rion o.a o o,,,,,,, ns . o.6 -
, q,
-0 5
l . . . . l 10 15 l . , . . 20 l Time (min) . Figure D.6(g). The energy balance obtained in run A10. J 1.4 - _ 1 1.2 - _ N 1.0 - _ m cr _ : 0.0 - _ 0.6 - _
. . . . l . . . . I , ,
-0 10 20 Time (min)
Figure D.6(h). The energy balance obtained in run Bl. D-16 I'
I t I 1
; ; l
~
1.4 -
~
1.2 - 1.0 0.8 - f l 0.6 -
- , . . . l . . . . l . . . . I
-0 5 10 15 Time (min)
Figure D.6(i). The energy balance obtained in run B2. I !I 1.4 -- j 1.2 -- I u se.g u . . e g m.e e N 1.0 - 0.0 - l 0.6 - _ I :
. . . . l . . . . I . .
-0 10 20 Time (min)
Figure D.60). The energy balance obtained in run B3. D-17 I
term behavior. While these more esoteric aspects may be of some interest in verification studies of detailed numerical simulations (such as those mentioned in Chapter 5), they are peripheral to our present purposes and will not be discussed here any further Rather, we focus on the average heat transfer results and the flux distribution on the curved boundary, only during the quasi-steady portion of the transients. 'Ihe Steinberner and Reineke (1978) and the Mayinger et al. (1975) correlations discussed in Chapter 5 were found to be in good agreement with these data [for upward and downward heat transfer, respectively] so they are included in the figures g that present them. Also shown on these figures are the 15% intervals around these correlations. 5 The results of the series B runs, addressing Prandtl number effects, are given directly in Chapter
- 5. So, without further reference, in the following we will be discussing the A series of runs only.
The results for upward heat transfer are shown in Figures D.7, D.8 and D.9. Figure D.7 contains the data from all isothermal boundary runs, except run A16, which is given separately in Figure D.8. This special status is assigned to this run because it represents the culmination of perfecting the experimental techniques, including the bypass flow and hence the largest coverage in the Ra' number. In Figure D.9 we can see that the flux distribution in the upper boundary g (the central portion occupies ~50% of the area) is very nearly uniform, and this is typical of all E runs. The results for downward heat transfer are shown in Figures D.10, D.11 and D.12. Figure D.10 contains the data from all the runs except run A16, which is shown in Figure D.11. In Figure D.12 we have collected the local fluxem normalized to the average flux, from all the mini-ACOPO experiments. On the same hgure we show the line that represents the experimental trends (Eqs. D.2 and D.3 shown below), and also the UCLA correlation from Appendix C. A generally , good agreement is seen, except for the higher peaking exhibited by the UCLA correlation for 6 > 80*. This, however, must be tempered by recognizing that our values are averaged over the width of the cooling units-the values shown at ~84* really correspond to an average over 78' < 6 < 90'. On the other hand, it is also interesting to note that the UCLA experiment cxhibits a somewhat broader stratification pattern, i.e., almost absence of an upper well-mixed portion (see Figme D.13 in comparison to Figure D.4). Runs A10 and A6 were carried out for exploring further these aspects. In run A10 we imposed a non-uniform wall temperature, as illustrated in Figure D.14. It did not appear to make any significant difference on the stratification pattern, the downward heat flux, or even the heat flux distribution, as illustrated in Figures D.15, D.16 and D.17, although it should be noted that the degree of imposed nca-uniformity was small in comparison to the bulk-to-wall E temperature difference-this is especially so because as shown by all previous experiments the 3 upper portion of the pool is dominated by the strong cooling from the upper boundary. D-18 I
E In run A6 we kept the upper boundary adiabatic, and this did have a pmfound effect. First, in Figum D.18 we see a totally different stratification pattern. As expected, we find an absence of a well-mixed upper pool portion, and an essentially linear variation over the whole depth of p the pool (in the Vg/V coordinates). In Figure D.19 we see that the effect of this pattern is to produce an excessively strong peaking, with values reaching up to 4. Finally, in Figure D.20 we see that the downwani heat transfer is perceptibly lower than that found in the uniform. wall l temperature runs, but interestingly enough, the sensitivity is not as great as perhaps might be I expected. The remarkable features of Figure D.12 are that the peak-to average heat flux is below 2 and that the data depict two distinct regions (or trends) connected with an inflection (or transition)
- Irgion. With reference to Figure D.4, it can be seen that these regions correspond exactly to the two regions of the stratification pattern. That is, an upper region, 65 < 6 < 90', which
[ corresponds to 0.40 < Vg/V < 1.0 and the lower remaining volume. De flux shape is rather curved over the lower region, but is proceeds with an abrupt reduction in slope and in essentially E a linear fashion (on the average) into the upper region. It is remarkable that such a two-region trend can.be discerned at the lower Rayleigh number data of Jahn (Mayinger et al.,1975) obtained at Ra' = 1.2 1010 in a semicircular (slice) geometry (see Figure 5.8 in Chapter 5). 7 In this case, the peak-to-average flux ratio was ~1.6. With the help of these considerations we arrive at a proposed correlation for the flux shape given by Nus (6) /6S 63 2 g a g
= 0.1 + 1.08 I l - 4.5 1 + 8.6 for
- Nugo (90'j 90'j 90' 0 < 90* - 0.6 (D.2) and Nua"(6) #T 6 8 y, ,
= 0.41 + 0.35 gg,j + gg, for 0.6 < gg, s im M y his correlation is normalized to unity and is shown in relation to the data in Figure D.12. In applications where local peaking is of inte. rest, we recommend that a reasonable upper bound can be obtained from 1
= 2.0 (D.4) r As a final point we would like to observe that the heat fluxes found at the outer portion of the horizontal boundary and the upper edge of the curved boundary are close to each other.
J This can be seen quite readily by applying the peaking factors from Figure D.12 (1.5 to ~2.0) L to the results in Figure D.11, and compare with Figure D.8. For example, at Ra' = 3 10", fmm Figure D.11 we read Nug. ~ 420; applying the peaking factors we get 630 to 840, and
~
L fmm Figure D.8 we read Nu'y ~ 750. - D-19
I D.6. CONCLUSIONS A new experimental approach to the problem of heat transfer from volumetrically heated enclosures has been proposed and verified. The approach is especially important in making 18 feasible experimentation at the very high Rayleigh number range (10 to 10") that is found in g, practical applications of severe accident management in certain nuclear power reactors (in-vessel 5 < retention). While a 1/2-scale experiment (the ACOPO) is in preparation, results obtained fmm a proof-of-concept,1/8-scale experiment (the mini ACOPO), verify and extend the Steinberner- , Reineke (1978) and Mayinger et al., (1975) correlations for upward and downward heat transfer respectively, to the already relevant Rayleigh numbers of up to 7 10". This is complimentary to the UCLA work (Appendix C) that already reached these conclusions for Ra' numbers up to 910 .13In addition, these data demonstrate that the pool is characterized by a stable (self-similar) stratification pattern, in which the upper half of the pool volume is at a uniform temperature, and that the heat flux distribution along the lower boundary can be expressed by Eqs. (D.2) and , (D.3). To bound the heat flux peaking at the upper edge of the curved boundary a value of 2 is recommended. This is somewhat lower than the 2.4 value found in the UCLA-experiments, and it may be worthy of further clarification. Finally, in the Series B runs covering the range 2.5 < Pr < 11.0, no independent Prandtl number effects were found (see Chapter 5). D.7. REFERENCES
- 1. Mayinger, F., M. Jahn, H. Reineke, and U. Steinberner (1975) " Examination of Thermo-hydraulic Processes and Heat Transfer in a CoreM. elt," Final Report BMFT RS 48/1.
Technical University, Hannover, W. Germany. As reviewed by F.A. Kulacki, Ohio State University, for the US NRC, march 31,1976. l
- 2. Steinberner, U. and H.-H. Reineke (1978)" Turbulent buoyancy convection heat tansfer with internal heat sources," Proc. Sixth International Heat Transfer Conf., Toronto, Canada, Aug l
1978. I E D-20 I
1000 , , , , , ,, , , ,, ,
- ./. - ,,,.
[ - g
,s*',',- .
/ ,.., _ ,. ,- .. .
, ,. ~ j. / .
a y' ...' . . y ' , ,- 1
,x .
**,r /,..
500 -
/,**.,',/
,./',,..*,.
,./, Steinberner-Reineke, Eq.(5.12)
, , , , . ...l , , , ,,,,,
88 10 ** 10 " 10 r Ra' L r Figure D.7. The upwani heat transfer obtained from all mini-ACOPO runs with isothermal L boundary, except run A16. i r ! [ , , , , , 1000 - /~ 1 r Steinberner-Reineke, Eq.(6.12) l L l F - l L. t ! o - - Z l 500 - t .
+1 II I
[ , I+llii+11II,+1 1I I j 88 88 IC 10" 10 ) l Ra' { Figure D.8. The upwant heat transfer obtained in mini-ACOPO run A16. The lines and plus [ signs at the bottom show incrementally 1 minute intervals during the cooling transient. D-21 [, H. __---.-__.___--_-__-__-______.-___-_____._--__-__-_____a
I I 1000 ' ' - - - - , , , , , , , E
~
Steinberner-Reineke, Eq.(5.12) - M
~ l g .. ^
, ; .5 .
g
~
p/ . a f..
- r. . .
- 2. f. ' ' ,,X '
500 .
~
,t./ ?
Outer Center
- - i . . . .I , , , , , ,,,
10 " 10 4 10 Ra' Figure D.9. The heat flux distribution in the upper boundary for run A3. The outer ring represents 50% of the area. 1000 ' ' . , , , , ,,, I
'l Mayinger, Eq.(5.22) l E
Soo . . .
's..
,g
) !
200 - . I 100
' > - - i ...I , , , , , ,,,
10 " 10 14 10 l W Ra' i Figure D.10. The downward heat transfer obtained from all mini-ACOPO runs with isothermal boundary, except run A16. D-22 I
~ -----
T l { 1000 , , , , , , , , , , , , , , [ . [ Mayinger, Eq.(5.22) _ 500 . 4
.,a ..
200 . f 100 ' ' ' ' 'l ' ' > > . 10'8 l 10
- 10
[ Ra' Figure D.11. The downward heat transfer obtained in mini-ACOPO run A16. y , , l g
/
o Mini-ACOPO Data / _ 2 ~ Mini-ACOPO Fit / UCLA, / -
. /
/
4 _
- / /
/ .
s4 # ' i _ '.., [ y y
-0 - - - - I . . . . I , , , , I , ,,,I , ,
-0 20 40 60 80 Angle (degrees) r
[ Figure D.12. The heat flux distribution over the lower boundary obtained in all mini-ACOPO runs with an isothermal boundary. Also included are the UCLA correlation (Appendix C), and a line through the mini-ACOPO data (Eqs. D.2 and D.3). The points are placed at the center of the arc covered by the respective cooling circuits. D-23 [
I I - 2 , . . . . . . . , , , . . . .
~
.. a .. -
O - O m a y 0 - O _
=
- o .
E o y _ -
)a - -
O 9 ' l -2 - - b o l
-o l
. . . . l l . . . . l . . , , I , , , ,
_4 . , . .
- 0.0 0.2 0.4 0.6 0.8 1.0 Vi /V Figure D.13. The stratification pattern in the UCL run at Ra' = 9 1013 ,
1
' ' ' ' ' > > i , . . . , , , , , ,
l l l o l
, 10 -
U o _ O . v o 8 _ l f& g
~
o - a 6 -
$ . o -
to - k 3 _ g _ l
- . . . l . . . . I l j
-0 , . . . , , , , l , ,
-0 20 40 60 60 l Angle (degrees)
Figure D.14. 'Ihe temperatum distribution imposed on the curved boundary of run A10. l l D-24 i lil l
2 . , , [ : 9 b y0 - - E l - kO -
" 8
-2
[ 4
~
b ~$ -
- O P, , ,l , ,,,l l l , , , , l
_4 , , , , , , , ,
- 0.0 0.2 0.4 0.6 0.8 1.0 Vi /V Figure D.15. He dimensionless pool stratification pattern obtained in run A10.
b 1000 , , , , , , , , ,,,
,,,I , ,
Mayinger, Eq.(5.22) - r' 500 -
~
... g 200 -
100 ' ' ' ' ' I * - - - > ,ii 84 10'8 10 30 16 Ra' Figure D.16. De downward heat transfer obtained in mini-ACOPO run A10. { D-25
I I I s i i r a u I I I I s r s s s , q Mini-ACOP0 Fit - 2 - l, a o
~ ~
Q O Z . O , N o S v
. 0 .
4 1 p Z _ _ o
. . . . l . . . . l . . . . I . . . . I
_o . . 40
-0 20 60 80
- Angle (degrees) i Figure D.17. The heat flux distribution found in run A10.
I 2 , . . . . . . . , . . . , , , , , , , , g g
.-O"-
o l - E y0 - g l _ o - E e l l g 6 B g" a 6 a o o - j [o a - 1
. . . . l I l
_4 . . . . . . . . . . . . l . . , ,
-0.0 0.2 0.4 0.6 0.8 1.0 Vi /V Figure D.18. The dimensionless pool stratification pattern obtained in run A6.
I D-26 II l
l . ( 4 , , , , , , . . , , , . , , , , .
$~
~
8 - . 3 - g-I e : E 8 - N O - g 2 - o-o -
]c ; -
Z
~ -
1 - 8 _o . ,0. . l
.!..l , . . . I , , , , i . .
-0 20 40 60 80 Angle (degrees)
Figure D.19. The heat flux distribution found in run A6. l 1000 , , , , , , , , , , , , , ,,, f - [ Mayinger, Eq.(5.22) - 500 -
* ~
q . Z -
/ \
200 - a { yen - 100 '
' - - - .l . . . . . . , .
58 10 10 ' 8 10'5 Ra' Figure D.20. The downward heat transfer obtained in mini-ACOPO run A6. D-27
I (( ADDENDUM TO APPENDIX D)) The purpose of this addendum is to present more detail on the development, with time, of the pool stratification pattern, and heat flux distributions, in mini-ACOPO. As explained already, mini-ACOPO A16 was run such as to minimize the duration of the initial transient; thus it also provides the best information on the development of the pool stratification pattern. This development is shown in Figure D.21, and indicates much more rapid approach (within 1 or 2 minutes) to the self-similar shape, than the other runs (see, for example, Figure D.4). This time is consistent also with that mquired for a few resident times of the fluid descending within the thermal boundary layers over the curved surface (path length ~40 cm, velocity ~1 cm/s, adjusted from the values measured by Steinberner and Reineke,1978, for turbulent boundary layers at somewhat lower Ra' numbers). The measund evolution of heat flux shapes with time, for runs A3, A4, A5, A7, A10, and A6 are shown in Figures D.22 through D.27 respectively. We note that with only the exception of the data in position 40 at late times (15 to 19 minutes) in run A4, shapes am consistently regular and evolve gradually, and to a small degree, flattening out somewhat, especially near the very end of the cooldown (this repmsents the low end of the Ra' numbers covered-see for example Figure D.8). It is noted again that the run with the adiabatic upper boundary (A6) is interesting for understanding certain aspects, as discussed already, but it is not relevant to the g reactor situation of interest here. E 2 , , , , , , , , , , , , , , , , , , ,
- I i
; I H 0 -
o _
+ ~
s 5
^
n s . I -2 :-- I ._ t' [ i + 1 min
. x 2 min t
h o 3 min - 58 0 4 min j8 4 o > 4 min 3 I _4 . . . , . . . , I , , , . I , , , , I , , , ,
- 0.0 0.2 0.4 0.6 0.0 1.0 Vi /V Figure D.21. Evolution of pool stratification patterns with time for run A16.
D-28 I
i 20 i I I I 6 min
~.. ~ ~- 8 min
.- ..-~. 7 min 1.5 -
- 8 min fC=
9 min -- 3 mm. z - N !
,, 1.0 -
4 /
; A 06 - <#
/ _
\
l 5',*,,
,,guua"p5
- 1 I f I 0.0
-0 20 40 60 80 Angle (degrees) ,
2.0 ; ; ; ; 10 min
...._ . - I 1 min
. _ . - - . la min (f4c-1.6 -
13 m6n
, 14 min ~,r#' <
is ,. q !, s . kg t .0 - l. i 4 .,/ o F* p*',a ; O5 - s><" -
' ! ! I
-0.0
-0 20 40 60 80
) r Angle (degrees) L ~ i i i i IS min 16 min
. . . . . , 17 mln "'-
15 - 18 min j - 19 min ./
.;Y$ "
x e q l .0 -
,1 , ' ,,A.< _
w a
*s'.
4 l, s - 0.6 -
.js' %~f _
I I I l
-00 ' >
-0 20 40 60 80
. Angle (degrees)
Figure D.22. Evolution of heat flux shapes with time for run A3. D-29
80 I 1 l l 5 min 6 min
.. -. 7 min v 1.5 -
a min sr#p.n-9 min /*'r 4 E y
% /..
g t .0 - g/ - o J[' = O.5 - 9h' ~
,g,,g .a" I I I I
- 0.0
-0 20 40 60 80 Angle (degrees) 20 I I i 1
10 min **u. s i il min '
--- 12 min .
13 min 1.5
</<<* *
.- . . . 14 min I -
x 1.0 - 3 + Z f O5 - y - 2 f..
"* I
/' :, , ,; , _
-0.0
-0 20 40 60 80
! Angle (degrees) 1 I i 20 l l l l 15 min ..-- l 16 min *' k l .5 -
!sN f -
g
, -- 19 min [
, E
- z
- N e 1.0 - - o . Z 05 - -
! g
-0.0 I b I I l
i -0 20 40 80 80 g Angle (degrees) Figure D.23. Evolution of heat flux shapes with time for run A4. , D-30 I
L l l l l 3 min
~
-4 min
.. ...._..- 6 mi n #'
j .5 - + 8 min
*----- 7 min r$,/.'.; .9 7
h s? s:tdW*f N g w 1.0 -
.g,,
4 '
'$ _ ./
O.5 - sh 6W($;fb'5 ,
~
I I I I
- 0.0 I
-0 20 40 Angle (degrees) 60 80 i
8 I i i i 8 min 9 min ['...-
+ + + - +
10 min l .$ - . I1 min
, 12 min /s l i u z N
g 1.0 - - F = l -- u 4 0.6 -
/p
~
.. J I I I I !
- 0.0
-0 20 40 60 80 Angle (degrees) i l
1
- i i i i
!3 min 1;;;;
14 min p
- IS min 43g 1.5 -
16 min -
.. .....- 17 min s
R ,/.~~1 q l .0 - P 4 s z O5 -
/
u
.?.% s-
_ n_ n
. -r fiY' l l 1
-0 20 40 60 - 80 Angle (degrees)
Figum D.24. Evolution of heat flux shapes with time for run AS. b D -
1 I 0 ; 3 min 4 min
- - 6 min .<5' l .5 -
6 natn
, 7 min gilgp * *' d n rt'571p; z . N , . 1.0 - -
t ./ o Z ..a.,f. . G O.s - , -
! w
,,c::2 =a' 4
I I I I
; - 0.0
-0 20 40 60 80 Angle (degrees) 3 1
20 g g [ ; J 6 min
, 9 min * .,, ,,,
a . . - . . . - . 10 min 1.5 - 11 min I 12 min #.. ' " ~ ' - i 4 ,
- ... s,,
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/
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. 0.6 -
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-0 20 40 60 00
- Angle (degrees) l l
I 20 , , , ; I l 13 min 14 min ., _,,,,,,,, - , 16 min ' l .5 - -- 17 mm - E
- t' t
n . Z / i . N / g 1.0 -
,/ -
- ",n .,
! c ' Z 05 -
.p***.e*,,* -
1
! ' 1,, i i 1
- 0.0 g -0 20 40 60 80 i Angle (degrees) i Figure D.25. Evolution of heat flux shapes with time for run A7.
i 1 D-32 I 1 l I I
r i V L < L E B l l 2.0 I { ' a min
*! mtn ,.
-- a min -"'
9 min
/'*? [
1.5 -
, 10 min l
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t .9;Y, ..f o l E ,;.f' O5 -
-' y'#~ -
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-00 l i I I
-0 20 40 60 80 Angle (degrees) a 20 r I I I l l
t I mtn . N: 1.5 t! $n '/ 14 min _ l 4 L_, :J Z ,< s E 1.0 - I i a 4
)
2 05 -
,/
"/
- 0.0 l I I l
-0 20 40 60 80 e
Angle (degrees) { Figure D.26. Evolution of heat flux shapes with time for run A10. 4 D-33 { I
t I r l l , I i i I 6 min i - 6 min
- - - - 7 min f a min /-
9 min /% s g 2 -
,e j.:
'- 1 4
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-0
-0 20 40 60 80 j Angle (degrees) 3 l l l l .
10 min
/
/ ;-
1I min /f
. . . . - . I2 min /c 13 min .
2 -
,a t m
l Z .I N S e , m
- r.
v,, - 1 o - 6,
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-0 " ^ .... a*5f ; ,
-0 20 40 60 80 Angle (degrees)
I I I I 3 _ 15 min j,' _ 16 min -
- -- 17 min 18 min ,
, --- - --- 19 min /
i z 2 - E I z 1 -
,/, -
p' s
, m.
._7r - ; ,
-0 20 40 60 80 W Angle (degrees)
Figure D.27. Evolution of heat flux shapes with time for run A6. D-34
[ [ [ [ APPENDIX E THE ULPU EXPERIMENTS { This appendix consists of four pans, as follows: E.1, Critical Heat Flux Through Curved, Downward Facing, Thick Walls L Nuclear Engineering and Design 151, 247-258, 1994 [ and E.2. The Coolability Limits of a Lower Reactor Pressure Vessel Head [ To appear in proceedings, NURETH-7 Saratoga Springs, New York, September 10-15,1995 I - and ((E.3. Critical Heat Flux Sensitivity to Flux Shapes and)) [ Recirculation Flow Rates e and L ((E.4. ULPU Configuration III Results)) [ [ [ [ E-1
t OVERVIEW The purpose of this appendix is to present the experimental data obtained in the ULPU-2000 facility. His facility is a large-scale upgrade of the original ULPU, built to investigate
. critical heat flux on extended vertical, thick walls under flow conditions relevant to the Loviisa "in-vessel retention" accident management scheme. The present ULPU-2000 facility is oriented to the curved portion of a hemispherical lower head, as in the AP600 design. The basic concept in this design is to use power shaping to effect an essentially full-scale simulation of critical heat flux (under the appropriate flow condition) in a 2-D slice; that is, a full-length quarter-circle geometry. The full elevation of the flow path, and flow phenomena in the annular space between the cavity wall and the reactor pressure vessel (the " riser"), are also simulated (in a 1-D approximation). The facility is capable of fluxes up to 2000 kW/m 2, easy recovery from film boiling without damaging the heater (that is, experiments can be run back-to-back within
. only a few minutes), and it allows easy visualization of the flow regimes on the heater surface and in the riser.
Experiments reported here cover two facility configurations. Configuration I is focused on the lower-most portion of the lower head, -30' < 6 < 30', in a conservative representation of the coolant condition - saturated pool boiling. Configuration II is oriented to full simulation; that is, including natural convection flow and local subcooling (due to the gravity head), and the full heater arc, 0* < 6 < 90'. While Configuration II involves an "open" access to the lower head, there are provision also for future Configuration III testing, intended to simulate any reactor specific vessel insulation or other reactor-specific geometric features. This appendix, then, consists of two parts, corresponding to the two configurations just mentioned. The details of the experimental concept, the power shaping principle, the facility description, and the measurement techniques can be found in the early portion of the first part (E.1). The main conclusions can be summarized as follows: With the completion of the Configuration II experiments reported here, we have established a firm estimate for the coolability limits of the lower head of a reactor vessel submerged in water and heated internally. The scale of the experiment, and the power shaping principle, ensure that these data, and resulting correlation, are directly applicable to the reactor. The correlation reveals a two-region behavior, q,,(6) = 500 + 13.3 6 kW/m 2 for 6 < 15' (E.1) ger(6) = 540 + 10.7 6 kW/m 2 for 15* < 6 < 00* (E.2) which has been related to the different flow regimes observed in the two-phase boundary layer in the respective regions The data can be equally well fit by a single equation ger(6) = 490 + 30.2 6 - 8.88 10-262+ 1.35 10-8 86 - 6.65 10-~564 kW/d (E.3) E-3 4
l l t l which has been used in Chapter 3 of the report. Application of these generic results to reactor situations should consider specific aspects of the geometry and surface conditions as follows: l (a) Geometry. As a modifier to the Configuration II geometry, this refers to the presence of insulation, the natural circulation flow path (especially water inflow toward the lower head surface, and any restrictions to the venting of vapor), and the presence of any obstacles within the two-phase boundary layer (either mounted on the vessel as, for example, for loose part monitoring purposes, or extemally imposed by something else coming to rest against the lower head during an accident). Any significant deviations from the Configuration II examined should be tested prior to using the present results. However, the Configuration I results qer = 300 kW/m 2 for 6<5 (E.4) ger = 310 + 12.6 6 kW/m 2 for 5* < 6 < 30* (E.5) provide another perspective, possibly useful if one was interested in a minimum bound realized under saturated pool boiling. (b) Surface Conditions. The AP600 lower head la made of carbon steel, and the external surface is machined (to 250 rms), primed, and pairted over after installation. According to the paint supplier, this coating is unstable in boiling water and would be expected to flake off soon in such an environment, exposing the as-machined metal surface. From a g point of view of water wettability, we expect this surface to behave as the fully-aged copper 3 surface tested so far in ULPU-2000. However, a prototypic piece of steel is now ready to be installed in ULPU, and we expect to fully illucidate this point within the first quarter of 1995. ' ((This appendix also contains two addenda prepared simultaneously and as a part of the responses to the first round of the reviewers' comments. The first addendum is Appendix E.3. l It covers the results of an extended experimental matrix in Configuration II with flux shapes that include those found in the sensitivity / parametric studies as well as variations thereof, and arbitrary variations of recirculation flow rates, obtained by throttling the inlet, to 50% of the normal (~130 gpm) flow rate, and to full stagnation. The results indicate that Eq. (E.3) is a robust conservative estimate appropriate for the evaluations performed in this report. The second addendum is Appendix E.4. It covers Configuration III experiments, built in accordance with the thermal insulation design just completed by Westinghouse (see Appendix K). In addition, this set of experiments included the effect of a prototypic heating surface, i.e., reactor vessel g grade steel with and without the normally employed paint. The results once more demonstrate E the roubustness of Eq. (E.3) and its applicability for our purposes.)) E-4
4 APPENDIX E.1 CRITICAL HEAT FLUX THROUGH CURVED, DOWNWARD FACING, THICK WALLS Nuclear Engineering and Design 151, 247-258, 1994. o ( I s. E.1-1
F L APPENDIX E.1 e L CRITICAL HEAT FLUX THROUGH CURVED, DOWNWARD FACING, THICK WALLS T.G. Theofanous*, Sanna Syri" and Tony Salmassi* Olli KymElEinen" and Harri Tuornisto" L
- Center for Risk Studies and Safety Department of Chemical and Nuclear Engineering University of California, Santa Barbara
[ Santa Barbara, CA 93106, USA "IVO International Ltd. 01019 IVO, Finland m ABSTRACT I Experimental data are presented that provide a lower envelope on the critical heat flux distribution e t over the external surface of a hemisphere submerged in water. The experiment was designed and run so as to provide an essentially full-scale simulation of a reactor pressure vessel lower g head. Thus the data, and the correlation derived from them, can be applied directly, and they I are supportive of the important severe accident management idea of retaining the core debris in the reactor vessel by external flooding ("in-vessel melt retention"). E.1 INTRODUCTION ~ u The purpose of this paper is to make available the first experimental data directly relevant to establishing the coolability limits (critical heat flux) of reactor-scale hemispheres submerged ( in water and heated intemally. The situation arises in the management of severe accidents, and a relatively recent idea that the relocation of molten corium could be arrested at the lower head [ of a reactor pressure vessel by external flooding, as illustrated in Figure E.1 (Theofanous et al., 1994). For this idea to work, it is necessary that the thermal load created by natural convection F of the heat-generating pool on the inside be below what could cause a boiling crisis (BC) on the outside. In relation to previous work on critical heat flux (CHF), the present situation involves two unique and important aspects. One is that the vapor generated by boiling remains confined by r gravity within a two-phase boundary layer all along the heating surface. Flow velocities and L phase distribution within this boundary layer depend very much on the local surface orientation to the gravity vector, and on the cumulative quantities of steam generated in all upstream positions. b The other unique aspect is that the heating surface, typically up to 15 cm thick, has a very E.1-3 .
1 I I l lh - l hC o*h I ' - _ Steel b: \ k . La er
& - M7w-_Mfg _"""'M _ ~
?,
% mMv .
l
- g. 7 .= Corium C
~
Se (0)
- # Pool g q,(0) g Figure E.1. Schematic of the in-vessel retention phenomenology and basic nomenclature used to describe it.
large thermal inertia. It is clear that both the hydrodynamic (" repulsive") mechanisms and i the surface-thermal contributions to it (capillary wetting effects, susceptibility to temporary / local dryouts) (Bui and Dhir,1985) can in the present situation be significantly different from anything g i examined in the past-however, the initial efforts by Henry and Fauske (1993) and Chu et al. E l (1994) are noted. Accortlingly, we have adopted an experimental approach that is to evolve gradually from overall parametric studies and simulations (of the reactor conditions of interest), to detailed investigation of local phenomena, and thus eventually to identification of the crisis mechanism and, hopefully, to an analytical model. The emphasis on simulations in the early part of this l program derives from two reasons. One is to afford an early identification and focus on the particular flow and heat transfer regimes relevant to the problem of practical interest. The other, l and perhaps more important one, is that the practical need for reasonably robust estimates of g CHF is imminent as reactor-specific accident management schemes are now up against key decision points and regulatory scrutiny (AP600, Loviisa). The results presented in this paper are intended to fulfill this immediate need. In addition, these results provide an initial perspective on mechanisms as a starting point for the more detailed investigations of the phenomena at the local level. It should also be noted that both of these reacton have lower heads with no penetrations, so the effects of such complications in geometry are left for future studies. g E.1-4 I
L i
'Ihe experimental work is carried out in the ULPU facility, and the overall program involves this facility in three significantly different configurations. The overall strategy in the design of
[ this experiment and its three configurations is given in the next section, while the details can be [ found in Section E.3. Experimental procedures and the test program are summarized in Section E.4. The experimental results are presented and discussed in Section E.5, and concluding remarks are provided in Section E.6. t E.2 EXPERIMENT CONCEPT , Not surprisingly, the basic concept for this experiment was derived from the unique features I of the practical problem considered, ac mentioned in the Introduction; namely, the thick wall and the two-phase boundary layer. The thick wall consideration is straightforwani, easy to satisfy and, in fact, it leads to certain important conveniences (in comparison to thin walls) in both the f construction and experimentation, as described in the following two sections. For the two-phase boundary layer, we wish to match, in the experiment, its local structure and dynamics to the local surface inclination, as they are to be found in the protonpe, all along the vertical are length from 6 = 0' to e ~ 90*. This cannot be accomplished in sub-scale models, while a full-scale representation (in an experiment with prototypic heat flux at all locations) is clearly impractical, if not impossible.' The approach used takes advantage of the axial symmetry in the prototype, in combination with a power-shaping approach in the experiment. The axial symmetry allows a " pie" segment representation of the hemisphere, but this is still, for a variety of reasons, a formidable experimental geometry to work with. By power-shaping we can effectively represent f the flow behavior in such a pie segment with a uniform (in thickness) vertical slice, which, as it l turns out, is experimentally feasible. We call this a " full-length" representation. A key conclusion of this paper is that this representation affords an essentially perfect full-scale simulation. Our task is to conduct simulation experiments that allow the determination of the critical heat flux g,,cr, in the reactor, as a function of the angular position 6 under the constraint of a f l specified power shape, say q,(6). Our approach is to make this determination for a discrete set 6.4 i = 1...n of values of the angular position, by a corresponding set of experiments, each simulating the prototype for the particular angular position considered. For this we set ( q,,er(6 ) = q,,cr(6 ) (E.1) l
- A full scale test with a torospherical lower head, in the CYBL facility, demonstrated a nucleate I boiling condition for uniform heat fluxes up to 200 kW/m 2(under subcooling corresponding to the gravity head).
l E.1-5 f 1
and require (i) that the superBeial vapor velocities (expressed as volumetric Bow rate per unit width) match up with those of the prototype for all 6 > 6m, and (ii) that for 6 < 6 l the vapor Bow rates build up gradually, so as to smoothly approach the value required at 6 = Gm, while allowing a " natural" development of the boundary layer in all of the l , upstream region. By satisfying these requirements, we ensure that the two-phae.e boundary layer is properly driven in a broad neighborhood of the location under consideration (Sm) as well as all of the downstream region. - The situation is somewhat complicated by the presence of subcooling and the dynamic aspects of vapor production and (partial) collapse. In the following, the derivation is limited for g convenience to saturated and steady conditions. It can be easily seen that that the same results 5 can be obtained under moderate subcoolings, as in the case of interest here, if one considers the total energy (sensible plus latent) flow per unit width, which, in turn, provides a more generalized similarity criterion, reflecting the fact that the convected sensible heat is also important in the
' local behavior of the two-phase boundary layer.
The relation of the constant-width test section to the pie-segment geometry is illustrated in Figure E.2. Let the superficial vapor velocity, at position 6, be denoted by J(6). One possible way of meeting the above requirements is by selecting,in the upstream region: W(6) s I g,(6) = q,(6)W(6m) = q,(6)sm.in for65;6m6 (E.2) 6 For saturated conditions (no condensation), the superficial velocities can thus be written as: 8 J,(6) = R' d6' g,(6') ms.* 6m (E.3) O J,(6) = R' g,(6') ' g de' (E.4)
- and their relative deviation can be derived to be:
AJ(6) J,(6) - J,(6) sin 6 E (E.5) J,(6) J,(6) _ sm 6m 3
'Ihis relation is shown in Figure E.3, wbich also includes the upstream lengths within which the " distortion" in the superficial vapor velocity is less than 10% or 20%. For 6. as small as 10',
the simulation is deemed to be acceptable, and it improves drastically as 6m increases, especially beyond 40'. Interestingly enough, it is this outer region,40' < 6 < 90', in which cumulative vapor flow can be expected to be the most important. E.1-6 I
-- 99=
[
- 67.5*
I [
-- 45' L
r em L - - 22.5* r
-- g
- Figure E.2. Geometric relationship between the constant-width test section in ULPU and the l pie-segment geometry, deduced from axial symmetry, for simulation. Both are shown unfolded, and 6m is the position at which the CHF is simulated.
The inner region,0* < 6 < 10*, can also be approached fmm a flux-matching standpoint alone; that is, by applying a uniform heat flux and setting 5 9p,cr(0) = q,,cr(0) (E.6) I [ is negligible and the most limiting CHF position is at 6 ~ 0*. We do not expect cumulative vapor flow effects to be important here, but it can be readil.y shown that now 8 - " j
=
,g
~ -1 for 0* < 6 < 10* (E.7) and if anything, this strategy should provide a conservatively biased simulation for this region.
For the downstream region, the similarity of local superficial velocities requires that, for L any position 6 > Gm, J,(em)W(6 )+ g,(6')W(6')R'd(6') = J,(6 ) + g,(6')R'd6' (E.8) y yg) E.1-7
I The distortion in superficial vnpor velocity with various 0m 1 i i [ 120
+ 0. - A J/J < 20% /
-+- Om -20 AJ/J < 10% ,
0.8
~
s 0m-30 / Om -40 / _
/ .'
Om -60 ; 0.6 p .
% Om=90 . .4 4
<J /
r a
-
- A 0.4 N/ .-
1 5
' ~~
0.2 20
....\ -
~ '
#~ ' ' '
0 O O 15 30 45 60 75 90 e. Figure E.3. Illustration of the distortion AJ/J, in superficial vapor velocity, as a function of upstream position, for various matching positions,6 . Also shown are the upstmam lengths within which the distortion is less than 10% or 20%. g which can also be written somewhat mom explicitly as g,(6')d6' = i, (1 - cos9m) ,;9g + q,(6') sin 6'd6' (E.9) I
,;9, g where q, is an " average" flux over 0 < 6 < 6m defined by I
sin 6m q,(g,)W(6')d6' (E.10) gP= Wm(1 - cose m ) o In the region O' < e m < 6 < 30', which is ofinterest in the experiments presented hem, and the relatively uniform q,(6) within it (see below), Eq. (E.9) can be shown to mduce to the simple result 1 g,(6)~gg,(6) 6. < 6 < 30' (E.11) and it is intemsting to note that this creates a discontinuity with Eq. (E.1) at 6 = 6m. This discontinuity arises because of the requirement to match the superficial velocity as well as the critical heat flux at Gm, and the need for choosing something like Eq. (E.2) for doing so. As we will see in Section E.4, this discontinuity can be repmsented in the heater design selected, E.1-8 I
b exactly at 6 = 30' or 60', and approximately at all other positions. Moreover, the importance ( of satisfying the downstream conditions can be checked by means of sensitivity runs around the
. result of Eq. (E.9).
h IAcal subcooling and vapor condensation effects clearly enhance the critical heat flux. To understand this behavior, we follow a two-pronged approach. One prong is to obtain a lower [ bound by running experiments at saturated, pool boiling conditions. De other prong is to allow for a natural convection flow loop in which the downcomer fluid, while saturated at the top of the facility, attains a subcooling equivalent to the gravitational head at the bottom of the test section. An important condition for this second set of experiments is to simulate the vertical void fraction profile over the entire length of the reactor vessel; it depends on the vapor supplied due to direct heating through the lower head, plus the vapor created all along the vertical vessel walls which are radiatively heated from the top of the molten corium pool (see Figure E.1). An [ impornnt object of these experiments is to determine the radial distributions (distance from the wall) of local subcooling and their evolution from 6 = 0' to e = 90'. Based on the above considerations, we arrive at the conceptual design, involving three distinct experiment configurations, as illustrated in Figures E.4 and E.5. Configuration I (to be [ denoted by C (I)) is for studying saturated, pool boiling in -30' < 6 < 30', and especially in the region around & ~ 0', which is not as well represented in the other configurations. Configuration [ II (C (II)) is for simulating the complete geometry (a full one-quarter circle) under both loop flow (includinn the effects of subcooling) or pool boiling (saturated) conditions. As seen in Figure E.5, this configuration is to represent an open-to-the-cavity geometry. A channel geometry, as it might arise from particular thermal insulation designs with an inlet at the very bottom (8 ~ 0'), can be created by introducing a baffle, as illustrated in Figure E.5, to obtain Configuration III L (C (III)). In this paper we present data from Configuration I only. E.3 DETAILED DESCRIPTION OFTHE EXPERIMENT De experiment (ULPU-2000) and the related technology in building the heater blocks [ evolved from the original ULPU work which was aimed at the vertical (side) wall of the reactor vessel and the exit restriction of the natural convection path in the Loviisa reactor (Kym11&inen [ et al.,1992). In that experiment the heater was limited both by design and available power to 1400 kW/m2, and CHF could not be reached for the range of conditions investigated. In the present experiment, both the power and the heater design were upgraded to allow a peak flux p l k of 2000 kW/m 2, hence the name ULPU-2000. Another important requirement in the present ! i ~ experiment, as explained in the previous section, was to have control of the power shape over L the whole extent of the heater surface, which is to cover, in Configurations II and III, the region p E.1-9 L ? I
1 I ULPU 2000 Configuration I I I Condenser Heat Input
}
$ ULPU.2000 Connguration II qp O O
( OO I Windows Riser Dowocomer Figure E.4. Schematic of Configuration I in 88 5' ULPU-2000. De heater blocks extend over ns ra IE'511 the region -30* < 6 < 30*.
/
\g, Heater block
\
t& "
. m Figure E.5. Schematic of Configurations II and III in ULPU-2000. He heater blocks extend over the region O' < 6 < 90'.
I E.1-10 I
0' < 6 < 00*; that is, a much larger physical dimension than in the original ULPU. Finally, certain important improvements in the installation of the heater blocks were made to essentially eliminate lateral losses and hence any departures from the desired 1-D behavior (i.e., heat flux and temperatures varying only with angle 6). Three heater blocks were built, each covering, nominally, a 30*are of a cin:le, with a radius of curvature of 1.76 m, which is well within the range of typical reactor dimensions. The actual are is 27*, for a total length of 0.83 m. The block height and width were chosen as 7.6 cm and 15 cm, respectively, such as to ensure sufficient thermal inertia and to minimize side-wall effects. One such block is illustrated in Figure E.6, and in a photograph, prior to assembly, in g 5 Figure E.7. The holes are 9.5 mm in diameter and allow two cartridge heaters (per hole) to be inserted, one from each side. The " fit" must be very good, while pmcision machining is also required in the accurate positioning of the holes, the 1.5 mm in diameter holes needed for the thermocouples, and the forming at the smooth, curved faces. Copper stock was selected as the raw material. Volage (217 V) is supplied to the cartridge heaters through 32 relays which are individually computer contmiled to cycle in the "on-off" positions so as to obtain any desired power distribution on the heater block.6 The total power obtained by summing the calculated power of each cartridge (from the voltage applied, the known resistivity, and the fractional "on"- time), agreed to within 1% of the total power supplied by the power generator. In Configuration I I, we have used two heater blocks (Figure E.4), which allows up to 16 power zones on each block. In fact, such fine resolution is unnecessary, and we use only eight power zones (i.e., 3.375' arc each). Temperatures are measured at eight corresponding positions along the length of each block.
- I 4
f
~
4 4 ,/1 . 1 1
' c _ u _ _4-
- I g Figure E.6. Heater block design, showing the holes for the cartridge heaters and the thermocou-E ples.
6 In all experiments the cycling time was 3.52 s, which is small when compared to the conduction time constant of the copper block (58 s). E.1-ll I
i l ! { l 1 l 1
\
I' l ~ r Q %.# , . .:~ **
~ * *-* * *
- j
~ T vX MT u5%:grs x n=
v;y 3 -y v ~ . , l . 1 E'
- I.
l '
\
l i Figure E.7. One of the heater blocks immediately after machining. l
- In Configuration I, each heater block fits onto the one (open) side of a similarly curved channel of a rectangular cross-section (15 cm on the side), as illustrated in Figure E.8. During operation, the blocks and channels am well insulated, and relative losses to the outside have been estimated to be negligible. On the sides the blocks overlap with the 2.5 mm stainless steel channel walls by approximately 13 mm, with a rubber gasket in between. Absence of steep temperature gradients in this region assums that any " bypass" losses to water are also negligible, i and this is confirmed by the near-perfect agreement of the four thermocoupies placed along the width of the heater block at each of the eight " axial" positions. As seen in Figure E.4, the
- channels are equipped with windows, for visualization. Also, the channels are equipped with I thermocouple " trees" arranged at various key positions (6 = 0 ,6 = 30 , etc.) to measure water temperatures. The overall experiment in Configuration I is shown in Figure E.9. At the ends i
of the U-tube ((15 cm each leg inside diameter)), we have installed condenser coils so that the
- facility can be operated open to the atmosphere without significant loss of steam (reflux mode operation).
The exact positioning of the thermocouples, the heating zones, and the related nomenclatures used in the subsequent discussions are given in Figure E.10. l E.1-12 I I
SEsP?W.& T Ztl % Wi" i c
,l T{ '"
=.
,{
... ...3 ..
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.9-
- 3, 7 4j , y e
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-. m . ., ,,
y ... .
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. y: } .Z .
. . n > . ~. , 7'w t-s qn L,
. ' s W. - '
*. .?
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~
^
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.. }
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- f;iW ; . ..= . .
'. _ ; , , ? $*.Q: ' . . ..
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. .. 7-w;- ., ,
L - . .. . . Figure E.8. The test section of Configuration I. - E.4 PROCEDURES AND TEST PROGRAM FOR CONFIGURATION I An approach to the boiling crisis can be recognized quite easily by sporadic, small (in both ~ amplitude and duration) departures of thermocouple signals; usually following a small increase in power level, a steady excursion indicating boiling crisis is observed. In taking data the aim is to bracket the CIIF betwen a value where BC occurs and a value which can be sustained for a sufficiently long time (see next section). The power, power shape, and all thermocouple signals - are recorded (at 0.5 IIz) so that a complete documentation of each run is retained. Video records before, during, and after BC are also obtained. This is possible because of the high heater thermal inenia which allows operation well past the BC. The temperature excursion can be arrested at will (by reducing the power); rewetting can easily be established; and experimental runs basically can be made back-to-back. This greatly facilitates the search u for narrowing the range between the CHFs and the fluxes at which nucleate boiling persists. - All experiments but one in the Configuration I program were run with saturated water at a L height of between 1.2 and 1.8 m in the U-tube, measured above the heater surface at 6 = 0* The one "other" run was made under transient subcooling conditions; that is, starting with a l water temperature of 20 *C and holding the power constant so as to deliver a uniform heat flux E.1-13
i i
.' O.) ; .-: }. _-l j 4
. .' . .7. ' .
1 i
.9 : ; ,;. .
i J { W i ,,
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1 q gg
}
Figure E.9. An overall view of ULPU-2000 in Configuration I. l of 400 kW/m .2 The saturated water runs can be distinguished by the power shape employed. One group involves a simulated flux shape, as discussed in Section E.2, and consists of three subgroups, corresponding to CHF " matching" at zones 1,3, and 5. These runs are denoted by the heating zone at which the matching condition is specified. That is, run SF-3 means a 11ux shape simulating CHF at heating zone 3 (18.75* < 6 < 22.5'). The other group is aimed at the region 6 ~ 0' (zone 8), and it was approached in three different ways, all employing a uniform flux around 6 ~ 0', but with different shapes in the downstream region. These runs are indicated by the last included zone of the uniform power segment, and the fractional power applied to thz downstream region. Thus, run UF-6-50% means a uniform flux in the region of zones 8,7, and E.1-14
l
'II* \\
l;I I l\ \ \ l f ffl t\\ Top view I II l \'\ \ ll l g;I,i li \ & J. .1.25 en Ifg l l l \ g to - . s.0 m I fg i gi i \ 3 's - - - 10 0 cu l lI gl ;l gl i; '\ ',\ '\ I , i \ g r""- / r I lI g ; ; l I l I l l l
\ \
l \ ;
; \ \ \
\
g I l
,/
s' I I I I \ \ I / I ;;g I l,t\ \ \ /
\;
lI I I I \ l l g \
\
; /
I I l /
# I I I
/ \ hac #
'sls1 ,3;2 I
4 8 g g 1
,/
ll 1 : :
\ ', v
\ rc, e
7l P +-l-li i 8 I5 4 is I2
,1
\
L 1.5 m i Side view i a 3.0 m i Figure E.10. The heating zones and thermocouple positions on a heating block. In Configuration I zone 8 of each heating block is adjacent to 6 = 0*, and zone 1 at 30'. 6 (-11.25' < 6 < 11.25') and 50% of this flux applied to the remainder of the heater blocks. Repeat runs are shown by the number in parenthesis at the end as, for example, by SF-3 (1), [ UF-6-50% (3), etc. He whole experimental program in Configuration I is summarized in Table r E.1. L ne reference reactor power shape (Theofanous et al.,1994) and the shape used in the { simulations are shown in Figure E.11 - the flat portion is due to the steel layer on top of the corium pool. Clearly, in the absence of the 30' < B < 90' irgions, these are only partial simulations; however, within the context of the Configuration I program, they are believed to be appropriate. The calculations were carried out with Eq. (E.9), and the resulting " wanted" flux shapes for runs SF-5, SF-3, and SF-1 are shown in Figures E.12, E.13, and E.14, respectively. Rese figures also show the fluxes delivered to each of the heating zones, and the resulting, E.1-15 {-
Table E.1. Summary of the Experimental Program in Configuration I, UlfU-2000, and Related Nomenclature Group Subgroup Remarks SF-5 4 runs SF SF-3 4 runs SF-1 4 runs I UF-1-0% 4 runs UF-5-0% 1run UF UF-6-0% 2 runs UF-7-0% 2 runs g UF-5-50% 1run 3 UF-6-50% 4 runs UF-7-50% 1run actual, fluxes following the " smoothing" effect of axial conduction. The latter were obtained by numerical simulations of 2-D conduction in the heater blocks using the boundary conditions determined in the respective experiments. From these figures, we obtain the correction factors of 0.85,0.89, and 0.95 for converting peak input to actually delivered peak fluxes for the three cases respectively. (The data reported in the next section incorporate this correction.) Rese figures also show the discontinuity at 6 = 6 mentioned in Section E.2. Because the heater blocks can be insulated from each other, it is easy to see that the discontinuity can be represented exactly E at 30' and 60' (in Configuration II or III, of course). In all interior points the discontinuity can 5 be represented approximately (because of axial conduction), but it is noted that Figures E.12 and E.13 are only illustrative of the experimental capability - no special efforts were made to represent the discontinuity quantitatively in these partial simulations in Configuration I. Dat is, the delivered " discontinuity" can be improved by suppressing even further the downstream power levels to the test section, as illustrated, for example, in Figure E.15, made to show the behavior in the UF-series of runs. (Here the position 6 = 0* *is of interest, and as seen in the figure, the correction due to axial conducti on is negligible in all cases.) Retuming to the internal discontinuity, it may be of interest to note that the " wanted" fluxes in Figures E.12 and E.13 do not appear to exactly follow Eq. (E.11). This is because of the finite discretization combined with the increasing trend of the prototypic flux shape (see Figure E.11), especially for 6 > 15*. I ! E.1-16
l } l 1000 . . . . l 800 - i c 6 . ,' - N ~
/
E
$ 600 -
/ -
l g
./ _
D . C 400 -
/ 5 a
n
/ -
v - Z -
',,.,e' 200 -
)
-0 ' - - I - - - - I - - - - I - - - - I -
L -0 20 40 80 80 iOO Angle O E Figure E.11. The mference reactor heat flux shape ( ) (from Theofanous et al.,1994), and the shape used in the simulations (......). L l l . t t _ 000 - F ^ g / [ - F l M 400 v
/ -
m .
....'.. I -
p . C _ V a L c - o 200 - ~~~~--J - lC - r Out ut flux - I Out ut flux wanted Input flux .
~'. . . . l . . . . I . . . .
-0
-0 10 20 30 Angle (Degrees) f~
Figum E.12. The wanted, input-equivalent, and the actual heat fluxes for runs SF-5. b E.1-17
_[ ,',, I l . 600 -
/ -
N Yl. . I g 400 - C . J.- . J.. ' 200 - [ -
'~~~ ~~~~ Output flux wanted -
The actual output fiux - l Input flux . 3 r ,---- , , ,
; , , , , i , , , ,
-0
-0 10 20 30 Angle (Degrees)
Figure E.13. The wanted, input. equivalent, and the actual heat fluxes for runs SF-3. 800 , , , , , , , , , y , , , g 600 - g - N
> . +.-
.M ,
v - y 400 -
- ./
D - u . c o .;;:.) Z 200 _ . . . . ,c . Output flux wanted . The actual output flux Input flux Y"- , g
-0
, , ! , . , , l , , , ,
E
-0 10 20 30 Angle (Degrees)
Figure E.14. The wanted, input-equivalent, and the actual heat fluxes for runs SF-1. i E.1-18 i I
( 600 g f -~" The input flux UF-7-0% The actual flux UF-7-0% ( The input flux UF-7-50% g The actual fluz UF-7-50% 400 - - d w ;~ y 'g,'N
$ 200 ',
g
\,,%~.% -
\
s [ '] . ;
~ -0 to 20 30 Angle (Degrees) 600 .g g The input flux UF-6 -0%
t The actual flux UF-6-0% The input flux UF-6-50% g The actual fluz UF-6-50% f k400 l .x j ' '; s,
- s..
Y 200 .'N.'--, g ' [ 'N l l '. - l
-0 to 20 30 Angle (Degrees)
L 600 g g The input flux UF-5-0%
.- .- n;innt' fin'nant c g The actual flux UF-5-60%
J f400 - - l 5
] 'E';'N
- s y 200 - '. N.,~.._,_,,
y
, \. -
~ -0 10 20 30 Angle (Degrees)
Figure E.15. 'Ihe input-equivalent and actual heat fluxes delivered in all UF-series of runs. (a) Runs UF-7-0% and UF-7-50%, (b) runs UF-6-0% and UF-6-50%, (c) runs UF-5-0% and UF-5-50%. E.1-19
I E.5 EXPERIMENTAL RESULTS AND DISCUSSION In the early shakedown experiments we saw successively increasing values of CHF over a period of one week. Having started with a clean, po?ished heater surface, this was due to the expected aging effects. Eventually this behavior stabilized, and since our interest is for a fully-aged carbon steel surface, only then did we enter the the actual test program described in the previous section. The thermocouple behavior during the approach to CHF and beyond its occurrence is illustrated for a typical case in Figure E.16. In each run we approached CHF from above, or from below, seeking the lowest flux yielding CHF and the high'est flux at which nucleate boiling would persist indefinitely. Quite soon it became apparent that the behavior is asymptotic . Dat is, small reductions in power below some level produce increasingly delayed BCs, as illustrated for the case of a series of UF-6-50% runs in Figure E.17. On this basis the nucleate boiling data points were obtained after a 50 min wait in nucleate boiling, and they may be taken to represent a reasonably conservative lower bound for CHF. In addition, a set of 120 min wait runs were made, at the end, to provide a more definitive lower bound. One might think of these latter data as corresponding to deterministically impossible CHF. The delay time may pmvide important clues on the mechanisms, but quantitatively it is not so important in that it spans a g less than 10% effect on the magnitude of CHF. E The data from all runs performed are summarized in Figure E.18 and in Table E.2. The g most important and interesting observation is that the simulation runs at positions 5, 3, and I line E up well among themselves and also with the lower bound of the UF runs at 6 ~ 0*. The other , key point is that even with rather wide variations in the downstream flux shape in the UF-series of runs, a reasonably consistent behavior, and lower bound of approximately 300 kW/m2 n CHF l ! is quite evident. The boundaries for the two CHF bounds defined above, as determined from the respective data sets, are shown in Figure E.18 and they can be described by: conservative bound l ger(6) = 300 kY /m 2 6 < 5* (E.12) E
= 300 + 12.66* kW/m 2 5* < 6 < 30* E detenninistic bound ,
ger(6) = 276 kW/m 2 6 < 5* 2 (E.13)
= 276 + 12.66* kW/m 5* < G < 30*
I E.1-20 I: ;
l
- g. , , , i g
. , , i g
T1 200 - T2 - I
-- T 3 /,\
m - i .'- - I o . . . . . . . . . . T 4. .- t g, e, -
- , *. l;/ se,'. -
a 5 ed 4 l 't \'. 1:
- 1. /
0if oj
/ i u
i:. 0 150 a,
"Y' r'//
1 ::
! !s G . t lI l h \ \;
e : :.
' '! 'I o n;I' E-* g .!
~
_A ..m<-'4
~f
.yc...s r. ' pf ,,/ . .;
.i ,j . . ;;,,
- g. ,,,,,.,A.. ....u. g , ,, . . .
100 ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' I ' ' ' ' 40 42 44 46 48 50 Time (min) Figure E.16. Heater surface temperature behavior as critical heat flux is approached, and the excursion associated with its occurrence. Test SF-3 (1), zone 3, thermocouple position as shown in Figure E.10. 400 i i i i i i e of 3gg _ o Nucleate Bolling _
.e
- e N
M 360 -
$ e a
M 5
] 340 , -
)
E I
- 1 0
320 - 4 300 0- 20 40 60 80 100 120 140 Time (min) Figure E.17. Illustration of the asymptotic CHF delay time behavior, in the UF-6-50% series I of tests. 1 E.1-21
I 800 i i i i i i 700 X e g 600 E h 3 1 - g 500 - 5 h 400 -
- CW -
< Nucleate Boiling 300 -o- 50 min. tests -
+ 120 min. tests 200 O 5 10 15 20 25 30 35 Angle (degrees)
Figure E.18. Summary of all the data obtained in Configuration I. Solid symbols denote oc- g currence of BC; open circles denote persistence of nucleate boiling for approximately 50 min; E crosses show persistence of nucleate boiling for 2 h. (At 0* angle, runs UF-6-0 and UF-5-0 are not shown.) E.6 CONCLUDING REMARKS Full-scale simulations of the critical heat flux distribution on the lower head of a ree.ctor vessel submerged in water are possible in the ULPU-2000 facility. In this paper we have pmsented data from Configuration I, repmsenting the lowermost (-30* < B < 30') spherical segment conservatively in saturated pool boiling. These data are enveloped by Eqs. (E.12) or (E.13) which can be applied directly as conservative bounds to the reactor case. In future testing (Configurations II and III) the effects of full geometry (0* < 6 < 90*), natural convection, l subcooling, and flow path geometry are to be considered, and detailed investigations of the local phenomena and mechanisms are to be carried out. As noted in Section E.4, a preliminary investigation of the effect of subcooling was carried 2 out in Configuration I. The heat flux was set at a uniform value of 400 kW/m (over the whole i -30' < 6 < 30' region) and the experiment was started with water at 20
- C (and the same level as all other runs reported in this paper). As the experiment continued, the water heated up gradually, leading to several distinct condensation regimes, both in terms of the intensity of E
l the resulting vibrations as well as in tenns of the observed two-phase flow phenomena near the E heating surface. Nucleate boiling persisted throughout. The heatup transient and CHF occurred ! E.1-22
l [ Table E.2. Listing of the Experimental Runs Perfonned in ULPU-2000 Configuration I, Heat Fluxes, and Respective Waiting 'Ilmes ! Test Nucleate Boiling Boiling Crisis 3 2 Flux (kW/m ) Time (min) CHF (kW/m ) Time (min) L UF-7-0 322 20 353 3 322 44 337 7 r UIL6-0 384 18 407 6 L 376 40 391 22 UF-5-0 422 24 437 2 r UF-1-0 322 30 329 12
- 346 10 338 6 307 20 322 4 UF-7-50 322 40 337 11 UF-6-50 322 41 337 9
- 307 75 276 120 -
322 120 337 38 UF-5-50 345 30 353 3 SF-1 656 21 693 2 635 50 693 3 671 44 693 2 678 42 693 23 SF-3 580 50 615 3 574 20 595 7 574 14 568 100 SF-5 483 50 529 1 490 16 509 13 502 42 522 5 470 120 - l (at 8 = 0') within some tens of seconds after reaching saturation. 7his is consistent with Figure E.17 and demonstrates the important effect of subcooling to increase the CHF. At this time we also have a preliminary result from Configuration III with one heated block at position 60* < 8 < 90' (see Figure E.4). In this experiment the flow channel used was as in Configuration I in pool boiling at saturation. Boiling crisis was obtained with flux levels around E.1-23
I l 1000 kW/m2, and the point of inception could be made to move across the length of the block by relatively small changes (less than 20%) in the power shape. Finally, mturning to the application, a perspective on the above results can be obtained with
- a reference to Figure E.11, indicating the predicted thermal loads distribution in the reactor. It can be seen that near the bottom the available margins am of the order of 200E From the pmliminary information pmsented here on the upper region, however, it appears that the margins could be of the order of a few tens of per cent. While experiments in Configurations II and i
III will clarify this point, it is already clear that contrary to the generally held opinion that the region 6 ~ 0* is limiting, the mal limitation may actually be around 6 ~ 90'. E.7 ACKNOWLEDGMENTS Support for this work was provided by IVO International Ltd and the Argonne National Laboratories, for DOE's ARSAP Program under contract no. 23572401. Mr. Sergio Angelini's collaboration in working out the similarity criteria, and Mr. Stephen Additon's help with many aspects of this work are also gratefully acknowledged. I E.8 NOMENCLATURE q J superficial vapor velocity heat flux l R' radius of curvatum divided by the latent heat per unit volume of vapor W width Greek 6 angle of surface inclination from horizontal Subscripts er critical e experiment g m matching point for experiment and prototype B p prototype (mactor) E.9 REFERENCES
- 1. Bui, T.D. and V.K. Dhir (1985) " Transition Boiling Heat Transfer on a Vertical Surface,"
Trans. ASME, Vol. 107, 756-763.
- 2. Chu, T.Y., B.L Bainbridge, J.H. Bentz and T.B. Simpson (1994) " Observations of Quench-ing of Downward-Facing Surfaces," Rep. SAND 93-0688, Sandia National Laboratories.
E.1-24 l
s
- 3. Henry, R.E. and H.K. Fauske (1993) "Extemal Cooling of Reactor Vessel Under Severe ;
Accident Conditions," Nucl. Eng. and Des. 139,31-43. *
' 4. KymRitinen, O., H. Tuomisto and T.G. Theofanous (1992) " Critical Heat Flux on 1 hick Walls of Large, Naturally Convecting Loops," ANS Proc.1992 National Heat Transfer Conf., San Diego, CA, August 9-12,1992, Vol. 6,44-50, (and in more complete form in IVO International Ltd. Rep. LO1-GT1-59).
- 5. Theofanous, T.G., C. Liu, S. Angelini, O. KymtlRinen, H. Thomisto and S. Additon (1994)
" Experience from the First Two Integmted Approaches to In-Vessel Retention Through Ex-ternal Cooling," OECD/CSNI/NEA Workshop on Large Molten Pool Heat Transfer, Greno-ble, France, March 9-11.
l l i E.1-25 l
APPENDIX E.2 THE COOLABILITY LIMITS OF A LOWER REACTOR PRESURE VESSEL HEAD Submitted to NURETH-7 E.2-1
4e-E-.sh+-m,ww_4 a,.m-y; ...a .%eAw._ _-----w.----- -- ------------ - . - - - - - I. I I I. I I I' I i l I l I' l ! I l I i I I i I I I
i APPENDIX E.2 THE COOLABILITY LIMITS OF A LOWER REACTOR PRESSURE VESSEL HEAD T.G. Theofanous* and S. Syri"
- Center for Risk Studies and Safety Department of Chemical and Nuclear Engineering University of California, Santa Barbara, CA 93106 "IVO International Ltd.
01019 IVO, Finland E.1 INTRODUCTION This second part of Appendix E is written as a sequel to, and in conjunction with, the paper given as the first part, reporting on the Configuration I experiments. The experiment concept, simulation approach, experimental facilities, and measurement techniques have aheady been l described therein. Thus, here we enter directly into the detailed aspects of the Configuration II facility and test program-Sections E.2 and E.3 respectively. The experimental results are presented and discussed in Section E.4, and the conclusions from the work on both configurations are given in Section E.5. E.2. CONFIGURATION II FACILITY he overall geometry of the experiment and related terminology are shown in Figure E.1. He three heater blocks (the primary heater) are fit (in the same manner as in Configuration I) on top of a two-dimensional chamber (15 cm wide) with a shape (in the other two dimensions) as shown. This chamber simulates an open lower cavity geometry (no reactor vessel insulation); it is 2 m wide (at the base) and 0.5 m in height at the short end. The chamber is made of stainless steel sheet,2.5 mm thick, and it is reinforced externally over the flat areas to sustain the substantial hydrostatic forces without any significant distortion. Bis test section stands bolted on shock absorbers capable of carrying 3000 kg, which in turn are anchored to the floor. The riser and downcomer are assembled from glass piping 6 m long and 15.2 cm and 7.6 cm in diameter respectively. He riser is equipped with a cable heater (referred to as the secondary heater) extending essentially over the whole length, and operating at a fixed power level of 24 kW. The purpose of this heater is to simulate the radiative power from the melt delivered through the wall of the reactor pressure vessel to the water in the annular space between the cavity wall and the reactor vessel. (The riser in the experiment corresponds to this space.) Finally, the E.2-3
I ! condensor at the top is to minimize coolant losses and allow operation with saturated water at the inlet to the downcomer. In Configuration II runs this was accomplished by direct contact condensation; that is, a fine spray of demineralized, room temperature water injected at rates sufficient to make up the steam loss to the environment (let out through a permanently open vent ! line). The condenser was also equipped with a safety relief valve which, however, did not ever g have to energize. 5 Condenser r ll ULPU-2000 I Configuration II I I
-- Riser Downcomer I
Bame to obtain Configuration til r
/
/
Ilester blocks
\
N
\ >
/
- '/ -.
(A Figure E.1. Schematic of the experiment arrangement in Configuration II. l In addition to the instrumentation employed in Configuration I (heater block thermocouples, thermocouple trees in water opposite the heater surface, and windows / video for visualization), in Configuration II we also had an electromagnetic flow meter for instant flow measurement in the g downcomer, and pressure transducers for pressure drop measurements in the riser for the overall 5 void fraction in the upper and lower halves of its length. E.2-4 5
4 f In keeping with Configuruion I, we assigned 8 heating zones per block, and counting from l { the upper end of the heater (6 = 90') as zone #1, we had a total of 24 zones. [In fact, because i the upper block had twice as many heaters - 4 rows as compared to 2 rows of the other two
- - it was assigned 16 relays for power control, but with coupled operations in pairs such as j to produce 8 heating zones.] Because the heater blocks were insulated from each other, it was possible to represent especially well the discontinuities dictated by the power shaping criteria !
(for similarity) of positions 30 and 60*.
- l l The whole facility, in operation, is shown in the photos of Figures E.2 and E.3.
l - . . . .
. 6 ; [;[.N J
. s ; y. # t .
- 1. a;. 1, a;; ., .
j.# 2y.. .. .
- i .
j / - in&g.n, . ! i
/
P
\ sp;,fjQf u l
r :Rnq I l 33g y J' 1 l , 3
'T
{ l
."p. -
f
- - ti ~1
,- t 4, l '
^*
!4 -
t % ! . f m- o 4 'I, ' E,*, I,i l l X ' i;
- l. t v-- J Je l
7: l, k'a W f f , ' . , ,, ' i
! hl '
I
- Figure E.2. De ULPU-2000 Configuration II in operation.
r E.3 OVERVIEW OF THE TEST PROGRAM All experimental and data acquisition and reduction techniques were the same as in Config- , uration I. Again, we found an aging affect from the initial, polished copper surfaces, with CHF increasing and then leveling off when the surface was fully oxidized. The data reported here are those obtained with the surface in this fully-aged state. We expect this to provide a good E.2-5
I I N [n igy r 7o g . ,i~
- L g W I^
Y l i n gte ' tW. t h 87 i 4 d
$ '.; i. ~ , ' i
.[
, j. .
'L. 't,[ .E'.? o : \
- ' 4 6 ..,
.s 3
-1
~
/- -
', ~-
w .. _ Figure E.3. He ULPU-2000 Configuration II test section. simulation for the aged, carbon steel reactor pressure vessel surface; however, an exact duplicate h of this material has been secured (from one of the prospective manufacturers) and is planned to be tested, by replacing one of the current copper blocks, for confirmation. All runs in Configuration II were carried out with sufficient water in the loop to close the natural circulation path. Bus, there was a relatively strong flow, depending on the total power 1m ' (typically ~ 80 kg/s) and subcooling at the base, corresponding to the gravity head (~10 K). Although the flow regimes near the heater surface in these runs were qualitatively similar to g those observed in Configuration I, here the CHF would occur typically within a few minutes or 3 not at all. It appears that the present conditions (flow, subcooling) do not favor a CHF-delay-time behavior, as found in Configuration I. Hus, zeroing in the CHF was now much easier; starting from the high end, the power was reduced after successive occurrences of boiling crisis (BC) l (each of those runs being only a few minutes long), until the last reduction (typically by a few I a percent) where the heater remained in nucleate boiling. Once it was established that the delay time was not a significant factor here, this nucleate boiling condition was allowed to continue, E.2-6 I
for most runs, for 10 to 30 minutes. A grouping of several successive BCs and a final period in nucleate boiling is referred to as one experimental run. Regarding the power shape, two types of runs were carried out: " uniform flux" (UF) runs, involving a number of zones around 6 = 0* at a uniform power (that is, simulating heat flux at 6 ~ 0*) while the remaining two blocks wem powered according to the power shaping principle; l and " shaped flux" (SF) runs, powered according to the power shaping principle, to simulate CHF , at specific locations (6 / 0*) along the test section. The reference power shape used here is the same as that employed in Configuration I, and it is shown in Figure E.4. However, certain modifiers from these general descriptions am necessary: (a) Because of the strong peaking in the reference shape, simply elevating the power level always produces CHF at 6 = 90*; that is, under reactor conditions, the position 6 ~ 90* is by far mom limiting than the very bottom of the lower head. Thus, to obtain the CHF at " 6 ~ 0* we had to reduce the downstream power very significantly. This was done, up to whatever degree was necessary, while maintaining the shape, however. Hat is, the highest power in the downstream (to the uniform flux section) region is still at 90*. [%is power level was denoted in the run identification number as a percentage of the uniform flux level imposed at B = 0*).] An example of what has been described above is given in Figure E.5. l (b) For SF runs, the same " compromise," for the same reason described above, was necessary for forcing CHF anywhere on the lower block (0 < 6 < 30*). l (c) For CHF in the upper block (60* < 6 < 90*), an essentially exact simulation could be obtained for the lower end of it (6 ~ 67.5"); but in order to force CHF at 90*, the upstream
^
l power profile within the third block had to be reduced somewhat. The reason for this is that in this upper region the mactor flux is rather flat, which translates to a rather uniform ! shape also according to the power shaping principle, thus yielding CHF at 6 < 90*. l About naming, we follow the same procedure employed in Configuration I. That is, we use a prefix, UF or SF, to denote uniform and shaped flux respectively. Following this there is a numerical index that for UF runs indicates the number of zones subject to the uniform flux, while for SF runs indicates the zone at which CHF is simulated. Uniform flux runs are only employed to simulate CHF at the bottom end of the test section (6 ~ 0*). Then, there is a third numerical index for UF runs only, indicating the percentage of increase in power at the upper end of the test section (6 = 90*) in relation to that on the uniform flux portion. Finally, the number in parenthesis at the end indicates the order in which repeat runs (if any) were performed; however, repeat runs were not run consecutively, but rather were intermingled among the various runs. u o l E.2-7
I' i Il I 1000 . , , , . - ' ' ' ' '
, ,,,,;,,,,l l l '.
800 - - g - E : / : N . .
$ 800
/ 7
. i .
x .
/ .
_o - i N 400 - m . o . .
- I: .
200 -
~ '
' ' ' ' I ' ' ' ' l ' ' ' ' l ' ' ' ' I ' ' ' '
-0
-0 20 40 60 80 100 Angle 0 Figure E.4. The reference reactor heat flux shape ( ) (from neofanous et al.,1994), and the shape used in the simulations (. . . . . . ).
l
..r-I 3000 UF-0-180 7. ..._:- - 3 g
- ~"'
~~~~~~~
Power shaping principle g . . N . v x 2000 - -
' ~
l j~~ 4 % .
.,4 . r~ .
c e 1000 - r--l .) lI: - -
,J
,_.a -
. L. _ . - - .. _ .
' ' ' ' l - - ' ' ' ' ' ' l ' ' ' ' l ' ' ' -
-0
-0 20 40 60 80 100 Angle (Degrees)
Figure E.5. Illustration of the power shape " compromise" necessary to force CHF at 6 = 0'. E.2-8 I I
% illustrate the above,
( UF-8-145%(2) means: (a) a uniform Bux run, simulating CHF at 9 ~ 0*, with all 8 zones of the ( lower block (i.e., zones 17 to 24) at the same power; (b) middle and upper biccks powend acwrding to the power shaping principle (as discussed above) and such that the power level at the upper end (90*) is 145% of that at 9 = 0*; and (c) { this is the second run carried out under these conditions, while ( SF-7(4) means: (a) a run simulating CHF in zone #7 (9 ~ 67*); (b) run with a heat Bux distribution according to the power shaping principle; and (c) this is the fourth run carried out under these conditions. A listing of all runs carried out in Configuration U is given in Table E.1. He flux shapes employed in each case are shown in relation to those dictated by the power shaping principle in ( Figures E.5, E.6, and E.7(a) through E.10(a). He conduction correction for UF runs is negligible (see Configuration I), and for the SF runs the actual fluxes delivend are shown in Figures E.7(b) through E.10(b). He corrections involved are summarized in Table E.2. Dese small corrections have been applied almady to the data reported. E.4 EXPERIMENTAL RESULTS AND DISCUSSION A reagh idea of the surface aging effect on CHF is given in Figure E.11. In it, we see that the effect is measurable even after ~4 hours of operation, but it is clearly leveled out, compared 2 r to the very initial value of 450 kW/m2 . Also, for 6 = 90*, the initial value was ~1.2 MW/m , as compared to the fully-aged value of ~1.6 MW/m2 . As noted already, this work is focused on the fully-aged surface condition, and these am the results reported and discussed below. l ne results from all experimental runs are shown in Figure E.12, and in tabular form in Table E.3. In Figum E.12, we also show the results from Configuration I. De following observations and comments can be made: ,
- 1. Configuration II exhibits a significantly higher tolerance to boiling crisis as compared to Configuration I. These are clearly the effects of flow and subcooling, and they amount to about 50% increase.
[ 2. For Configuration II, the variation of CHF with angular position seems to be composed of two, remarkably linear, regions. We believe these to be reflective of the significantly ( different flow regimes observed in the respective regions. 1 E.2-9
- _ _ _ - _ - _ _ _ _ _ _ _ _ __ __ __ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ __ m _
I
- 3. The CHF level at the upper end (1.6 MW/m 2) is remarkably higher than anything observed previously - under any orientation. This is contrary to the " conventional wisdom" that flat plate (horizontal) CHF is generally applicable.
Further, it should be noted that: (i) the nucleate boiling point shown for 6 = 45' was obtained at l the maximum available power in the middle block at the time. Now, a third row of heaters has l been added to it, and we expect to carry out experiments in this area shortly - and to confirm that the results lie on the same linear trend for this " upper" region; (ii) in Table E.3 we find three runs in which CHF occurred after a few minutes; however, note that all three cases wem for the lowermost region (0* < 6 < 15*), and that the differences were rather small (2-4%). This again is another indication, or symptom, of a different mechanism in the lower region identified in the data trends (Figure E.12). The lower envelope for the Configuration II data in Figure E.12 can be expressed by: 2 ger(6) = 500 + 13.36 kW/m for 6 < 15* (E.1) ger(6) = 540 + 10.76 kW/m 2 for 15* < 6 < 90* (E.2) However, the data can be fit equally well with one equation: ger(6) = 490 + 30.26 - 8.88 10-262 + 1.35 10-868 -6.65 10-846 kW/m 2 (E.3) His line is shown in Figure E.12. E.5 CONCLUSIONS With the completion of the Configuration II experiments reported here, we have established a firm estimate for the coolability limits of the lower head of a reactor vessel submerged in water and heated internally. The scale of the experiment, and the power shaping principle, ensure that i these data, and resulting correlation, are directly applicable to the reactor. De correlation reveals ! a two region behavior [Eqs. (E.1) and (E.2)] which has been related to the different flow regimes observed in the two-phase boundary layer in the respective regions. E.6 ACKNOWLEDGMENTS This work was funded by IVO International Ltd. (supporting S. Syri) and the U.S. Depart- g ment of Energy's Advanced Reactor Severe Accident Pmgram (ARSAP) through ANL subcon-tract No. 23572401. We are also grateful to Sergio Angelini, Tony Salmassi, and Mitch Frey, for help with design and construction of Configuration II, and to Jeff Smith, for helping with the construction, running of the latest portion of the experiments, and helping with the data reductions. Mr. Stephen Additon (TENERA) played a key role in programmatically supporting thisproject. E.2-10 I I
Table E.1. Listing of Runs Carried Out in Configuration II Group Subgroup Remarks ! l SF SF-1 3 Tests SF-7 3 Tests SF-17 3 Tests SF-21 2 Tests UF UF-3-180% 1 Test UF--3-220% 1 Test UF-8-145% 2 Tests UF-8-180% 1 Test Table E.2. Heat Flux Correction to the Input Flux due to Axial Conduction Run # CHF Position Correction Factor All UF O' 1 SF-21 15' O.965 SF-17 30' O.992 SF-7 (4) 67.5' O.947 SF-7 (3) 67.5' O.985 SF-7 (2) 67.5' O.962 SF-7 (1) 67.5' O.94 SF-1 90* 0.998 l l E.2-11 l l t - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
} I Table E.3. Listing of the Experimental Runs Performed in ULPU-2000 I Configuration II, Heat Fluxes, and Respective Waiting Tunes. Test Nucleate Boiling CHF Boiling B.C Tune 2 2 Flux (kW/m ) Time (min) (kW/m ) (min) UF-3-180% 461 15 517 498 2.5 3.5 l 479 14 UF-3-220% 479 15 UF-8-145% (1) 545 1.5 526 3.5 g 508 47 3 UF-8-145% (2) 527 120 573 1.5 564 1 E 555 2 5 536 3 UF-8-180% 498 15 SF-1 (1) 1485 10 SF-1 (2) 1504 30 1617 1 1579 2 g SF-1 (3) 1579 10 1617 2.5 SF-7 (1) 1231 30 SF-7 (2) 1246 30 l SF-7 (3) 1282 10 l l SF-7 (4) 1299 60 1335 2 1317 1335 1.5 1 l SF-17 (1) 932 10 g SF-17 (2) 914 30 932 2.5 3 SF-17 (3) 914 30 SF-21 (1) 789 30 862 1 g l 843 2 5 1 816 2 SF-21 (2) 762 30 789 13 g I l l I E.2-12 I
O
.; ...g . . . .
g
. UF-8-180 % .
UF-3-180 % i-- UF-3-220 %
---"~~.
r"~~ - g 1000 - UF-8-145 % - E D ac
~
f ...
~
w ...r-
- g
- s - i ~
;;; ,_ J
.s 500 -
e r- ..: o -
;I: .
s- - . . ; E i 8 E f f I 1 i . I 1 I ia 1 i E 1
-0 20 40 80 80 100 Angle (Degrees)
Figure E.6. Heat flux profiles imposed on UF-type runs. The shape required for " simulation" for these runs is shown in Figure E.5. l l E.2-13
I I 6000 , , , , g g Input flux - SF-21 J~~ .
. ---- Power shaping principle ............r-t~,i--
I a : E 4000 - N y . I x .
- s .___
o .
% 2000 -
x o . l_f~ 1,.. _i-'-'~~,.. '
-0
-0 20 40 60 80 100 Angle (Degrees)
Figure E.7(a). The actual power shape for run SF-21 compared to that derived from the power shaping principle. I 1000
,g ,,,,g, , , ,
g, ,, ,
~~ ~
600 - - N . . 6 . . s ~j kx ' 600 - M . .
$ 400 _
i f~' a g - e o . Z . 200 -- 3 -
. .a Input flux -
;. Output Flux -
-0 ' ' ' ' I '! ' ' ' ' I - - - ' I ' ' ' '
~
-0 20 40 60 60 100 ..
Angle (Degrees) Figure E.7(b). 'Ihe effect of axial conduction in the beater block in modifying the input flux shape for run SF-21. E.2-14 I
I l 5000 , , , , g
,g , , , , , , , ,
g
, g ,
Input flux - SP-17 ....i~~' -
------ Power shaping principle ---'-'~
4000 - _" N . - g . - s . -
> 3000 - -
v x . - u . -
- 3 . - -
C 2000 - - 5o : : l-l_f ( x . - l 1000 - - t -
. d-- __ _
c l I I ,,,l I _o , , . , , , , . . , , , . . . .
-0 20 40 60 80 100 Angle (Degrees)
Figure E.8(a). The actual power shape for run SF-17 compareil to that derived from the power shaping principle. 1000 , , , , , , , , , , , , , , , , , , , ,
- v. .
800 - N . N . y 600 - m . x . 400 - r - g - x : ,. 200 -- LJ -
,. Input flux -
Output Flux -
- J .
l _o . . . . .. . , I , , , . ! . , , . l . . . .
-0 20 40 80 80 100 Angle (Degrees)
Figure E.8(b). 'Ihe effect of axial conduction in the heater block in modifying the input flux shape for run SF-17. E.2-15 \ __ ---_ - - -- --
I 1500 , , , , g
,g , , ,
,g , , , ,
g I
'Q . .
(>1000 - - W 5 _ _ g g .
- r. .
. E
= -
, ..i
%o 500 -
x -
~
.. Input flux ~
Output Flux
' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' '
-0
-0 20 40 60 80 100 Angle (Degrees) l Figure E.9(a). The heat flux profile according to the power shaping principle for CHF at 6 =
67.5' and effect of axial conduction. I 1500 , , , , , , I ,l l l
~
E (> 1000 d . x . E '..
~ .
g To 500 -
- g
= "
,, .2 .
. Input flux ~
Output Flux
-0 ' ' I ' ' ' 'I ' ' ' ' l ' ' l ' ' ' '
-0 20 40 60 80 100 Angle (Degrees)
Figure E.9(b). The effect of axial conduction in the heater block in modifying the input flux shape for run SF-7. E.2-16 I i I
L I l 2000 , input flux - SF-1 Power shaping prmciple g 1500 -
, , , . . . - "]
E : N ' 3: - l f., ! x 1000 - l 2 . , c - g - v
= 500 -
l I I ' l
-0
-0 20 40 60 80 100 Angle (Degrees) f Figure E.10(a). The actual power shape for run SF-1 compared to that derived from the power shaping principle.
1500 - - _ 7.. .,!
~
S - .J N - l % .1000 y C zI
", ,. .a 0 500 - "'" -
m .
,a j
Input flux Output Flux I ' ' ' ' ' ' ' ' ' ' ' ' ' '
-0
-0 20 40 60 80 100 Angle (Degrees) l Figure E.10(b). The effect of axial conduction in the heater block in modifying the input flux shape for run SF-1.
l E.2-17 l
I e50 i * ' I
! i l .
800 ~~~~~~i
~i ,
} -~ I~ ~~ ~ ~
E 550
^
e -
*~
E I !
- I E . !
C + l l 500 w
- 3
$. o e soang c=e < san 450
. - c . .-
O Nurame Sonng iO 20nn { 400 4 8 12 16 20 0 Operating TIrne (hrs) Figure E.ll. Illustration of the surface aging effect in Configuration II, for times greater than 4 hrs. [ Data for earlier times are not shown.] All data refer to boiling crisis at 6 = 0'. 1 2000 ! w 1600
~ - " ' ' - ~ ' ~ -- ~ ~ - - - - - - ~
- ~ - --
3: 1200 e - 1 E ,,,
/ _c...,0.......
e Batmg case
,,. _ g j
- f' j- + e60 nn Nucleate Bodmg 1(y _l' - - - - - - - - -
+ e60 nn Nucleate Bahng 400 -- Configuration 1
'{-~~+--~~---~~-- 4 sonag c,mi.
- a - 560 nn Nuckme Somng x $60 an Nuchme Bomng 0 20 40 60 80 100 Angle (degrees)
Figure E.12. Collective presentation of all critical heat flux data in both Configuration I and Configuration II experiments in ULPU-2000. The line shown for Configuration II is Eq. (E.3). ne B.C. points at 6 ~ 0' have been displaced to the right for clarity of presentation. l E.2-18 I
, APPENDIX E.3 I CRITICAL HEAT FLUX SENSITIVITY TO FLUX l SHAPES AND RECIRCULATION FLOW RATES 1 e E.3-1 V i
s i L APPENDIX E.3 r CRITICAL HEAT FLUX SENSITIVITY TO FLUX SHAPES AND RECIRCULATION FLOW RATES f A new series of experiments was carried out in ULPU, to examine sensitivity of the critical [ heat fluxes to the flux shape and the natural circulation flow rates. The experimental facilitity was in Configuration II, as described in Appendix E.2, except for increasing the power control resolution (by adding relays to the control circuit) to 48 zones. In the runs described here L each zone corresponds to an are length of 1.875*. We have also changed the nomenclature; now, the zone numbers begin at 0* and increase with angular position, so that zone 0 is over ( l O' < 6 < 1.875* and zone 48 over 88.125' < 6 < 90'. ( Flux shape sensitivity is examined using, besides the base case flux shape shown in Figure E.1 (note that it is somewhat different from the shape used in Appendix E.2, as illustrated in the same figure as the "old shape"), several variations around it, as well as shapes associated with the parametric cases considered for the reactor. Flow rate sensitivity studies were carried out by throttling the downcomer so as to obtain about 60 gym, or about half the flow normally obtained (~130 gpm) with the flow path completely open. In addition, the case of zero flow was examined by letting the level drop sufficiently so as to interrupt the natural circulation flow path. 1000 , . , , New Shape Old Shape - 800 - N E : : N _ g 600 - -
- l :
x _ _
.3 - -
I h 400 - - y
~
U - Z . 200 - - I I l I _o . . . , . . . . , , . , , , , . , ,
-0 20 40 60 80 l Angle (degrees) l Figure E.1. The presently used base case flux shape in relation to that used in Appendix E.2.
\ l E.3-3 l - _ _ . _ . - _ _ .
1 I The experimental matrix is summarized in Table E.1, together with the resulting CHF values. The second column indicates the origin of the reference flux shape used in each case. The actual flux shapes used am shown, together with the shapes that would be required according to the power shaping principle, in Figures E.2 through E.19. l The results are shown in graphical form in Figures E.20 and E.21. Figure E.20 contains the comparison between all present full-flow data with the CHF correlation obtained in Appendix E.2. This figure shows that the correlation represents a robust lower envelope even under some not insignificant variations of the heat flux shapes. But this figure also shows that there is l a significant additional tolerance to CHF under a strongly peaked heat flux at the top. The sensitivity to the flow rate can be seen in Figure E.21. It is very interesting that the zero flow case produces a negative effect only near the top and even then, it is only a ~20% reduction. g Note that the zero flow case in effect eliminates the cavity subcooling as it is operated under a m significantly lower water level (~2.0 m vs 5.6 m from the bottom of the lower head). These results indicate that simply immersing the lower head of the AP600 would be sufBcient to remove the thermalloads from a base-case-like scenario with very signincant margins. I I I I I I l I l E.3-4 I l l I
r [ Table E.1. Sununary Of The ULPU (Configuration II) Experimental Program on Flux Shape and Recirculation Flow Effects ID Reference
- Maximum Flow
{ Number" Shape CHF Medium Flow No Flow Angular Position CHF CHF (Actual)" (kWhn2 ) (kW/m2 ) (kWhn2 ) (') ( L ZOOA Figure Q.1 508 545 0 564 0 658 0 (200B) 498 0(6) ( (ZOOC) 602
$64 0 0
j 1 208B Figure 0.1 718 649 15 8 770 15 d Z14A Figure Q.1 902 866 26 902 26 Zl9B Figure Q.1 1125 1005 37 [ 1139 37 1072 37 (Zl9C) 1072 991 37 I Z24A Figure Q.1 1205 1096 45 1191 1083 45 1151 45 1042 45 L (Z24B) 1179 45 (Z24C) 1228 45 Z30A Figure Q.1 1116 1064 56 l 1104 56 Z35A Figure Q.1 1263 1190 66 1263 66 r 1255 66 L Z35C Figure 7.16 1340 66 (Z40A) 1186 75(90) g 1318 75(80) i 1340 75 Z40B Figure Q.1 1489 1370 75 (240C) 1310 75(85) Z42A Figure 7.15 1523 78 48A Eq. (5.30) 1480 1263 90 1622 90 f 1118 90 L Z48B Eq.(5.30) with cut 1353 90
- Flux shapes based on calculated reactor shapes, as follows:
{ e Normal print number. Base case calculation as in Figure Q.l. e Number in parenthesis. Sensitivity variations around the base case. e Number in bold print. Parametric cases examined for the reactor.
'The number indicates the zone number at which CHF is being simulated. Total 48 equal size zones starting with zone 0 at O' and ending with zone 48 at 90'.
% actual boiling crisis position is shown in parenthesis when it is different from the expected one.
E.3-5 {
8, , , , , , , , , , , , , , , , ,
- l ,, l
............... Prineiple (15) / i' ,<
E Experiment 3
~
Real Heat Flux -
' is... ' ' -
3 6 - Q ~
,l -
,o ..
u . a '
.m
..- . m a 4
,i- _ g M l -
o s==4 / A - i
/ -
a -
/ -
@ 2 -
x - g.. - . . . . . . . . " , . . -
' I. I
~
- ' ' I - I l
-0 - - - - - - . . . .
-0 20 40 60 80 Angle (Degrees)
Figure E.2. The actual input and delivered flux shapes in comparison to that obtained from the I power shaping principle for run 200A. 8 , ,., , , , . . . . i . . . , . i i g ,, j
'9 \
............... Prineiple (15) , t, ,.#
Experiment
,- i c ,
- \..
.3 6 -
1 "p _
,a.
- 4 -
a 4 t .m- ..- Q 4 - x ! p -
.,/ -
- a k ,' -
a ; - l c 2 - .. ' v ' _ --- .77.;,. .,.. . . . . . . . . . . .
-0
' ' ' I ' ' ' ' I ' ' ' ' I ' '
-0 20 40 60 80 Angle (Degrees)
Figure E.3. The actual input and delivered flux shapes in comparison to that obtained from the I power shaping principle for run Z00B. E.3 6 I
[ 8 , , , , , , , , , , , , , , , , , , [ - Principle (15)
/\
Experiment
/ j
c ,- i [ .3 o p 6 -
,i \ ... ... . - .
.o u
a
.n O 4 -
s- - x - l - Q - l . C - j o - c . [ a 2 - x -
....-.....,..) ,., ,,,,,.............. .
,..< \3.. . .- ", _
I
-o ' ' ' ' ' ' ' I ' ' ' ' I ' ' ' ' I ' '
-o 20 40 60 80
( Angle (Degrees) Figure E.4. The actualinput and delivered flux shapes in comparison to that obtained from the ( power shaping principle for run 200C. 8 , , , , , , , , , , , , , , , ,
- 4 Principle /i Experiment / \
@ Real Heat Flux ,-
i ,,.... - - ! .- 6 u a , y -
.o, -
a
.u -
t
,g -
p 4 - g - 0., l . w - l . a - l M ' 2 [
,/ -
x - 1 [ _o
-_ g,,,l ,
, , , , I , , , , I , , , , l , .
-0 20 40 60 80
( Angle (Degrees) { Figure E.5 The actual input and delivered flux shapes in comparison to that obtained from the power shaping principle for run 208B. E.3-7 [
?
i I 6 , , ,
, , , , , i g j
. . . . . . . . . . . . . Principle ,4, -
Experiment ,/ i Real Heat Flux ,' , i , 3 ,/ \ , ... , .
,$ 4 -
,-, 3 C .- .
a
.5 _ ..-
- g A _
. 5 M ,
y . i -
~
A 2 -
/
a , d - / o / - Z -
.4.,
, . ..e
, , I , , , , I , , , , I , , , , l , .
_g ,
-0 20 40 60 80 Angle (Degrees)
Figure E.6. The actual input and delivered flux shapes in comparison to that obtained from the I power shaping principle for run Z14A. g g I 3 - --- Principle , . '<I -
- Experiment ,/ \ ,_
Real Heat Flux ,f" i .. , ' ,
,i t . ..
3 - p
,o -
..s' .
.b 2 -
.en a - ,-
x ,- Q - l k - l 4 c o 1 Z - -
.s
* ' ' I ' ' ' ' l ' ' ' - I ' ' ' ' l ' '
-0
-0 20 40 60 80 Angle (Degrees)
Figure E.7. The actual input and delivered flux shapes in comparison to that obtained from the power shaping principle for run Z19C. E.3 8 I
[ j ; [ 3 -
------ Principle ,./\ -
Experiment ,/ \, ,<. c [ y o .
,/
,/ i
\,.****..,,..- .
y -
.o
,s'
[ b 2 -
.D .
o ,....- . x ' [ y .
,i k -
/ -
4 1 - (G a/.,' ym.:,*... [- g . s- 1 _ J' '
,.e,.<J _
... * ~'~; ' ' ' ; ' ' ' ; ' ' ' ; '
-0 ' ' ' '
-0 20 40 60 80 Angle (Degrees)
Figure E.8. The actual input and delivered flux shapes in comparison to that obtained trom une ( power shaping principle for run Z19B. 2.0 , , , , , , , , , , , , , , , , , ,
. I I l l _
.......... - Principle Experiment -
f Real Heat Flux ,/\ ' - L . 1.5 -
/ i "m .
.- \, ..... -... r
.a
[ b -
,g .
m 1.0 f g ; ... ,... ', - e.. . .. , - x . Q . . l . . C , l ' a - l . [ @ 0.5 - i ,.< - l Z -
.l' i
.r 1 1
. 1
_o,o , , ! , , , , I , , , , I , , ,,I , , p -0 20 40 60 80 L Angle (Degrees) Figure E.9. The actual input and delivered flux shapes in comparison to that obtained from the ( power shaping principle for run Z24A. E.3-9 [. W
2.0 , , , , , , , , , , , , , , , ,
- ~
.............- Prin eipl e Experiment
~
Real Heat Flux
' ~
@ fi 1.5 , .
a 1 m -
\...,_.....'
,o .
3 .
.g -
p 1,0 - g -
. / \, . ' -
p .
,.. l .
C -
/
s .
- / .
8 0.5 - 2 -
' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' '
-- 0. 0
-0 20 40 60 80 Angle (Degrees)
Figure E.10. The actual input and delivered flux shapes in comparison to that obtained from the power shaping principle for run Z24B. 2.0 , , , , j
; j _
~
............... Prin eiple ~
Experiment . Real Heat Flux ~
@ fi
~'
1.5 , . .
,o p
.b
,9 .
p 1,o - e..... ,.. x -
/ \,, : ' -
0 j l E !
/ .
a ; . 0.5 ,' m . l o,o
-0 20 40 l , , , ,
60
! , , , , I 80 l
Angle (Degrees) Figure E.11. The actual input and delivered flux shapes in comparison to that obtained from the power shaping principle for run Z24C. E.3-10 l 1 l ? _____.-.____ - - __ _ __.
[ 1.5 , , , , , , , , , , , , , , g g Principie . Experiment .<
@ Real Heat Flux ,,f' ,i
{ - - h 1.0 - r.- - - fm - 7..)'\i.;.*'. ' . . - t.. - p . A 0.5 - a g - o y . I
- 0.0 ' ' ' ' ' ' I ' ' ' ' ! ' ' ' ' I '
( -0 20 40 60 80 L Angle (Degrees) - Figure E.12. The actual input and delivered flux shapes in comparison to that obtained from the [ power shaping principle for run Z30A. 1.5 , , , , , , , , , , , , , , , , , , L _ ......... .. Principle .
~
Experirnent [ @ Real Heat Flux - 3 l j h
,m 1.0
\,..
.', \, *
\ ,_.....'.
o - M Q . N 0.5 - a e - - v _ Z - - a0
-0.0 ' ' ' ' ' ' ! ' ' I ' ' ' ' ! ' '
-0 20 40 60 80 Angle (Degrees)
Figure E.13. The actual input and delivered flux shapes in comparison to that obtained from the { power shaping principle for run Z35A. E.3-11
1.0 , , , , , , , , g ,.f, t ! -
'--~~"~.....-
..... ........ .. Pri n cip t e I -
Experirnent ! c 0.8 - Real Heat flux l E O - ,
*y - i..e - -
0 - A .. 3 0.6 - - 5 : : x - j. - D 0.4 - J. g - a .- cg Z 0.2 -
~ '
' ' ' ' ' I ' ' ' ' I ' ' ' ' I ' '
- 0.0
-0 20 40 60 80 Angle (Degrees)
Figure E.14. The actual input and delivered flux shapes in comparison to that obtained from the power shaping principle for run Z35C. 1.0 , , , , I l . -
....... ..... Prin ciple j -
Experirnent t C 0.8 - Real Heat Flux - O - - p t p - I - p - i'. ' -
~
'C 0.6 - \
l I %.-
\:.... .... . 4 -
O - - x - ! c 0.4 - - l t [ - cp - Z 0.2 - l $ - r
~ ~
' ' ' I ' ' ' I I
- 0.0 - ' ' ' ' ' ' ' ' ' '
l l
-0 20 40 60 80 l Angle (Degrees) l Figure E.15. The actual input and delivered flux shapes in comparison to that obtained from the power shaping pdnciple for run Z40A.
E.3-12
L 1.0 , , , , , , , , , , , ,
,,. ,, ,. g
. ............ Principt e j Experiment -
g 0.8 - Real Heat Flux - a - U -
.c
- t. . '
t
'r t 3 0.6 -
; A
.m C4 i....,.,,.. -
I H - L J 0.4 - g . . g . - y . m 0.2 [ _o,o < , , , , , I , , , , I , , , , I . . g -0 20 40 60 80 L Angle (Degrees) g Figure E.16. The actual input and delivered flux shapes in comparison to that obtained from the L Power shaping principle for run Z40B. 1.0 , , , , , , , , , , , , , , _ ; ; ; , i,.. .; ; _ L -
............... Prin ciple
. ~ l' -
j - Experirnent t :.., r C 0.8 - Real Heat Flux - i L .2 s U -
.,.' I -
~ Ja .
.) t .
C o,e _ m i ,e y . , lt . . ,, ' C3 _ , x - L 2 0.4 - g _ g . Z 0.2 - { l
~
_ g,g . . . . , , , 1 , . . . I . , , . I . .
-0 20 40 60 80 Angle (Degrees)
Figure E.17. The actual input and delivered flux shapes in comparison to that obtained from the [ power shaping principle for run Z40C. E.3-13 [
I 1.0 , , , , , , , , , , , , , , , _ ; l g p ,., j; ; ,. 3 ,
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Figure E.19. The actual input and delivered flux shapes in comparison to that obtained from the power shaping principle for run Z48A. E.3-14
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[ ; i l 400 - -- '- r 1 i . 0 O 20 40 60 80 100 Angle (degrees) r Figure E.20. Comparison of all present full flow data with the correlation in Appendix E.2. The L open circles are for flux, a shape representative of the Extreme Parametric (discontinuous, high peak at the top). r L 2000 , e 130 GPM 1600 C 60 GPM - S .. .. X OGPM 3
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l I (( APPENDIX E.4]} ULPU CONFIGURATION III RESULTS 1 l 1 E.4-1
(( APPENDIX E.4)) ULPU CONFIGURATION III RESULTS The Configuration III specifications as shown in Figure E.1 were obtained from Figure K.3a. He baffle simulating the lower part of the reflective insulation was introduced such as to allow the minimum clearance of 9" (22.86 cm) at an angular position of 30' The riser is 15.24 cm in diameter as compared to the 15 cm annular gap allowed around the reactor vessel by the insulation. Finally, an exit restriction (10 cm diameter) was introduced as shown to reduce the flow area down to ~40% of that available in the riser (as in the case for the reactor). Dese riser and restriction dimensions correspond well to the prorated values based on the minimum simulated circumferential fraction in ULPU. This minimum is obtained for a matching angle of 90' and corresponds to 1.2% of the reactor circumference. The riser and restriction areas then become 220 cm2 and 84 cm2 respectively, with equivalent diameters of 16.7 cm and 10 cm respectively. Two sets of experiments were performed: the first focusing on the effect of changes in flow i geometry (baffle and exit restriction), and the second on the combined affect (of this change) with heater material and surface. In particular, for the second set the heater block was constructed from prototypic A508 ASTM standard class 3 steel, purchased from one of the potential suppliers of the AP600 reactor vessel (Japan Steel Works, Hokkaido). Half of the block surface was left as bare steel, while the other half (15* < 6 < 30') was painted with the paint normally employed to protect the vessel material (a Carboline G6504L paint employed at a thickness of 0.002 0.001 inch or 0.05 mm 0.025 mm). The paint was cured at 450 *F (232 *C) for 3 to 4 hrs, prior to installation. Contrary to what we were able to learn prior to the actual use of it, this paint appears to bond very well, creating a highly tenacious coating even under prolonged boiling and successive boiling crisis events. Sample microphotographs of the surfaces of all tluce materials-copper, steel, and Carboline paint on steel, after use in ULPU-are shown in Figures E.2 through E.4. The results are compared to Eq. (E.1)- This is Eq. (E.3) of Appendix E.2)-in Figure E.5. l 2 ger(6) = 490 + 30.26 - 8.88 10-26 + 1.35 10-86' - 6.65 10-864 kW/m 2 (E.1) The copper data were obtained with the first heater block (0* < 6 < 30') in a " fresh" condition (cleaned to a fine polish), while the other two blocks were fully aged from the exper-iments reported in Appendix E.3. The power shapes were based on the base case simulations as described in Appendix E.3. The new geometry can be seen to clearly enhance the CHF E.4-3
I I I I I Vent Spray q Exit Restriction H Condenser
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Figure E.2. Microphotographs of the copper heater surface, after exposure in the ULPU tests described in this appendix. Magnifications of 10X and 63X at top and bottom mspectively. E.4-5
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f i l I I E i I i i 2000
- Eq.(E.1) 4 O Steel / Paint Nucleate Boiling g 1600 -
l i N g S Copper Boiling Crisis l i s it, 1200 - l- ~ g f g-
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[ performance. For position 6 = 0' the enhancement is in that the geometry effect is seen to just [ about compensate for the fresh surface effect, which for copper, as explained in Appendix E.2, is rather significant. I 'Ihe steel data were obtained with the heater block at the low position (0* < 6 < 30'), as it is here that surface / material effects would appear first, if at all. All three data points in Figure [ E.5 are shown as nucleate boiling fluxes, because boiling crisis was not obtained for any of them. The reason is experimental difficulties due to the relatively lower thermal conductivity of steel compared to copper; at high fluxes this causes problems with gasket integrity. This will be { overcome in the future, but it did provide a limitation within the tight schedule of completing this appendix in the course of the review. Thus, we began with position 6 = 0* (flux shape shown in Figure E.2 of Appendix E.3), and stopped the power ascension (to conserve the gaskets) as soon as the confirmatory level of heat flux (compared to Eq. E.1) was reached. We then moved ( to position 6 = 22' < 6 < 28' with the flux shape shown in Figure E.6 of Appendix E.3. Power was increased until the gaskets failed, at which point we had to abandon the test. Fortunately, as [ seen in Figure E.5, this occurred quite close to the target values (Eq. E.1), thus the confirmatory nature of this test can be considered basically completed. Further elaboration can be expected from our ongoing experimental and analytical efforts aimed at the fundamental mechanism and [ prediction. r L r t L L I ( L I L [ E.4-9 L f ?
APPENDIX F THE CYBL EXPERIMENTS Ex-Vessel Boiling Experiments-Laboratory and Reactor Scale Testing of the Flooded Cavity Concept for In-Vessel Core Retention l Part I: Observations of Quenching of Downward-Facing Surfaces Part II: Reactor-Scale Boiling Experiments o'f the Flooded Cavity l Concept for In-Vessel Core Retention Proceedings, Workshop on Large Molten Pool Heat "IYansfer Grenoble, France,9-11 March 1994 . F-1
[ APPENDIX F Ex-Vessel Boiling Experirnents-Laboratory and Reactor Scale Testing of the Flooded Cavity Concept for In-Vessel Core Retention Part I: Observations of Quenching of Downward-Facing Surfaces T.Y. Chu, B.L. Bainbridge, R.B. Sirnpson, and J.H. Bentz Sandia National Laboratories Albuquerque, New Mexico Part II: [ Reactor-Scale Boiling Experiments of the Flooded Cavity Concept for In-Vessel Core Retention g T. Y. Chu, J. H. Bentz, and S. E. Slezak L Sandia National Laboratories and Walter F. Pasedag, USDOE { ABSTRACT F L Flooding a reactor cavity and immersing the reactor pressure vessel in water to extract [ decay heat from core debris following a severe accident is appealing as a safety feature. A flooded cavity is an accident management concept currently under consideration for r advanced light water reactors (ALWRs) as well as for existing light water reactors " (LWRs). It was also implemented in the design of the now deferred Heavy Water New Production Reactor (HWR NPR). One of the uncertainties in the evaluation of the flooded cavity concept arises from the uncertainties in the boiling heat transfer outside of the reactor pressure vessel (RPV) bottom head. Because of the upside-l down geometry, the vapor generated in boiling cannot readily move away from the hot surface; rather, it must flow along the surface to the edge before it is released into the bulk liquid. Based on two-phase boundary analysis, it can be shown that the heat transfer process could be scale dependent. 'Ihe present paper presents the results of two g experimental studies of the ex vessel boiling process. The first experiment, presented in past 1, Observations of Quenching of Downward-Facing Surfaces, summarizes the results of a series of quenching experiments to examine the boiling curve of relative L large (comparing to existing experimental studies) downward-facing surfaces. The critical heat flux was found to be approximately 50 W/cm2 . The nucleate boiling { precess was found to be cyclic in nature. The second experiment, presented in Part II, F-3 E L
I Reactor-Scale Boiling Experiments of the Flooded Cavity Concept for In- Vessel Core Retention, summarizes results of reactor-scale ex-vessel boiling experiments performed in the CYBL facility. Experiments with uniform and edge-peaked heat flux distributions up to 20 W/cm 2across the vessel bottom were performed. Boiling outside the reactor vessel was found to be subcooled nucleate boiling. The subcooling is mainly due to the gravity head which results from flooding the sides of the reactor vessel. The boiling process exhibits a cyclic pattern with four distinct phases: direct liquid / solid contact, E bubble nucleation and growth, coalescence, and vapor mass dispersion (ejection). The 5 results suggest that under prototypic heat load and heat flux distributions, the flooded cavity in a passive pressurized water reactor like the AP-600 should be capable of cooling the reactor pressure vessel in the central region of the lower head that is addressed by these tests. I I I I I I Il . F-4 l l
[ PART Ir OBSERVATIONS OF QUENCHING OF DOWNWARD-FACING SURFACES T.Y. Chu, B.L. Bainbridge, R.B. Simpson and J.H. Bents c F.
1.0 INTRODUCTION
The design of the Heavy Water New Production Reactor (HWR NPR) as well as the Ad-vanced Light Water Reactor (ALWR) incorporate a flooded reactor cavity as an accident man-agement feature to prevent melt-through of the reactor vessel in the event of a core meltdown accident. It is expected that boiling heat transfer on the outer surface of the bottom head will remove the decay heat from the molten core. One of the uncertainties in the evaluation of the flooded cavity concept arises from the uncertainties in the boiling heat transfer outside of the reactor pressure vessel (RPV) bottom head. Because of the upside-down geometry, the vapor I generated in boiling cannot readily move away from the hot surface; rather, it must flow along the surface to the edge before it is released into the bulk liquid. L nere is experimental evidence that the boiling process depends on both surface inclination (Nishikawa et al.,1984; Guo and El Genk,1991) and scale (Babin et al.,1990). According 2 [ to the classical study of Nishikawa et al. (1984), at low heat fluxes (< 7 W/cm ) increasing (toward horizontal) surface inclination was found to increase the effectiveness of heat transfer, E but the surface inclination effect diminishes at high heat fluxes (> 17 W/cm2 ). Other studies tend to confirm this general trend (Chen,1978; Guo and El-Genk,1991). Despite the observed near independence of nucleate boiling from inclination for downward-facing surfaces at high heat fluxes, critical heat flux (CHF) was found to decrease monotonically with inclination (Guo and El-Genk,1991, Vishnev et al.,1976; Beduz et al.,1988). The 7 deterioration of CHF accelerates as the surface inclination approaches horizontally downwani-facing. Anderson and Bova (1971) obtained boiling curves for downward-facing circular disks L with diameters ranging from 5 cm to 30 cm in saturated R-11. They found that the critical heat flux varied inversely with the disk diameter. E L While the above mentioned small scale experiments show some alarming trends, recent , experiments give rather encouraging results. De integral experiments of Henry et al. (1993a) l L demonstrated that for highly subcooled water, nucleate boiling heat flux from a 30 cm diameter f curved surface exceeds 100 W/cm2 . Steady state experiments by neofanous et al. (1994), using I~ a section of a two-dimensional slice of an AP-600 like reactor vessel, showed that the critical L El-1 r l
)
1 J
heat flux from downward-facing surfaces in saturated water is in the range of 30 W/cm2 . This 2 value is quite favorable compared to the heat dissipation requirement of 10 20 W/cm for in-vessel core retention estimated by Henry et al. (1993a,b). l In the present study, quenching experiments have been performed to examine the boiling processes from downward-facing surfaces using two 61-centimeter diameter test masses, one with a flat test surface and one with a curved test surface having a radius of curvature of 335 cm, matching that of the Cylindrical Boiling (CYBL, See Part II) facility test vessel. He scale of the experiments is between that of reactor-scale and typical centimeter-scale bench experiments (Chu, et al.,1992,1993), but it is by far the largest experiment of boiling from downward-facing surfaces. Boiling curves were obtained for both test surfaces facing horizontally downward. The boiling process showed some unique features not observed in boiling from upward-facing surfaces. F.2.0 EXPERIMENTS g A series ofintermediate-scale quenching experiments was performed to examine the boiling E processes from downward-facing axisymmetric surfaces. These experiments were performed 3 as a presurser to the reactor-scale experiments that have recently been performed in Sandia's Cylindrical Boiling (CYBL) facility. Two test masses made of 6061 aluminum were used. They were made from 61 cm (24 in.) diameter stock approximately 10 cm (4 in.) thick. He first mass was a simple upright cylinder with a flat bottom (Figure E1). ne second mass was similar to the first, except that the bottom surface had a radius of curvature of 335 cm (132 in.) (Figure E1), matching the crown radius of the CYBL test vessel. He experimental masses were heated to an elevated temperature between 160'C and 330'C, and then plunged into a pool of water at saturation. The vertical surfaces and the top of the experimental masses were insulated to limit the boiling to only the downward-facing surfaces. Figure E2 shows how the masses were machined such that the VisiloxR silicone rubber insulating layers were set into the surface so that the test surface extended all the way to the edge of the test mass, and the two-phase flow across the test surface would not encounter an abrupt obstruction or change of material. l De test masses were instrumented with seven pairs of near-surface thermocouples. Each pair consisted of a thermocouple at a depth of 0.64 cm (0.25 in) and one at a depth at 1.27 cm (0.5 in). ne near-surface thermocouples were located at radii 1.27 cm (0.5 in) to 27.94 cm (11 in) as shown in Figures El and E2. The thermocouples used were type K,1.6 mm (1/16 in.) diameter stainless steel sheathed thermocouples with grounded junctions. These thermocouples l El-2 l I
were chosen because they will be used in the reactor-scale CYBL experiments. For ease of installation, the near-surface thermocouples were installed from the water side. Observations during the quenching experiments indicated that the presence of the thermocouples did not cause f significant disturbance to the overall characteristics of the boiling process. Here were also three thermocouples 1.27 cm (0.5 in) below the top surface of the test mass for interior temperature measurements. ; { he test surface was machined to a No. 32 rinish and then brushed with a fine steel brush. Figure F.3 shows the typical surface texture as machined and after brushing. To ensure identical { ~ starting conditions for each experiment, the surface finish was renewed before each experiment by brushing. Each mass was supported from above by a rod screwed into the top. The other end of the rod was connected to an air cylinder that allowed for vertical motion. The sample was first heated by six two-kilowatt cartridge heaters to the desired initial temperature. After a brief waiting period, when the temperatures were observed to equilibrate, the experiment was initiated by extending the air cylinder and plunging the mass into a test vessel filled with water. He test vessel was a Lexan 8 box,91 cm on each side. He box was filled with de-ionized water to a depth of 60 cm, and the test surface was immersed approximately 15 cm below the water surface. Two auxiliary heaters were used to keep the water at saturation. The [ 8 quenching process was videotaped through windows in the bottom and the side of the Lexan tank. A Hewlett Packard model 3852, 5-1/2 digit integrating analog-to-digital converter was [ used for data acquisition. The sampling interval was slightly under 0.5 seconds. F.3.0 EXPERIMENTAL OBSERVATIONS As a test mass is quenched from an elevated temperature it goes through film boiling, ' transition boiling, critical heat flux, and finally nucleate boiling. r he liquid / vapor interface during film boiling appears to be relatively stable. The surface can best be described as a visually smooth film with superimposed small amplitude waves, as shown in Figure F.4. The initiation of transition boiling from film boiling is signaled by the appearance of groups of bulges in the vapor film moving around the edge of the test surface. Eventually, the number and locations of bulges around the edge increase, and the bulges move I inward to extend across the entire surface. { l
'IYansition boiling is characterized by intermittent direct liquid / solid contacts and a lig- J uid/ vapor interface with growing and receding bulges, as shown in Figures F.4 and F.5. Over time, the interface appears to have a rather uniform appearance. He typical dimension of bulges is of the order of I cm. De intermittent solid / liquid contacts appear as swirling clouds moving F.1-3
I' around the surface. The cloudy appearance is probably associated with the rapid vaporization at the contact sites. As the mass cools further, the critical heat flux (CHF) is reached. The CHF regime is characterized by cyclic explosive vaporization. Shown in Figum F.6 is one such cycle. The cycle starts with a surface covered completely with a vapor film. A small indentation appears in the film probably leading to direct liquid / solid contact. This initial disturbance results in an ever expanding circular region of intense vaporization. As the circular region expands, the vapor film outside of the circle is pushed beyond the edge and released into the bulk liquid. As shown in the side-view in Figure F.7, the vapor mass extends as much as five centimeters away from the g surface. The periods of this cyclic event for the flat specimen and the curved specimen are 0.29 m and 0.27 seconds, respectively. In time, the explosions become less intense and less far-reaching. While the vapor film thickness still undulates, the amplitude becomes much less. Subsequently, the mass enters the nucleate boiling regime. Visual observation indicates that nucleate boiling from downward-facing surfaces is a cyclic process. Starting with direct liquid / solid contact, bubbles nucleate at various sites. These bubbles grow and coalesce into larger bubbles (Figures F.4 and F.8). For the flat surface at high heat fluxes (q > 10 W/cm ),2 the coalescence phase ends with nearly the entire surface covered with one single vapor mass. At high heat fluxes, the ejection phase is vigorous and chaotic. The large single vapor mass may break into several pieces and slide off the surface in several directions or shed away as a l single entity. However, over time, the process appears to be quite rhythmic and the directions in which the vapor masses leave appear to be random. At high heat fluxes, nucleation takes place g immediately at the freshly exposed surfaces left by the shedding fragments of the large vapor 3 mass. Therefore, the ejection phase of the first cycle and the growth phase of the second cycle actually overlap in time; the surface is partly covered by large retreating vapor masses of the first generation and the new bubbles of the second generation nucleating and growing in between the retmating large vapor masses (Figure F.9). At intermediate heat fluxes (3 W/cm2 < q < 10 W/cm 2) bubbles do not always grow to cover the entire surface before the ejection phase (Figure F.10). For low heat fluxes (q < 3 W/cm ),2 the nucleation sites become far apart and bubble coalescence becomes increasingly local in scale. Eventually, at lower heat fluxes, the surface is 1 covered with a few growing bubbles lumbering toward the edge of the surface with a significant portion of the surface in dimet contact with the bulk liquid. For the curved surface, the cyclic process still applies. However, as a result of the geometry the shedding of the vapor masses from the surface is more regular, always taking a more or less radial direction, especially at , lower heat fluxes. It is also interesting to note, for the curved surface at low heat fluxes, the F.1-4 I
l l b , bubbles take a crescent shape as they move toward the edge of the surface, as shown in Figure F.10. He thermocouple data are processed with an inverse conduction code SODDIT (Blackwell et al.,1987) to obtain boiling curves. SODDIT is a finite difference code that can be used to solve one and quasi two-dimensional direct and inverse heat conduction problems. When solving inverse problems, the unknown surface heat flux is calculated by minimization of the squared error between the temperatures measured at specified locations and the corresponding computed { temperatures. In addition, mom than one future time can be used in the heat flux calculation to reduce the effect of measurement error and noise. During preliminary experiments, it was discovered that while the cooling rates over the test { surface were masonably uniform during film boiling; the rates started to diverge considerably as transition boiling approached. Transition boiling occurred first near the edge of the test surface and moved inward. Therefore, the heat transfer within the mass became multi-dimensional. As a result, different locations on the surface underwent critical heat flux at different times, making it highly inaccurate to use the SODDIT code to calculate the surface flux. However, if the initial temperature wem in the range of transition boiling, the temperature msponse over the surface became nearly uniform. This is probably mlated to the nearly uniform appearance of the surface l during transition boiling (Figure F.5). Themfere, two sets of experiments were performed. High temperature quench from 330 C was used to obtain the film boiling to transition boiling portion p L~ of the boiling curve, and low temperature quench from 160 C to 170 C was used to obtain the transition boiling to nucleate boiling portion of the curve. l i E L A composite boiling curve for the flat specimen from thn:e low temperature quench exper-iments and one high temperature quench experiment is shown in Figure F.ll. The critical heat flux is found to be between 40-60 W/cm 2; the corresponding superheat is approximately 30 C. The spn:ad of the data represents an experimental uncertainty of approximately 20%. This [ critical heat flux is higher than those reported for previous experiments using 15-m test masses (Chu et al.1992b). We feel that the previous results are in error because data rates were too low, and - ; quenclag; curve failed to resolve the high cooling rates associated with the critical heat flux. The present CHF values am also higher than those obtained by Guo and El-Genk (1991) quenching a 50 mm copper disk. We believe the Guo and El-Genk CHF value is low because of the effect of the insulation rim around their quenching specimen. As shown in Ishigai et al. (1961) experiments, the CHF value decmases by almost a factor of two with the size of the insulating rim around the Guo and El-Genk test specimen. He 10*C superheat corresponding 10 W/cm2is in good agreement with previous quenching experiments (Chu et al.,1992b) as well as the results of Nishikawa et al. (1984) and Guo and El-5
El-Genk (1991). A boiling curve is also calculated for the curved specimen (Figure F.12). The critical heat flux is essentially the same as that for the flat surface. He nucleate boiling portion of the curve is slightly below that for the flat surface. This is consistent with previously observed l trends of the effects (Nishikawa, et al.,1984, Guo and El-Genk 1991) of surface inclination. It is interesting to note that there appears to be a rather distinct change of slope of the boiling curve near 10 W/cm2 . His transition is analogous to the transition from the isolated bubble regime to that of slugs and columns for upwani-facing surfaces, as first pointed out by Lienhard (1985). As described earlier, for heat flux less than 10 W/cm2 , the bubbles do not always grow large enough to coalesce into a large vapor mass to cover the entire surface before the ejection phase. But for higher heat fluxes, the ejection phase is always associated with a surface-size vapor mass. There are also changes in the rhythmic / cyclic behavior of the boiling g process associated with the transition. The general trend is for the cycle period to increase (as 3 well as the nucleation site density to decrease) with decreasing heat flux. Between critical heat 2 flux and 10 W/cm 2, the cycle time increased by about 17%. Whereas, between 10 W/cm and l 2 5 W/cm , the cycle time increased by more than 30%. F.4.0 CONCLUDING REMARKS Quenching experiments have been performed to examine the boiling processes from downward-facing surfaces using two 61-centimeter diameter test masses, one with a flat test surface and one with a curved test surface having a radius of curvature of 335 cm. Boiling curves were obtained for both test surfaces facing horizontally downward. The critical heat flux was found to be essentially the same, having an average value of approximately 50 W/cm'. This value, while smaller than the accepted value of CHF for upward-facing surfaces (typically 100-130 W/cm 2), is larger than those obtained from correlations derived from smaller scale experiments (Guo and El Genk,1991; Vishney et al.,1976). He critical heat flux is significantly higher than the estimated heat fluxes required for in-vessel core retention for the HWR NPR (Jedruch,1992) 2 2 and for light water reactors (Henry, et al.,1993a,b); those values are 16 W/cm and 20 W/cm , respectively. De liquid / vapor interface during film boiling appears to be relatively stable. The traveling g bubble pattern observed by Bui and Dhir (1985) on vertical surfaces was not observed. He 3 , liquid / vapor interface can best be described as a visually smooth film with superimposed small amplitude waves. Wansition boiling is characterized by intermittent direct liquid / solid contacts and a lig-uid/ vapor interface with growing and receding bulges. Over time, the interface appears to have a rather uniform appearance. The typical dimension of bulges is of the order of I cm. El-6 I 1
t De critical heat flux regime is characterized by cyclic explosive vaporization with circular expansion pattems. He periods of this cyclic event for the flat specimen and the curved specimen are 0.29 and 0.27 seconds, respectively. b The nucleate boiling process is found to be cyclic with four relatively distinct phases: direct liquid / solid contact, nucleadon and growth of bubbles, coalescence, and ejection. De general trend is for the cycle time to increase with decreasing heat flux. { Traditionally, experiments aimed at investigating basic mechanisms of boiling and theoret-ical treatments of boiling have concentrated on upward-facing flat surfa:es. Other geometries { have been treated as extensions of upward-facing surfaces. However, the current experiments re-veal rather unique flow patterns compared to those observed from upward-facing surfaces. While [ there are similarities in the initial nucleation and growth of bubbles, there appear to be substan-tial differences in the mechanisms of late-phase growth, coalescence and detachment of vapor p masses in the nucleate boiling regime, and in the appearance of near surface two-phase flow, approaching CHF. Although many of the key mechanisms of the current hydrodynamic stability based theory of CHF are not operational in downward-facing boiling, both boiling processes generate the characteristic boiling curve. It is appropriate to recall a recent lecture by Bergles (1992): " nucleate boiling still defies accurate prediction [and] ...there is a lack of agreement on the mechanism of critical heat flux." He present observations, although qualitative, suggest ' that perhaps by examining upward-facing and downward facing boiling in parallel experiments, it would be possible to single out a common set of mechanisms that give rise to the boiling L curve. These mechanisms can then be considered necessary and sufficient to build a mechanistic model of boiling. I~ L F.
5.0 REFERENCES
I Anderson, R. P., and L. Bova,1971, "The Role of Dowfacing Burnout in Post-Accident Heat Removal," Trans. Am. Nucl. Soc., Vol.14, p. 294. Babin, B. R., W. Linear, and G. P. Peterson, (1990), " Cooling Electronic Component with Hermosyphons," Thermal Modeling and Design of Electronic Systems and Devices, HTD-vol. 153, ASME, New York, N.Y., pp. 89-94. Beduz, C., R. G. Scurlock, and A. J. Sousa,1988," Angular Dependence of Boiling Heat Trans-fer Mechanisms in Liquid Nitrogen," Advances in Cryogenic Engineering. Vol. 33, pp. 363-370. Bergies, A. E.,1992, "What are the Real Mechanisms in Pool Boiling?" Pool and External Flow Boiling, Eds., V. K. Dhir and A. E. Bergies, ASME, New York, NY. Blackwell, B. E R. W. Douglass, and H. Wolf,1987, A User's Manual for the Sandia One-pimensional Direct and Inverse hermal (SODDIT) Code, SAND 85-2478, Sandia National Lab-oratories, Albuquerque, NM. F.1-7
I Bul, T. D., and V. K. Dhir,1985," Film Boiling Heat Transfer on an Isothennal Vertical Surface," J. Heat Trans., Vol.107, pp. 764-771. Chu, T. Y., R. C. Dykhuizen, and C. E. Hickox,1993, Scoping Studies of Boiling Phenomena Associated with the Flooded Cavity Design of the Heavy Water New Production Reactor, SAND 912383, NPRW-SA01-7, Sandia National Laboratories, Albuquentue, NM. l Chu, T. Y., R. C. Dykhuizen, and C. E. Hickox and B. L. Bainbridge,1992, " Boiling from Downward Facing Surfaces with Applications to Ci: Flooded Cavity Concept," ANS Proceedings, 1992 National Heat Transfer Conference, San Diego, CA, HTC-Vol. 6, pp. 367-375. Guo, Z., and M. S. El-Genk,1991, "An Experimental Study of the Effect of Surface Orienta-tion on Boiling Heat Transfer During Quenching," Proceedings ASME Winter Annual Meeting, Atlanta, GA, Dec. 2-5. Henry, R. E., J. P. Burelbach, R. T. Hammersley, C. E. Henry and G. T. Klopp,1993a, " Cool-ing of Com Debris within the Reactor Vessel Lower Head," Nuclear Techo9]pogy, Vol.101, pp. 385-399. Henry, R. E., H. K. Fauske,1993b, " External Cooling of a Reactor Vessel Under Severe Acci- E dent Conditions," Nuclear Engineering and Design, Vol.139, pp. 31-43. 3 Ishigai, S., K. Inoue, Z. Kiwaki, and T. Inai,1961, " Boiling Heat Transfer from a Flat Surface g Facing Downwani," Proceedings of International Heat Transfer Conference, Boulder, Colorado, 3 i 1961, p. 224-229. Jedruch, J.,1992, Post-Melt Heat Flux Estimate in 670 MWt NPR Lower RV Head, EBASCO Services Inc. Report, New York, NY. l Lienhard, J. H.,1985,"On the Two Regimes of Nucleate Boiling", J. Heat 'IYans., Vol.107, pp. ( 262-264. Nishikawa, K., Y. Fujita, S. Uchida, and H. Ohta,1984, "Effect of Configuration on Nucleate Boiling Heat Transfer," Int. J. Heat Mass Transfer, Vol. 27, pp.1559-1571. I Heofanous, T.G., S. Syri, T. Salmassi, O. Kymaltinen, and H. Tuomisto,1994, " Critical Heat Flux Through Curved, Downward Facing, Rick Walls," Proceedings, OECD/CSNI/NEA Work-shop on Large Molten Pool Heat Transfer, Nuclear Resean:h Center, Grenoble, France, March, 1994. Vishnev, I. P., I. A. Filatov, Y. A. G. Vinokur, V. V. Gorokhov, and V. V. Svalov,1976, " Study of Heat Transfer in Boiling of Helium on Surfaces With Various Orientations," Heat Transfer
- Soviet Research, Vol. 8, No. 4, pp.194-108.
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1 b PART II: REACTOR-SCALE BOILING EXPERIMENTS OF THE FLOODED CAVITY CONCEPT FOR IN-VESSEL CORE RETENTION T.Y. Chu, J.H. Bentz, S.E. Slezak and Walter F. Pasedag F.
1.0 INTRODUCTION
ne success or failure of in-vessel core retention has a profound effect on the progression { of severe accidents, and because engineering the capability to flood the reactor cavity can have a significant impact on plant design, it is essential that there be a solid technical understanding of reactor-scale, downward-facing boiling heat transfer before risk assessments or safety qual-ifications can credit a flooded cavity with ensuring in-vessel core retention (Okkonen,1994, Rouge and Seiler,1994). But with only small scale downward-facing boiling data (Chen,1978, Nishikawa, et al.,1984 Beduz, et al.,1987, and Guo and El-Genk,1991) and without a vali-dated analytical model to extrapolate existing data, reactor-scale testing is the only viable means for confirming the required heat transfer capability. For this reason, the Department of Energy (DOE) New Production Reactor (NPR) Program funded Sandia National Laboratories to develop a reactor-scale facility and to perform confirmatory testing of the effectiveness of boiling heat transfer of the flooded cavity design for the Heavy Water New Production Reactor (HWR-NPR). F L The facility is named CYBL, short for Cylindrical ]! oiling (facility). Despite the indefinite de-ferral of the HWR-NPR program, DOE continues to sponsor the CYBL testing program through E the Office of Nuclear Energy (DOE-NE) because of the value of a reactor-scale vessel cooling u demonstration for Advanced Light Water Reactor (ALWR) applications. [ Sandia has recently completed a series of tests for DOE-NE in support of the Advanced Reactor Severe Accident Program. The objectives of the present testing program are to conduct r tests which demonstrate the required cooling capability for the central, most downward-facing L region of the passive PWR lower head. Part II of the paper presents results of ex-vessel boiling experiments performed in the { CYBL facility. CYBL was developed as a reactor scale facility for confirmatory research of the flooded cavity concept for accident management. CYBL has a tank-within-a-tank design; the inner tank simulates the reactor vessel and the outer tank simulates the reactor cavity. Because the facility was initially developed for the NPR program, the test vessel head is torispherical L rather than hemispherical, to conform to the NPR design. Experiments with uniform and edge-peaked heat flux distributions up to 20 W/cm2 across the vessel bottom were performed. De edge-peaked heat flux distribution experiments are designed to examine the sensitivity of the E2-1
l I ex- vessel boiling process to a non-uniform heat flux distribution similar to the predicted edge-peaked distribution resulting from melt convection (O'Brien and Hawkes,1991, KymElHinen et al.,1993, and Asfia and Dhir,1994). He current estimated range of cooling requirements for l ' 2 the AP-600 reactor is 10-20 W/cm2 (Henry et al.,1993a,b). The target heat flux of 20 W/cm for the tests is based on providing d.ita at prototypic heat flux levels covering the uncertainty within the current cooling requirement estimates. He test planning included an evaluation of the fact that the CYBL vessel is datter at the bottom than the hemispherical bottom head typical g of many U.S. reactors. He general consensus from a workshop of experts held at Sandia in July 5 1993 is that CYBL results would be conservative when applied to surfaces with steeper angles of inclination (i.e., hemispherical heads will be more efficient in ex-vessel boiling as they curve l upward more rapidly). Heat transfer results including heat flux, surface temperature and bulk water temperature as well as observations of the characteristics of ex-vessel boiling are reported. The results l 1 suggest that under prototypic heat load and heat flux distributions, the flooded cavity in a passive pressurized water reactor like the AP-600 should be capable of cooling the reactor pressure vessel in the central region of the lower head that is addressed by these tests. l F.2.0 EXPERIMENT CYBL has a tank-within-a-tank design; the inner tank simulates the reactor pressure vessel, the outer tank simulates the reactor cavity (Figures Ela and Elb). He inner tank, made of 1.6-cm- thick 316 L stainless steel, is 3.7 m in diameter and 6.8 m high. The outer tank is 5.1 m in diameter and 8.4 m high, made of 0.95-cm-thick 316 L stainless steel. At present, the inner test tank has a torispherical head, but the test fixture is designed to accept a test vessel of any configuration with a diameter of 3.7 m or less. He present torispherical bottom has a crown l radius of 3.35 m and a knuckle radius of 0.66 m. He energy deposition on the bottom head is accomplished with an array of twenty radiant lamp panels. Each panel measures 0.3 m by 1.2 m, and consists of a flat aluminum reflector and two bus bars for installing up to sixty-three 480 V,6 kW linear quartz lamps. The reflector and the bus bars are water cooled. The panels are organized into twelve individually controlled g heating zones (Figure E2). Each numbered zone has two panels except the four panels (1,9,6, 3 and 12) on the outer rim of the array By adjusting the power input to each zone, the density of lamps of each heating panel, and the three dimensional configuration of the panel array, the heat flux distribution can be customized to the needs of the experimenter. The maximum total power l!l available is 4.3 MW from a 6 MW supply with the limitation based on the present connecting cables between the substation and the power supply. E2-2 I
I For uniform heat flux tests, the double-panel heating zones (2,3,4,5,7,8,10, and 11 zones in Figure F.2) are all operated at the same power and the four single-panel heating zones (1,6, 9, and 12) are operated at 75% of the power of the double-panel zones. Therefore, the power density at panels 1, 6, 9, and 12 is 1.5 times that of the other panels. For an edge-to-center j heat flux ratio of 2, the center four panels (zones 3 and 4) are off and the rest of the zones are
; powered at 120% of the power required for uniform heat flux tests to achieve the same maximum heat flux. The maximum achievable heat flux was determined from system design experiments to be about 40 W/cm2 , l The CYBL test fixture is installed over an observation pit. The 51 viewing windows,
- ' ranging from 30 to 60 cm in diameter on the side and bottom of the outer vessel, allow the
- boiling process to be observed from a variety of directions. Nearly three-hundred data channels l 4 are used to monitor vessel and surface temperatures as well as water temperatures. Temperature gradients from in-depth and surface temperature measurements are used to calculate local heat i fluxes. A map of thermocouple array placement and thermocouple locations on the bottom head 4
, is shown in Figure F.3. Arrays A and B are 7.5' on either side of the O' axis and arrays E and F are 7.5' on either side of the 90' axis. Arrays C and D are along the 30' and 60' axes ,l respectively. Five thermocouples located 15 cm away from the surface, following the contour of the bottom head, are used to measure the bulk water temperature. A thermocouple tree monitors the temperatum of the water as well as the steam temperature at fifteen vertical locations over the entire height of the outer vessel. All except the surface thermocouples are 1.6 mm (1/16 in) stainless steel sheathed thermocouples with grounded junctions. He surface thermocouples are intrinsic thermocouples made from the same 1.6 mm sheathed thennocouples with the last 2.5 cm stripped to bare thermocouple wires. The two bare wires are welded individually onto l l the test surface; the distance between the wires is typically 2-3 mm. This installation lessen the effect of the presence of thermocouples on the surface and the temperature reading represents a
'I locally (3 mm) averaged surface temperature. A ten-camera video system is used to view and record the boiling process. Additional cameras are used to monitor key systems in the facility. The data acquisition and control system
- l plots selected heat transfer data as well as operating parameters in real time. De system is also
. used to " scram" the test power, should thermocouples detect conditions that indicate departure from nucleate boiling. Also monitored for operational safety are the cooling water flow rates and temperatures for all the cooling water circuits. F.2-3
1 F.3.0 EXPERIMENTAL RESULTS A total of three test series have been completed in the CYBL facility: the NPR series urider the DOE-NPR program, and the NE1 and NE2 series under the DOE-NE program. A summary J of all the tests is given below: Test Heat Flux
- Flux Distribution ;
2 l W/cm ' NPR-A 16 uniform NPR-B 16 edge-peaked NEl-UA 16 uniform I NEl-UB 18 uniform NEl-UC 20 uniform NE2-A 8 edge-peaked g NE2-B 16 edge-peaked 3 NE2-C 17 edge-peaked NE2-D 18 edge-peaked E NE2-E 20 uniform E
- Peak heat flux for edge-peaked tests.
I For all the experiments performed, the water level is 5 meters above the bottom center of the test vessel. Because of the 5 meters of gravity head, the bulk condition near the bottom head area was subcooled, and in all cases, the entire bottom head was in subcooled nucleate boiling. The purpose of the present paper is to report the main observations of the experiments and results that have direct impact in the evaluation of the flooded cavity design. Representative heat flux and surface temperature distribations are reported here to illustrate the general trend of the data. Detailed heat transfer analysis as well as correlation /modeling of the heat transfer process will be reported in the future. The heat flux distribution from two uniform heat flux tests (NEl-UA,16 W/cm2 and NE2-E, I 20 W/cm2) and one non-uniform heat flux test (NE2-B) are shown in Figure F.4. Arrays A/B g and E/F are two orthogonal arrays on the bottom head, Figure E3. Arc distances from 0 cm to 5 146 cm correspond to the crown region and the knuckle region extends from 146 cm to 218 cm. The edge of the crown region has a surface inclination of 25.7'; surface inclination reaches 90' at the edge of the knuckle region. Within each region, the surface inclination increases linearly l with arc distance. The heat fluxes are calculated from temperature gradients given by in-depth thermocouples at 0.95 cm into the surface and the surface thermocouples. Temperatures and E2-4 l I
L 1 temperatum gradients used are averaged over a 200-500 second interval. For the uniform heat flux tests, NEl-UA and NE2-E, the heat flux over the entire surface is constant to within about l 10% to an arc distance of 168 cm. Along the 0*-180* and 90*-270* axes, there is a gradual l l drop of about 20% to a distance of 213 cm and a sharp drop to zero at 229 cm. The drop off is riightly faster along the 30' and 60* axes (as well as symmetrical directions in the other j quadrants), by about 25% at 213 cm. For the non-uniform heat flux case, the heat flux peaks around 168 cm from the bottom-center location. He peak is relatively broad; the heat flux is W within 90% of the peak value 30 cm on either side of the peak. Surface temperature excess (over saturation temperature) as measured by arrays A/B and i E/F are shown in Figure F.5. Because there is a 90 cm change in elevation along the surface (from bottom center to the rim of the bottom head), there is a coriesponding change in local saturation temperature of approximately 2 K. Therefore it is more appropriate to examine the l surface temperatute excess over local saturation temperature. It is interesting to note thr.t in all cases, including the non-uniform heat flux experiment (NE2-B) where the heat flux is lowest at i the bottom center, the surface temperature excess is still highest at the bottom center location. His suggests that the bottom center area is least effective in heat dissipation. The heat transfer data from the CYBL experiments are compared with the result from the quenching experiment in Figure F.6. Here appears to be general agreement between the two experiments, although, g 2 3 the surface temperature excess at CYBL bottom center for 20 W/cm s approximately 2.5 K j higher than the surface temperature of the quenching specimen. There is not enough data to judge if this is a scale effect. The effectiveness of boiling heat transfer can be examined quantitatively using the data of the NE2-E experiment. Shown in Figure F.7 is the heat transfer coefficient based on temperature excess over local saturation temperature as a function of surface location. While the applied heat flux is essentially constant over the surface (between arc distance 0 and 168 cm) the heat trarisfer coefficient increase monotonically with are distance. He heat transfer coefficients obtained by l 2 s Nishikawa et al. (1984) for 20 W/cm s 1.3 W/cm -K in their laboratory-scale experiments; this value is higher than the heat transfer coefficient for the bottom center area, but lower than the values in the knuckle area. This comparison suggests that scale and geometry do have an i effect on the heat transfer coefficient. l We effect of heat flux distribution on heat transfer ce.n be examined by comparing experi-ments NEl-UA and NE2-B. The peak heat flux is appmximately 16 W/cm2 for both experiments but NEl-UA has uniform heat flux and NE2-B has edge-peaked heat flux with an edge-to-center heat flux ratio of approximately 2, Figure F.4. He surface temperature excess is slightly less near the bottom center area for NE2-B as a result of lower heat flux near the center. The heat l F.2-5 l
I transfer coefficients for the two experiments are compared in Figure E8. It is interesting to note that in the region between arc distance 137 cm and 183 cm where the heat fluxes for both experiments are comparable, the heat transfer coefficients for both experiments are quite close (increasing from 1.4 W/cm2-K to 1.6 W/cm 2-K). De result suggests that for the present range of l heat fluxes, the local heat transfer coefficient is not a strong function of the shape of the surface heat flux distribution. In other words, the heat transfer coefficient near the outer radius of the vessel appears not to be strongly effected by the net heat input (vapor generation) upstream g (close to the vessel center). As we will see in the next section, this is a direct consequence of 5 the general phenomenology of the ex-vessel boiling process. F.4.0 PHENOMENOLOGY OF EX-VESSEL BOILING I The ex-vessel boiling process is best described as subcooled nucleate boiling. Visual obser-vations indicate that the boiling process near the bottom center is cyclic in nature ar.d has four distinct phases: direct liquid / solid contact, bubble nucleation and growth, coslescence, and vapor mass dispersion (ejection). Because of the axi-symmetrical configuration, the flow patterns are l axi-symmetric. The general direction of flow is in the radial direction. This radial flow gives rise to an onlerly progression of the four phases as a function of radius from the bottom center of the test vessel. The progression of flow patterns has the appearance of waves of vapor emanating E from the bottom center of the test vessel, although vapor is actually produced over the entire W surface. Two sequences of video frames illustrating this cyclic progression for heat fluxes of 2 8 W/cm2and 14 W/cm are shown in Figures E9 and E10, respectively. The field of view is approximately 2 meters. he frequency of the cyclic / pulsating pattern in the bottom center region increases with heat flux but the rate of increase decreases with heat flux (i.e., the frequency only increases very slightly at high heat fluxes). The cyclic / pulsating pattem is much more regular temporally and spatially at higher heat fluxes. Here is not sufficient data to determine the demrcation between l 2 high and low heat fluxes but it is above 8 W/cm2 and less than 10 W/cm . It is interesting to note that this demarcation is near the heat flux where the boiling curves from the quenching experiments changes slope (see Figures E11 and E12, Part I). Furthermore, the general trend g of the variation of cycle frequency and heat flux is also observed in the quenching experiments. 5 2 The frequency is approximately 2 Hz for heat fluxes above 10 W/cm . Each cycle starts with nucleation near the bottom center region; in time, bubble nucleation progresses outward from the j bottom center. De growth of the bubbles eventually results in a coalesced circular vapor mass of as large as one meter in diameter, Figure E10. Similar to the trend in frequency, the size of the vapor mass increases rapidly with increasing heat flux for low heat fluxes, but only increases E2-6 1 1_ _ _ _ _ _ _ - _ - _
L ' slightly at higher heat fluxes. For the range of heat fluxes tested, the maximum thickness of the r L central vapor mass varies approximately from one to three centimeters. The vapor mass disperses in the form of an expanding flat ring rising along the surface (Figure E10). However, eventually the configuration becomes unstable and the ring thickens and breaks into smaller arc segments. De broken vapor segments condense in the surrounding subcooled water leaving essentially no trace. De radial location of this condensation zone is quite well defined; the corresponding radius increases with heat flux. As a result, the boiling i { process beyond the condensation zone is to a large degree decoupled from the cyclic pulsation of the center bottom and is observed to be essentially steady in nature. His is probably the reason that the heat transfer coefficient is not influenced significantly by the upstream heat flux 7 distribution, Figure E8. The vapor in the outer region also condenses in the bulk water a very short distance E beyond/above the bottom head region. While the subcoling corresponding to the 5-meter gravity head is approximately 12 K; the actual observed subcooling of the bulk water near the bottom L center is in the range of 9-10 K. The amount of subcooling decreases with heat flux. This reduction in subcoling is probably the result of condensation and convective mixing. Figure Ell I is a plot of the vertical temperature distribution of the bulk water for test NE2-E. The rim of the 1 bottom head corresponds to 0 on the distance axis and the bottom center of the vessel head is at - -91 cm. The water steam interface is at 409 cm. Noz the temperature bulge near the rim of the bottom head (0 cm location) due to vapor condensation. Locations above the rim of the bottom head are essentially occupied by single phase subcooled liquid until within approximately 60 cm of the interface. Intense vaporization takes place in the top 30 cm of the water. Figure E12 is a schematic of all the important physical mechanisms of the ex-vessel boiling process. There appears to be no qualitative difference in the boiling process between the non-uniform heat flux and uniform heat flux cases. The bottom center region still exhibits the typical cyclic pattern. r here is still a well-defined condensation zone separating the cyclic central region and the steady ' twaphase outer region. In a "real" accident, the vertical portion of the reactor vessel wall is heated by radiation and convection. De condensation zone near the bottom head rim would certainly be modified. F.5 CONCLUDING REMARKS Re ex-vessel boiling pmcess is best described as subcooled nucleate boiling. The boiling ! pattern is divided into two regions: a cyclic / pulsating bottom center region and an outer steady two-phase boundary layer region. Condensation takes place at the edge of both regions. He bulk l l of the water in the annular space between the reactor vessel and the cavity wall is single- phase E2-7 _ _ o
liquid. Intense vaporization takes place near the top surface of the water. The subcooling is mainly due to the gravity head of the water flooding the simulated reactor cavity. But the degree of subcooling is modified by the complex ex-vessel boiling pattern. Because of condensation, , the outer rim of the bottom head is to a large degree decoupled from the cyclic pulsation of the bottom center area, the heat transfer coefficient is found not to be significantly influenced by the ) upstream heat flux distribution. The results of three CYBL test series and the critical hett flux study of Theofanous et al. ] (1994) suggest that under prototypic heat load and heat flux distributions, the AP-600 flooded cavity should be capable of cooling the reactor pressure vessel in the central region of the lower g head that is addressed by these tests. W There is general agreement between the heat transfer results of the quenching experiments and the CYBL experiments. It is interesting to note that the quenching experiments also exhibit similar cyclic behavior in the nucleate boiling regime but the temperol and spatial regularity certainly could not have been predicted from the quenching experiments. The comparison with l the Nishikawa et al. (1984) results suggests that geometry and scale does influence the ex-vessel ; boiling process. The CYBL experiments demonstrated that the ex-vessel boiling process is dominated by spatial structures of rneters in scale. Therefore, the reactor-scale tests performed in CYBL should prove valuable for an accurate assessment of the potential of ex-vessel boiling for in-vessel core retention. l The CYBL facility can be used in the future to investigate reactor-scale vessel coolability issues not addressed by the current test series. Issues that could be addressed include: the coolability of a hemispherical vessel head; the impact of vessel penetrations or vessel insulation; g the effect of an only partially flooded cavity; characterization of the two-phase boundary layer, E sensitivity to higher heat flux levels; and the effect of water subcooling and recirculating flow on vessel coolability. l F.6.0 ACKNOWLEDGEMENTS
'Ihe authors would like to thank Steve Additon of TENERA for many insightful comments and suggestions. This work was performed at Sandia National Laboratories and supported by the U.S. Department of Energy under Contract No. DE-AC04-76DP00789.
F.
7.0 REFERENCES
Beduz, C., R. G. Scurlock, and A. J. Sousa,1988," Angular Dependence of Boiling Heat Trans-fer Mechanisms in Liquid Nitrogen," Advances in Cryogenic Engineering, Vol. 33, pp. 363-370. F.2-8
i l Chen, L T.,1978, " Heat Transfer to Pool-Boiling Freon from Inclined Heating Plate," LgA Heat Mass Transfer. Vol. 5, pp.111-120. Chu, T. Y., J. H. Bainbridge, J. H. Bentz, and R. B. Simpson,1994, Observations of Ouench-inn of Downward-Facing Surfaces, SAND 93-0688, Sandia National Laboratories, Albuquerque, NM.
; Chu, T. Y., R. C. Dykhuizen, and C. E. Hickox,1992, Scocing Studies of Boiling Phenomena Associated with the Floodad Cavity Design of the Heavy Water New Production Reactor.NPRW-SA92-2, Sandia National Laboratories, Albuquerque, NM.
i Guo, Z., and M. S. El-Genk,1991,"An Experimental Study of the Effect of Surface Orientat on ~ on Boiling Heat 'IYansfer During Quenching," ASME Winter Annual Meeting, Atlanta, GA, Dec. 2-5, 1993. Henry, R. E., J. P. Burelbach, R. J. Hammersley, and C. E. Henry,1993a, " Cooling of Core
- Debris Within the Reactor Vessel Lower Head," Nuclear Technology, Vol.101, pp. 385-399.
Henry, R. E., H. K. Fauske,1993b, "Extemal Cooling of a Reactor Vessel Under Sevem Acci-dent Conditions," Nuclear Engineering and Design. Vol.139, pp. 31-43. Kymnininen, O., H. Tuomisto, O. Hongisto, and T. G. Theofanous,1993 " Heat Flux Distribution from a Volumetrically Heated Pool with High Rayleigh Number," Proceedings, NURETH 6, . Grenoble, France, October 5-8,1993., pp. 47-53. Nishikawa, K., Y. Fujita, S. Uchida, and H. Ohta,1984, "Effect of Configuration on Nucleate Boiling Heat 'IYansfer," Int. J. Heat Mass Transfer, Vol. 27, pp.1559-1571. O'Brien, J. E., and G. L Hawkes,1991," Thermal Analysis of a Reactor Lower Head with Core l Relocation and External Heat 'IYansfer," AIChE symposium Series 283, Vol. 87, pp.159- 176, National Heat Transfer Conference, July 28-31,1991, Minneapolis, MN. Okkonen, T.,1994, "In-vessel Core Debris Cooling through External Flooding of the Reac-tor Pressure Vessel," Proceedings, OECD/CSNI/NEA Workshop on Large Molten Pool Heat Transfer, Nuclear Research Center, Grenoble, France, March,1994. Rouge S., and J. M. Seiler,1994, " Core Debris Cooling with Flooded Vessel or Core Catcher Heat Exchange Coefficients under Natural Convection," OECD/CSNI/NEA Workshop on Large Molten Pool Heat Transfer, Nuclear Research Center, Grenoble, France, March,1994. Theofanous, T. G., S. Syri, T. Salmassi, O. KymEllinen, and H. Tuomisto,1994, " Critical Heat Flux Through Curved, Downward Facing, 'lhick Walls," Proceedings, OECD/CSNI/NEA Work-shop on Large Molten Pool Heat Transfer, Nuclear Research Center, Grenoble, France, March, 1994. E2-9
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