ML20134H488
| ML20134H488 | |
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| Site: | 05200003 |
| Issue date: | 01/31/1995 |
| From: | Angelini S, Theofanous T, Yuen W CALIFORNIA, UNIV. OF, SANTA BARBARA, CA |
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| DOE-ID-10489, NUDOCS 9611140117 | |
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{{#Wiki_filter:- i l l t l DOE /ID-10489 THE STUDY OF STEAM EXPLOSIONS j l January 1995 IN NUCLEAR SYSTEMS t 1 i i T.G. Theofanous, W.W. Yuen, S. Angelini and X. Chen 1 i l J i i
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i i l 1 DISCLAIMER This report was prepared as an annount of work sponsored by an agency of the Unned States Govemment. Nether the Unned States Govemment nor any agency thereof, nor any of their .44, . makes any warrarny, express or imphed, or assumes any legel hability or responsibility for the accuracy, compimenses, or usetuiness of any niormamon, apparatus, product or prooses escioned, or represents that hs use would not ininnge prwately owned rights. Roterences herem i
. to any specdAc commerolai product, process, or service by trade name, trademark, manutacturer, or othenvies, does not necesserty coneutute or imply its endorsement. recommendamon, orfavonna by the Unned States Govemment or any i agency thereof The views and ogwuons of authors expressed herem tio not necessanly state or rotect those of the Uruled States Govemment or any agency i th*'*88 a
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( l DOE /ID-10489 THE STUDY OF STEAM EXPLOSIONS IN NUCLEAR SYSTEMS l I i l T.G. Theofanous, W.W. Yuen, S. Angelini ! and X. Chen l l
. 4 Final Draft January 1995 Centerfor Risk Studies and Safety Department of Chemical and Nuclear Engineering University of California, Santa Barbara Santa Barbara, CA 93106 Prepared for the 4 ,# U. S. Department of Energy Idaho Opemtions Office CREE Under DOE Subcontract No. 23S72401 i
I ?! j ABSTRACT } i The purpose of this repon is to present an overview of the steam explosion issue in nuclear L reactor safety and our approach to assessing it. The key physics, models, and computational 3 tools are described, and illustrative results are presented for ex-vessel steam explosions in an j/ open pool geometry. An extensive set of appendices are also provided to facilitate access to ' f previously reponed work that is an integral pan of this effon. These appendices include key developments in our approach, key advances in our understanding from physical and numerical experiments, and details of the most advanced computational results presented in this repon. ( Of m2, a significance are the following special and unique features: 1 (a) A consistent two-dimensional treatment for both premixing and propagation which in prac-g tical settings are ostensibly at least two-dimensional (as opposed to ID) phenomena. v (b) Expenmental demonstration of voiding and microinteractions which represent key behaviors P .r in premixing and propagation respectively,
- f j (c) Demonstration of the explosion venting phenomena in open pool geometries which, there-
[ fore, can be counted on as a very imponant mitigative feature. (d) Introduction of the idea of penetration cutoff as a key mechanism prohibiting large-scale premixing in usual ex-vessel situations involving high pour velocities and subcooled pools, e This report is intended as an overview and is to be followed by code manuals for PM-1 ALPHA and ESPROSE.m, respective verification repons, and application documents for reactor- !{ specific applications. The applications will employ the Risk Oriented Accident Analysis Method-j ology (ROAAM) to address the safety imponance of potential steam explosions phenomena in 4 evaluated severe accidents for passive Advanced Light Water Reactors (ALWRs). Vn b ,i
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CONTENTS Page ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
- 1. INTRODUCTION AND TERMINOLOGY . . . . . . . . . . . . . . . . . . 1-1
- 2. GENERAL TRENDS AND OVERALL APPROACH . . . . . . . . . . . . . 2-1 l 3. THE KEY ELEMENTS OF THE COMPUTATIONS AND THEIR
! VERIFICATION STATUS ........................ 3-1
- 4. ILLUSTRATIVE CALCULATIONS .................... 4-1
, 5. PULSE-WIDTH SYSTEMATICS ..................... 5-1
- 6. CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . 6-1
- 7. REFERENCES 7-1 APPENDIX 1. MULTIPHASE TRANSIENTS IN THE PREMDONG OF STEAM EXPLOSIONS .................... 1-1 l
APPENDIX 2. PREMDONG-RELATED BEHAVIOR OF STEAM EXPI.OSIONS . . . 2-1 l APPENDIX 3. ON THE FUNDAMENTAL MICROINTERACTIONS THAT SUPPORT THE PROPAGATION OF STEAM EXPIDSIONS . . . . 3-1
- APPENDIX 4. THE PREDICTION OF 2D THERMAL DETONATIONS AND RESULTING DAMAGE POTENTIAL . . . . . . . . . . . . . . 4-1
. APPENDIX 5. THE PROBABILITY OF ALPHA-MODE CONTAINMENT FAILURE UPDATED . . . . . . . . .. . . . . . . . . . . . . 5-1 APPENDIX 6. THE STUDY OF STEAM EXPLOSIONS IN NUCLEAR SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1 APPENDIX 7. THE PREDICTION OF DYNAMIC LOADS FROM EX-VESSEL STEAM EXPLOSIONS .................... 7-1 APPENDIX 8. DETAILED RESULTS OF SET II PREMDONG CALCULATIONS . . 8-1 i APPENDIX 9. DETAILED RESULTS OF SET II EXPLOSION CALCULATIONS . . 9-1 1 l l { ! V i
)
- - -- . - - _ - _ . - - - _ _ _ . . .= . - . . - . . . .-. .
ACKNOWLEDGMENTS This work was supported under the ROAAM program carried out for the US DOE's Ad- ) vanced Reactor Severe Accident Program (ARSAP), under ANL subcontract No. 23572401 to UCSB. The authors appreciate the cooperation during the performance of this work and the inputs to this document by Mr. S. Sorrell (DOE, Idaho Operations Office) and Mr. S. Additon (TENERA). l l i l l l 1 Vii
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i
1.0 INTRODUCTION
AND TERMINOLOGY The purpose of this report is to provide a concise statement' of the " steam explosions problem" and an approach to it intended for use in the licensing arena." The " problem" involves interaction in the pouring mode of contact; that is, the molten corium pouring into a pool of water. [ Stratified configurations can also lead to explosions; however, it is well understood that 1 1 they are of limited energedes because of the limited mixing (coupling length scale) possible in the explosion time scale.] We speak ofin-vessel and ex-vessel explosions depending on whether this contact occurs in the lower plenum, or in the reactor cavity, respectively. The two situations are similar in that both involve the release of significant quantities of melt following failure of , l the stmeture contaming it. In the in-vessel case this structure develops naturally, as a result i of melting of core materials and refreezing in the outer, cooler core boundaries, forming the so-called " crucible." In the ex-vessel case the temporarily (in the absence of external cooling) I retentive ta cture involved is the lower reactor pressure vessel head. There are also important differences. Typically, the in-vessel case involves low velocity pours in near-saturated water pools, while in ex-vessel situations we have much higher velocity melts pouring into subcooled pools. Currently, and in light of the licensing activities for the US advanced passive plant designs, in-vessel explosions are ofinterest to the AP600, and ex-vessel explosions to the SBWR. In both l cases we are interested in the resulting pressure dynamic loads on adjacent structures-in the i case of AP600, for assessing lower head integrity, which is an imponant aspect of the in-vessel retention severe accident management strategy, and in the case of SBWR, for assessing the ! integrity of both the protective shield and the lower drywell walls, which constitute a part of the 1 1 containment pressure boundary. The two geometries are schematically depicted in Figures 1.1 ' and 1.2, respectively. i The pressure loads on the structures result from the pressure waves emanatmg from the explosion zone. These pressures are generated as a result of the intense thermal interactions between the coolant and core materials during an explosion event. The pressure is " radiated" through the surrounding water, eventually reaching and loading the boundaries. At a non-yielding (rigid) boundary, and for the conditions of interest, such a pressure wave will be reflected, doubling in magnitude, while a free boundary (a water-air interface) allows unloading, i.e., an invened, negative reflection (see, for example, Figure 4.14 and related discussion in Section 4.2). Intermediate situations, such as, for example, along the interface between the explosion zone and surrounding water give rise to intermediate behaviors; that is, a reflected wave that feeds back into the explosion zone, and a transmitted wave that radiates energy outwards. Clearly, the
- This means we adopt a style of presentation that is readily accessible to the non-expen and is focused on the goals stated. Other pertinent literature is referenced in a comprehensive manner in Appendices 1 through 7.
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i explosion cannot be uncoupled from the transmission problem, and the water that surrounds the explosion zone plays the role of a " coupling medium" in the full sense of the woni-i.e., the wave dyrsmics in it affecting the explosion process itself. In other words, to correctly calculate dynamic loads in the present geometnc setting, what is required is a multidimensional calculation that captures the wave dynamics over the whole physical domain ofinterest. As a consequence of these compression waves, surrounding mobile or failed materials are set in motion, yielding the so-called " expansion" phase of the overall explosion phenomenon. I 1 The explosion process itself, also refered to as " propagation," needs a sufficiently strong local disturbance (a " trigger") to initiate it, and it lasts only milliseconds. The spatial distributions of melt, steam, and water at the time of a trigger event define the explosion "premixture" (see Appendices 1 and 2). The "prenuxing" transient, that is, the flow and heat transfer processes that lead to any particular premixture, is a result of the pouring process described above; it i takes place in a time frame of seconds, and it can, therefore, be considered " frozen" during a propagation event. l In addition to the volume fractions, to fully characterize a premixture, we need also the respective characteristic length scales of the three phases. In general, these length scales will be a function of position, too, and they are important in defining the local interfacial area concentrations, and through them the extent of interphase interactions that to a large extent govem propagation. For the melt, in particular, these length scales evolve through " breakup," which is induced by interfacial instabilities due to body force fields and differential velocities within the mul-tiphase, multidimensional premixing zone (see, for example, Figure 1.3). These are " coarse" scales, varying from centimeters to a few tens of centimeters at the source of the pour, down to dimensions, eventually stabilized by surface tension, of a few millimeters. However, breakup is a rate process, and the resulting final breakup may be limited by the depth of the interaction zone and/or solidification phenomena (especially for low superheat oxidic melts). I During propagation, these coarsely mixed melt masses are subject to " fragmentation," a process responsible for sustaining and amplifying the explosion (see, for example, Figure 1.4). Fragmentation is an interface phenomenon, it produces fine particles in the micron to hundreds of microns range, and the positive feedback is obtained by the intimate contact obtained as these fine particles mix with the coolant in the immediate vicinity of parent-particle interfaces. It is important that this process leads to a localized contact; the mass ratios of the coolant and fragments involved in fact determine the magnitude of this feedback. This is the constitutive law needed to characterize this "microinteractions" process (see Figure 1.5 and Appendices 3,4 and 6). 1-4 L ----_ _ _ _
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Figure 1.3. Schemati: representation of a premixture, indicating key parameters of interest. During an explosion a wave propagates through this mixtme collapsing the steam volume and ) 1 forcing melt-water contact. This contact is characterized by the interfacial area concentrations, which depend on the local length scales. For a disturbance to become an actual trigger it must lead to a cascade of local interactions that become coherent and escalate into a high pressure wave, sweeping through the premixture (" propagation"). It is very important to distinguish the different fragmentation regimes; early in this triggering process prevailing pressures are low and phase-change-induced velocities are l much higher than what can be obtained by thermal expansion at the supercritical pressures that l characterize the main propagation event. Similarly, we expect the microinteraction regimes, and the respective constitutive laws, to be quite different also. To correctly calculate escaladon one needs the constitutive laws throughout all those early regimes, in addition, of course, to the magnitude of the initial disturbances and the premixture characteristics as defmed previously. Spontaneous triggers can be obtained by liquid-liquid (melt-coolant) contact, which is promoted by coolant subcooling and turbulence, and/or by impact pressure as, for example, when the melt hits solid structures. It is very important to note that for ex-vessel explosions both mechanisms are combined when a high velocity melt hits the surface of a subcooled water pool. This is the origin of the " penetration cutoff" idea put forth in Appendix 7. t 1-5 d
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2.0 GENERAL TRENDS AND OVERALL APPROACH Our task is to obtain reasonably bounding estimates of stmetural loads, and we must begin with reasonably bounding meh release conditions also. Thus, besides the geometry of the interaction, we begin with the melt pouring rate, an effective pour area, characteristic melt length scales (s), and the melt composition (ympnies) and superheat. Our first step is to determine the extent of voiding in the resulting succession of premixtures and to evaluate the potential for an explosion being triggered during the evolution of the premixing transient. Besides water subcooling, the degree of voiding obtained depends on the development of the melt length scales (due to breakup). The larger the interfacial area concentration (small length scales, high volume fractions), the higher the degree of thermal and momentum coupling between the melt and the coolant fields, and this coupling facilitates the heating of water and void formation. In addition, this coupling decelerates the melt, which under some conditions can lead to a buildup of the melt i i volume fraction in some regions of the premixing zone. With increased voiding, premixtures become more resistant to triggering, and once triggered they exhibit reduced energetics. However, o as a compensating factor, the higher interfacial area concentrations can lead to more intense interactions within an explosion wave. Conversely, while lower interfacial area concentrations may produce slightly voided premixtures that can be cally triggered, they can only provide limited feedback and hence reduced overall strength in explosions. We take advantage of this compensating effect to develop an approach that treats breakup in a more-or-less parametric l fashion. Considermg, as noted aheady, that the potential range of length scales involved is relatively limited (from a few centimeters to a few millimeters), the parametric approach to breakup is not as open-ended as it may appear at first. This is because, due to turbulence and other gross motions, even a 10 or 20 cm jet would be expected during its fall in an ex-vessel geometry to suffer at least some gross breakup to the sub-10 cm scales. Further guidance for parametric coverage is that deeper pools allow more breakup time and thus more of an approach to the lower end of the length scales; however, subjected to these longer exposures such small particles I would tend to solidify, at least partially, which effectively would remove them from participating l in an explosive event. Accordingly, we treat premixing by means of a three-fluid formulation, and with specified melt length scale (s). The focus is to understand the key momentum and heat transfer interactions among the three fields, especially from the point of view of premixture voiding pmduced. Our - l approach is to confirm this understanding by means of experiments that are well-enough char-l acterized to allow unambiguous comparisons between measurements and predictions. This was i 2-1 _ =_ _ _ - J
1 accomplished in the recent past in the MAGICO experiment, involving the pour of a high temper-ature (up to 1000 *C) metallic particulate into a pool of saturated water, and the measurement of the void fractions throughout the mixing zone. The results confirmed predictions made with the PM-ALPHA code, and a summary can be found in Appendices 1 and 2. In a new experiment, the MAGICO-2000, which has just become operational, we are focusing on subcooled pools and high velocity pours, as they are ofinterest to ex-vessel explosions. In this experiment the particulate is ZrO2 or Af O 2 at 3 temperatures up to 1500 *C, with the density diffemnce between 1 the two particulates providing (according to pretest predictions) diverse momentum interaction conditions for model testing. An example that such an approach to breakup is quite consistent with the expenmental evidence available can be found in the interpretation of the available FARO expenments carried out with 30 kg of oxidic corium simulant poured into a slightly subcooled water pool at a pressure of ~50 bar (Appendix 2). At the other extreme is the approach taken for the THIRMAL code, with its detailed mechanistic breakup interpretation and structure. In it, a melt jet erodes due to entrainment of fine droplets off its lateral surface, and complete " breakup" is defined when the jet is depleted l by this mechanism. Thus at any given time the calculation produces axial profiles (1D) of l the size of the interaction zone, the diameter of the remaining (nonfragmented) jet, and of the volume fractions of steam, water, solidified particles, and still-molten melt droplets within the zone. The zone is surrounded by undisturbed water. While the detailed dynamics of such a complex model is rather difficult to sort out by direct comparison with experiments, some global comparisons with FARO data appear to be favorable, and such an approach provides an interesting complement to our " particle-cloud" approach in delineating the potential boundaries of premixtures as initial conditions in a propagation calculation. Moreover, the three-fluid model recently has been extended to bridge the gap between j the original fixed-particle-size formulation and the discrete approach employed in THIRMAL. This extended model accounts for breakup and entrainment of melt globules into the coolant stream, and a corresponding decrease of the fuel field particle size, (i.e., length scale transport) so that in the corresponding limits it can be reduced to either the PM-ALPHA or the THIRMAL approaches. More importantly, however, it can cover the whole ground in between, and in keeping with the parametric attitude in this area described above, this can be considered to provide a rather comprehensive coverage. This approach and the first results can be found in reactor-specific calculations currently under preparation (Theofanous et al.,1995a,b). 2-2 L_ ____ _
l l Triggering, in general, is even more difficult to predict than breakup.6 A great part of the difficulty lies in facing a wide range of local conditions, within a premixture, while assessing l the likelihood of a vapor blanket collapse (a necessary condition to initiate triggering) and the magnitude of the resulting disturbance (pressure pulse). Perhaps an even greater difficulty is in determming whether such a disturbance, again depending on the local premixture conditions, will develop into a propagating event, or whether it will simply die out. As alluded to above, this facet of the difficulty is due to lack of the constitutive laws of microinteractions, in the low pressure and small disturbance environment of the early escalating phases of a trigger. However, this also must be viewed in the context of really not knowing the melt length scale distributions in detail (the breakup issue discussed above), and by implication also the local void i fraction distribution. In other words, we see that " triggering" and " breakup" are closely related, not only conceptually, as both are instability-driven, but also mechanistically, in that detailed knowledge of both simultaneously would be necessary to predict when a prenuxing transient can be interrupted, giving way to an explosion. Accordingly, we also treat triggering parametrically; that is, we assume that it will happen, and we vary its tmung over the duration of the premixing transient. This means that we envelop structural loads by studying propagation in a set of premixtures defined by variations in a two-parameter space, the melt length scale (or the initial length scale and the rate of breakup in the mom recent formulation), and the timing of a trigger. For low-to-moderate depth pools it is easy to bound the behavior by letting the trigger occur when the melt hits the pool bottom. Physically, this is a likely trigger anyway, but also at this condition a near maximum quantity of melt has been pmmixed (as compared to any earlier triggering). In l addition, the deeper melt penetration mmimizes explosion venting effects (see Appendices 3 and l 6) and maximizes structural loads. For very deep pools, say over 5 meters, this approach (of delaying the trigger) becomes increasingly unduly conservative, and somewhat more involved in accounting for the new mitigating factor that comes into play: melt freezing. Nonetheless, such an accounting is still feasible. There is, however, also an idea (see Appendix 6) that these more difficult to deal with circumstances also imply a regularity in triggering that prevents deep penetrations. The idea is that vapor blanket collapse is forced by the high velocity melt entering the water pool. High 6 It may be noted, however, that certain regularities seem to have been well enough established to be used in safety analyses - as is the high pressure cutoff used in the Sizewell case (Turland ' et al.,1994). An excellent discussion of past work and current understanding has been prepared by Fletcher (1994). 2-3
l subcooling helps this vapor blanket collapse process, but in addition it gives rise to intense condensation shocks which in themselves constitute significant pressure pulses. There is ample empirical evidence in the literature (experiments with pouring various melts in coolants) indi-cating such trends, but this idea has not been pursued specifically before and remains to be, therefore, quantified. We are pursuing this now, and if substantiated, we expect to argue with high confidence that under this special set of conditions we expect a series of shallow attempts to penetrate, intermpted by small steam explosions, resulting in extensive melt quenching and paniculation, so that the melt ends up highly (evenly) dispersed on the drywell floor. Once an explosion is triggered (in a particular premixture) the magnitude of the resulting energetics can be computed with the ESPROSE.m code. With the present model, the behavior is not a strong function of the trigger (see Section 4.2), mther it depends on the constitutive law for the microinteractions for which we have the SIGMA experiments (Appendices 3 and 6), and a good comparison with an experimentally observed detonation in the KROTOS facility : (Appendix 7). Moreover, the results are not sensitive within a reasonable range of variation in this constitutive law, which makes the whole problem of parametric variations tractable. With a much broader database from SIGMA expenments, which are on-going (a key aspect here also is melt superheat), more widely applicable constitutive laws could be developed which might enable prediction of triggering. The more limited set of experiments currently available, however, is sufficient to support a simpler, more conservative model, much like the present one, which is nevertheless expected to support conclusions regarding the impact of steam explosions in ALWRs. l 2-4 L_
l 3.0 THE KEY ELEMENTS OF THE COMPUTATIONS AND THEIR VERIFICATION STATUS l The purpose of this section is to summanze the above discussions so as to create a global ; view convenient for putting the vadous components of the assessment process into perspective. The three main steps in this process-melt initial conditions, premixing, and propagation-are taken up in the same order below. In each case we list the key physics, the respective models, and what can be said about their verification status. In addition, we discuss potential questions of l adequacy and indicate what else may be needed or desirable. Ourintent is to provide an overview only-the subiect of verification is approached in detail in a repon specific to this purpose (Theofanous et al.,1995c). Also, this information should be reviewed, in conjunction with the l results in specific reactor applications because, depending on the particular circumstances, these i results may be impacted to a greater or lesser degree by these qualifications (Theofanous et al., 1995a,b). The material for the melt initial conditions is summarized in Table 3.1. Also shown are what precisely is needed (results) to quantify these conditions for any panicular application. In general, the thermal loading and release path formation can be considered reasonably well l understood based on past experience, and if not precisely predictable, we expect it is possible to reasonably envelop the behavior by means of a few splinter scenarios. On the contrary, almost nothing is known about melt flowing around (submerged) stmetures, and this should be l considered as a significant qualification in any attempt to quantify premixmg in the presence of ! such structures in the melt flow path. l
- For premixing, a summary view is provided in Table 3.2. With the exception of the MUPHIN, MIXA, and ALPHA experiments, everything in this table has been discussed al-ready. In the MUPHIN experiments, single spheres or arrays of a few spheres are inductively heated to high temperatures (~1000 *C) while water at velocities up to 5 m/s or steam-water !
two-phase mixtures at velocities up to 9 m/s flow over them. A comprehensive data base has been accumulated and correlations supponed by theory have been developed in excellent agree-ment with these data (Liu,1994). These conclations are presently being implemented into the l code. l The MIXA experiments are in concept somewhere between MAGICO and FARO. This is because they have been mn with a melt (uranium-molybdenum thermite) which, however,
- was made to prefragment by passing through a graphite grid, while high speed movies allow presumably a reasonably good definition of melt length scale (s) at the entrance. These data
, have not been made available, but if this definition is good enough, and if the length scales are 3-1
8 Table 3.1. Melt Initial Condition-Sununary View Key Consideration and Related Physics Models Basis and Verification Status
. Ihermal loading at melt pool boundaries ,
-Natural convection Conelations Nu = f(&) COPO, UCLA, and mini-ACOPO/ACDPO expenments
[Theofanous et al.,1994] e Melt release path PNC exmm. ;. [Saito et at,1990)
-Melt attack, Crust formation
-Penetration failure, Plugging vs Ablation TMI expenence y Deformation, and External forces to -Creep failure Finite element IMI analyses [Witt 1994]
-Heat losses to water (if present) Film boiling, Radiation ULPU expenments [Theofamous et al.,1994]
MUPHIN experiments [Liu,1994] e Melt Bow around structures j
-Flow distribution through lf vapor venting irrportant, perforated plates under melt _ need feedback to melt inertia, gravity forces, and pour rate vapor venting ;
Note: Scripted items are in progress. r Results: Melt Pour Rate (rhf ), Effective Pour Area (Af ), Effective Melt Length Sceh (Lf .) and Velocity (V f.) entering the premixing zone . i
l
' Table 3.2. Premixing--Summary View Key Consideration and Related Physics Models Basis and Verification Status e Multi 6cid thermal and 3-fluid,2D, PM-ALPHA [ App 2) Integral verification with momentum interactions 4-fluid,3D, PM-ALPHA MAGICO [ App. I and 2] and MAGICO-2000 (Possibly also with MIXA)
PM-ALPHA - CIIYhES comparisons [ App 5] e Boiling and Condensation Film boiling, MUPlHN expenments, including direct contact condensation, high subcooling and high velocities [Liu,1994) radiation transport { e Multiphase drag Friction factor correlations and " Cold" MAGICO-2000 runs collective-particle behavior e Breakup
-Taylor instabilities Interfacial area tranrport Guided by sanple test cases under
-Helmholtz instabilities with parametric source ideal conditions
-Thrbulence terms Some global, indirect testing with
-Condensation shocks FARO experiments [ App 2], and ALPHA emeriments Note: Scripted items are in progress.
Results: Space time distribution of volume fractions and leng:h scales Melt- #(7,f) f I(7,f) f Water: Gr(F,f) Le(F,t) Steam: 8,(F,f) L,(F,f)
/
/
p -- - - - - - - - - - - - - _ _ _ _ - - . -- -
l l small enough to narrow sufficiently the ranges potentially present in the premixing zone (that is, if funher breakup is not too important), we could have what we need for an unambiguous comparison with prediction. What is interesting about these experiments is that the melt reached temperatures over 3500 *C, which makes the water sufficiently transparent to produce a poten-tially imponant non-local radiative energy deposition mechanism. We have recently introduced a model in PM-ALPHA to account for this mechanism, so we are ready to consider the MIXA data when they become available. On the other hand, it should be noted that no local premixture characterization (such as local void fraction, or fluid velocities) was made in the MIXA tests. Rather, total steam flows leaving the interaction vessel were measured, which allows an overall, indirect comparison with predictions. The ALPHA experiments involve releases of coherent masses of thermitic melts into water pools at low and intermediate pressures. In some runs estimates of void fractions, averaged over the premixture zone as a whole, have been deduced from the pool level rise, and these are now used as a basis for integral comparisons with PM-ALPHA. As such, these provide an interesting complement to the FARO and MIXA comparisons, but in addition, they are potentially useful as the basis for triggering and escalation considerations. Among the ALPHA tests we find some with prefragmented melts (using a grid as in MIXA), but again it is not clear to what extent the inlet particle characteristics (length scales, volume fractions) are available. l Finally, for propagation, we have Table 3.3. Again, most of the material on this table has been discussed already. The only clarification needed is that so far the SIGMA experiment has been run with metallic melts and only for the high pressure conditions relevant to already propagating events. We believe that this is sufficient for a conservative approach to energetics. On the other hand, we believe there is good reason to expect that oxidic melts, especially if they are of low superheat, as expected in reactor accidents, would be much more difficult to trigger, and if triggered, they would tend to participate much less efficiently (than highly superheated metallic melts). Experiments in SIGMA designed to address this issue have been scheduled for the near future. Incidentally, we should note that the aluminum oxide in the KROTOS experiments inentioned in Table 3.3 was highly superheated. 3-4
i Table 3.3. Propagation-Summary View Key Consideration and Related Playsics Models Basis and Verification Status e Microinteractions (Local mixing 3-fluid,4-phase (ESPROSEm)[ App 7) Integral verification with KRO103 [ App 71 of coolant and fragments) Fragmentation kinetic correlation SIGMA experiment [ App 3) Mixing volunnes correla: ion SIGMA czperiment [ App 61 e Wave dynamics, including 2D ESPROSE.m hydro Integral verification with KRO10S tests [ App 7) reflections Wrificerion in ID with SIGMA emeriment Verification in 2D with analytical solutions e Numerical accuracy of Numericaliteration pd ie Time step and nodalization studies pressure source in explosion in ESPROSEm Comparison with czact solutionfor a specially constructed test problem Note: Scripted items are in progress. Results: Peak explosion pressure: P, .,(t). Pbol kinetic energy: K(t) Pressure loads on pool boundaries: P(n,t) where a is any point on boundary L
- - - c- - - __---,. - --- -. _ . -.
l l 4.0 ILLUSTRATIVE CALCULATIONS l Specific applications to reactor-scale conditions have already been performed on various occasions. The procedure is to carry out a set of PM-ALPHA premixing calculations and f continue over with ESPROSE.m by selecting one or more trigger times and positions in the premixing transients. For in-vessel interactions, we have demonstrated the water depletion phenomenon and also I have produced some very interesting comparisons between PM-ALPHA and CHYMES that resolve an alleged disagreement and sensitivity to constitutive laws [ Appendix 5]. So far, we also have run ESPROSE.a calculations which demonstrate the imponance of venting, and pressure wave dynamics in general, as shown in Appendix 5. Now, we also have the first in-vessel explosion calculations with ESPROSE.m.* For the purposes of this repon, we concentrate only on ex-vessel explosions. Ex-vessel explosions have been run previously with PM-ALPHA /ESPROSE.a calculations, whereby the important concept of " explosion venting" was introduced [ Appendix 4]. Calculations for a similar set of conditions were performed subsequently with PM-ALPHA /ESPROSE.m [ Appendix 7]. We refer to these as Set I calculations; they demonstrate the " explosion venting" concept even better under the much higher explosion source predicted by ESPROSE.m. This set of calculations is complemented here by another set (Set II) chosen to represent conditions somewhat closer to the SBWR. It is emphasized, however, that the purpose is still illustrative of main trends, rather than developing a safety case for the SBWR. This will be done in a specifically focused manner in a separate document (Theofanous et al.,1995a). With both sets of calculations taken together, we are exploring in a rather comprehensive fashion the key parameter to explosion venting: pool depth. Also, we explore, but to a lesser degree, the effects of water subcooling and melt pour rate, while we hold constant the melt (oxidic) temperature (3050 K), melt panicle size (1 cm) and system pressure (1 bar).d The
- T.G. Theofanous and W.W. Yuen, "The Probability of a Reactor Pressure Vessel Failure by Steam Explosions in an AP600-Like Design," Letter Repon to ANL, September 1994.
d One parametric at 3.5 bar gave essentially the same results. Of the other two parameters, the melt panicle size is imponant and in particular practic-1 applications it should be explored thoroughly in the manner described in Section 2. The effect of the other parameter, the melt temperature is rather straightforward. Oxidic melts may vary by one or two hundred degrees above or below the value used; however, such variations are inconsequential from a point, of ' view of thermal energy coutent, and hence they are not significant to the resulting energetics. For metallic melts the initial temperature can be considerably lower with correspondingly lower thermal energy content, thus yielding lower energetics. The melting point of iron-ztrcornum i; in the 900
- to 1350 *C range, and the superheat in general is expected to be limited to 4--I l
run specifications for premixing are summarized in Table 4.1. The identification code shown represents: Premixing (Set #) - Water Depth / Water Subcooling/ Pour Rate Factor. 3 The pour rate factor is a rough multiple of a reference pour rate of 10 kg/s. A couple of additional clarifications for these runs are in order: (a) The melt inlet velocities were obtained from a free-fall acceleration from the point of release and an initial velocity of 1 m/s, down to 1 meter above the water surface, where the upper edge of the computational domain was positioned. The requisite melt pour rates were obtained by specifying the appropriate values of the melt inlet volume fractions, (b) The PM-ALPHA calculations were actually carried out with a computational domain diameter of 4 meters. According to tests performed with the code, this convenience does not introduce any perceptible difference in the results. Propagation calculations were carried out mamly by providing a relatively strong trigger at the time and point where the melt first hit the pool bottom. The trigger was effected by releasing the pressure from a 100 bar steam-filled computational cell. Calculations carried out v.ith 10 bar to 200 bar triggers produced essentially the same explosions. Initial conditions were provided by PM-ALPHA, except for ignoring the amoung of freezing calculated in a!1 but one case where only the still-molten fuel was utilized. The one case in which only molten fuel was considered is denoted by an (m) in the run identification number. The explosion mns are identified in the same manner as the premixing runs, except for changing the prefix to E.m (for ESPROSE.m) and l adding a fourth number to indicate time of triggering, in seconds. That is, E.m(I) - 1/80/0.75/0.5 l is an ESPROSE.m calculation initiated from premixmg run PM(1)- 1/80/0.75, with a trigger at 0.5 seconds after the initiation of the pour. The full specification of PM-ALPHA and ESPROSE.m nms, including code versions and l other key inputs, is summarized in Tables 4.2 and 4.3, respectively. The results of Set-1 calcula-tions may be found in Appendix 7. In the following, we present and discuss the results of Set-II calculations. 4.1 The Premixing Results In exammmg the premixing results, of primary interest are the development of voids, the amount of melt accumulation obtained due to deceleration in the pool, and the degree of freezing due to heat losses to water. All of these can been seen in detail, with respect to time development, under 200 *C. However, it is also noted that for a creep rupture lower head failure there are no firm estimates of superheat (it could be considerably larger). As noted in Appendix 6, the l chemical reactivity of zirconium with steam could provide potentially an energetics-augmenting l factor, however, this could not occur in iron-rich melts because of the " diluting" effect of the l low-reactivity iron. 4-2
s Table 4.1. Key to the Premixing Runs Performed With PM-AIMIA Poe! Pow Pool Water Mek Meh inlet Run LD. Diameter Diameter Depth Subcooling Ptwr Rate Wlocity (m) (m) (m) (C) (kg/s) (m/s) Set I 6 0.6 1 20 750 8 PM - 1/204.75 6 0.6 1 20 1500 3 PM - 1/20/1.5 h 6 0.6 3 20 750 8 PM - 3/20m.75 ! 6 0.6 3 20 1500 8 PM - 3/20/1.5 l Set II 7 0.5 3 80 560 11.6 PM - 3/80m.5 7 0.5 3 0 560 11.6 PM - 3 Alm.5 ! 7 0.5 5 20 560 11.6 PM - 5/204.5 7 0.5 5 80 560 11.6 PM - 5/80m.5 ! i t
.- ~~.- ,- -. . - - . . _ . . . . . - - - . _ . - . . - - . - - - . _ . . . _ _ - . - .
b l
)
Table 4.2. PM-ALPHA and Input Specifications l for Calculation Sets I and H ! i PM-ALPHA, version MOD.1 l Fuel Temperature (K) 3050 3 i Fuel Superheat (K) 50 l System Pressure (bar) 1 i Particle Size (cm) 1 i
'l I l Table 4.3. ESPROSE.m and Input Speci6 cations !
for Calculation Sets I and H ESPROSE.m, version MOD.0 Fuel Temperature (K) 3050 Entrainment Factor 4 l for all 4 runs, in Appendix 8. Here we present sample results, primardy in a comparative manner, among runs, such as to make evident important trends. Also, the additional detail afforded by these color plots should be useful in understandmg the results shown in black and white in Appendix 8. The important and expected effect of water subcooling on void formation is illustrated in
. Figures 4.1 and 4.2, for the 3 and 5 meter deep pools, respectively. These comparisons are taken l st the time of melt arrival to the pool floor, but as can be seen in Appendix 8, the 20 *C water pools do not develop any void, even well after this time. On the contrary, with saturated water we observe that the void extends essentially over the whole mixing zone and it can be seen in Appendix 8 that this behavior is simdar for the duration of the transient. We also observe that the main fuel mass is in a water depleted region, while the " leading edge" seems to develop a region of low voids (< 10%), and somewhat accumniatad but radially spread out fuel. This is reminiscent of the " vortex ball" observed experimentally in such jet-like penetrating flows. This portion of the premixture can be considered quite favorable to triggering and propagation. On the other hand, we observe that even a relatively small subcnoling (20 *C) can suppress voiding to '
l l quite a large extent; interestingly enough, a limited voided region develops immediately behind the leading edge, quite late in the transient (~1 s) and it remains quite localized in the same 4-4
l ? j manner for the remmi* of the tunsient (~1.5 s). Again, we notice a local region of fuel accumulation from an entry value of 3% to a high value of 6% just behind the leadmg edge. From another perspective, we can observe that the voids did not develop until after ~0.9 s and after the melt penetrated the pool by ~4 meters. That is, under the pour and pool subcooling conditions considered, voiding would be expected to be negligible for pool depths of up to ~4 m eters.
'Ibe main reason for this strong effect of subcooling is that the melt flow induces a pool circulation, with cold water from around the mixing zone being entrained and flowing downward together with the melt, as illustrated in Figure 4.3(left). This motion can be reversed [see Figure 4.3(right)] only if there is a strong void, as in the saturated case, which leads to the ETHICCA phenomenon introduced in Appendix 2. Otherwise, the water experiences different exposure times to the melt as it flows down, and this is why the void first appears behind the leading edge. As discussed previously (see Appendix 2), these behaviors are dominantly two-dimensional and cannot be captured at all by one-dimensional formulations.
Melt freezing is very important, especially for the low superheat oxidic melts, not only because frozen material simply cannot participate in an explosion, but also because the presence of significant solids fraction could also effectively " shield" the melt from water within the propagation time frame, as well as signinc=ady increase the melt viscosity, thus interfering with I both fragmentation and the microinteractions. 'lhe freezing pattem obtained in the four runs discussed here is illustrated in Figures 4.4 to 4.7, at the time just before applying the trigger. For reference, the total fuel distributions are pmvided in each case, as well. By comparison among these 4 figures, we can discern the effects of water subcooling and pool depth (exposure l time). In all cases, the amount of freezing is not negligible, however, as expected, the pool depth is the dominant factor. 'Ihe fracdon of the total fuel in the premixture that is found to be frozen are 38%,40%,42% and 44% for the four cases of Figures 4.4 to 4.7 respectively. As we will see below, the impact of this freezing on energetics is rather significant, and to cover the range of uncertainty in this area we have a new option in PM-ALPHA that provides the other extreme of conduction-limited freezing. In this version the conduction equation is solved for each particle such that its surface temg. hue and any phase change occurring within it (an inward moving front) are updated at each time step, accordmg to the cooling history. This minimizes the heat losses fmm the particle, as compared to the standard PM-ALPHA model that considers a uniform particle temperature, while on the other hand allows freezing before all superheat is lost. 'Ihe net result is a partial compensation and a relatively minor effect on both l the quantities frozen as well as on the premixture void. As an example, the effect on freezing for run PM(II) - 5/80M.5 is shown in Figuie 4.8. 4-5
k PM(N)4900.5 PM(N)490.5 e
;, i
*
- gr. ? ' sa
** t' ..
- Ff ,
.. ; )
. 'f _ , . .- .
.,. : cc w.ma2.sumu o- e a= .. .
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) == .. )$8 .D 7 , c- t . 3 ', , .
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,sc
.' /., A4,- ,, ., p .-
h,( Pf) g$ .a
=
s7_f<
=
- [i ..%h: ; 6,. f) -
Fuel 2,
~'
Fuel Void Volume Voki Volume Fraction Fraction Fraction Fraction Figure 4.1 Comparison of fuel volume fraction and steam void fraction distribution developed . after 0.65 seconds of premixing in runs PM(II)- 3/80/0.5 and PM(II)- 3/0/0.5. i - . _ m -.__ ._ _ ._ -_s. _ _ _ . _ _ _ . _ _ _ _ . _ _ _ _ _ _ . _ . _ _ _ . _ _ . _ _ _ _ _ . _ . _ _ - . - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _._-m__ ____ _ _ _ _ _ _ _ _
L k l I PM(N)-5/800.5 pqpm3 4 !! i t il _t ** 1
" u _
== ,- . .. L i
*=
7
-. >2 .
av s om l
*7 ;
e,
- .. g' ; "*
l N Jl[f t ,- ,. .. JI ems t : m pa j f{. , ..
*> q =j@
.. => fg s ., t ..
t I
- i. .ij du ! -
'th
] a ; ':M[
~
I Toted Fuel B. I i i Void Volume Vf Total Fuel E' Void lI Volume i Fraction h - _ _ _ . . ..) Fraction Fraction __ {_ _l Fraction j i Figure 4.2 Comparison of fuel volume fraction and steam void fraction distribution after 1.15 seconds of premixing in runs PM00 - 5/804.5 and PMGD - 5/20/0.5. r i. _. _ _ _ _ _ _ _ _ . _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ .______.______________r-
1 l l l i PM(II)3/80/0.5 PM(ll)-3/WO.5 44 _ - ' ,_ [f ]
, ... m -
~
. ,f,(V
! j .hg. ,
l,,' v~ 7;;f ,
" ' I
.I. '. ji pl . .
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. s7: .
1 w)u(;:..
.' C -
f:'.' =
- g: if4: -
.. .l t.
. ne -v j , tY-- *
~%ff4\s?~
Vold -'- Water Volume Flum Void I 's -'! Water Volume Flux Fraction , , (cm/sec.) Fraction , (cm/sec.) Figure 4.3 Comparison of the calculated pool circulation pattern at high Geft) and aero (right) subcoolings (in runs PM(II)- 3/80/0.5 and PM(II)- 3MD.5, respectively).
r- - 4 4 i
- i. .
l t i i
.. i
.- i
.._..-_.._._.4Q_._,_m
. .= l 4- .
f:. ..
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j;; W\ '\ .- g,n ij ! .-
.s g\ .. q.
'4 +s3 A ,. ;' -h '
}' '-j,.';'. 1~f Solid Fuel ,
Total Fuel Volume Void ym Void , Fraction Fraction - 2 Fraction s Fraction r I Figure 4.4 Spatial distribution of total fuel (left) and solid fuel (right) volume fraction for mn PM(D)- 3/80/0.5, at 0.65 s. 1 a r i I k
L
- 3. I .. ,,
. ! ;f -
;3
' *** =
.. ; ,ll ..
.. .s
. gi .. .- .. .,
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' y. u _
,n Fuel Solid Fuel Void
'-~'
Volume Void
- -- Volume ,
Fraction Fraction Fraction - - - - -- - - -- -. Fraction , Figure 4.5 Spatial distribution of total fuel (left) and solid fuel (right) volume fraction for run PM(II)- 3/0/0.5, at 0.65 s. , I i i 6 i t i i
l \ (
- w ..
e . - .. ..
! *~
[ V1
.. j i .
4
-1 p
3
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u ,
= - 1 :I :
j., p . [
., t s ~
n .. i I
' f f ,I l l f Solid Fuel 1 Total Fuel void Fraction g- i' voium.
Fraction void Fraction T., (y;;/p! voium. Fraction Figure 4.6 Spatial distribution of total fuel (left) and solid fuel (right) volume fracdon for run PM(II)- 5/80/0.5, at 1.15 s. i. 5 l
i I
.. 4 l, .. ,_
p..
= :----- ..gp -
u 6 - 4= ..
===
,, ,r . ,, .
.. J == n . .
?
2
. f'o ..
pu '
*= u ff)' ..
y ee a 3 l
'~
== se ,t{ , .y::)y .-
i i y: f .w .
== c>
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1 i
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q%#.7 . i.. - !,% [y : -'
- &fu ' Y M y'
- r - /
Total Fuel h sV Bolid Fuel Vold \:N/ Volume Void V8 Volume Fraction Fraction Fraction Fraction i. t Figure 4.7 Spatial distribution of total fuel (left) and solid fuel (right) volume fractions for run l PM(II)- 5/20/0.5. [ l i I e
i P l l'
. - - - - . m~s x.
a est
** ./ d'
[l.
.'* p
- i. ,
d, jj < .. *. , p; p ,, {' ! . , , , t; y . 1 R1 ,,
L ..
,N'
'7 Solid Fuel Solid Fuel Void Fraction
( l" Volume Fraction Void Fraction Ta[ 9 J Volume Fraction i Figure 4.8 Companson of the calculated frozen fuel volume fraction distribution in PM(II)-5/80/0.5 between the standard PM-ALPHA model (left) and the new conduction-limited phase change mod 51 (right).
~ _ _. - _ _ _ . _ _ _ _ _ ____._.___.____
These premixtures provide, we believe. a reasonable range of conditions for a first scoping of explosive behavior in SBWR-like geometries. As noted above, breakup to smaller (<1 cm) particle sizes would provide a higher interfacial area for microinteractions and thus enhanced energetics in an explosion; however, during premixing, this higher interfacial area would also favor void formation and higher degrees of melt solidi 6 cation, thus introducing important com- 1 pensating effects. A partial exploration of these effects is to be presented with Set-III calculations (Theofanous et al.,1995a), and a more comprehensive invcatigation is planned immeAiately af- ! 1 ter PM-ALPHA has been tested against the early results from MAGICO-2000, with new Set-IV calculations, speci6cally focused on this (compensating effects) topic. ( 4.2 The Propagation Results l In examining the propagation results, of primary interest are the development of the ex- l plosion and radiated waves, the role of venting in this development, and the resulting pressure pulses at the pool boundaries, which are needed for assessing the potential for structural damage. ! These pressure pulses are summarized in Figures 4.9 through 4.13 for the 5 explosion calcu-lations performed, respectively. The detailed development of the pressure waves, for all five runs, can be found in Appendix 9. In what follows, we examine comparatively the wall pressure pulses and then relate these results to the explosion and pool response as a whole, by means of j selected results from Appendix 9. ! First, we note that, as expected, the pulse width is larger for the deeper pools. In fact, comparing the otherwise corresponding runs E.m(II)- 3/80/0.5/0.65 and E.m(II)- 5/80/0.5/1.15, i we see that a nearly doubling of depth produces a nearly double pulse width, while the peak i pressures are very similar. Also similar are the staircase-like structure of pressure decay in the j upper half of the pools due to wave reflections. As we will see below, this behavior is quite ; predictable in terms of the pool aspect ratio and the relation of its acoustic time to the time-duration of the driving pressure pulse. What is not so simply predictable from acoustic theory i fundamentals is the magnitude and character of the driving pressure pulse itself-it is here that the full, and unique, ESPROSE.m capability to couple the explosion zone with the surrounding pool response in a full 2-D manner is indispensable. i The effect of accounting for freezing can be seen in Figures 4.11 and 4.12. For a reduction in total fuel quantity of 38%, we observe a reduction in peak pressure, and in total impulse since the waveforms remain the same, by about a factor of 2. This is clearly a major effect, and it would be even more pronounced for smaller melt particle sizes. The effect of voids can be seen by comparing run E.m(II) - 3/80/0.5/0.65 with E.m(II)- l 3/0/0.5/0.65 and run E.m(II)- 5/80/0.5/1.15 with E.m(II)- 5/20/0.5/1.15. 'Ihe first two reflect the 4-14 i
r i r l l l ll l l , z=6.2cm z = 156.2 cm - - c - I-1 en . g200 - 200 ~
- i. . . i- . . . . .
- a. -
\
0 2 4 6 8 0 2 4 6 8 l z = 56l2 c . z = 206.2 cm ; ; 5200 i- .
.- 200 1-
-{
- a. -
1
. l 0 2 4 6 8 0 2 4 6 8 i z = 106.2 z = 256.2 cm : .
e . E200 i- <- - - - 200 -
~: .i- .
1 I e _ 0 2 4 6 8 0 2 4 6 8 Time (ms) Time (ms) Figure 4.9. Pnssure pulses at various heights along the pool side wall, obtained from mn E.m(II) l
- 3/80/0.5/0.65. Total wall-average impulses at the six locations am: 43.8 kP2 s (z = 6.2 cm);
42.7 kPa s (z = 56.2 cm); 38.5 kPa s (z = 106.2 cm); 32.0 kPa s (z = 156.2 cm); 25.1 kPa s (z , ) = 206.2 cm); and 18.5 kPa s (z = 256.2 cm). ' 4-15 l
3 i e 200 200 z = 6.2 cm. - - z = 156.s em - : ! c ' ~ m Q100 - -- - 100 ;- :- ; i Q- . : . 0 2 4 6 8 10 12 0 2 4 6 8 10 12 200 . 200 z = 5 6.2 c.~ m
~
z = 206.s em - - tr -
- : i m .
Q100 - - -- i- +- 100 y
~
-i; .- '
- n. . .
l 0 2 4 6 8 10 12 0 2 4 6 8 10 12 l 1 l 200 200 . z = 106.s cm z = 256.2 cm . . . l e . m '" ' Q100 , 100 ;
-l- ,
t
}- l 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Time (ms) Time (ms)
Figure 4.10. Pressure pulses at various heights along the, pool side wall, obtained from run E.m(II) - 3/0/0.5/0.65. Total wall average impulses at the six locations are: 31.1 kPa s (z = 6.2 cm); 30.2 kPa s (z = 56.2 cm); 27.2 kPa s (z = 106.2 cm); 22.7 kPa s (z = 156.2 cm); 16.9 kPa s (z = 206.2 cm); and 9.9 kPa s (z = 256.2 cm). 4-16 l l
t l l l l 2.=.6.2. j i c 400 400 2.=.268.7. cin . 3.. m - m
~200 n.
?- 200 -
- - - -r -
l :
} .
0
- O 5 10 0 5 10 2.= 93.7 ni. -
400 2 =.35E 2 cm. . c 400
- m -
m
~
200 n.200 0 ) 0 l 0 5 10 0 5 10 l m400 2.=.1.81. cin . ... .- 400 2. = .4.43 [7. cin . . . . . . ;... 5 m
-1 200 . . . .. . ... r. .
200 . . ... ... ..a.... .+ .. l . l 0 I 0 0 5 10 0 5 10 Time (ms) Time (ms) Figure 4.11. Pressure pulses at various heights along the pool side wall, obtained from mn E.m(II) - 5/80/0.5/1.15. Total wall-average impulses at the six locations are: 107.3 kPa s (z = 6.2 cm); 102.0 kPa s (z = 93.7 cm); 88.0 kPa s (z = 181.2 cm); 68.9 kPa s (z = 268.7 cm); 45.6 kPa s (z = 356.2 cm); and 18.8 kPa s (z = 443.7 cm). 4 4-17 l l l i l - .
l J l l l l o i z = 6.2 cm . : z = 268.7 cm. . _200 l m 200 -- -
-+- ,
t a - 0 5 10 0 -5 10 z = 93.7 c : z = 356.2 cin :
% 200 200 LD., . : i -
- a. :
0 5 10 0 '5 10 z = 181.2 cin z = 443.7 cin egoo 200 . . . ......;.............. a1
)t : ,U' 0 5 10 0 5 10 Time (ms) Time (ms)
Figure 4.12. Pressure pulses at various heights along the pool side wall, obtained from mn E.m(II) - 5/80/0.5/1.15 (m). Total wall-average impulses at the six locations are: 39.6 kPa s (z
= 6.2 cm); 37.8 kPa s (z = 93.7 cm); 32.9 kPa s (z = 181.2 cm); 25.6 kPa s (z = 268.7 cm); 16.4 ,
kPa s (z = 356.2 cm); and 6.7 kPa s (z = 443.7 cm). i 4-18 i l .. l
}
l I 1 i l t i 400 . .z .=. 6.2 cm . . . . . . . . ;. . 400 2.=.268.7 i.. ... . . . .:. . c
. qs . 1 m *
~ -
-i- -
2bo i-c.200 I
- 1 l :
l 0 0 4 t 0 5 10 0 5 10 1 400 z.= 93.7.cm . : . . . . . 400 2.=. 356.2 :...... .:. . e : g
~
i- - 1- 200 - n.200 - - - - 1-0 5 10 0 5 10 400 2.=.181.2 :. ....;. . 400 2.=.443.7 cmj . . . . . . . .;. . . e45 *
.g * -
o.200 i- 1- - 200 - -
-i - :-
0 - 0 0 5 10 0 5 10 ! Time (ms) Time (ms) l Figure 4.13. Pressure pulses at various heights along the pool side wall, obtained from mn E.m(II) - 5/20/0.5/1.15. Total wall-average impulses at the six locations are: 90.2 kPa s (z = 6.2 cm); 87.7 kPa s (z = 93.7 cm); 77.7 kPa s (z = 181.2 cm); 60.2 kPa s (z = 268.7 cm); 39.3
- l. kPa s (z = 356.2 cm); and 16.6 kPa s (z = 443.7 cm).
i 4-19 i
, .r- - .. . - - - - ' ~~^
i ; i behavior at the two extremes, zero versus very high void, while the other two depict the more subtle effect of the presence of small, spatially-limited voided regions. Thus from Figures 4.9 and 4.10 we see the tremendous damping effect of high voids (this has been discussed previously by Medhekar et al.,1991, Theofanous and Yuen,1994, and Fletcher,1993), while from Figures 4.11 ; and 4.13 we observe that limited, local voids have only a temporary retarding effect on the f explosion. As far as total impulse, the most severe case is that of run E.m(II) - 5/80/0.5/1.15, where the lowermost portion of the pool boundary is subjected to ~107.3 kPa s while the average I impulse of the whole boundary is considerably less (71.8 kPa s). As a general perspective on these numbers it is noted that in the 100-150 kPa s range the structural stability of reinforced ; pedestal walls begins to become a concern. For a freestanding steel sheet as in the SBWR lower l drywell corium shield, the structurally-important impulses are in the range 150-250 kPa s. In discussing the wave mechanics, we begin by considering run E.m(II) - 3/80/0.5/0.65 in l sufficient detail to follow the processes of escalation, direct venting of the explosion zone, the l l radiated pulse, reflections off the walls, and eventual venting. These are typical behaviors of all l l the other runs, as can be found in Appendix 9. Referring to Figure 4.14, the early escalation is shown by the pressum distribution at 0.8 ms, but the pressure buildup within the interaction zone is arrested by radial expansion (lateral venting) while, as illustrated by the distribution i at 1.2 ms, it has progressed already to a very large degree even before the propagation front has arrived at the pool top surface. The bottom reflection and pressure doubling can be seen at time 2 ms. This figure also makes evident the venting effect of the free air-water interface and the special soliton-like structure of the radially moving wase, which is even more clear at 2.8 ms. This structure is due to superposition of the comprestion waves coming from the explosion zone and of rarefaction waves coming off reflections frm Le tree surface, and it can be demonstrated analytically. By 3.6 ms, the main body of the pool is seen to be vented, while a radial pressure wave is being reflected off the side boundaries doubling in magnitude. An inward moving (radial) pressure pulse is generated, but it is gradually " eroded" both off its top and its behind by venting processes as seen by the sequence at 4.4 and 4.8 ms. At 4.8 ms, what appears as ari~ inner core of the pool (basically spanning the region in which the explosion took I place), is rather voided, and it is here that the converging pressure waves dissipate, as seen at ; 6.4 ms. In a much deeper pool that has been only partially penetrated by the melt, the lower regions contain no voids, so the radially incoming waves mentioned above can be focused to a significant degree to finally dissipate only upon rebounding into an outward radial wave. l In the large-void case of E.m(II) - 3/0/0.5/0.65, on the other hand, the damping behavior dominates throughout and the explosion never quite develops. This is manifested as a sequence 4-20
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i of " attempts" to escalate, that endup fiz71ing into the void. This behavior can best be seen on the detailed printout in Appendix 9; an abstraction of it only is rendered in Figure 4.15. j The damping effect of limited / local voids as seen in run E.m(II) -5/20/0.5/1.15 is illustrated m Figure 4.16. At 0.8 ms the escalated wave hits the bottom of the void area; at 1.2 ms it is j seen to be going around it, while dampening significantly; at 2 ms the escalation is strongly resumed, but at 3.6 ms it is seen to quickly vent in all directions, including downwards, aided by the local voids. Even including the effect of reflection from the wall, the overall pressure reduces. As can be seen in Appendix 9, from then on the behavior is similar to what has been described above. l The effect of pool depth (or aspect ratio) can be seen from Figure 4.17 (run E.m(II) - 5/80/0.5/1.15) when it is examined in relation to Figure 4.14. Basically, the greater depth delays the upwards venting of the explosion which, therefore, sustains the radial pressure wave for a longer time, as seen by the distribution at 1.2 and 2 ms. Upwards venting begins as the radial wave is about to impinge on the side walls (2.4 ms), and it is not very significant until the main wave is already reflecting radially inwards (3.2 ms). This leads to the dissipation phase, which is simdar to that in Figure 4.14, except that because of the greater depth the outer bottom comer l is vented last, and only when rarefaction waves off the free surface (moving downward) and off the central void (moving radially outward) arrive at this location. This is shown by the sequence 4.4 ms,4.8 ms,6.4 ms, and 8.4 ms in Figure 4.17. Finally, the effect of a reduced quantity of fuel in moderating the severity of the explosion may be seen in Figure 4.18, comparing the early escalation in the two corresponding runs: E.m(II) - 5/80/0.5/1.15 and E.m(II) - 5/80/0.5/1.15 (m). Also, the late escalation between these ; two runs is compared in Figure 4.19. It is remarkable how simdar the wave structure is, except for the magnitudes, owing to the reduced quantities of melt driving the interaction in the case where the frozen material calculated from PM-ALPHA has been excluded. 4-23 l
i t
;k, ll i
500- 500, Pmax = 3227 Bar i Pmax = 963.9 Bar s 400, t = 1.2 ms 400- t = 1.6 ms ; liI ; c - f \ E.300- $.300- f li l i A ; A 100- - 100-6' 6 60 . 60 40 40 g M . M M . M [
'1 i
500' 500,
- Pmax = 775.6 Dar Pmax = 830.9 Bar 400- t = 2.8 ms 400, t = 3.2 ms g \ e p
E.3m- E.300 l ,
!25- .t l im-cl200-300, l
I 1 \I 60 80
.0 .0 20 20 20 l 20 Figure 4.15. Illustration of the repeated attempts to escalate in the presence of an extensively voided premixture. Run E.m(II) - 3AVO.5A).65.
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- 20 m a lllll20
~ "'
- -- ::r - -
so ll so f Figure 4.17. De pms' sum wave dynamics in a deep pool as seen from run E.m(II)-5/80m.5/1.15.
400 I[4N ' 400- I[8N"' ~ . - so 2c 20 E' lll 2, t w < iN4N Is74N ' " r l l200- 200,
);
'] _
Figure 4.17. (continued)
pi' l I Pmax = 922.6 Bar Pmax = 404 Bu 400- t = 0.8 ms L 400- t = 0.8 ms sm. Pmax = 810.8 Ba f [ ' 300, Pmax = 861.8 Bar g 4m- i- i.s ms j 400 , = i.s ms ,l [m- , 4 la, h l2m-I t m-
- t00- t y 200, !
l d' ! l= IV
, m , a ll *
- a a a a Figure 4.18. The early escalation phase in runs E.m (II)- 5/804.5/1.15 (on the left) and E.m(II)
- 5/80N.5/1.15 (m) (on the right).
l l
- 500, 500'
Pmax = 371.9 Bar Pmax = 296.6 Bar
, \
400, t = 2.8 ms 400, t = E8 N l a 20 Wm '" l 20 Pmax = 416 4 Bar Pmax = 220 Bar i 400- t = 3 6 ms 400, t = 3.6 ms ! d300- [300-f200- 4 l200- i k L, 1(' , 6, 8 6 Figure 4.19. Comparison of the late escalation phase between runs E.m(II)- 5/80W).5/1.15 and l E.m(II) - 5/80/0.5/1.15 (m). [ t
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5.0 PULSE-WIDTH SYSTEMATICS The wave dynamics results and discussion presented above can be generalized, for the purpose. of estimating a pdod the timing of the impulse on the sidewall, as follows. For shallow pools (aspect ratio less than 1), the outgoing pressure wave reaches the wall
' after the explosion wave has vented off the top, thus the pressure pulse should be contained between the wave arrival time (equal to the acoustic time in the horizontal duection) and the
- incremental time required for relief in the vertical direction (equal to the acoustic time in this direction). For the 3-meter-deep pool considered here, the acoustic times are 2.4 m and 2 ms in 1
the horizontal atxt vertical directions, respectively, and according to the above, the main pressure pulse should be observed between 2.3 and 4.3 ms. As seen in Figure 4.9, this is indeed the case. For deep pools (aspect ratio greater than 1) the outgoing pressure wave is sustained, from - behind, well after it reaches the wall and until the explosion is vented off the top. Relief then requires an additional acoustic time in the vertical direction. For the 5-meter-deep pool considered here, the acoustic times are 2.3 ms and 3.3 ms in the horizontal and vertical directions, respectively, and according to the above, the pressure pulse in this case should be contained between 2.3 and 6.6 ms, and as seen in Figures 4.11,4.12 and 4.13, this is indeed the case. i l l t I i i II f w 5-1
--- - _ _ _____.___ _ ____t __ - 3.---r . -- .
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l 6.0 CONCLUDING REMARKS l l i The purpose of this work was to summarize, under one cover, an approach, the analysis tools, l i their verification status, and preliminary illustrative results for assessing the damage potential of j ex-vessel steam explosions. l The approach is based on treating conservatively aspects of the phenomenology considered j too vague, or uncertain, for the time being (such as bmakup dynamics and triggering), while l focusing on physically demonstrable aspects such as void formation in premixing, and explosion ! venting in open pool geometries. Most importantly, the self-compensating relation of particle size with void formation and melt freezing was identified, and the idea of " penetration cutoff" of high velocity melts in subcooled ex-vesse' pools has been put fonh. Unique aspects of the analysis tools are a 2-D capability, which is considered essential to repmsent the key physics of both premixing and propagation, and a physically meaningful explosion concept, that of "microinteractions." Verification is well along the way. Key testing in the immediate future will be with the MAGICO-2000 data, while from SIGMA-2000 we expect a substantial data base to support the constitutive formulation in the microinteractions model. l We also expect to provide some initial experimental evidence on the penetration cutoff idea, also , in the near future. l The results provided here demonstrate clearly the role of voids in dampening an explosion; they give a perspective on the conditions under which such voids can be expected to develop; and they demonstrate the role of explosion venting in mitigating structural loads. In addition, we provide a simple procedure for estimating the timing of the pressure pulse on the pool boundaries; however, the amplitude transient is demonstrated by means of these illustrative results to be a much more complicated matter requiring the full hydrodynamic coupling between the explosion zone and the surrounding medium, as done in ESPROSE.m I i ! 6-1 l i
7.0 REFERENCES
- 1. Fletcher, D.F. (1994) " Propagation Investigations using the CULDESAC Model," Proceed-'
ings of the CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994, pp.180-192
- 2. Fletcher, D.F. (1993) " Steam Explosion Triggering: A Review of Theoretical and Experi-mental Investigations," Proceedings of the International Seminar on "The Physics of Vapor Explosions," October 25-29,1993, Tomakomai, Hokkaido, pp.111-117.
- 3. Liu, Changchun (1994) " Film Boiling on Spheres in Single- and Two-Phase Flows," PhD Thesis.
- 4. Medhabr, S., M. Abolfadi and T.G. Theofanous (1991) " Triggering and Propagation of Steam Explosions," Nuclear Engineering & Design 126,41-49.
- 5. Saito, M., et al. (1990) " Melting Attack on Solid Plates by a High Temperature Liquid Jet
- Effect of Crust Formation," Nuclear Engineenng & Design 121,11-23.
- 6. Theofanous, T.G., C. Liu, S. Additon, S. Angelini, O. Kymn1sinen and T. Salmassi (1994)
"In-Vessel Coolability and Retention of a Core Melt," DOE Report DOE /ID-10460 (Peer Review Version).
- 7. Theofanous, T.G. and W.W. Yuen (1994) "The Probability of Alpha-Mode Containment Failure Updated," Pre ** dings of the CSNI Specialists Meeting on Fuel-Coolant Interac-tions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994, 331-342.
- 8. Theofanous, T.G., W.W. Yuen, JJ. Sienicki and C.C. Chu (1995a) "The Probability of Containment Failure by Steam Explosions in an SBWR-Like Lower Drywell," ARSAP report (in ymy== ion).
- 9. Theofanous, T.G., W.W. Yuen, JJ. Sienicki and C.C. Chu (1995b) "The Probability of Lower Head Failure by Steam Explosions in an AP600-Like Reactor," ARSAP report (in ynyumion).
- 10. Theofanous, T.G., W.W. Yuen, H. Zhao, I. Jansson and W. Frid (1994) "A Study of Ex-Vessel Steam Explosions in Swedish BWRs," First CSNI Specialist Meeting on Selected Containment Accident Management Strategies, Stockholm, Sweden, June 13-15, 1994.
- 11. 'Ihrland, B.D, D.F. Fletcher, K.L Hodges and G.J. Attwood (1994) "Quantification of the Probability of Contamment Failure Caused by an In-Vessel Steam Explosion for the Sizewell B PWR," Proceedings of the CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994, 309-321.
- 12. Witt, R.J. (1994) "Iacal Creep Rupture Failure Modes on a Corium-Loaded Lower Head,"
Nuclear Engineering & Design 148,385-411. 7-1
. . .. . -. . . - . .- -. -.. _. .. .. . =- . . . . .
j J 4 7 i l APPENDIX 1 l MULTIPHASE TRANSIENTS IN THE PREMIXING OF STEAM EXPLOSIONS Proceedings of the Fifth International Topical Meeting l On Reactor Thermal Hydraulics - NURETH-5 September 21-24,1992, Salt Lake City, Utah Volume II, pp. 471-478 1-1
. _ . _ _ ____._m_. _ _ . _ _ _ _ -__.____ __ . _ _._. _ _ -. _ _ . _ . _ _ _ . _ ,
l MULTIPHASE TRANSIENTS IN THE PREMIXING OF STEAM EXPLOSIONS S. Angelini," E. Takara,* W. Yuen" and T.G. Theofanous Center for Risk Studies and Safety C e-io ; of Chemical and Nuclear Engineermg University of California, Santa Barbara, CA 93106 Telephone (305) 893-4900 - Fax (805) 893 4927 l' ABSTRACT (the so-canarl " closure" relations) in three? systems, with the one phase in Alm boiling. Initik results have his paper describes the Arst attempt to experimentally quan- been by Liu et aff he second effort is to ex-tify the multiphase transient associated with the
- amine ing of steam explosions- a hot particulated (heavy se integral aspects of the premaning process with l
falling, in film boiling, into a coolant pool, which thus emphasis on the performance of the three-fluid modelling approach. For this purpose we use an already paniculated forced, to rapid vapontation. De process is, characterized hot vness (particles of a given size) instead of a liquid, and by maxms-zone-averaged and local void-frecuon transients, seek to characterize in detail the spatial-temporal evolution as well as mixinpfront advancement histories, and the data are found to be m good agreement with predictions carried of the three-phase mixing zone created when these particles out with our PM-ALPHA code, in particular, these tests are dumped (as a cloud) into a liquid coolant pool. This i confirm the ted water de etion phenomenon which is the subject of this paper. Finally, the third effort is to is a crucial actor in limiting energetics of large-scale test the prediction in experiments run with molten " fuel" steam explosions. thus including the " fuel break-up phenornena during pre-mixing.- It is ex ted that the FARO experunents at the T m,~.o Joint h Center (ISPRA) and the ALPHA
- 1. INTRODUCTION experiments at the Japan Atomic Energy Research Insti-tute (Tokai) will provide data uste for this purpose.
Essentially all practically relevant steam explosions oc- It should be mennoned, however, by its very nature, l cur in the poun,ng mode of contact. Large, energetic ex- the breakup, process can only be indirectly inferred from i I plosions can only evolve from (or propagate through) "ad- these expenments (i.e., vapor producuan rates), and it is equately" dispersed states created in this pouring / mixing expected to remain uncertain m its details-cevertheless, process. In analogy with chemical explosions these states its effect on the water-depletion phenornenon, and thus on are referred to as "premixtures." A premixture is charac- energetics, can be bounded by parametric evaluations. terized the spat al distribution of the " reactants," the l " hot" " cold , liquids (ahematively referred to as " fuel"
" II. EXPERIMENTAL FACILITIES and " coolant" and a third "inen" coa-a---*. the "v De role of th)is third component is duah Arst,it ces
- ne basic concept of the experiment (called MAGICO) compressibility which has a dissipative effect on tri g, is illustrated in Fi 1. 'Iens-of-kilograms quantities of escalation and stion of an explosion; it im- mm-siae steel are heated to a unifonn high (up to plies depletion of iquid coolant (the " working" fluid) and 1000 *C currently) ; ...,~. ., then transferred into an in-thus reduced energetics even if an explosion were to oc- tern = ham contamer equipped with a dumper mechanism, cur. This latter aspect was first recognised by Henry and and within a few seconds are released into a pool of sat-Fauske,3 and it was a key ingredient in the quantincation urated water in a lower-plenum-like geometry. De intent of steam-explosion-induced containment failure by Deo. is to match (except for the betakup) the water-depletion fanous et al.8 Dese initial predictions were made with a regimes of the reactor m a 1/g-scale geometry, and numer-l transient, two-dunensional, two-fluid model, i.e., with the scal simulations (PM-ALPHA) ase used for,this purpose. <
assumption that the vapor and liquid coolant behave as a De m8F **perimental parameters are panicle siae, par. homogeneous-equ.libn.um i mixture. In subsequent work 3 ticle ...,~, .re, pour diameter and particle entry velocity. this assumption was relaxed by the use of a three-fluid in addition, we intend to vary the particle cloud density and model, whichis , similarly-depleted (m water) pre- the lower plenum geometry (by including internal struc-mixtures. Clearly,it is important that these predictions are tures). In the followmg we provide some details of the confirmed experimentally. ex r;. 4,,;.1 equipment and the measurement techniques. > i his ex -g;.,e. tally-oriented effort consists of three For this experiment the oven cavity was equipped with ! j parts. De Brst is to examine the interface transfer laws a ceramic cylinder (1.67 m long, 8.2 cm in diameter) that could be loaded, plugged at both ends, and rotated during
- heating to r
- Also with the Depanment of Mechanical and Environ- high .. prevent the steel balls from sticking together at
.;.s. De rotation also helped obtain temper-
- mental Engineering utm uni ormity. Integnty of the ceramic cylinder requires l
l-3 l
4 i i ma i CMrTE III. MEASUREMENT TECHNIQUES g Y 4 i m t w Eoiars As mentioned above, the key measurement in these j CONTAINER experiments is the space-time evolution of the liquid frac-i ovgu tions, in the two-dimensional evolving mixing zone, during 1 ------
~
the short (less than I second) transient. [An indication of ] what is involved is given in Figure 3]. Such measurements j . mEnAc'nON were made at the global level; that is, averages over the 4 VESSEL whole mixing zone, as well as at the local level; that is, on 8
"" "*'ang z" a sample volume of ~ 1/4 cm at severallocations within
] 3 the nuxing zone. Tle presence of hot particles introduced ! a different son of dilficulty for each of these two measure-ment approaches-correspondingly they were susceptible to Figure 1. Schematic of the MAGICO experiment. different kinds of limitations. This made them complimen-l d that heat-up be regulated closely at less than 150 'C tary to each other, specifically with regards to the portion ' of the transient (carher vs. later) best suited to each. Each hour-13 hours are required for a 1000 *C run, includm cooldown. When the desired temperature level is reached, measurement is discussed funher below. the one end of the cylinder is unplugged, and the whole oven is tilted so that by gravity flow the balls are trans-ferred to the intermediate container (this rocess lasts about Y 2 min.). Future tests with aluminum oxi particles will al- V - Iow temperatures up to the maximum oven capacity, which i i is 1400 'C. The inwire container (21 cm in diame-ter)is equipped with several thermocouples located such as M ".t ", to allow a good charactenzation of the initial temperature of the iculate at the moment it is released. Both the [c t
~
no ' (initially in the oven) temperature and this, actual, 3 temperature are recorded, and typically they differ by less + than 100 'C. Sudden and uniform release is achieved by I a solenoid-operated air-cylinder operation that, by a slight movement, aligns the holes of two orated plates that j ; ! 1
- make up the bottom of the interm ate container. In the
- present set-up, the holes are 1.1 cm in diameter, placed on 'e'
~
^ ~ ' '
_.~ 1 a square 1.27 cm pitch. In future tests this pitch will be , varied to obtain different cloud densities. The maximum " 3 C g pour diameter is 20 cm. . l The lower plenum scale model (the interaction vessel) . J was fabricated from steel and is equipped with an observa-tion window. Preliminary tests indicated that the behavior F F - 1 l ) is quite similar to that obtained in a plain rectangular ves- I s i sel (406 mm on the side, with a height of 355 mm), and ' j the use of such (made of tempered glass) was made,in the i
- experiments reponed herein, to allow easy and complete l visualimion. The whole experimental setup is shown m i
- Figure 2. Not discemible are the FLUTE components (see ,
i next section) as they are located just behind the interaction 4 l l vessel. Not shown is the data acquisition system which is i* m. . ) i located in another room. '7 l ,~ - V y . [&nsy ,.,1i ut. 2 E. . i mag # 1 : p 6.eneo co'mu ,
-[**"1 y ,
( . j ~y 3 . s y . 2 mm . w- m---
- Figure 2. An overall view of the MAGICO experimental Figure 3. Snapshots of a typical premixing transient in setup. MAGICO. The times are 0.33,0.66, and 1.0 seconds.
i 1-4 j
Since the melt volume fraction in the mixing zone is besides providing the local structure it is complementary to less than 2% (this is estimated from the pour area and the the volume-averaged one also in this respect. particle delivery rate, and is consistent with the results of P,M-ALPHA calculations) the hquid (water) volume frac- Even though less than 2% by volume , the presence tion m it can be deduced from measurements of the zone- of the hot, solid particles present serious difficulty in the averaged void fraction. By mass contmuity this can be measurement of local liquid (void) fractions. A new instru-l related to the apparent merease m volume of the surround- ment, FLUTE, had to be invented for this se.55 n e l ing bquid which, in turn, can be obtained from the observed principle of this measurement can be exp d with the I level nse. Such data were obtamed throughout the transient help of Figure 4. The idea is to measure the intensity of by closeup high speed movies (camera #1 in Figure 2). In fluorescent light emitted from a local fluid region, activated addition, the whole mteraction vessel, and especially the by ultraviolet radiation (a dye, fluorescein, dissolved in the whole free liquid surface, were observed with high speed liquid being the active ingredient). The size of the measure-camera #2. Void fraction data were reduced in two different ment volume is controlled by the distance L between the ways. One referred the measured void volume to the whole fibets (the acceptance angle 6, is 29'). Because the fibers nuxing zone volume, while the other made use of the whole are very fine (1 mm in diameter) their presence provides i volume under the pour area (a cylinder with a cross section hardly any disturbance to the flow. For this application ( the same as that of the pour area and a height equal to the (because of the hot, solid panicles) the fibers are protected instantaneous height of the hq by very fine steel tubing, and they also need to be securely The first will be referred to as ,uid, in the mteraction vessel).
' mixing-zone averaged void supported, as illustrated in Figure 5. De suppons are made fraction, while the latter as ' pool. height-averaged" void to offer minimal cross-sectional exposure in the main flow fraction. Clearly, the two should agree, when the melt-front direction, and we believe that the disturbance introduced just touches the pool bottom and begins to accumulate on by their presence is insignificant. He data rate is limited it. As seen m Figure 3, the mixin zone maintains the only by the capability of the data acquisition system. In the cross section of the pour area, thus gor the mixing-zone- hresent configuration, this is 8 kHz, but an upgrade to 80 averaged' void fraction the nuxing zone front only needs z is readily possible.
to be tracked. De error in estimating the water position is ti mm, thus the " pool-height-averaged" void fraction nis instrument offers a unique capability, in general, data involve an absolute error of 2%. De " mixing-zone- for the measurement of local, essentially instantaneous, lig-averaged" void fraction measurement uncenainty is primar-uid volume fractions in highly transient, multidimensional, ily impacted by properly following the mixing zone front. dispersed two phase flows. In the present application, the l sohd particles mtroduce some additional consideration with It is estimated that this was done to within il em, which regani to the choice of fiber (L in Figure 4). Panicle in-translates to a rather significant error initially, decreasing gradually to about i10% (relative error) near the end. Er- terference with both the emitting and receiving light heams increases with L (Note, however, that such interfersee is fors due to air entrained with the particles are negligible as verified by pours of cold panicles that produced no mea- not present from vapor and gas / liquid interfaces'). from surable level rise. At still later times, the interface breaks numerical simulations (Monte Carlo type) we find that for up in the manner illustrated by the third snapshot in Figure L = 4 mm, a melt volume fraction of 2%, and very low void fractions, this interference leads to a maximum abso-
- 3. This often happens at around the time the mixing-zone lute error in void fraction of about 10%. That is, for real front reaches the pool bottom, but sometimes earlier also.
Clearly, this marks the end of the time period for this son void fractions of ~10%, the FLUTE reading may be a; high of data. as 20%. However, as the void fraction increases, diminish-ing portions of the panicle interference are attributable to a
. From a Practical standpoint, this is also the , time pe- juantity of liquid " shadowed" and thus the absolute error ecreases. As a consequence, we expect that the relative nod of interest for steam explosion energetics-tf an ex-plosion has not been tnggered up to this pomt, it should error at void fractions over 30% to be under 10%. It is be at the pomt of impact, rather than at any later time. noted, however, that some funher work is required to firm Still, it is interesting to follow the void fraction transient up these estimates. On the other hand, as this interference for somewhat longer. He local void fracuon measurement effect is diminished by reducing L, liquid " trapping" be-tween the fibers can lead to errors. We call this fiber in-r r,a,;;- i
- sie v- guses -
pm,p e , .s,,. I L_ h l -
- 3_p -
o w.e --
+=f s A[p .
-{ s;;~;] o'\----
- ?!
Figure 4. Schematic illustration of FLUTE. He measurement volume is F,. 1-5
i l j Table I. Expenmental Mattix frr Runs with Global Lig- {( Ng%* ,, , y uid Praction Measurement (1.5 mm cromalloy A151-52100 h, particles)
'.,[{.c L .'
e h '.'"7; *^ ; mes O== Puises Peel Depeh henfall Peer
,mm. > ,' T_ T.. paq l
[. 3 01 600 Se0 2$ l$ #
,! - 35 i
- O = = = 11 s E
,. 4, n = 2 3 e 'i E Q
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= != = !! E E 2
111 313
=
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,Q s,?
' 'P[1 " Q( ] y D6 800 700 15 1s 12 Table IL Experimental Matrix for Runs with Local Liquid Figure 5. He FLUTE fibers and suppons for two simulta. Fraction Measurement (2.4 stainless steel particles,25 cm neous measurement locations in the mteraction vessel. pel depth, 20 cm pour *=m and 15 cm freefall dis-tance, except for runs 204 and 401, set at 5 cm and 3 cm, resPectively) terference;it tends to produce erroneously higher values at bqmd fraction. From expenments, we found this error to be significant for 4 == 1 or 2 mm. Thus, the measurements a.,
T
- o. E at w o.o <= o
- t. u- a' w 9.o 9-o L
reponed here were made with I == 4 or 5 mm. -- me sa0 su o s i, as s In any case, it should be recognized that these are g g g [j j j'j jj
- first and um,que (at this time) measurements, with a brand zu := m 24 4 se 14 4 new instrument, and clearly in need of further verification. El E E lj E jj
- One aspect of this is poss,ble i by the order-of-magnitude g g g gj j g gj
- com sons with the nuxmg-zone-averaged measurements, as em m 34 6 3, 34 s and y more detailed comparisons of both sets of measure- 3 2 % jj j y gj j ments with numerical simulations (PM-ALPHA). A further do ** # is i l' ** I attempt at such veri 5 cation is currently made by the use of E E is Il 5 'Is I'l I x rays. = = = lj j g }; j IV. EXPERIMENTAL RESULTS AND INTER- *"'**""''""'"**"'""**^'
PRETATIONS Measurements with FLUTE require a totally dark envi. interaction vessel cross-rectional area). He panicle ve-ronment, thus the runs with high speed movies were carried locity at the point of release (inlet to the flow fields) was out as a separate series. Run numbers and respective ex. obtamed from the, high speed movies as 72 cm/s, and it perunental conditions have been listed separately for the was found to be mdep-det of the quantity of material two sets of runs in Tables I and IL From Table I it can be in the intermediate vessel (presumably the partic!c's sliding seen that nominal panicle temperatures varied in the 600 to against each other as they enter the holes m the bottom of 1000 *C range (the panicle temperatures quoted in this ta. the intermediate vessel controls the release rate). The par-ble are those measured in the intermediate vessel just prior ticle volume fraction in the same location was found from to the initiation of the pour); the rest of the expenmental volumetric release rate of particles to be 1.87% and 2% matrix covered variations in pour diameter, pool depth, and for the 2.5 and 1.5 mm balls, respectively. In the calcu-freefall distance. He freefall distance refers to the distance lations, the two-phase zone front lagged the panicle front between the panicle release point and the pool surface-this by about 3 nodes. To check for numerical diffusion we variation creates different panicle velocities at the point of implemented also a Langrangian treatment, as a side to the pool entry, in the FLUTE runs (Table 2) the main effect main calculation, and the results were found to be in good studied was the fiber spacing, but other vanations included agreement with both the calculated Eulerian particle front were particle temperature and measurement position. and the particle front motion obtained from the movies. In all runs the water was at saturation--it was brought From such numerical simulations, the two experimen-to a boil by 2 immersion heaters located at 2 corners of the tally deduced void fraction transients were computed for the interaction vessel (these heaters are visible in Figure 3). conditions of each experimental run-these are the " 'c-tions" shown with the expenmental data in what f Ilows. In the following, the experimental results are presented An illustration of the calculated developed of the mixing m conjunction with predictions using the PM-ALPHA code, zone and the void fraction distributions in it may be seen The three-fluid formulation used in this code and the set of in Figure 6. Note that the qualitative features are simi-constitutive laws in it have been completely specified;3 the lar to those of Figure 3, although maybe somewhat more predictions are made on this basis. The flow field (which pronounced. includes the freefall space) was discretized by 2.5 cm (ax-ial) by 2 cm (radial) nodes, in axisymmetric cylindrical The complete set of results may be found in Theo-geometry (the radial dimension was chosen to represent the fanous et al.7 Representative results only are included here. I-6
l l l , 1 l l
~
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1~-. l __--k Figure 6. Calculated development of mixing zone and void fraction distributions in it for the conditions of run 102 at times of 0.35,04,0.45, and 0.5 seconds following the initiation of the release. ing' on the time axis. De results for two runs with mea-Mixing-zone-averaged and pool-height-sveraged results surement positions at 2 different depths (see Table II) are from four typical runs in the 100-series are shown in Fig- shown in Figures 11 and 12. An additional reduction was ures 7 through 10. As may be seen in Table I, these illustra-performed by averaging the so-smoothed rt sults from 9 dif-tions cover the effects of particle temperature, pool depth, ferent mns (2 equivalent FLUTE positions in 7 of these freefall distance, and pour diameter. De mixing zone aver-age results extend roughly up to the time that the zone front runs), and these results are shown in Figure 13. De FLUTE reaches the pool bottom (note that for the shallow pool run signals show the first arrival of the hot particles by the in-terference signals already discussed in section 3. Synchro-
#106 the time scale of the data is about one-half of that for nization between the experimental and predicted traces is the other three runs). The calculation shows an initial rapid increase and an eventual leveling off in the void fraction as accomplished by establishing coincidence of this instance to the arrival of the hot panicles at the measurement loca-the pool bottom is approached. Dis is because at higher void fractions steam is able to vent off the top (see Figure tion in the calculation. We see in the measurements a rather complicated structure, but the general trends are consistent 6), there is less water " feeding" the mixing zone at its front, and heat transfer (and vaporization) degrade because of in- with the predictions. This is particularly evident in the multi-run, or ensemble, average as indicated in Figure 13.
crease in void fraction. Note that the radiation component More specifically, in the calculation we observe an initial of the heat transfer at these panicle temperatmes is not as rapid rise when the two-phase front reaches the measuring strong as what would be expected for the very high temper-ature fuel in reactor situations. In general, these trends are location, a more moderate increase for a period of time well past the panicle arrival time at the pool bottom and a shon born out by the experimental data, with the only nmable and sharp peak followed by a rather marked fall. In tne exception, possibly, the case of run 113. In this r; the experimental data, the initial rapid rise is somewhat marred pour was ~1/3 that of the other three runs, and the same trend of significantly higher void fractions at the tail end of by the fiber interference; however, it is still quite evident, the transient was also observed in the other mns (114,115, Note that this early period is well covered by the global < 116) of this group. The reason for this difference remains void fraction data discussed above. More clear is the inter- l mediate period of moderate rise. As noted already, in this ' to be clarified. Turning next to the pool-height-averaged range of high void fractions the interference error is reduced void fractions, which also are shown in these figures, we drastically, and this is very important because we thus ex-note that the numerical results show initially a rapid rise, tend the measurements into the region for which the global but peak and " level off" within a short time after the parti- void fraction measurements were not possible, it is also cles begin to accumulate at the pool bottom. An oscillatory very interesting to note that in the overlapping region there structure, of varying amplitude, on this " level" pan is also appears to be good consistency between these two measure-observed. The experimental data are seen to reveal clearly ments. Finally, at the very end of the t'ansients shown, the this early rising trend, but unfonunately they stop short of data do not exhibit as pronounced a fall-off as found in the the peak-as explained earlier, this son of measurement is prediction; indeed, even discerning such a fall-off in the not possible after the pool surface begins to break up. His data is rather subjective. is where the local measurements are very helpful, and they are discussed next. V. CONCLUSIONS At 8 kHz, FLUTE provides essentially instantaneous l readings of the local liquid fraction-because the sampling An experimental facility and related experimenta! tech- ! volume is so small, the signal often shows either 100% niques have been demonstrated to provide a viable vehicle i liquid or 100% vapor. These readings were time-averaged for the study of the extremely complex multiphase zone cre. l over 10,20, and 50 millisecond time intervals while " slid- ated by the interaction of a hot paniculated phase poured I I-7
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0: ' j 0 0.05 0.1 0.15 0.2 0.250.30.35 0 0.05 0.1 0.15 0.2 i Titae (e) Time (e) Figure 7. The pool-depth-average (top) and mixing-zone- Figure 8. The pool-depth-average (top) and mixing zone-average (bottom) void fraction tra.wients for Run #102. average (bottom) void fraction transients for Run #106. , l t E 1 , - -
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l O.1 e + prediction - 3 -+- prediction f e g o experiment 0.1 F e e experiment O: -t' O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Time (e) 0 0.05 0.1 0.15 0.2 0.250.30.35 Time (e) Figum 9. The pool-depth-average (top) and mixing-zone- , Figure 10. The pool-depth-average (top) and mixing-zone-average (bottom) void fraction transients for Run #112. avenge (bottom) void fraction transients for Run #113. l 1 1-8
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i mm. i.3 mm.<.,u Figure 11. The local void fraction transient for Run #301 Figure 12. The local void fraction transient for Run #406
- position #1, as deduced by 10 (top), 20 (middle), and 50 position #1, as deduced by 10 (top), 20 (middle), and 50 i
(bottom) millisecond time-averaging of the 8 kHz FLITTE (bottom) millisecond time-averaging of the 8 kHz FLUTE signal, signal. i l-9 1
r l a into a volatile liquid. Initial indications are that the pro-cess dominated by heat transfer and the resulting vapor i i i I~~~ n.'"'""" l i production, in ,is not sensitive to details of the phe.
~
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nomenology. mparison with predictions made by using
.s /) the FM-ALPHA code are encouraging. At this time, the t experunental data and related computations presented here ;
L. ' provide only a very initial quanti 6 cation; however, the wa-C ./ ter depletion phenomenon, in general, seems to be firmly s estabhshed now. i
> k t e.e - -
y . ACKNOWLEDGMENTS 3 J u - -
'Ihis work was supported by the U.S. Nuclear Regula-i tory Commission under Contract No. 04-89-082. ,
",[ ,' '
, ,', ,', ,', . REFERENCES
,i.. t.,
j.
- 1. R.E. HENRY and H. K. FAUSKE, " Required Initial l
Conditions for Energetic Steam Explosions," Ebel- , Coolant Interactions, HTD-V19, Amencan Society > 1 se of Mechanical Engineers (1981). t
- 2. T.G. THEOFANOUS, B. NAJAFI and E. RUMBIE, l ?.Lul "An Assessment of Steam-Explosion-Induced Contain-i ,e rnent Failure. Part I: Probabilistic Aspects," Nuclear g Science and Engmeermg, 97, 259-281 (1987).
/ 3. W.H. AMARASOORIYA and T.G. THEOPANOUS, f" -
e' -
"Premixmg of Steam Explosions: A Three-Fluid Model,"
.g ,/ " Nuclear Engmeering and Design 126, 23-39 (1991).
# o. - -
'j 4. C. LIU, T.G. THEOFANOUS and W. YUEN, " Film j Boiling from Spheres in Single- and Two-Phase Flow,"
3 1992 National Heat Transfer Conference, San Diego, n -
/ -
August 9-12,1992.
.A 5. S. ANGELINI, W.M. QUAM, W.W. YUEN and T.G.
.l u i e
*IHEOFANOUS, " FLUTE: Fluorescent Technique oe e.s e4 es e.s s4
*"* (') for Two-Phase-Flow I.Jquid-Fraction Measurements,"
Proceedings 1991 ANS Winter Meeting, San Fran-cisco, CA, Nov.1991.
- 6. H. YAN, W.W. YUEN and T.G. THEOFANOUS,"Ihe
" Use of Fluorescence in the Man ement ofIAcal Liq.
i i i i uid Content in Transient Flows," To ap-j'd,,,, j in Pramelings of , Salt I.ake City, UT,
~
mbt:r 1992. g
- 7. T.G. 'INEOFANOUS,W.W. YUEN,S. ANGELINI,X.
3 - CHEN and E. TAKARA, " Steam Explosion Funda-e e. -
,./ -
mentals and Energetic Behavior," To be published as
} ~,,~ a NUREG/CR report.
j i u 3
-e j .
1 n - ee L- ' ' ' ee n en ee n sa hme (e) l Figure 13. The local void fraction transient obtained by averaging the time-smoothed signals (obtained as in Figures - 11 and 12) of 9 similar runs. . 1-10 l
l l l l APPENDIX 2 PREMIXING-RELATED BEHAVIOR OF STEAM EXPLOSIONS Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions Santa Barbara, CA, January 5-8,1993 NUREG/CP-0127 March 1994,99-133 i l i s 2-1
.- - _ . _ . . - - . - - . . - . . _ - - - - . . - - -- -. - ,- - -. - _ - ~ -
PREMIXING-RELATED BEHAVIOR OF STEAM EXPLOSIONS S. Angehni,' W.W. Yuen* and T.G.11:eofanous Center for Risk Saubes and Safety, Depamnent of niamwal and Nuclear Engineenng Universny of ruhai=. Santa Barbara, CA 93106 lblephone (805) 893-4900 - Fax (805) 893-4927 ABSTRAC1 i
" steam bubble" is due to the high heat trasfer rams and Three recently - published 1xemixing experimanes, the ==aariatad staminf that " drive" the water out while at the MAGICO, MIXA, and FARO, are discussed comparatively, same t me it is being vaporized. This manns that large gn ,4,,a= of meh cannot coexist with large gaan**ia= of and two of them, the MAGICO and FARO, are analyaed
- with the help of the computer code PM-ALPHA.1he resuhs weer in a coarsely mixed aa8-===*iaa i.e., in a condition of these analyses are shown to provide gnantantive interpre- the is cananeive to an emeiaiw thermal interaction. On tations of the data , and to suggest raadirianalmamanmmanta the one hand, such largely voided premixtines are not eas-in further experinnents to enhance the insights thus ob- Dy susceptible to triggering, and on the other hand, even tamed. Also, a qn=**mtive radiography +=^="a is de- assuming that an explosion can develop, h would be very scribed and apphed to MAGICO for the,mamannement of inefficient. This aHows for putting boundmg limits on in-chordal-averaged void fractions in the snixing zone. Die teracting masses from arbitrarily large pours, and thus k resuhs are in excellent agra===w with PM-AIEHA predic- has served as a central alamant of the arpmant against the tions, '.ims --F =: the previously reported good com- a mode cantainmant failure in the past (Theofanous et al.,
parisons with the local (point) measurements of PLUTE. 1987; Steam Explosions Review Group,1985).1his is im-ponam because then, and this remams nue now, Ime-phase, L IN11tODUCTION core-melt progression uncertaintian do not allow a rigorous argumant to be made against massive molten corium dumps Premixing is the multiphase transient obtained dunng into the lower plenum. l the pouring of a high temperature mek in a liquid coolant; given an appropriate tngger, this transient can be trans-fanned into an explosion (cammanly referred to as a " steam 1he weer depletion phanamanaa was first conjectured explosion"6). An explosion can be triggered at any time by Henry and Fauske (1981), and Bankoff and Han (1984) by an externally supplied pressure pulse, or k can occur made an attempt to compute it. A first actual quantierinan
;- - 9y as a resuk of a local thennel interaction if was offered by Abolfadi and Theofanous (1987), using a pomnent canditians for such are obtained dunng the pre- two-fluid model, and this was further refmed by a three-mixing. In any case, the premixing transient provides the fluid fornatatina and the PM-AIJHA code (Amarascariya initial canditiaan for the explosion (or so-called "escala- and 1heofanous,1991). An indarandant but aimdar three-'
fluid for=niarian also has been pursued under the CHYhES tion" and " propagation" phases) and as such k provides the code ! . ' , basis for assessing "what constautes an adequate trigger," - effort in the UK (Fletcher and Thya-and the "mafninide of the energetics obtained from a re- garaga,1991), and the first comparisons with the above-l sulting explosion." la general, these initial condaions can mannanad PM-ALPHA resuhs have just been pubhahad i be charactensed by the space-tune vanations of the volume (Pleicher,1992). Eacept for not accounting for subcoohng, ' these CHYMES resuhs can be ;- , t. to be support-fractions of the three coristihaank (melt, water, and steam); however, of pamcular sg 3==e is the so. called " water ive to PM-AIEHA and the predict:( water depletion phe-depletion" -W nomenon (Theofanous et al.,1993). The first " ---' - var"*iaa of this phanamanan was made in the MAGICO The water depletion phenomenon sden m the fonna- 63 ; ; a little more than one year ago (Theofanous et i tion of a high void (steam) fraction region in the major al.,1991), and a detailed pneestation of the first two so-central portion of large-scale snek pours in water. This ries d experuness agaher with PM-ALPHA pradieriana . was given in the recent NURE111-5 mestag (Angehni et !
- Also with the Depamnent of )Amehanical and Faviron- al.,1992). The initial data from another premixing exper- 1
- menta1Engmeering iment, the MIXA, tied to the CHYMES venfication effort, l 6 were also praannad in the same meeting (nanh== et al.,
Such apla=ia== can occur with a vanety of" hot"/" cold" i 1992), and the first data from the FARO experunant at the liquid pain, but wahout loss of generahty we will speak I CRC, Ispra have just become available (Magallon, et al., best of a "mek" and " water" 1992; Magallon and Fah==nn,199't). Clearly, the major 2-3
i l new developments in this area will occur as these and sub- In both these experiments, the interaction progresses essen-sequent data are studied and interpreted with the help of tially at atmospheric pressure (i.e., there is no feedback from these codes. The main purpose of this paper is to discuss steaming). He same approach of measuring the steam gen-these experiments from such a standpoint and to take some cration rate is also intended for FARO; however, the two initial, illustrative, steps in this direction. tests reported so far were performed with a closed interac-tion vessel which, as explained later in this paper, provides II. OVERVIEW OF THE PREMIXING EXPERIMENTS analysis-testing opportunities not previously anticipated nor As noted above, there are three premixing experiments available so far from the other two tests. Briefly, with a that are currently active (a fourth one is planned in Greno- cl sed vessel, the thermal interaction leads to pressuriza-ble, France). Of these, the MAGICO and MIXA are specif- tion and an interesting boiling feedback due to the mduced ically designed for this purpose. De stated scope of FARO nse m saturation temperature. In these tests, this feedback is not specific to premixing; however, it provides an inter- was further accentuated by radiation heat transfer to the esting complement from this standpoint, also, to the steam in the cover gas space. In addition, FARO is run MAGICO and MIXA expenments. Indeed, viewed as a at high pressures (~5 MPa), which provides oppommities gmup, these three experire nts provide a nice sequence (but also corrplications) for testing integral predictions in from the well-defmed conditions of MAGICO (fixed par- that constitutive laws are not as well known at elevated ticle sizes), to MIXA (prefragmented melt pours into more- Pressures (1.c., film boiling from spheres in subcooled wa-or-less regular streams, and apparent capability to observe ter and high pressures). Regarding other measurements m particle sizes in flight), to the rather poorly defined melt both MAGICO and MIXA, the interactions have been ob-conditions entering the water and no possibility of direct served visually (by high-speed photography), which makes observation of the ensuing interaction in FARO. Except per- Possible melt-front ,and two-phase zone tracing, and per-haps for the relatively small (compared to reactor) quantities haps even particle size measurements in MIXA (the extent cf melt, the FARO is quite prototypic, and very valuable to which this can provide the full information needed is yet for this reason, to its main purpose: to determine the extent to be determmed). In FARO, no such data are possible, but cf quenching possible in the lower plenum at high pres- s me rough idea of melt-front advancement and level swell sures, and the extent, if any, of thermal attack on the lower seems to be possible to extract from thermocouple signals, head. As usual, gaining in prototypicality creates loss of Regarding melt temperature and delivery conditions, definition, both in initial / boundary conditions, as well as in there are some interesting differences to be noted. In MIXA, cbservations/ measurements that characterize the interaction, the melt is heated up to ~3600 K. At such high temper-and this loss is quite detnmental in achieving the basic un- atures, the optical depth of the emitted radiation in wa-derstandmg necessary for analyses to be usefulin predictmg ter increases rapidly so that non-local deposition of radiant the behavior in reactor accidents. On the other hand, one eneq;y becomes very important. For realistic simulations, would be amiss expecting to securely bridge the gap be- one must treat the mixing zone as an absorbing-emit:ing tween the well-defined experiments and the reactor without medium taking into account spatial variations in melt and the actual experience of dealing with the less well-defined liquid volume fractions, and one must even include,in the but more pmtotypical tests. We believe that it is very fortu- scale of MIXA, the surrounding liquid zone,if any, and the nate that these three independently-developed programs are container boundaries. For the FARO test (melt at 2650 *C) l so congment to the overall purpose. and the reactor case, on the other hand, such effects are i The major aspect of this view is that MAGICO is suit- negligible. We are currently modifying PM-ALPHA for able for the unambiguous testing of the three-fluid formula-this specialized heat transfer regime of MIXA, and for this tion, especially of the phase-change and momentum inter. rea5 n. n C mParisons are available at this time. Turning action parts, while the MIXA and FARO can provide im- t melt delivery, m MIXA the pour is prefragmented (by j Passing it over a grid made of graphite bars) and charac-portant perspectives on the extent and rate of melt breakup , ter zed kg6 scaks, velocities, and volume fraction) from under two different melt-entry conditions. All tests involve , high-speed movies; m FARO, the melt is allowed to pour the pounng of a hot mass (in liquid or solid particle form) by gravity through a 10-cm nozzle and to contact water af-int) a liquid pool, but.in addition to the above, there are other interesting differences well-suited to the overall task ter a fall of ~2 m through the cover gas (steam and argon) of understanding premixing in all its major aspects. A brief space. Melt delivery times are estimated, presumably by account of these other aspects is given below. thermocouple data, but at this stage, it is not clear how this is done, nor what are the uncertamues myolved. Regarding measurements, the MAGICO is focused on local steam volume fractions, as this is the key variable III. OVERVIEW AND ORGANIZATION OF THIS PAPER charactenzmg a premixture from the explosivity/ energetics As noted already, the main purpose of this paper is point of view (neofanous et al.,1993; Yuen and Theo- to study the results from the MAGICO and FARO experi-fanous,1993). 'Ihis is a very difficult measurement, but it ments with the help of PM-ALPHA. There is also an exper-became possible using FLUTE (Angelini et al.,1992) and imental component in addressing the local void fractions in X rays (la:er in this paper). In MIXA, on the other hand, MAGICO by an X-ray diagnostic technique, as an indepen-an integral measure of the thermal interaction is obtained dent check on the FLUTE data reported earlier. To preserve by measuring the steam flow rates during the transient and some cohesiveness of presentation, this W-7 h ,t exper-obeemng the overall level swell in the interaction vessel. imental component is relegated to the appendtx. 2-4
-. . - . __ _ -. __ _ =.
! In the discussion of the expenments, we assume that V. CONSIDERATION OF THE MAGICO EXPERIMENT the reader is already famthar with the original papers on A. Simulation Aspects ! them, i.e., Angelini et al. (1992) for MAGICO, and Ma-gallon and Hohmann (1993) for FARO. Our presentation The basic concept of the expenment is illustrated in begins, in each case, with the aspects relevant to the sim- Figure 1. Tens-of-kilograms quantities of mm-sized steel ulations and how they were effected, and in the main part balls are heated to a uniform temperature (up to 1000 *C), i focuses on the comparisons and related interpretations. For then transferred to an intermediate container equipped with ! completeness, we also provide a recently-implemented nu- a darnping mechanism, and within a few seconds are re-merically advantageous treatment of phase-change in PM- leased into a pool of saturated (atrnospheric presswe) water. ALPHA- [ne complete formulation is also included, for He Pool cross section is rectangular,40.5 cm on the side. convenience, in the appendix.] Starting from this intro- he major expenmental parameters are pool depth (15,25 l ductory PM-ALPHA topic, the presentation proceeds from and 50 cm), particle size (1.5 and 2.4 mm), particle temper-MAGICO to FARO. ature (600 to 1000 'C), pour diameter (12 and 20 cm), and particle entry velocity (corresponding to free fall from 5,15, IV. THE PM-ALPHA CODE and 25 cm, wMi an inidal velocity oW2 rn's). h initial velocity was obtained from high-speed movies and found to In the original formulation, the rate of phase change be independent of. particle size or the panicle depth in the (J) was calculated such as to maintain the liquid phase intermediate container. From this and the measured total i saturated at the local pressure. This was accomplished by mass pour rate, the particle volume fraction at the outlet of l specifying (J > 0 for vaporization) the intermediate container could also be obtained as 1.87 and 2.5% for the 2.4 and 1.5 mm particles, respectively, Temperature losses in the intermediate container were mi-y , #1 [P_e,)g _y (g) nor, and the actual temperature of the particulate just before 7, (p/ ' being released was reported. where 9 is the usual specific heat ratio, p, is the satura- i e, , cwn tien piessure of liquid temperature, and p is the actual local " i pnnure. The parameter r, is a relaxation time for ther- ggag con %NER l modynamic equilibrium, and this model could couple very nicely with the iteration process given the correct amount of WEN l phase change accounting, implicitly, for pressure changes. .~,~ ' We found it convenient to choose this relaxation time equal Iss to the time step, but the results are not sensitive at least up to 5 times as large. With this model PM-ALPHA could ac-commodate a subcooled liquid, but numerically in a some- l
**e Phase naxing Zoes j what cumbersome way. On the other hand, the above for- l l mulation has occasionally caused criticism because of its Figure 1. Schematic of the MAGICO expenment. I heuristic nature. To eliminate this nuisance and at the same time achieve an explicit treatment of phase change, as a rate Hus, fw any panicular expenment, all conditions nec-pmcess,i.e., reflecting non-negligible amounts of superheat 'SS"fY.fw the sunulation are exactly specified, and only as well as subcooling, we replace Eq. (1) with: one nunw appmxunation and one mmor non-tdeality need to be mentioned, ne approxunation myolves representmg the rectangular cross section of the pool by a circular one of diameter equal to the side of the rectangular tank. He Pour area is also circular, and *.his allows the simulations to J = h, - he [R,(T, - T,) + Rr(Te - T,)] . (2) be performed in axissymmetric cylindrical geometry. De
~
non-ideality involves the presence of a few cold balls in the front of the falling particle cloud. Rese are the balls that When the liquid and vapor are at their thermodynamically fill the holes in the 6-mm-thick plate of the dumping mech-stable states (i.e., saturated or subcooled liquid, saturated anism; they are cold because of heat losses to the plate, or superheated vapor), the transfer coefficients (R, and R,) and they fall in a " formation" with a considerably larger l t are evaluated based on a set of constitutive laws that are particle volume fraction than the rest of the cloud (this was oInsistent with the flow regime approach used previously. confirmed experunentally). Certainly, these balls cannot in-When the two phases are predicted to be in thermodynami- fluence the interaction itself, but one needs to be aware of cally unstable states (i.e., superheated liquid and subcooled tdem for some timing details and especially for interpret-vapor), R, and R, are adjusted upward to recover thermo-ing the very initial FLUTE signal as previously discussed dynamic equilibrium. Sample calculations camed out with (Angelini et al.,1992). Eq. (2) and this approach are in excellent agreement with the previous results [t.e., based on Eq. (1)]. For conve-y mPloy g nience, the complete model after this m~htion is given trated in Figure 2. All geometric features and inla condh in Appendix A. tions are specified for each experunent, as d&dabove, 2-5 l
except for the vent openings. Since in the expenment the patterns for the conditions of MAGICO runs #702 (25-cm pool top was completely open to the atmosphere, the only pool,2.4-mm balls,800 'C) and #905 (50-cm pool,1.5-mm requirement is that these vent openings are chosen of large balls, 800 *C). Rese runs were chosen for the purpose of enough area to avoid any pressurization in the vapor space. explaining the prediction of a " reversal of water volume Cell sizes are 2.0 cm in the radial 6rection and 2.5 cm in flux" phenomenon, which we believe relates to, and ex- , the axial direction, which gives 10 radial cells and 12-26 plains, an expenmentally-found sudden increase in steam ! axial cells, dependmg on tank deptil and free-fall region. generation rate under certam conditions during the premix- ! Node size studies showed that this is adequatt ing transient. More specifically, we believe that reversal of water flux causes a strong counter-current melt-water . contact and an associated rapid increase in steam genera- l tion rates; accordingly, the resulting phenomenon is termed Energetic Transfer of Heat in a Counter-Current Ambient l (ETHICCA).
" " lU " The reversal of water volume flux is illustrated in Fig-I ures 3 and 4 for runs #702 and #905, respectively. [In 8
these figures, spatial maps are given for only one-half of 8 the flow field-symmetry.] In the initial stages, we can see
,' v.,, that the generated steam moves upward and out of the mix-F ing region, while the water is being pushed down and to the sides. This creates a counterclockwise motion in the liquid !
i E jM - 3 around the mixing zone. As time goes on, the behavior l 6 E i iii i of the' steam remains basically the same, except for being l i
~
yJ * !E : lifted from farther down the pool in a pattern that follows
- 2 # the particle cloud front penetrating the pool. However, the water volume flux undergoes two major changes, one at 0.2 and the other at 0.6 seconds. At 0.2 s in the interaction,
! 3 water is seen to begin to move upward within the mixing zone, apparently being " lifted" by the steam flow. The mix-ing region is therefore becoming depleted ofliquid for three
' reasons: vaporization, water being pushed down and to the Figure 2. Blustration of the flow field utihrrA in PM- sides by the particles, and water being lifted by the steam.
ALPHA for the interpretation of the MAGICO expenment. The implied intemal stagnation region is clearly visible in , Figures 3b and 4b. The other change occurs around 0.6 ! De expenmental data consist of mixing-zone-average s, when the water around the mixing zone revenes sense void fractions obtained from high-speed movies (from the of " rotation" (note that these are an irrotational motions) level rise around the mixing zone), and local void-fraction and begins to flow into the mixing zone! At about the transients using a new instrument, the FLUTE. Both of these same time with this flow reversal, the high-speed movies quantities can be easily obtained from the resuhs of the show a relatively violent breakup of the pool surface, as PM-ALPHA computations for comparison with the data, if by a suddenly increased steam generation rate; this is and such comparisons have been reported previously (An- the ETHICCA connection mentioned above. Quantitatively, gelini et al.,1992; neofanous et al.,1992) with very good this sudden change in steammg rate is illustrated in Figures agreement. Also, chordal-average steam volume fractions 5a and Sb, and in detail is seen to depend on particle size can be obtamed for comparisons with the projection-type and pool depth, and we expect on particle temperature also. information obtamed from X-ray radiography, as described However, we believe that the most important parameter af-in Appendix B. These comparisons are also very good. As fecting ETHICCA is the pour-to-pool diameter ratio, and a next step in this study of MAGICO, we examine some in the limit to where this ratio is 1 ETHICCA should van-of the more detailed features of the interactions as revealed ish; prelimmary calculations confirm this expectation. De in the computations and relate them, when possible, to the particular mechanism, in elementary terms, is due to the structure of the mixing zone as seen by direct visnaliration. buildup of gravitational head between the inside (voiding) of the mixing zone and the outside water (hence, absolute B. he Detailed Structure of Interactions in MAGICO value of water pool depth is also important), and is another manifestation of the decisively non-one-dimensional nature l The premixing transient is a vastly complicated pro- of premixmg transients. l cess, which besides the primary quantity of interest, the space-time evolution of the void fraction, has a number Apart from the water volume flux evolution, the of other interesting features Rese features relate to the ETH1CCA can be tracked from the evolution of the steam detailed motions and associated interactions, and they are volume fraction in time. This is shown in Figures 6 and q sigmficant in creatmg the conditions within which the void 7 for runs #702 and #905, respectively. These figures are ! fraction pattems develop. We study these motions here given in two forms, a synoptic one in 6ij and 7iJ for visu-in terms of the calculated steam and water volume flux miiring the whole transient, and a quantitative one in 6a-h 2-6 i l
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i .e . . l 1 l Figure 3a. Evolution of steam volume flux in numerical emniarion of Run #702. Upper two rows, times (from impact of balls on the water) are .004 s, .054 s, .104 s, .154 s .204 s,254 s, .304 s, .354 s; lower two rows, e times (from impact of balls on the water) are .404 s, .454 s, .504 s, .554 s, .604 s, .654 s, .704 s, .754 s. s 2-7
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l i .t s...... l Figure 3b. Evolution of water volume ihn in smi. sial mirrmlanon of Run #702. Upper two rows, times (from impact of balls on the water) are .004 s, .054 s, .104 s, .154 s, .204 s, .254 s, .304 s, .354 s; lower two rows, times (from impact of balls on the water) are .404 s, .454 s, .504 s, .554 s, .604 s, .654 s, .704 s, .754 s. 2-8
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j i i Figure 4a. Evolution of steam volume flux in nummcal minitation of Run #905. Upper two rows times (from e impact of balls on the water) are .004 s, .054 s, .104 s, .154 s, .204 s, .254 s, .304 s, .354 s; lower two rows, times (from impact of balls on the water) are .404 s, .454 s, .504 s, .554 s .tiO4 s, .654 s, e"/04 se .754 se e l 1 2-9 l l i t I l i i I
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4e4 . .l \ . Figure 4b. Evolution of water volume flux in numencal simuhn of Run #905. Upper two rows, times (from
- impact of balls on the water) are .004 s, .054 s, .104 s, .154 s, .204 s, .254 s,304 s, .354 s; lower two rows, thnes (from impact of balls on the water) are .404 s, .454 s, .504 s, .554 s, .604 s, .654 s, .704 s, .754 s.
1 I 2-10 ! \
1 and 7a-h with the void fraction contours labelled. From are studying film boiling from spheres in steam-water two-l these figures, we can visualize the growth of the mixing phase flows including conditions of elevated pressures (Liu zone and the breakup associated with ETHICCA. In addi- et al.,1992). tion, they may be seen to be remarkably similar (in shapes) to sample snapshots taken during actual runs and collected m Figures 8 and 9. In particular, notice the agreement m VL CONSIDERATION OF THE FARO EXPERIMENT the violent breakup of the pool surfaces seen to occur at around 0.4 s m run #905. his experunent involves the pouring, under gravity, of tens-of-kilograms quantities of UO2 /ZrO2 melts at high no
, ' ' ' temperatures (~2700 'C) into deep water pools (~1 m) at
{ high pressure (~5 MPa). He interaction is contained in a l l closed cylindrical vessel ~3 m in length and 0.47 or 0.71 To m in diameter for the Scoping Test (ST) and the Quenching
! 8' -
Test 2 (QT2), respectively. The initial pool temperature a
- is well-characterized, and the water depth is given as 0.87 and 1 m for the ST and QT2, respectively. Thus, the flow i
l ,, _ field can be simply represented for simulations with PM-3 - ALPHA, as illustrated in Figure 10. The length of the [ gas space was slightly reduced to preserve the total test 3 vessel volume (accounting for the melt catcher volume in 8 s - it) to the values of 0.64 and 1.3 m8 given for the ST and i2 QT2 conditions, respectively. His whole flow field was discretized, uniformly, into 5 radial and 60 axial cells (Ar =
, , , , 4.7 cm, A: = 6.1 cm). Cylindrical symmetry was assumed.
o.o c: e. o. .. i .' he only aspects of the simulations that require some elaboration are concerned with melt delivery, with certain Figure Sa. Mass of steam ejected through venting cell in numerical simulation of run #702- transient behavior' prior to the melt reaching the water pool surface, and with melt breakup in the interaction. He dis-
** cussion of these aspects is limited here to the case of the i i i i Scoping Test, as only this test could be analyzed in the short time available since the release of these data (Magallon et al.,1992). However, the treatment is expected to be similar 3 ,o ..
to the QT2 simulations that will follow in the near future. I 91 j ne melt delivery time is given as 0.28 s, for a total E release f 18 kg of melt. Using this release rate and the l
. no -
_ melt-exit nozzle diameter (10 cm), we find an inlet melt ve- l j locity of 1.07 m/s. Under free-fall, the melt front is found
.o to have traveled 0.67 m by the time the tail-end of the pour j is entering the gas space; the melt front at this time,0.28 s a
8' - after initiation of the pour, is still 1.15 m above the water pool surface. Based on this, the calculation is initialized at 0.28 s with the experimentally measured value of the pres- _, e i i sure in the gas space (~5.1 MPa) and the fuel distributed ;
-o.o or o. o.e o.e i.o along the indicated column in Figure 10 with volume frac- 1 r= W tions and velocities in each cell obtained by accelerating Figure $b. Mass of steam ejected through venting cell in the respective " parcel" under gravity, with the quoted ini-numerical simulatioH of run #905. tial velocity, so as to arrive at the' respective location at the appropriately available travel time (0 5 t $ 0.28 s).
Note that the innermost cell diameter is very nearly equal To conclude, it would appear interesting now to carry to that of the melt-exit nozzle; thus, all melt is taken to be out more focused investigations suggested by these results; contained within it. specifically by measuring velocity profiles in the water sur-roundmg the interaction zone, and by visualizing the inter. The other aspect of the simulation that requires some nal (void fraction) shapes within the zone itself (see Ap- elaboration is the treatment of meh-to-gas radiation heat pendix B). Both are well within the technology currently transfer. This is peculiar to a closed system, with large tvailable for MAGICO, and such studies are planned for cover-gas space, at high pressure, as is the case here, and the near future. Incidentally, we also plan experiments its importance has already been noted by Magallon et al. with aluminum oxide particles (different density than the (1992). An a prioritreatment of this aspect would only be steel ones used till now) of much higher temperatures. Fi- possible if the extent of melt breakup, and its emissivity, nally, in a companion experimental / analytical program, we were known, which of course, is not the case. However, our i 2-II
1 l _= 1 i l ume fraction in numerical simulation of Run #702. Times (from impact of b on the at , I i
# ^^
w A y --- I
--C2
-c
~
1 i i 2-12 i
i
\
l l l l
)
i l __ M A i 1
& l l N-i
\ l l l Figure 6c. Evolution of steam volume fraction in numerical simulation of Run #702. Tunes (from impact of balls on the water) are .204 s, .254 s. l l
& 'A?
I cm. o l l m 1 J M ; f l Figure bd. Evolution of steam volume fraction in numerical simulation of Run #702. Tunes (from impact of balls on the water) are .304 s, .354 s. 2-13 l l
N
$ {
h
~g Figure 6e. Evohnion o steam volume fraction in nummcal simulation of Run #702. Tunes (from impact of W/c
\
as T re 6f E on of o\\ 2 vo ume fraction in numerical simulation of Run #702. Tunes (from impact of 2-14
T l J dB D1 Yk d Fgure 6g Evo on of m ef% ume fraction in numerical simulation of Run #702. Tunes (from impact of ( s J 8
/
8
= = _ _ _
kk 2-15 . -. . -= .
_~ l I l b on w ) 004 . , .10 , .1 4 , , s, 3$ s. p N (
- l. ss 4
,h /, s , # k\ b d I,2:* %" L";",:%""".2"*sM "51 *"As?.2"2 :,'."" " * "" """ *
- 2-16
J fo . s - n o4 i 5 t l a 1 u , s - i4 m s01 - l a - ie c -
- rr
- ea -
_ mue)r nt - a iwn - ke en* m ne oh - i t
- t
- cn -
ao r f sl el e mb lu f oo _ vtc ma ap em t si fo m nro i of( u es t _ l om _ _ v E Ti b5 709 _ e r# , un g iu FR f _ o s. _ n . o45 m i t a0 a l u , m s _ mu l i a s0 cnre 4 0 _ ss e a m ue)r nt a i nw ne a ioh _ t t cn ao r fel l s mba _ luf oo am f vt c _ ma ap em t si m fo m a nrfo i o( m l t s ue om a vi ET . . a5 709 m e r# un g . iu FR Y ;:
ta \
.8%
un i
}J '
{ k .!3 f
'?
t
\
[ \\. a i o h c "w" i i'
\
Ao
, $h \
g e~ cwL5 ! I Od 7 l. 'k k 2< \ a n. iN '$
.il 1
4 4 i
.13 L'
1 4
}'8 us
,, 1 45
e1 s
hN }& s n c }$ si aa cu I 2-18 \
4s '
.W
(' 7T( M b, O , r. jj iln1 I i ni i 11 f o I
\
\
O4 i 3% ' 3 *;
!O P p:-
\
is \ bk f y u a 1 l MNe-2-19 l l __
I O ei R tw N -
$p s
3 . E a k) \ a 1 n i1 ' r2 45
# 1 1 41 si 4 gs 3, g 3
s ( k '
.4i 5
'n b.
p 5 %. 3 Y " 5* hg
~
1,1 d
,e q
$F .
\ i N n 9 o 2-20
l e ;;p-l l[ , ___ J E!!!e! Figure 7i. Evolution of steam volume fraction in numerical simulation of Run #905. Tunes (from impact balls on the water) are .004 s, .054 s, .104 s, .154 s, .204 s, .254 s, .304 s, .354 s. ! w-p _-- - d l y I 4
/ f W
/ h !
3 [' V W Figure 7j. Evolution of steam volume fraction in numerical simulation of Run #905. Times (from impact of balls on the water) are .404 s, .454 s, .504 s, .554 s, .604 s, .654 s, .704 s, .754 s. l 2-2I
* * ' ' ~
a s f. f s, ;
' ' N.:
~
~
I N : M { N.
,j I ~?' 4 , . yk
; 1 e. i '+
t e g , 41 #,
, 7 . . g .j Ts :
N
.c+, . j, ' '
t + i 4s4. * . i _ . .
. . ,ars, y
9 *
.4
%}
'I . sp'<
e . i e 3 .. - l l ., A Y d ' .13 I -
. W sY' f yp[) - ' :
M y , a 1l .. q .
- i
(*4\ . l s.
- g .
.i ,
~
- I .c- ' ,;t .
,_'y h-! ';)$ . ., ) b g.' - -
.~,L
' ~
.p .,
f ,, a y ( ), ~ f.;;g S l_ . .;, . Q. 4 ', ' ' . N' :g. . _ .
" ~ ~-
Figure 8. Snapshots of Run #205 (identical to Run #702). Times (from Figure 8 (Continued). Snapshots of Run #205 (identical to Run #702). l impact of balls on the water) are .27 s and .57 s. Times (from impact of balls on the water) are .87 s and 1.17 s.- l
.~ -
t i [ . a , - f
, , :, . . . ; .y .
, w k
.ig, .
l ( .
* ,9
~
i { t ' s h , l : . 5 I .. --
~
.u r- . "
p ... N , _
- A
.._, m , - . _ . - . _l- r - "-
Figure 9. Snapshots of Run #905. Tunes (from impact of balls on the j water) are .1 s and .4 s. l l I e-
.\
^; * '
y[4$ A _s , . p
'. , . ? . .
?$'t
,:J f '{
p .f ,
- f. p7 f +' '
Jl; nl &,i
. .; g. % '
_ Q, . -- f; .
*. sw ,
- l. py, : ' ' -l e: ,, ;a
~',,
?
we = muut st ' Figure 9 (Continued). Snapshots of Run #905. Tunes (from impact of balls on the water) are .7 s and 1.0 s. l t 2-23 i I _ _ _ . . _ . . . _ _ . . _ . _ . _ _ . _ _ _ _ _ _ . _ . _ _ _ _ _ _ . _ . _ _ _ _ _ _ _ _ . . _ .
'. ' p ,' . .,,-
4 3 , + w::'J;l.i. 4'. 4 j e g it, V
. 4 4 6 c.. l
& n
$; . % n Y: i ),
3, x r
. y
'~
.y
$ '.7 ,'
p. e. r
% ;f, q m-
,. J fe t
- 3. .- ,
8 (*. < y' - ,
.j ,
jf '
. N5 A)' _$
~
J l s k- f l ' ~
. ~
l 1 g ' g ,' ,% ey l y ,1 . > a
- 1 A1 Figure 9 (Continued). Snapshots of Run #905. Ttmes (from impact of balls on the water) are 1.3 s and 1.6 s.
i j J' , eg. a g;gr y w yg
..w- r*
j %. .. p ?gty % [,' '! *
%SJ. .; .
i re s;, ,
,p *
(
'. .,.ij?
g y i, . 9.. ! 4 p ' ! ,e . , Ei. h.f
~
. x
- '- y}- ~
t i
~ "~ ,9.;;;
m l
.:;fg Yl l @ . ,1;.
- 1; . Q s ,, U (0$ ._
.. ~
Figure 9 (Continued). Snapshots of Run #905. Ttmes (from impact of j balls on the water) are 1.9 s and 2.8 s. l 1 l r 2-24 l l
. - - . - . . _ . - - . . - - ~ ~ - - . ~ . - - . - - . - - - - - - .- - - - ~
l h of 4.01 MW and a 6Ef /dfvalue of 3.6 cm-1. The lauer ! is obtamed fmm l 1 Ef aT'*/- = 4 dj pf where mf/pf si the total fuel volume, and 4 is the total j i rate of radiative heating of the gas. Using an emissivity of a L rnl 0.7, the above yields a melt perticle size of 1.2 cm, which ! N is censinly a reasonable degree of breakup of the ensuing ' meltjet under the condaions of this experiment (crusts were ! observed within the nozzle as well as in the meh catcher). Finally, regarding further melt breakup wahm the in- l teraction zone, by consideration of Weber number craena, ! and with a melt-entry (the pool) velocity of 4 m/s, we esti-mate an initial breakup to mm-size particles. However, as , the liquid pool is ,= n :-i and set in downward motion 3 ! (see earlier discussion on MAGICO) by the high velocity : l "rwarm" of particles, the relative velocities decrease, and '! l- the continuous phase density decreases, which would tend l l to this extensive inhial W. N the calcula-353 cm l tion reported here, we chose a value of 0.5 cm. It happened . t' that this first choice gave a good (compared to the experi- ! ment) timing for traversing the 0.87 m depth of the pool and also a good agreement with the interaction features of the
- j. calculation (pressunzation)., The fr- = i debris found c
in the melt catcher was reported to have a mean panicle ; l size of 4.5 mm; however, from the photographs and the { ! discussion,it appears that this fry =-M debris represents ; r only a relatively small fraction of the total melt; much of l it collected as a "congiornerate in contact with the bottom plate. 'Ihis part was certainly still molten when it contacted ; the plate" (Magallon et al.,1992). Thus, the chosen size j , of 0.5 cm may not be unreasonable, and as seen below, the ! degree of quenching obtamed in the calculation with such a particle size appears to be consistent with a large fraction U of the mass arriving in still mohen form at the catcher. 47 cm :I As a Snal point in this discussion, we need to mention , 8 ' ( that we do not agree with the discussion in the quick-look report (Wider e al.,1992) about the role of Argon gas (used Figure 10. Illustration of the flow field utilized in PM- initially as a cover gas) and about the transient phenomena ALPHA for the 'oa,.y--on of the FARO experiment. associated with the small expansion of the gas volume due to the opemng of valve SO2. First of all, the Argon atom is interest in these tests is pnmarily on the melt-coolant in- considerably heavier than the steam molecule, and there is teractions, and the melt-to-gas heat transfer is relevant only no way for it to struify under the conditions of the exper- , in prong the proper boundary conditions (subcooling iment as claimed. Second, startmg from 0.4 MPa pressure I induced due to pressurization) for this interaction. Our ap- at 80 'C, as starwl, the Argon partial pressure at 265 *C proach, therefore, is to sort out the melt-to-gas heat transfer should be ~0.7 MPa, and with the partial pressure of steam from the early portion of the pressunzation transient (prior (at 265 *C) should add up to 5.77 MPa, which is signifi-I to melt contacting the water) in such a way that it can be cantly higher than the measured value of 5.33 MPa. 'Ihis consistently " merged" with the fuel-coolant interaction por- is not surprising given the method and poner of heatag tion. This is done by findmg from the early pressunzation and likely heat losses. 'Ihird, after openmg the valve, the rate an effective value of the product of "sneh interfacial system pressure decay was arrested at ~5.07 MPs by wa-area densay" times the mek emissivity (i.e.,6Ef /df) and ter flashing to steam, as it should, however, because of the using it to emmate radiative power for all subsequent times, Argon gas pressure, the pressure could not increase sig-however, accountag for the reduction in total area as the nificantly above this value by flashmg, as clanned bi the c melt " column" becomes submerged in the water pool In quick-look report. [ Free surface vaponzation could provide l actual numbers, at ~0.3 s, the pressurization rate of the some aMitional steam; however, it would be too slow to j gas (0.83 MPa/s) imphes a uniformly applied heatup rate make a difference at the time frame (< 1 s) ofintatet.] We 2-25
i conclude that the pressunzation above 5.07 MPa is solely place in the expenment. This type of information would due to radiative heating, and steaming, of course, after melt- be most helpful in carrying out premixing calculations for water contact. Dat is, the situation is quite straightforward, reactor conditions. and the rnethod of simulation described above is quite ap-propriate. 2 . , , , , He results of the calculatio'ss are discussed next. Start-ing from the " bottom-line" results in Figures 11 and 12, we see the comparisons with the data on the pressuriza-
- g 1.5 -
tion transient and the pressurization rate, respectively. The li agreement is remarkably good. In Figure 13, we see the g ' water subcooling (at a position away from the interaction - 1 -
+ ,
zone) building up rapidly as a result of the pressurization,
- g a feedback quite important to the phase change processes it3 within the mixing. zone. The temperature rises quickly to 0.5 -
PM-ALPHA saturation as the fuel penetrates deeper into the pool. He + Approx. Dein pressurization mechanism, initially due to radiative heating , , , , , cf the gas space, gradually reverts to the supply of super- o heated steam from the interaction zone. This can be seen o o'2 0'4 0.6 0 1 1.2 from Figure 14 showing the " sinking" history of the melt in Time (s) '8 the water pool, Figure 15 showing the change in radiative heating of a typical volume element in the gas space as a Figure 12. Comparison of calculated pressurization rate result of this " sinking" of the melt, and Figure 16 showing with the FARO data from the Scoping Test. the temperature transient of a typical cell in the gas space. His temperature transient is very consistent with that mea- o , , , , , sured experimentally In Figure 17, we see the buildup of .
-5 - ,..
fuel volume fractions at the bottom cell; the timing is in _ excellent agreement with the data. The level swell reported E .1 o
- 2 ;
for this experiment is 13 cm, which is also in remarkable - agreement with the calculated value of 12 cm. Finally, a > = - 15 sampling of the evolution of calculated fuel and volume . ' 2
. -20 -
fraction distributions at different times during the transient 2 are shown in Figures 18 and 19, respectively. Because of I 25 '
- 2 the large aspect ratio of the full facility, the distributions ;
-30 below the initial water level are only shown in these fig-ures. ' ' ' ' '
35 o 0.2 0.4 0.6 0.8 1 1.2 1.2 ,_ , Time (s) PM-ALPHA
- 1 -
+ Approx. Data -
Figure 13. Calculated buildup of water subcooling, as a result of the pressunzation transient, at locations away from g 0.8 -
+ -
the mixing zone. E
~
. o.6 - -
S 20 , , , , , [ 0.4 - - 0.2 - - 15 - ,' ,,,,,,,,,, g over , o
' ' ' e i g ----- under ,
o 0.2 0.4 0.6 0.8 1 1.2 :F 10 -
/ -
Time (s) a' f Figure 11. Comparison of calculated pressure history with the FARO data from the Scoping Test. 5 -
/ -
,/
To conclude, these are very promising comparisons for ' ' ' - ' 0 a first calculation, and they indicate rich possibilities for o 0.2 0.4 0.6 0.8 1 1.2 further more detailed calculations and interpretations. In Time (s) parucular, we hope to examine the role of different degrees tf breakup during the interaction with water, and hence to Figure 14. The calculated " sinking" of the fuel " column" be able to backup more conclusively what actually took into the water pool. 2-26 i
VII. CONCLUSIONS 1o ' ' ' The water depletion phenomenon in prenuxing tran-i sients has been simulated in MAGICO, measured by FLUTE 8 - and by quantitative X-ray radiography, and predicted by
=
~ PM-ALPHA. Moreover, PM-ALPHA seems to also predict some key multidimensional intemal features of the flow
! 6 -
8 field and thermal interaction regimes that appear to be con-E 4 sistent with what is observed in MAGICO. These latter re- _ sults suggest additional exp- =1 work in MAGICO for o" further insights into the detailed phenomena. By design, 2 -
- MAGICO allows no free parameters in analytical model predictions and is well-suited for ===%=e testing of the -
j o
, , , , threeduid and phachange aspects he fannMon. At o 0.2 0.4 6 0.8 the other extreme, the FARO experiment with r viyT,1c s 1 1.2 high te...r .. materials, high pressures, and unknown melt particulation during the transient provides some inter-esting challenges to analytical interpretations. We show, Figure 15. . Illustration of the danunishing of the radiative by means of comparison with the results of the Scoping heat source to a typical cell in the gas space, as a conse. Test, that PM-ALPHA can be fruitfully applied in a rather quence of the melt sinking, per Figure 14.
straightforward manner Perhaps more 6.pni-sly, these interpretations offer significant new insights on the effect of subcooling, as a feedback mechanism in closed (or con-650 ' ' ' ' ' stramed) systems, on the extent of vapor production and resulting voiding pattern. Future work will carry further these results to understandmg the breakup and associated thermal interactiori behavior, p 600 - 2 ACKNOWLEDGMENTS H 660
- This work was supported by the U.S. Nuclear Regula-2 ,
tory Commission under Contract Number 04-89-084. ; i REFERENCES 500 ' 0 0.2 0.4 .6 0.8 1 1.2 1. Abolfadi, M.A. and T.G. Theofanous (1987) "An l Assessment of Steam :.xplosion-Induced . Containment I Failure. Part II: Premixing Limits," Nuclear Science and Engineering 97,2.82.
- Figure 16. Calm 1=*=d temperature rise in a typical cell in
! the gas space away from the water surface.
- 2. Amarasooriya, W.H. and T.G.Theofanous (1991)" Pre-l mixing of Steam Explosions: A 'Ihree-Fluid Model,"
\ Nuclear Engineering and Design 126,23-39. 1 - ' ' ' '
- 3. Angelini, S., E. Takara, W.W. Yuen and T.G. ~1heo-fanous (1992) " Multiphase Transients in the Premix-0.8 - -
ing of Steam Explosions," Proceedmgs NURETH-5, Salt Lake City, UT, "-ge
-- 21-24,1992, Vol. II,
; o.e - -
471 478. C. o,4 4. Bankoff, S.G. and S.H. Han (1984) "An Unsteady One-l Dimensional Two-Fluid Model for Fuel-Coolant Mix-0.2 - - ing in an LWR Meltdown Accident," r ;.4 at U.S.- Japan Semmar on Two-Phase Dynamics, Iake Placid,
, , , , , New York, July 29-August 3,1984.
O o.2 0.4 o.s o.e 1 1.2 ). ""' (*) 5. rwh==. M.K., AP. Tyler and DE. Fletcher (1992)
"Experunents on the Mixing of Molten Uranium Diox-i ide with Water and Initial Comparisons with CHYMES Figure 17. . Calculated arrival rate of melt into the melt Code Calculations," Proceedags, NURETH-5, Salt catcher.
< Lake City, UT, September 21-24,1992. e i 2-27 f
-_ _ - - .e
! t 1 l ! cra i tte l '1 pm i l ti ta ca 3 I B l ! ta ta E l E l Em tl l 1 ,5 l t t ::U Eb a ! I hlll
)
- i E
i l tra ra t ! i ! T q i 1 tsi . r:0 ta , EH EE to C3 ( ta ta ta t : { [tl .0 f tu ca ca ta c:rn - ta to ta ta
]J v _
v m w l t Figure 18. Melt Volume fraction distributions at selected times in the simulation of the FARO Scoping Test. i Tunes (from the initial melt release) are 0.53 s,0.63 s,0.73 s,0.83 s,0.93 s and 1.03 s for plots reading from left to right and top to bottom. 'Ihe width of the plot is 47 cm, and the height is 97.6 cm, corresponding to the l volume of the test vessel below the initial water level. ; 2-28
l o l U, dnl /Ak /0h
%,J p) "
k
. ., 9 l l l l /feb MJEtk kN N <
2-29
F
- 6. Fletcher, D.F. (1992)"A Comparison of Coarse Mix- APPENDIX A: FORMULATION OF THE PM-ALPHA ing Predictions Obtained from the CHYMES and PM- MODEL ALPHA Models," Technical Note, Nuclear Engineer-ing and Design, 135,419425.
- 1. CONSERVATION EQUATIONS
- 7. Fletcher,D.E and A.Ryagaraja(1991)"neCHYMES Here are three separate phases: namely, coolant vapor, Co e Mixm odel," Progress m Nuclear Energy, coolant liquid, and fuel (melt) drops. ney will be referred to as gas, liquid, and fuel, respectively. Each phase is rep-
- 8. Henry, R.E. and H. K. Fauske (1981) " Required Ini. resented by one flow field with its own lockl concentration tial Conditions for Energetic Steam Explosions," Rel- and temperature. Rus, we have three continuity equations, Coolant Interactions, HTD-V19, American Society three momentum equations, and three energy equations. In the usual manner, the fields are allowed to exchange energy of Mechanical Engineers.
and momentum with each other, but only the steam and wa-
- 9. Liu, C., T.G. Theofanous and W. Yuen (1992) " Film ter fields are allowed to exchange mass. With the definition Boiling from Spheres in Single- and Two-Phase Flow," of the macroscopic density of phase i.
ANS Proceedings 1992 National Heat Transfer Confer-ence, San Diego, CA, Aug. 9-12,1992, Vol. 6,211- p'g = 6,pg for i = g, t, and f, (A.1) 218. and the compatibility condition,
- 10. Magallon, D. et at (1992) " FARO LWR Programme, Scoping Test Data Report," Technical Note No 1.92.135, Institute for Safety Technology. 8s + 8' + 81 = l' ( A 2)
- 11. Maga 11on, D. and H. Hohmann (1993)"High Pressure these equations can be interpreted rather directly (1shii, Corium Melt Quenching Tests in FARO," CSN1 Spe- 1975).
cialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993.
- Continuity Equations.
- 12. Steam Explosion Review Group (1985) "A Review Gas: ,
of Current Understanding of the Potential for Con- -Bt+' v . (p',u,) = J (A.3) tainment Failtre Arising from In-Vessel Steam Explo. sions," NUREG-1116, U.S. Nuclear Regulatory Com-mission. Liquid: a
- 13. neofanous, T.G., B. Najafi and E. Rumble (1987)"An hp' + 7 * (9'"t) * -I t (A 4)
Assessment of Steam-Explosion-Induced Containment Failure. Part 1: Probabilistic Aspects," Nuclear Sci- Fuel: ence and Engineering,97,259-281. Op' l- + y -(p'f uf) = 0 (A.5)
- 14. neofanous, T.G., S. Angelini, R. Buckles and W.W. Bt Yuen (1991)"On the Prediction of Steam Explosions Energetics," Proceedmgs,19th Water Reactor Safety e Momentum Equations.
Information Meeting, October 24,1991. Gm
- 15. Reofanous T.G., W.W. Yuen, S. Angelini, X. Chen, W.H. Amarasooriya, S. Medhekar and H. Yan (1992) O at (p',u,) + y . (p',u,u,) = -6,vp - F,,(u, - us)
" Steam Explosions: Fundamentals and Energetic Be-havior," to be published as NUREG/CR-5960 by the - F,f(u, - uf) + J(H[J]u, + H[-J]u,) + p',g (A.6)
U.S. Nuclear, Regulatory Commission.
- 16. neofanous, T.G., W.W. Yuen and B.W. Sheron (1993) Liquid:
'The Probability of Alpha-Mode Containment Failure Updated," CSN1 Specialists Meeting on Fuel-Coolant 6 Interactions, Santa Barbara, CA, January 5-8, 1993. g(#' tut) + V '(P',us ue) = -0,vp + F,,(u, - us)
- 17. Wider, H.U., et al. (1992) "The FAROfLWR Experi-
~ III("' - uf) - J(H[J]u, + H[-J]u,) + p',g ( A.7) mental Programme," JRC Technical Note No. L92.139.
Fuel:
- 18. Yuen, W.W. and T.G. neofanous (1993) "ne Fun, damental Mechanisms and Structure of Dermal Det- g onations," CSN1 Specialists Meeting on Fuel-Coolant -(p' uf) + y . (p'f uf uf) = -6f vp + F,f(u, - uf)
Interactions, Santa Barbara, CA, January 5-8, 1993. Of f
+ F,f(u, - uf) + p'jg (A.8) 2-30
l l l l l e Energy Equations. l Gas j """" '"a"f < o.s n,,,.
,,,,n opw .
~
a '06 3s g(p'I,) + y -(p'I,u,) = -p g+y-(6,u,) = s 0.3 c.s < . < o.7 0.7 s . [G h
+ J(H[J]h + H[-J]h,) - R,,(T, - T,) + Qf, (A.9) t
,g*gI a. Y y hJh 00 00 0
*go ' p!G'T '
i uguid: 2 '8
- 8 (psit ) + V - (pjIru s) = -p + v .(6,u e) E= 0= 5=
- J(H[J]h, + H[-J]h,) - R,,(Te - T,) + 4ft (A.10) Figure A.I. Schematic diagram of flow regimes considered in characterizing interface transfers.
Fuel: We use the exchange laws available for two-phase sys-tems after making suitable modifications to account for, as a g first approximation, the effect of a third phase. In calculat-p(P'fI I) + V -(p'Iff uf) = -4f,- 4ft (A.11) ing interfacial momentum exchange, one needs to know the pmjected area concentration of the dispersed phase. Also, in calculating interfacial heat exchange, one needs to know In the above equations H[J) is the Heavyside step function the interfacial area concentration. In a two-phase system, that becomes unity for positive values of the argument and these area concentrations can be estimated fmm the length zero otherwise, and J ts given by scale and the volume fraction of the dispersed phase. How-ever, the presence of a third phase reduces the area con- l centration as the third phase must also share the same area. l 1 J= [R,,(T, - T,) + R,,(T, - T,)) Therefore, we modify the area concentration, by a factor, dgj; dij representing the effect of the phase k on the area concentration of phase i for its interaction whh phase j. His is calculated from the respective volume fractions as l It should be pointed out that diffusive transport within G each field (shear stresses and conduction) has been ignored 4i1 = gj+jgg (A.12) in the above formulation. Indeed, resolution of the shear layers would impose quite more extensive demands on the Note that with this definition pij lies between 0 and 1. computation in both nodalization and the physics of turbu-lence processes responsible for such transport. Although II.A Interfacial Momentum Coupling this is certainly an area for further improvement, we doubt that it will materially change the results for the particular The interfacial momentum coupling is primarily due to process quantified here. drag. For the bubbly flow regime (o < 0.3) we have also included the added mass effect as given by Wallis (1969) II. THE EXCHANGE LAWS #8 1 p, = 3 - 6,p,j u, -s u lSti p( , - 4) l (A.13) he interfacial exchanges of mass, momentum and en-ergy are clearly regime dependent, and uncertamties remain For 6f< 0.3 the drag force is based on Ishii and Zuber even for two-phase flows. For now, our appmach aims to (1979). Specifically, incorporate first-order physics that account for the major flow and heat transfer regimes as identified by simple crite-ria of fuel volume fraction, ef, and gas void fraction, o, i.e., p ,3,g jpj % l u - uj l (A.14) 4 f, o = 6,/(6, + Fr). The flow regimes are shown in Figure A.I. For 6 <f 0.3 we consider the fuel particles immersed where suffices i and j refer to dispersed and continuous l in a two-phase gas-liquid flow, whose own flow regimes are phases, respectively. He drag coefficient for churn flow l defined by the value of the void fraction: o $ 0.3 (Bubbly), (0.3 < o < 0.7)is defined by: 0.3 < a < 0.7 (Chum-Thrbulent), and a 2 0.7 (Dmplet). For 6f2 0.3, as the fuel particles are densely packed, we i = g, j = t, Cog # = $(1 - o)2 andl=4f#
# $ _3p considered a flow of gas and liquid thmugh a porous bed i 3 (y J of fuel particles.
(A.15) 2-31
l l Fe dispersed flow we have: and (Witte,1968; Liu et al.,1992) i ap h, = 2.98 #' ' #' b #- l uf - u, l Co.j = (4 1 + 17{G7(f(ag))'/ _ (A.16) (A.28) where ne emissivity value E = f 0.7 is selected for the calcula-tions of typical interest. Heat transfer from fuel to gas in l i = p, j = t, a 5 0.3 f(ag) = (1-a)' 8 (A.17) this regime need not be accounted for separately. ! For a > 0.7, we assume a vapor-continuous rgime in
- = t, j = g, f(og)=a, a > 0.7 (A.18) which heat is u=ofsisi to liquid drops by irradiation and I i = f' j = g'i' f(og) = (1 - ef)3 8 to the gas by convection. The gas is allowed to superheat (A.19) and ccavect heat to the liquid drops which boil at saturation.
i and ti is obtained from Hus: glu,-u,12I d 8 for i = g
)
y 12 for i = t 4f, = min (nsetj, nfrt}) aEf Es(T) - Tl) (A.29) and For the " dense fuel regime"(ef > 0.3) we use lammar 4f, = nf 4f,rt}h',(Tf - T,) (A.30) l and turbulent permeabilities (Sissom and Pitts,1972), where n, = 68,/rtj and h' is, given by Bird et al. (1960): i = g, t for Gf < 0.3 F4f=Fff+Flf (A.21)
- t h',= (A.31) f 2 + 0.6Re /2Pr}/8f 150g I,#I ,p g for Re; < 1000 F,'f = (A.22) where 0 for Re's 21000 Re, = #' I "' - "# ! t #
P, M and and for 6f 2 0.3 y , f 1.75h #"{"'I for Re', > 10 (A.23) h', = 0.91c,fp', l u, - uf l Re','-8 83Pr,-8/8 for Re',' 5 50 I (0 for Re's 510, (A.33) h', = 0.61c,fp', l u, - uf l Re','-"3Pr,-2/3 for Re, > 50 Re; = Gf # # l "' ~~ "# l (A.24) (A34) Mi Where It is noted, however, that this regime is of very limited '# "' - " # i Re',' = (A.35) i relevance to computations of practical interest. 68f, He factor E, in Eq. (29) was 1.=vdus4 to empirically de-II.B Interfacial Heat Transfer and Phase Change grade the radiation heat transfer to liquid by the portion that cmild not k abW. For e caWons we typicaHy
%e distinction of the fuel-to-coolant heat transfer mech-anisms is made again on the basis of the flow regimes. He tue ,= . t c nservat vely as t ns.
i key distinction is whether or not there is sufficient water Similarly, for vapor-to-liquid heat transfer we have: ) in the coolant phase to completely engulf the fuel particles, For a < 0.7, with vapor as the dispersed phase thus a gas void fraction enterion is used. For a < 0.7, beat transfer to liquid is estimated by Rs, = cand,,rts5 2 {2 + 0.6 Re /8Pr'/8f (A.36) superposition of radiation and film boiling heat fluxes. Hat 9, R,, = 2n,+,,rt&* 1 while for o > 0.7, with liquid (drops) as the dispersed 4f, = nf(h, + h,)rt}4f,(Tf - T,) (A.25) phase R,,=nept,rtj {2 + 0.6 Re /2Prj/8f (A.37)' 60 Tj-Tl nf = , h, = aEf - T, (A.26, A.27) Re,=2cin,ps,rtl 2-32
~ ~ - - = . - . - - - _ - - = - - - . - - - . - - - . - - . - . - - - . - . - . - - .
I In the above the coefhcient er was introduced as a way to ! 1992 Nanonal Heat Transfer Conference, San Diego, control the liquid wier a in cases where these simplified August 9-12,1992.
- 3. Ishii. M. (1975) "Ihermo-Fluid Dyname Theory of ,
Two Phase Flow," Eyrolles. NOMENCLA*IURE
- 4. Ishii, M. and N. Zuber (1979) " Drag CoefEcient and Ca drag coefEcient et control coefEcient Relative Velocity in Bubbly, Droplet or Particulate Flows," AIChE J. 5,843.
e, specific heat at constant pressure , i Ef emissivity of fuel particles 5. Sissom, L.E. and D.R. Pitts (1972) Elements of Dans- i Er absorptivity of water droplets Pwt Phenomena, McGraw-Hill, New York. F factor for inter 6cial momentum exchange E accelennon d gravity 6. Wallis, G.B. (1969) One-dimensional Two-phase Flow, . N McGraw-Hill, Inc., New York. Heaviside sep function h heat transfer coefEcznt; speci6c enthalpy 7. Wiese, L.C.-(1968) Ind. Eng. Chem. hdamentals ;
.h, f enthalpy of evaporation 7,517. '
I speciAc internal energy "8 f conducu i APPENDIX B: INDEPENDENT VERIFICA110N OF 71IE f ion,& scaie r = s as^suasus"Ts n number of particles (or drops) per unit volume Pr The season for creanng the FLITI'E is that our efforts Prandtl number in using absorbmg radianon to image the whole muung P. P8*ssme zone during the design phase of MAGICD did not yield Q rate of heat transfer per unit volume promising results. The working concept in this effort was R heat transfer coefEcient between the phase (liquid to make use of two different 7- and X-ray energes and or vapor) and interface the differences in atenuanon between the water and the Re Reynolds number matenal of the balls so as to simulemaaansly measure both. T temperature Although in principle this approach is fme, in pracace, it t time results in a stiff sysem of equanons that yield large errw u velocity vector amplification in the solution, and thus it was abandoned. Wey critical Weber number for bubble / drop breakup We returned to it recently after the completion of the Greek a first phase of the expenmental program in MAGICO that void fraction of vapor (per unit volume of coolant) made use of FLUTE. The tempproach appemed hopeful, be-7 surface tension between vapor and liquid; specific sically because actual expenence with MAGICO inclemmart heat ratio 6 that the particle volume fractions in the mixing zone are in volume fraction (per unit volurne of total mixture) p the 2 to 3% range, thus creanng the possibility of"seeing" viscosity through limited (sporadic) areas of this zone without ball e microscopic density p' interference. Namencal expenments anempting to recre-macroscopic density a ale reahzation of the particle cloud and the optical paths Stefan-Boltzmann coefEcent thmugh it revealed that this was indeed the case. These ex-6 area concentration factor, defined in eq. (A.12) perunents also provided guidance on how to opnam the Subscripts wientation of the X-ray shot and the sarce-Wt h a added-mass effect tance, taking advantage of the hole panern in the dumper c l l convection Pate. ! f fuel ! g- gas (steam) In actual implementation, we used a flash of " soft" l f liquid (water) X rays timed at the desired instant within the preauxmg I transient in MAGICO. The image is recorded on a 13- x r radiation a saturanon 18-cm film positioned to cover the region of intrest in the mixing zone. By changing the timing of the flash and the Superscripts film position, we can map out a premixing transient in any f laminar flow tempwal and spatial detail desired-this is possible because t turbulent flow of the excellent reproducibility of the MAGICO runs, as al-ready demonstrated by the FLUTE maammements and the ! REFERENCES high-speed movies. We have limited our goal here to the ,
- 1. Bird, R.B., W.E. Stewart and E.N. Lightfoot (1960) independent check of the FLUTE results, and only a few !
Hansport Phenomena, Wiley, New York. me tw mis . In se pmoess d de-w & madw upecu d&is echmque, we have
- 2. Liu, C., T.G. Theofanous and W. Yuen (1992) " Film made quite a few runs that successively appeared more and
- Boiling from Spheres in Single- and Two-Phase Flow," more promising. A great deal of the success depends on 3
' 2-33 i
1 l l
/ ' 49rg I
.s ;f , ram *wy %
d h ";
.? ,
p> $43 %, .,;g ; h ^^y v,l 7% 4 4, % [ vQ3 : j'4e (,; n ;;p(p ^ d g 4';f~'itf
,A e *>,( l fI j ; ^ y,,, , ..
f y~y ; gc n Aw3c#1t,,Yl{g~ . f )#
& N YEE 4 3
4 P- 4 l$g/ 't l go+,\ ~ ~xp($ g Q+ ,? T& {'e % (%
!?
1 - ~% = n;.4+'**,'
' V*y '
t'
- l' - J ' .; ~
, Y j & j I Figure B.I. Print of the X-ray film taken in Run #1005. 1' l 8 g !
).tg% .
- k. '
3o54o. . 8 a, g , 40 &45s 4* f h *'.' I
'/ >45
=- 55o5
=
4 J a i % l l 1 i Figure B.2. Void fraction distribution obtaireo from X-ray analysis of mn #1005. The region i t covered is -1.5 < r < 5.5 cm and 19 < r < 25 cm. j 4 2-34 l i i
establishing adequate safeguards and procedures to ensure that the image obwined can be directly related to a cali- sphere boundaries were excluded, we used as an additional bration image obtained with a stepwise variation of void in criterion that the fraction of unaffected readings within a the optical path. Besides, we confirmed that the effect of group we: above some value-otherwise, the space associ-ated with the particular group of (20) pixels was taken to be X ray scattering from the steel balls (they are not present, clearly,in the calibration shot)is negligible. At this time, interfered by the presence of steel. He data analysis was the technique is well-developed, and we have one run in the repeated with f values of this fraction set to 25,50, and 75% with very consistent results, indicating absence of the MAGICO series (the 1000-series) to discuss here. Rather l than carry out the many special FLUTE runs needed to boundary-type influence being addressed by this operation. i cover the information on the X rays, our approach is to use The results from film segments covering the region PM-ALPHA as the means of comparison; the PM-ALPHA 19 < < 25 cm (i.e., a 6-cm slice of the pool top; is i interpretations are the ultimate purpose in any case, measured from the pool bottom) over two radial segments, l -1.5 < r < 5.5) cm and 5.5 < r <.11.5 cm presented his MAGICO test, #1005, was run with the 2.4-mm here. Spatial void fraction maps (using the 50% criteria steel balls at 600 *C poured into a 25-cm-deep pool of sat. discussed above) are shown in Figures B.2 and B.3 for the urated water from a he:ght of 21 cm. The X-ray shot was above two radial regions, respectively. The plank spaces timed at 0.52 s after initiation of the pour, which cone. in these maps indicate regions at ball interference. Imme-sponds to just about when the particle front hits the pool diately, we can notice that these results indicate void frac-bottom. De X-ray image obtained is shown in Figure B.I. tions in the general range measured by FLUTE (Angelini et It is notewonhy that individual balls are recognizable, even al.,1992). In a more detailed examination, we have plot-i when they partly overlap, and we believe with a pattem ted these results against PM-ALPHA predictions for four l recognition technique, we will have, from such shots, the different radial computational cells (at r = 1,3,5, and 7 I parucle number densities as well. Also in this figure, small em) at three axial positions (r = 18.75,2L25, and 23.75 j areas where balls are completely absent are clearly distin- cm), as shown in Figures B.4. In these figures, the PM- ! guishable, and it is in these areas that with the application of ALPHA results were obtained by an appropriate chordal- j the water / void calibration curve we can obtain the chordal. average equivalent to projecting the cylindrically-symmetric average void fractions. , void fraction distribution, as effected by the X ray on the l film. De X-ray results were obtained from the spatial maps ne " reading"and analysis of these films was done on by averaging all measured values within the cell being con-6- x 6-em film segments in order to obtain the high reso- sidered. The agreement is quite remarkable in all cases. It lution required-this gave a pixel size of 0.12 mm. These 1 is also interesting to note that the " water flux reversal" phe- l readings were analyzed in groups of 20 pixels. For each nomenon discussed in Section 4 is quite evident in Figure I such group, an average value of void (and hence of void B.4d; the insurge of water causes a precipitous drop of void fraction) was obtained by using the calibration curve and fraction at the outer edges of the mixing zone. The X ray a criterion excluding readings indicating the presence of happened to be taken just prior to this time, but it is clear spheres. Moreover, to ensure that reulings too close to the now how to best time the X-ray shot in the next run. k[ ;*
'%5,.g. .
I i b , g, **
; 3o540s a d, 4osass lp #
l h P 455-50s i
, Sos b
e l 44 i hr
- h 4lB Figure B.3. Void fraction distribution obtaired from X-ray analysis of run #1005. The region covered is 5.5 < r < 11.5 cm and 19 < < 25 cm.
2-35 i
- . . . . - . ~ . - .
. , . . - ~ . - . - _ . - . - . _ . . - . - . . . . . . . . . . - . . - - _ -
f I 0.6 , , . . 4 I I i z = 18.75 cm
'5 z = 21.25 cm 1 = 23.75 cm \.
O e z = 18.75 cm '"
~ ~ ' - * ' ,/ \ '
0, , o = 21.25 cm / f 5 a U 0.4
# z = 23,75 cm ,/
/Jo - i Vj-s ./- ,
d -
/ ,
u / 4 f s. - q/s // d O
;../.\/g'
- c
~ :
j [ h D.2 - f' i O : . t J l
- l o
t' ,
; , /
~ ~ -
'~~" ""~ ! ' ' ' ' ! ' ' ' '
O.0 O.0 0.2 0.4 0.6 Time (s) i Figure B.4a. Comparison between pmiiction and X-ray measurement for run #1005 for cell ! centered at r = 1 cm and three different heights. ; i t l 0.6 . , g f 7. = 10.75 cm ! ------- z = 21.25 cm /* * '. **,-* * ! ........ 2 = 23.75 cm /
- z = 18.75 cm / '- ' /'~ \
g o = 21.25 cm / / '. i z = 23.75 cm ,.
/ .. - \, r .
.O
- . / .
O 0.4 -
-s /-- '.
v'/- j I d :\- L. / i
~.\.c,/ r-'"I# \ '
! .d . l .- t - o :
-- l d 0.2 - -
U O : a : i
**.? '
i
~~j~~ #,/I 00 O.0 0.2 0.4 0.6 l Time (s) i f Pigure B.4b. CWaaa between prediction and X-ray measurement for run #1005 for cell f centered at r = 3 cm and three different heights.
- 2-36 I
. . . . - . - . - - - . = - - - . - . . ..
l I i 0.6 y g . t= 10.75 cm z = 21.25 cm
.......... : = 23.75 cm
- e
- z = 18.75 cm * .
g o a = 21.25 cm # I ' i 1 z = 23.75 cm N #["'~~N i
..o.
# ,/ , \.i ,[- J 0.4
- r l f -
j$ y \, j e 6 d
/./ \ f,/
A s, . i $ i
)
g l
.. 0+/ \ -
l
\
e l o 0.2 -
- / -
1 1 O ! 1 A l I .' / -
./ / -
} .
g,g
, . -' -4 l . . . l . . . .
l 0.0 0.2 0.4 0.6 l Time (s) Figure B.4c. Compenson between prediction and X-ray measurement for run #1005 for cell centered at r = 5 cm and three different heights 0.6 .. g g r
= 18.75 cm z = 21.25 cm e
-: = 23.75 cm s = 18.75 cm k
(#// 'k o \ l C z = 21.25 cm o i a = 23,75 cm
\
U 0.4 -
\
o - C A
/
j
\ .
1' aj'\j\ l 6.g . v.
~
l C 0.2 - - ! o / O f - l
/ , ',
0.0 i O.0 0.2 0.4 0.6 Time (s) Figure B.4d. CV- between prediction and X-ray measurement for run #1005 for cell centered at r = 7 cm and three different heights. 2-37 l
l l APPENDIX 3 l l ON THE FUNDAMENTAL MICROINTERACTIONS THAT SUPPORT THE PROPAGATION OF STEAM EXPLOSIONS l l Proceedings of the l Fifth International Topical Meeting l On Reactor Thermal Hydraulics - NURETH-5 September 21-24,1992, Salt Lake City, Utah Volume II, pp. 627-636 l 1 1 W 3-1
ON THE FUNDAMENTAL MICROINTERACTIONS THAT SUPPORT THE PROPAGATION OF STEAM EXPLOSIONS W.W. Yuen,' X. Chen" and T.O. neofanous Center for Risk Studies and Safety I4 A...s; of Chemical and Nuclear Engineering University of California, Santa Barbara, CA 93106 Telephone (805) 893-4900-Fax (805) 893-4927 ABSTRACT a highly devsloped detonation, and perhaps mort im-portantly, whether this escalation is possible within the his paper makes available the first experimental data Physi, cal constraints of the practical system underinves-on the fragmentation kinetics of hot liquid drops in another tigation. liquid (coolant) under the influence of sustained pressure j pulses. We observe the effect of " thermal" on "hydrody- his then is the main theme of this work, with some 1 namic" fragmentation and micromixing mechanisms, as de- more specific considerations inicluding: the details of mi-duced by the rates and morphology of the resulting parti- cromixmg environment around each drop as it fragments, cle " cloud." We show how propagation can be quanti 6ed the dynamic aspects of the pressure and velocity fields be-within the framework of a numencal model, and on this hind the shock front (especially in the so-called reaction zone), and the fundamentally non-one-dimensional charac-basis some interesting interpretations of an ex rimentall observed triggered " detonation" in the KR S facility (y- ter of the process. Our experu' nental approach is based on m the detailed observation of droplets forced to inStact with ISPRA) are offered. the coolant in a simulated steam explosion environment-especially with regard to sustained, pressure waves that I. INTRODUCTION characterize the reaction zone. His is accomplished in a i
- a. ions are It is known that under certain conditions " hot" lig- hydrodynamic shock code, carried out with our computer tube.ESPR All analytical '. - bSE j
uid drops can violently interact (" explode") after coming in documented by Medhekar et al.1'8 contact with a surrounding " cold" and volatile liquid (the
" coolant"). Rese thermal interactions are the co vence Previous related work can be briefly sum ==AM as rotto,s.
cf rapid and fine fragmentation (of the drop) and ac-compan,ying mixing with the surrounding coolant. Such Therrnally-Induced Fragmentation. Most of the interactions are known to be initiated by the contact of the work in this area has been aimed to delineate and interpret two liquids; such contact can be observed either sponta- the so-called temperature interaction sone. No fragmenta-neously (for appropriate combinations of temperatures) or tion rate data exist, but inferences on fragmentation (and it can be caused by forcing the collapse of the intervening interaction) rates have been made from comparisons of cal- j vapor blanket, as for example, by a sharp pressure pulse. 8 culations with Nelson's data on the growth and collapse It is also known that droplet fragmentation can result from j cycles of vapor bubbles from triggered single-drop melt- - purely hydraiynamic causes (i.e. in isothermal systems) in water interactions. Such interpretations have been offered an induced rapid acceleration environment, as the one that , by Kim and Corradini4 and by Inoue et al.8 among oth- ! accompanies a large pressure wave. In the detonation wave ers. In particular, the Kim-Corradini model is intended to - of a steam explosion clearly both mechanisms are present, be predictive; in it the fragmentation time is obtained from yet their relative role, and hence the actual kinetics that the penetration of the drop by liquid coolant jets arising control the various stages of escalation from the initiating from the " spikes" of Taylor waves at the interface upon trigger event to a " full-strength" detonation, remain to be reconciled. collapse and rebound of the vapor blanket. In a simple inter is More s ifically, while the v I'""pretation of this model the jet velocity is obtained initial stages of a taneous y triggered explosion w I be dominated by AP ly-induced fmgmentation, and while at the other ex- g ,fj 1p,(1 + pg/p,)1/2 j }afs - treme of a fully developed detonation into the supeeriti-cal pressure region only hymvoi. . breakup is relevant, which yields a fragmentation time iso f nothing is known about the intermediate, escalation, regime-This regime is crucialin that it determines whether the R4/Uj < fs < De/Uj (2) premixture conditions can support an escalation into In the above, AP is the pressure rise across the shock fron't. Nete that this model makes no distinction for the duration
- Also with the Department of Mechanical and Environ- of the pressure pulse or of the droplet temperature, and it ment Engineenns does not explain how these nueroscopic jets can survive the 3-3
intense heating environment, but rather penetrate the droplet Burger et al.,88 one-dunensional simulations lead to consid-all the way through. For example, for a corium melt drop crable inconsistencies-with the exception of ESPROSE, 10 mm in diameter, and a shock pressure rise of 200 bar, all other published detonation models are restricted to one the above yields a fragmentation time of 50 to 100 ps. dimension. [ Wote that this is short compared to the residence time in . i the reaction zone, and too long regarding the microjet's he presentation in this paper is I potential response to the intense heating. De first is concemed with the recastm,made g of Eq. (4)ininthree, dif- parts. ferential form; that is, expressing the fragmentation rate Hydrodynamiently-Induced Frngmentation. Ex. in terms of the instantaneous Bond number. His is done perimental work in this area, for the relevant liquid-liquid with the help of ESPROSE made to simulate the single-system, is scarce and not well documented; worse, it ap- drop response as observed in the shock-tube experiments pears to be contradictory. On the one hand Baines et al.s that formed the basis for Eq. (4). ,In the second part we and Kim et al.' working with mercury and gallium drops present new experimental data, obtained in the same shock-in water have reported (visual determination) fragmentation tube facility but with molten tin drops superheated by dif-times consistent with old results obtained in gas-liquid sys- ferent amounts and subjected to pressure waves of van-tems; namely, the boundary layer stripping mechamsms and us magnitudes, such as to span the tential range of a dimensionless fragmentation time
- tj' of thermal vs hydrodynamically controlle mechamsms. A prehmina.y interpretation of these data (hydrodynamic vs.
thermal fragmentation mechanisms) is also provided with pe 5/2 the help of ESPROSE and the instantaneous Bond number fi = f U, -
~ 4 to 5 (3) formulation derived in the first part. Finally, in the third Dd Pd part these fragmentation kinetics results are supplemented with a non-equilibrium treatment introduced in ESPROSE On the other hand, Theofanous, Saito and Efthimiadis,* to " simulate" and discuss a " detonation" observed in the using flash X-ray diagnostics reported, for a mercury-water KROTOS facility at the European Joint Research Center in system, significantly lower breakup times. Rese results ISPRA (Italy). This example also illustrates the importance were correlated in terms of a Boi l' dependence, motivated o.f two-dimensionality even for apparently one-dimensional by a Taylor instability mechanism, as situations.
f = 10.3 Bo,_ y4 (4) II. THE INSTANTANEOUS BOND NUMBER FORMULATION For example, for a Bond number of 10' this yields a di-mensionless breakup time of ~1, or four to five times faster neo ration of the hydrodynamic shock tube (the SIGMA fac ty) was simulated with ESPROSE by intro-than boundary layer stripping. For a Bond number of 10 8 ducing a small enough mercury mass in one computational the resuh is ~2 and still more than a factor of 2 faster. Both shell to correspond to the one drop used in the experi-the X-ray photos and the quantitative analysis of them has ments. The facility and experimental techmque have been been documented by Theofanous et al.' described previously.24 Briefly, a prescored diaphragm is ruptured, to suddenly release the pressure from the 1.2 m Fragrnentation in Detonation Models. Not surpris- long driver section mto the water-filled 3 m long expan-ingly, the formulation of fragmentation in detonation mod-elling has been widely varied. To start with, the fonnulation sion section. The tube is designed for pressures up to 1000 in the original, steady-state, detonation model of Board and bar. In the particular experiments considered here (isother-mal at room temperature) the mercury drops were initially Hall'8 made use of Eq.(4), with a coefficient of 22, known stationary (resting on a thin teflon piece) and the fragmen-at the time from experiments with gas-liquid systems. Mod- tation states were determined from flash X-ray radiograph em transient detonation models have also made use of hy- obtained for different delay times after the arrival of the drodynamic fragmentation; Dyagaraja and Fletcher 18 used shock. The fragmentated mass on these X-ray films was a uniform fragmentation rate based on Eq. (3), but, for determined' from the mass found in the " particle cloud" by unknown reasons, with the constant set equal to 1; Med- quantitative image analysis. (This method is demonstrated hekar et al. ,2 used the Reinecke-Waldman fragmentation for tin drops in the next section). The driver pressures in rate correlations 2 (developed also frotn gas-liquid work) this set of experiments were set at 200,333 or 466 bar. We with a dimensionless fragmentation time of 1 (motivated could match the data well with an mstantaneous fragmen-from Eq. (4)). It shotr!d be noted that all these (gas-liquid) tation rate given by data were obtained with steady flow conditions (by impos-ing an instantaneous acceleration and thus a fixed free- dMg ~frDj(t)lUs(t)- U,(t)l stream velocity behind the shock) while for liquid-liquid s/2 di 6t*6 systems the relative velocity changes during the fragmen-tation time is very significant. In a detonation calculation this is further aggravated by the highly variable pressure with a dimensionless breakup time given in terms of the and velocity field histones behind an escalatmg shock front. instantaneous Bond number by Finally, besides the fragmentation kinetics, another ually important aspect in detonation modelling is to prope y re- t[ = 14.8 bot8/ , (6) flect the rmeromixing between the finely fragmented debris and the coolant available to mix in the immediate proximity. Note that in the implementation of Eqs. (5) and (6), all his is particularly important in fuel-dilute premixtures (as fluid properties and flow velocities are evaluated at their is commonly the case) and also in interpreting experiments instantaneous values. The results are shown against the that may not be truly one-dimensional. As expenenced by experimental data in Figure 1. 3-4
I h Similar calculations were carned out for the bound-ary layer senppm 1 ' ' discussed above.g and the Remecke-Waldman correlations
"* In these calculations the cm.M. were used in their differentiated form and with the instantaneous 0.8 -
p - flow / drop parameters during the transient. The results for g different combinations of pressures and fragmentation time are collected in Figure 3. We observe that E - a -
^
[0.6 A (a) the Reinecke-Waldman formulation cannot be made to agree for any choice of t;, and l f0.4 - g ['{"'" - (b) although for particular conditions there are particular
' o 8' choices of f; to pmduce reasonable agreement, no sin-0.2 -
x [ _ gle choice can cover the whole range of the conditions of interest. j O; i Further testing of the pneently proposed fwmulation under { 0 5 10 15 mme extzme condidmis of Bond number vanadon durin '
,,i s a ,- the transient (for example, by shaping the pressure pulse g -
this can be done by inserts m the dnver section) is deemed desirable. l Figure 1. Computed fragmented mass (o, D, x) in com- ' parison to experimental data in the mercury / water system (isothermal). The solid line is 13.7 ta Bo'/'. III. DROPS FRAGMENTATION OF MOLTEN TIN The detailed resuhs from the 200 bar simulation are summarized in Figure 2. In particular, we can observe the For these experiments the SIGMA facility was equi changes in relative velocity, particle diameter, and the re- with a melt generator, a device that could produce re-sulting variation of the Bond number. The evolution of the lease a single (occasionally split into two equal parts) drop of mohen tin at required temperatures of up to 1000 *C (at debris volume fraction distributions is also shown- this is this time). Data were obtamed at low (360 *C), mtermedi-of significance in gaining some perspective on local mixin) ate (670 *C), and high (1000 'C) temperatures, and at two obtained and resulting pressure feedback effects responst- shock (pressure) levels,66 and 200 bar. The drop tempera-ble for sustaining a propagation. The computed liquid and droplet velocities are m good agreement with the data. The ture (auoted at the time of shock impact) was reproducible computed shock front exhibits minimal numerical diffusion, with 120 'C. In all experiments the drop mass was fixed Cnd its speed is also in excellent agreement with the data. at I g and the water pressure and teuiperature at 1 bar and The node size in this computation was I cm and the time 85 'C (to prevent spontaneous interactions), respectively. step,0.01 ms, The shock was timed to hit the drop while it is within view of the shock tube window. This timmg could be adjusted so i ase , , , t . t , , , . 300 . c.s -
-I u e m. o j a 0.0 160 -
-
- 0.0 -
0.0 - a 1 100 - - h 0.4 -
- 0.4 -
50 - 02 - CJ k
- 0 '
0 ' 0 O 200 400 800 000 1000 0 1 e 3 4 tes 270 27s See 283 200 s esse ens amesse a sono I is 0.e
, , te , , .
is - , ,
- g. .
' ~
ls - l 0.4
=
e - ls g - g 8 c
. 1> -
e 0 0 1 2, 3 4 1
==.2.* mi 3 4 9 1 2
*='>==*
3 4 Figure 2. Detailed results from an ESPROSE simulation of a mercury drop subjected to a 200 bar shock in water. The distance s is along the length of the shock tube starting at the top of the driver section. The position of the diaphragm is at = 250 cm (in this simulation a longer tube, than in the experimental one, was chosen to allow a longer evolution of the transient before reflected waves arrive back at the drop). The pressure front is given in time incrernents of 0.2 ms. In the debris volume fraction plot, the time increment is 0.4 ms. In the time plots, the origin is at the shock amval time to the droplet position. 3-5
R/W Model with t , s 1 B/L Stdpping with t , a 1 1 ' ' ' e O 'O g A C'"#*"*" 0.8 - o.S - o 00 a0 - O o'a o o 340 Be ; O O 200 Sw I O.6 -
, o se en I
- 0.6 - 0 o,' a -
o O g 6
'. g 4 Correetion 2- 0.4 - -
3
- o.4 -
o6 g ,,,y o 0.2 - , o o 0.2 [ o too ser 6 3eo en
,o a esta 0 :._ :
OL ' O 1 2 , 3 4 5 0 $ , . 10 15 R/W Model with t' =8 BIL Stripping at 200 Ser 1 . , 1 . . . , c=,emaan g O se n= a 0.8 - - 0.8 - - o too e-A A se n= _
- 0.6 - a ses g - o 0.6 -
a - 3 o 2 o 0.4 A o 0 g Corresenen 3- 0.4 - o o 3 o , , , ,, D D
- go a o , , , , ,
a 0.2 - n o,a - 0.2 o 3 a omia - 0 Aod ,' , , , , , 0 L._ 0 5 10 15 0 4 16
,q. 8
,q.12 20 Figure 3. Comparison of the Boundary Layer Stripping and the Reinecke-Waldman correlations (for various choices of t!) with the experimental data in a mercury / water system.
that the drop remained in view for times up to 2 ms follow- significant). He X-ray image was digitized by a scanner ing impact. In the present configuration, the pressure / flow creating a two-dimensional array oflight intensities. Rese conditions of the water in the viscinity of the dro et remain data were then processed by the computer using the cal-unchanged for up to 2.5 milliseconds, at which me the re. ibration curve (with appropriate normalizations, based on flected shock travelling back from the bottom of the tube the witness pieces) to obtain a two-dimensional array rep-arrives. As noted already, however, by appropriate modifi- resenting the spatial distribution of tin mass. A test of the c tions in the driver section a wide range of pressure pulse accuracy of the procedure is the extent to which these cal-shapes can be obtained. Also, a two-phase flow emiron. culated masses add up to the known total drop mass (1 g, ment around the drop can be generated by means of steam or 0.5 g for the case of split drops). From the results ob-injection at the bottom of the tube. Such experiments are tained so far (discussed below) this test was met beyond cunently in progress. also, the initial pressure (in the ex- our expectations. Because of the non-linearities involved, pansion section) can be varied-such experiments are now visual inspection of such films can be quite misleading, and planned for the future, such quantitative results are essential to understanding the
. fragmentation process.
As m. the mercury / water ex riments discussed above, data were obtained from singl flash X-ray ex Additional information about the extent and intensity different times along the fragmentation process.posures Since all ofatthe interaction, in an overall sense, is available from c:nditions are highly reproducible, these data provide the the debris which is collected with an especially constructed time-wise evolution of a " representative" drop as well. In plastic " pan" located some 10 cm below the interacting these older experiments, the unfragmented portion of the drop. These data have not been analyzed in detail yet, drop could not be adequately penetrated, even with hard X- but ically they are composed of two groups of masses-rays (30 kV in the Hewlett-Packard generator). nus, only one ly fragmented at micron-size round spheres and the the fragmented mass (debris cloud) could be quantified. In other ghly porous, but macroscopic in dimension, parti-the present experiments with tin, the whole drop can be cles. In the 1000 *C runs, for which these data are avail-penetrated, even with soft X-rays (24 kV, using the soft X- able, this macroscopically fragmented mass amounted to ray tube), and the whole image, including the unfragmented 50% and 40% of the drop mass for the 66 and 200 bar part, could be quantified. The procedure involved the use of runs, respective . Bus, as a first indirect measure it a a calibration curve obtained from exposing a tin stepwedge pears that at 1 'C about one-half of the drop is fine and two (later three) " witness" pieces to allow for vari- fragmented, with a bias for more fragmentation at the higher (bility in the exposure (small) and film development (quite shock pressures. 3-6
All the X ray results obtained so far can be found in Before discussing these data, it is useful to have in Figures 4 through 7. The 100-series runs in Figure 4 were obtained with shock pressures of 66 bar (1000 psi), whilethe mind Figure 8,' which shows in real time the expected frag-300-series results obtained with shock pressures of 200 bar mentation of a tin drop according to the hydmdynamic frag- [ mentation model (the instantaneous Bond number formula-(3000 psi) are in Figure 5. In these figures the top line,is tion discussed in the previous section). Also, it is useful i for tin drop temperatures of 1000 *C while the bottom kne to consider the digital X-ray " reconstructions" (i.e., mass i for 670 *C. In Figures 6 and 7 we have collected certam distribution) for runs T109, T312 and T313 as shown in I " older" experimental data obtained during the development i Figure 9. The total mass computed for T109 and T312 was of the experimental techniques. As such the conditions for 0.98 g and 0.89 g, respectively, while for runs Til3, which I these "old" data are not very reliable, but they are included was apparently a split drop, the mass adds up to 0.49 g. here because of certain interesting features in the fragmen-tation morphology they exhibit. !IIIIII8I Tiot T110 f1M Tio5 i l 1
, .p.
W M T337 ' N Figure 4. X-ray snapshots from the runs with 66 bar shocks. Figure 5. X-ray snapshots from the runs with 200 bar Tin temperatures of 1000 *C and 670 'C for the top and bottom rows, respectively. Times (in ms) following shock shocks. Tin temperatures of 1000 *C and 670 *C for the arrival: T109-1 Tl10-1.5 Tl14-1.5, T105-2, top and bottom rows, respectively. Times (in ms) following T101-0.5, T103-1, T104-2, TlOS/0-2. shock arrival: T314-0.75, T316-0.85, T312-1, T313-1.5, T306-0.75, T303-1. T307-1.5, T304-2. i l Figure 6. X-ray snapshots from the low temperature (360 *C) Figure 7. Snapshots from miscellaneous runs. Shock pres-j runs with 66 bar shocks. Times (in ms) following shock ar- sures of 66 and 200 bar for the 100- and 300-series, respec-i rival: TlXI/G-0.25, Tl X2/0-1.5, TlX3/0-2. tively. Tm temperature 1000 *C for Til3 and 670 *C for i
! all others. 'Ilmes (in ms) following shock arrival:
T307/0-1.5, T304/O-2 T104/o -2 Ti l 3-1.5. I
- i 3-7 I
1 , , , 0.8 - 3 o 0.6 -
~~E p 200 Bar
~
g
~
0 0.4- - ' wno 3 33e ear - ad S l 0.2 - se Bar O * !,s O 1 2 3 4 $$d 5 time (msec) VU o Figure 8. Hydrodynamic fragmentation in tin / water system. 4@d 6
, 10 mm ,
ESPROSE with the instantaneous Bond number formula- e i g j ti n. g 1 o
== o !
E $ P 5 10 mm g , 10 mm , E ' ' o ! l E o E S o o hi o E N o u E o n o - Figure 9. Digital reproductions of the X-ray films for runs T109 (above), T312 (top next column) and T313 (bottom -- next column). The numbers in the shade-scale are in em. Note that the diameter of a 1 g spherical tin drop is 0.66 cm. Figure 9. (continued) 3-8
ne following observations can now be made: but with the void concentrated in the inner radial node. The (a) At low tin temperatures (360 'C), even at 2 ms, the molten tin ~1 ft was distributed evenly along the center of the tube. fragmentation observed under a 66 bar shock is negli-gible. His is consistent with Figure 8. He object of this numerical exercise is to show the importance of local non-e (b) At intermediate tin temperatures (670 *C) fragmenta- of fragmentation kinetics, quilibrium tion is again negligible (up to 2 ms) under a 66 bar and of their inter (within the coolant), velopment of triggered explosions. nus, theplay in the de-ESPROSE shock, but a catastrophic breakup is seen to occur at just before I ms under a 200 bar shock. This is clearly code (model fully specified in Medhekar et al.x,2) was used thermally dnven as it is far faster than that expected with the tollowing changes. from the hydrodynamic mechanism (see Figure 8) and (a) In place of the original phase change model used to is also suggested by the morphology (see Figure 5). As drive the system to eguilibrium through a relaxation seen by the result of T304, by 2 ms "there is nothing time constant, we put m a phase change rate obtained le ft." from the difference in heat flux transported through (c) At high tin temperatures (1000 *C) thermally driven each phase to the interface. The constitutive laws for fragmentation seems to set m already at 66 bar (it is these fluxes are as in the original model. 1.5 ms) but, again,it is faster essentially at complete 200 bar (see T312 in by ~ Figures 5 and 9).(b) he fragmentation kinetics were based on the hydrody-namic fragmentation correlation described in this pa-(d) In both T10,1 and T109, both taken at I ms,it appear per (based on the instantaneous Bond number). This that somethmg; is already beginning at the mterface- choice was made because, as shown above, a formula-see also T109 m Figure 9. Ho, wever, it is also clear that tion for thermally-driven fragmentation under the con-there is a significant delay time before thermal frag- ditions of interest is still lacking, and also because of mentation can be seen to be clearly in progress. This the panicular purpose of the illustration intended here. delay time seems to be decreasing as shock pressure A difficulty with one-dimensional models, as encountered and/or tin temperature increase. by Burger et al.25 in an attempt to interpret this same KRO-(e) FinallY, attention is directed to the interestin8 and TOS test, is that even in apparently 1,-D geometries (as mrymg mo hologies seen in tests T114 and T303 the present one) they are forced to nux the debns with (seeming to too much water.-thus " quenching" the escalation. One the ; fully developm, ave caught g event) the, very and m tests T105 early and T304stages ofother a hand, by using less water (in each axial node) the I (showmg the final, high dispersed stage). Also very actual compressibility of the system is distorted. In the mterestmg is test T104/ sho, wing an upward-directed present calculation, this can be partly overcome by using fragmentation event with quite a lot of detail on the two radial nodes (the inner one of radius 2.375 cm). ! interfacial structure. Even with the above description, some of the phase It is clear from these resuhs that neither Eq. (1) nor Eq. changc, dynamics early on cannot be captured, as very small l (6) capture the essential physics involved in the thermal or pantrues of {ragrnentmg fuel contact very sman quanti-combmed thermal-hydrodynamic regimes of fragmentation. nes of the adjacent water thus leadmg to very high local Moreover, the various interdependencies on shock pressures n n-equilibnum m the coolant /debns field. To generate a and melt temperatures seem to be rather complex. Based ferentpective on Llus, several calculations were run with dif-en this, it can be expected that even the pressure pulse Sed fractions of the fra duration (in fact shape) will play an imponant role in the given tly to vapor producuonthegmentmg rest of thedebris energy energy process. Clearly, more such data are necessary if this key is su plied to the coolant in the node to which the debn.s ingredient to predicting the escalation and potential intensity is r cased For tMs fracuon, set at M, a of detonations in explosive premixtures is to be adequately escalation was calculated in less than 0.25 ms.g strong Similarly, j Pi nned down. f r this fracuon at 5%, the calculated explosion was much stronger than observed experimentally in just 0.5 ms. A l fraction of only 2.5% was necessary to match the observed ' IV. DISCUSSION OF AN EXPERIMENTALLY propagation. In this case, the total fragmented mass in the OBSERVED DETONATION 3.75 milliseconds of the calculation was only 354 g (out of In this section we apply ESPROSE to perhaps the only a total total massof 6.5in kg), used t he direct vaponr.ation process wa reasonably characterized detonation observed expenmen- 8.85 g. With no direct vaporizanon, the propagation fizzled tally. It was run in the KROTOS facility in ISPRA.15 In out. His calculation is contrasted to the one that produced it,7 kg of mohen tin at 1075 'C was dropped (in the form agreement with the data in Figure 10. The companson with of a jet) into a vertical pipe (9.5 cm in diameter,1.09 m the measured pressure traces in KROTOS is shown in Fig-long) full of 85 *C water. When the first melt arrived at ure 11. the bottom, an explosion was triggered by rupturing a di-aphragm and thus releasing 15 cc of compressed mtrogen at Several points can now be made. 120 bar into the lower end of the tube. The explosion was (a) ne KROTOS test discussed involved a very mild ther-recorded by pressure transducers found all along the tube. mal interaction; however, it was adequate to maintain We used the term " reasonably" rather than "well' character-the imposed trigger pulse. ized, above, because an important quantity, the steam vol-ume fraction along the tube during the premixing, was not (b) Unless the cons,titutive law used for condensation m. measured. However, this can roughly be estimated from the this calculanon is very inaccurate, it appears,that only shock wave trajectories measured experimentally 88 Such a slight thermalinteractions are needed to mamtam the void fraction distribution is used in the present calculations, Pulse in strongly tnggered experiments. His raises the 3-9
]
140 140 1 120 - 120
- 100 - 100 -
80 - 80 . 0.6 - 60 - 60 -
" " ) 0..
huAk
, iiitu'M
. , k%- A
([(U 0 0 0 60 100 150 0 80 100 150 0 50 e n,g 100 150 aM aM 140 140 1 120 120 - 100 - 100 - 1 00 .
. I 00 -
{u - la h j ddhb a i 0.. .
>: m m : ma
- 0., .
0 60 100 150 0 50 100 150 0 50 100 150 Pigure 10. ESPROSE simulations of the KRO7DS test with (bottom) and without (top) direct vaporization from the debris-coolant interaction. He first and second figures in each row are for the inner and outer radial nodes, res Print interval 0.25 ms. He third figures in each row show the void fraction in the inner radial node. question of what is the relationship to a full detonation. ACKNOWLEDGMENTS Regarding the adequacy of the condensation laws, the possibility of shattenng the ;;as/ liquid interface and its effect on heat transfer remains to be examined. His work was performed for the U.S. NRC under contract 04-89-082. Dr. S. Medhekar and Mr. R. Buckles (c) The issue of local micromixing and vapor produc. helped with the early development of the melt generator are tion / condensation in the pressure field withm the "reac- related experimental technique. tion" zone needs further study, in conjunction with the fragmentation kinetics. Toward this purpose, future NOMENCLATURE studies besides X-ray diagnostics will employ direct visualization. Bo = f Cop,D 4W, - Ug)2/a Co drag coefficient V. CONCLUDING REMARKS D diameter g density his study makes available the first experimental data M rnass on exploding dreps in an environment that simulates tha R radius of a propagating steam explosion. It also shows that frag. f* dimensionless time mentation kinetics, and the micromixing behavior with the to time required for breakup surrounding coolant, can be quantitatively derived by an X- t; dimensionless breakup time l ray imaging technique. The results show very interesting U velocity interplay (s) between thermal and hydrodynamic in origin fragmentation mechanisms. However, additional data are Greek 1 required before the necessary clues for theoretical develop- AP pressure rise across shock front ments can be discerned. p density a surface tension Further examination of hydrodynamic fragmentation kinetics supports the quantification proposed earlier by De- Subscripts ofanous et al.' Using this correlation, and a non-equilibrium j coolant microjet phase change treatment in a 2-D simulation of a KRO- e continuous phase, or coolant TOS test by ESPROSE, we conclude that it depicts a barely d dispersed phase, or droplet sustainable propagation (involving very small quantities of fragmented melt). Suggestions for further investigation of local non- fr o initial value just after passage of shock equilibnum phenomena in conjunction with fragmentation r droplet-to-coolant Maive value kmetics m stmulated steam explosion " reaction zones are made. 3-10
_. _ ._ __ .. ._ __.m _ _ _ _ i 120 120 , , 120 - 100 100 -
- k1 -
---- k0 100 -
,g "~ k0 dets ~~ kl . data ~ 42 i l
80 -
- "~ k2.dela
{ SO ,
.0 t
.0 q .
.0 t ee -
s, 49 ' s .' 40 - j ,f., s, 40 ,. j 20 - 20 s" - 20 ' '* . . . . -
, g.
* , f ,.I '
O O O O 1 2 3 4 8 6 7 8 0 1 2 3 4 5 6 7 4 0 1 2 3 4 s e 7 e ene peeg one pese one >= set 120 , , , , 120 , 110 f 100 - k2 l- 100 -
- k4 -
100 m .
~~ k3 dats l --. k4.seta ."""""
g .0 . g .0 - g .0 -
.0 .
.0 -
- .0 -
g i, 40 -
- ,, 40 1. -
,, 40
.e.-...****.....
20 -
! - 20 - --.....* .
t0 -
, D , ,
, . -v" v . , ,
O 1 2 3 4 5 6 7 0 0 1 2 3 4 6 8 F s 0 1 2 3 one 4 pseep 5 6 7 4 ene posee une post 1 120 120 , 120 i 100 - ko 100 - k1 - 100 -
- k2
.. . k0.dsm "~ kl . data .. . h2 este g .0 g .0 g .0 - -
.0 ; .0 - .0 -
- . l 40 s; 40 f I. - 40
- f4 -
20 - e~. ..- 20 l . . * - to . -
?% ~ - ~'* ,"**,,, .f,l .
, , , , , , , , . , , ,?:' ** *,'
0 1 2 3 4 5 6 7 8 0 1 2 31 4 5 6 7 g 0 1 2 3 4 5 6 7 8 - ene peso one pneeg ein p=eg I 120 120 , 120 , 100 - 100 - 100 k3 l - _g
- h6
,, -~ k3. data l .. . k4.date --~ kl.Wate 80 ,
.0 .
.0 . .0 .
40 ;(. , ! s, - 40 - j'.., - 40 - to *L...,..... - 20 -
*'**-......- - 30 y- .
.. . - m...ef .....
0 1 2 3 4 8 8 7 s 0 1 2 3 4 5 s y e 0 1 2 3 4 5 6 7 8 ene poes, one peng one peeg i l Figure 11. Comparison of the pressure traces taken in the KROTOS test with ESPROSE results (outer radial cell). l Top two rows "without" and bottom two rows "with" direct vaporization (corresponding to the heat from 2.5% of the fragmenting debris). ~ l 3-1I J
. - _ - . - ~ - - _ . - .. - - . - - . _ - . - - . - - . _ . - . _ - - . . - -- --
i I ' REFERENCES 9. T.G. 'nIEOFANOUS et al.," LWR and HitiR Coolant
- The Containment of Severe Accidents,"
I 1. S.MEDHEKAR, G-3306, My 1983. M. ABOLFADL and T.G. THEOFANOUS, "higgering and Propagation of Steam 10. SJ. BOARD and R.W. HALL, " Propagation of Ther- ! Explosions," Nuclear Engineering and Design 126, t mal Expansions Part 2: A Theeretical Model," Berke-41-49 (1991). ley Nuclear I. abs, RDf8/N 3249 (1974).
- 2. S. MEDHEKAR, W.H, AMARASOORlYA and T.G.
j THEOFANOUS," Integrated Analysis of Steam Explo- 11. A. ~nIAYAGARAJA and D.F. FLEICHER," Buoyancy- l Driven, Transient, Two-Dimensional 'Ihermo-sions," hunigs Fourth Intemational Topical Meet- Hydrodynamics of a Melt-Water-Steam Mixture," Com-ing on Nuclear Reactor 1hermal-Hydraulics, Karlsruhe, puters L Fluids 16,59 (1988). j FRG, Oct. 10-13,1989, Vol.1,319-326. 4 12. W.G. REINECKE and G.D. WALDMAN, "Investi a-
- 3. L.S. NELSON and P.M. DUDA," Steam Explosion Ex- tion of Water Drop Disintegration in a Region Beh nd l periments with Single Drops of Iron Oxide Melted with ,
Strong Shock Waves," Third Int. Conf. on Rain Ero- j a COs Laser," NUREGICR-2295, September,1981. sion and Related Phenomena, Hampshire, UK (1970). ; l 4. HJ. Kim, and M. L. CORRADINI, "Modelling of Small 4 Scale Single Droplet Fuel Coolant Interactions," Nu- 13. M. BORGER, W. SCHAWALBE and H. UNGER,"Ap-
- clear Science and Engineermg 98,(1988). plication of Hy and Thermal Fragmenta- !
tion Models and a State Thermal Detonation ! l 5. A. INOUE, M. ARITOMI and Y. 'IDMITA, "An An- Model for Molten Salt- Vapor Explosions," Int. i ! alytical Model on Vapor Explosion of a High Temper- Meetmg on "Ihermal Nuclear Reactor Safety, Chicago, ature Molten Metal Droplet With Water Induced by a Illmois,1982. Pressum Pulse," Proceedings Fourth International top-i ical Meeting on Nuclear Reactor 'lhermal-Hydraulics, 14. P.D. PATEL and T.G. THEOFANOUS,"Hydrodynam- ' j Karlsruhe, FRG, Oct.10-13, Vol.1,274-281 (1989). ics Fragmentation of Drops," J. Fluid Mech. 103, I 207-223 (1981). { 6. M. B AINES and N.E. BUTI'ERY," Differential Veloc. l sty Fragmentation m Liquid-Liquid System," Berkeley 15. M. BORGER, K. MOLIER, M. BUCK, S.H. CHO, i Nuclear Labs, RD/B/N 4643 (1979). A. SCHA~I2, H. SCHINS, R. ZEYEN and H. HOH- l MANN, " Examination of Thermal Detonation Codes
- 7. D.S. KIM, M.BORGER, !
G. FRQHLICH and and Included Fragineraation Models by Means omg- '
' H. UNGER, " Experimental Investigation of Hydrody, Pmpagation namic Fragmentation of Gallium Drops in Water Flows," gered,,
ture, Nuclear Enaaanng ?xperinnent in a Tin / Water Mix-and Design 131, 61-70 Proceedings International Meeting on Light Water Re- (199I)- actor Severe Accident Evaluation, Cambridge, MA, Aug. 28-Sept.1,1983, Vol.1,6.4-1. 16. M. CORRADINI, Personal Communication (1992).
- 8. T.G. THEOFANOUS,M. SAITO and T. EFnf1MIADIS, "The Role of Hydrodynamic Fragmentation in Fuel Coolant Interactions," Fourth CSNI Specialist Meet-ing on Fuel-Coolant Interactions in Nuclear Reactor Safety, Boumemouth, England, April 2-5,1979, CSNI Report No. 37, Vol.1,112, Paper #FCl4/PS,1979.
l 3-12
'l e 1, t j APPENDIX 4 THE PREDICTION OF 2D THERMAL DETONATIONS AND RESULTING DAMAGE POTENTIAL i Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions Santa Barbara, CA, January 5-8,1993 NUREG/CP-0127, March 1994,233-250 l l l 4-1
[ THE PREDICTION OF 2D THERMAL DETONATIONS AND RESULTING DAMAGE POTENTIAL W.W. Yuen and T.O. Theofanous Center for Risk Studies and Safety Department of Chemical and Nuclear Engineering University of California, Santa Barbara, CA 93106 Tel. (805) 893-4900 - Fax (805) 893 4927 ABSTRACT he basic concept of thermal detonation was put forth about twenty years ago (Board and Hall,1974), and it has he main purpose of this paper is to introduce a new remained unchanged in its basis since. In it, the basic feed-concept for the processes responsible for the escalation and back that sustains the detonation wave is derived from npid propagation of steam explosions. The concept recognizes that initially only a small quantity of coolant around each I"*"***"* # "* Y. Premixed " fuel" behind the pres sure wave f the explosion in the manner tilustrated m,- coarsely premixed melt mass " secs" the fragmenting de-bris coming off it, hence it is called the concept of "mi-agure . As usnated, the fagments are taken to rnix homogeneously with the coolant. Subsequent work intro. crointeractions." We also derive the analytical basis for it, define the nature of the requisire constitutive laws and re- duced a more detailed two-fluid formulanon (Sharon and
. . ScVera Ementati n ICE i mes (W et lated experimental data, and demonstrate that this concept
. . al.,1984; Patel and %eofanous,1981; Yuen et al.,1993; as essential for the prediction of steam explosion energet-Kim and Corradmi 1988), transient escalation from an ini-tes in large-scale premixtures in 2D geometries. We also tial trigger in a one-dimensional geometry (Burger et al.,
provide the first numericalillustrations of this concept,im-1993; Abolfadt and Theofanous,1987; Fletcher and nya-plemented in the computer code ESPROSE.rn. Further, garaja,1989; and Chu and Corradmi,1989) and also in a we provide the first numerical results of steam explosions m 1 two-dimensional geometry (Medhekar et al.,1989), but the l large water pools, i.e., ex-vessel explosions. Dese results concept of homogeneous mixing of the fragmented debris reveal two important mechanisms for explosion " venting with the coolant was retained throughout. and thus for reducing the dynamic loads on adjacent struc-tures. We conclude that, taken together, the "microinter- i actions" and " venting" make realistic predictions of steam ' 4V i1 U L ' ' explosion loads feasible and within reach in the near future. O $g 8 V W M
.h l e
O e* $~ $, Ng. 4M INTRODUCTION $ 7 , - Now that the computation of realistic premixture con-ditions seems to be well within reach (Angelini et al.,1992; Denham et al.,1992), the possibility of predicting the det-onation event itself, for use in safety analyses, cannot be
\
overstated. Particular (and important) aspects of such pre-dictions include: susceptibility of a given premixture to -- triggering, rate of escalation, peak pressures developed, and impulse delivered to the boundaries. These are new aspects Figure 1. Schematic of current modeling of thermal of cunent interest, especially to advanced reactor designs detonation following the original Board and Hall concept. (i.e., the passive ALWRs) in which one is concerned about direct explosion loading of the lower head, pedestal walls, Direct expenmental evidence that this concept is incor-l and immediately adjacent containment pressure boundaries. rect has recently been made available (Yuen et al.,1992). l In addition, this more in-depth understanding of the deto- In this study, the basic fragmentation / mixing morphology l nation process can be expected to further buttress previous of exploding drops in a simulated detonation-wave environ-I energetics assessments focused on in-vessel missile gener- ment was studied by quantitative X-ray radiography. This i ation (the alpha-mode containment failure) and carried out study revealed strong thermal effects on fragmentation and mainly by global energetics arguments (i.e., based on the a mixing pattern that begins in the immediate vicinity of quantities of fuel participating in an " explosive premixure" the drop and spreads, gradually involving more and more as in Medhekar et al.,1991. Turland et al.,1993 and The- coolant and debris. Blustrative examples of these data are ofanous and Yuen,1993). given here in Figure 2. De so-emerging concept of "mi-4-3
I 4 i i , ) i l iw l a: < ,, ! Figure 2. Example of fragmentation / mixing morphology of an exploding tin drop i (1000 and 670 *C for the top and bottom rows, respectively) in a simulated ! explosion environment (200 bar), in the SIGMA facility (Yuen et al.,1992). d i crointeractions"is schematically depicted in Figure 3. Hav. To further clarify the concept, we should point out i ing introduced this. concept the main purpose of this paper is that consideration of the microinteraction zone irstroduces l to show how it can be implemented in a multifield formula- non-equilibrium within the liquid (coolant) phase as a key l tion, including consideration of the constitutive laws needed aspect in the feedback process that allows a local (trigger) l to characterize the microinteraction zone, and to provide the event to escalate to an explosion. Also, it is important to l first illustrative numerical results. 'Ibe code reflecting this note that the coolant outside the microinteraction zone, and i new concept is called ESPROSE.m. where "m" stands for hence not thermally participating, is fully involved in the I microinteractions. - hydrodysamics, i.e., compression waves and associated ve-l locity fields. It should now be c. lear that within the old l s computational frame " producing" an explosion would re-
# # kY. M quire artificially large amounts of fragmentation and even 9 9 g;g %
i I so, the time-signature of the realistic pressure pulse could I # < not be wyauducsi. Furthermore, it should be clear that this problem cannot be fixed (even in ID calculations) by j increasing, artificially, the fuel volume fraction. j "Ihe above comments also imply a clear distinction be-i tween the microinteractions approach and other approaches I __ accounting for non-equilibrium phase change (condensa-tion)in the coolant. For example,in the appmach employed ! Figure 3. Schematic of the concept of "microinteractions" in TEXAS (Chu and Corradini,1989) or ESPROSE.a. the in a propagating large-scale explosion. energy of the fragmenting debris or a specified fraction of j 4-4 I I
it, respectively, is taken to produce vapor, which is then one directly through the explosion zone and the other by allowed to condense at rates controlled by a heat trans. " reflections" off the free pool surface as the pressure waves fer coefficient. This involves thermally the whole coolant of the explosica " radiate" through the water pool toward mass with the fragmenting debris which is not what hap. the pool boundaries. Another purpose of this paper is to pens in reality. In particular, anificially low heat transfer quantitatively illustrate these " venting" effects. coefficients must be utilized in order to reflect the limited thermal participation of the surrounding water implied in the microinteractions concept. Moreover, the appropriate amount of non-equilibrium is not known appriori and can. ; , (a) not (neither has it been attempted) be captured by means of g (b)
" tuning" a heat transfer coefficient. g_--- p %s y he two-dimensional feature of the ESPROSE code s h =
$Q has been utilized in a first attempt at reflecting very roughly the limited coolant participauon with the fragmenting debns k_g ]E in a precursor to this present effon (Yuen et al.,1992). Al-though a step in the right direction, this approach
- is also Figure 5. Illustration of the two " venting" mechanisms in open to criticism because it effectively fixes the quantity ex-vessel explosions, of water participating and hence, again it cannot rtproduce the conect signature of an explosion. More imponantly, ne timing of the developments described above in this " remedy" is only possible in ID geometries, i.e., the relation to this meeting allowed only the separate demon-radial nodes are used to allow the required degree of con-tact between the melt and liquid coolant, as illustrated in stration of the "microinteractions" and of " venting." he Figure 4. "microinteractions" concept was demonstrated in a ID KROTOS-like geometry using ESPROSE.m. and the " vent-ing" was illustrated in a 2D ex-vessel interaction geometry using ESPROSE.a. In the near future these two aspects are 8 to be combined into a 2D ESPROSE.m capability which,
... ,. 8.......
,8 ,. %.. h f..........
together with the PM-ALPHA code (for premixing), will allow the first meaningful predictions of steam explosion loads in reactor geometries. THE FIELD FORMULATION OF THE MICROINTER-ACTION ZONE CONCEI'T ne original ESPROSE code (Medhekar et al.,1989) was based on a 3-fluid (3-field) formulation, the three fluids being " fuel panicles," " steam" and a " water-debris" mix-Figure 4 Blustration of the limited fuel-coolant comact ture. The field equations and constitutive laws were the afforded by ESPROSE.a. That is, using a 2D computational sune as those of PM-ALPHA (Amarasooriya et al.,1991; mesh for a quasi-ID geometry. Angelini et al.,1992) supplemented by a debris continuity 1 In fact, non-one-dimensional behavior is crucial in the + 7 * #b6"' " I' 0) consideration of large scale explosions, not only because re-alistic large scale premixtures are strongly non-one-dimen-gp e i sional (Angelini et al.,1993). but s'.so because in reactor
-Ofl- + y . p'f uf = -F, (2) l geometries the premixture zo se is surrounded by significant and a constitutive law for the fragmentation rate:
quantities of water w hich pro rides the coupling medium be-tween the explosion zone and the surrounding structures. A 66f dM realistic consideration of the dynamic loads on these struc- Tr = 77 I (3) tures requires the dynamic couphng of this medium to the where explosion zone, as schematically illustrated for the case of dM an ex vessel explosion in Figure 5. His schematic makes uf} l W - u,,f l(#l#'}g evident two intuitively expected mechanisms of" venting"; T" 6t; and the " fragmentation time" and the instantaneous and
- Ris formulation also included an augmentation of the Bond numbers are defined by fragmentation rate to roughly reflect thermally-driven frag-9.6~- 13~7 BoO and a* l u' - uI l2 2'I mentation (Yuen et al.,1992), and the assignment of a frac- ' Bog = 8 -
tion of the thermal energy of the fragmenting debris to di-rect vapor production, as mentioned above. The ESPROSE (5) code version reflecting these features is referred to as ES- His instantaneous Bond number formulation was shown to be consistent with experimental data (from the SIGMA fa-PROSE.a. cility) where fragmentation is dominated by hydrodynamic 4-5 L_ __ _ . --
l 1 instabilities (Yuen et al.,1992). These comparisons also simulations already at pressures of 100 to 200 bar, while l demonstrated that the numerical scheme captures well the the real interest in steam explosion energetics is for much j shock features (steepness, speed) of the hydrodynamics. higher pressures. 1 This aspect of the treatment presently includes an "artiS-On the other hand, in the microinteraction zone the de-cial viscosity" in the manner discussed by von Neumann and Richtmyer (1950). bris, some liquid in the vicinity entrained with it, and any 1 vapor produced would be in such intimate contact that to a l in the augmented version of this model (ESPROSE.a), first approximation, they can be treated as an homogeneous we introduced an enhancement of the fragmentation rate mixture in thermodynamic equilibrium. In this approxima- [Eq. (3)] by a factor ff to reflect the experimentally ob- tion, then, the microinteraction zone is treated as a field. served contribution of thermal fragmentation (Yuen et al., This field grows with time as it receives debris, from the 1992), and modified the phase change model to allow some fragmenting fuel drops (the " fuel" field), and liquid coolant fraction, f,, of the fragmenting debris energy to go directly from the "m-extemal field." Thus we arrive at a three-to vapor production. This formulation, field formulation, the three fields (or " fluids") being " fuel particles," the "m-external field" and the "microinteraction 1 zone." The equations are given in the appendix. A fur-J= _ {R,(T, - T,) + Rt(Te - T,) ther elaboration could be made by separating further the ,
+feFe(If -Io(T,))} microinteraction zone into two (debris-water and steam) or l (6) even three (debris, water, and steam) 6 elds, which would l
when a < 0.,d , also allow for departures from " local" equilibrium. The nu-merical implementation of the resulting 4- or 5-field model is quite feasible; however, the potential advantages of such D/t = nf(h, + he)rfjQif(Tf- Ts) an elaboration and therefore its need are best assessed after
+ F,(1 - f,)I f+ f,F,la(Ts) (7) gaining some further experience with the 3-field microin-teractions model, especially in regards to the constitutive and when a 2 0.7 treatment of the microinteraction zone,in relation to exper-iments run specifically for this purpose, as described next.
It = min (nfatj, nfrt})aEf E,(T) - T/) Along with the field equations given in the appendix,
+ (1 - f )F, {(1 - a)I f+ oI (T,)}
f + f,F,I (Ts)(S) f WC SPecify the constitutive laws for mass transfer, at all two- l Seld intrfaces. We distinguish between the case of fully-collapsed void immediately behind the propagating front and that in which a signi5 cant void remains. The former Qf, = nfh ',rt}&f ,(Tf - T,) case is the most significant in terms of its positive feedback
+ of,(1 - f.)(I, I f(Tt)) (9) to the explosion,it typically arises in premixtures consid-ered explosive (o < 30 or 40%), and it is the only case in-enhances the degree of interfacH non-equilibrium, but va- vestigated so far at the fundamental level (i.e., the SIGMA por is still allowed to condense, through a heat transfer experiments described by Yuen et al.,1992). The latter case coefficient [as seen in Eq. (6)], which thermally couples it is basically dissipative (i.e., Medhekar et al,1991; Fletcher, to aH the water in a computation cell. In other words, this 1993) as its high compressibility tends to attenuate pres-formulation forces condensation for as long as there is any sure waves and the low densities are ineffective to produce subcooling in the water, in the cell, taken all at the same signincant fragmentation rates. The emphasis at this stage temperature (T4 ). Regarding the factor ff, we expect it to of development is given in the former case, the latter case gradually decrease as pressure increases, and to essentially being treated in a more approximate fashion.
approach unity at supercritical pressures. The definition of In the fully-collapsed void case, the initial volume frac-the various exchange parameters is presented m, a previous work (Medhekar et al.,1989). tion of the microinteraction field is essentially zero, and it grows as debris and entrained fluid from'the m-external By contrast, tiie concept of microinteractions is to al- Seld enter it--the rates at which this is happening represent low for non-equilibrium within the liquid phase itself, and the key constitutive features of this model. For the frag-this is accomplished by introducing another field comprising mentation rate we use a generalization of Eqs. (3) and (4), all the liquid which is "too far" (outside the microinterac- including the thermal augmentation factor ff. 'Ihe detail tion zone) to thermally interact with the fragmenting debris. is given in the appendix. We expect that the entramment To fully appreciate the importance and need for this sepa- of the m-external field will depend on its relative velocity rate field (called here the "m-extemal" field, i.e., the coolant to the fuel field, and the amount of speciSc volume expan-Beld external to the microinteraction zone) one needs to re- sion (i.e., dilation due to thermal or phase-change effects) call that typical premixtures are rather lean in fuel (typically of the microinteraction zone. Further, we expect that these less than 10% in a volume fraction), and as pressure builds two mechanisms (rates) will interact and funher data (than up (in the explosion front) the liquid-to-vapor density ratio those presented by Yuen et al.,1992) in the SIGMA facil-approaches unity-thus mixing induced by the large local ity extending especially the range of conditions to higher velocities associated with evaporation at low pressures es- melt temperatures and shock pressures would be required sentially disappears. This was clearly seen in the SIGMA to open up the real fundamental understanding in this area. 4-6
Such work is currently in pmgress. De technical approach QUASI-ONE-DIMENSIONAL EXPIDSIONS AND THE relies on the simultaneous use of several diagnostics in- KROTOS EXPERIMENTS cluding quantitative flash X-ray radiography (providing the l debris fragmentation rates and growth of the microinterac. Integral type explosion experiments are cunently car- l tion zone), high speed movies (givmg an idea of the extent ried out in the KROTOS facility at the European Joint Re- 1 of phase change), pressure measurement in the immedi. search Center in ISPRA (Hohmann et al.,1993). Rese I ate vicinity of the exploding drop (providing the transient experiments involve the pouring of tin or aluminum oxide i thermal interaction feedback), and the fmal debris size dis. melts into a tube filled wi'k water, the sudden release of ! a compressed gas volua the bottom of the tube, and tribution (pmviding another measure of the intensity of the explosion). The simultaneity of the transient measurements the measurement of the 1mure transients of the resulting is emphasized because beyond the morphology the microin, explosions along the length of the tube. He tube is 10 teraction model must also match the resulting thermal feed. cm in diameter and 2 m long, thus the geometry is essen-back. Finally, it is noted that by introducing steam bubbles tially one dimensional. He trigger is well-characterized by into the shock tube we can obtain a wide range of liquid the expansion of the known volume and initial pressure of
" flow" velocities and shock pressure combinations as appro- some compressed gas at the bottom of the tube. He melt priate in exploring the important regimes of escalating ex. is released in a controlled fashion from a well-known ini-plosions. For the time being, the nature of the ESPROSE.m tial temperature, and the water temperature is uniform and solution can be illustrated by making the volume of the en. known. Because of all these features, these experiments are trained m-external fluid to be proportional to the volume of very attractive for testing explosion concepts /models. This the fragmented fuel. The entrainment rate per fuel particle, is especially so because the most recent KROIDS-28 test th.,is thus given by using aluminum oxide melts produced very energetic ex-plosions and very high (supercritical) pressures. The main shortcomings currently are on the quantitative aspects of th, = f, g f \ (10) data " prediction" comparisons, in that the local melt and di \p// steam volume fractions along the tube are not mersured directly, and in that the range of the pressure transducers !
where the factor f, is parametrically fixed to various values, was exceeded in the latest and most interesting explosions. i.e.,1,2, . . 5. Even so, these are the best charactenzed experiments so far and it is worth pursuing their detailed understanding with For any region left with significant void behind the E*"
- pressure front, this void is assigned, as an initial condition, to the microinteraction zone. In such regions fragmentation In a recent publication (Yuen et al.,1992) we con-rates do not contribute significantly, but rather the behav- sider KROTDS-21, a test with molten tin at 1000 'C. V!c ior is controlled by the rates of condensation, i.e., vapor- concluded that this was a rather mild interaction, contribut-liquid mixing which can also be viewed as an entraintnent ing to maintain the strong trigger imposed rather than to of the m-external field into the microinteraction zone. Un- lead to a rapid escalation. Here, we consider the tests with der the intense condensation conditions behind a shock, we aluminum oxide melts (KROTOS-26 and KROTOS-28).
expect shattering of interfaces and it.rge liquid subcoolings, . i.e., enormous condensation rates. To bracket the behavior, let us tegm. with an .dealized i case of arb.itrarily spec-ified, uniform melt and steam volume fractions-6f = 0.05 we consider three different constitutive treatments in such and a = 0.01, respecuvely--under the typical KROTOS regions (a) an entramment rate given by Eq. (10), (b) an trigger: the sudden release of a 12 MPa nitrogen gas of 15 entramment rate sufficiently large to incorporate all the m-cm8. The ESPROSE.a calculation was run with ff = 1, external field to the microinteraction zone within a specified f, = 0.05, and for the ESPROSE.m we used ff = 1 and time constant r,, i.e., f, = 1,2,4 and 6. The results are summarized in Figure
- 6. Note that ESPROSE.a calculates a relatively mild inter-rh, = 2 (11) action, basically preserving the imposed trigger, while ES-
#' PROSE.m predicts rapid escalation to comparatively much larger pressures. Also note how strongly the factor f, af-where ms is the mass of liqu.d coolant (at any particular i
fects the " signature" of the explosion, as well as 6e peak position, or computational call), and (c) a zero entramment pressure. This is inherent in the physics of the consti<utive rate but an enhanced heat transfer coefficient, between the law for the microinteractions utilized here. microinteraction and the m-external fields, to roughly rep-For KROTDS-26, the initial conditions were specified l resent transient condensation effects (i.e., g behavior) as usirig the tirning of the premature trigger,in relation to the well as shattering of interfaces. start of the melt pour, the guidance from PM-ALPHA ceJ-ne third and final important element of the constitu- culations and the speed of the pressure shock observed ex-tive treatment is in the drag laws of the " fuel" field. De perimentally in the explosion. The specification used in an treatment used previously in ESPROSE.a is maintamed. It ESPROSE.a calculation is given in Figitre 7. He calcula-has been tested extensively with SIGMA expenments (Yuen tion was carried out with ff = 5 and f, = 0.05. he results et al.,1992) and will be expanded when additional experi- are given in comparison to the experimental data in Figure mental data become available. 8. The positions of the pressure transducer (K0 to K5) are 4-7
- - - . . . _ . - - . - ~ . _ .
- . . - . . . . . . . _ . - . - . .~ _
ESPROSE.s 1000 , , , , f v= 0.05 _ s00 - l t ! E 600 - 400 - i 200 - l i o uu tu m\ . . , l 0 10 20 30 40 60 l s (em) , ESPROSE.m ESPROSE.m ! 1000 , , , , 1000 .,- , , , ; 800 - e
- 800 o .
- b. 5
- 600 -
. 500 -
I - l 400 l 400
& L 200 . 200 .
0 -'I- 0 ' l- - '- - ' O 10 20 30 40 50 0 10 20 30 40 50 - (om) x (om) ! ESPROSE.m ESPROSE.m 1000 , , , , 1000 , , , , _ a00 - I.
- 4 .
800 - I, " 0 .
)
a
- 1 500 -
- 600 -
. l t i l 400 -
- ! 400 -
200 f . i g00 . O t ,k... .,k. .. , o 0 10 20 30 40 60 0 10 40 50 s (cm) 2 0, ge,3) 0 Figurel Illustration of the role of microinteractions in the escalation and propagation of steam explosions. These. calculations refer to a KRO' IDS-like geometry and trigger with f6 = 0.05, a = 0.01, All cases were run as ID with ff = 1. 'Ihe f, and f, in the ESPROSE.a and ESPROSE.in models respectively are shown in each case. l l l 4-8 1 i )
._~.- - - - - - . _ . - _ . - . - - - . . - - . . - - . . . - - . - . - . . . _ - . - - - . - -
inside Cell Outside Cell 1 ,- , , , , ,- ,- 1 m . ,- , , ,- ,- - 0.s - 0.s - 0.s - 0.s - e a 0.4 - i 0.4 -
- I t !
1 0.2 - 0.2 - t o
... ... i 0 20 40 s0 s0 100 120 140 1s0 0 20 40 60 s0 100 120 140 160
*(=) : tm) i 1 i- ,. ,- , , ,- , 1 ,- ,- , ,- , , ,-
f 0.s - 0.s - i Os - 0.6 -
't 't i- 0.4 -
0.4 - \ [ 0.2 - 0.2 - 3 0 0 ' '- - ' O 20 40 so s0 100 120 140 160 0 20 40 so s0 100 120 140 1s0 ; n(m) (m) ' Figure 7. Initial conditions for the KRO10S-26 calculations. ' l , 1 ( 1 i described in Hohmann et al. (1993). Note that the trigger dicted. The ESPROSE.m calculation was run in ID and ! propagates essentially undiminished through the lower part with the ID initial conditions fmm Figure lla. The re-of the shock tube (a = 0), it tnggers an explosion at the l suits are shown in Figme 11b. Because of the transducer ' very top (K5), which then pmpagases downwmd. We note cutoff, the comparison is only qualitative, but it is impor-that the pressure amplitude at position K5 is reasonably well tant that the microinteractions model pre & cts pressures well W As the shock propagases downwards it seems over 500 bar, as found in the ev . ;. In very rough : to be attenuated at position K4, but drives the transducers terms the pulse widths are also comparable, whatmg that - out of scale at all lower positions. Given that K5 is the a very energetic explosion is pre &cted as in the experiment. , origin of the explosion, and that the melt did not penetrate Clearly, this initial comparison is very promising for both
- l. below K4, the " topping-out" of the transducers KO to K3 the expenment and the calculation. To meet this promise the l would appear to be suspect. So, this comparison is only of expenment should improve the reliability (and range) of the
- qualitative significance, pressure measurements, and provide data that provide a bet- -
Much more interesting is the test KROTOS-28, in which tu chzadon M se premixtme &c., melt d seam the trigger functio 5ed as intended--i.e., after the melt reached volmne a distributions at se time d se Ingger). At the bottom. For this case we ran both ESPROSE.a and ES- se same dme, se calculades shmid be improved by se PROSE.m calculations. The initial conditions were speci. incorPwann d new constitudve laws fw smeminieracdas fied in the manner described above. For the ESPROSE.a as they become available from the SIGMA experiment. run the initial conditions are shown in Figure 9, and the paramesers ff and f, were set to 5 and 0.05, respectively. The results are compared to the expenmental data m Figure VENTING PHENOMENA IN 2D EXPIDSIONS
- 10. Note tha't the explosion was initiated at position K1 and The purpose of this section is to quantitatively illustrate I escalased rapidly along the tube to pressures over 500 bar, the " venting" processes mentioned in the introduction. The "toppmg off" the transducers. The mechamcal damage ob- situations of interest are reactor cavities with diameters in i served (Hohmann et al.,1993) seems to be consistent with the 6 to 10 meters range and pool depths of 1 to 3 meters. j such high pressures and pulse-widths. Note that even with For these illustrations we chose the diameter of 6 meters j the augmented treatment of ESPROSE.a and the relatively and pool depths of I and 3 meters. The quantity of pnmary large value of ff = 5 the explosion is grossly underpre- interest is the pressure pulse on the side walls. l a
I I 4-9 l l l
I l L f i l l : 250 , , , , , 250 , , ( 200 - _ no .
- 200 -
_ ns : %
-- ko. data ~~- k3. data l i
k 150 - j . f 150 - l ', , . e i : ! .! 100 , ; . 100 . ! - 8- ., ; i. ; ' 50 so ; ;* \ , ', ,'
- '.,...*.*...,,.....j o a ' *' ' ' ' '
0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 ! ma= la==4 in tonne l 250 , , 250
, ., . , , , , , n , ,
200 "I
- k. J - k'
"-- kl. data y 200 -
.! ..-. k4. data r k 150 L f .
[ 150 - J ,
- 100 -
! J 100 . J
, g i 50 - *
. , ,f -
50 -
'., 2
' ' ' \' '
- 0 o i 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 ene Muse ene meno 250 , ,
, , - . . , 250 , , , ,
k2 ! '! *
- k5 3 200 -
_ . k2. data 200 -
! * ~~* k5. data l l .,
k 150 - l J f 150 - - 100 - I ' 2 100 - 2 8- l -
' #, , i. .
50 - ' .
..- 50 -
.! ? .
0 o i 0 0.5 1 1.5 2 2.5 3 0 0.5 1 15 2 2.5 3 une peses ans ine,4 Figure 8. Comparison of an ESPROSE.a calculation of KROTOS-26 test with experimental data of pressures measured along the tube length. 1 i l 4-10
_.~ , _. _ _ _ . . _ . - . _ . _. -.___._ _ ~._ _. . . _ . . - _ _ - _ . _ _ _ . . _ _ _ _ . . _ . - - - - l ! f ! Inoldo Cell Outside Cell 1 .. . ,- , ..- ,- ... 1 , , . ... ,. ,. , 0.s - - 0.s - - t 0.8 - - 0.6 - s < a f 0.4 - 0.4 - - l 0.2 - 0.2 - - L I l
' ' - ' " ..a. o .n
- O 0 ;
i , 0 20 40 40 80 100 120 140 100 0 20 40 80 00 100 120 140 100 I (m) g, 3 ; l l 1 , . ,. . ,- , ,- 1 ... ,- , i- .. , ,- 0.5 - - 0.8 - - ! 0.6 - - 0.8 - - O '8 r i- 0.4 - - 0.4 - 2 1 0.2 g 0.2 - - 0
- '- '- '- ' L' - 0
'- ^'- '- '- - '- -
0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 180 m (em) s (ce) , Figure 9. Inidal conditions for the KROTOS-28. ESPROSE.a calculations. ! , ~ The melt pouring conditions are very much system and roundmg fluid and the free surface can be surmised from l scenario specific, thus we make no attempt to represent any- Figure 14. For the 3-meter pool case the c. g=t -g
- thing in pikolar here-for illustradon purposes only, we type of information is found in Figures 15,16 and 17, re- -
j assurne a pour of 0.6 meters in diameter with velocities of spectively. 'Ihe vennng processes are quite evident in both ! 9.7 and 7.1 m/s at 0.2 and 0.4 m above the water surface cases fmm Figures 14 and 17, and they manifest themselves ! l (" inlet" to the computational flow 6 eld) for the 1 and 3 me- in Figures 13 and 16, by the relatively low pressure at the l ter pool cases, respectively. In both cases the melt (UOs wall as compamd to that in the explosion zone. It is also properties) volume fraction at the inlet was taken as 0.05, clear that this venting is more pmnounced in the 1-meter and the particle size was fixed as 1 cm. The premixing tran- case, as expecsed. In parallel with propenng the 2D ver-sient was calculated with PM-ALPHA and the explosions sion of ESPROSE.m. we are working toward a theory to were triggered at the time the fuel reached the pool bot- generahre these 2D venting aspects for convement funne tom, by suddenly releasmg the pressure of saturated steam use. i at 120 bar from one of the computational cells. The calcu-lation was carried out using ESPROSE.a (with ff = 1 and f,, = 0.05) because the 2D version of ESPROSE.m is, at CONCLUSIONS this tirne, sdll be,ing tested. e As in the case of premixing, propagation is a funda- , From the results of the previous section, we expect mentally non-1D phenomenon, domir.ated by miemin-l that ESPROSE.a will underestimate peak pressures in the teractions. l explosion zone, thus we emphanie that these results are e " Venting"is a key feature of ex-vessel explosions, and only illustrative of the " venting" in a separate-effects man- it plays a key mie in mitigating the dynamic loads on ner. On the other hand, we must also emphane that the the side boundaries of " shallow" (1 to 3 meter) pools
; trigger employed in these calculations is quite %2 and in reactor cavities.
not necessarily representing the true explosivity of these ,g g ; premixtures.- Again, the idea is to focus on the ' explosion venting * #8Pects of such Wes. depends on the formulanon of adequate constitutive ( laws for the microinteractions. Relevant experiments
- 'Ihe' initial conditions for the explosion in the 1-meter (single-drop explosions in a simulated detonation front l pool are depicted in Figure 12. "Ihe calculated pressure environment, i.e., sustamed pressure pulse with a de-1 pulses along the side boundary are shown in Figure 13, and tailed diagnostics on the micminteraction zone) are 4
the dynamics of the explosion zone interacung with the sur- cunently in progress in the SIGMA facility. 4-11
600 , , , , 600 , , , , 500 - -# j'. O - 500 - k3 r.
; } [g!g
~- ko. data .. . k3 data 'l
;: ; 400 :
g 400 300 l 5'g;W a='=awa senan.s
! ,.een.s 300 -
i
- a.
200 - - 200 -
! 'I.: -
100 ,,,,=--.....*," i 100 - ,j . t
' ' 'I 0" '
o O 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 en.in.no w go ,o 600 , , , , 500 , , , , 500 . k1 . 500 - - ke l ,r -- -- -
--- kl . data "-- k4. data l l g 400 - -
T 400 -
,L -
- e. F- ; n.e 300 -
l *. ,1
* - 300 - -
- s. 200 -
- i- 200 -
j -
- a. ; -
~
100 - l I./, . 100 - -
, .. o . , ,
0 0 0.5 1 1.6 2 2.5 0 0.5 1 1.5 2 2.5 nneinamo ""='""*'8 600 , , 600 , , M , M 500 --- k2. data . 500 -
.. . k5. data :
- 'I - - -
g 400 - l j g400 . , 300 - l ;..; saneswerm.s meannwn - 300 - jj -
< 200 - ; -
- i. 200 - -
l 100 - 100 -
- i 0 0 i 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 i uneta==0 en (mese Figure 10. Comparison of an ESPROSE.a calculation of KROTDS-28 with expedmental data of pressures measured along the tube length. l 1
J 4-12
1 , , , , , , , 0.1 , , , , , , 0.s - 0.0a - - 0s - c.0s - - a e t 0.4 - 0.04 - 0.2 - 0.02 - 0 > ' ' ' ' ' ' 0 0 20 40 80 00 100 120 140 180 0 20 40 60 80 100 120 140 160 m (es) atem) Figure lla. Initial conditions for the KROTOS.28, ESPROSE.m calculations. 1400 , , , , 1400 , , 1200 -
- k0 -
1200 - U 2
--- kO. data ~ k3. data 1000 -
1000 - 2 g 800 g mammwn wanedvase mammen 2 E 800 - "****' 2 eenshes 600 - N 2 600 - 2 400
- r. *
!ur s ,,,
l . 400 - 2 l 200 - 200 - l .'*'* ' 2 0 w-- , . _- ,
' ' ' 'l '
0 O 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 i 8""8""*# to's tause 1400 , , , , 1600 , , , , 1200 -
- A1 -
1400 -
- k4 -
..... kl. data 1200 "-- k4. data ;
1000 - - ' { 0 - - {1000 w e amamwn - 800 - - 600 2 600 g, ," , n. 400 - - 400 - l - 8 ., t I O 0.5 2 2.5 0 0.5 1 1.5 2 2.5 1,,,, p,1.5 ,, m'= ta=*e 1400 , , , 1400 , , ,
- k2 -
1200 k5
-1200 ----- k2, data
---* k5. data 1000 - J 1000 - 2
- 300
- 2 300 - 2 600 - -
600 - 2 c.. .... j 400 -
, .),
* .../y
400 -
j 200 - i - 200 - ll 2
, , , , e' O 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 som mese sme (meme Figure lib. Compenson of an ESPROSE.m calculation of KRO1DS-28 with experimental data of pressures measured along the tube length.
( l 4-13
.__ _ .- _ ~ . . - .- _ - _ _ . . = - . . . .- . - - . . . -
t t k l 2t ; ' '- t es . 0 : Q q a:. C ls-3 t,' s
=6' i l $ j>~ t '
l I l -
, s
". '*, tl' i % Cj ,., &
l I
%% , y# #
e + g.
+ s
+
s- e.%w 'e < l Figure 12. Initial conditions for the ex-vessel,1-m deep pool, ESPROSE.a calculation. , l l
^
l l 25 , , 25 , , , l I to - l - a. 5cm l! - 20 - l-: . s5 cm l _ Y Y I E 15 - - 8 15 - - 10 - - 10 - . 0
. . b. , L
- - - ----J 0
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 i #e (""c) une (umsc) 25 , , , , , , 25 , l 20 l . 25 cm ij 20
!I - r-*5 = 1 -
i . I . l 8 15 - 8 15 - - 2 10 - to - 2 5 2 5 ( 0
. N. . 0 i
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 time (amec) time (meer) ; 75 , , , , , , 25 , , , , , 20 - l- r . 45 cm l - 20
,-l- 2 105 cm l l I
b . t . B 15 - f E 15 - 10 - 2 to - -
)
l ; 5 - 5 - o 0 O 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 time (mene) time (mmec) Figure 13. Calculated loading 5 on lateral pool boundary for a 1-m deep pool. ESPROSE.a with ff = 1 and fe, = 0.05. 1 4 - 14 l l
l l l l 1 l 1 PRESSURE AT TIME = 0.0015 SEC. PRESSURE AT TIME = 0.0030 SEC. l $~ ls 1 Is ls 24 s
- 2. .s t
0 0 4 !s - t !s M Rs %s i t g .
*yE '
& P 1 e * + u q e .o. u+
Sw #r 4
%w s, 4 PRESSURE AT TIME = 0.0045 SEC. PRESSURE AT TIME = 0.0060 SEC.
1 ks ks l ks is
- i. a s s,s 3 e
- 4. 't ' 4t-s
~
%s l 5s ,
4
- l s, >
+ i
* ,* *p 3
* + u+ ,
u+
% * +
i r '%r ,, 4
%w ,, 4 l
l J 4 Figure 14. Calculated transient pressure distribution of an ex-vessel explosion for a 1-m deep poc! using ESPROSE.a. 4-15 l l
l t 4 C k l c i' ! t h /
/
- u t. , I.-
e',, s .
- //
t 2O . 3,' l f ' ' s f
/' !
lti l -
~g, gp I
~
s: su->x;, + *
" ,9'* s e
s~
.p- + ,
'e
~s *
*p p s ,
q%s s + ,** e Figure 15. Initial conditions for the ex-vessel,3-m deep pool, ESPROSE.a calculation. 20 , , , , , 20 , , , , 16 - l- a = 5 cm l - 16 ' l- 2 = 185 cm l t k E 12 - - 8 12 - - l - g e - - b b 4 - - 4 . . 1 0 0 O 1 2 3 4 5 6 0 1 2 3 4 5 6 time (mec) timme (masc) 20 , , 20 , , ,
,, . l- . 5 cm i . ,, -l - -245cml I T g 12 - - 8 12 - -
g - - 8 - 4 N 2 4 . . o 0 O 1 2 3 4 5 0 0 1 2 3 4 5 6 time (muse) ttuse (muse) 20 , , , 20 , , , , 1.~Ll- r = 125 cm l -
- 1. LI-2 305 cm I -
a a E 12 - - 6 12 - - s - - s - - 4 - - 4 - 0 1 2 3 4 5 8 0 1 2 3 4 5 6 some (mune) tiens (manc) l l Figure 16. Calculated loadings on lateral pool boundary for a 3-m deep pool. ESPROSE.a with ff = 1 and f, = 0.05. ; 4-16
i l , i PRESSURE AT TIME = 0.0014-SEC. PRESSURE AT TIME = 0.0030 SEC. ! Is- Is l is is I. t. ~ I. .s t 0 0 , l t !s A !s l 4 ts sd 9 -,- . Is si I: :: ;! :
! l i'
, 2 :zs:1 ---
jp.g- : : - - i.:A ; ,> i lllli.:. :
- A
' ==: ' , ,
., e-
.;r .
j,. l, ,,,, l-.
!v s
,,- , ,, ::A: - - : -
*'g +'
v
,:.:' j: : ' ' ,+ '*
s*
/ #*',% + .!!!!!!:: ' -
, . '* /
, g ;qi,;, . .
' ' + , s+
l PRESSURE AT TIME = 0.0044 SEC. PRESSURE AT TIME = 0.0060 SEC. i ks ks is M( - i-l 1 g' b 1 ? g' y , j- fl j s - s l 4! 4 !s j
.y lllII! .!
)
ts ' Is
^
.::!!!il I ;: ;
[ _-:--- - l , ' >~ 5j ' .
. . . - :.:. im il
-r A s
,'> l
- . . 6
; $i:. ::i , , ,,
.t: , ,, , :. *
*'g + ii; :;;. . , , , *'g + j '* /
v g m ;: . .
- . . + , s+ w g #
s+
~4 .
i 2 Figure 17. Calculated transent pressure distribution of an ex-vessel explosion for a 3-m deep pool using ESPROSE.a. 4-17 i l . ,
APPENDIX: IORMULATION OF ESPROSE.m FIELD Fuel: MODEL 6 g(p juf) + y . (p'f uf uf) = -8f vp + F.f(u. - uf) I. CONSERVATION EQUATIONS + F,f(u, - uf) + p'f g - Fruf (A.9) There are four phases: namely, " micro-interaction" fluid, coolant liquid, fue! (melt) drops, and fuel debris. They e Energy Equations. will be referred to as m-fluid, liquid, fuel and debris respec-m-Fluid'- tively. Each phase is represented by one flow field with its own local concentration and temperamre. The debris is 0 6t (p'.I.,, + p',I assumed to be part of the m-fluid in thermal and hydrody- 3 g>(T.)) namic equilibrium. Thus we have four continuity equations, + y . [(p'.I. + p' gI 3 g>(T.))u.] = three momentum equations, and three energy equations. In g the usual manner, the fields are allowed to exchange energy, -p momentum and mass with each other. With the definition
-g(8.) + y . (8.u.)
of the macroscopic density pl of phase i, + Eh, + Jh.
- R.,(T. - T,) + 4f. (A.10) pj=8pg for i = m, t, f,and db, Liquid:
6 (A.1) O and the compatibility condition, g(plls) + y -(prisu,) =
- 8. + 8, + ef + 8 46 = 1 (A.2) -p (8,) + y . (8,us) these equations can be written rather directly (Ishii,1975). - Eh, - Jh, e Continuity Equations. + Re,(T, - T,) + 4f, (A.11) m-Fluid: Fuel:
g,,* + y - (p' u.) = E + J (A.3) a Of g(p'ff I ) + y . (p' ffI uf) = -4f. - 4f, (A.12) Liquid: ag e In the above equation, H(J) is the Heaviside step j + v . (pjus) = -E - J (A.4) function that becomes unity for positive values of the ar-gument and zero otherwise. When T. < T., the m-fluid Fuel. is liquid and J is set to be zero and T, is an " equivalent" interface temperature given by ap} gg
+ y -(p'f ut) - Fr (A.5)
T = R.,T. + R,,T, R., + R,, Debris-
#d' + y . (p'gium ) = Fr When T. > T., J is an evaporation rate given by Of (A.6) 1 o Momentum Equations. J = h. - h,[R. (T. - T,) + R,,(T, - T,)]
m-Fluid: It should be pointed out that diffusive transport withiu g each field (shear stresses and conduction) has been ignored
-((p'.
&t
+ p's )u.) + v . ((p'. + p,'3)u.u.) = in the above formulation--they are expected not to be im-portant.
- (8. + 846)vp - F.,(n. - us)
- F.f(u. - uf) + Eu, + Fruf II: TIIE CONSTITUTIVE LAWS
+ J(H[J]u, - H[-J]u. + (p',,, + p',3)g (A.7) The interfacial exchanges of momentum and heat are clearly regime dependent, and uncertainties remain even
. for simple two-phase flows. Only experiments specifically Liquid.,
oriented to this problem and detailed local measurements g will provide the basis for the appmpriate assessment, parde-
-(pju,) + v . (p,usur) = ularly if one of the phases is the " micro-interaction" fluid.
at For now, our approach is to treat the m-fluid as a " pseudo" 8,vp + F.,(u,,, - ne ) - F,f(ut - uf) gas and utilize a similar set of constitutive laws as in a
- Eu, - J(H[J]u,- H[-J]u.) + pig (A.8) previous work (Medhekar et al.,1989).
4-18
For the mass transfer from the fuel, the fragmentation h specific enthalpy rate, F,, is calculated based the instantaneous Bond number h', heat transfer coefficient formulation as described in a previous work (Yuen et al., I specific intemal energy 1992). De relevant equations are J evaporation rate t length scale 7,, , g dAf (A.13) th, entrainment rate of microintraction fluid by a fuel wif di drop n number of fuel particles (or liquid droplets) per unit where volume dM dM dM P P'***" 7 = o.(7)" + (1 - a.)(7), (A.14) 4f, heat transfer rate between fuel and vapor Qfs heat transfer rate between fuel and liquid with Rr, heat transfer coefficient between liquid and the liquid /m-fluid interface dM 4 / R., heat transfer coefficient between the m-fluid and ( 7 ),= wt} l6t[,, G - G l(###'} ifs # * " " ' ' the liquid /m-fluid interface (A.15) T temperature i time Equation (A.14)is a generalization of the single phase t; fragmentation time fragmentation rate utilized in the previous work (Yuen et u velocity al.,1992) with a. being the " void fraction" of the m-fluid defined by Greek i a void fraction g" a. " void fraction" of microinteraction fluid
- a. = +" (A.16) e volume fraction p microscopic density The " fragmentation time" and the instantaneous and Bond p' macroscopic density numbers for each phase are defined by a surface tension or Stefan-Boltzman constant r, entramment time constant used by ESPROSE.m Subscripts ti,6 = 13.8 Bo,'/' and Boi= ' l ug - uf l8 g (A.17) , vapor (steam) used in ESPROSE.a For the mass transfer between the m-fluid and liquid, s coolant (m-external fluid) i the entramment rate, E, is assumed to be directional pro- = microinteraction fluid !
portional to the fragmentation rate in the preliminary cal. , saturation properties ' culations presented in this work. Specifically, ACKNOWLEDGMENT E = f,F, #!- (A.18) The ESPROSE.a code utilized in the calculations pre-pf sented in this paper is an advanced, developmental version of the ESPROSE code developed for the U.S. Nuclear Reg-with f, being an empirical entrainment factor which can be ulatory Commission under contract number 04-89-082. varied parametrically. REFERENCES NOMENCLATURE 1. Abolfadl, M.A. and T.G. neofanous (1987)"An As-Bo Bond number sessment of Steam-Explosion-Induced Containment Fail-Cg drag coefficient ure. Part II: Premixing Limits," Nuclear Science and fragmentation rate for a fuel drop Engineering 97,282. entrainrnent rate 2. Amarasooriya, W.H. and T.G. 'Iheofanous (1991)" Pre-Ef emissivity of fuel particles mixing of Steam Explosions: A nree-Fluid Model," Et absorptivity of hqmd droplets Nuclear Engineering & Design 126,23-39. F factor for mterfacial momentum exchange F, fragmentation rate 3. Angelini, S., E. Takara, W.W. Yuen and T.G. Theo-
- f. entrainment factor used trf E SPROSE.m fanous (1992) " Multiphase 'IYansients in the Premix-ff enhancement factor of fragmentation rate ing of Steam Explosions," Proceedmgs NURETH-5, f, direct vaporization factor used in ESPROSE.a Salt Lake City, UT, September 21-24,1992, Vol. II, g gravity 471-478.
4 -19
i
- 4. Angelini, S., W.W. Yuen and T.G. Theofanous (1993) 15. Medhekar, S., M. Abolfadl and T.G. %eofanous (1991)
" Premixing-Related Behavior of Steam Explosions," " Triggering and Propagation of Steam Explosions,"
CSNI Specialists Meeting on Fuel-Coolant Interactions, Nuclear Engmeeting and Design 126,41-46. Santa Barbara, CA, January 5-8.
- 16. Medhekar, S., W.H. Amarasooriya and T.G.Theofanous
- 5. Board, SJ. and R.W. Hall (1974)" Propagation of her-(1989)" Integrated Analysis of Steam Explosions," Pro-mal Expansions Part 2: A heorencal Model," Berke-ley Nuclear Labs, RD/B/N 3249. ceedings Founh International Topical Meeting on Nu-clear Reactor Thermal-Hydraulics, Karlsruhe, FRG, Oct.
- 6. Burger, M. et al. (1984)" Description of Vapor Explo- 10-13,1989, Vol.1,319-326.
sion by hermal Detonation and Hydrodynamic Frag-mentation Modeling," Int. Meet. of Rermal Nucl. Re. 17. Patel, P.D. and T.G. neofanous (1981)"Hydrodynam-actor Safety, Karsruhe, Sept.1984. ics Fragmentation of Drops," J. Fluid Mech.103,
- 7. Burger, M., M. Buck, K. Muller and A. Schatz (1993)
" Stepwise Verification of hermal Detonation Mod- 18. Sharon, A. and S.G. Bankoff (1981) "On the Exis-els: Examination by Means of the KRO'IOS Experi- tence of Steady Supercriticalplane Thermal Detona-ments," CSNI Specialists Meeting on Fuel-Coolant in- tions," Int. J. Heat Mass Transfer,24.
teractions, Santa Barbara, CA, January 5-8.
- 19. Theofanous, T.G., B. Najafi and E. Rumble (1987)"An
- 8. Chu,C.C. and M.L Corradini(1989)"One-Dimensional Assessment of Steam-Explosion-Induced Containment Transient Fluid Model for Fuel / Coolant Interaction Anal.
ysis," Nuclear Science and Engineering 101,48-71, Failure. Part I: Probabilistic Aspects," Nuclear Sci-ence and Engineering, 97, 259-281, (Also, including
- 9. Denham, M.K., A.P. Tyler and D.F. Fletcher (1992) peer review comments, in NUREG/CR-5030,1989.)
" Experiments on the Mixing of Molten Uranium Diox-ide with Water and Initial Comparisons with CHYMES 20. heofanous, T.G. and W.W. Yuen (1993)"ne Proba-Code Calculations," ANS Proceedings NURETH-5, bility of Alpha-Mode Containment Failure Updated," j Salt Lake City, UT, September 21-24,1992, Vol. VI, CSNI Specialists Meeting on Fuel-Coolant Interactions, 1667-1675. Santa Barbara, CA, January 5-8.
- 10. Fletcher, D.F. (1993) " Propagation Investigations Us- 21. Turland, B., D.F. Fletcher, K.I. Hodges and GJ. Attwood ing the CULDESAC Model," CSNI Specialists Meet- (1993) "Quantificaton of the Probability of Contain- I ing on Fuel-Coolant Interactions, Santa Barbara, CA, ment Failure Caused by an In-Vessel Steam Explosion January 5-8. for the Sizewell B PWR." CSNI Specialists Meeting
- 11. Fletcher, D.F. and A. Ryagaraja (1989) "A Mathe. on Fuel-Coolant Interactions, Santa Barbara, CA, Jan- I matical Model of Melt /Waer Detonations" Applied uary 5-8. I Mathematical Modelling 11.', 333-350.
- 22. Yuen, W.W., X. Chen and T.G. Reofanous (1992)"On
- 12. Hohmann, H., D. Magallon,11 Schins and A. Yerkess the Fundamental Microinteractions nat Suppon the (1993)"FCI Experiments in the /Juminumoxide/ Water Propagation of Steam Explosions," ANS Proceedings l System," CSNI Specialists Meeting c:: Fuel-Coolant NURETH-5, Salt Lake City, UT, September 21-24, Interactions, Santa Barbara, CA, January 5-8. 1992, Vol. II,627-636.
- 13. Ishii, M. (1975) Thermo-Fluid Dynamic Theory of
- 23. von Neumann, J. and R.D. Richtmyer (1950)"A Method Two-Phase Flow, Eyrolles, France.
for the Numerical Calculations of Hydrodynamical
- 14. Kim, H.J. and M.L. Corradini (1988) *Modelling of Shocks," J. Applied Physics 21,232-237.
Small Scale Single Droplet Fuel Coolant Interactions," Nuclear S:ience and Engineering 98,16-29. 4-20
l l l l l l l l APPENDIX 5 THE PROBABILITY OF l ALPHA-MODE CONTAINMENT FAILURE UPDATED Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions l Santa Barbara, CA, January 5-8,1993
- NUREG/CP-0127, March 1994,330-342 l
l l 1 5-1
l l l ! l THE PROBABILITY OF ALPHA-MODE CONTAINMENT FAILURE UPDATED i T.G. 'Iheofanous and W.W. Yuen Center for Risk Studies and Safety t University of California, Santa Barbara, CA 93106 l Tel. (805) 893-4900 - Fax (805) 893-4927 ABSTRACT ! agreeable) closure rather than as a result of explicitly spec-l Since the on.g inal quantifican.on of the likelihood of e fail- ified and generally accepted active concems on it. This is j ure in NUREG/CR-5030, major expenmental and anaiyti- quite evident in the first systematic evaluation ofit by an ad i cal developments have taken place. By taking advantage or hoc panel of experts, the Steam Explosions Review Group l these developments, we beheve it is possible to reduce the (SERC,1735), some eight years ago, as well as in the latest substantial conservatisms in the on,gm, al quantificanon, and quantiScation ofit as a pan of the NUREG-II5O study two ta thus conclude that even vessel failure by steam explo- years ago. Specifically, in SERG, we find panel member l si:ns may be regarded as physically unreasonable. We have assessments that, with only a few exceptions, agree that o
- illustrated how tius can be done within the onginal frame- failure is of adequately low likelihood not to pose serious work, as well as m a complementary framework that takes containment integrity concems, while the NUREG-1150 ex-
- advantage of current integral analysis capabilities. On this pen panel on this issue agreed that these SERG assessments
[ basis, the a-failure issue is now npe for final resolution; were appropriate and made use of an aggregate (based on what is needed is a complete set of calculations supporting arithmetic averaging) of them in the quantification. The a revised quantification of CRI and CR3 and a final review NUREG-1150 results indicate that the probability of a fail-step in the ROAAM process. ure (conditional on core melt) is under 1%, with an upper bound (95" percentile) estimate of "a few" percent. The ! INTRODUCTION reasons for further attention on this issue can be listed as t follows-Since hs definition and initial quantification in WASH. 4
- 1. Quality and Robustness of Assessments. Indi- i 1400, the a-mode containment failure has maintained a vidual assessments in SERG were based on widely variable unique place in risk analyses of nuclear reactors and related reasoning and to a great extent on judgment.
safety research. It involves an energetic fuel-coolant inter-action that takes place in the lower plenum of a pressurized 2. Treatment of Outliers. Individual SERG assess-water reactor (PWR): the generation of an internal missile ments of probability varied over many orders of magnitude, l that loads the upper head of the reactor vessel to failure, the including some extremely small as well as some ratherlarge t generation of an external missile, and containment bound- (the few exceptions noted above) values. I ary (upper dome) impact. The energetic interaction presup. 3. Interpretation of Results. The SERG-aggregate poses a massive pour of mohen corium from a crucible-held mean value of 0.8% and the above-quoted NUREG-ll50 geometry into the lower plenum; the energetics of the inter- result (under 1%) may mean different thmgs to different nal missile depend on a number of dissipative phenomena People, and not necessanly always a negligible concern. associated with the momentum and structural interactions It is wonh noting that these specific, quantitative, concerns leading up to and including upper head loading and failure; were framed in the context of the scenario described above; and the external missile (the detached vessel head or ponion l cf it) must destroy or " sweep-away" the missile shield be- it can be espected that their resolution will provide the fore it can begin to rise toward impacting the containment. impetus and kip address explicitly other less tangible as-pects of this use Mcluding multiple explosions and other The problem is significant because it gives rise to the pos-sibility of "early" contamment failure, and it has become (than pouring) m i , of contact, especially as they arise in l consideration of acc.acnt management actions (Theofare_4, an " issue" because the complex phenomenology has been 1991). addressed variably and on occasion with conflicting results. An initial step toward resolving the concems listed In interesting contrast to most other major containment above was made five years ago (Theofanous et al.,1987, integrity " issues" (in severe accidents), the a failure has to be referred to as NUREG/CR-5030) under an approach ev 1ved as a rather benign one, that is, more as a matter of formalized later as the Risk-Oriented Accident Analysis cmission rather than one of commission. In other words, Methodology (ROAAM) - Theofanous and Yan (1991), more as a result of failure to deliver a definitive (generally Meanwhile, the methodology has been employed to the 5-3
l 1 into the lower plenum) drops well below that pres- Safety of Nuclear Instal!ations: Future Direction, sure range. In any case, ambient pressures of a few Proc of Int. Workshop on the Safety of Nuclear in-bars will have to be considered and this will require stallations of the Next Generation and Beyond, Chi-experimental data with respect to premixing and cago, USA, August 28-31,1989, International Atomic energy conversion obtained under such conditions. Energy Agency Report IAEA-TECDOC-550, pp. 361-371 ACKNOWLEDGEMENT l Jacobs, H.,1989 Steam explosions during light water i The auther is grateful to Dr. Lisa V5th for thoroughly reactor meltdown accidents, Proc. of 3rd int. Semi-reviewing this manuscript. nar on Containment of Nuclear Reactors, Los An-l geles, CA, August 10 - 11,1989, pp. 302-320 REFERENCES Jacobs, H.,1993. Analysis of Large-Scale Melt-Water Allison, C. M., C. H. Heath, L. J. Siefken, and J. K. Mixing Events, Proc. of CSNI Spec. Mtg. on Fuel Hohorst,1991, SCDAP/RELAP5/ MOD 3 Code Devel- Coolant Interactions, Santa Barbara, USA, January opment and Assessment, Proc.19th Water Reactor 5-8,1993, to be published Safety Information Meeting. Bethesda, USA, October 28-30, 1991, US Nuclear Regluratory Commission Krieg, R. and B. G611er,1992, private communication Report NUREG/CP-0119, pp.199-210 Krieg, R., H. Alsmeyer, G. Jacobs, H. Jacobs, J. Eibl, Bird, M. J.,1984, An experimental study of scaling F. H. Schl0ter, T. Klatte,1992, Extreme Loadings of in core melt / water interactions, 22nd Natl. Heat inner Structures of Next Generation PWR Contain-Transfer Conf., Niagara Falls, USA, August 1984 ments, Proc. of Fifth Workshop on Containment In-tegrity, Washington, USA, May 12-14,1992, US Nu-Bohl, W. R.,1990, An investigation of Steam-Explo- clear Regluratory Commission Report tion Loadings with SIMMER II, Los Alamos National NUREG/CP-0120 (SAND 92-0173), pp. 323-335 Laboratory Report LA-10639-MS, March 1990 Meyer, L. and K. Rehme,1993, private communi-Broughton, J. M., Pui Kuan, D. A. Petti, and E. L. cation Tolman,1989, A Scenario of the Three Mile Island Unit 2 Accident, Nuclear Technology 87 (1989) 34-53 Peppler, W., F. Huber, and H. Will,1993, private communication Corradini, M. L., B. J. Kim, and M. D. Oh,1988, Va-por Explosions in Light Water Reactors: A Review Sengpiel, W.,1993, private communication of Theory and Modelling, Progress in Nuclear Ener-gy, Vol. 22, pp.1-117 Steam Explosion Review Group (SERG),1985, A Re-view of the Current Understanding of the Potential Corradini, M. L.,1991, Vapor Explosions: A Review for Containment Failure from In-Vessel Steam Ex-of Experiments for Accident Analysis, Nuclear Safety plosions, U.S. Nuclear Regulatory Commission Re-32 (1991) 337-362 port, NUREG-1116, June 1985 Courtaud, M., M. R6ocreux, P. Hofmann, and H. Ja- Theofanous, T. G. et al.,1987: cobs,1993, in-Vessel Core-Melt Progression Phe- T. G. Theofanous, B. Najafi, and E. Rumble, An As-nomena, Proc. of ENS Topel. Mtg. Towards the Next sessment of Steam-Explosion-induced Containment Generation of Light Water Reactors, The Hague, Failure. Part 1: Probabilistic Aspects, Nucl. Sci. Eng. Netherlands, April 25-28,1993, to be published 97 (1987) 259-281 1 M. A. Abolfadi and T. G. Theofanous, ! Edwards, A. J., J. B. Knowles, and R. B. Tattersall, An Assessment of Steam-Explosion-Induced Con- ' 1988, Molten Fuel Studies at Winfrith, U K Atomic tainment Failure. ) l Energy Authority Report AEEW-R 2301, January 1988 Par 1 11: Premixing Limits, Nucl. Sci. Eng. 97 (1987) 282-295; Ehrhardt, J. and 1. Hasemann,1991, private commu- W. H. Amarasooriya and T. G. Theofanous, nication - An Assessment of Steam-Explosion-induced Con-tainment Failure. Eibt, J., F. H. Schl0ter, T. Klatte, W. Breitung, F. Er- Part Ill: Expansion and Energy Partition, Nucl. Sci. bacher, B. G611er, R. Krieg, W. Scholtyssek, and J. Eng. 97 (1987) 296-315; Wilhelm,1992, An improved Design Concept for G. E. Lucas, W. H. Amarasooriya, and T. G. Theofa-Next Generation PWR Containments, Proc. of Fifth nous, An Assessment of Steam-Explosion-Induced Workshop on Containment Integrity, Washington, Containment Failure. Part IV: Impact Mechanics, USA, May 12-14, 1992, US Nuclear Regluratory Dissipation, and Vessel Head Failure, Nuct. Sci. Eng. Commission Report NUREG/CP-0120 97 (1987) 316-326. l (SAND 92-0173), pp. 337-363 l Turland, B. D., D. F. Fletcher, K. I. Hodges, and G. Gesellschaft f0r Reaktorsicherheit (GRS), 1990, J. Attwood,1993, Quantification of the Probability of Deutsche. Risikostudie Kernkraftwerke, Phase B, Containment Failure Caused by an In-Vessel Steam Verlag TUV Rheinland, K6ln Explosion for the Sizewell B PWR, Proc. of CSNI Spec Mtg. on Fuel Coolant interactions, Santa Bar-Hennies, H. H., G. Kessler, and J. Eibt,1989, im- bara, USA, January 5-8,1993, to be publiahed proved Containment Concept for Future PWRs, in: 5--4
l resolution of two other major issues---Mark-I Liner Anack Predactions, respectively. At a much larger scale, the FARO (heofanous et al.,1991) and Direct Containment Heating Quenching Test series is now also beginning to produce the (Pilch et al.,1992)--while new data and calculations antic-first results. We will argue that these developments provide ipated by, and relevant to, the original quantification have the firm basis needed to drastically reduce the conservatism recently become available. Guided by the methodological built in the quantiScation of Figure 4. insights from these funher applications of ROAAM, our purpose here is to re-examme the NUREG/CR-5030 quan- Energy partition, during the early yield phase of the tification, in light of these new data and calculations, with CIPl osion, in NUREG/CR-5030, was based on what was an eye toward an ultimate resolution. though} to be a conservative treatment of explosion ener-getics in combination with the structural response of the OVERVIEW OF THE ORIGINAL QUANTIFICATION lower head. The simple idea was that an explosion ener-l AND THE NEW DEVEIDPMENTS getic enough to produce an upper-head-threatening missile The probabilistic framework employed in NUREG/CR- should be able to fail the lower head that contained it in 5030 is shown (in current notation and with the practically the first place; such failure provides downward relief and I unimportant limit of molten core available omitted)in Fig- thus significant mitigation of energy in the upward-dtrected ure 1, and it can be understood in terms of the explosion missile. The quantification is reproduced in Figure 5. The scenario described in the early pan of the introduction sec- " break"in slug energy due to lower head failure is seen to tion, with the help of Figures 2 and 3. Of critical impor. occur at ~1 GJ of total mechanical energy release, and this tance to the quanti 6 cation, is the " upper-central" ponion of is consistent with other independent studies. Still, the mech-this framework including, in panicular, the quantification anism depends on the time scale of the energy release, and of premixtures (CRI) and of the energy panition associated at can, therefore, be (it has been) questioned in a quanti 5-with lower head failure (CR3). Indeed, these also happened cation based on equilibrium thermodynamics that bypasses to be the focus of the criticism received in the review pro _ the dynamse aspects of the interaction. It is now possible cess, as documented in NUREG/CR 5030, and accordingly, to account for these dynamic aspects and thus address this these will be the focus of the present reexamination here. In question directly. Several developments have contributed passing, we note that the overall framework and,in genera', !o this new capability, including: experience with several the approach, has been wc!! received; moreover, a similar independent one-dimensional detonation codes (Medhekar approach has been taken in addressing this issue within the et at,1991; Fletcher and Thyagaraja,1991; Burger et al., licensing proceedings of the Sizewell plant in the UK. The 1993), smgle-drop fragmentation data under conditions rel-details of this study are to be snade openly available soon evant to an established detonation wave (Yuen et al.,1992), (Turland et al.,1993), but it is our understanding that the re- the first quantified expenmental demonstration of a strong sults indicate an adequately low likelihood (of containment detonation with At 2O3 melts (Hohmann et al.,1993) as failure) for licensing purposes. This can be taken as gen- Compared to mild ones obtained with tin melts in previous erally reinforcing of the NUREG/CR-5030 conclusion that works, and an experimentally-tested analysis tool, the ES-such failures are " physically unreasonable," but the extent PROSE code, that when interfaced with PM-ALPHA cra of actual synergism obtained can only be understood after f Ilow the triggering and escalation of an explosion in two a detailed comparative study of the two quantifications. dimensions from realistic pmmixtures and in relevant re-actor geometries (Yuen and Theofanous,1993). We will Premixing, in NUREG/CR-5030, was quantified strictly on the basis of computations. In panicular, a two-fluid argue that these developments provide a firm basis for the model was used to compute the transient penetration of consideration of lower head integrity, and the related energy fuel panicles in a locally homogeneous steam-water mix- partition question, under physically meaningful explosions in the lower plenum. ture, allowing for two-dimensional motions and to thus demonstrate the water-depletion phenomenon envisioned by With this integral capability at hand, from a method-Henry and Fauske (1981). Assuming that fuel surrounded ological standpoint, the question arises as to whether the by highly voided coolant (say,50 to 70%) cannot effectively lower-central portion of the framework affected should be participate in an explosion, limits to the quantities of fuel condensed into one single operation, as illustrated in Fig-premixed (and thus able to explode) could be obtained for ure 6. This structure is attractive because it captures in a arbitrarily Ltrge pours. The resulting quantification, allow- consistent manner the " size" of the explosion in terms of ing for highly generous margins above the quantities de- premixture chamteristics and respective level of energet-duced from such computations to judgementally cover un- ics. In the aginal quantification, this could be done only in cenainties, is shown in Figure 4. Imponant subsequent de. a prelimincy way, ny making the conversion ratio a func-velopments include: a new and more general three-fluid for- tion of tho e,v.q, stored in the premixture (CR2). Also, l mulation and computer code, the PM-ALPHA, that confirms this app aach centmuet to capture the main variable char-l the conservative nature of the original quantification (Ama- acterizing the 7nas',iv,: ness" of the melt pour. In panicular, rasooriya and Theofanous,1991); a comparative study of we note that this is ade4 vte tu rviect " side" versus " bot- ! reactor-scale premixing calculations between PM-ALPHA tom" pours as well as otter variaMes in accident character-i and the independently developed CHYMES code (Fletcher, istics such as system presse: y lower plenum subco'o ling 1992); and the MAGICO (Angelini et al,1992) and MIXA by defining an appropriate set of splinter scenarios (Theo-(Denham et al., It r92) experiments designed specifically for fanous and Yan,1991). An important disadvantage of such comparisons with the PM-ALPHA and CHYMES codes a condensation, on the other hand, is tnat it could detract 5-5 l l
szeof Pour Mene of Men m Premixture Area w Pour Aree pr CRr ' h
\J Mene of Men in Premanure AMEE 4 uman Thermal Energy of Met in F=M hd Enwgy in Fraana'an l'
Upward Slug Energy Mechanical Energy i Mechanical Energy Release CM3 I i Not Enesgy in Vesosi Head Upwerd Slug w l Enwgy Slug Enessy i g I'"' I Vessel Head Missile Enwgy W Not in Vessel < Not Enwgy in vessel Head I cms l Masile Enugy Aner shield impen veneet Head n i Missile Enugy Vessel Head Mmeiis Enmay l
#7 l cns Containment Failure Frequency W Mmeios Enavy Aner Shield impact Missile Energy CRT
%)
Contaanment Fadure Frequency Figure 1. Probabilistic framework for the assessment of a failure as pro-posed in NUREG/CR-5030. pdf and CR refer to " probability density function" and " causal relation" in the ROAAM terminology. 5-6 l I
nessu 1
.., g.?.f%N=k. .
O' C..g.'cbn..'.,',', n-57-
/r - - -
r w n sma m -T 80LT FAIL 1JRE as l ./ l.: ' l N I o 6l l o
-maumia 4 . .= 4 UrPER INTERNAL , .
STRUCTURES (UIS) . h ** f *,--conc.in 8 I 9 , l
-- a 1 wa '
t
.. . "J."
. sm.sv coac.ar
, -[.,1.
(7 % ' "*
" "kE--!e
, , , , , , ,- g,.;..
m . i - t2 ft ., / ' L.
. ~. .- e ,
- :...-,~.- umeR core et4Te i. > .
o
* * *s cactmannewnnL j ( *
.ge i f rAwne ,
u-------' "f;','
.p A v f.
- p. ;cgw. .,e -<
; com . ../ ., %,,.,
9 Figure 2. Key mechanisms and termmology for a steam Figure 3. Geometry relevant to the ex-vessel portion of a explosion event (in-vessel portion). steam explosion event in a large dry contamment. 3.0 . , , , 20 ' ' ' E - { 2.5 2 o
-y 15 - -
2.0 - - E W Q- ~ ~ 10 0
- s - -
2 en 1.0 - p - o 5 - - E
- a. 0.5 - -
2 0 ' ' ' O.0
. . .0 7.5 10.0 12.5 0 2 4 6 Core Support Failure Area (m 2) Mechanical Energy Release (GJ)
Figure 4. CRI according to NUREG/CR-5030. A flat dis- Figure 5. CR3 according to NUREG/CR-5030. A normal tribution was assumed between the 5 and 95% limit lines distribution is assumed between the 5 and 95% limit lines shown. The point refers to a calculation presented later on shown. in this paper. 5-7
just been published (Fletcher,1992). Melt volume fraction distributions were very consistent, and even premixed-mass transients up to the melt contact time with the lower head Mass of Melt in Premixture were found to be in excellent agreement; however, dis-Size of Pour Area vs turbingly large discrepancies on the spatial evolution of the Pour Area steam volume fractions were also noted. He author at-pd/2 CR1 tributed these discrepancies to differences in the drag laws employed in these two codes but offered no specific rec-
@ ommendations for resolution. To us, these discrepancies became a significant cause of concem, especially in light of our opinion of the importance of void fractions, as de-Upward Slug Energy tailed above, and the prior use of PM-ALPHA to quantify pdf5 premixing for the actual assessment of a failure.
In fact, the cause could be traced to an organic differ-ence between the two codes: CHYhES cannot allow for l the presence of subcooling, while PM-ALPHA does. More e speci6cally, in CHYMES, the local rate of boiling is taken as a local latent heat requirement; i.e., in CHYMES's nota-tion (Fletcher and Thyagaraja,1991), Figure 6. A condensed version of the upper-central portion cf the probabilistic framework in NUREG/CR-5030, mak-m, _ o.%
._ f,) g ing use of currently available integral analysis capability.
where the o's are the melt and water volume fractions, h from one of the key aims of ROAAM; that is, allowing for is the heat transfer coefficient, hf , is the latent heat of va-as many independent quantifications of each component of Ponzation, and L. is a melt length scale used to estimate the framework as possible. For example, an independent the heat transfer area. By contrast, m PM-ALPHA, boil-contribution to the quantification of premixing could not be ing occurs at the rates necessary to bring the water locally made to the condensed framework. Conversely, the break- to santration In praedcal tenns, this means dat de water down of the resuhs from integral analyses, for the purposes cannot sustain any signincant amount of superheat, which of the original framework, should always be possible while is, f course, the physically meaningful behavior. More-still retaining the essential features of consistency (or de-ver, CHYMES cannot anow for condensation, while m PM-ALPHA, steam is allowed to condense, as it should, pendencies). For these reasons, we propose the condensed framework as a complement to rather than as a substitute if it happened to flow through a subcooled water region. for the original one. complete constitutive package can be found m An-gelim. et al.,1993.] The importance of subcooling is not limited to scenarios with an initially " cold" pool of water; QUANTIFICATION OF PREMIXING gravitational head m deep pools (as the one in the lower De fundamental parameter in quantifying a premix- head) implies a non-negligible subcooling even in "satu-ture is the void fraction. From a bounding equilibrium ther- rated" cases, but more importantly, even modest increases modynamies standpoint (i.e., Hicks-Menzies), the implied in pressure due to the limited venting area from the lower working-fluid depletion drastically reduces the thermal-to- plenum (the area leading into the downcomer) can produce, mechanical energy conversion (Amarasooriya and neo- through the induced subcooling, a most significant feed-fanous,1987), while from an explosion dynamics stand- back effect on boiling. In the absence of this feedback, point, it interferes with both the triggering and the escala- as in CHYMES, the calculation in a sense " runs away," tion processes. This interference is further augmented by since any large quantities of steam are taken to escape, not two-dimensionality (Medhekar et al.,1989; Yuen and Theo- accounting for the higher and higher pressure increases re-fanous,1993), and vice versa, two-dimensionality is essen- quired to actually deliver this escape. To demonstrate this tial to the prediction of void fraction distributions (Angelini as the root-cause of the discrepancy under investigation, we et al.,1993). Accordingly, this discussion and a related ex- ran PM-ALPHA with only the one change needed to make perimental program are focused on void fractions? The it mimic the CHYhES phase-change formulation; namely, analysis tool is PM-ALPHA, and its performance against we used Eq. (1) for boiling and set the condensation rate these experunents has been presented in a companion paper identically to zero. He current comparison with CHYMES (Angelini et al.,1993). The only other comparable analysis is shown, side-by-side with the comparison produced by tool available at this time is CHYMES, and the first com- Fletcher (1992), in Figure 7. Note the remarkable agree-parisons of its predictions, with those made previously by ment even at the " microscopic" level,i.e., the shape of the PM-ALPHA for reactor-scale premixing calculations, have 0.7 contours. The pressure field responsible for these impor-tant differences is shown in Figure 8. In a vice-versa com-
- Note: " void fraction" refers the " steam content" to the parison, we ran PM-ALPHA with CHYMES's drag laws; as
" coolant volume," while " steam volume fraction" refers the shown in Figure 9, the differences are rather minor Clearly, " steam content" to the total (three-phase) mixture volume. CHYMES's "run-away" boiling rates pushed the calculation 5-8
>U 3
m ;
/
m
~Y y'Ni l
' \/ Figure 8. The calculated pressure field at 05 s into the premuung transient.
I into a regime that accentuated these drag-related differences l in Fletcher's comparisons. Further insights into "what is important" were obtained !
, l from a series of related calculations made within the same
, ,' ;, context. In particular, we investigated fuel emissivity, gr l gravitational'y-induced subcooling, and condensation. The results are summanzed in Table 1 and the figures indicated s l on this table. We conclude that only the treatment of sub- l' c ling is me essendal diffmence regarding me praedcal CHYMES aspects of application to reactor conditions, while in every other aspect, CHYMES provides indirect support to PM-ALPHA for both the numerics as well as the formulation of premixing of steam explosions.
With the numerical and physical aspects of the three-fluid formulation in PM ALPHA well scrutinized, we are prepared to take the next major step in the quantification of premixing. In this, we persist in the fixed-particle size treatment; we expect that the real behavior can be cap-tured/ bounded by appropriate parametric variations of par-ticle sizes, and this is all that is possible until a reasonably defensible approach to accounting for melt breakup behav. ior becomes available. For the particular calculation re-ported here, we chose the case considered above (fuel pour diameter 1.60 m, inlet velocity 1 m/s, inlet void meh frac-tion 0.5, melt temperature 2500 *C, and pressure 0.1 MPa), except for modifying the shape of the liquid pool boundary into the hemispherical shape of the lower head (same max-imum depth). To better resolve the curved portion of the boundary, the grid size was reduced by a factor of 3 (a 30 by 27 mesh). Otherwise, aspects of accuracy and conver-gence (time step, spatial discretization, convergence criteria Figure 7. A side-by-side comparison of calculated steam in the numericaliteration) are well at hand and need not be volume fraction distributions at 0.5 s, for the premixing elaborated here. A sample of the nmin results, including a problem of Amarasooriya and Theofanous (1991), predicted couple of snapshots (at times of mid- and full-penetration by PM-ALPHA (a), CHYMES (b), and PM-ALPHA mod- of the water pool by the melt front) of melt and steam vol-ified to mimic CHYMES' boiling model (c). ume fraction distributions and the premixed-mass transient, 5-9
. - . . ~ . . _ . . . - _ , . _ . - . _ . . . - ~ - ~ - .- . . . . . ~ . . . . . - - . . . -
l l i I 1 i 3 , i l 2 r-af ;
-- ..m- e l
I i r Figure 9. The effect of drag laws in the calculation of premixing. (a) PM-ALPHA, (b) PM-ALPHA with CHYMES' drag laws. ! { Table i Sensitivity to Various Treatments in the CHYMES and PM-ALPHA Formulations, - Deduced by Making the Change indcated to the PM-ALPHA Code f i PARAMETER PM-ALPHA CHYMES VALUE CASE OF PROCESS BASE VALUE FOR SENSITIVITY COMMENTS l Fuel 0.7 0.85 Slight Effect Emissivity See Figure 10 ll Condensation Allowed Set to Zero in - Addition to Case I Change Moderate Effect Spreading l of the Voc NearTop lil Gravitational Allowed Set to Zero in Subcooling Addition to Case 1,il Changes Negligible Effect l ( S-10 l
~
4 are shown in Figures 12 through 14. Again, we notice the ! i famihar fuel spreading and mixing zone voiding patterns.
- y V The premixed mass is seen to depart early enough from the total quantity of melt poured to reach a peak value of
~2.5 tons at about the time that the melt front touches the j
4 lower head (~1 s). Shown in Figure 4, this calculation j provides an indication of the very large degree of conser-vatism embodied in the NUREG/CR-5030 ganti6 cation. A L 7-- " systematic set of calculatwwis for the complete requentifica-tion of premixing are currently in progress, but we expect ; i both 5 and 95% bounds to be reduced by at least a factor i of 2. Within the context of the original quanti 6 cation, the i ' impact of such a reduction is in revealing further signift-cant margms, as discussed in Section 4, and thus to further 1 :' con 6rm the NUREG/CR-5030 conclusion that a failure is
" physically unreasonable.**
l' QUANTIFICATION OF ENERGY YIELD c , With 1.3 GJhon and a conservatively boundmg con-version ratio of 20%, the 2.5-ton premixture found in the i ,
!- particular PM-AIEHA calculation of Section 3 implies a !
Figure 10. 'Ihe calculated steam volume fraction for the md**=1 energy release of 0.65 GJ, that is, a value way l premixing problem of Amarasooriya and 7heofanous (1991), too small to threaten the lower head. Conversely, for an j with increased particle emissivity.. energy yield of 1.5 GJ we would need a mass of ~6 tons j which, based on the discussion of Section 3, cannot be an-1 ticipated te be physically possible under any cucumstances i relevant to reactor accidents. Clearly, only a small portion i (the one under 1.5 GJ) of the CR3 quanti 6 cation in Fig-une 5 is relevant, and by reference to the NUREG/CR-5030 quanti 6 cation of CR4 reproduced here as Figure 15, it is j - rather clear that the upper head is not threamned either. In fact, based on our experience of the effects of water depletion and two-dirnensionality, we expect that the above i i estimates are highly conservative and that the real margms t to vessel failure are even larger.1his is illustrated below by an integral calculation that accounts for the dynanucs of the energy conversion pmcess, along the lines of the alternative framework of Figure 6. [A systematic set of calculations along these lines needed to quantify pdf7 in this framework are underway.] Using ESPROSE.a the premixture of Figures 12 and 13 was triggered by means of snManly releasing the con-tents of a computational cell pre;surized (by steam) to 12 MPa. The timing of the trigger corresponds to melt ar- _ rival and contact of the lower head; its location is taken at the bottom of the axis of symrnetry; and its magnitude is Figure 11. The calculated steam volume fraction for the pre- chosen to ensure a strong initial escalation (based on ex-mixing problem of Amarasooriya and Theofanous (1991), perience with the KROTOS AlsOs calculations discussed with increased particle emissivity and zero corvinnaarion by Yuen and 'Iheofanous,1993). In this calculation, we chose the fragmentation (ff) and vaporization (f.) param-eters (see reference above) as 1.0 and 0.05, respectively, and the calculation was run with all flow paths, in or out of the lower plenum, sealed, and all boundaries rigid. This maximizes the loads on the lower head and,in particular,it ^ provides an upper bound estimase of the impulse that could be delivered if the explosion was consW=-i frorn above by a hydrodynamic mass (i.e., a slog of material) inssead. The results are summarized in Figures 16 and 17. 5-11
melt volume freehon tame = 0.300 Steam volume freetion to 0.300s
=W ,
e s u I
~I f,
2
)
i melt volume freeben times 0 600 Steam volume fraction to 0.800s 1 i ) i I
. I
[
-rs , !
=iQA j l g ,
i 1 t i melt volume frecuen times 0 900 Steam volume fraction to 0 700s ; 1 p
^ -
( i
@ ~ !
R ! I M - l I
. i o
o Figure 12. Calculated meh volume fracdon distribution at Figure 13. Calculated steam volume fraction distribution at : different times into the transient. different times into the transient. 5-12 1 l
8 , , , , 7 ' ; i j 6 ; 5 m at - o 4 - 2 PRESSURE AT TIME = 0.0015 SEC. [- 3 ' a <o.7 q l 2 ' ; Is 1 ; a Es 0 - 0 0.2 0.4 0.6 0.8 1 1- I time (see) e , l 0 $s . I Figure 14. Premixed mass transient compared to the total Q- - quantity of melt poured. $s
![ l s a e a
'@ y 3.0
,s) ~
ig '
. ~
{ 35 ._,. . + EE 2.0 -
>g - % +
.5 g
- 9-E"y 1.0 -
E z<N PRESSURE AT TIME = 0.0030 SEC. ,
' ' ' ' l 0.0 O.0 1.0 2.0 3.0 4.0 5.0 Upward Slug Energy (GJ) I' Figure 15. CR4 according to NUREG/CR-5030. I*
7 I The basic results of this calculation,i.e., the evolution e - of thi pressure field, are summarized in Figure 16. Some 0 $s partiede results, the pressure transients at five points along 4. . the lower head, are shown in Figure 17. We note the generi- ls cally benign character of this calculated explosion; an initial , trend to escalate seems to die out rather quickly as the wave Is . encounters the highly voided mixing zone, while a larger amplitude wave is seen to propagate around the periphery 3, of the mixing zone where there is fuel but the void is low. - ' l Further, we see that this wave is reinforced by reficctions . off the curved boundary of the lower head in a complicated
- e^ /
r ,, wave interaction pattem that exhibits the effect of void in j the mixing zone. A sample of wall pressure pulaes is pro- ** 4*
- i vided in Figure 17. Again, we note that the pressure pulses are rather low and clearly of no consequence to lower head integrity. These results are presently tested against a new model, ESPROSE.m (Yuen and Theofanous,1993), that ef-fects unique opportunities for representing the basic physics Figure 16. Evolution of an explosion in the lower head of the steam explosion phenomenon, under total confinement.
5-13 1_______
CONCLUSIONS Since the original quantification of the likelihood of a I failure in NUREG/CR-5030, major experimental and ana- ; lytical developments have taken place. By taking advantage of these developments, we believe it is possible to reduce the substantial conservatisms in the original quantification, i and to thus conclude that even vessel failure by steam ex- ! Pl osions may be regarded as physically unreasonable. We PRESSURE AT TIME = 0.0045 SEC. have tilustrated how this can be done within the an,ginal j framework, as well as in a complementary framework that , takes advantage of current imegrr.1 analysis capabilities. On ! g' 5 this basis, the o-failure issue is now ripe for final resolution; ! what is needed is a complete set of calculations supportmg i a revised quantification of CR1 and CR3 and a final review i
$' step in the ROAAM process.
7~I - ACKNOWLEDGMENTS '$ g He ESPROSE.a code is an advanced, developmental version of the ESPROSE code, which together with PM-I E,- ALPHA and related premixing calculations reported here ' 4' were supported by the U.S. Nuclear Regulatory Commis-I sion under contract number 04-89-082. REFERENCES
- 1. Amarasooriya, W.H. and T.G. neofanous (1991) " Pre-
. mixing of Steam Explosions: A Eree-Fluid Model,"
+ , ,,, J Nudear Engineering & Design 126, 23-39.
Md*
- s#' 2. Amarasooriya, W.H. and T.G. Theofanous (1987) "An Assessment of Steam-Explosion-Induced Containment Failure. Part III: Expansion and Energy Partition,"
Nudear Science and Engineering,97,296-315.
- 3. Angelini, S., W.W. Yuen and T.G. Theofanous (1993)
" Premixing-Related Behavior of Steam Explosions,"
CSNI Specialists Meeting on Fuel-Coolant Interactions, PRESSURE AT TIME = 0.0060 SEC. Santa Barbara, CA, January 5-8,1993.
- 4. Angelini, S., E. Takara, W.W. Yuen and T.G. Theo-fanous (1992) " Multiphase Transients in the Premix-gs ing of Steam Explosions," Proceedings NURETH-5, Salt 1.ake City, UT, September 21-24,1992, Vol. II, i g, 471-478.
]
- 5. Burger, M., M. Buck, K. Muller and A. Schatz (1993)
, $s " Stepwise Verification of Thermal Detonation Mod-t . els: Examination by Means of the KRO' IDS Experi- ,
ments," CSNI Specialists Meeting on Fuel-Coolant In-0( q teractions, Santa Barbara, CA, January 5-8,1993.
, , l ls
- 6. Denham, M.K., A.P. Tyler and D.F. Fletcher (1992)
" Experiments on the Mixing of Molten Uranium Diox-t
's ide with Water and Initial Comparisons with CHYMES Code Calculations," ANS Proceedmgs NURETH-5,
. Salt Lake City, UT, September 21-24,1992, Vol VI, 1667-1675.
. 7. Fletcher, D.F. (1992) "A Comparison of Coarse Mix-
.- */
D' ing Predictions Obtained from the CHYMES and PM-Mk**" + s ALPHA Models," Nudear Engmeering and Design, 135, 419-425.
- 8. Fletcher, D.F. and A. Dyagaraja (1991)"The CHYMES Coarse Mixing Model," Progress in Nudear Energy, Figure 16. Cont. 26 No.1,31-61.
5-14
l l l l l l l I i l l l l 350 ... ... ,. 350 ... ... 300 - 300
- 2 = 85.05 cm q .
p 250 - l 2 e 250 - 2 l E 200 -
} ,
I 4 200 L 2 2 I
' 1 t 150 L 2 '
( 150 - i 100 - 2 A 100 - 2 50 2 50 i ; O 0 " 0 1 2 3 4 5 6 7 0 2 3 4 1 5 6 7 l time (mm) time (mm) ; l 350 1 1 , ... .,. 350 ... ... ... ... . . ... 300 - z = 2835 cm l 2 300 ; z = 116.55 cm l 2 I e 250 - 2 c 250 - - l 200 - 3 2 200 ' i t ' t 2 l 150 l 150 i l 5 100 '
- 2 A 100 - 2 !
50 - i 50 ' 2 0 ^-" O l 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 time (mm) time (mm) 350 ... ... ... ... . ... 350 .. . . .
... ... i.
300 - z = 53.55 cm] 2 300 -l z = 148.05 cm l 2
; 250 ' 2 e 250
- 2 200 -
200 4 t t j 150 ' ' i - 2 l 150 s 100 '
-- 2 5 100
- 2 l 50 - 2 50
- 2
^^ " ^^^ '
0 0 O 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 time (==> time (mm) Figure 17. Transient loadings at various positions along the containing boundaries of the explosion in Figure 16. I f 5-15
- 9. Henry, R.E. and H.K. Fauske (1981) " Required Ini- 16. Deofanous, T.G., W.H. Amarasooriya, H. Yan and tial Conditions for Energetic Steam Explosions," Ibel- U. Ratnam (1991) Failure in a Mark-I Containment,"
Coolant Interactions, HTD-V19, American Society NUREG/CR-5423, U.S. Nuclear Regulatory Commis-of Mechanical Engmeers. sion.
- 10. Hohmann, H., D. Magallon, H. Schins and A. Yerkess 17. Deofanous, T.G., B. Najafi and E. Rumble (1987)"An (1993)"FCI Experiments in the Aluminumoxide/ Water . Assessment of Steam-Explosion-Induced Containment System," CSN1 Specialists Meeting on Fuel-Coolant Failure. Part I: Probabilistic Aspects," Nuclear Sci- l Interactions. Santa Barbara, CA, January 5-8,1993. ence and Engineering,97,259-281. (Also, including
- 11. Medhekar, S., M. Abolfadl and T.G.Theofanous (1991) Peer review comments, in NUREG/CR-5030,1989.)
" Triggering and Propagation of Steam Explosions,"
- 18. %eofanous, T.G. and H. Yan (1991) "ROAAM: A Nuclear Engmeermg & Design 126,41-49. Risk-Oriented Accident Analysis Methodology," Pro-
- 12. Medhekar, S., W.H. Amarasooriya and T.G.Theofanous ceedings, International Conference on Probabilistic (1989)" Integrated Analysis of Steam Explosions " Pro- Safety Assessment and Management (PSAM), Beverly ceedings Fourth International Topical Meeting on Nu- Hills, CA, February 4-7,1991, Vol. 2,1179-1185.
clear Reactor hermal-Hydraulics, Karlsruhe, FRG, Oct. 19. Turland, B., D.F. Fletcher, K.I. Hodges and GJ. Attwood 10-13,1989, Vol.1,319-326. (1993) "Quantificaton of the Probabihty of Contain- ,
- 13. Pilch, M., H. Yan, M. Allen and T.G. %eofanous ment Failure Caused by an In-Vessel Steam Explosion ;
(1993) "Ihe Probability of Containment Failure by for the Sizewell B PWR," CSNI Specialists Meeting Direct Contamment Heating," to be published as a on Fuel-Coolant Interactions, Santa Barbara, CA, inn-NUREG/CR report by the U.S. Nuclear Regulatory uary 5-8,1993. ; Commission. 20. Yuen, W.W., X. Chen and T.G. Theofanous (1992)"On l
- 14. Steam Explosion Review Group (1985) "A Review the Fundamental Microinteractions hat Support the of Current Understanding of the Potential for Con. Propagation of Steam Explosions," ANS Proceedmgs tainment Failure Arising from In-Vessel Steam Explo. NURETH-5, Salt Lake City, UT, September 21-24, sions," NUREG-1116, U.S. Nuclear Regulatory Com- 1992, Vol. II, 627-436.
mission. 21. Yuen, W.W. and T.G. Theofanous (1993) "The Pre-
- 15. Theofanous, T.G. (1991) "The Role of Fuel-Coolant diction of Two-Dimensional Detonations and Result-Interactions in Severe Accident Management," ing Damage Potential," CSNI Specialists Meeting on Appendix A in NUREG/CR-5682, U.S. Nuclear Reg- Fuel-Coolant Interactions, Santa Barbara, CA, January ulatory Commission. 5-8, 1993.
5-16
i 1 i i l l { l APPENDIX 6 I THE STUDY OF STEAM EXPLOSIONS IN NUCLEAR SYSTEMS \ l Proceedings of the International Semimr on ! The Physics of Vapor Explosions October 25-29,1993, Tomakomai, Hokkaido Japan, pp. 5-26 i I I l I i
- 1 j
i i i b 6-1 i
THE STUDY OF STEAM EXPLOSIONS IN NUCLEAR SYSTEMS T.G. neofanous Department of Chemical and Nuclear Engineering Center for Risk Studies and Safety University of California. Santa Barbara, CA 93106 ! tel. (805) 893-4900 - fax (805) 893-4927 i l l l ABSTRACI' Almost exclusively, past work has been fo-- I. Recent developments in the des! cm n suaHed emode containment fa4 3 " of nuclear ure, whose mechamstic sequence is illustrated m ! systems require a mom detailed examination of Figures 1 and 2. That is, an in-vessel steam ex-l steam, explosion energenes than has been neces-sary m the past. Of particular interest now are plosion that can cause uppet reactor vessel head the dynamic aspects of explosions and the resultmg loadmg, and failure, of suca intensity as to pro-duce a large missile energetic enough to reach and dynamic loads on adjacent structures. A compre-hensive approach toward such a goal is described penetrate the containment boundary some 40 me-ters above. Two papers (Turland et al.,1993 and and sample results are provided on 2D explosions from the recently proposed micromteractions model Theofanous and Yuen,1993) in the CSNI Special-ist Meeting on Pael-Coolant Interactions held in (the ESPROSE.m code) and on the chemical sug-Santa Barbara Isst January (henceforth to be re-mentation of steam explosions with highly reactive metals. ferred to as the CSNI-SB Meeting) directly ad-dressed this issue. These papers conclude, and the INTRODUCIlON meeting summary concurs that "a-failure is highly unhkely and may be impossible." The key method. Although steam explosions can occur in a vari- ological element in these studies is a probr.bilistic ety of industrial and environmental circumstances, framework; that is, decomposition of the problem their study has been, by far, the most intense in the into sequential " elementary" processes, and sepa-context of nuclear reactor accidents. His is be- rate quantification of each in a manner that allows cause of the potentially catastrophic consequences independent contributions, his sets the stage for of an early and massive containment failure, steam successive refinements and eventually convergence explosions being one of the handful of mechanisms (on each process), which is necessary before we potentially leading to such failure. The theoretical can consider the assessment mature and the issued possibility is apparent from the total amount of the resolved (Theofanous,1993). While the above-energy involved (~100 tons of melt at ~3000 K), mentioned papers,together with NUREG/CR-5030 but the assessment of likelihood is an extremely constitute the begmnmg steps toward such a goal, j difficult task that requires consideration of how the we now have a demonstration of how such a pro-i melt and water are brought together, how they mix, cedure can be brought to completion, in another, under what circumstances they can explode, how similar in many respects problem, known as the the mechanical energy release depends on the par- " Mark I Liner Attack" (Theofanous et al.,1991; ticular parameters that characterize the melt / water neofanous et al.,1993a). (and steam) mixture, and how this energy is "fo-cused" to produce mechanical damage. De bifur- Much other work on panicular aspects of the cations are clearly too numerous to allow an ap- problem and at various stages of completion or proach based on " prediction"(i.e., fully mechanis- planning (including new computer codes) was pre-
.. tic modelling) neither can one adopt the empirical sented at the CSNI-SB meeting, and even more approach taken in risk analyses of similarly com- work on fundamentals as well as on verification as-plex problems (seismisity, carcinogens in the en- pects (prototypic material expenments, code com-vironment, etc.). His redoubles the need for fun- parison exercises) was recommended in the meet- 3 damental understanding, but this must be pursued ing summary. It can be reasonably expected that in !
!. in a focused way if one is to capture the essence an intemational cooperative climate this work will
- of the behavior within practical resource and time bring the subject of o-failure to a sufficiently deep i l constraints. This means that the methodology is understanding as to be regarded as having reached also imponant, especially in allowing the syner- maturity. This, I believe, will be a much needed
- gism from international cooperation-a theme to development toward public acceptance of nuclear 4
- which this Seminar is devoted. power.
6-3 l
On the other hand, the proceedings of the CSNI-(,,, SB meeting, to appear shortly in print, including the summary agreed upon by the some sixty partici-n Hl1 y pants, provide a comprehensive status report that needs no further interpretation. With this in mind,
/ ', u u 7_ w ,,,u,, I decided to orient my talk to a personal progress br Jn n n n gi g report; that is, what is new from Santa Barbara g* since we last reported in the CSNI-SB (Angelini et al.,1993; Yuen and Theofanous,1993; Theofanous
< and Yuen,1993). I will touch upon a wide range
' .4",J"&s"Ei of topics, as we are trying to address the subject ,
_d . i in a comprehensive manner, within the domain of '
, , our overall approach, of course, and I will try to i
-m=:owa explain how this approach is related to some emerg-j uouo sun ing application areas of practical interest. I hope
,__..; r that even though not a review, the result is reason- l l _, ~ _~-: _' _-
. : ably consistent with the general title and position
! j -___ '*.[' ,_ .
of this presentation in the program. l
.m_u encona w. I i ' d i 1. THE COOLABILITY VERSUS EXPLOSION
[h~.gdh*/- DILEMMA G
" Y^u"E"'.
, A severe accident cannot be considered ter- i 4,* + mmated unless the molten core (heat-generating) I materials reach a stable, coolable configuration. It recently has been recognized (Theofanous,1988;
==ssu Tuomisto and Theofanous,1991; Henry et al.,1991) l that this can be achieved in the lower head of the l reactor pressure vessel if the vessel is submerged Figure 1. Key mechartisms and terminology for a in water (see, for example, Figure 3). This is es-steam explosion evem (in-vessel portion), pecially so in the absence of lower head pene-trations, as is the case of some pressurized wa- :
[ 'cMf b rai/.. A t;,;.L. yll
-l ter reactors (PWRs), but it may even be possible in the presence of penetrations [which would en-compass also the boiling water reactor (BWR) de-l l
* %::. '*h , .) signs] if they were to be externally supported (so l c./lE 4.)
y - - ll 4l 1, that they do not fall out, under their own weight, after they have melted at the nozzle weldment). I g The two particular efforts pursuinF this approach I v 6[*', l of " accident managen: cat" are for the operating
"" ^"
. s _r; Loviisa reactors (Tuomisto and Theofanous,1991;
[.4 - J[is..m., Ky nEininen, et al.,1992; KymulHinen, et al.,1993) r e and be the newly-designed advanced passive PWR, the AP600 (Hammersley et al.,1993; Theofanous t 3 ;.t:. et al.,1993b). [Both cases involve " tight" reactor I-AF 7 Fq" %. r cavities in relatiori to the available water supplies-melting of the ice condenser in Loviisa, and abun-g ..r,m, m-gs / . a9 ,.. ..... . ;;g-m . . dant and passively available water from the emer-I
] ~7534,%
i P %
$ i gency core cooling system in the AP600.] Be-sides confining the radioactive material, this ap-l [u~ M C g %7Ph.! proach has tremendous advantages in eliminating the need for tracking the accident, and related con- l
.M. .c,.
. . 'd tainment integrity issues, into the even more dif-ficult realm of ex-vessel evolution. However, to i
'.\ l l v i
- f. actually achieve this advantage, besides coolability
%',,,. .. . / 4 4 .,<- (i.e., integrity of lent thermal loadm,the vessel g conditions) wewall mustunder demon- the preva-
[ C' strate that the lower head can survive applicable mechanical loads from any steam explosions po-Figure 2. Geometry relevant to the ex-vessel por- tentially arising during the relocation process. And tion of a steam explosion event in a large dry con- clearly, both demonstrations must be mr.de a: a high tamment. conficence level. 6-4
l l consistent with the gravity-driven melt pour into a ! confined geometry. Rather, the point we wish to l C make is that the consideration of these new ele-7 Aq} ments is not trivial, and it should be seriously un-i dertaken only if the in-vessel retention case could ! j ; not be made sufficiently robust. l All these problems, including the ones con-l ; nected with lower head integrity, disappear, of course, , if the reactor cavity is to be kept from flooding, !
- e e ,
but this would pose a whole set of new issues con-j cerned with ex-vessel coolability. (y_ ]l y ' JQ C - This coolability versus steam explosion en-ergetics dilemma is everi more intriguing in the Q i ? Qg i case of BWRs. Here, the reactor vessel has to be . h) high above the containment floor (see Figure 5), [h}I fg - g W
*d E*7py?f injection the lower head is dense with control guide and in-strument tube penetrations, and so far there has not been a serious consideration of an accident manage-e e w d, .
Rea: tor cavity ment approach relying on in-vessel retention. Re-Tunnet garding ex-vessel phenomena, the approaches have Figure 3. Schematic of reactor cavity flooding. spanned two opposite extremes. In one, called
" post-flooding," the cavity (or lower drywell) is kept dry until the lower head fails, and it is flooded {
Such structural evaluations require the dynamic i load histories, which involve the dynamic aspects soon after the melt is released and spread out on ) of the explosion itself, as well as its coupled re. to the floor. This climinates the possibility of ener- l sponse to the motions induced in the surround- getics because even if some fraction of the core de- l ing media (water, structures). In the context of bris were to relocate after flooding, such relocation l a-failure, our interest in lower head failure was would be very gradual (controlled by melting cor- i as a potential relief mechanism, and the evalua- responding to decay power levels) and at no time ! tion was carried out roughly on the basis of esti- l l mated mechanical energy releases (Reofanous et i al.,1987; Turland et al.,1993)- and minimizing g gl"
'a the likelihood of such failures was conservanve. .r::. _ ge The present context demands a much more realistic, E yj dynamic-loads-based, evaluation, and now maxi- {,;! M j
I mizing the potential for failure in the assessment @@y ' A T i sa ane is the conservative trend. sm Panes 7
-E I
! W g*
While these sorts of evaluations are in progress ! Md l b M'. ! f7 the need to consider ex-vessel steam explosions, al- ua I though unlikely, remains open. Should such a need \ ll J a. = w. arise, we would be confronted with certain new el- g6 i 'bpp ' " " ements, including: melt pouring under gravity into a highly confined geometry (see Figure 4), pres-M
@;i cm.
ygj"y sure buildup and coupling of the premixing tran-sient with the pour process itself, and a highly con-
@s;M
_ . . _ g@g strained (by the geometry and water depth) explo- bj~dy l }I.WJ
!W sion. Moreover, if the reactor cavity is buried in J#fch $1 F" the ground, as in the AP600, what we are look- %!q '/ 9j3.(!b ing for here is gross motions of the reactor ves- 5".E [.,Q ' M M&g?
sel rather than structural failures. It is gemature a C= ,y **!f e at this time to judge the potential severity of this .g y .rff situation, especially recognizing, among other mit- 'I igative aspects of these new elements, that the very attainment of significant in size premixtures is in- Figure 4. He " tight" cavity geometry in the AP600. 6-5
involving any significant quantities of melt in pre- , , mixture (in " flight"). 'Dtis approach, for example, oco ., was initially intended for the " simplified boiling /e%Cf" ]f water reactor" (SBWR), but it appears to have been abandoned because other considerations, related to l ,,,,, c"'*'.T, *'c ( i , ... design basis accidents, lead to scenarios with mod- I.
' t crately deep water pools (1 to 3 meters) prior to i
{
/ ca, l ,
," 1 lower head failure. In the other extreme, called
" deep-flooding," the lower drywell is kept full of 1 i b '. ,,.
,}l _
d l water at depths up to ~10 meters, so as to provide i Jm"a 7" ']j contact (of the released melt with water) of suffi- e i , ._ . _ Q 1 cient duration as to ensure breakup (particulation) $ and quenching prior to arriving at the floor. This ]1 U+ O !l I ca "" - is the approach taken in the Swedish (ABB atom) j J, T design of BWRs, and it is still an option for the i { _ oE 6 l SBWR. Quite aside from the coolability merits of j,,,,k,['""I __ f _
,_b each approach (see, for example, Theofanous and N = = * ,
Corradini,1993) in the presence of any significant wm quantity of water (say, over ~1 m) one must ad- EUI" dress steam explosion energetics. In constrast with Figure 5. Schematic of a BWR pressure suppres-the PWR case discussed above, the lower drywell sion containment, illustrating the reactor vessel in m these BWR designs is not buned m the ground, relation to the lower drywell geometry. and the explosion geometry is relauvely open (a pool with a large open space above it); thus, in-stead of gross vessel motion, what one is lookirig for here is structural loading at the pool bound-aries, which in some cases may be reactor vessel um,,, support elements [such as a pedestal (see Figure ** 5)], or, in part, the containment pressure boundary / itself (see Figure 6). [ Note, however, that in the latter case the boundary is, in addition, protected D- aemp y / ky p by a shield, a cylindrical steel shell of substantial $P J thickness.] As another interesting aspect, note that b. the quenching potential increases with pool depth, co
- / l but so also does the inertia constraint and hence the resulting loads, if melt could penetrate deeply into
- l j such pools. [More on this later.] f
. - ~ ~
g., .' ] ~ To put these integral assessment, or risk as-
- e*MMMahd8*1 pects into the proper perspective, we must also con-sider what is mvolved m specifymg the melt pour ggggg{ggggggg' -
conditions in each case. For the in-vessel explo- i sions (PWRs only) evidence is accumulating (i.e., Figure 6. Detail of the lower drywell geometry in see, for example, Turland et al.,1993, and Pilch the SBWR. et al.,1993) that the side versus bottom melt pour bifurcation is very likely to reduce to either a TMI- the respective mqnitude of the heat sinks involved like (see Figure 7) moderate, in both size and rates, could in some cases make a bottom release physi- " side" pour for most so-called " wet" scenarios (i.e., cally unreasonable, thus eliminating the need for a where core degradation occurs with some water in bifurcation altogether (for example, we believe this the lower extremity of the core and core-support to be the case for the AP600). For the ex-vessel structures), or a very gradual melt. rate-controlled situations in the BWR case, the preponderance of pour (no possibility of energetic behavior) in a few evidence indicates local instrument tube (or drain- l so-called " dry" scenarios (i.e., where core degra- line) failures (see Figure 8), either early or long i dation occurs with the water level below the core after the relocation process, which produce mod-support structures). Plant-specific features, on the crate rate pours, i.e., 0.7 m /8 min (Theofanous et particular design of the core-support structures and al.,1993a; Rempe et al.,1993). However, much 6-6
more massive pours (up to 4 m 8/ min) and the pos- ,- ; sibility of creep rupture failure also have been con- ' O. - sidered in an effort to bound the range of physi-cally possible behavior for the Mark I Liner Attack problem (Theofanous et al.,1991). Both of these
/'- : '%]:-
[.-f " l areas-the PWR in-vessel relocation and the BWR (
\ (g m. l
] l!yj' E"-= c*=s ex-vessel release-are now ripe for a systematic, plant-specific evaluation, with significant benefits
\ r i". ' -
I q l Unf4" in better focusing the conditions under which both L l coolability and steam explosions need to be ex- ' ! amined. This focusing is, I believe, essential in ~ l * - - " ' " " creating a proper balance between the various ele- ~ "~ ~ ments of the assessment (i.e., uncertainty in initial Ml conditions versus uncertamty in the mixmg and ex- , ; plosion models themselves), while diminishing the p-chances that non physical conservative elements in the evaluation could interfere with the optimal res. Y# T b= g;l",-
=-
pn. olution of the coolability versus energetics dilemma 4 ","""" M's
]hlp -.-; h presented above. sq l sr
,,,. l _ . .
I ~a _n'
' l. g- h.,h'**"""
i.a h[
"1" i
!G;"." m - *-
g g e a ! 'A._ :+*"" ... 1 I 50C$0f s i i i 2 ; i cr_! - i
. co ,,, m, .- n , u,,, ,, ,,,,
uJ- ]-[ g i
% ! Figure 8. BWR lower head penetration.
In 1 ! .I
"{ l Q ldj:
; i {-"~9 Figure 9. The in-vessel case involves low veloc-g 56Si W d'"gg A ity,1-2 m/s, mainly oxidic (UO 2/ZrO )2 melt pours, a which flow through a rather narrow space to enter
!.", .",T' 5g--
f
.- y e ., the lower plenum after settling through one or more g perforated plates (design-dependent). In most ac-c.,,,,,,,- l ,
cidents the water in the lower plenum would be
,"*,'",",,'~7,,,,,
j
} m__ , , saturated, although subcooled conditions could oc-cur in some special cases of partial operation (in h.,_jg"T/
~
; [Mp-~ timing, both onset and duration) of the emergency U' / (I hn tM T core cooling systems. By contrast, the ex-vessel case involves highly subcooled pool conditions and Q very high melt entry velocities (10 to 15 m/s). In this case the melt is more likely to be basically
^*'7,,,,"",,,,
W gg '
- - - - metallic, an iron-zirconium eutectic, although oxi-
' 9:d! C dic melts or mixtures of oxidic / metallic melt have I
not yet been precluded. We can immediately rec-kli(%jU[j I 00 ognize two highly different breakup and premixing
!j i regimes. In the in-vessel case the perforated plates i
govern the radial spreading of the melt and the as-sociated melt length and velocity scales, which in Figure 7. Illustration of the TMI-like sideway core turn determine the degree of voiding (water deple-crucible failure and melt relocation pattern. tion) in the mixing zone. In the ex-vessel case we , expect a highly dynamic breakup pattern, as both
- 2. KEY FEATURES OF THE PROBLEM AND the high velocities and the high subcooling favor lo-AN OVERALL APPROACH cal blanket collapse, rapid local pressure generation and fine scale fragmentation, thus preventing deep
'Ihe basic geometric configurations discussed pool penetration. On the other hand, these same above and related dimensions are summarized in key features dictate that with only coarse mixing
( 6-7 l t
l g -- .
~~ ._ m
~ , -
l - 1 - g I m sA Mv 'v, e q ,,7 *a e g !
*
- i
* %.. Y _y 8 to 10 m Figure 9. Schematic of key geometric configurations for steam explosions of current interest.
(length scales from a few to tens of millimeters) the vance to the current risk analysis needs for quantifi- , water depletion in the mixing zone would be neg- cation of dynamic pressure loads on adjacent struc- l ligible. As a third key feature we could consider a tures, especially for ex-vessel interactions. The one jet penetration regime, as modelled by THIRMAL is called " explosion venting"; it applies to open (Sienicki et al.,1993) or by BQrger et al. (1993). pool geometries with a large aspect ratio, and the Even though it is unlikely that such jets could sur- venting refers both to the dimet venting of the ex-vive this intensely forced penetration, it is interest- plosion zone (mitigating the " driving" component ing to note that with their very limited interfacial of the load) as well as to reflections (unloading) of area available they do not really pose any energetic the pressure waves off the free surface of the pool concerns in the present setting. The significance of (mitigating the transmitted component of the load). t pool penetration is in defining the quantities of melt The other key behavior, already mentioned above, that could potentially explode as well as the depth applies to high velocity contact of the melt with of the explosion (the inertia constraint), while wa- highly subcooled coolant, and it is meant to de-ter depletion is important not only in separating the scribe the destruction (fragmentation and quench- !
. melt from the working fluid, but also in reducing ing) of the coarse melt masses by forced, small the susceptibility of premixtures to triggering and scale, but intense interactions. We call this behav-escalation (Theofanous and Yuen,1993; Fletcher, ior " penetration cutoff".
1993). It is now possible to visualize how the system-Turning next to the task of risk analysis, it is atics of large scale premixtures could be explomd clear to us that any models and predictions devel- in terms of the melt pour velocity and coolant sub-oped for this purpose must rely upon well estab- cooling. The qualitative behavior is illustrated in lished behaviors and trends (the problem " system- Figure 10. The water depletion boundary is taken atics", one might say) rather than the microscopic to represent the space of conditions which create ; details necessary to describe this overwhelmingly extensively voided premixtures. Its actual posi- i instability-driven phenomena. As made evident in tion can be obtained by means of premixing cal-the CSNI-SB meeting, the " water depletion" phe- culations (i.e., using the PM-ALPHA code), and nomena is playing such a key role, and arguably it consideration of the melt length scale creates an-did so even before it was experimentally demon- other (difficult to illustrate) dimension, in that for strated. The resistance of premixture to trigger- given velocity and subcooling larger scales pene-ing at high ambient pressures (one might call it trate deeper and produce less void, but provide less
'~'
the "high pressure cutoff") has also played such interfacial area for fragmentation during an explo-a role-even though not fundamentally understood sion. For small length scales, on the other hand, the yet, the empirical evidence is diverse and unam- magnitude of penetration is limited by heat losses biguous enough to ellow such use (Turland et al., (quenching) and slowdown (due to momentum ex-1993). Here, we propose to add to this list of key change with the coolant); thus the premixtures are behaviors, two more. They are of particular rele- smaller, but richer in fuel and more highly voided. 6-8
l CHYMES code calculations)-for a comparative assessment, see Theofanous and Yuen (1993). The h phenomenon also has been experimentally verified in the MIXA and MAGICO experiments (Denham {
"Pencfration Cutoff" l y et al.,1992; Angelini et al., 1992,1993)-in the
,b _
lg case of MIXA, indirectly, by visual observations S TA o and by measuring the steaming rates, and in the j
=
I$ l "' case of MAGICO, directly, by measuring the local (using FLUTE) and the global (using the pool level j l rise) void fraction transients. I Y,1 Premixtures \lj At the CSNI-SB meeting we also reported pre-
.. g ,f,7 ofsize "L" ;2 liminary measurements oflocal/mstant chordal- av-Depletion" I erage void fracnon measurements with quantitauve
> radiography (attenuation of soft X-rays). At this Water Subcooling time the technique has been developed such that it is highly reliable and conveniently applied to Figure 10. Conceptual frame of an approach to provide a two-dimensional void fraction distribu-bound the range of physically possible premixtures. tion map over the entirety of the mixing zone in l MAGICO. [ Currently, we are generating the X-The penetration cutoff line refers to phenomena rays using a single flash generator, so we obtain outside those considered in previous jet breakup one such map, at the desired time, during each ex-studies, and carefully designed experiments would perimental run.] ' Die results obtained for particle be necessary to quantitatively describe it. temperatures of up to 1000 *C are consistent with These four key behaviors are in the focus of the previous FLUTE results and with PM-ALPHA l
our current efforts in Santa Barbara, carried out as code predicuons. a part of DOE's Advanced Reactor Severe Acci-A sample radiograph of a particle cloud falling dent Program (ARSAP). Specifically, the work is through air is shown in Figure 11. Using the same oriented to the advanced " passive" designs, which calibration, scanning, and data reduction software are panicularly protected against accidents evolv-as used for deducing void fraction in premixing, ing in pressurized primary systems, thus we place we can deduce from this figure the particle vol-considerably less emphasis on the " pressure cut- ume fractions as function of axial position (fall I off". We have new experimental results on water distance). The comparison with the prediction is depletion in MAGICO, and experiments in a new shown in Figure 12. A sample radiograph of a premixing facility with capability up to 2000 *C premixture in MAGICO, with initial particle tem-(the MAGICO-2000) are about to begin. We also perature of 600 'C, taken is after initiation of the now have the first actual demonstration of explo- experiment is shown in Figure 13. Sample results sion venting using the ESPROSE.m code-based of the reduced data compared to PM-ALPHA pre-on the concept of"microinteractions" introduced in dictions are shown in Figures 14 and 15, for two Santa Barbara last January (Yuen and Theofanous, rows of cells near the top (10) and the bottom (18) 1993). We study these microinteractions by sub- of the mixing zone, respectively. The second index jecting single melt drops in simulated explosion in these figures refers to the four radial cells used environments, in the SIGMA facility (Yuen et al., to discretize the radiograph. The agreement is seen 1992). In a related exploratory effort, we began to be reasonable. The predicted effect of increasing the study of chemically augmented explosions (i.e., the initial particle temperature by 200 *C is small, steam explosions with highly reactive metals such and as shown in Figure 16, this is born out by the as At or Zr), and have the first fundamental data ex-experiment. hibiting clear chemical reaction effects under well controlled conditions in SIGMA. In the following, I , Based on this experience, our new tluust is provide an overview of these developments. Work in achieving experimentally void fracnons m the l on penetration cutoff has not begun yet. 0.8 to 0.9 range, and exploring the effects of much i higher inlet velocities, particle density and water
- 3. WATER DEPLETION IN PREMIXTURES subcooling. For this purpose we have built the MAGICO-2000 facility, with capabihty of up to Originally proposed by Henry and Fauske 2000 *C. The particulate is A(2 0 3or ZrO 2of se-(1981), water depletion (or voiding) of premix- lected particle sizes in the 2 to 10 mm range. The tures has been quantified recently (PM-ALPHA and pool depth can be up to 1 m, and inlet velocities of 6-9
1 i
- , y.. .
% ,' ,- **$i.'
.,h 1
' 7
; , , 4- l
*g..-:.
. . s
.. l l
t
.e 1
- 9 -f*r,s.
s,.. 9. . %;,.'
/- , -
*s ,
, ,t '3
- 4 e< , ..
l : s
.h'.e._g% 7 y, ~ .
- . . .4 4.*.,
, . '~ . .
- < - . , / , , 4 ,, .
, ' ,5 -
.py .
, q
- y. y ao
', ~
~
.. ~
r
-(. .- %
.~ , .
t {
\ .
a 3 g ~ . =, , 4
~ . . A l .. .,
i- ' N _ . rA" E..'3 1
. f r<_m
, . . . . L
. ;, % . . . . * - x - -
i j Figure 11. An X-ray radiograph of a steel panicle cloud falling through the air in MAGICO. i 6-10
I fr:gmIntation ow i at ~1.0 and ~2.0 ms for 100 ' ' ' ' ' _E the 20.7.and 6.9 MPa runs, respectively; and for t; 2-D avg these times, Figure 18 indicates entrainment fac-g 80 - e x-ray 4 - tors of ~3 to 4. A more ImH=d analysis of these [ radiographs is expected to provide information on , E 60 -
, the timewise evolution of this entrainment factor, }
e , and further experiments are twded at still higher , 40 - e . . - melt temperatures to fully characterize the beh::v- ' E ior. For the time being, we believe that an entrain-E 20 - ment factor of 4 is reasonable for use. in scoping g analyses. Moreover, the use of such a value with O ESPROSE.m applied to the KROTOS-28 detona-0 2 4 6 8 10 12 tion yields results very consistent with what has Layer been observed experimentally. i Figure 12. Comparison of measured particle vol- We have discussed explosion venting previ-ume fraction variation with axial distance (" Layer" ously (Yuen and Theofanous,1993), but in terms of axis on the figure) from Figure 11, with the predic- the ESPROSE.a code, whose modelling approach, tion. as it was made clear, is very limited. Here, we consider the same example cases of 1- and 3-meter up to 7 m/s can be achieved by selecting the free subcooled pools, under the same pour conditions. fall distance. A PM-ALPHA prediction for an alu- Sample results are summarized in Figures 20 and minum oxide pour of 2000 *C is shown in Figure 21, from which one can easily see the venting, both 17, indicating that the desired operation at the very directly from the explosion zone, as well as from high end of void fractions should be achievable. the transmitted waves. Our efforts are now directed These expenments are to commence in about two to beuer understanding this key behavior, and once months. understood to systematize and generalize it for easy use. In parallel, we are pursuing in detail the mi-
- 4. MICROINTERACTIONS AND EXPLOSION crointeractions in the upgraded SIGMA-2000 facil-VENTING ity.
The idea of microinteractions was introduced 5. recently (Yuen et al.,1992; Yuen and Theofanous, EXPLOSIONS WITH HIGHLY REACTIVE METALS 1993) to reflect the observations in the SIGMA fa-cility that the mixing of fragmented debris within a Essentially " buried"in past work on aluminum propagating hont is very localized around the par- explosions one can find sporadic references to ent particles. This drastically affects the pressure " flashes" of light and the possibility of chemical feedback, and hence the escalation of the explosion augmentation of the explosion yield. The sub-and the resulting pressure pulse characteristics, as ject became of great interest recently to the nu-demonstrated by sample calculations reflecting this clear community during the design of the New Pro-idea, through a 3-field model in the ESPROSE.m duction (Heavy Water) Reactor. This, as well as code (Yuen and Theofanous,1993). We now have other " production" or high flux research reactors, the 2D version of ESPROSE.m. and make use of have cores that are constituted mainly of aluminum it here to demonstrate explosion venting. metal, whose reaction with water is highly exother-
.. mic and presents the theoretical possibility of aug-As an imtial approach (and pending further menting the explosion yield by about one order of experiments m SIGMA with melt temperatures up magnitude. The work presented here was done in !
to 2000 *C) the constitutive law for the micromter- this context and for the purpose of examining the actions has been modelled by using an entrainment fundamental mechanisms involved. Moreover, as 3 i factor, that is, the rate water entrained in the mi-noted in the CSNI-SB meeting summary, it now crointeraction zone being a multiple of the drop would be desirable to consider such behavior with fragmentation rate (Yuen and Theofanous,1993). zirconium in assessing steam explosion issues in A first, rough estimate of this entrainment factor nuclear power reactors. I can be obtained from the observed growth of the debris-cloud volume, with time (which is illustrated Our approach was simply to expose molten l in Figure 18) in the SIGMA experiments (Yuen et aluminum drops (~1g) to a steam explosion envi-
- al.,1992). According to the radiographs, complete ronment (in the SIGMA facility) and observe the t
6-11
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Shot 19,24 kV,4/13/93 Y
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- 600 C, .24 cm, t = 1.0 s FLG #: N3144
- Figure 13. Sample radiograph of a premixture in MAGICO.
6-12
1 l 10 1 lait 10-1 right i i i 1 , , , , l 0.0 - 0.8 -
- g j 0.6 -
0.6 i - O f 2
'I 0' ~
0.4 - i 0.2 - 0.2 - 0 ' ' ' ' 0 ' ' 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Time (a) m, g,) 10-2 left 10-2 right 1 , , 1 , 0.8 -
. 0.8 -
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. j 0.6 -
t E . 3 04 3 0.4 - f 0.2 -
. 0.2 - * .
0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Time (s) Time (s) 1 10-3 left 10-3 right
, , , , 1 , , , ,
l 0.8 -
. 0.8 -
j s 1 j 0.6 -
- t: 0.6 -
I s n. 2 i' m. 3 0.4 0.4 3
> > l 0.2 -
. 0.2 -
l 0 0 ' O 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l Time (s) Time (s) 10-4 left 10-4 right 1 , , 1 i , . . . . 0.8 - - 0.8 - 5 ! l 0.6 -
. 0.6 -
0.4 - 0.4 3 - 0.2 - . 0.2 - . 0 ' 0 ' ' ' 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Time (s) he (s) l ! Figure 14. Comparison of chordal-average void fraction distributions in the upper portion of the premixmg zone (from the radiograph of Figure 13), with PM-ALPHA predictions. The vertical lines are experimental values, including measurement uncertainty. l 6-13
10 1 1:ft 18-1 right 1 . . . 1 , , , , i 0.8 - - 0.8 - I 5 - j 0.6 - - 5 0.6 -
$ b
- q 0.4 - , k g 0. 4 -
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' 0 0
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1 , , , , 0.8 - 0.8 - - 8 3 0.6 [ j 0.6 - t - 2 3: c - 0.4 - q 0.4 - - 1 02 - 0.2 - - t
, , 0 o 0 0.2 0.4 0.6 0.8 1 O 0.2 0.4 0.6 0.8 1 Time (s)
Time (s) 18-3 left 18 3 right l f . . . . [ 1 , , , , 0.8 - 0.8 - -
! 0.6 -
j o.6 - - j - a , a q 0.4 - - g 0.4 - 0.2 - 0.2 - -
' ' ' )
' 0 0 0 0.2 0.4 0.6 0.8 1 l 0 0.2 0.4 0.6 0.8 1 Time (s> l nm. (s) 18 4 right 1 . . . . ;
0.8 - I . T 0.6 . - d . q 0.4 - 0.2 - - 0 0 0.2 0.4 0.8 0.8 1 Time (s) l Figure 15. Comparir.on of chordal average void fraction distributions near the bottom of the premixing zone (from the radiograph of Figure 13), with PM-ALPHA predictions. The vertical lines are experimental values, including measurement uncertainty. 6-14 i t _ _ - -- -
.-- - ~ . . - - - - . .. - - , ,
5 1 , 1 , i 10 2 gioc 102 3:00 j 0.8 10 2 s:Co 0.8 . - -- 10 2 8200
- j 4
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5
.i, 0.4 -
,,...~~',,,Il -
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.- > j. !'
- 0.2 - 0.2 - l . 1 A d 0 ' ' ' 0 0 0.2 0.4 0.6 0.8 1 0 0.2 Time, (s) 0.4 0.6 0.8 1 j Time (s) i 4 i i 1 < i 1 , , , u 2 eioo u.2 saco , u-2 eico 0.8 - u-2 i stoo e' " 0.8 - u 2 saco .,.
.... 112 i e200 , e 112 r 8100 ,'
-$ a
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g 0.6 -
,./ -
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/ -
- 5 ,,'., l] $ ,., l" 00 *
, 'I ,
~
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' ,,I
, g -
$ .~-
l 02 " l ~ 0.2 - l :l - 0
' ' ' 'l '
0 ' ' , 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Time (s) Time (s) Figure 16. The effect of initial particle temperature on void fraction. The vertical lines are experimental values, including measurement uncertainty.
\ C7 0 f 5 i , ,
j , a 4 - V / , 3 - ,# -
>g _ / ,'
d
,/ <
/
N
~
1q & ...g'.'---a- P=6 9 MPa,T=1000*C - I
---9-- P=20.7 MPa, T 670*C l s
-A- P.20.7 MPa, T 1000*C t I l t 0
cn . 0 0.5 1 1.5 2 2.5 3 Time (ms) Figure 18. Exploding drop cloud volume, in the SIGMA experiment, as a function of interaction . Figure 17. Pretest predictions of void and parti. time. V* is the initial drop volume. cle volume fractica distributions in the MAGICO-2000 experunent, with an aluminum oxide pour at 2000 *C. 6-15 m
. . . . - - _ _ ___~ _~ . _ . .. . _ _ _ _ _
1400 , , , , 1400 , , , , 1200
- ko 2 1200 - U 2 '
~- k0. data '
~~- k3. data ,
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)
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0 o 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 i== < ci .m.i % - Figure 19. The prediction of KROTOS-28 test, with the ESPROSE.m code. Note: The transducers went out of scale at ~500 bar, and from the extent of material deformation the pressures are expected to have exceeded 1000 bar. 6-16
. . . . . - . . . - . - _ . . . . . . . . . . ~ . - . - - - . . . . . . - - . . -- .. - .. - . - . _. - . - -- - - -. - . _ . _ .. . __
l l ! l l i
.6 ms. P.= = 400 bar 1.0 ms. P.o = 850 bar i
i 4 l i i i i ] =_- 1.4 ms. P.~, = $00 bar l i l Figure 20. Illustration of Explosion Venting from a 1-meter-deep pool. The explosion was triggered at the bottom-center of the pool. 6-17
1 13 ms,Pe.= .12M W I Tw 12 ms. P-,
- 17# #
1 1.8 ms, Pmer
- I
\
4 , Figure 21. Illustration of Explosion Venting from a 3-meter-deep pool. The explosion was triggered at the bottom-center of the pool.
\
6-18
behavior as a function of initial melt temperature at ambi:nt pressure, and dramatizes well enough and shock pressure level. He SIGMA facility has the distinction we have been pointing out (Yuen et been described previously (Yuen et al.,1992), and al.,1992; Yuen and Theofanous,1993) and further modifications employed in this application are indi- emphasized in this presentation, about fragmenta-cated in Figure 22. The'most important modifica-tion and resulting microinteractions in the trigger tion was in a new melt generator (shown in Figure and early escalation phases on the one hand, and 23), which allows melting in an inert atmosphere the energetic, propagation phase on the other. As to temperatures up to 2000 *C (hence the name, explained already, our approach to the practical, SIGMA-2000). Details of the experiment and the risk aspects, of the problem emphasizes the dy-procedures employed have been described by The- namics and energetics of steam explosions (rather l ofanous et al. (1993c). than the triggerability of them), and this defines the ne results indicate three debris' morphologies, main thrust along the lines of microinteractions, and correspondingly we have defined three interac- and denvm, g the constitutive laws for them from tions regimes, as shown in Figures 24,25 and 26. the SIGMA-2000 sunulations. With this, the ana-In a pressure-temperarme map, Figure 27, the data lytical capability of PM-ALPHA and ESPROSE.m. show a sharp temperature threshold for both the and an approach based on the four " key behav-
" ignition" and " combustion" regimes, but very lit- 1 rs" described above, we are prepared to address tleif any pressure dependence in the range explored the emergmg practical needs of steam explosion (66 to 400 bar). In the high speed movies both the assessments m nuclear systems, ignition and combustion regimes are clearly ev-ident with flashes of " white" light-the duration REFERENCES and " size" of the flash are smaller in the ignition regime, which indicates that the chemical reaction
- 1. Angelini, S., E. Takara, W.W. Yuen and T.G.
region can be localized in some portion of the drop Theofanous (1992) Multiphase transients in the , and then extinguished. However, within about a premixing of steam explosions, Proceedings l 100 C range, we see a transition to a complete NURETH-5, Salt Lake City, UT, September combustion event, where 100% of the drop mass 21-24,1992, Vol. II,471-478. [ Nuclear En-is found to have been chemically reacted. In this gineering & Design (m. press).] regime the debris looks like a black, fine powder, 2. Angelini, S., W.W. Yuen and T.G. Theofanous with more than 80% of it in the 0-10 p range. X-(1993) Premixmg-related behavior of steam ray diffraction analysis showed it to consist of a explosions, CSNI Specialists Meeting on Fuel-and y alumina, the y alumina being amorphous- Coolant Interactions, Santa Barbara, CA, Jan-like and indicative of freezing at extremely high uary 5-8,1993, cooling rates. We are currently workm.g on the theoretical 3. Bilrger, M., S.H. Cho, E.V. Berg and A. Schatz interpretation of these results, but some basic ob- (1993) Breakup of melt jets as pre-condition servations are already possible. for premixing: Modelling and experimental verification, CSNI Specialists Meeting on Fuel-
- 1. Because of its low density, high thermal con- Coolant Interactions, Santa Barbara, CA, Jan-ductivity, and high surface tension, aluminum uary 5-8,1993.
is quite resistant to fragmentation.
- 4. Denham, M.K., A.P. Tyler and D.F. Fletcher
- 2. He sharp temperature threshold for combus-(1992) Experiments on the mixing of molten tion indicates that the behavior is driven by uranium dioxide with water and initial com-chemistry, rather then chemistry coming on parisons with CHYMES code calculations, Pro-top of a base fragmentation event.
ceedings, NURETH-5, Salt Lake City, UT,
- 3. The fundamental question is really reduced to September 21-24,1992.
whether we have a vapor phase combustion, or whether the combustion energy drives the hy- 5. Fletcher, D.F. (1993) Propagation investiga-drodynamics to produce fine-scale fragme,nts tions using the CULDESAC model, CSNI Spe-cialists Meeting on Fuel-Coolant Interactions, that react m a feedback process. Santa Barbara, CA, January 5-8,1993. CONCLUDING REMARKS
- 6. Hammersley, R.J., R.E. Henry, D.R. Sharp and The " interaction" regime found in the SIGMA- V.S. &inivas (1993) In-vessel retention for the 2000 aluminum experiments is fundamentally dis- AP600 design during severe accidents, ICONE tinct from that found with triggered drop explosions Meeting, San Francisco.
6-19
- 7. Henry, R.E., J.R Burelbach, R.J. Hammersley behind shock waves in water, To be issued as and C.E. Henry (1993) Cooling of core debris a DOE-ARSAP repon.
within the reactor vessel 1:wer head, Nuclear 19. Theofanous,T.G.,W.H. Amarasooriya,H.Yan Technology, 101,385-398. and U. Ratnam (1991) De probability of liner
- 8. Hemy, R.E. and H.K. Fauske (1981) Required failure in a Mark-I containment, NUREG/CR-initial conditions for energetic steam explo- 5423, August 1991.
ty of Mech ahEn 20. eo 8' T ' 99 nt i m o
- 9. Kymninmen, O., H. Tuomisto and T.G. Theo- advanced passive light water reactors, Report fanous (1992)" Critical heat flux on thick walls prepared for ENEA/ DISP, Italy.
oflarge, naturally convecting loops, ANS Pro-ceedings1992 National Heat Transfer Confer. 21. neofanous, T.G., B. Najafi and E. Rumble ence, San Diego, CA Aug. 9-12,1992, Vol. {1987) An assessment of steam-explosion-6'44-50~ induced containment failure. Pan I: Proba-bilistic aspects, Nuclear Science and Engmeer--
- 10. Kymulumen, O., H. Tuomisto, O. Hongisto ing 97,259-281 (1987).
and T.G. %eofanous (1993) " Heat flux distri-bution from a volumerrically heated pool with 22. heofanous, T.G. and W.W. Yuen (1993) ne high Rayleigh number, Proceedmgs NURETH- Probability of alpha-mode containment failure 6, Grenoble, October 5-8,1993. updated, CSNI Specialists Meetmg on Fuel-Coolant Interactions, Santa Barbara, CA, Jan.
- 11. Pilch, M.M., H. Yan and T.G. Theofanous uary 5-8,1993.
(1993) The probability of contamment failure by direct containment heating in Zion, Draft 23. homisto, H. and T.G. Theofanous (1991) A NUREG/CR-6075, SAND 93-1535, June 1993. Consistent Approach to Severe Accident Man-agement Pmceedmgs Specialist Meeting of
- 12. Rempe, J.L. et al. (1993) Light water reactor Severe Accident Management Programme De-lower head failure analysis, Draft NUREG/CR- velopment, ENEA/ DISP, Rome, Italy, Sept.
5642, April 1993. 23-25,1991. Nuclear Engineering and Design
- 13. Sienicki, J.J., CC Chu, B.W. Spencer, W. Frid (to appear).
and G. L5wenhielm, (1993) Ex-vessel melt- 24. Wrland, B.D., D.E Fletcher, K.I. Hodges and coolant interactions m deep water pool: stud- GJ. Attwood (1993) Quantification of the prob-nes and accident management for Swedish ability of containment failure caused by an BWRs, CSNI Specialists Meetmg on Fuel- in-vessel steam explosion for the Sizewell B Coolant Interactions, Santa Barbara, CA, Jan-uary 5-8,1993. PWR, CSNI Spalists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, Jan-
- 14. Deofanous, T.G. (1988) Some considerations uary 5-8,1993.
on severe accident management at Loviisa, IVO 25. Yuen, W.W., X. Chen and T.G. Theofanous Repon prepared by Theofanoas & Co. (1992) On the fundamental microinteractions
- 15. Deofanous, T.G. (1993) Dealing with phe- that suppon the propagation of steam explo-nomenological uncenainty in risk analyses Pro- sions, Proceedings NURETH-5, Salt lake City, ceedings, Workshop I in Advanced Topics in UT, September 21-24,1992, Vol II,627-436.
Reliability and Risk Analysis Annapolis, Mary- Nuclear Engineering & Design (to appear). land, October 20-22,1993. 26. Yuen, W.W., and T.G. Theofanous (1993) he
- 16. Theof anous, T.G., H. Yan, M.Z. Podowski, CS. prediction of 2D thermal detonations and re-Cho, D.A. Powers T.J. Heames, J.J. Sienicki, sulting damage potential, CSNI Specialists C C. Chu, B. W. Spencer, J. C Castro, Meeting on Fuel-Coolant Interactions, Santa Y.R. Rashid, R.A. Dameron, J.S. Maxwell and Barbara, CA, January 5-8,1993.
D.A. Powers (1993a) The probability of Mark-I contamment failure by melt-attack of the ACKNOWLEDGMENTS liner, NUREG/CR-6025 (in press). . This presentation is based on the tools and
- 17. Theofanous, T.G., S. Additon, C Liu, experience gained from the steam explosions O. Kymulunen, S. Angelini and T. Salmassi portion of our DOE ARSAP program. I would (1993b) ne probability of in-vessel coolabil- also like to acknowledge my current colleagues in ity and retention of a core melt in the AP600, this work, Prof. W.W. Yuen, S. Angelini, S. Chen, Draft report of DOE Advanced Reactor Severe P. Di Piazza at UCSB and S. Additon (TENERA),
' Accident Progun. as well as Dr. H. Amarasooriya (Scientech) and
- 18. %eofanous, T.G., X. Chen and P. Di Piazza Dr. S. Medhekar (PL&G) in the past.
(1993c) Ignition of exploding aluminum droplets 6-20
t High Pressure Nitrogen Shock Tube i i i
/ Relief Valve Blasting Cap Pressure
& Diaphragm Gege "i
Heater J \ i 3 r ' Check Valve Nitrogen l l - Solenoid Valve Compressor 3 " Gas l l ~Diermoccuple .' i Argon P.T. le ! " Computer j l ' i !!! ! RF Power Supply P.T.2 e l : M ' i 3
- "' ~~ l
- Laser I Ph,oto Cell , , . :.
P.T.3 e i j':.:.:' l See fig. 23 l E'! .
- 8
\
*. . j Trigger Of The . Drop Cather Blasting Cap :
_ s' W ,'- i W: . . i' Water i fMt?&?#f%sCU l Figure 22. Schematic of the SIGMA-2000 facility. t 6-2I t I
Thermocouple I.ine
& Pressure Balance Tube Argon Ges
( = Teflon Tube l l :::,
- , ,::::. Holder 1
- ::::::: Induch.on
- , ,::::. Holder 1
_ ':: '5' , ., Cc11 Thermocouple ,, ',!!!!! !!!!!!! m*=ui , Hole (~) s
..h. f Purgo Hole y y'
s r ss gl gg/;p 9
= #" raphite Crucible e
4 -: - - yN s : :S - n
" , \ g :
Eg A%~ l j, ]',jg:Iiii t Insulau.en
\.. gj :
; Aluminum
-s , ,
\ 4 gy -
i N - ' e x ne - 3 M, e'i s itU;i
- e en%[" !;i! Teflon Ring N e M n 'Wuf iyi
~
! i r y ;.-
iik-um
;g 7 g;i gg g.. .
- y. ..r ::n =
g g, e il C
~
=
c,
, riiii e: ,
e - ' s l'i:
- isi Figure 23. 'Ihe SIGMA-2000 melt generator.
>, . a. ~. you - .
, .S.; , - g -ga. . .
sa 1,. g<.j n 7 *..#8 g
<- 4 g
,l** ; , *
*l* ? . .- - +,y ,
. . ,4 , _;
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. .' :.e ; e, ;t g , s gn. 4. ;. , g i
. .,, e
.w ,
-. ,. .,, t.<' . ;. ,; w
; ~j Q,n, .. , - ,
5 .,y. ,,A g . . s.4,
~ [t
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,,A,,
- se * *
.,. e. -,. . .by# ..
A. e% =rs. *ww w4 mo - < 4 . . =
. *~,.3 .-. .. .=
. . RUN 354 wie. .noede m gee me.
Figure 24. Morphology of the debris with 100% conversion to " powder", resulting from the
" combustion" regime.
6-22
1..__________._____________--- I o i 1 i
' l i
, o ' l i - 1
'g.. . ,
4,
.- ~ * ,
j l / l 4 l l s ! Rt T 107 1 I Figure 25. Morphology of the debris with muumal, or no breakup (" popcorn") and absence of l
" powder". This results from the " interaction" regime. I I
i l i I i i l l
,1 1
l i
]
,4,,. :
, , . .y
. * .s' i % s . ' ? g s - ,- ,,
, . 1 e.' '
.m 1 .
c . -
- 1 e
a
^%
f -
.s
- 5, V ,, .
4 Rt N lot, Figure 26. Debris morphologies with " popcorn", " granulate", and " powder" components. This
- results from the " ignition" regime.
I 1 1 i l 6-23
500 i i e combustion (cc) {
+ Ignition (cc) -
y400" a interaction (cc) - 6 A Interaction : 2 s 300 o ignition ^ 0.
- O combustion :
@ + 4 e
m . _ D- 200 A a ^
- 8 5 : :
O -
.c- . _
W 100
- a A a A *eo :
0 a 600 800 1000 1200 1400 1600 1800 Temperature ( C) Figure 27. Map of the various observed explosion regimes in " melt temperature" " shock pres-sure" coonimates. The solid symbols are for computer-controlled runs. 6-24
l l l l l l l APPENDIX 7 t I THE PREDICTION OF DYNAMIC LOADS FROM EX-VESSEL STEAM EXPLOSIONS Proceedings, International Conference "New Trends in Nuclear System Thermohydraulics" Pisa, May 30 - June 2,1994, pp. 257-270 i , i i l l l 7-1 1
THE PREDICTION OF DYNAMIC LOADS FROM EX-VESSEL STEAM EXPLOSIONS T.G. Theofamous and W.W. Yuen* Center for Risk Studies and Safety Department of Chemical and Nuclear Engineering University of California, Santa Barbara Santa Barbara, CA 93106, USA
*also with Department of Mechanical and Environmental Engineering r
i i ACSTRACT THE SIGMA AND KROTOS EXPERIMENTS l The purpose of this paper is to quantitatively demon. In the SIGMA experiments (Yuen et al.,1992) we j strate the " explosion venting" as an important mitigs- can observe the fragmentation morphology and associated l tive mechanism in energetic ex-vessel fuel-coolant inter- microinteraction phenomena of molten drops subjected to
- actions. The illustrative calculations are carried out with simulated explosion environments. This is accomplished l a model based on the recently-introduced microinterac. in a hydrodynamic shock tube, capable of generating sus-tions concept,in the first 2D implementation of the ES. tained pressure waves of up to 100 MPs and a duration j PROSE.m code. The constitutive law for microinter- of ~2 ms. We employ quantitative X-ray radiography, I acti
- ns was obtained from the available SIGMA exper, and the results obtained are in the form of Figure 1. Ap-i iments, and the integral modelis shown to be consistent proximate mixing volumes can be obtained from these with the KROTOS experiments 21 and 28. These experi. data, and the results available so far are summarized in ments are adequately well characterised, both in terms of Figure 2. Within ~1 to 1.5 ma the drcps are completely initial conditions as well as in resulting propagations, and fragmented, and we observe an *entrainment factor" (the th y are unique in yielding in the same apparatus the two volume of water involved in the microinteraction sone di-
, extr:mes, from mild propagation to strong supercritical vided by the volume of the debris) of ~4. Further, more l detonations. detaihd analysis of the data is necessary to deduce the whole time evolution. From qualitative observations we INTRODUCTION deduce that this " final" value is approached from above, and since peak pressures increase as the entrainment fac-l l This paper is a sequel to Yuen and Theofanous (1993) tor decreases, we believe the choice of a constant value at j j in pursuing the idea of "microinteractions" to the full im- ~4 or 5 is appropriate for these first calculations, as it is plementation of a 2D model for ex-vessel explosions. [For expected to be somewhat conservative. j l convenience, the formulation, with some minor modifi- The KROTOS experiments (Hohmann et al.,1993) ' l c: tion since our first publication, is restated here in the are carried out by the controlled pouring of various melts ! Appendix.] Toward this purpose we use the SIGMA ex- into a vertical tube (9.5 cm in diameter,1.25 m in height) periments to quantitatively extract a first order estimate filled with water and releasing a pressure pulse from the of the basic constitutive law for microinteractions, and bottom of the tube upon melt arrival at this location, the two key KROTOS experiments to demonstrate the ef- Pressures are measured along the length of the tube at , fectiveness of the three-fluid ESPROSE.m formulation to five locations. So far, experiments have been run with tin ' capture the basic behavior. This includes a mildly explo- and aluminum oxide melts, and among them runs 21 and I sive interaction with tin (KROTOS-21) and a highly en- 28 appear to have been the most succtanful and replet6u-srgetic detonation with aluminum oxide (KROTOS-28). tative of the principal trends. In KROTOS-21, run with On this basis we believe that propagation modelling has molten tin at 1000 *C and triggered with 15 cma of 120 tow entered the realm of physical reality, and since pre- bar nitrogen gas, only a mild, barely sustained propaga-mixing has already achieved this status (Angelini et al., tion was observed (Yuen et al.,1992). In KROTOS-28, 1993; Fletcher et al.,1993) the whole prospect of calcu- run with 1.45 kg of molten aluminum oxide at 2400 *C, lating the dynamics of energetic steam explosions appears the samd trigger produced a highly energetic explosion promising. that exceecied the range of pressure transducers (~500 f l 7-3 l
equitely ull characterized in all three rapects: initial conditions, tQs;rr, and resulting propag: tion; and they i are unique in yie 5e in the same apparatus the two ex-tremes from mild propagations to strong detonations. The KROTOS-21 experiment was analyzed previ-ously by means of ESPROSE.a in a pseudo.2D approach (~ {c to roughly account for the microinteractions (Yuen et al., 1992). Here, we employ the ESPROSE.m in the manner s -- used in an earlier preliminary interpretation of KROTOS- l g 28 (Yuen and Theofanous,1993); that is,in ID and with ; the equivalent initial conditions used previously in the
. , i 5 pseudo.2D approach. Since this earlier calculation of
' ~ -
- KROTOS-28 was carried out with a preliminary version (o of ESPROSE.m,it is updated here with the current ver-sion (ESPROSE.m Mod 1) also.
is It should be noted that the initial conditions of melt 2 and steam volume fractions, 4% and 14% respectively, so mm % g assumed in our calculation of KROTOS-28 are some-l l ~g what different from the 8% and 4% values (respectively) l
, quoted by Hohmann et al. (1993). The difference in melt q $ volume fraction is due to the density assumed-we use 3.9 g/cm8, which is the density of pure aluminum ox- ,
Lg ide, while Hohmann et al. used 2.6 g/cms, which we find l N - in Hodgman et al. (1961) to correspond to a crystalline !
\ solid called Bayerite, including bound-water molecules.
Because the specific and latent heats have been supplied 1 I I per unit mass, this difference is not in itself very signif-Figure 1. Mass distribution of a fragmentm.g tin drop icant. However, it does produce a " correction" to the (1000 'C) from SIGMA run T312, as obtained from the steam void fraction, deduced from level swell data, from analysis of an X-ray radiograph at 1 ms after the arrival the 4% value quoted by Hohmann et al. to a value of of the shock wave (200 bar). The numbers in the shaded 8E This correction is in the right direction if we also scale are in cm. Note that the diameter of a 1 g sphencal consider the shock propagation speeds deduced from the tin drop is 0.6 cm. [From Yuen et al.,1992.] experiment--600 to 1000 m/s for estimated shock pree-sures f at least 1000 bar (the transducers overranged at , 5 ' ' ' ' 500 bar). Indeed, for a 1000 bar shock we can calculate
/ speeds of 1600,1200, and 900 m/s for steam volume frac-
)
tions of 4%,8%, and 14%, respectively, which is another
/ , indication against the 4% value, and that it probably was 3 -
as high as 145
$2 -
[ 'g
/ -
Some remarks on the choice of the fragmentation fac-tor (see Appendix) are also in order. For the high pres-
' . ,.- sures found in KROTOS-28 we do not expect very strong i e #,,, - -c ' '
f'd ((((,' " thermal" effects, so we believe that a fragmentation fac-tor value of unity is appropriate. On the other hand, o
, , , , i KROTOS-21 produced very weak explosions and rela-0 0.5 1 1.5 2 2'.5 3 tively low pressures, which were shown in past SIGMA Time (ms) experiments (run at comparable melt temperature and shock pressure conditions) to involve strong thermally-Figure 2. Exploding drop cloud volume, in the SIGMA induced augmentation of fragmentation (Yuen et al.,1992).
experiment, as a function of interaction time. V' is the Thus the choice ff = 3 may be more appropriate here, initial drop volume, but to illustrate the effect we have carried out a calcula-tion also for ff = 1. bar) and appears (from the resulting structural damage The predicted pressure transients at transducer lo-and destruction of pressure transducers) to have exceeded cations up along the KROTOS test section are compared 1000 bar. In both tests the whole quantity of melt was to the measurements in Figures 3 and 4 (for the two premixed, and in the case of KROTOS-28, essentially all tests, respectively). It is clear from these comparisons of it was recovered in finely pulverized state (60% un- that the calculations correctly reBect the decisively dif-der 250 p, 90% under 2 mm). The local void fraction ferent behavior observed in the two tats. Quantitatively, distribution (prior to triggering) was not measured, but the agreement is also reasonable, especially after recall-rough estimates can be obtained from overall measure- ing that according to the observed structural damage the ments and from the observed wave propagation speeds. KROTOS-28 test may have indeed produced pressures in Consequently, these experiments can be considered ad- the 1000 to 2000 bar range. We enn now conclude that 7-4 L _ _ _ _ _ _____ _..
1 > 120 , , , , - 80 , , , , , I 100 I W - so
-- ko. data f . . . k3 k3. data Ia60 l %,
2 ga 30 h ,, . s
.' , / **,
i
;,, . i.s : - ..
- d. 40 1 ..... ,,'*<
(.'
'- 20 -
" - k.
0 O 1 2 3 4 5 6 a 0 0 l 2 3'%- 4 5 6 aus em.o 1
,3 120 , , , , , 120 , , , , ,
100 - - k1 '
- ke ~
--- kl. data * -* k4. data g .0 - ,, . s -
g .0 -
.0 - : s0 -
- s. 40 - 4 ;
E 40 - *' I,1 20 -
"**....., 20 -
J ,,W
,, ....- .i n
_i ? I. = 1 g
, L .I 0 1 2 3 4 5 6 0 1 2 3 4 5 6 ,
one emme exis emog 120 , , , , , 120 , , , , , 100 - 2 - 100 . - ks :
- -- k2. data .. . k5. data g .0 -
gn - - a '.* a - j d; 40 - - 4. 40 - -
; e, 20 -
l -- .... ,, - 20 - l %z.
-H .....--:--....
O 1 2 3 4 5 s 0 1 2 3 4 5 s aus peso eam >m=4 i Figure 3. The results of two ESPROSE.m calculations for KROTOS-21 compared to the experimental data. l 1 l high temperature (and superheat) melts in constrained and Theofanous,1993) by means of ESPROSE.a. The (1D), low void fraction geometries can produce highly su- premixing calculations were carried out with the PM-percritical, energetic detonations. The comparisons show ALPHA computer code (Angelini et al.,1993). For clar-thit this experimental fact is captured well within the ity in comparison between runs, we have adopted a run modelling frame of ESPROSE.m, which thus opens the identification code which is given by: [ Premixing (I) - way for investigating (under realistic
- driving" conditions) Pool Depth (m)/ Water Subcooling (K)/ Pour Rate Fac-
, a whole spectrum of reactor-specific features, such as tor), where the pour rate factor represents the pour rate as ! multi-dimensionality, scale, and the role ofinternal voids, a rough multiple (rounded to the first decimal) of 1,000 l free surfaces, and solid boundaries. An initiating effort kg/s, the typical order of pour rates of interest. The in this direction, which for the most part is outside the present set of calculations is identified as set I for easy scope of practical experimentation, is made in the next reference in relation to future sets addressing other as-section. pects of the behavior, or other applications. I ILLUSTRATIVE REACTOR EX-VESSEL EX- ner as the premixing runs, except for changing the prefix PLOSIONS to E.m(I), and adding the trigger time (in seconds). For Specification of the Calculations example run E.m(I).1/20/2/0.07.was triggered after 0.07 see nds of premixing. The trigger was applied by relens-Here, we consider a typical ex-vessel geometry 6 me-ing, suddenly the pressure from the center computational ters in diameter and water pool depths of 1, 2 and 3 cell at the pool bottom assumed to be steam filled at 100 meters. This is the geometry considered previously (Yuen 7-5
. . . ~ .
I 2000 , , , , , 2000 , , , , 3 - k3 1500 - - 1990 -
--- k3. data
-- Oh -
1200 - - f1200 -
- w. _ -
800 - - goo . . 400 - 400 - . 0
* ' " "), '.52 ' '
0 ' '
- ?.
O 0.5 1 1 2.5 3 0 0.5 1 1.5 2 2.5 3
'"" #") en. (m o 2000 , , , , , 2000 , , , , ,
1600 - - 1600 - -
._ k1 data """""" k[
k1200 - - k1200 - - 800 - - 800 - N -
~
400 - 400 - - 0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 l nam >=.4 saa >=.4 1 l 2000 , , , 2000 , , , , , 1600 - *--* k2 data - 1600 Z ~ k data k1200 - ___ k1200 - 800 - - 800 - -
- n. n.
~~
400 -
.) [~ 400 -
{v -
' 1' ' ' ' ' ' ' '
0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 , u.a. >=.e e, e o
)
Figure 4. The results of an ESPROSE.m calculation for EROTOS-28 compared to the experimental data. Bar. The trigger time were selected to be approximately case of a pool depth of 1 meter. [ Incidentally, the ap-the time at which the leading edge of the penetrating fuel propriate pour rate for BWR releases at vessel failure is ! jet arrived at the pool bottom. expected to be ~500 kg/s.) The melt is taken to be oxi- ) Four premixing and five explosion runs are presented die at a temperature of 3100 K (~100 superheat) and the ! in this work. A complete listing of the conditions and re- particle diameter is assumed to be constant, at I cm,in spective identification codes are given in Tables 1 and 2. all calculations. The primary purpose of these calculations is to illustrate For the discretization we use a 10 x 10 cm grid. The the effect of pool depth and internal voids on the explo- time step for the premixing calculation is 10-4 second. 4 sion dynamics and on the resulting loading of the pool For the ESPROSE.m runs, a time step of 2 x 10-' is l boundaries (i.e., to demonstrate the " explosion venting" used. Numerical experiments show that these time steps ; idea). The calculations here are thus carried out for the and discretization are adequate for the purpose of the I same pool subcooling (20 'C) and the same melt pour present calculations. The PM-ALPHA calculations were I conditions - that is, a 0.6 m in diameter pour, with melt actually carried out with a computational domain of only* I arriving at the water pool at ~10 m/s and a volume frac- 1.8 m in diameter. According to test calculations this I tion of 0.05. This corresponds to a pour rate of ~1000 convenience does not introduce any perceptible difference kg/s (a pour rate factor of 1). In addition, we present in the results. Since wall reflections are expected to be results of calculations at twice this pour rate (obtained important in the overall pool dynamics, the full geometry by increasing the inlet melt volume fraction to 0.10) in the is employed in the ESPROSE.m calculations. I 7-6 4 i
l
'Ihble 1. Key to the PM-ALPHA Calculations j Pool Depth Water Subcooling Pour Rate Inlet Velocity (m) (K) (kg/s) (in/s) Run LD.
I 1 20 2000 10 PM(I)-1/20/2 i 1 20 1000 10 PM(I)-1/20/1 ! 2 20 1000 10 PM(I)-2/20/1 3 20 1000 10 l PM(I)-3/20/1 ; I l 1 1 Table 2. Key to the ESPROSE.m Calculations I l Premixing Run I.D. Trigger "Ilme (s) ESPROSE.m 1.D. I l PM(I)-1/2W2 0.07 E.m(I)-1/272/0.07 I PM(I)-1/20/1 0.07 E.m(I)-1/20/1/0.07 PM(I)-1/20/1 0.14 E.m(I)-1/2W1/0.14 : PM(I)-2/20/1 0.40 E.m(I)-2/20/1/0.40 PM(I)-3/20/1 0.70 E.m(I)-3/20/1/0.70 Premixing Results melt freezing can be an important factor in limiting the The melt and steam volume fraction distributions at magnitude of the energetics. This effect will be analyzed the times selected for triggering are illustrated in Figures more precisely in future works. In the present work, both 5,6,7, Sa, and 9a. We can readily observe a slight ac- the 2-meter and 3-meter ESPROSE.m runs assume that cumulation effect on the melt, due to its deceleration by frozen fuel does not participate in the fragmentation pro-thi water. The void development is seen to be a strong cess. function of the contact time - for the 1 m case voids are completely suppressed, the 2 m case exhibits a cen- Propagation Results tral voided region extending all the way to the top, and Key results of the propagation calculations are sum-in the 3 m case this axial void is seen to be pinched off marized in Figures 11 through 18-they include the dy-chile the void associated with the penetrating fuel " head' namic loads on the pool boundaries for the five cases ex-b seen to grow further. In all cases, however, the leading amined (Figures 11 through 15), sample results of the edge involves low void fractions (less than 10%), and this pool dynamics responsible for these loads (Figure 16), b where a trigger can be most effective in building up a and an indication of the variability in these " internal de-significant explosion wave. Space limitations do not allow tails on such things as fuel distribution, the total quantity for a detailed description of the phenomena responsible being the same, (Figures 17 and 18). We discuss briefly for the various " phases" of void development, but an in- each of these three aspects in turn below. dic: tion of the importance of two-dimensionality allowing While the load histories, such as those in Figures the "entrainment" of subcooled water around the melt- 11 through 15, are necessary for detailed finite element entry location is given in Figures 8b and 9b. The momen- computations of structural response, a rough apprecia-tum exchange effects responsible for this entrainment and tion of the severity can be gained from respective height-th) pool surface depression observed in the same figures averaged impulses and the loading times involved. The' are currently under investigation in the MAGIGO-2000 loading times depend on the pool size and aspect ratio, exp;riment (Theofanous,1993). and as seen from the numerical results, they are 1, 2, l For the 2-meter and 3-meter case, the effect of melt and 3 ms for the 1,2, and 3 meter deep pools examined freezing becomes important because of the iccreased ex- here. These pulse-widths can be obtained also quite sim-posure time to subcooled water. As illustrated in Fig- ply from a consideration of the pool acoustic times in the ure 10 for the 3-meter case, the liquid fuel quantity in vertical and horizontal directions, as follows. the pool begins to become asymptotically limited. Since For shallow pools (aspect ratio less than or equal to solid fuel cannot participate efficiently in an explosion, 1), the outgoing pressure wave reaches the wall after the i i 1 I 7-7
1 l explosion wive has vented off the top, thus tha pressure pulse should be contained between the wava arrival time (equal to the acoustic time in the horizontal direction, y ~2 ms) and the incremental time required for relief in TLG9N the vertical direction. For the 1 meter,2 meter and 3
+
NW" meter deep pools, these times are ~0.7,1.4 and 2.1 ms, IW which lead to pulse times in reasonable agreement with those in Figures 11 through 15. l The impulses were computed by integrating the pres-r- p sure histories in Figures 11 through 15 and averaging the results at the five wall elevations. For the three 1-meter cases, the results range from 2 to 4.4 kPa.s, while the 2 and 3-meter cases produced 34 and 69 kPa s, respectively. While it is emphasized that the purpose of these calcula-tions is none other than illustrative, it may be interesting to note that for such narrow pulses reinforced concrete walls of the type employed in reactor pedestals may be able to withstand impulses above 100 kPa s. Figure 5. Steam and fuel (marked) volume fraction dis. A depiction of a more-or-less complete evolution of a tributions for premixing run PM(I)-1/20/2 at t = 0.07 calculated explosion, including some features of key im-sec. portance to escalation and resulting energetics, is given in Figure 16. Figure 16(a) shows an early rapid escala-tion and the beginning of an attenuation pro (ess as the pressure wave propagatcs, literally, "around" the voided
.l- ._[ region. However,the void eventually collapses, the fuel
]
within it gets involved, and Figure 16(b) shows the net results of this sequencial fuelinvolvement and expansion u -- g processes (both into the internal void, as well as into the j surrounding liquid). Also, the beginning of the expan- ' sion (venting) off the pool free surface is evident in Figure
" 16(b). By 2.2 ms [ Figure 16(c)) these venting processes are developed well enough to cause a significant decay within the explosion zone, which monotonously contin- )
ues in the next three figures: 16(d), (e) and (f). In these figures we also see the reflection of the radial wave off the side boundaries and the formation of a radially inward focused wave (Figure 16(f)]; however, the upward venting continues, and for the explosion zone it is so strong that
. . it allows for this inward wave to completely dissipate, as Figure 6. Steam and fuel (marked) volume fraction dis- shown in Figures 16(g) and (h). Space lim;tations do not tributions for premixing run PM(I)-1/20/1 at t = 0.07 allow the inclusion of these details from the other cases 8'**
considered; however, the general features are very similar to those noted above. j On the other hand, the specific features, especially regarding escalation and the role of internal voids, cen , e -w vary sigmficantly depending on the fuel and void distri-
? 6 butions in relation to the pool boundaries (both free and fixed) and the position of the trigger. The purpose of Figures 17 and 18 is to provide only a very brief indica-I I' tion of the " rich" behavior possible in this respect. The two runs were initiated from premixtures involving the same total quantity of fuel, by allowing for a half as long premixing time for the run with a pour rate factor of 2.
- - - These figurec show a stronger early escalation in the morc g~ 7 dilute, deeper penetrating melt case (see Figure 7); the
( more concentrated fuel region (see Figure 5) does lead. E to a stronger la+e escalation in run E.m(I)-1/20/2/0.07, l however, this is all too close to the free surface (vent-ing) and is less important to wall loading. This can also Figure 7. Steam and fuel (marked) volume fraction dis- be seen by the second peak in Figure 11. The total im-l tributions for premixing run PM(I)-1/20/1 at t = 0.14 pulse 3.2 kPa.s is still lower than the 4.5 kPa s obtained in sec. the case of E.m(I)-1/20/1/0.14. Along the same lines, we l l 7-8 ,
- - _ . . . . . _ . . . . =_ _- . . . .
L d
/ . . .. ......
/
\ .
j j j j ,.....
\ \
l . .
$)f j I'..$...
g e . U k. o ::::
. . .. : : ' Q,' ,l l, t,......
. ..,r , , . .......
i I i Figure 8a. Steam and fuel (marked) volame fbaction dis- Figure 8b. Steam volume fraction (
) and volumetric tributions for premixmg run PM(1)-2/20/1 et t = 0.40 liquid f'ux distributions for premixing run PM(I)-2/20/1 sec. at t = 0.40 sec. The maximum vector represents 4.73 m/s.
EQ 5 a
, ,y y .e
......,gg g,......
l
, g.,, . ....
n
.g i .... , , , . ....
J;\y n ::: tg0 1 1 Figure 9a. Steam and fuel (. narked) volume fraction dis- Figure 9b. Steam volume fraction ( ) and volumetric
- tributions for premixing run PM(I)-3/20/1 at t = 0.70 liquid flow distributions for premixing run PM(I)-3/20/1 sec. at t = 0.70 sec. The maximum vector represents 6.05 m/s.
i i 7-9 l .
t Meeting on Full-Coolant Interactions, Sants Barbars, CA, January 5-8, 1993. I i e i i e a i IIOHMANN, H., MAGALLON, D., SCHINS, H and YERKESS, A.1993 - FCI Experiments in the Aluminu-totat 0.8 -
..... Ilquid moxide/ Water System. CSNI Specialists Meeting on ,
{ Fuel-Coolant Interactions, Santa Barbara, CA, January 0.6 5-8, 1993. H s < MEDHEKAR, S., AMARASOORIYA, W.H. and THEO-FANOUS, T.G.1989 - Integrated Analysis of Steam Ex- , } 0.4 - - plosions. Proceedings Fourth International Topical Meet-E ing on Nuclear Reactor Thermal-Hydraulics, Karlsruhe, 0.2 - - FRG, Oct. 10-13,1989. Vol.1,319-326. l THEOFANOUS, T.G.1993 - The Study of Steam Ex- ; l l o
' i ' i i i i plosions in Nuclear Systems. Proc. Int'l Seminar on .
l 0 0.1 0.2 0.30.4 0.5 0.6 0.7 0.8 Physics of Vapor Explosion, Hokkaido, Japan, October f l sm. M 25 28, 1993. ! YUEN, W.W., CHEN, X. and TH EOFANOUS, T.G.1992 Figure 10. Total fuel and liquid fuel mass in the pool for - On the Ibadamental Microinteractions That Support f premixing run PM(I)-3/20/1. the Propagation of Steam Explosions. Proc. NURETH-5, Salt Lake City, UT, September 21-24,1992, Vol. II, also expect the magnitude of the trigger to play per. 627-636. i h:ps an even more significant role; however, such effects YUEN, W.W and THEOFANOUS, T.G.1993 - The Pre-l are outside the scope of realistic investigation until the diction of 2D Thermal Detonations and Resulting Dam-i ; r: levant early escalation conditions are addressed in the age Potential. CSNI Specialists Meeting on Fuel-Coolant l SIGMA experiments (and the microinteraction law). Interactions, Santa Barbara, CA, January 5-8,1993. j CONCLUSIONS APPENDIX: FORMULATION OF ESPROSE.m This paper has been written as a sequel to that of FIELD MODEL Yuen and Theofanous (1993), pursuing further the idea of microinteractions, and implementing it in 2D explosion CONSERVATION EQUATIONS i There are four phases: namely, "nu,ero-interaction" I calculations in the ESPROSE.m code. The rnost impor-fluid, coolant h, quid, fuel (melt) drops, and fuel debris. tant result is the quantitative demonstration of "explo-They will be referred to as m-fluid, liqu,d, fuel and debris i sion venting" as a mitigative feature of ex-vessel explo. ! sions under appropriately severe peak pressures. The re- .spectively. Each phase is represented by one flow field with its own local concentration and temperature. The l sults also depict the occurrence and role of voids in the , debris is assumed to be part of the m-fluid in thermal and premixing zone, and dynamic coupling with the surround-hydrodynamic equilibrium. Thus we have four continuity , l ing liquid to produce the loading on the sidewalls neces-equati ns, three momentum equations, and three energy l sary for structural evaluations. While comparisons with equations. In the usual manner, the fields are allowed to l ongoing experiments (MAGICO-2000, SIGMA-2000, exchange energy, momentum and mass with each other, l FARO, KROTOS, ALPHA), as well as other verification With the definition of the macroscopic density pj of phase activities, are continuing, the present results indicate, for the first time, the feasibility of assessing in a physically I meaningful way the damage potential from ex-vessel ex-l plosions. pl=0,p4 for i = m, t, f,and db, (A.1) and the compatibility condition, ACKNOWLEDGMENT I Support for tiiis work has been provided by the U.S. em+ 0, + #f+ eo = 1, (A.2) Department of Energy's Advanced Reactor Severe Ac-these equations can be written rather directly (Ishii,1975). l cident Program (ARSAP) through contract DE-AC07-
. Continuity Equations.
931D13200 and ANL subcontract #23572401. .
- m. Fluid:
REFERENCES of, + Y "'""'" } bi ANGELINI, S., YUEN, W.W. and THEOPA NOUS, T.G. Liquid: 1993 - Premixing-Related Behavior ofSteam Explosions. gp,r CSNI Specialists Meeting on Fuel-Coolant Interactions, y + V - (#'ur) = -E - J (AA) Santa Barbara, CA, January 5-8, 1993. g. HODGM AN, C.D., WEAST, R.C. anc' SELBY, S.M.1961
- Handbook of Chemistry and Physics. The Chemical bp'_
og
+ V * (P)uf) ~ fr (A 5)
Rubber Publishing Co., Cleveland, Ohio,1961. Debris: FLETCHER, D.F. and DENHAM, M.K.1993 - Valida-tion of the CHYMES Mixing Model. CSNI Specialists afet + V * (P'au na) = b V0) l 7-10 !
g 100 z = 5 c;m 100 z = 65!cm l A 0 1 2 3 4 0 1 2 3 4 j j 0 100 z = 25!cm 100 z = 85 cm ' i c- .A 1 0 1 2 3 4 0 1 2 3 4-e 100 ' 100 z = 45!cm
- z = 105 cm i c.
l 0 1 2 3 4 0 1 2 3 4 Time (ms) Time (ms) , Figure 11. The pressure-time history at various elevations on the side wall for run E.m(I)-1/20/2/0.07. . I' l t 1 c 50 50 z = 65;cm ! z=5cm
- c. A i 1
0 1 2 3 4 0 1 2 3 4 g 50 z = 25lcm 50 z = 85icm A A-0 1 2 3 4 0 1 2 3 4 c 50 z = 45!cm . 50 z = 105 cm ! 0 1 2 3 4 0 1 2 3 4 Time (ms) Time (ms) l Figure 12. The pressure time history at various elevations on the side wall for run E.rn(I)-1/20/1/0.07. l a 7-1I
O ' z = 65.:cm g 100(z = cm -- 100 - - - - :- L 0 2 3 4 9 fL , 1 0 1 2 3 4 l i O z = 25!cm : z = 85:cm ; y100 100 - - - :- ,- ; n. 0 0 M l 0 1 2 3 4 0 1 2 3 4 : l O z = 45:cm
- z = 105 cm l g100 100 - - - -
j
- a. '
) l 0 '
0 1 2 3 4 0 1 2 3 4 Time (ms) Time (ms) Figure 13. The pressure-time history at various elevations on the side wall for run E.m(I)-1/20/1/0.14. l I etu 500 z = 5 c.m 500
.i z = 125 cm -
ca a : - h : 0 2 4 6 8 0 2 4 6 8 e 500 z = 45icm 500 m ; ; z = 165 cm ; ; E i i - i : i a 0
.M :
0 2 4 6 8 0 2 4 6 8 em 500 z = 85lcm 500
; ; z = 205 cm ; j :
E a . !. !
. .! i.
0 0 2 4 6 8 0 2 4 6 8 Time (ms) Time (ms) Figure 14. The pressure-time history at various elevations on the side wall for run E.m(I)-2/20/1/0.40. l l 4 7-12
l ; i O z=5cm i z = 185 cm 8500 s- - 500 -
- 4. 4-3- .
e
- 0 2 4 6 8 0 2 4 6 8 I
i c z = 65!cm . . z = 245 cm ! 8500 T- <- 500 -
-{
n. 2 NI O 4 6 8 -0 2 4 6 8 ! l I e z = 125 cm : : z 305 cm i : g 500 .......g... t I
- 3. . . ......
5oo . .=... 3 ... .. 3 ... ....:..... ... . a . , 0 2 4 6 8 0 2 4 6 8 . i Time (ms) Time (ms) t i l Figure 15. The pressure-time history at various elevations on the side wall for run E.m(I)-3/20/2/0.50.
- e Momentum Equations. '
Fuel: I m-Fluid: a 8 E(P'ffI ) + V - (pf'f I uf) = -hf. - hf (A.12) g((p' + p'3)u.)
, + V - ((p' + p',3)u.u.) =
- (8. + P,e)Vp - F.,(u. - us) In the above equation, H(J) is the Heaviside step function that becomes unity for positive values of the ar-
- F./(u. - uf) + Eu, + F,u/ Eument and zero otherwise. When T. < T,, the m-fluid
+ J(H[J]ue - H[-J]u. + (p' + p4'3)g (A.7) is liquid and J is set to be zero and T, is an " equivalent" Liquid. interface temperature given by g(pju )s + V -(p'u4ur) , = T, = R.,T. + Rt,Te gm + gt.
" FrVp + F.t(u. - us) - Esf(ut - uf) When T. > T,, J is an evaporation rate given by
- Eur - J(H[J]us - H[-J]u.) + pig (A.8) i Fd- J " h. - he
** . - T,H &,Y - T,)]
Of(pf uf) + V -(p' f uf uf) = -# f vp + F f(u. - uj) It should be pointed out that diffusive transport within each field (shear stresses and conduction) has been ig-
+ F4f(ur - uf) + p'f g - Fruf (A.9) ~ noted in the above formulation-they are expected not i
{ o Entrgy Equations, to be important. ' m-Fluid: THE CONSTITUTIVE LAWS
-(p'. I. + p', I,.(T.)) 'i.Ne interfacial exchanges of momentum and heat are bt clearly regime dependent, and uncertainties remain even
+ V - [(p'.I. + p'46I d*(T.))u.} = fo, ,i,. ple two-phase flows. Only experiments specifically
'8 oritated to this problem and detailed local measurements
-p g(8.) + V -(em u.)
, will provide the basis for the appropriate assessment, par-
+ Eh, + Jh. ticularly if one of the phases is the " micro-interaction"
- R.,(T. - T,) + 4f. fluid. For now, our approach is to treat the m-fluid as a (A.10)
" pseudo" gas and utilize a smular set of constitutive laws Liquid:
as in a previous work (Medhekar et al.,1989). 8 For the mass transfer from the fuel, the fragmen-g(PII )4 + V -(Pileue) = tation rate, F,, is calculated based on the instantaneous i
'a- Bond number formulation as described in a previous work
-P M(8')+V*(8'"') (Yuen et al.,1992). The relevant equations are
- Ehe - Jh i F, = 60 dM-(A.13)
+ R4,(Te - T,) + hf (A.11) r di l 7-13 i
. _ _ _ _ . . . - . _ _ _ . . .m .m . . 1 .._. ....~__m_. . _ . . - _..-_...m.. . . ~ . . - _ ~ _ _ . _ _ . ._.m._.. .. . . . _ _ _ _
I gt)-21 tor 1 *0 40 E m(tF2Wibo 40 1000 1000, ' 800 Pmas
- 1498 Sar j 000< Pmer 4194 Bar y t o t ms 'i' E 800 y g 800-t = 34 ms 3 3 la 10 cq . (g) a m 10 cq 8 m 10cq (g) : W 10 cm) +
E.glF2M1*0 40 E.m(fF2.3104) do , I I 1000, 1000 000, Pman a 2466 Bar i 900- Pmas a 327.6 Bar y t e 18 ms . J t e a ms E 400 [ g 800 I 400 ' 400 3: j "3: ,, s 0:10 cm) (b) s > 10 cm) :W to og ({} s > 10 cg E.m(fF212Dr1DO 40 E,m(IF2.2M 40 1000. 1000
- m. Pma. . m. , .00 P, . m . Ba, t
- 2.2 ms f
- 4 e ms
; 400 -
400,
300 - , ' 200 n'
., . so 60 a p 10 sq 8 P 'M (C) s in to m) (g) ts 10 cm j E.m(f>2201M 40 E.m(0 tw1b0 40 l
1000- 1000, i 300 Pman 444.1 Bar 800 Pmas e 220.3 Br y t o 2.8 m T t
- 62 ms
( 000- 6 E00 s p ic '" (d) '"'"> 8 5 *") (h) a m '8 a) Figure 16. The development and venting of explosion in run E.m(I)-2/20/1/0.40. 7-14
. , ~ ~ . - - - . . . - . . . - ~. .- ~ ~ - --, -- - - - -. --
I"DO I g own.1@t.0 0 to M 1 l
, ,, 500 <
#
- 5 Ba' 400 Pmas = 285 5 Se l_' a l_. t-63 60 I 8 8 s E meti-1,2310 0 f 4 l a m(i) 1310414 i t
! $30 500 400
)pman .1192 Sar '
400, Pmas
- 150 7 Bar I
i l-], t . ii ms . 1. i . a s ms '
,4 r i so0, -
m.
.p 100, ! 100, p; ; _ ..
3 3 3 B Figure 17. The development and venting of explosion in run E.m(I)-1/20/1/0.14. l 2000, iOOO,
.00 Pma. . ast i a, sec. Pma. . sits e.
T t
- 0 a ms T t
- 2 ms
( 800 & 600 f a 300, i 200-I. E g gjh 60 g E 40 40 20 20 g
-23 a p 10 cm) a ta to cm) :(a 10 cm) is 10 cm)
, E m0)-1,202 0,0 C7 E mpFt@2M C7 1000 1000, 800 Pmaa = $15.3 Bar 800 Pman
- 195 9 Bar to tJ ms -
t e t t ms la &m a- e0 o I e e -( a (Wu , c so , e ,
* @ N @
a m to em) a is 10 cm) a ta to cny a p 10 cm) Figure 18. The develepment and venting of explosion in run E.m(I)-1/20/2/0.07. 7-15
where crnissivity of fuel particles Ef dM dM Er absorptivity ofliquid droplets l F factor for interfacial momentum exchange 7 = a.(7)m + (1 - o di)(dM)#m (A.14) Fr fragmentation rate f, entrainment factor > ff enhancement factor of fragmentation rate (dM)# =ff4 l6t;,,// n, - nf l(pfpg)t/2fo, g= ,,f g grgwy j dt h specihe enthalpy (A.15) h', heat transfer coefficient with ff being an enhancement factor for fragmentation I 8pecific internal energy . rate, which can be varied to account for, specifically, the J 'V8Poration rate ! effect of thermal fragmentation. t length scale Equation (A.14) is a generalization of the single phase th, entrainment rate of microintraction fluid by a fragmentation rate utilised in the previous work (Yuen et fuel drop , al.,1992) with o. being the " void fraction" of the m-Huid n number of fuel particles (or liquid droplets) per defined by unit volume ; p pressure
#" 9/, eat transfer rate between fuel and vapor j
,_ , e r+ 8 (A.16)
Qf, heat transfer rate between fuel and liquid ; The " fragmentation time" and the instantaneous Bond Re, heat transfer coefficient between liquid and ! numbers for each phase are defined by the liquid /m-fluid interface ! R., heat transfer coefficient between the m-fluid and ; the liquid /m-fluid interface ! Bog = 3C,p4 l u. - ufif l, 7 T temperature i ti,s = 13.8 Bog-1/4 and g gim, ! (d.17) t; fragmentation time t For the mass transfer between the m-fluid and lig- t * ,,, minimum fragmentation time uid, the entrainment rate, E, is assumed to be directional u velocity ; proportional to the fragmentation rate in the calculations Greek i presented m this work. Specifically, a void fraction r
- a. " void fraction" of microinteraction fluid l E = f,F,E (A.18) Aff delay time for fragmentation .
#1 e volume fraction I
with f, being, for now, an empirical entrainment factor p microscopic density obtained from the SIGMA experiments, as described in p' macroscopic density ; Section 2. a surface tension or Stefan-Boltsrnan constant ; Subscripts - NOMENCLATURE a debris h Bo- Bond number f e lant (m-external fluid)
'"E * '"
m microinteraction fluid Y E fragmentation rate for a fuel drop entrainment rate uturatim prwtim e initial value I 1 l l 7-16
i i i i APPENDIX 8 1 DETAILED RESULTS OF SET II PREMIXING CALCULATIONS I l l l l l l j 8-1 1 I l
1
- APPENDIX 8 DETAILED RESULTS OF SET II PREMIXING CALCULATIONS l Each page of this appendix contains a plot of the fuel volume fraction and steam void fraction distribution at the time indicated. When the fuel is beginning to solidify, a second '
plot of the " liquid" fuel volume fraction and steam void fraction is shown on the right, to illustrate the degree of solidification. l In the plot of the total fuel volume fraction and steam void fraction, the darker lines are contours of the fuel volume fraction. They correspond to values of 0.01,0.02,0.03,0.04, 1 f 0.05,0.06 and 0.07. & same notation applies to the plot of the liquid fuel volume fraction and steam void fraction. l I h lighter lines are contours of the steam void fraction. hy correspond to values of 0.1,0.3,0.5,0.7 and 0.9. For clarity, the contour lines of the steam void fraction are not labelled. Note that the contours are shown starting from the line of the lowest specified value. l For example, in a plot of tott.1 fuel volume fraction in which only three contour lines are shown, they are lines corresponded to volume fractions of 0.01,0.03 and 0.05 respectively. W identification of runs for these figures is as follows: Run I.D. Page No. , PM(II)- 3/80/0.5 . . . . . . . . . . . . . . . . . . . 8-4 PM(II) - 3/0m.5 . . . . . . . . . . . . . . . . . . . . 8-25 PM(II)- 5/80/0.5 ................... 8-46 PM(II)- 5/20/0.5 ................... 8-75 8-3
I. f
; e z* e Q
s
!. U
! 5
- a i>
l 9 R O l N m b C i 2 ' a O
.- I_
J = t* 5 t E 0
- c 5 0
- E b
8-4
,e - -4,4-h-.4-.4 s,-.4 ,p,, 4 e-A $4__& *,++E---e-- -J,4J- 4 4 M* a4 Sam. x = -4% ar-J e- A w.A.4,_4 wm s, A..a m-a,e .
I i I l 1 5
~
2 l
\ l I l E
3 s s i l t e.
=
w I
. I 9
=
b i 71 j i i l 9 1 E j s l i W4 8-5
1 i
)
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= II I 1) i s
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l {1 > i
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E 3 l 5 1 i > b M i
=
v S I t E
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5 5 S l 1 l l r j s i 8-7
4 .- 4are-A A 4 w +__J.--*we - 4 er 4-4 iw" _4-A *-- .a .um , p., 2 4 ,e--.-- A 4 r i i H O l h E
- 1l J ll j .,
o l h i y i
~
W . l
=
v 2 n. 8 O h E s x -
)
E 5 N 2 8-8
, h . -wa. a.< 4- m 4. ----e- se.- a,ed.--4 %J, -- ,4 -_ - - , -ea 4 -4 A -d. _,
A. mmmA i t 1
- l e
! = >
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i, .
~
! E I s a l i t
=
v 2 A i l l l e o h E
=
- l E l 2
l i l l l i 8-9
i 8 2 e
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E i 1 Q + v
- n. -
E 5 1
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1 l 8-10 l
. - . . . . . , . . - . ~ - . - . _ - . . . - . . . . . . , . . . .
.7
. - .- --... , ~ . .
l l 2 d i e 5 1
=
1 l I E I s .1 C 2 n. f Id 8
=
s N 2 l i i a 5 l 8-11 1 l
- __ r
e 8 O O I
=
c s ,
% ?
3 em i+- l 2
- n. :
I i e I g '
~ ,
D 0 3 s T P w-
- 8-12
& -j ,__.p e4 , m_ .,,o_ $ __a 4 _ y 4 ,4._. a .4 .. - - 4 6 h _ p .a ut - ,&..,4... A ._m. c4Am a 44 ,. &a _ _
E a I a s i l it) 1
=
2 f 1 l l l l I 1 l
=
l l t! !
;s 1
a l l 1
-e.
N J 8-13 f 1 ._ .
__ - L - -. .. - L .Jw - 4 A .J A_a + .i I E O e E
=
1 .- t , , . 1 (C ( E
- s s i s3 l l
i 1 1 l i k I
=
w 2 n. 1 i 8 O R
=
I 1 1
~ms d-t n~
w E J s 5 i t 8 - 14
2 O 9 E a
= _
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6
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s t I t
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r I i i N
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s i j
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l 8-16 { ' l
. . - . - - , . . , - . , , - . , . . - , . . . . . . - - ~ .
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1 E I E , W c 2 n. r 1 E
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i I I I 8-17
'l i
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=
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I a : I ! 1 ! I 1 I v 2 c. I b l S 8-18 l
w ,swi t.--Je.4J. Ah eu4->w +- #- 4 _s,m dh--,_JW 24wam h s , hp 4 AsAAe M.-b-+h MN4WLh1& 4m- .Am=do.hhw.w'4..maJ-M d 2 6d4 s M-A .d-A A am 1%-.+m A J m A Aps,
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w __.y-- > _-+:9 4med-5A--4-aA-+ r4- Je 46 s4.- . - . +<Aa. -A,5-.,-e.4M45 .L.5. - l4-- A#o.e4.h J hb-.h. A S. 4 4 mmr,h -@.be.- wm- 4. 2-.e2,& A,s4_-. _.A& -.,p.A.u 1 a I. R a I i j i=i==EiE5it: V i _== J-E s m i C 2 n. Id 8 I l l NN @ 4 8-23
M - , - J- ,, -, a - - - - t .,u b -_ - A 4 S Y
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$ ! 7 ,
a i 2 3 .T b 8-24
i 1 i a E 8 u 3 E : 1
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E I t I J O m C 2 a O f
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1 1 a-25 ! 1 3 f J
'l l
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=
w 2 n. 1 6 9 I j D 2 i \ __. V i k a i I l t 8-27
a- a -y 2 e 4,u., 4 44,p4_-- _ te#-A.,_ .,44_MJ s -J,,4-.,.e ,,A,4 ,'--,d.- & e g,=-.h .rs As aAr,, A -u , -.aw*A. ...Agi 4 _eu S O 8 C
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d APPENDIX 9 DETAILED RESULTS OF SET II EXPLOSION CALCULATIONS 9-1
l APPENDIX 9 DETAILED RESULTS OF SET II EXPLOSION CALCULATIONS l Each page of this appendix contains a figure with a pressure distribution in a water pool j subjected to a steam explosion. Each figure is identified by the run code, as discussed in the body of the report, and the time elapsed since application of the trigger. For convenience, the maximum pressure on each figure is also given. The bottom, center of the pool is identified by the position of the trigger at t = 0. The numbers shown on the axis correspond to grid points of the computational mesh. In all runs of Set II the computational cells are 10 cm x 10 cm. For quick reference, the page index below can be utilized. l l Run I.D. Page No. E.m(II) - 3/80S.5S.65 . . . . . . . . . . . . . . . . . 9-4 E.m(II) - 3/04.54.65 . . . . . . . . . . . . . . . . . . 9-25 E.m(II) - 5/80/0.5/1.15 ................. 9-56 E.m(II) - 5/80S.5/1.15 (m) ............... 9-87 ! E.m(II) - 5/20/0.5/1.15 . . . . . . . . . . . . . . . . 9-118 l l l l i i I l l 9-3
E.m(ll)-3/80/0.5/0.65 ' i
- l i
j j 500' t = 0 ms Pmax = 100 Bar 400s
=
s300s e o y200s 100s 60 W 10 0 0 9-4
i f E.m(ll).3/8@.5/0.65 t 500s t = 0.4 ms Pmax = 478 Bar 400-
# f
@300s 1 t a
8200~ e a. { l 100s l O> , 60 40 60 , 50 ! 40 20 30 20 10 0 0 l t l i 9-5 l 1 t , w w- , . _
I l l E.m(ll)-3/80/0.5/0.65 . I l 500s t = 0.8 ms f l Pmax = 902.6 Bar , 400s l i e t
@300s ,
y f t l y200s , i p IE t 100s t 03 / \ .; ;:;;i-M-l:g _ 60
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l i I$i i D i V ?
$300,
, g/
e g g200s i 100, ' I i 0, 60 1 40
- l AO 20 30 l 29 a
i 1 1 9-7
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i l i E.m(ll)-3/80/0.5/0.65 1 500' t = 1.6 ms Pmax = 1047 Bar 400s /l 4 e 5300s s e # s b f y200s , E \Ifj. 100s t .
~--'e', , ,'", , ,
60
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40 -::;g); __ ::___ _ _;; ::;.(. 59 49 20 20 10 0 0 - 9-8 l
l l E.m(ll)-3/80/0.5/0.65 . I 500s t = 2 ms Pmax = 539.2 Bar
)
i e i
$300s -
c) 5 y200s ct 100s ' l
/
r 03 40 f 50 40 20 30 20 10 0 0 , i I t i I 9-9
i E.m(ll)-3/B0/0.5/0.65 ' i i ] 500' t = 2.4 ms I Pmax = 364.7 Bar 400s
$ 300, E }200, ex i
60 60 40 30 20 to s 0 , i 9-10
l i 1 i l l E.m(ll)-3/80/0.5/0.65 l 500' t = 2.8 ms Pmax = 301.9 Bar 400s , e
$300s i e
g i 200s 100, ' %, l / 0' 60 4 40 1 60
. 50 l 8 40 30 l 20 to
/ 0 0 - i m 1 o 9-1I {_ _ _ _ _ _
1 l I l I E.m(ll)-3/80/0.5/0.65 500s t = ?.2 ms Pr'1ax = 318.9 Bar 400s e $300s e 5 E,200s 100s 8 I s 4 i
\ -
0> 4 60 s 50 t 40 20 ', - r - , ~ ' 30 0 W~ o 0 0 l 9-12
I t l l l t E.m(ll)-3/80/0.5/0.65 - i 500' t = 3.6 ms ! j lax e 34g g 400, l
@300, l E f200,
( 100, l d I O' ( 60 L v , 40
'( .
60 50 / 40 / 20 . .
'- 30 20 to
/ 0 '0 , i 9-13
E.m(II)-3/80/0.5/0.65 ' 500' t = 4 ms Pmax = 217.6 Bar 400s
= $300s c>
y200s ic 100s i
, ,~ = '
0 '
, 50 40 20 20 10 0 0 -
9-14
i E.m(II)-3/80/0.5/0.65 ! l t I 500' t = 4.4 ms ! Pmax = 206.8 Bar l 400s I l ! c l l $300s 5 l N200s e o 100s i l 0> 60
\
l
- 40 Il llll'li.
l i T 60 l 50 l i , l 20 ', ,
, 30 20 Y 10 j 0 0 L
i l i l i 9-15 l l
l l l Em00-3/80/0.5/0.65 i l 500s t
- 4.8 ms Pmax = 253,7 gg, 400s c
$_300 s E 2 y200s et ' s 100s j 0> . 60 'N ( ^
,~ g9 40 x 50 ;
[f' il _w . 30 4o 20 ;--
~
=. 20 j9 6
9-16
I l l l l l E.m(ll)-3/80/0.5/0.65 1 r 500' t = 5.2 ms Pmax = 298.4 Bar l 400s l =
$300s l
2 a l M200s 2 c. 100s , f f U
~
6 j l' . l, * ' z h5hiti;;._ __ 40
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20 39 j 0 0 - l 1 I i 9-17
l m E.m(ll)-3/80/0.5/0.65 500s \ t = 5.6 ms Pmax = 221.2 gar 400s = $300s o 5 y200s E 100, t
' \ i 0, t 60 40 .
~ 60 l 20
~ ~
Nr W" -s
= '
30 40 I
'F '01 O O l
9-18
E.m(ll)-3/80/0.5/0.65 , 500' t = 6 ms Pmax = 139.4 Bar 400s = $300s y200s ct 100s 60 0 . i M 9-19
E.m(ll)-3/80/0.5/0.65 . 500' t = 6.4 ms Pmax = 70.82 Bar 400s e 5300s y200s ct 100s A 0, m 60 C 40
- 60
~ 50 20 W "
20 30
-W 10 0 0 9-20
l l I 1 i l E.m(ll)-3/80/0.5/0.65 l 500 1 t = 6.8 ms r Pmax = 39.01 Bar ' 1 400s I i C
$300s I
l 5 i y200s ic : l l 100s
.A 40 60 W 10 0 0 -
l l I l l i i l 4 9-21
l l E.m(ll)-3/80/0.5/0.65 l 500' t = 7.2 ms Pmax = 81.13 Bar 400s e
- 5300, e
a y200s ct 100s 40 60 W 10 0 0 1 9-22
E.m(ll)-3/80/0.5/0.65 500' t = 7.6 ms Pmax = 44.1 Bar 400s e
@300s y200s a
100s 4 h
"' Mem%
0> _ 60 I 40 50 40 20
=
30 W 10 0 0 . 9-23
f i E.m(ll)-3/80/0.5/0.65 500s t = 8 ms Pmax = 29.34 Bar e d300s 4 b i y200s i et 100s 0> 60 m..0 o , 9-24
1 1 1 l 4 4 d I a J l d l E.m(ll)-3/0/0.5/0.65 i i 500s Pmax = 100 Bar 400s t = 0 ms eto m
- 300-G w
U
$200-w b
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9-25
i E.m(ll)-3/0/0.5M.65 l 500s Pmax = 285.1 Bar i l 400' t = 0.4 ms l C , m - m
~ 300- I Q
w
)
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l . 20 a I i l 9-26
l l 4 l l i 1 E.rr.(ll)-3/0/0.5/0.65
)
1 500s ; i i Pmax = 2364 Bar
~
400s t = 0.8 ms e to E300- ' E l a i , , l 8200~ l E
- o. i 100s I I p
l ..
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20 ^i.i:;;;;;;;3;;;i::. gg l i l l l 1 9-27
l E.m(II).3mo,g 500, , l
**X = 3227 Bar '
400, t=12ms e m 6300, 8 a , f200, l a , i 100, ; g
' .y:q::; _
0> , .:;iii;7:fi:
^ :: ;
-- :;i:::.
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9-28 1 - _
l E.m(ll)-3/0/0.5A).65 . t i 500, i
*BX = 963.9 gg, 'i i
400 1.6 ms )' o en . 8300, ! 2 ,
- o ni200, E
[ , i 100, y / 0, %:)?;::::: 60 : . ::. : I
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20 l l' l l 4 4 9-29
E.m(II)-atojo,5py,gg , 500s
/
Pmax = 1880 Bar 400' t = 2 ms e , tu 6.300, h l O )' i
$ l .
}
8200~ S 8 I a. 100s 0:, / 60 ' I 40 40 20 20 I i i
)
9-30
l l l 1 1 1 E.m(ll)-3/0/0.5/0.65 500s / Pmau & t 400, % mg ~ i e j l gg0o, /
' 200, /l l )'
l I ( 100, .~. s'hp'_;;
"-. /
~.
Os /
/f
- 60 ' L
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~
20 l l l 1 l I 9-31 l
1 i E.m(ll)-3/0/0.5/0.65 rj i l 500s Pmax = 775.6 Bar 400' t = 2.8 ms / e \' tu 8300s ' e a 8200- i e
- a. s 100, I 0,
,y H=
S J , 1
' 60
" 40 20 20 WED 9-32
E.m(ll)-3/0/0.5/0.65 ' 500s { Pmax = 830.9 Bar -' 400- = 3.2 ms ' E l @ 300- 3 } , ! I l 8200s 0 sue 9-33
E.m(ll)-3/0/0.5/0.65 500s Pmax = 470.7 Bar 400s t = 3.6 ms @300s ( h200s f 60 M 9-34 l l
! l E.m(ll)-3/0/0.5/0.65 l i l 500s l Pmax = 497.3 Bar l , 400- t = 4 ms l 8.300-co ) i l 55 [ n200s 40 60 9-35
E.m(ll)-3/0/0.5/0.65 ' 500s Pmax = 507.7 Bar 400s t = 4.4 ms j ! e t $300s
- s h200s I e \ \
100s ; \hfl i I l I i 0>s b 60 i kl /' ;. 40 . 60
.i* -
40 20 r _ y 20 9-36
E.m(ll)-3/0/0.5A).65 f 500s l Pmax = 477 Bar 400' t = 4.8 ms
$300-l 8200-60
{- 9-37
.. _. . .. . _. ..-. =_ .- . . . .- . . . _ _ . _ . . - ..- - - . .-
*00WO/0.Sm.gg 500, Pmag 400, I e S g ml51 Ba, g '
e o / 200, 100,
;j f4 /
03 60 ' g 60 40 40 20 20 / 9-38
I 1 l l E.m(II)-3/0/0.5/0.65 . t j 500s ! Pmax = 627 Bar 400s t = 5.6 ms e , m i m300s - 2 ; ,
$200s '
w .
~
l 100s P , l ' \ I l l 03 - l ! 60 4 40 60 l 40 20 20 I - l I ! l t i P f 9-39
l I E.m(ll)-3/0/0.5X).65 - l 500s Pmax = 445.3 Bar 400s t = 6 ms e i $300, e ., a , N 200,. Y 8 ' 100, i 0, : 60 inh
- s-;:: :www ,
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l , 1 l E.m(ll)-3/0/0.5/0.65 l l l l 500s ! Pmax = 332.7 Bar l 400s t = 6.4 ms l c ! m 1 l m 300s ' E
" 1 9
8200s l w b l
\
l 100s -
))
40 60 9 1 l 9-41
I i I f i l E.m(ll)-3/0/0.5/0.65 l l 1 , l l 500s Pmax = 388.9 Bar 400s t = 6.8 ms ecc E300s F e a
$200s e
Q- 1 100s - l, , J l 60 40 60 40 l 20 i- , 20 i j 9-42
h E.m(ll)-3/0/0.5/0.65 , 500s i Pmax = 215.6 Bar I 400s t = 7.2 ms ! e m E300s e a
$200s e ,
- n. L 100, On 60 40 20 t
9-43
-~
l l
}
E.m(ll)-3/0/0.5/0.65 1 500s Pmax = 124.9 Bar 400s t = 7.6 ms E @.300s !$200s e a. 100s 6 .s. l 9-44
I I I E.m(ll)-3/0/0.5/0.65 500s Pmax = 86.74 Bar 400- t = 8 ms e cts
@300s E
a l 8200-E c. 100s g _ - _2 03 60 mg - - = -
=' 60 40 ~.
=- -
~
a 40 ; 20 h -- ~- 7 20 l w l I 1 1 9-45
E.m(ll)-3/0/0.5/0.65 500s Pmax = 69.46 Bar 400s t = 8.4 ms , m E300s 2 a <
$200s e
a. 100s
' l 6 _
40 -
-7 60
- 40 Y
20 20 l 9-46
1 l L E.m(ll)-3/0/0.5/0.65 l l l E Jos l Pmax = 56.69 Bar 400- t = 8.8 ms i e ! cts
- 9.300s
- e l 5 8200s e
c. 100s sA 40 '60 l
~_7 20 f
4 9-47
4 1 E.m(ll)-3/0/0.5/0.65 500s ; l Pmax = 131.8 Bar 400s t = 9.2 ms e cc 59.300s e a
$200s e
n. 100s l f
-"E A 0>
6 "" % 60 40
)
~
60 20 ' 1 l 1 9-48
i i l l l l l l i I l l l E.m(ll)-3/0/0.5/0.65 l i l l i l 500s Pmax = 41.59 Bar l 400s t = 9.6 ms e cc
@.300-8 m
l2200s e
- c. .
100-40 60 l l I ? I 9-49 l
1 1 1 I E.m(ll)-3/0/0.5/0.65 500s Pmax = 60.08 Bar 400' t = 10 ms e cc 50300-e a M200s e n. 100s
#, _LA 0>
60 __w ~ 5TA ~A
} l ' = --- ' -
40 20 __'"W . 20 6 9-50
E.m(ll).3/0/0.5A).65 500-Pmax = 57.09 Bar l 400' t = 10.4 ms - e , (U I E300s
- l s i 8200s 8
a. 100s 60 i 9-51
1 i E.m(ll)-3/0/0.5/0.65 500s i Pmax = 38.78 Bar 400' t = 10.8 ms i i e CU 9300s ! e a 8200s e
- a. i 100s A
0> m 60 l 9-52
i l l .i i E.m(ll)-3/0/0.5/0.65 i l i i i l 500s Pmax = 42.46 Bar 400~ t = 11.2 ms e m ' i E300s
- E o !
4 - 8200~ e n. 100s (
, 0> --
j 60 1 40 - 60 i
% 40 20 x -
- -- 20 9-53
1 l 1 l l 4 l E.m(ll)-3/0/0.5/0.65 i 1 500~ Pmax = 54.42 Bar 400- t = 11.6 ms e (U m 300s e a M200s e. a. 100s 4 '60 l I 9-54
. _ _ _ _ _ - - - _ . .. _ _ _ . _ _ . . _ _ _ . _ _ _ _ _ _ _ . _ ~ . . _ _ . _ _ _ . _ _ _ _ . . . _ _ _ .
1 j ' 4 i. F j E.m(ll)-3/0/0.5/0.65 4 4 l 1 1 i 500s Pmax = 43.03 Bar l l 400- t = 12 ms 4 e
- c5 1
E300s
- e a
Fn200s e . i 3 o_ i
. 100s I
60 I 9-55 L.- - -
I E 1 l E.m(II)-5/80/0.5/1.15 500s 1 Pmax = 100 Bar 400s t = 0 ms e cu l Eq.300 s e u ) 8200s a w b
^ ,;,,,sall,b ^:i 1'~ lOfi::. .
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. ~ ~*!!!?)Q:ft:4lllll='*^20 9-56
E.m(ll)-5/80/0.5/1.15 500s Pmax = 656 Bar 400- t = 0.4 ms E E300s j e
- s 8200s e
n. 100s 0, 60 40 60 40 20 20 6 9-57
i E.m(ll)-5/80/0.5/1.15 a tr 500- ; , Pmax = 922.6 Bar 400' t = 0.8 ms . S I
/
E300- n 200-c t
\ j 0> -
60 40 60 40 20-20 6 I 9-58
E.m00-5/80/0.5/1.15 e
)
500' \ .'.
\
Pmax = 919.6 Bar it 400- 15 1 2 ** 3' 300-e 3 -, I g200-e { \
- c. .,
100- 9
, t 0> '
60 , 40 40 20 20 h 9-59
1 l l i E.m(ll)-5/80/0.5/1.15 t 500s I I Pmax = 810.8 Ba! l 4gg' t = 1.6 ms s' i 4 cCU ' g E300, fjN )jf. ,j ;jf E - j 2
' \ I M200s t
\ I j e '
I f a. i 100s 1 I '
\
\
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49
-: :gj97jlliiv:::-- pg 9-60
-. 4 _ A i-.5 . 43 a _% 2m-_ a .h .a 4 A A.hs.a_.w____ha_A4 .4 ,_a J.J m.s 4g _4._.._ 4-.4 ,_ X. _ 3M ,A_ , _.s..__
l t i E.m(ll)-5/80/0.5/1.15 : l 500s Pmax ,490 Bar - 400, ta2 c , l) l kS00, e , , m S00s / i 100, !
$Ues Os ~'
~:
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60 .O . 1 i iI--[.:[-$r:::.;.,. 40
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20 *x i$jl:lj;)yq.;.; -::m :n;; x :::::::;:::i.:.
- m:-s::::::;::
-- - .. _x:;
4 J 9-61 4
E.m(ll)-5/80/0.5/1.15 500s 6 Pmax = :199.5 Bar 400s t = 2 4 it.s e c3 E300s T
/* '
e ' a , 8200s e
- n. ,
100s 1 : O, 60 , c{ am f l4:::..
;:: gy;;g;j;i
;i;;illtiii:jg:l~p;:. 60 i :-
40 llll$15!!"~~~
~~~
40 20 ~*!UU..i!.!!!!!'s:.:::::::.N.
- : :.:.: '!gn 9-62
l l l l E.m(ll)-5/80/0.5/1.15 500s Pmax = 371.9 Bar 400s t = 2.8 ms S / 8300,
/
e a y200~ E luu, . ,g s i 0>
\ ,
i
, J
' -.M
. ' l 60 40 --
* ~
#' 740 20 ' ,
=
f 9-63
E.m(ll)-5/80/0.5/1.15 500s Pmax = 413.1 Bar 400- t = 3.2 ms 300~ "uiiq 00 [ 6 \ # 4 - y 60 40 4 --
' 40 20 7 20 9
9-64
I E.m(ll)-5/80/0.5/1.15 500s l ' Pmax = 416.4 Bar l 400' t = 3.6 ms 8 "in l~ 8300- ; e ' C 200s j 100s > 0> 60 N
' M 60 40
' 40 20 t..
20 i 9-65
E.m(ll)-5/80/0.5/1.15 500-Pmax = 403.6 Bar 400- t = 4 ms W n I m.300 - 'in,,".i,,, i / 2 s Po200s ' (
- 9. l }
o_ I 100s I \,
} p 6 \ \ ( -
='60 40' \
E# 40 2d" y' kb 9-66
I t l 1 E.m(ll)-5/80/0.5/1.15 l l 1 500s Pmax = 345.2 Bar 400' t = 4.4 ms e l N 8.300s 'li l e I D N l $200s 1 e l o. ( l 100s 4 l r i L
' I 0>
, 60 N \ t m l . " 40
,- - 60
,- - 40 20 . y
- . % ,- 20 1
l a 9-67
E.m(ll)-5/80/0.5/1.15 500s Pmax = 453.8 Bar 400s t = 4.8 ms m ' E300-8 h a ' 8200s ,
, , j 2 ,
a , q ( 100~ s( N 6 \ t 4 { 40
\
~ y ?"60 40 20
-p 7 '20 9-68
l l l E.m(ll)-5/80/0.5/1.15 l 500s . Pmax = 697.3 Bai .1 l 400s t = 5.2 ms h ( , W hj m 300s J sI e h f l 5 ) q[' p,1 8200s e I s ,
)
l l 100s s s
- f t j j
l 0> \ 60 \ , 4 J '-- 60 40 l , 40 l 20 _- 20 9-69
r
.y l
l l l l I E.m(II)-5/80/0.5/1.15
\
500s Pmax = 618.6 Bar 400- t = 5.6 ms j j to 8300s - ( , 1 I ? a , \ 'f
/
$200s n i h ; e f >
- a. ~
- a. Q \ \
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100s '. 1
\
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60 N ' 40 f 60
\ 40 20
_7 20-y 9-70
I l I l E.m(ll)-5/80/0.5/1.15 500s Pmax = 357.3 Bar 400s t = 6 ms e $300- j- # p 1 k , V $200~ ' e l l \
- n. i '
)i; <
100s l i . L nniil
~
( J l 0 e i 60 N ' 40 m ci / [ 60
' 40 20 g#@>lV~20 ..
9-71
~\
E.m(ll)-5/80/0.5/1.15 500s Pmax = 402.9 Bar 400- t = 6.4 ms W ! E300s / f e
/
f200s , 9-72 l l
l I l I 1 l E.m(ll)-5/80/0.5/1.15 l l l l 500s Pmax = 312.3 Bar 400s t = 6.8 ms m 300s e a . 8200s i e I
- a. l 100s 0> l 1
60
~
' ' 60 40 -
, 40 20 l 20 i l l l
l s 9-73
I 1 I E.m(ll)-5/80/0.5/1.15 500s Pmax = 333.3 Bar 400' t = 7.2 ms e
$300s 2 $200s e
o. 60 my ~ 20 9-74
t I l \ i E.m(ll)-5/80/0.5/1.15 t i i 500s Pmax = 381.5 Bar 400s t = 7.6 ms e m m
- 300-2 l c l 8200s e
w i 1 100- ::s?::
. .:: ::. : ;:: :::?:.
3 .
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i
E.m(ll)-980/0.5/1.15 500s Pmax = 444.5 Bar s 400s t = 8 ms D ; m E9,300 s j e
~
- s
, Q200s e n. 60 m 9-76
l 1 i s 4 J 4 l 4 l l 1 4 k i i i j E.m(ll)-5/80/0.5/1.15 l l s I i I 1 i i 1 : j 500s I Pmax = 137.1 Bar
- 400s t = 8.4 ms 1 C 1 m 3
m
- 300s J w "3
8 200s w b . 100s ,
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E.m(ll)-5/80/0.5/1.15 500s Pmax = 280.3 Bar 400- t = 8.8 ms e j $.300~ l l e l l $200-1 e 1
- 1 1 7
40 60 9-78
E.m(ll)-5/80/0.5/1.15 I 500s Pmax = 314.6 Bar 400' t = 9.2 ms e (U m300~ w ,,
)
M200-ew 100s : .i:!:: r:.
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1 i E.m(ll)-5/80/0.5/1.15 ! 500s 1 Pmax = 316.2 Bar 400' t = 9.6 ms l
- e <
ce 9300s ) e a !
$200s t e
- n. "
100- g 0> 1 gy .~; 60 _
- 60 40
~_s 20 9-80
l E.m(ll)-5/80/0.5/1.15 l 500s l Pmax = 87.4 Bar 400s t = 10 ms e to 9.300s e a
$200s e ;
o. 100s g_ 0> ~.- ~
'60 40 --
20 i 6 l 1 .$ 9-81
4 '4 M 4 4 4 1 4- .i i i. t 4 4 E m(II)-5/80/0.5/1.15 i
- t i
4 1 i 500-1 Pmax = 218.9 Bar j 400' t = 10.4 ms
- c j (U 1
m300s d @ w k ) i; toOnn t.-Uvw l' w i CL 4 100s s . . .::5?idi! !::.
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i l E.m(ll)-5/80/0.5/1.15 l l l i 500s , i i ! Pmax = 223.6 Bar 400s t = 10.8 ms ! ! C m E300s e 1 5 l
$200s l e ,
- a. l l
100s -
.: go 20 20 i
i l l l 4 i i i i 9-83 L__________. _. ,- - . ._. . - . , - -
J 1 .i l 4 1 a i. j E.m(ll)-5/80/0.5/1.15 l-4 i i l 500s ; Pmax := 53.77 Bar i 400s t = 11.2 ms i ! _ i h l @ 300s
- e ,
, a l j $200s )
, e a. 4 100s ^ 1-l 0> . - ! 60 l 60 40 40 20 20 9-84 ! l
W 1 E.m(ll)-5/80/0.5/1.15 500s Pmax = 192.9 Bar l 400' t = 11.6 ms ' = I i cc E300s 2 m - 8200s e . 100s 6 1 1 i 9-85 i
l i l l l l Em(ll)-5/80/0.5/1.15 500-Pmax = 67.76 Bar 400- t = 12 ms j @,300-E . o l 8200-e n. 100-60 9-86
i i i 6 i 1 l
- E.m(ll)-5/80/0.5/1.15 (m) 1 i
1 e I l 500s ! I Pmax = 100 Bar : 400- t = 0 ms i e(V ! 9.300s ; 6 ' c
$200~ 3 e t n.
100- , l t 03 f 60 40 60 40 l 20 I 20 i l 9-87
4 4 i f i l' i
- l 2
l E.m(ll)-5/80/0.5/1.15 (m) i i i 500s 4 j Pmax = 196.4 Bar i 400' t = 0.4 ms 1 - E l @.,300s i e
- o <
- 8200s )
> e )
1 i j 100s fI 1 i i t
- 0>
j 60 40 60 - 40 20 . 1 1 20 t a
)
i,
~
1 i r i ! t i 4 E i A 4 I , I 9-88 1
I J
- )
E.m(II)-5/80/0.5/1.15 (m) ; 1 500s l l' max = 404 Bar l j 400- t = 0.8 ms !< t ece , l E300s d ! e 1 m s i $200s l 8 u- } i 100s l t -l 0> ! 60 1 60 40 40 20 20 l 9-89 l
E.m(ll)-5/80/0.5/1.15 (m) ; L 500-400-Pmax = 687.2 Bar t = 1.2 ms [ I e e . ED.300s . i ! e ' t 8200- ! e (' l 100~ - .-~:: ;: ;;;: . .
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i i I l l 9-90
, - _ . - . - -- - . - - - ~ -
- I i
j -i j ! i i i 1 i E.m(ll)-5/80/0.5/1.15 (m) - l 'y ! 8
/
l 500~ f >{ I Pmax = 861.8 Bar I 400' t = 1,6 ms f j m h, i 8.300s 8 ) i l, a I, i 8200s i i e i
- a. t 100- i
., 1 J 0> i l
1 60 N i 40 60 40 20 I 20 J 9-91 i
l l l E,m(ll)-5/80/0.5/1.15 (m) , 4 500s Pmax = 597.3 Bar 400' t = 2 ms E '
- q. ,
E300s g ' y \\ $200s \ , e , 1 100s f i t , t 64 I f 03 60 40 , 60 40 20 , 20 i I 9-92
E.m(ll)-5/80/0.5/1.15 (m) 500s Pmax = 402.4 Bar 400~ t = 2.4 ms e $.300s e $200~ e ( 100- '
,jg, .
.:;lif' .;- ;::;;; .
0> 'd/
- 60 --l V;:.~ 7;; .
y . ;: ;.;;;;;:: ::: (')
. 99 40 .
- f. - 49 20 ~ i:i ::? I:)/l ::;: .i--:::-' 2g 9-93
{ i i E.m(II)-5/80/0.5/1.15 (m) i 500s Pmax = 298.6 Bar 400s t = 2.8 ms e i m E300-E l 2 12200s - 1 y _ 1< : -
~~'*' # '
100s j j
. :s . \
~ . . .
0> .g:::: ::._ . l IIl kb. . _ -. - -;/-f: 40 .: ___ . , 49 20 ~ ~ Y. .:I'<:: , ... g9 gum l i l 9-94
b E.m(ll)-5/80/0.5/1.15 (m) 500s ' Pmax = 263.5 Bar 400- t = 3.2 ms I E300- r E 2 f 8200-e ct 100s 6 \ s
' - 60 40 -
r' 40 20 - I 9-95 l l I
E.m(ll)-5/80/0.5/1.15 (m) 1 500s Pmax = 220 Bar 400' t = 3.6 ms
=
to E300s T. D
!2200s e
n. 100s W 0> 60 \ .~ 40 _
- 60
_ -- 40 20 , '
- _ - - 20 9-96
i E.m(II)-580/0.5/1.15 (m) 500s Pmax = 199.2 Bar 400s t = 4 ms e m
- E300s
- e a
$200s e
- c. -
100s "'illll M 6 \ { u 60 40 ~- " 20 I 9-97
E.m(ll)-5/80/0.5/1.15 (m) 500- 1 Pmax = 220.6 Bar 400s t = 4.4 ms E @300s $200s ? c4%\ 100-6 \ 40 60 2b' NO 20 9-98
j E.m(II)-5/80/0.5/1.15 (m) l 500s Pmax = 251.2 Bar 400s t = 4.8 ms S E300s 2 2 200s
,,q m
100s , s i e8"N i 40 40 20 - 7_ - 2g 9-99
E.m(ll)-5/80/0.5/1.15 (m) 500s Pmax = 271.4 Bar 400s t = 5.2 ms E m 300s e : 2 8200s e
- a. ,
100s - 0> 60 N 40 *. 60 40 20 20 I i l 9-100
i a 1, 2 , . t 1 1 r a \. a t I
- E.m(ll)-5/80/0.5/1.15 (m) ,
1 1 . 500- : l Pmax = 244.5 Bar , j 400s t = 5.6 ms i 4 i m 300s -- 4 ! G w D r i- $200s ; i W w l k e k
- 100s 6 \
40 60 r
.... 40
- 20
- 20- .
Y , r 1 2 -. 0 4 9-101
t r E.m(ll)-5/80/0.5/1.15 (m) l 500s Pmax = 214.8 Bar 400s t = 6 ms ! e
- m l @.300s
! e l Ei 12200s e n. 100s 4;l { 0> i 60 N ! 60
. 40 20 29 9-102 '
i 1 l i E.m(ll)-5/80/0.5/1.15 (m) 500s Pmax = 176.3 Bar i 400s t = 6.4 ms e tu
; E300s 8
- o 8200s E
n. 100s asi% 6
\. I 60 40 -
" 40 20 20 f
9-103
i < l l l i E.m(ll)-5/80/0.5/1.15 (m) l l l 500s Pmax = 133.1 Bar 400' t = 6.8 ms e i
$300s 2
2 12200s
" 'IlIIIIIII 6
l 9-104
1 i E.m(ll)-5/80/0.5/1.15 (m) 500s
- Pmax = 121.9 Bar 400- t = 7.2 ms i e m
9.300s : e a
$200s e
n. 100s 6 llll 40 ' 60
, 40 20 --p w 20 l
9-105
1 E.m(ll)-5/80/0.5/1.15 (m) 500~ l Pmax = 136.7 Bar 400~ t = 7.6 ms e
$300~ $ l n200~
e l 60 N
- cv 20 9-106 l 1
1 4
)
i 4 d E.m(ll)-5/80/0.5/1.15 (m) - i i 4 l 500s
- Pmax = 343.4 Bar 400- t = 8 ms c .
cts E9.300-a
$200s '
e o.
+
100s ] _
-~
Od b 80
- 60 40 =-
40
' 20 u 20 i
e l a a 9-107
E.m(ll)-5/80/0.5/1.15 (m) 500s Pmax = 270.9 Bar 400s t = 8.4 ms S 9.300s 8200s e h] i b ' 6 I t 9-108
I l 4 f E.m(ll)-5/80/0.5/1.15 (m) : 500s Pmax = 362.4 Bar 400s t = 8.8 ms - m I 501300-a) ! s ; 12200-2 l
- c. :
' i 100s i
l 0> 60 ; i 60 40 40 I 20 20 l l l 9-109
l E.m(ll)-5/80/0.5/1.15 (m) ! 500s Pmax = 296.2 Bar A00' t = 9.2 ms i C et! E300s e t?200~ e Q-100s 60 l w 20 l l l l I 9-110
( M i i s
- 1 4 l
? ,i l l W i I l E.m(ll)-5/80/0.5/1.15 (m) i i e i L 500s i Pmax = 128 Bar
- 400s t = 9.6 ms L
1 eto ! m
- 300s
,t e 1 1, 2 ' i 8200s e > v w
- a. l s
100s . o..
._ ; j i 'L ^:L l -; _ ._ :: : i::~!~?::
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t 4 E.m(ll) 5/80/0.5/1.15 (m) i 500s . Pmax = 121.3 Bar ; 400' t = 10 ms j ect , E300-2 a
?200~
e n. 100s p g- . 60 40 ,
'y -; 40 20 v 7 20 w
9-112
4 1 1 1 1 j ' a ) 4 i . j E.m(ll)-5/80/0.5/1.15 (m) J i i 5 b t
- 500s Pmax = 108.1 Bar
!, 400s t = 10.4 ms 6
- e to
- m 300-m .
8200s e c.
- 100, . . ::
3: :: . j . ., z. . l' 0> h. ::-::$%.. v.. I . J?DI::'i;:::.. i 60 ..::::? 862: :::;;i;;;i;; -fi-::1.i: : i! : ;fi:li: .
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i 4 I i - i j I t i 0 t I i 4 9-I13
' l 4 1 i I ? ! l 4 l 1 l j E.m(ll)-5/80/0.5/1.15 (m) l 4 1 4 500s Pmax = 38.37 Bar 400s t = 10.8 ms c3 m 300s e a 8200s e n. 100s 60 I 9-114
4 i i 1 i s j i l E.m(ll)-5/80/0.5/1.15 (m) l 1 i 1 1 i j 500s a Pmax = 264 Bar i 400s t = 11.2 ms ! i m j @,.300s e a , 8200~
- i. e :
i a. l 100s j i i i >
- 0::. i
- 60 l
! 60 l 40 i
- 40 i 20 ,
i 20 . 4 ! I ! I l l i t . I l i i 4 I 4 a 9-115 i i 4
. . - , _ _ , .- _ .-e .. . . - . - _ - , _ -
J e i i ! J s ! i ! i . j t 4 I . E.m(ll)-5/80/0.5/1.15 (m) l i 500s Pmax = 42.36 Bar 400- t = 11.6 ms , tu CD
- 300s u
O ' 8200-e i 6 100- ..
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i i i l E.m(ll)-5/80/0.5/1.15 (m) l !. 500s j Pmax = 38.26 Bar
- 400s t = 12 ms i -
! E300s ! i 2 l 3 a .
- 8200s
2 i a- i
- 100s l i l 3 0>
60 \ 60 i 40 l 40 > 20 i l 20 i .
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} l 1 4 9-117 l
i E.m(ll)-5/20/0.5/1.15 l 500' t = 0 ms Pmax = 100 Bar 400s e $300s N200s e n. 60 l l I 9-118
d 1 i j i , j E.m(ll)-5/20/0.5/1.15 l t i i 1 j 500 ' t = 0.4 ms j Pmax = 354.9 Bar 400s O i S300s i o , ! E200s l
- e u-i l 100s
- O>
- 60 50
' 40 60 50 l 30 40 20 30 I- 20 10 10 i - [ l I 1 i e 4 4 i a' 9-119
I t i I I I I 1 l
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, (
400s l 6 j S300s e f a " , y200s E hh ? \ 100s > hsh 4;h;'/.I;./7;;:/i:I:~:. ) .. 03 ll ; li L ::L :L :l:l:iii ::..
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9-121
J, J 1 il 5 1 i E.m(llF5/20/0.5/1.15 l 1 l j < ' \ [ ! h I 1 J 500s 6 , I t = 1.6 ms Pmax = 1956 Bar / I i 1 1 ' i 400s I 1 \ , r 6 lj w l ! 5300s 't i V Il l j 2. a ; l y200s i t ( \ 100s y ) :iii ?::. f .
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30 to-aiglgliiilltii:::^ 20
~~
':i i 10 9-122 :
l l I E.m(ll)-5/20/0.5/1.15
- q r ij i
4 l 4 500' t = 2 ms Pmax = 1491 Bar j t / l , 400s ' I
$300s I
t . 1 ^
% l @200s E
l, 100s , i 0, i
- =-
N 60 40 ?- - 60 30 f 0 30 7I "yg 20 10 9-123
E.m(ll)-5/20/0.5/1.15 h( l [t 500'l t = 2.4 ms
)-
i Pmax = 1594 Bar , l 400s i f l e
$300s f
y200s ,.. i 100, z. 0> ' 60 i ......:. .: .___ 50 m- : ::. 40 l -' 00 60 30 - _::: 5hh5ES"4n~ 20 . - 30 0 t o ~ :!::Y:'*=' 3 9 9-124 - - )
E.m(ll)-5/20/0.5/1.15 i 500' t = 2.8 ms jl Pmax = 1011 Bar 400s - O co300s e 200s ' d i f t i 100s ' f l} I y 6 \50 \ f * ( f f 60 40' "
) '
30 40 20 "- 10
@ ~ C G "~20 W 10 9-125 l
E.m(II)-5/20/0.5/1.15 e 500' t = 3.2 ms Pmax = 576.4 Bar 400-l -= h,300s , E s 8200s f 'I 2 1 -( 100s )
'%g jj ,
' ~'
03 )
/ I s 60 50h } ,
( 60 40
, 5 - ,
_ l l ,h#-50 l
.L 30 mi er
, 40 20 30 20 10
~
~' j o 1 1
I l 9-126
E.m(ll)-5/20/0.5/1.15 500' t = 3.6 ms Pmax = 393.4 Bar 400s c s . (o" 300 s g nMI'"Ill n
?200s i e \
- o. ,
\
100s i
\
6 \50 \ . 40
\
4
} m -
50 30' 40 20' w' 30 20 10 'W 10 M 9-127
E.m(II)-5/20/0.5/1.15 ; i l 500' t = 4 ms i Pmax = 395 Bar l 400s g 300s y oilQlj lIll!!!! y200s a. 100s ,
\
6 \
# 60 4b ,
l 20 7 ' '30 10' 10
)
i 9-128 l
I E.m(ll)-5/20/0.5/1.15 500' t = 4.4 ms Pmax = 436.3 Bar 400s e , s300s e 'l," j 3 - t I, g
$200s l,
2 t f' a.
\ \ '
t 100s '
\
( !
\
6 \50 \ s -
# 60 40 , s
-p' 50 30 40 20 "' 30
# '20 10' W '10 i
9-129
E.m(II)-5/20/0.5/t.15 i 500 ' t 4.8 ms Pmax - 398.8 Bar 400-g300-2 ,, b ' o 101 4 8200~ e ' $ s '! t 1
\
100~ (. s 1 6
's 6 >\ 50 .
s 40 s 60 s 50 30 ',.. 40 30 20 ' 20 10 10 l l i 9-130
E.m(ll)-5/20/0.5/1.15 500' t = 5.2 ms ( Pmax = 452.3 Bar e I j
$300s 1 200s
<. 1 ; ( ( ;
1=~ 1
;f l p4
,p 50 ,
\
40 60 50 30
' 40 20 20 10' 10 9-131
E.m(ll)-5/20/0.5/1.15 500' t = 5.6 ms Pmax = 389.8 Bar 400s c ' $300s N 5 . i q s 5 - $200s "" i g l
$ i !
100s i . ( '
)
( < N ] j( . 6 \50 ,
*<' 60 40 ,
50 30 , 40 20 30 1 20 ; 10 ' 10 9-132
E.m(ll)-5/20/0.5/1.15 500' t = 6 ms Pmax = 422.9 Bar 400s
=
$300- I l .,
[ '
\
7 2
')
y200s e I k [q E ' i j . i 1, 100s i, f q r 03 s r 60 50h .' 40 ~ 60 50 30 ' 40 20 20 10 10 m I 9-133
l l E.m(II)-5/20/0.5/1.15 i i 500' t = 6.4 ms Pmax = 398.3 Bar 400s j = g300s J ) , 5 V \ y200s ( {
]f), -
I n
)
100s
)!
ff " ,
\ )
I h 6 h, 50 - -. 60 40 - s < 50 l 30 ' ' 40 20 - 30 ' 20 10 # 10 9-134
? E.m(ll)-5/20/0.5/1.15 - 500' t = 6.8 ms Pmax = 352.1 Bar 400s e h s E300s ( b i 200s yi , L
)
0-l
)
I 100s u,, . h \ 0 i N 60 50\ ' ____-- 60 40 , 50 20' 30 g 10 10 e 9-135
l E.m(II)-5/20/0.5/1.15 - i 500' t = 7.2 ms Pmax = 1259 Bar 400s e $300s ,, ? 8 t \' f 10 ~- 10 l j 9-136 ,
E.m(ll)-5/20/0.5/1.15 500' t = 7.6 ms Pmax = 1075 Bar 400s
$300s 'f 6 s 10 -# 10 l
9-137 i
.I E.m(ll)-5/20/0.5/1.15 .
'H p4
/
) \
500' t = 8 ms Pmax = 802.8 Bar , -, 400s g i t E.300s e}}