ML20236S798
| ML20236S798 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 06/30/1996 |
| From: | Ivanov K, Macian R, Gary Robinson PENNSYLVANIA STATE UNIV., HARRISBURG, PA |
| To: | |
| Shared Package | |
| ML20236S793 | List: |
| References | |
| NUDOCS 9807270235 | |
| Download: ML20236S798 (225) | |
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{{#Wiki_filter:--_ -- --- --_ - _ - - - _ - - - - - _ - - - - _ - _ - - ------ ------- - --- - --- l Analysis of Boron Dilution Transients in the AP600 : i l l Final Report June 1996 l l i i 1 l l l l l l l J l Prepared by : l l Rafael Macian Kostadin Ivanov Gordon E. Robinson 9807270235 DR 900720 The Pennsylvania State University ADOCK 05200003! PDR . 3
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TABLE OF CONTENTS Ea2t2 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................ .11 to 12 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 1 to 1 1
- 1. 2 R e fe re nc e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... . . . . . . . . 1 2 to 1 2 2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 t o 2 18 2.1 Description of Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 to 2 8 2.1.1 Thermalhydraulic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 to 2-2 2.1.2 Neutronic Analysis. NEM Code . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 to 2 7 2.1.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8 to 2 8 2.2 The High Order Solute Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 to 2 18 2.2.1 The Upwind Numerical Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 10 to 2-10 2.2.2 High Order Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 1 to 2 13 l
2.2.3 Implementation of the Solute Tracker in the Solution Scheme i ............................................ . . . 214 to 215 l 2.2.4 The Turbulent Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 16 to 2 16 !. 2.2.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 17 to 2 18 3 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 to 3-28 l 3.1 AP600 TRAC-PF1/ MOD 2 Thermalhydraulic Model Description . . . . . . . . . . . . . . 31 to 3-2 l 3.1.1 P rimary Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 to 3 2 l 3.1.2 Secondary Side (Balance of Plant) . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 to 3-4 l 3.1.3 Reactor Vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3- S t o 3 7 ! 3.1.4 Modifications of the Basic Steady State Deck . . . . . . . . . . . . . . . . . . . 3-8 to 3-8 3.1.5 Modifications to the AP600 Transient Docks . . . . . . . . . . . . . . . . . . . 3 8 to 3-18 3.1.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14 to 3-14 l 3.2 AP600 Neatronic Core Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 19 to 3 22 i 3.2.1 Basic Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 19 to 3 19 l 3.2.2 Core Neutronic Noding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 19 to 3 28 L l. 3.2.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22 to 3 22 4 Benchmarking and Test Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1 to 4 48 4.1 N EM Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1 to 4 2 ll 4.1.1 Benchmarldng information . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . 4 1 to 4-2 l 4.1.2 A.erences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 to 4 2 q l 4.2 Solute Tracking Test Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 to 4 17 j 4.2.1 One dimensional test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 to 4 10 4.2.2 Multidimensional Test Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11 to 417 4.2.3 Expenmental Assessment of the Multidimensional i; Solute Tracker Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4- 18 to 4 24 4.2.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 25 to 4 25 4.3 AP600 input Deck Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 26 to 4 57 , 1 4.3.1 Themialhydraulic Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . 4 26 to 4 47 1 i i 1 l l
i l 4.3.2 Neutronic Benchmarking . . . . . . . . . ......... ........ . . . 4 48 to 4 56 4.3.3 References . . . . . . . . . . . . . . . . . .......... . . .. ...... 4 57 to 4 57 5 Dilution Transients . . . . . . . . . . . . . . . . . . . .................. ......... . . 51 to 5-53 l i 5.1 Standard Decay Heat Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1 to 5 14 i l i 5.2 Low Decay Heat Calculation . . . . . . . ......... ... .............. 515 to 5-33 ) 5.3 Maximum Slug Size iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-34 to 5-47 ) 5.3.1 Loop 2 Pump Restart (Direct Mixing) . . . . . . , . . . . . . . . . . . . . . . . 5-35 to 5-42 l 5.3.2 Loop 1 Pump Restart (Backmixing) . . . . . . . . . . . . . . . . . . . . . . . . 5 43 to 5 47 5.3.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-44 to 5-44 5.4 Possibility of Recriticality during a LONF Transient . . . . . . . . . . . . . . . . . . . . 5-48 to 5 53 1 5.4.1 Correction of Critical K., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-48 t o 5 4 9 !
- j. 5.4.2 Analysis of Minimum Core Average Concentration for Recnticality . . 5 49 to 5-53 l
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1 to 6-3
- Appendix A. Vessel Boron Distribution for the LONF Transient . . . . . . . . . . . . . . . . . . . . . . A 1 to A 6 l Appendix B. Evaluation of the TRAC PF1/ MOD 2 AP600 Model . . . . . . . . . . . . . . . . . . B-1 to B 5 I
l Appendix C. Input Decks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C 1 to C-126 i j Appendix D. Attached Document. High Order Solute Tracking in System Codes . . . . . . . . . . . . . . . D-1 i l l i i i I 1. i l l ii
4 i Summary l A study of boron dilution transients in the AP600 System has been made. The objective was to l identify potential stagnation scenarios and to obtain a conservative estimate of clean coolant plug sizes that ! can be injected into the core without resulting in fuel damage. In addition, the results can be used to select recovery strategies in case dilution is suspected in one of the loops. The analysis has been made with a full AP600 primary side model that also includes passive safety
- systems. A coupled three-dimensional thermalhydraulic-neutronic description of the core has been employed l
l together with a high-order solute tracker to better resolve the transport of unborated plugs from their location in the primary side to the core. The results have shown that, under standard and low decay heat conditions, the passive safety l systems are able to maintain natural circulation flow for enough time, so that the concentration in the primary ( side remains higher than the critical operating concentration. On the other hand, the neutronic analysis has . shown that the core average concentration needed for recriticality is much lower than the entical j concentration. Therefore, lacking a physical mechanism that can inject large quantities of clean coolant into ! the system, recriticality does not appear to be of concem. l The possibility of local reactmty insertions, with the resulting fuel damage, has been addressed by analyzing the so called Finnish scenario. Pump restart of the loop with unborated plugs has rendered a maximum size of clean coolant plug to prevent fuel damage. In addition, pump restart of tlw loop without the unborated plug, has shown that the dilution process is much less severe, providing a possible strategy for recovery when dilution is suspected in some of the loops. I l t l ( . 6
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1 Introduction 1,1 Introduction The possibility of boron dilution events in PWRs has been of concem for some time. In particular, one of the design basis accidents desenbes the inadvertent dilution of the pnmary coolant as a result of the malfunction of the Chemical and Volume Control Systems (CVCS) or operator error. Nevertheless, there have been several studies (1.1 1), (1.1-21, [1.1-3), that have addressed the issue that under certain conditions, unborated plugs of coolant could circulate through the core, resulting <n a reactivity induced I accident (RIA) with the possibility of fuel damage. 1 in 1990, Diamond et al. (1.1 1) reviewed a number of potential RIAs expected in both PWR and BWRs. They evaluated the probability of occurrence and the seventy of ten types of RfAs for PWRs (Westinghouse plants) and seven for BWRs. The results showed that only two BWR accidents had both the potential for causing fuel damage and a high probability. Although the remainder RIAs were very unlikely, the authors acknowledged that, some of the RIAs could cause a plug of dilute water to pass through the core, thus generating a power excursion that might resud in fuel damage. h particular, some potential scenanos resu. ting in localized unborated plugs in the RCS have been identifiec [1.1 1), [1.14) They require the formation of a stagnant coolant region within the RCS, and some physical toechanism which, by injecting unborated water in the region, will greatty reduce its boron cor, centration. Once this situation is reached, any recirculation of the plug into the core (i.e. pump restart, natural circulation enhancement, etc.) may generate a large localized reactivity insertion along the path of the plug in the core. Some of the physical mechanisms for deboration and transport of the plug point to human error, whereas others result from the formation of reflux recirculation pattoms in the RCS (especially in the steam generators), and finally others postulate the leaking of clean water into some regg>n of the RCS (e.g. pump seats). As some studies have shown [1.14), most of the plausible scenanos that can lead to conditions favorable for RfAs, are dependant on system design and performance of its safety systems. For instance, the likelihood of stonng clean water in the loop seal depends on the existence of this part of the RCS in the system under study. Most of the previous analyses of such events have re sumed a perfect and instantaneous m(xing of the diluted water with the whole vessel inventory (1.1 1]. The resultmg frarment is then dnven by a slowly changing boron concentration, which leads to an almost linear increase in reactivity. Some imponant boron dilution transients cannot realistically be analyzed under such assumptions, because the boron field they generate inside the core is heterogeneous, as the mixing of the diluted plugs of coolant flowing towards the core is not instantaneous and complete. Initial analysis of such scenancs (1.14] have shown that the potential exists for fast local reactivity increases when sucn dilute plugs flow through the core, even if the core average concentration is not low enough to dnve the core to entical condrtsons. They can result in fuel darbage depending on the concentration, extension, form, etc. of the plug. This means that the seventy of 1.t t__
l I i l 1 i l l the accident depends on the instantaneous flow situation in the RCS, and , in particular, on the distnbution j of the boron field inside the core [1.12]. In summary, the detailed study of RfAs requires analytical tools l able to resolve both the thermalhydraulic and neutronic core responses and the accurate transport and mixing processes of the diluted plug. Several authors [1.1 1], (1.1-2), (1.13) have put forward a new j l l approach to this kind of dilution scenano, based on a more realistic consideration of the solute transport and l mtxing prccesses. The study presented in this report is based on such approach. The code selected for the I coupled thermalhydraulic and neutronic analysis is TRAC PF1/ MOD 2v5.4/NEM, whereas the accurate ] calculation of the transport of diluted plugs has been addressed by implementing high order numencal methods for sharp front resolution in place of the standard low resolution solute tracker of TRAC PF1. ; I The present report aadresses some of the concems related to RIAs in the AP600. In particular it will analize the LONF transient as a base line calculation to study the possibility of stagnation when the ! passive safety systems actuate. This wdl give an indication of the most probable places in the RCS where low boron concentration plugs are expected to form and remain. The base line calculation will be used as a starting point to study the transport of unborated coolant , pockets from their location in the RCS to the core. The ob tective is to obtain the maximum unborated water volume that can be allowed and maintain the core inlet boron concentration high enough to preclude reenticality. 1.2 References 1.1 1 Diamond, D.J., et all,' Reactivity Accidents. A Ran==== ament of the Design Basis Event, Brookhaven National Laboratory NUREG/CR-5368 January 1990. 1.12 Jacobson, S., Risk Evalum' inn of local Dilution Transients in PWR, Ph.D. Thesis, Linkoping University,1992. 1.13 Hyvannen, J., 'An Inherent Boron Dilution Mechansism in PWR*, Finnish Center for Radiation and Nuclear Safety (STUCK),1992. 1.1 4 Diamond, D., et al.,' Probability and Consequences of Raped Boron Dilution in a PWR', NUREG/CR-5819,1992. 12
2 Methodology The analyses of boron dilution transients in the AP600 RCS desenbod in this report are based on a coupled desenption of the thermalhydraulic and neutronics system behavior for all the cases presented, together with the use of an enhanced high order solute tracker, in one-dimensional and three-dimensional components for some of the analyses, j l The thermalhydraulic desenption is provided by TRAC PF1/ MOD 2v5.4 [2.1 1), which as stated later. I allows for three-dimensional simulation of the flow in the vessel, while treating the flow in the rest of the system components as essentially one-dimensional. The onginal code has been modified to include a three-dimensional neutronics descnpiion of the core by using a three-dimensional neutronics module based on the Normal Expansen Method (NEM). Such methodology requires the creation of a detailed thermalhydraulic model of the system and also a three-dimensional neutronic desenption of the core. In addition. a high-order solute tracker method developed at PSU and incorporated in TRAC- j I PF1/ MOD 2 has been used for those transients where fast transport of coolant into the vessel cames a plug of unborated water into the vessel and through the core in a short time. The effects of numencal diffusion inherent to the solution procedure of TRAC PF1/ MOO 2, would smear the plug excessively, thus introducing a larger degree of uncertainty on the minimum boron concentration of the coolant entenng the core. 2.1 Description of Codee 2.1.1 Thermelhydraulic Analysis. TRAC-PF1/ MOO 2 v5.4 l ! The TRAC PF1 computer code was developed at Los Alamos National Laboratory (LANL). The code is capable of performing advanced best estimate thermal hydraulic calculations for PWRs. It contains a full six equaten two-fluid model in aodition to two mass continuity equations capable of tracking non. t condensible gas in the vapor field and dissolved solute in the liquid field. The equations are generally l solved in a 1<$lmensional form. However, 3-dimensional flow can be simulated with the TRAC Vessel component (normety in r-6 z geometry). The closure of these equations is obtained by a senes of models and correlat ons whch cover the range of physcal phenomena expected to occur dunng LOCAs and other transients in pressunzed water reactors and in reduced scale facilities (2.1 1]. In addition to the thermalhydrault simulation, the code prodcts the neutronc core response by means of a point kinetes neutronc tredel. This model, while suitable for trans:ents where the vessel conditons remain relatively homogeneous, is not appropnate to desenbe the core power response in a highly heterogeneous thctmalhydraulc environment. Under such conditions, the neuttome feedback in different regions of the core depends strongly upon the local environment surrounding the fuel elements. 21
t The degree of accuracy needed to simulate this can only be achieveo with a three dimensional desenption. For this reason, the original point-kinetics model was replaced by the NEM 3 D Neutron Kinetics model described in Section 2.1.2. The 5.4 release version of TRAC-PF1/ MOD 2 was incapable of running the base USPWR LBLOCA l with scram beyond approximately 28 seconds after the pipe break. At this time a combination of several
]
problems resulted in failure of iterations to converge, and reduction of the time step size below an reasonable minimum value. These flaws existed in version 5.3 also preventing ii from completing this transient. . The last LANL analysis of the USPWR v as with modifications to version 5.3. Unfortunately these modifications were'not publicly documented, r4nd not propagated into version 5.4. Los Alamos was able to trace the exact contents of the code used for their last analysis, confirming one problem that we had located and pointing out one other not yet been located by PSU. The main problem identified by PSU was the failure to converge in the iteration used to determine the critical heat flux temperature (T.). The correction was a simple change in the convergence test for l the iteration. The problem had not been detected by LANL due to differences in the treatment of machine l-roundoff error between Cray supercomputers and IBM RS4000 Workstations. A more subtle but more severe problem discovered during our effort was the fact that the water packing logic was not fueG,6i6iii in the downcomer of the vessel. LANL had partially corrected this probkem in their correction to version 5.3. However, the scope of their water packing modifications would have limited the effectiveness of the logic in s.'tuations involving sudden numerically induced pressure drops. They have since accepted the more restricted PSU correction for use in subsequent code versions. During their last USPWR calculations, LANL discovered a problem in some special coding for i interfacial shear in the downcomer and forwarded the information to PSU. The existing code left the i interfacial shear in a Blausius correlation (separated flow) for all conditions. The correction allowed transition to a bubbly interfacial drag at low void fractions. Unfortunately, the LANL fix resulted in a discontinuous change in the drag coefficient at the transition point. We have tested a version of the correction that provides a continuous transition. However, tr,a contmucus transition resulted in shorter quench times for the rods. Without more information on the impact of various possible corrections to this problem, we deceded to use the LANL fix for this analysis. it is the more conservative of the two current . options, i l { l 22 i [. 2 I
l l 2.1.2 Neutronic Analysis. NEM Code i i The 30 kinetics model used in this analysis was developed by Bemard Bandini [2.12] at Penn State ! l University. In order to provide multidimensional transient neutronic analysis capability, Bandini developed l an algonthm based on the Nodal Expansion Method (NEM), capable of handling steady-state and transient ! calculations as well as 3D Cartesian and cylindrical geometries. The NEM method is one of a variety of recently developed nodal coupling schemes, where the solutions to the transverse integrated three-dimensional diffusion equation are approximated by a polynomial expansion. This method was developed 4 in West Germany in the late 1970's by H. Finnemann [2.13] at Kraftwerk Union (KWU). In this scheme, the solution to the transverse integrated diffusion equation in each node is approximated by a fourth oder . 1 polynomial expansion. ; ' i ! The nodal method equations are derived from the general diffusion equation by integrating over l t large homogenous nodes in each direction. The result is three one dimensional nodal balance equations. j in order to solve these equations numerically, one must develop some relationship between the node i i average fluxes and the node surface currents. The relationship should be a simple set of equations which I involve only the node average fluxes and partial currents. A coupling relationship such as Finnemann's, which has a higher order than a simple linear flux gradient on a node, allows the use of larger mesh spacing than that used in standard finite difference approximations. 2.1.2.1 Steady State Development and Testing in his thesis, Bandini outlined the details of dermng the two energy group, fourth order, quadratic NEM in 3D Cartesian geometry in steady state and transient versions. The derivation begins by introducing the general fdrm of the steady state multi group neutron diffusion equation a e , vo,+,- z,+,4 ms.,+,4,r v,.z .+,, o <2.11> ; o g et , o1 where:
$, a neutron flux in group p D, a group g diffusion coefficient I, a group g removal cross section E, , a probability of a neutron scattering from group g'to g K = multiplication eigenvalue x, a fracten of fissen neutron entering group g ,
u, e average number of neutrons produced by group p'flasion Eg a group g' fission cross secten 23
l After developing the steady state NEM, Bandini tested his work by comparing results of his code to those of several two and three dimensional benchmark problems, including: The 3D IAEA PWR Test Problem which models a one-eighth core symmetric two zone PWR reactor made up of 177 fuel assemblies including a 20 cm axial reflector and a partially inserted control rod in the center fuel region.
- Tne 3D LRA BWR Test Problem which modeled a two zone BWR reactor containing 312 fuel e'ements includag a 30 cm axial reflector and a off-center control rod. j
- Finally the 3D LMW Bench Mark Problem which models a one-eighth core symmetric reactor with 77 assemblies and nine control rods, four of which are inserted to the mid plane of the core.
Based on these results Bandini concluded that the fourth order NEM was suitable for calculating the steady state power distribution in Cartesian geometry using very coarse mesh spacing. 2.1.2.2 Transient Development and Testing Although the implementation of NEM used in our version of TRAC-PF1/ MOD 2 (locally designated TRAC-NEM) permits any number of energy groups, this application only uses two groups. For clarity we will write the specific two energy group form of the multidimensenal transient neutronic diffusion and precursor equations. The fast diffusion equation: fi i i er in Y nNi sa k es O The thermal drffusion equation: 3 E *** ' ' ' (2*3) V, at E The precursor equations: a d=1,0 (2.1-4) g jC5,(vE,$, + v E,$,)- A,C, where: V, a energy group g neutron velocity
$, a time and space dependent neutron flux in group g 0, a group g ddfusen coefficient 24 l
l
I ,, . m group g absorption cross-section
~ I ,, a group f to 2 scattering cross section C, a time and space dependent group d neutron precursor concentration p, a fraction of fission events which produce group d neutron precursors p a sum of p,'s A, a decay constant for neutron precursor group d D a total number of delayed neutron precursor groups Bandini tested the NEM stand alone code on several two and three dimensional test problems (2.1-4), including:
The 2-D TWIGL Seed-Blanket which models a 160 cm square unreflected seed blanket consisting of three fissile material types. The transient consisted of a ramp or step change in the thermal absorption cross-section in one of the material types. The cairidation yielded very accurate results (1% error) for even large time step sizes. A second test performed was the 3D LMW transient problem. This model is similar to the previous LMW problem except this time the control rods are removed to cause a transient. Once the calculations were completed the maximum error Bandini reported in the power shape distribution was 5.5%. l' '2.1.2.3 NEM/ TRAC Coupilng i in order to understand how the NEM and TRAC-PF1 codes are coupled, one needs a general j knowledge of the progression of a TRAC-PF1/ MOD 2 thermal hydraulle time step. In each TRAC time step l there are three separate stages; the pre-pass stage, the outer iteration stage, and the post pass stage. ) During the pre-pass stage of time step n, TRAC calculates the material dependent properties and j convective heat transfer coefhcients based upon the condstions at the end of the n f time step. Next, in the outer-iteration stage, TRAC solves the ID and 3D fluid <fynamic equations, providing values for the basic flow variables at time level n. Finally, in the post pass stage, TRAC solves the fuel rod and structure q heat conduction equations to obtain rod and structure temperatures at time level n. The actual cross-section calculations for the NEM subroutines take place between the outer iteration and the post pass slagss. In the if time step, the outer iteration stage solves the fluid-dyname equations based on the fuel rod temperatures, material properties and heat transfer coefficients evaluated at time level n f. The cross secten routmas are then executed uomg time step tef fuel rod temperatures and time ; step N moderator condihons. At this point, the NEM routines calculate the nodal power distrbutior. in the core for time step n. Finally, to complete the time step n solution TRAC executes the normal post-pass l subroutines, calculating the fuel rod ternperatures using the newly calculated nodal power distribution as
. a heat source for the fuel rods. Time step N is then complete and FRAC is ready to proceed to the pre-1 25 i I
pass stage for time step n+f. In the case of the steady-state calculation, the NEM/ TRAC coupling follows a similar calculational procedure. A TRAC steady state is basically a transient run to the point that key variables stop changing significantly. The primary difference from a transient is that the heat conduction ! calculations can be executed with a higher time step size than the fluid calculations to obtain a quickar relaxation of rod and structure temperatures to their steady-state values. In a manner consistent with this technique, the transient neutron diffusion equations are dropped during a steady state, and replaced with l a solution of the steady state diffusion equation at each time step. The final result is a consistent set of nodal powers and thermal properties. l 2.1.2.4 Cross Section Feedback The NEM code that Los Alamos made TRAC compatible contained a thermalhydraulic feed back model which was primarily based on variations in moderator density, moderator temperature and fuel ' temperature and secondarily on vanations in coolant soluble-boron concentration. The cross-section feed l back mechanism used can be expressed as: d I - A + Sp + Cp' + DT, + ET[ + Fs,x10 (2.15) where: I e any two group macroscopic cross section or diffusion coefficient A +F a constant polynomial coefficients p a actual cell averaged moderator density l T,,, a cell averaged moderator temperature T, a cell averaged fuel temperature s, a coolant soluble boron concentration (parts per million by weight) This method has proven 14 be inadequate when a wide varianon of core thermalhydraulic condebons are orpected during a transient. Runs invariably reach a point where the NEM module obtains negative values for some crose sections and predicts some negative local power densities, resulting in a fatal code failure. To solve this problem a table interpolation routine was added to the cross section feed-back calculations. This rouline aNows the user to determine which thermalhydraulic parameters are important for each specsfic transient and to create a cross section table library to cover the ranges expected. Up to four independerit parameters can be used at one time in this routine. For this study three independent ! parameters were chosen, moderator density, fuel temperature and boron concentration. Bounds for the tables were obtained by checking the Reference LONF transient [2.1 11] in order to insure that they fell within the bounds of the tables. The table interpolation method has been shown to perform very well for a series of applications carried out at PSU [2.17), (2.1 10). i 26
l 2.1.2.5 Cross-Section Calculation l The TRAC /NEM input deck requires cross sectional data as input. Several standard Cross section { l calculation codes can Le used to generate this information, e.g. LEOPARD [2.15), CASMO-3 [2.19], etc.. l LEOPARD (abbreviation for Lifetime Evaluating Operations Pertinent to the analysis of Reactor Design) is a computer program that determines fast and thermal cross sections using only basic geometry i . and 'emperature data, based on a modified MUFT SOFOCATE model. The code optionally computes fuel depletion effects for a dimensionless reactor and recomputes the cross sections before each discrete bumup step. The PSU-LEOPARD code was further modified so that it can analyze the Westinghouse !' VANTAGE 5 fuel assembly designs by implemsating a methodology capable of handling the complex Westinghouse bumable poison designs, Pyrex BP, WABA, and IFBA [2.1-8]. This improved version of PSU-LEOPARD was benchmarked to EPRI CPM 2 for various Westinghouse bumable poison designs with their associated environments at different fuel enrichments and diferent exposurec, The Westinghouse designed i Beaver Valley Unit 1 and Unit 2 reactors were chosen as the reference core designs in this study. These analyses showed very good agreement between PSU LEOPARD and EPRI CPM-2 results. The PSU-LEOPARD code together with the nodal simulator ADMARC were used to analyze most of the cycles of the Beaver Valley Unit 1 and Unit 2 reactors. Good agreement was obtained also wdh tne operational results for all of these analyses. I !: The above described modified version of PSU-LEOPARD capable of simu; tion of the IFBA designs l has been adapted and tested on IBM RISC Systemal000 workstations. Further options for branch and average depletion calculation cases have been implemented into the code as well as dump and restart processing. The code has been integrated into the cross sechon tables generation procedure required by the coupled TRAC-PF1/NEM code. Since this code version was benchmarked only for core follow and fuel management calculations a benchmarking to CASMO 3 results has been accomplished for transient and accident conditions. The reference design is AP600, BOL of EQ Cycle. Benchmark analyses show good j agreement for the initial steady state calculations. The cross sechon library generated with PSU-LEOPARD gives maxsmum devindon in normeRzed powers of about 7 percent when compared to the results predicted
.with the library generated with CASMO 3. Both libraries predict the same power shapes following the l ' Westinghouse reference results.
l l i 27
l 2.1.3 References 2.11 Schnurr, N. M., et al., ' TRAC PF1/ MOD 2 Theory manual', Los Alamos National Laboratory Report l LA 12031-M, U.S. Nuclear Regulatory. Commission Report NUREG/CR 5673 (1992). : 21-2 Bandini. B. R., 'A Three Dimensional Transient Neutronics Routine for the TRAC.PF1 Reactor l
- j. Thermal Hydraulic Computer Code'. Ph. D. Thesis, Penn State University,1990. l j 2.1 3 Finneman, H. et al. ' Interface Current Technique for Multidimensional Reactor Calculations *.
Atomkomenergie 30, p.123,1977. 2.1 4 Bandini, B. R., et al., 'Venfication of the Three dimesional Nodal Transient Neutronics Routine for the TRAC-PF1/ MOD 2 Thermalhydraulic System Analysis Code' LA UR-921210. Los Alamos National Lab.1992. l 2.15 Levine, S. H., Kim. S. S., 'PSU LEOPARD Users Manual', The Pennsylvania State University. L 1987 l' 2.16 Ivanov K. N., A. J. Baratta, and B. R. Bandini, "Three-Dimensional NEM/ TRAC-PF1 Rod Ejection Benchmark Analyses," Trans. Amer. Nuc. Soc. Vol. 73, p.343 (1995). 2.17 Ivanov, K. N., et al. "TMI MSLB Analysis Using TRAC PF1 Coupled with Three Dimensional Kinetics", Proc. of ICONE 4, Vol. 3, p. 33 (1996). 2.18. Zhian, Li, "An Automate Optimal Pressunzed Water Reactor Reload Design Expert System *, PhD
- Thesis The Pennsylvania State University (1993).
2.19 Edenius, M., B. Forsson, 'CASMO 3 A Fuel Assembly Bumup Program', Users Manual, STUDSVIK/NFA-89/3. 2.1 10 Macian, R., Taylor. T., Mahaffy, J., "Large Break Loss of Coolant Accident Analysis Using TRAC-PF1 and Three-dimensenal Kinetes', presented at NURETH 7 Conference, Saratoga Spnngs, NY, 1 September 1995. I i ! 2.1 11 AP600 Loss of Normal Feedwater Transont Information, Westinghouse Memos NTD-NSA TA 95-l 127 and NTD NSR&LA LEH 95 037 (Supplemented by AP600 Boron Transient Calculations using TRAC PF1, Westinghouse Memo NTD NSR & t>. LEH-95-096 dated Apnl 24,1995), dated Apnl 13.1995. I l o e- - e. i e 8 i 28 , r-
2.2 The High Order Solute Tracker Several System Codes, i.e. TRAC-PF1/ MOD 2 [2.21), TRAC BF1 [2.2 2], RELAPS [2.2 3], CATHARE [2.2-4), include the capability of tracking a soluble field, usually a neutron poison, to simulate the negative reactivity insertion resulting from the poison flowing through the core. The solute is treated as a separate field modeled by a single hyperbolic transport equation in which molecular and turbulent diffusions are neglected in particular, TRAC PF1/ MOD 2 computed the solute field at the end of the time step in a post-pass operation after the velocity field has been obtained (2.2 5), so that its solution does not directly affect the general solution procedure. As with all the convective terms in the TRAC-PF1's conservation equations, the convective term is explicitly differences on a staggered grid with upwind donor-cell spatial differencing [2.2-6), while the time gradient is first order differences. According to Rider [2.2 7], this method is quite stable, but suffers from numerical diffusion due to its first-order spatial accuracy. Rider recognized that the use of this method to solve the conservation equations may be acceptable in many applications, since most of the uncertainties in such system codes reside in the two-phase closure relationships. But, in cases where the detailed description of the spatial and temporal distribution of the solute field is required, the method is less than sa'Jsfactory. An example can be found in shutdown studies where fast transport and dilution of soluble poison into the core, artificially enhanced by the numerical diffusion, may render non-conservative results from a safety point of view. In general, any transient that requires accurate tracking of a heterogeneous solute field within the vessel will be adversely affected by excessive numencal diffusion. In addition to the shortcomings reported above, the solute transport equation in TRAC-PF1/ MOD 2, as in most system codes, does not desenbe any mixing effect in the solute field caused by the turbulence in the main ik:w As reported in [2.2 8) one of the factors believed to reduce the severity of the transients with large boron free water plugs is the turbulent mixing that takes place at the vessel inlet. Moreover, in situations where a diluted coolant plug is accumulating in the lower o8enum, an effectrve mixing between the water already in the vessel and the ir,cciiding dilute plug can substantially reduce the reactivity insertion. The implementation of any physical diffusion mechanism in the solute equation requires the reduction, and if poseinte elimination, of the numerical diffusion associated with the upwind differencing scheme. Rhode et al. (2.2 9) reported that it is well known that a portion of the discrepancies with measurements of many turbulence models may lay in false numencal diffusion, which can overpower the very effect under investigation. Simeter comments can be found elsewhere in the literature, it is clear from the ideas expressed above tnat the description of the spatial and temporal evolution of the bcron field in the vessel, which requires the implementation of a mecharusm capeble of simulating physical turbulent diffusion, should be affected by as little artificial numencal diffusion as possible. 29 4
2.2.1 The Upwid Numerical Scheme l ; The upwind numerical scheme, also known as donor cell differencing, is a widely used method to numerically solve the conservation equations describing the advoction of scalar or vector fields. Its populanty lays in its robustness and the property that it produces positive definite solutions, which is very important to guarantee the stabihty of the solution of systems of conservation equations.
' Methods based on central space discretization (e.g. second-order central differences), do not I distinguish upstream from downstream, and the physical propagation of perturbations (e.g. solute fronts) is j not inherent to the numerical method. In regions of smooth behavior of the flow variables, these methods can be applied with any order of accuracy without any oscillatory behavior; but they generate oscillations in the vicinity of discontinuities [2.210). Additional artificial diffusive terms have to be added to these schemes in order to damp the oscillations, thus affecting the accuracy of the original method.
I Upwind schemes try to overcome the oscillatory behavior by introducing the physical properties of the flow equations into the discretization process, in particular, the apphcation of these methods to the solution of scalar transport equations is based on the sign of the convective veioody, whch contains physical l information about the actual flow direction. This parameter controis the form of the scheme, by providing, in fact, the asymmetric character that mwnics the actual downstream physcal transport process of the scalar. According to [2.210], methods based on upwmd weighted schemes can represent discontinuities better than i centered schemes of similar order of accuracy that use artificial viscosity terms to dissipate the oscillations l near discontinuities.
. The properties of robustness and relative good accuracy near discontinuities have made this class of methods widely used in CFD and System Codes. The atulity to accurately resolve discontinuities, however, is directly dependent on the order of the scheme. In this sense, a large number of codes have l
l implemented first order upwind, which, although able to resolve sharp gradients better than centered method t combined with artificial dissipation (i.e. Lax Friedrichs) of smier order of accuracy, is itself affected by art.ficial numencal diffusion. This diffuseve character may render these codes unsuitable to track sharp i
- i. gradients of scalar quandlies with the degree of accuracy required for certam applications.
l. 2 10
I 2.2.2 High Order Methods Some of the approaches to the tracking of solute fields used in plume dispersion studios are based on Lagrangian-like particle tracking; but it will not be considered here. since its application to System Codes is not deemed very effective in terms of computational efficiency; especially for long transient simulation (see l [2.211]. [2.212]). Such methods are generally based on stochastic approaches requiring the tracking of l large ensembles of " concentration particler' in order to be statistically accurate; this would require too much l l computation time when applied to transient simulations, since the calculation should be perfo:med every time step to account for the dynamic charceter of the flow field being simulated. Most current System Codes make use of the local approach by integrating the transport equation in time and space over cornputational cells, control volumes, into which the fluid field is meshed. Unfortunately, there are difficulties acsociated with the nurnerical solution of this type of equations by this approacn, especially when discontinuous solutions arm expected [2.213] (e.g. solute fronts). Methods based on simple finite difference approximations can yield wrong results when such discontinuities are present [2.2-14] Several methods are available to solve hyperbolic conservation laws (e.g. firt :': Tent [2.215], spectral viscosity methods [2.216], front tracking methods [2.2-17], etc.), but, since the purpose of this review is to find suitable methods to improve the actual methodology in System Codes,'only the finite-difference schemes used by these codsa wiH be addressed. The first attempt to improve the accuracy of the numerical methods were based on cell centered second or higher-order differencing schemes, i.e. Lax Wendroff, Beam Warming, etc.. The major problem with these methods is their tendency to show oscillatory behavior before and/or after discontinuities. Obviously, this is of great concem when implementing them in a finite dstforence based code in order to resolve sharp gradients, boccase the elimination of the smeanng of discontinuities would be substituted by unstable solubons, whose amplitude and frequency depend on flow and numeric parameters and order of the approxarnation [2.218). In complex System Codes, where such parameters vary frequently as the system evolves during a transient, the use of numerical methods that can lead to instabilities should be avoided if possible. For this reason, it was decided to search for other methods that could provule good resolution in discontinuities, but would also show no oscillatory behavior in their vicenty. More sophisticated numerical schemes to resolve sharp discontmuses than those discussed abon, have been developed in recent years. Two of the most important famshes are the Goudonov-type and the High Resolubon methods. The basic Goudonov type method obtains a riumerical solution that is piecewise constaat in each mesh ceN at f,,. The con interfaces separate constant states at time (,. The time evolution of the solution from (,to f,,,, is obtamed from the solution of a the Riemann pmblem at the ces face. The new piecewise constant approximations are obtained by averaging the exact Riemann solution over each 2 11
I l l' l l l respective cell. The basic Goudonov method is, thus, a first-order spatial approximation because of the l constant assumption of the solute field in each cell. Since the exact solution of the Riemann problem is expensive to obtain, several approximate Riemann solvers have been proposed (e.g., the Goudonov type schemes by Osher [2.2-19] and Roe [2.210]) to be applied to the basic numerical method described above. As shown in [2.219), both methods are first-order, however, since the discontinuities are smeared out. Thus, they are not suitable for the accurate tracking of solute fronts. High resolution methods, are in general, second-order accurate in regions where the solution is i smooth, and give oscillation free results around discontinuities. These schemes satisfy a convergence criterion known as Total Variation Diminishing (TVD), which mathematically assures that for a given time, t,,. the total variation of the numerical solution will be bounded in the spatial domain, and that, as time I advances, the value of the total variation of the solution will decrease. The ultimate effect is the suppression j of oscillations near discontinuities. The most used high resolution schemes which satisfy the TVD condition are the Flux Limiter methods [2.2 21], [2.2 22]. They incorporate some form of limiter for the numerical flux at the cell face. The definition of nurnerical flux stems from the form in which a conservative numerical method can always be expressed as a balance in a time step, where the variation of the scalar within the ! l computational cell is caused by the flux of the scalar across the cell faces. The flux limiter approach uses l a classical high-order flux function (e.g. the Lax Wendroff flux) which gives accurate results in regions of ( smooth selution, and a low order flux (e.g. the basic upwind rnethod). The combination of both into a single flux is expected to reduce to the high-order flux in smooth regions, provedmg accuracy, and to the low-order flux near discontinuities, thus avoiding oscillations. In order to achieve this last property, the second order flux, also known as antidiffusive flux [2.2 23], is limited by a function, L(r) , in such a way that the limited ; antidiffusive flux is maximized in amplitude (providing very low nurnoncal diffusion), while being low enough so as to assure that the method is TVD, and oscillation free. Several limiters have been proposed by Roe [2.2 24] (Superbee), Van Leer's [2.217], Chakravatrthy and Osher [2.2425], etc.. They all show very good behavior near discontinuities. Roe's Superboe highly compressive trEnsfer function is by some measures the best of all [2.217). In fact, Rider and Woodruff [2.2 26] have implemented this limiter into TRAC- ; PF1/fAOD3 with good results in one dimensional solute traciong. Unfortunately, the method does not perform so well in three dimensenal geometry. This is related to the result by Goodman and LeVoque which proves that linear TVD schemes in two or higher dimensens are at most first order accurate [2.2 23). Another family of TVD methodt the Slope Lmter methods [2.2 23), generales the basic Goudonov technique by replacing the piecewise constant representation of the solution by a more accurate approximation, based on a slope functon. The problem in this case is to find a suitable slope. In addition, a slope limiter function can be used to reduce the value of the slope near discontinuities or the extreme po!3ts, so that the method is TVD; but then it will revert to first order accuracy. l- 2 12
l A different approach to the traditional TVD differencing schemes was proposed by Leonard [2.2 27). The method, known as OUICK (for steady state) and QUICKEST (for unsteady flow), is appropriate for highly convective flows. It is reported to considerably reduce numerical diffusion while avoiding the stabikty problems of central differencing. It requires, however, more operations per node than traditional methods but it can provida highly accurate solutions with coarser grids than those required by conventional schemes of comparable accuracy. The scheme uses a control-volume formulation with cell edge values of the scalar field computed from a quadratic interpolation using the two adjacent nodal values plus tne value at the next upstream node (a total of three interpolating values). According to Leonard, the scheme is more accurate than central differencing while retaining the basic stable convective sensitivity property of upstream-weighted schemes. The results presented in [2.2-27) comparing OUICK and QUICKEST to first upwind and second order central differencing show considerable improvement in tracking sharp discontinuities with a reduction of the computation time of the order of 100. This method has already been used in turbulent modeling by Rhode [2.2 28) in order to diminish the false diffusion uncertainty in the results. Recently, Leonard has introduced two new methods based on the concept of a universal flux timrter analogous to the flux limiters used in TVD methods (see above). The result has been the development of a multidimensional steady state high speed convective algonthm, based on the old QUICK method, called ULTRA SHARP [2.2-29] The concept of universal limiter has been extended to unsteady flow grving the ULTIMATE strategy [2.2 30), which can be applied to explicit conservative advoction schemes of any order of accuracy. Results shown in [2.2 30) prove that second-order methods (including well known shock-capturing or TVD schemes) are generally inferior to the third-order ULTIMATE-OUICKEST strategy, especially for smooth varying gradient profiles. Finally, a different approach to those presented above was followed by Smolarkieviez [2.2-32], [2.2-33). The proposed scheme has a multidimensional character, and is based on the first order upwind scheme. This guarantees the positive definite character of the method, while, at the same time, conferring staberty and robustness. The method has an iterative character based on the application of the Taylor series expansion to the upwind scheme, each iteration increasing the solution's accuracy. The simplest version of the method is second-order accurate both in time and space and, according to [2.2 33), gives results of comparable accuracy, while reducing the computational time compared with more complicated high-resolution schemes. If necessary, however, the degree of accuracy of this method can easily be extended both in time and space by extending the Taylor series expansion and incorporating new forms in the formulation. . Y f O *
~ '
2 13
2.2.3 Implementation of the Solute Tracker in the Solution Scheme Explidt time integration for the solution of partial differential equations introduces some numerical j r l restrictions in order to guarantee the stability of the scheme used, namely, the CFL condition that requires l the Courant numbers in each computational cell to be less or equal thr n one. This condition restricts the maximum time step size that can be used, depending on the flow velocities and mesh structure. Most System Codes have tried to avoid this constrain when solving the fluid flow equations by employing i l numerical schemes that are fully implicit in time (CATHARE), semi-implicit (RELAPS), or quasi-implicit ! l (TRAC PF1 with SETS). As a result, large time step sizes can be achieved, while preserving stability and l ! robustness, which sometimes violate the CFL stability criterion. l it is also well known that a fully implicit or semi-implicit integration of the simple advoctive transport equation for a scalar quantity will suffer from numerical diffusion if upwind spatial differencing, or any low I order scheme, is used to numerically compute the transport of the scalar by the flow. Most of the codes j make use of the upwind approach in order to keep the codes stable and robust enough for most applications. This feature, however, greatty affects the accurate tracking of any scalar moving with the flow, since the artificial numerical diffusion introduced by low order spatial differencing is substantial for implicit and semi implicit time integrations. Moreover, this non-physical diffusive transport linearly grows with the ! time step size, usually large in implicit and semi-implicit codes. l' An altamative to reduce the numerical diffusion is, hence, to use explicit time integration whers l solving the scalar transport equation. In addshon, if a high order scheme is to be applied, an explicit approach is also reasonable, since most of the high-order schemes are based on this kind of time differencing. A strategy to implement an explicit scalar field tracker in a impilcit or semi-implicit System Code has been developed and applied to TRAC-PF1/ MOD 2. The basic scheme is based on the decoupling of the main solution of the fluid flow equabons fmm the solubon of the scalar transpott equation, and the explicit solution of the latter withm the imphcst time step size. The solute tracking process starts after the code initialization of the main system variables and geometric charactenstics. The use of a high order method requires a more autensive treatment of the boundary informabon between components than a code based on the upwind scheme needs. For this reason the boundary data structure has to preserve information for j several cells of conbguous components, and be able to identify branch cells in TEE like components. In addition, the interfaces between three-dimensional and one dimensional components have to be defined. In this respect, a simple upwnd couping has been used in the implementat6on developed for TRAC-PF1/ MOO 2, but more complex schemes are also posette. This information should be stored for the durabon of the run and be available to the high-order tracking routmos. 2 14
i l The actual explicit high order tracking procedure is streamlined in the computational process, but care has to be taken to merge the implicit or semi implicit character of the fluid solution, and the expliert l nature of the solute tracking. This can be achieved without perturbing the overall solution procedure, since the solution of the scalar advection equation, be it one or multidimensional, does not affect the flow field. Only in cases where the solute concentration modifies the neutronic response of the core, i.e. boron injection or dilution, does the tracking affect the flow field, but its effect is exerted by the power history, which in tum determines the temperature field. This, however, does not modify in any way the implicit solution scheme and, therefore, the solute transport equation can be solved independently. Following this approach, the explicit scheme can be inserted within the implicit time step, and the CFL condition satisfied by using a smaller time step for solute tracking than the flow field solution time step if necessary. Two different high-oroer methods have been implemented in TRAC-PF1. The third-order accurate QUICKEST ULTIMATE has been selected for the one-dimensional component because it is fast and its performance in one-dimensional solute transport has been tested and compa W against other high-order methods. The results have shown superior performance to most commonly used methods (2.2-30). Its application to multidimensional flows is not as well tested, especially for non-steady situations. Moreover, the possibility of negative values in the boron field if the flux limiter cannot be sur:cessfully applied to three-dimensional flow, has led to the selection of Smolarckievicz's method for the three-dimensional components. Its positive definite character precludes negative boron concentrations, and its inherent multidimensional character, together with a relative easiness of implementation are good properties for the coarse noding schemes used in systern codes, in addition to the properties mentioned above, both methods are explicit methods that contain the desirable property of reduced numerical diffusion as the Courant number grows. Finally, the coupling of these two different methods was made through the bourxfary conditions at the junctions of the one-dimensional components with the source connections in the three-dimensional TRAC. PF1 components. A more detailed anahsis of the methods and the reasons for this choices is presented in App. D. i l l l 2 15
i l l I l 2.2.4 The Turbulent Diffusion Model l The mode implemented in TRAC PF1/ MOD 2 is based on a length scale approach proposed by l Deissier. The basic form of the equation is, from dimensional analysis [2.2-35) : c = c(U,I v ) = n' UI(1 -exp( -n' UI/ v }) (2.21) l where e is the turbulent viscosity. The velocity scale U and length scale, I ,should be selected to characterize the flow. The parameter n is an expenmental constant. The equation contains an exponential term to account for wall effects on the turbulent viscosity. This term satisfies the experimental requirement that the effect of the rnolecular viscosity, v ,should become small for large values of the length scale,1. According to [2.2 34), this equation with n=0.124 gives results for flow and heat or mass transfer in tubes and boundary layers that are in good agreement with experiments. Since the flow characteristics inside the reactor vessel resemble those observed in closed channels, where the flow is wall-bounded, the proposed model was chosen to simulate the turbulent mixing effects in the downcomer and the lower plenum. The law of the wall was added to account for the possibility of narrow spaces or regions where the distance to the walls would influence the turbulence of the flow, in the actual code implementation, the length scale has been assumed as half the hydraulic diameter of the fluid cell. Since the cells are three-dimensenal in nature, the equivalent hydraulic diameter, hd = sqrt( bd', + bd', + hd', ), has been used. The velocity in the turbulence correlation is the modulus of the actual three-dimensional velocity in each cell. For one-dimensional components (i.e. pipes), the correlation used is based on an experimental correlation obtained from (2.2 34). This correlation is dependent on the Reynolds number of the flow inside a pipe, when the flow is completey developed. For this reason, no law of the wall was used in this case. The mathematical structure of the correlation is similar to the equation above, but the experimental constant is based on the Reynolds number of the flow in the pipe. As mentioned above, the law of the wall, 3 10' 1.36 qge) . * (2.22) a g .i h *' represented by the exponential function, is omitted for one-dimensional components. I 2 16
2.2.5 References 2.2 1 Schnurr, N. M., et al., ' TRAC-PF1/ MOD 2 Theory manual', Los Alamos National Laboratory Report LA 12031 M, U.S. Nuclear Regulatory Commission Report NUREG/CR-5673 (1992). 2.2 2 Borkowski, J. A., (Ed.) et al., ' TRAC BF1: An advanced best-estimate computer program for BWR accident analysis', Idaho National Engineering Laboratory Report EGG 2626, U.S. Nuclear Regulatory Commission Report NUREG/CR 4356 (1992). 2.2-3 Allison, C., (Ed.) et al., 'RELAP5 MOD 3 Code Manual', US Nuclear Regulatory Commission Report NUREG/CR-5535 (1990). I 2.2-4 Barre, F., Parent, M., Brun, B., ' Advanced Numerical Methods for Thermalhydraulics', CSNI Specialist Meeting on Transient Two-Phase Flow, Aix-en-Provence, France (1992). 2.2 5 Mahaffy, J. H., 'A Stablility-Enhancing Two-Step Method for Fluid Flow Calculations', Joumal of Computational Physics, 48, 326 (1985). 2.2 6 tiles, D. R., and Reed, W. H., Joumal of Computational Physics,28, 77 (1978). , 2.2 7 RMar, W. J., 'High-Order Solute Tracking in Two-Phase Thermalhydraulics', 4th intomational ; Symposium on CFD, Davis, CA, September 1991. i 2.2 8 Oosterkamp, K. P., 'k-e Modeling Of Deboration Transient in a PWR', Presented at the ANS/ ENS Intemational Meeting, November 1982. l 2.2 9 Rhode D. L. And Stowers, S. T., 'Combustor Air Flow Prediction Capability Comparing Several l Turbulence Models', Joumal of Pmpulsion,5,242 (1988). 2.2 10 Hirsch, C., Numencal Computation Qf jn19m8[ and Extemal E] Sag, Vol. 2, Wiley and Sons, Chichester (1990). 2.2 11 Georgopoulos, P. G. And Seinfeld, J. H., 'Nonlocal Description of Turbulent Dispersion', Chemical l Engineering Science, 44,1995 (1989). 2.2 12 Thomson, D. J., ' Criteria for the Selection of Stochastic Models of Particle Trajectories in Turbulent Flows', Joumal of Fluid Mechanics, 180, 529 (1987). 2.2 13 Hirsch, C., Numerical Computation 2 fjnlema! and Extemal E)ggg, Vol. 2 Part IV, John Wiley & Sons (1990). 2.2 14 Berkenbosch, A. C., et al.." Finite-Difference Methods for One Dimensional Hyperbolic Conservation l Laws', SIAM J. Numer. Anal., 28, 30 (1989). ! 2.2 15 Johnson, C., et al., 'On the Ccovergence of Shock Capturing Streamhne Diffusion Finite Element !' Methods for Hyperbolic Conservation Laws', Met. Comput.,54,107 (1990). 2.2 16 Tadmor, E., 'Corwergence of Spectral Methods for Non-linear Conservation Laws', S/AM J. Numer. Anal.,28,30 (1980). 2.2 17 Schwartz,8. K. and Wendroff, B., ' Aztec: A Front Tracking Code Based on Gouoonov's Method' Appl. Numor. Math., 2, 386 (1988). 2.2 18 Leonard, B. P., The ULTIMATE Conservative Difference Scheme Applied to Unsteady One-dimensional Advoction', Comp. Meth. Apol. Mech. Eng., 88, 17 (1991). 2.2 19 Osher, S., and Solomon, F..' Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws', Math. Comput., 38, 339 (1982). 2.2 20 Roe, P. L,' Approximate Riemman Solver, Parameter Vectors and Difference Scheme', J. Comp. Phys., 43, 357 (1981). 2.2 21 Van Leer, E , Towards the Ultimate Conservative Differencing Scheme,11. Monotonicrty and 2 17
i ! Conservation Combined in a Second Order Scheme', J. Comp. Phys., 14, 361 (1974). l l 2.2 22 Engquist, B. And Osher, S., 'High Resolution Applications of the Osher Upwind Scheme for the l Euler Equations' AIAA paper presented at the 6th CFD Conference (1983). 2.2 23 Sweby, P. K., 'High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws'. S/AM J. Numer. Anal., 21, 995 (1984). 2.2 24 Roe, P. L., Lectures in Applied Mathematics, 22,163 (1983). 2.2 25 Osher, S., and Chakravarthy, S. R., 'High Resolution Schemes and The Entropy Condition', S/AM J. Numer. Anal., 21, 955 (1984). ! 2.2-27 Leonard, B. P., 'A Stable and Accurate Convective Procedure Based on Quadratic Upstream l Interpolation', Comp. Meth., Appl. Mech. Eng., 19, 59 (1979), 2.2 28 Rhode, D. L., and Stowers, S. T., 'Combustor Air Flow Prediction Capability Comparing Several Turbulence Models', Joumal of Propulsion, .5, 242 (1988). 2.2-29 Leonard, B. P., and Mokhtary, S., 'Beyond First-order Upwinding: The Ultra-Sharp Attemative for 2.2 Non Oscillatory Steady State Simulation of Convection', Int. J. Num. Meth. Eng., 30, 729 l (1990). 2.2-30 Leonard, B. P., The ULTIMATE Conservative Difference Scheme Applied to Unsteady One-dimensional Advoction', Comp. Meth. Appl. Mech. Eng., 88, 17 (1991). 2.2 31 Leonard, B. P., and Niknafs, H., ' Cost-effective Accurate Coarse-grid Method for Highly l
- Convective Multidimensional Unsteady Flow', Proceedings Si thi .QfQ Symoosium 90 l Aerooroouision. MA.,36 kasig Research Qgager, Cleveland, OH, April 1990.
2.2 32 Smolartuevicz, P. K.,'A Simple Positive Definite Advoetion Scheme with Small implicit Diffusion', Monthly Weather Review, 3, 479 (1983). 2.2 33 Smolarkievicz, P. K., 'A Fully Multidimensional Positive Definite Advoetion Transport Algorithm ! l with Small Implicit Diffusion', Joumel of Computational Physics, 54, 325 (1984). l 2.2 34 Nauman, E. B., Chemical Reactor Enaineerina. New York, Wiley,1987. 2.2 35 Frost, W. and Moulden, T, ed.,830@ggh g[ Turbulence, New York Plenum Press,1977. I i I O 2 18
l l O ' The following sections contain information that is proprietary to Westinghouse and have been 1 submitted under separate cover- I J
'3.1.1 3.l.2 3.1.3 l 3.1.4
! 3.1.5 3.2 The following figures contain information that is proprietary to Westinghouse and have been submitted . -; under separate cover: ! 1 3.1 , j 3.1 !
- 3.1-3 l l 3.1-4
- 3.1 -5 3.1-6 3.1 7 i 3.1-8 ;
l 3.2-4 ; I 3.2 ! 3.2-6 i 3.24- l 3.2-8 i i l l I L { L 1
l l l [ 1.9 Enrichment 1
#N 4.7 4.8 , enes bumed 158 128 2 feed 4.7 4.8 4.8
- 158 80 128 feed 2 1 4.8 4.8 4.8 4.8 80 128 128 80 2 feed 2 1-4.8 4.8 4.8 4.8 4.8 80 80 80 80 80 1 2 1 2 feed 4.7 4.7 4.7 4.8 4.8 158 158 158 80 80 1 feed 2 feed 1 l 4.8 4.7 4.8 4.8 80 158 80 128 feed 1 feed 1 Feed Realon 12 @ 4.7 w/o l as @ 4.8w/o i
l Figure 3.21 Equilibrium Cycle Core Design 3 23 u___ ________
l EQ CYCLE BOL AVERAGE ASSEMBLY BURNUP 1 2 3 4 5 6 7 1 18416 44641 0 39548 18712 24491 0 2 44787 0 36010 0 43046 0 23155 3 0 36918 23594 34901 16565 38269 0 4 39794 0 35010 21709 33354 0 24633 5 18765 40666 16504 33415 0 20795 6 24511 0 38066 0 20051 7 0 23333 0 24475 l I Figure 3.2 2 EQ CYCLE BOL Average Assembly Bumups 3 24 I i l l t______-_____-________ _
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' 4 Benchmarking and Test Problems l
4.1 NEM Benchmarking 4.1.1 Bench narking information The Hot Zero Power rod ejection benchmark provides a stringent teot of the NEM transient routine and its coupling to the fuel rod heat conduction solution methodology. Because actual reactor-core temperatures and power distributions are difficult to measure accurately under such severe transient I cc,nditions, the results from running TRAC PF1/NEM have been compared with the results of running two j established neutronics/thermalhydraulic space-time codes HERMITE and ARROTTA (4.1-1). Steady-state and transient calculations with one and four racRal nodes per assembly (npa) NEM models have been performed. Comparisons of steady-state calculations of initial and asymptotic conditions showed very good ! agreement in the calculated eigenvalues (ig.) and normalized assembly power (NP) distributions. Good i agreement has been obtained also "oetween the prodctions from TRAC-PF1/NEM, HERMITE, and ARROTTA during all phases of this transient. Agreement was in the areas of time dependence of total core power and peak assembly power density, as well as the time dependence of the core-average and peak-assembly fuel temperatures. The normehzed assembly power distribution at 0.39 s into the fransient (near the power peak of the transient) has been studied and compared aiso. The ARROTTA normalized assembly ' i
- powers agree to within 5.02 % with those of HERMITE while the TRAC PF1/NEM normalized assembly !
powers agree within 0.55 % with those of HERMITE. In conclusion, this PWR HZP rod ejection simulation j indicated that the coupled TRAC-PF1/NEM code produces results within the rance of results obtained by I l . HERMITE and ARROTTA. l In order to further test the coolant thermalhydraule coupling, a Main Steam Line Break (MSLB) transient study has been accomplished using TRAC-PF1/NEM for TMI-1 Nuclear Power Plant (NPP) [4.12]. The MSLB accident in a PWR is characterized by significant =pece time effects in ths core caused by asymmetric cooling and assumed stuck out rod during the reactor trip. Th!s MSLB analysis sseumed the .I instantaneous gudiotine break of a main steam line upstream of the main steam isolation valve. The reactor i
-is at EOC when the moderator temperature coethcient (MTC) is most negative. The concurrent failure of a feedwater regulating velve to the effected steam generator is also assumed. A reactor scram occurs on high neutron power or low system pressurs. The most reactrve rod is assumed to be stuck out. Feedwater (FW) to the affected steam generator is terminated by closure of the FW block valve at 55 seconds. High
- pressure injection is assumed not to activate. The TRAC-PF1/NEM results for initial steady state conditions j- . have been compared with the SIMULATE 3 results and the agreement is acceptable. During the transient
' a comparison of the 3-D kinetics results to a compatible point kinebes predictum has been performed.
TRAC PF1/NEM incorporates 3 D transient local nodal power information while in the point kinetics model, 41
only core average and not local thermalhydraulic feedback is used. This study demonstrated that the 3-D core transient modeling providec margin to re<riticality over a point kinetics approach during a MSLB analysis. 4.1.2 References i l l 4.1 1 Ivanov, K. N., A. J. Baratta, and B. R. Bandini, "Three-Dimensional NEWTRAC-PF1 Rod Ejection Benchmark Analyses," Trans. Amer. Nuc. Soc. Vol. 73, p.343 (1995). 4.12 Ivanov, K. N., et al. 'TMI MSLB Analysis Using TRAC-Pf1 Coupled with Three-Dimensional Kinetics", Proc. of ICONE-4, Vol. 3, p. 33 (1996). I I 4 I 42
t i 4.2 Solute Tracidng Test Problems The testing of the methods used in one and multidimensional solute tracker implemented in TRAC- l PF1 MOD 2 have been based on a set of test problems, where the diffusion introduced by the methods was compared to the diffusion inherent to the implicit upwind method currently employed in TRAC-PF1/ MOD 2, i in addition to the test problems described in the attached report in Appendix C, additional analysis were carried out. The study of the one-dimensional method was directed towards the comparison between ! the numencal diffusion introduced by the method, and the actual turbulent diffusion caused by turbulent flow l In pipes. For this comparison, the correlation for one-dimensional components described in Section 2.3 was < used. The multidimensional tracker was analyzed by comparing its performance of a test problem l suggested by Peterson [4.21]. This test problem shows the numerical diffusion in the axial direction (along the flow) and the one introduced by the 'skewedness' of the flow with respect to the computational grid. 4.2.1 One-dimensional test The one-dimensional test is based on a technique adapted at PSU called the C-Curve j methodology. The analysis of the perfo rnance of a numerical method regarding the numerical diffusion I introduced in the transport equation solutions can be addressed in a variety of ways. A mathematical formulation for the diffusion coefficient can easily be obtained for certam simple methods, whereas it can be very difficult for others. This is especially true if non-linear numerical flux limiters are used to avoid over and undershooting in the solutions provided by high-order numencal methods. For this reason, a rnethodology was developed to be applied to cases where the actual diffusion coefficients are not easily obtainable, or the problem being modeled has varying cell sizes, velocities, etc.; ' l a situation typical of system codes like TRAC PF1 MOO 2. The purpose of the rnethodology is to characterize quantitatively the diffusion associated with a given numenceJ method when applied to the modeling of scalar transport in system codes. The C-Curve "rl+2'cgy is based on experimental techniques used to quantdy the extent of non-ideal flow inside Chemical Reactor Vessels (Levenspiel 1972) [4.2 2]. The C-Curve represents the normalized concentration vs. time response at the outlet of the vessel when an impulse of concentration is injected in the incoming flow. Mathematically, this curve is a statistical Distnbution. For constant vekxnty flow, the Mean Residence Time of the " plug" in the vessel is defined as : 4-3
- characteris6aAxialLegth tu (4.21) velocity l
whereas the Mean Time of the C Distribution is defined as : tcdr
=-
E 'oC oO's t* = *o E c, A t, (4.2-2) l 1o* An essential parameter in the methodology is the Variance of the distribution : J(t-l,')cdt ft*cdr - E t, C, a t, 7 a o o o= =
- - -[c= E c,s t, -t c (4.23) fcdt o
fcdt o l The variance is directly related to the diffusive nature of the flow inside the vessel, and its value is often used to match experimental to theoretical curves. The variance is additive for independent flow regions (the diffusion is locally produced), so that one can write: c', = o', + o', + ... + o , + o' (fornregionsinseries) (4.2-4) where, the subindex out and in represent the outlet and inlet regions. l The application of this methodology to characterize numerical diffusion is based on the assumption that the transport of solute modeled by a numerical method in a purely convective form (no real diffusion added) can be assimilated to Plug Flow conditions. The Plug Flow assurnptions requires that the diffusion at any point in the system be a function only of local conditions, in case of numerical methods solving purely convective problems, one can maintain that the numerical diffusion at a given computational cell is l l a function only of the conditions (velocity, time step size, cell size) at this cett (center and edges). The statistical basis of the original experimental model, on the other hand, stems from the hypothesis that physical turbulent diffusion is a statistical process similar to molecular diffusion. Therefore, the independence of the local turbulent transport on the rest of the system conditions makes it possible to apply statistical tools to analyze the diffusion process. This local Independent approach, as mentioned before, is supposed to be also applicable to numerical diffusion. l t _ _ _ _ _ _ _ __-_ __ ___ __ _-_ _ _ _ _- ____ __ -
The model is mainly used in chemical engineering to characterize AXIAL diffusion by assuming diffusive transport being described as analogous to Fick's Law. The solute transport equation, thus, becomes : aC BC a*C
- + up = 0 (4.2-5)
, This equation is similar to the one-dimensional solute transport equation with an additional diffusive transport, that can be associated to the numerical diffusion introduced by a numerica'. method in the ! solution. Equation (4.2 5) can be made dimensionless, rendering : t t 8 ._ MeanResidenceTune t ! x x BC D SC BC (4.2-6)
~
l *" VesselAnallagth L W~Yu a, ~5 I l The dimensionless parameter, D/Lu, characterizes the diffusion of the solution. In a real vessel, I this would be the turbulent diffusion, in a numerical solution, this is the numerical diffusion. (note that vessel is used hers in a general sense; it can be a one-dimensional model, but also a three dimensional model with predominantly axial flow). , i The dimensionless parameter, D/ul, measures the extent of axial diffusion introduced by the ' ! numerical method when solving the transport equation for a given problem and flow configuration. l D
-O Plug Row. Very little diffusion (4.2-7)
Mixed Row. Lame cMfusion l \ UL The model represents satisfactorily flows close to Plug Flow conditions. Numerical methods used in solute transport modeling usually satisfy this condition when modeling Convective Transport only, i Therefore, testing the numerical method solution for the transport of a " plug" of solute, should allow the computation of the diffusion parameter. Therefore, the application of the methodology to numerical diffusion analysis is based on the characterization of the parameter D/bt for the numerical method used and the system being modeled, by obtaining the C-Curve of the model. Numerical experiments can be designed to obtain the extent of diffusion introduced by the numerical method for a given geometry.The additivity property of the variances allows for the use of any 45 l
Tracer input Signal (with known variance), to extract the variance of the C-Curve (see Eq.4.2-1): A o' = a - c', (4.28) The parameter, D/ut, can be obtained from the variance of the C Curve. Thus, for small diffusion, the parameter is related by the analytical solution of the dimensionless transport equation (Eq. 4.2-6) by - D A o, = Ao' =2 g (4.2-9) I ! and for large diffusion flows, (only available for open vessels, i.e. undisturbed flow at boundaries of vessel), (- the parameter is given by: l i s D D A o, = A o' =2(g)+8(g) (4.2 10) t The derivation of these expressions was made by Levenspiel and Smith (1957) and Aris (1959). The methodology described above was used to obtain a quantitative measure of the degree of improvement in the one-dimensional high-order model, by comparing the parameter Diu for the standard TRAC-PF1/ MOD 2 SETS based upon SETS-upwind and the new method. In addibon, in eider to benchmark the method with respect to turbulent diffusion, an experimental correlation for pipes and closed channels ) was used for high and low Reynolds models (4.2-3]. The High Reynolds nurnber was taken as 5.0e+5, the 1 maximum within the scope of the correlation (from Levenspiel and Nauman) [4.2 2). l Tables 4.21,4.2-2 and 4.2 2 show the results of the applicabon of the C Curve methodology to the characterization of a one-dimensional numerical method, regarding the degree of numerical diffusion introduced in the solution. They show the results for a series of test problems based on two one dimensional components connected with 10 cells each (20 cells totaQ. The flow has constant velocity and the main parameters for the test are shown in the table. The transport of a step of concentration is analyzed for 1, 5 and 10 seconds injechon (1sinj, 5sinj and 10sinj), and different time steps (0.05,0.01, 0.5 and 1.0 seconds). In this way the performance of the method can be tested against different Courant numbers (column labelled Cr #). The case for the one second time step had to be prepared with a larger lag in the injection to give time for the flow to stabilize the time step (20 seconds lag). In order to validate the method, lhe origmal TRAC-PFIMOD2 SETS method was analyzed, and its diffusion parameter computed from the statistical analysis shown above. At the same time, the ; corresponding diffusion parameter mathematically derived for implicit upwind was also calculated for each 4-6
l l problem. Table 4.21, shows that the methodology proposed can effectivey compute the diffusion introduced by a given nurnerical method with a high degree of accuracy: an error less than 1% in all the cases. This error can be m1ribuied to the numerical integration used to compute the variances and from the sampling process. The lu: gest discrepancies were observed for the case where a time step of 1 second was used, and the inbetion started at 5 seconds. The reason is that, by the t;me the plug of solute started its trip, the time step size was not yet stable. Therefore, the diffusion computed by the method describes this effect of varying Courta. numbers during the solute transport, and the value of the diffusion parameter is slightly coerent than tne one given by the truthematical formula because the latter assumes a coristant time step. Fir' ally, it is also clear that the npres,sion for low diffusion flow (Eq. 4.2-9) is the most appropriate to use with numerical diffusion. Table 4.21 shows that the rhethcd is able to resolve the irnplicit character of the upwind method in TRAC-PF1 MOD 2. The error with respect to the mathematical value for the implicii diffusion le always less than 1%. This assesses the methodology that is then applied to the QUICKEST ULTIMATE method implemented in TRAC-PF1 MOD 2. Tables 4.2 2 and 4.2-3 show the results for Low and High Reynolds
- number flows.
l The results show that for rnost of the cases the di"usion introduced by the method is less than the turbulent diffusion associated with the flow (based on the correlation described in 2,3) for or,a-dimensional components (see column Num/Turb). The results are improved by increasing the Courant number, as expected from an explicit method. In all cases the num6tical diffusion introduced by the me' hod is mucn smaller that the nurr'erical # fusion introduced by the original TRAC PF1 MOD 2 method (see column imp /Ok). For most of the problcrm, the numerical diffusion introcuted by the method is less (or atmost equal) than the corresponding turbulent diffusion coefficient. In any case, the differences could be included withM the experimental error of the measurements. In addition, because of the explicit character of the method, the diffusion is lowered by increasing the Courant number value, that is, by increasing the time step size in an actual calculation performed with a system code. As a conclusion, the onedimensional rnethod substantial:y reduces the numerical diffusion in the one-dimensional transport of solute. In most cases, i.a. for large enough Courant nurrbers, this reduction is enough to make possable the use of a turbulence modelin one dimensional components. 47 l
i i.ts get !!c 22f cat est 3 33..; ;;: a : :as ::: - g 1
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L i 4-9 ) e . _ _ _ _ _ . _ _ . _ . . - - - - - - _ _ _ . - _ . _ _ - _ - -
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-mm ag * ~mv-mm w,
- st R gfM x = = 8
- 5858.- j taarga
.w.. .* m -ey fwril'rvil;si.E.r$nm 2 tiv. n a 9.. .
4444*57* - c !l.:lEl:lIl)[g[ I IIR N l 24 g: El t l3! ! 5 55158E I f
- H i s aoos s sf!!
*O - 8s5
.g k
o. g i com .co ..e ood a a. j l' 5 . 2 {j j { SEI egg edi r te = =; IE! E!~ i !!I Y El i 9, xx-s~ - s.
=M i , "
sse l 4 i 3>. ! :as:sss:er*as
- sus sig gsE :us 3 j
.Q E
l o$ [ jij glii]! EEE BEE 05 ss no
.R
- S e. Roo
~
= -
.s.a.a. a. s. s .s. s .s .I..H E.. li.t 3 e [
. .!!8})5REE.8EE,
~x n- - se.B
- F 2 4e m ) 222ftdddf.21C NRR 33"5541 1 '-
3 {<l
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.n.. .n. .sa.i .
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l 1 t l Table 4.2 3 Application of the C-Cuive Methodology to OUICKEST-ULTIMATE. High Reynolds No. f- ; 4-10 L u _ __ -.- ____
! 4.2.2 Multidimensional Test Problem
~
The test problems for the multidimensional solute tracker (see Section 2.3) are based on the problems proposed by Peterson [4.2-1]. They are devised to characterize the numerical diffusion in the flow direction, and the cross-diffusion resulting from the skewedness of the flow with respect to the computational grid. This diffusion is important in multidimensional flows of practical intarest, since in most of them the direction of the flow will change in the solution domain. An example of this is the flow in the reactor vessel. I The test problem consists of the simulation of the transport of a two-dimensional exponential plug ) with a one cell maximum height of 10.0. The plug. placed at the origin of coordinates, is moved across the ) solution mesh in three directions by changing the x and y velocity components. The Courant numbers have been kept the same as in the original paper : Case 1 : Courent x = 0.125 Courant y = 0.0 l Case 2 : Courant x = 0.125 Courant y = 0.063 i Case 3 : Courant x = 0.125 Courant y = 0.125 The results have been compared to the explicit upwind method, which, because of its explicit character, will introduce lower numerical diffusion than the implicit upwind used in TRAC PF1/ MOD 2. Figure 4.21 shows the initial extension of the transported plug. Figures 4.2 2 to 4.2-6, compare the results for Smolarckievicz's multidimensional method and those from the explicit upwind method. It is clear that the diffusion introduced by Smolarckievicz's method is much smaller than that from the upwind method The spread of the initial profile is much smaller in the high order multxhrnensonal solution. Figures 4.2 7 and 4.2 8 show another variant of the problem, where, instead of transporting a plug, the flow transports a plume of magnitude 1.0 injected at the origin of coordinates. The comparison to the upwind results is also favorable to the high order multidirnensional rnethod '.mplemented in TRAC-PF1/ MOD 2. The plumes maintain a narrower profile, which indicates a much lower cross diffus'en. i i l i t i 4 11
i i I i 2D-Test Problem Pure Convection Upwind. Cx=0.125. Initial State 40 , , . , , . , ,. , 30- - 20- - x - j 10- - 0-h -
-10 ., , , ,
-10 0 10 20 30 40 X
l Figure 4.21 Initial Plug Two4imensional Shape 4 12 i L_______._._____.._____________
2D-Test Problem Pure Convection Upwind. Cx=0.125. Sc=1.1 No VCorr.192 steps
. ~
30- - 20- - h l 10, - 0- - l 1
-10 ,- ,- ,- , ,-
-10 0 10 20 30 40 X
Pure Convection Upwind. Cx4.125.192 steps 4c . ,- ... . 30- - l l 20- - i l h - - 10- - 0- 2' -
-10 . ,- . ,- . ,- . -
-10 0 10 20 30 40 X
Figure 4.2 2 Two Dimensional Test Problem. Cx=0.125, Cy=0.0 t 4 13 L_________.._._ _ _ _ _ _ _ _ _ _ _
2D-Test Problem Pure Conv. Smolarkievicz. Cx=0.125, Cy=0.063. NoVC. Sc=1.1.192 steps 40 . . 30- - 20- - N - 10-' i - 0- -
-10 , ,
-10 0 10 20 30 40 X
Pure Convection Upwind.Cx=0.125.Cy=0.063.192 steps 40 , 30- - 20- -
',,....h*
n . h!./ ';... , . ( ' ., i.' . ~j 'jl \; ') 10- .. -
...~.......-
1 o- - t ! -10 ~ ,- i- .- , , l -10 0 10 20 30 40 \
- Figure 4.2 3 Two Dimensional Test Problem. Cx=0.125, Cy=0.063 4 14
i J l 2D-Test Problem Pure Cony. Smotarkievict. Cx=0.125. Cy=0.125. NoCV. Sc=1.1.192 steps d') .,. .,- . .,- ,. l l . l ! 30- . T- - l x . l 102 . i 4 .
~
i l' -101 ,. ,. ,- . l -10 0 10 20 30 40 l X Pure Convection Upwind. Cx=0.125, Cy=0.125.192 steps c , ,. ,- , .,- ,- f p""Uta. l ',
+ *j i;( h. {' . ,
\ '" . . ' ' ) l ,
pp ,
./
-j/
7
.i es..,..e x
i l 102 - 0- - l L !
-ic . ,. . ..- .
.. , i
-10 0 10 20 30 40 !
x j I Figure 4.2 4 Two-Dimensional Test Problem. Cx=0.125, Cy=0.125 - 4-15 l _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . .__ __ _ _ _ _ . _ . _ _ _ _ _ . _____J
l L L 2D-Test Problem I Pure Conv. Smolecuevicz. Sc=1.1. Cs=0.12$, Cy=0.06.1.192 steps 40 ,- ,- , , 3H 20- .,,,-
* ~
l ] ip . l-0-
/ -
\
l 1
-10 ,- , , ,
-10 0 10 20 30 40 X
Pure Convection Upwind.Cx=0.125 Cy=0.0625.192 steps 40, . ,- , ,- , i ! 30- - l l 20- - x . : . ! Ik " l
- ~,
p . L -10 , ,- . ,- ,- ,- .
-10 0 10 20 30 40 I.
X Figure 4.2 5 Two Dimer.sional Problem (Plume). Cx=0.125, Cy=0.063 4 16 L___=__-____.
l t i i l 2D-Test Problem l Pure Cony. Smolarckievicz. Sc=1.1. Cx=0.125. Cy=0.125.192 steps 4C .- , ,- . .- - i 30. 20- - - E
^ .
{
\
ik - l l \ l .g. 02 -
-10 . ,- ,- - ,- ,
-10 0 10 20 30 40 I
l l Pure Convection Upwind. Cx=0.125. Cy=0.125.192 steps l 40 ,- ,- ,- .,- 1 i 3Q . . . . 2p - I g . i 10- -
.)
4 k -
-m- , , .- .
-10 0 10 20 3D 40 X
Figure 4.2-8 Two-Dimensional Test Problem (Plume). Cx=0.125, Cy=0.125 4 17 ? L____________-_____________.
4.2.3 Experimental Assessment of the Multidimensional Solute Tracker Model Benchmarking of the three-dimensional solute tracker and mixing correlation implemented in' TRAC-PF1 in order to increase the accuracy of the boron dilution analysis presented in this report was made by simulation of the experimental boron dilution transient i.pMed by Alavyoon et al.(4.2-4). These experiments were carried out at Vattenfall Utveckling AB (VUAB) with a 1/5 scale model of a three loop Westinghouse i PWR. The scenario analyzed in these experiments is the injection into the vessel of an unborated plug of coolant located in the cold leg by restarting one of the RCP. The scaled model used in the experiments has three loops. The main loop represents the cold leg where the unborated plug has accumulated, whereas the two side loops connect the downcomer with the upper part o' the core region. During the course of the experimental 1 runs, both side loops remain open, and flow through them appears as a result of pressure differences The relevance of the results of the simulations is clear, since the transients analyzed in this report ! are similar. to the pump restart scenario studied in the expenmental setup, where, as the authoss l l acknowledge, for the flow characteristics expected in the models. the transport of chemical species, e.g. boron, is mainly due to advoctive and turbulent diffuswa transports. l l 4.2.3.1 Basic Description of the Experimental Facility According to Ref.[4.2-4), the experitnental model has a main inlet, representing the cold leg, and two addit.onal side loops connecting the downcomer to the upper core regions. The three loops have the same flow area and are located on the same horizontal plane. Addnional piping and supporting equipment cortpletes :he system, l l The actual 'unborated plug is simulated by a 0.064 m' plug of salt water in the main loop, whose fro.1 is situated 1.9 m from the entrance to the downcomer. The flow rate through the main pipe is controlled by the start up of the pump, while the flow through the side loops (7 to 10% of the main flow) appears as a consequence of the pressure difference between the downcomer ard the core. Experimental data is available for the flow rate in the three loops, and will be used to precisely match this parameter in the computer simulation. l l; The inlet concentration measurements are based on a conductwity probe placed 0.35 m from the downcomer entrance. Maps of core inlet concentrated, obtained from 61 probes placed across a horizontal plane mdway between the bottom plate and the core inlet are also provided. Ai,coisig to Ref.[4.2-4), for a given temperature ard low salt concentration, the water conductmty can be expressed very accurately by a linear function of the concentration in this way, accurate concentration plots can be obtained as the 4-18
i l transient progresses. Finally, plots of the spatial (ensemble) average of the normalized concentration across the rneasuring section at the core inlet are also available. (. 4.2.3.2 TRAC Model Description 1 The TRAO-PF1 model of the VUAB facility includes the most important components of the experimental setup, l.a. vessel, main and side loops, injection pipe and outlet pipe. The rest of the supporting components has been discarded, since they can be satisfactorily replaced by boundary conditions. Thus, the pump has been sirnufated by a FILL component whose mass flow rate vs. tirne table l mimics the injection flow reported in the original paper. In addition, since no information about pressure j losses was provided, the flow through the secondary loops connecting the downcomer and the upper plenum was also rnodeled by FILt.s that controlled the mass flow rate exiting the downoomer at the injection
' level. Information about these flows was provided in the original paper, R6L(4.2-4]. Finally, the outlet pipe boundary cordtion is a BREAK component at the reported atmospheric system pressure.
The vessel rnodel consists of the three-dimensional TRAC VESSEL wigent. The noding scheme
- - e, c.
l is composed of hydraulic cells. This noding scheme is a comehow more detailed than the one used in the AP000 rnodel described elsewhere in this total number of cols is, nevertheless, withm l usual detailed vessel models used by system codes the TRAC PF1. The larger number of azimuthal sectors in the experimental simulation was a necessity because of the complexities in the downcomer flow introduced by the two side loops. This situation is not present in the AP600 rnodel, which has an independent downoomer modet in addition to the rnain vessel. I Geometrical data for the experimental model has been obtained in part from the information offered in Ref.[4.2-4]. The intomat structures in the lower plenum and in the core region were not described in the original paper. However, since the authors reported that the facility was a 1Ai scale mock-up of a three-loop ! Westinghouse PWR reactor, the area and volume fractions and the hydraulic diameters for the regions with intemal structures was obtained from a Los Alamos three-loop Westinghouse PWR TRAC E F1 vessel moitel i available at PSU. Only tie run retorted as High Reynolds Number run was modeled, since the results shown for the 1.ow Reynolds Number run show a distorted injection step, with no indication of the possible causes. The l TRAC run will simulate the actual transient from an initial stagnant condition, as reported in Ref.[4.2-4), that L is, no steady state run was made, since the initial steady state contSilons assume a stagnant system. Coolant temperature and prosaurs were set to 300 K (25*C) and 0.01013 MPs (1 atm) r;+ifi throughout the entire system. 4 19 )
The initial plug of salt water was placed in the inlet pipe within 10 equal length one-dimensional cells of 0.064 m' each. Of these cells, the one closest to the vessel has its cell face at 1.9 m from the downcomer inlet as reported in the paper. The meshing of the region between this cell and the vessel connection'is such that the point where the inlet concentration was expenmentally measured corresponds to the center of one of the cells at 0.35 m from the connection to the vessel. In this way the concentration readings reported in Ref.[4.2-4) should correspond to those computed by TRAC during the simulation. Finally, the average concentration at the core inlet is obtained by using TRAC's capability to extract volume averspedinformation i for a group of component cells by using signal variaLes. The concentration is averaged throughout the oxial plane of the level of the vessel representing the core inlet, whose midplane coincides with the location at which the actual 61 conductivity probes were placed. The simulation will inject borated water (1000 ppm) in a clean system. The experimental paper reported results as if they were clean plugs of water injected into a borated vessel. However, the physical system is similar to the model used in the TRAC PF1 simulation, i.e., infection of saft water into a clean vessel. For this season, the results presented in the paper have been transformed into a manner that allows direct comparison to the results provided by TRAC PF1. In this sense, the normalized (1.0 = injection concentration)
- depletion" of cnte inlet boron concentration has been read as an actual increase in salt concentration : 1.0 - [ normalized dilution), and then multiplied by 0.001 in order to compare with the results from the TRAC PF1 simulation. The multiplication by 0.001 reduoos the normalized experimental values to the equivalent of 1000 ppm as the injection concentration. TRAC-PF1 cannot use 1.0 as boron concentration, because it would plate out the excess of boron down to the saturation concentration for the system thermalhydrau6c conditions. In the same menner, the inlet concentration was reported in the paper as conductivity measurements. However, since, as the authors point out, there is a linear relationship between the conductivity measured by the probes and the salt concentration, the information provided can
- j. easily be normalized to 0.001 as the intet salt concentration, thus making the experimental results directly comparable to the TRAC-PF1 results. !
l l 4.2.3.3 Simulation Results l As mentioned above, only the High Reynolds Number run was simulated. Two solute trackers were l used, i.e. standard TRAC PF1 tracker based on implicit upwind, and the high-order scheme implemented l I in TRAC PF1 and described in App. D. Only the high order run employed the turbulence model described in Section 2.2.4. In this way, the code used for in high order run was sesentially the same as that used to compute all the boron dilution transients described in this report. The obpective was to compare the depersson of the solute plug from ils infecbon in the vessel to the core inlet. The depersion of the plug is directly related to the turbulent diffusion along the flow path followed
)
4 20 L__ _ __ _ _ _ _ _ _ _ _ _ _ _ - . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . - - _ _ _ _ _ _ _ _ _ _____ _ - - - - - - -
?
~ by the plug within the vessel (see Ref.[4.2 2] and (4.2-3]). However, dunng the course of our investigations, it was found that the distnbution of solute in the core inlet is also very dependent of the flow pattern in the downcomer, the lower plenum and the core inlet. It was not possible to obtain a very accurate prediction of the velocity field within these three regions if compared to the results reported in Ref.[4.2 4] for simulations with PHOENICS and mesh sizes ranging from 40000 to 320000 cells, although the average field and flow pattoms within the vessel were well predicted. Such detailed meshing pattoms are impractical in real system code simulations. But, nevertheless, the results obtained with the coarse vessel model desenbod above showed that average concentrations can be well predicted with high-order solute tracisers and appropnate turbulent diffusion models. Matching the correct local distribution of solute at the core inlet, however, requires a good prodction of the flow from thn point of injection in the downcomer to the core intet.
It was found that, in order to obtain an accurate velocity field, extra refinements would be necessary in the vessel meshmg scheme, especially in the downcomer region where the jet of coolant coming from the primary leg h4s the downcomer walls spreading into a highly turbulent two dimensional flow pattom. Figures 4.2 7 and 4.2 8 display the most important results. The first plot shows how the one-dimensional high-order tracker predicts a very accurate plug transport through the inlet pipe, even with accelerating flow (i.e. pump restart). The salt water plug enters the vessel with a similar degree of disperson as that observed in the experimental run. The simulation with the standard TRAC-PF1 tracker shows the effects of a larger numerical diffusion, which reduces the maximum value of the plug's concentration before l entering the vessel. The small driferences in the width of the expenmental and high-order profiles, is caused l by small differences in the injection volumetric flow rate curves, expenmental and the one implemented in l the input decks. It was found that small modifications of the values read from the curves in Ref.[4.2 4) used to build the tables for the TRAC input decks, would result in noticeable widening of the predicted profiles. This is related to the way the experimental curve is obtained: by tocol point measurement of conductivity. l The faster the plug moves, the narrower the square profile. The results presented in Fig 4.2-7 show the best approximation to the experimental volumetric flow rate curves we could achieve. The degree of dispersion introduced by the numerical simulations can be assessed by the slope of the sides of the profiles and the
- he*ght of the curwee. In this regard, the code used to perform the analyses desenbod in Section 5, yields similar slopes to those of the experimental profile, in fact, as will be shown in Table 4.2 4, the dispersion of the computer simulation is smaller (0.420200 vs. 0.654866).
The dispersion predicted inside the vessel can be analyzed from the results displayed in Fig. 4.2 8.
. The higner, narrower peak of concentration prodcted by the high order simulation is indicative of a lower predicted turbulent diffusion (mixing). The peaks for both simulations are located at the same time as the j expenmental one, which reflects a well predicted average flow field in the downcomer and in the lower plenum. Moreover, the solute plug reaches the core mlet at approximately the same time in the high-order simulation and in the expenmental run (- 8.0 s). j 4 21
_ _ _ _ _ _ _ _ _ _ - - _--:- i
A more detailed quantitative analysis of the results discussed above is based on the application of the concepts introduced in Section 4.2.1. The variance (or ' spread * ) of the soluw concentration curve at I the core inlet is related to the degree of mixing along the path of the plug. Obtaining a quantitative $easure of the dispersion from the variance of the concentration vs. time curves, similarly to what was done for one-dimensional configurations in 4.2.1, it is also possible in multidimensional situations, when the inlet and outlet measurements are well defined. In this particular case, the inlet concentration is well defined by the results of Fig. 4.2-7. The core inlet concentration is an average for the entire core inlet section, which could l be assimilated to a rneasurement of the concentration at the end of a pipe of wide flow area. We dispersion l resulting from the multidimensional character of the flow is then assimilated to an equivalent dispersion h a one-dimensional flow path, whose length is an average length traveled by the multidimensional flow. A1 average velocity can be obtained from this length and the average time of the solute concentration curve, Finally, application of the methodology described in 4.2.1 will yield a quantitative measurement of ttm dispersion, thus allowing comparison of experimental and numerical results. The average length from the point of measurement of the inlet concentration to the core inlet I midplane, /, is approxirnately 2.36 m. The average velocity is computed from the average time for the r> lug traveling from the point of measurement at the vessel inlet, and from the average length. The average time is obtained as the mean time, f, , of the solute concentration distribution at the core inlet in absolvte time (i.e. from f = 0.0 s ) minus a ' lag' time, that is, the time it takes for the front of the plug to reach tf4 vessel inlet concentration measurement point (approx. 4.0 s). I 1 I
#, , "I e -( (4.2 11) where the tc is computed from Eq. 4.2-2.
Avg. Variance Variance Estirrate Run Vol. of Vessel of Cote Variance Ddf. Integral Ws) Inlet Plug inlet Plug Coeff. Expenmental o.40s7 o.as4ese 2.ososed p.gk o.020057 o.000737 Basic TRAC o.4314 o.72ssas 1.sao4a2 i gp o.020067 o.0007s3 H.O. TRAC +T.D. o.42a7 0.42020s o.7ss717 @y
- o00s105 o.00o743 Table 4.2-4. Statistical Analysis of 3D Simulations 4-22
i l The statisteal analysis presented in Table 4.2 2 is based on a similar approach to the one desenbod l in Section 4.2. The variances of the solute concentration profiles were obtained from the data presented in Figures 4.2-7 and 4.2-8 . Equation 4.2 3 was used to compute the variances, and equation 4.2-8 was applied to obtain the variance associated to the dispersion of the flow from the probe at the vessel inlet to the measurement section at the core inlet. The average velocity was obtained by dividing the average length of the path of the flow inside the vessel by the average time, Q. The Estimate Diffusion Coefficient is an approximation of the actual effective diffusion coefficient that in a one dimensional flow setting with [ constant velocity would yield a similar dispersion of the incoming solute plug. This value is useful to quantitatively estimate the magnitude of the diffusion observed in each of the three runs analyzed, thus i l making possible their comparison. Finalty, the value of the integrated concentration is useful to assure that the amount of solute flowing through the core inlet in the experwnental run is conserved in the numerical l l simulations, and no extra solute is " created" due to numerical effects. ( From the results presented in Table 4.2 4, it is clear that the high-order run (H.O. TRAC +T.D.), l performed with the numencal model described in App. O and the turbulent mixing model discussed in l l Section 2.2.4, conservatively predets a lower mixing in the downcomer and lower pienum than the one observed experimentaty. Comparison of the variances yields a sirrelar conclusion as the one obtamed from the analysis of Fig. 4.2 4, that is, the mixing is conservatively underpiedcted. The reason may be found in the empirical character of the constants associated with the turbulent mixing rnodel, and the fact that the l- TRAC-PF1 simulation, even with the high order solute tracker, is not able to accurately resolve the effect of the inlet coolant )st impinging in the downcomer walls on the turbulent mixing and flow pattom. These two reasons could account for the lower mixing predicted t:V the numencal simulation when compared to the
- experimental results.
On the other hand, it is clear from the results that the use of a high-order method improves considerably the sharpness of the solute plug tracking. The standard SETS t,pwind tracker (Base TRAC-PF1) prodcts a diffusion of the same magrutude as the experimental one, even without a turbulent diffusion model or a jet impegmg model. The less dNfuente character of the high-order simulation makes the results described in Section 5 conservative from the point of view of mixing. The unborated plug sizes prodcted by TRAC-PF1 with the high-order solute tracker and the turbulent diffusion model for the transients analyzed can be considered smaller than the actual plug sizes that would yield the limiting mwwmum concentration at the core inlet. This assertion is supported by the sirrularities between the expenmental test analyzed and the actual dilution transients studied: they are both pump restart scenarios in Westmghouse PWR vessels. 4 23 L____-______________-________________
i i 1 l Inlet Concentration , 0.0013 ,. , , , . . r
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......, I ..I, ..7..
i
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4 .. i. . . . . . . > bP ! ... :.... . 3 .. -.....,... i 6
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. I t
- E l l 1
o ,...4... ..... ; . l.. . .! ... . .! ... ... .. ....... ....-..I. :
.. . .i ..' 4. ~ ...i... .....
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! t >
i e i E ...t,,, ! i. t Ii .. !. . ...'...,. l 4 , g . i j i
! 4
. .+.
?
t i. I h .{,f. !
.. . . . , . . .. ;. . .. I . .. j. . , ..
j , i
. . . . . > . . . . A.
t . , t i
.I .<, ...
. . . -. ....as......
~..........,...
.....t....+...t.-...;.
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. /.;. . - . . . + . . . . . . .. : ...,..4....;...
.4
, . &.. ...i.. . . . ;.. .
4 e* .e 1 l i < i
- 1. . . _ ...:, . . . ,.
t
. . i.
.i .,
,9.s . i i s. ,I - i > , . ! !
s 0 . 0 10 20 24 ! ? time (S) ! l I 1 ! Figure 4.2 7 Normalized inlet Concentration i i Core Inlet Concentration 0.0005 . 3 ; , , . .
'- f i i -
1 . j ' i : i : hp 0.00045- -lj ,
!. -+-. -
i l
, .- +1 i ! -
I ! l l H. Order +T.D.
- + -- l i
0.0004- - < -
, li.r
--+ --
! +- i i Sed. TRAC
* ' L' e 0.00035-r+t ! !
- J.t yt. '.- t p-'
l
. C. ; i j e Q,QQQ3 .;.. .. . j . .. ...4.. ........ ; .. . . . . . . . . . . . . . . . . . -. . . . . .
05 i .. j ..e 7. . . 4.. : 4 . b f r : I - ) i
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, 0.M25- :-
i i .
!i .! J+ v, ' ir ".--- - ,---
- : . i i- - --- - -
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4
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; i - '. ~ -
! i i
- 0. M -
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+--- 5 --
+1- F-0 + ' i
- i ! -
. i 1
Q 0.00015- - " 4 -
! I '
+
i
^ -~--+- l
^- -+ +
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+ .
6 i. t--- 1 j t . - Q,g j. .
. ... . . 1. . !
.. 4.. .. . ; . .,.;...i..... 4 . . a . . .i !
t
. .I
+
i
/
I [.-. 1 Se - m ~f . i n n- r .- =. .g -e I * \ -' r m-~ ~ i .
'--r -
.e. .. .
i i : n .. v v i . 5 0 10 20 24 time (s) i Figure 4.2 8 Core inlet Normalized Volume Average Concentration i 4-24 C__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .1
4.2.4 References 4.2 1 Peterson, P. F.,'A Method for Predicting and Minimizing Numerical Diffusion *, Numerical Seat Trans/er, Part B,21, pp. 343-366,1992. 4.2 2 Nauman, E. B., Chemical Reactor Enoineerina. New York, Wiley,1987. 4.2-3 Frost, W. and Moulden, T, ed., Handbook g[ Turbulence. New York, Plenum Press,1977. 4.2-4 Alavyoon, F., et al., ' Experimental and Computational Approach to investigating Rapid Boron Dilution Transients in PWR', First intomational Meeting on Boron Dilution Transients, State College, PA, October 1995. t 4 t l l l l 4-25 1
I 4.3 AP600 loput Dock Benchmarking - i 4.3.1 Thermelhydraulic Benchmarking l I 4.3.1.1 Staady State i The ben 0hmarking of the Steady State model was based on the comparison of the main system i parameters predicted by TRAC with the reference values for Thermal Design Conditions (TDF) proposed,as the initial conditions for the a ' nalysis [4.3-3). The Steady State was achieved at 102% nominal power by controlling the pump speed with the constrained steady state TRAC-PF1/ MOD 2 capability. The target mass flow rates at the impeller cell e a s c.O interfaces were set equal to[ -l g a, c-nd the final pump speeds were[ .Jrd/s for the pumps in Loop 1, and{ s$or Loop 2. Tables 4.31 through 4.3-4 display the results for the steady state conditions. The values ! included within brackets correspond to the reference TDF values (or the percentage of error). The results show very good agreement with the reference TDF state [4.3 2]. See App. B for a more detailed discussion. f k l f 4*N
I i 4.3 AP600 input Dock Benchmarking 4.3.1 Thermelhydraulic Benchmarking 4.3.1.1 Steady State , The benchmarking of the Steady State model was based on the companson of the main system
- parameters predicted by TRAC with . the reference values for Thermal Design Conditions (TDF) proposed,as the initial conditions for the analysis [4.3 3].
The Steady State was achieved at 102% nominal power by controlling the pung speed with the l constrained steady state TRAC-PF1/ MOD 2 capability. The target mass flow rates at the impeller cell-
-%o 40 interfaces were set equal to( j and the final pump speeds were[ .)rd/s for the pumps in Loop'1, and{ s$or Loop 2.
l Tables 4.31 through 4.3-4 display the results for the steady state conditions. The values
- included within brackets correspond to the reference TDF values (or the percentage of error). The results show very good agreement with the reference TDF state [4.3-2]. See App. B for a more detailed . l discussion. j 9
l , i i l. t l b_1_____________________ _ _ _ _ . _ _ _ _ _ _ __ _ _ _ _ . __ _ _ _ _ _ _ _ . _ _ _ _ _ . _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _
l Conditions in the VESSEL for TDF Reactor Power 102 % Nominal Pressurizer Pressure 15.07 MPa 2186 psia ( 0.6%) Core inlet Total mfr. 8540.0 Kg/s~ 67.7789 Mlbm/h Core Outlet Total mir. 8540.0 K0/s 67.7789 Mibm/h l Low Plenum T avg. 548.90 K 528.35 *F i Core Inlet T avg. 549.00 K 528.53 F ( 530.4 *F ) l
- . Core Outlet T avg. 591.10 K 804.31 F ( 805.1 *F )
Lower Plenum P avg. 15.34 MPa 2224.87 psia Core Inlet P avg. 15.31 MPa 2220.52 pois Core Outlet Pavg.: 15.26 MPa 2213.28 pela Upper Plenum Pavg. 15.31 MPa 2210.38 psia Table 4.31 Vessel Conditions for TDF Conditions in the LEGS for TQF Mass Flow Rates Hot Leg 1 4618.0 Kg/s 36.6355 MlbmM Hot Lag 2 4818.0 Kg/s 36.6355 Mlbm/h CoPJ Leg 1a 2308.0 Kg/s 18.3178 Mlbm/h (18.32 MibmM) Cold Leg 1b 2300.0 Kg/s 18.3178 Mbm/h (18.32 Mibmm) - Cold Leg 2a 2300.0 Kg/s 18.3178 Mlbmm (18.32 MibmM) Cold Leg 2b 2308.0 Kg/s 18.3178 Mlbmm (18.32 MlbmM) Table 4.3-2 Conditions in the, Legs for TDF. Mass Flow Rates 4 27
l Conditions in the LEGS for TDF Liquid Temperatures Hot Leg 1 588.6 K 599.81 F ( 600.0 *F ) Hot Leg 2 588.6 K 599.81 F ( 600.0 *F ) Cold Leg 1a 548.9 K 528.35 F ( 530.4 *F ) i Cold Log 1b 548.9 K 528.35 F ( 530.4 *F ) Cold Leg 2a 548.9 K 528.35 F ( 530.4 'F ) Cold Leg 2b - 548.9 K 528.35 F ( 530.4 'F ) Table 4.3 3 Conditions in the Legs for TDF. Liquid Temperatures i Condmons in the STEAM GENERATORS for TDF 10 % Tde Mugghg :10% Redaden in Mem. Asese 10%Redussen of MuW Vetsnes 10% Reducten in Nasher of Tese bem 4307 to 5875.30 Sisam GeneralerLoop f Boiler inlet Mass Flow Rate 1864.00 Kg/s 14.7939 M1bmh Liquid Level: 14.31 m (87% NRS) 48.95 ft Feed Water Flow : 540.80 Kg/s 4.2921 MlbmM Steam Flow : 540.70 Kg/s 4.2913 Mlbmh i Steam Line Pressure : 5.30 MPa 768.70 psia Liquid Mass Secondary Side: 54487.18 Kg 120123.70 lbm (44.1%) Steem Generator Loop 2 Boiler inlet Mass Flow Rate : 1865.00 Kg 14.8018 MibmM Liquid LeVol: 14.31 m (67% NRS) 46.95 ft Feed Water Flow : 544.40 Kg/s 4.3207 Mtbmh Steam Flow : 539.90 Kg/s 4.2850 Mibmh Steam Line Pressure : 5.30 MPa 788.70 psia Liquid Mass Secondary Side: 54701.06 Kg 120595.19 lbm (+0.5%) Table 4.3 4 Conditione in the Steam Generators for TDF 4 20
4.3.1.2 Transient Benchmark. Loss of Normal Feedwster (LONF) The benchmark of the transient decks was performed by simulating the Loss of Normal Feedwater Transient (LONF) whose reference results were provided by Westinghouse (4.3-3]. The transient was run up to 5000.0 s past the point where the system reached the minimum core temperature at about 3000.0. An aditional 2000 seconds were run to assure that the lowest system temperatures were, in fact, the minimum for the transient, and that the natural circulation flows reached a relatively stable condition. Since the main events controlling the transient behavior take place within the first 1000.0 seconds after reactor SCRAM, the legth of the transtent will allow benchmarking of the transient decks against the LONF Reference run. One of the important characteristics of this transient as analyzed in the present report,is that off-site power is not lost, that is, the pumps keep running at nominal speed after the SCRAM signal has dropped the control rods into the core. The SCRAM is assumed with one stuck rod, as desenbod in Section 3.2. The time sequence for the main events for the TRAC senulation and the Reference LONF transient (4.3-3] are shown in Tables 4.3-5 and 4.3-6. The small discrepancies in timing can be attributed to two main 4 causes, i.e. the difference in initial conditions and the more detailed TRAC system model that may be able l to resolve certain physical phenomena which do not appear in the Reference run. Figures 4.31 to 4.3 25 show some of the system maia parameters for both the TRAC simulation and the Reference run. The actions of controllers and trips as simulated by TRAC appear to rnimic quite closely the sequence observed in the Reference run from SCRAM (Fig. 4.31 and 4.3 2) to the turbine valve closure (Fig. 4.3-12)
- The transient starts with the loss of Feedwater to the steam generators at 10 seconds. Figure 4.3-1 shows this avent happening 10 seconds into the transient. The feedwater flow is completely shut down at about 18 sewnds. Since the turbine valve remains open, and the reactor has not yet received the SCRAM l signal, both steam generators boil off, while the secondary side pressure remains constant (see Fig. 4.3-2).
Tho different steem generator pressure behavior with respect to the Reference case (Fig. 4.3 3), where I the pressure raises steadily, is most probably due to the more detailed TRAC model used for the secondary side of the steam generators. The constant pressure scenario is physically consistent with the boiling of the steam generators, while the turbine and main steam valves remain open. Figures 4.3 4 and l 4.3-5 show how the decrease of secondary side inventory follows a similar trend in the Reference case and in the TRAC simulation. The zero level in Fig. 4.3-4 is only indicative of the level crossing the lower level tap, that is, some liquid inventory remains in the secondary side, as predicted by the Reference run. The drop in steam generator water level trips the low low steam generator level signal at 87.8 s 4-29
in the TRAC simulation, while the reference run predicts this event at 83.8 s. This small difference is most probable related to differences in the steam generator models employed in each run, and the fact that the initial conditions are not exactly the same in both cases. Figures 4.3 6 and 4.3-7 show how the SCRAM signal is activated at about the same time, i.e. 90.12 4 (TRAC) and 85.8 s (Reference). Within less than one second,90.84 s for TRAC and 86.6 s for the Reference case, the pressurizer SRVs open (see Fig. 4.3 8 and 4.3-9) as a result of the spike in
~ system pressure foliowing the almost complete loss of heat sink in the steam generators. Both simulations
( show a very similar pressure behavior. The Reference run predicts the opening of the steam generator SRVs, but this is caused by the " anomalous
- pressure prediction during the boiling off of the secondary j side inventory. TRAC simulation does not predict this event for the reasons stated above.
The maximum pressurizer inventory is reached at 87.8 seconds in the Reference run, and 90.0 seconds in the TRAC simulation. Figures 4.3-10 and 4.3-11 are not direcdy comparable, because Fig. 4.3-10 shows level and Fig. 4.311 inventory. Nevertheless, the pressurizer inventory change displayed in both plots is similar. Finttiy, the reciosing of the pressurizer SRVs is predicted also at about the same time by tath simulations, i.e. 92.06 seconds for TRAC and 89.1 seconds for the Reference run. At the same time the SCRAM signal is activated, the trip wiivwT;riv the turbine valve shuts it down. Figure 4.3-12 shows the increase of steam flow during the secondary side blow off, and the sudden stop of the flow after SCRAM. However, the main steam line valves (MSIV) remam open, and Fig. 4.3-13 shows the interchange of steam between the two steam generators later in the transient until the MSIVs close at 602.08 seconds because of a low T Cold signal. l The low-low steam generator level signal also actrvates the PRHR system. After 62.0 seconds i delay, at 155.44 r, the PRHR isolation valve opens. The Reference run predicts this event at 143.0 seconds Lscause of the initial discrepancy I.i the SCRAM timing. Figures 4.314 and 4.315 show how the l mass flow rate and the power transferred to the !RWST [4.3-4) are well predicted by TRAC during the period while the pumps are silE opeitting. After the pumps are tripped by the Low T Cold signal, the mass i flow rate is overprodcted by TRAC (Fig. 4.3-14), but the power is closer to that predicted by the Reference ! run (Fig. 4.315), since the IRWST model was optimized to obtain the power transfer as close to the reference run as poesble. As a result, the thermalhydraulic response of the system as simulated by TRAC, is quite close to that of prodcted by the Reference run. The Low T Cold signal trips the CMT isolation valves at 602.08 s (568 s in the refen x:e run), starting the ir.joc. ten of highly borated water in the downcomer, and the flow through the pressurA balance lines con'metod to the cold legs of Loop 2. The flow from the CMTs starts at 624.76 s,22 s after the low T Cold iignal. Figure 4.3-18 displays the flow for each CMT line. Comparison to the values displayed in 4 30
i Fig. 4.3-19 (in this case for both CMTs combined) show similar maximum injection rates after the valves ! open, and roughly the same rates of injection in the reference run arid in the TRAC simulation. These rates ! determine the flow in Leg 2, as will be shown in Section 5.1, and, ultimvely, the boron distrhution within the pnmary system. The low T Cold signal also activatet the MSIV trip. The steam geriorators become isolated from one another, and both loops are now thermally corinected 071y through the vessel. The system thermal response predicted by TRAC, as shown in Figs. 4.3-20 and 4.3-21, is very close to that of the Reference run (Figs. 4.3-22 and 4.3 23). The minimum values of the hot leg temperatures are very close: 505 K (450 'F) for the reference run and 510.0 K (460.0 'F) for TRAC. In the 1 cold legs, the temperature history is close to the reference run for Legs 2a and 2b, but Leg 1a and 1b i l present a larger drop in the TRAC simulation. This behava, together with the different pressure behaver observed in Fig. 4.3-2 for the steam generator in Loop 1 predicted by TRAC, leads to the conclusion that the flow in this steam generator is lower in the TRAC simulation than in the Reference run. The amount of hot coolant coming from the hot leg through the steam generator U-tube is higher in the Reference run, and its mixing with the cold coolant flowing from the PRHR piping, increases the ternperature of the hot legs. Less hot flow from the U-tube, as calculated by TPAC, will render less heating of the coolant from l the PRHR piping, and result in the lower cold leg temperatures observed in the TRAC simblation. Finalty, it is important to note that the TRAC simulation also predicts the increase in temperature that follows the minimum values at about 4000 to 4500 seconds (see Fig. 4.3 20 and 4.3 21) as a tesult of the decrease in CMT injection flow. The results discussed above show that the LONF transient computed by TRAC, and used as a baseline calculation for the dilution sttrjias desenbod in Sechon 5, can be r.cosidered a good ( representation of the system thwmalhydraulic response for this transient whon compared to the Reference LONF from the AP600 SSAR document (4.3 3). In addition, the benchtnarking also proves that the input decks used in the analysis are a good model of the AP600 system design currently adopted at the conclusion of the work. ( a.31 l____ _ _-- ' _____ ___ ____ _ )
l I l-L [. i i~ l Event Chronology during the TRAC-PFIMOD2 LONF Simuistion I Time Event 10.08 s Loss of Feedwater (MFW valves are closed) 87.83 s Low-low Steam Generator Level signal (2 second delay) l 88.84 s Hi@ Pressurizer Pressure ( > 16.588 MPs ) (2 second delay) l l, 90.12 s Reactor SCRAM i 90.12 s PRHR is sctivated by Low SG Level (62 second delay) l ! 90.36 r, Pressudzor SRV 1 opening signal ( pressure > 16.960 MPs ) E i lI' 90.36 a Prosaurizer SRV-2 opening sinal ( pressure > 16,960 MPa ) J 92.06 e Pressurizer SRV 1 and 2 Close (pressure < 16.680 MPa ) 155.44 s PRHR isoladon valve opens ! 601.08 s Low T Cold signal (2 second dolcy) l 602.08 s CMT looletion Vaks trip (22 second delay) l !.- 602.06 s MStV trip is ad/ated. MSIV close 624.76 s CMT lsolation V9ves Open l 1
; 624.76 s RCP trip (15 second deley) l 830.79 s RCPs start coast <kwn.
f Table 4.3-6 Event Cnronology for TRAC LONF Transient L i u l' fs 4-sa
I. l l l t Event Chronology during the Reference LONF Simulation l- [ Time Event l . 10.00 s l Loss of Feedwater (MFW valves are closed) 83.80 s Low-low Steam Generator Level signal. Reactor Trip reached ' 85.80 s Rods Begin to drop 86.60 s Pressurizer Safety Valves open I
~
87.30 s SG Safety Valves open 87.00 s Maximum Pressurizer pressure reached 89.10 s Pressurizer Safety Valves reclose 89.20 s Maximum Pressurizer water volums reached 143.00 s PRHR actuation on low SG water level (wide range) 188.00 s SG Safety Valves reciose 568.00 s CMTs actuation on low T-cold 'S' signal 568.00 s Steamline isolation on low T cold 'S' signal 583.00 s RCP trip on low T ooid *S* signal 8870.00 s Pressurizer Safety Valves open 18574.00 s Pressurizer Safety Valves recicas Table 4.3 6 Event Chronology for Reference LONF Transient [4.3 3] I A-33
t i I Steam Generator FeedWater Mass Flow Rate l 1.2e+03 . , . . ' j -l 5j ! Ii
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I. 3 .i ! i , c ' i; l 200 . -r- , . ! 10 100 te@3 le+04 time (s) l Figure 4.3-2 Steam Generator Pressure. TRAC Girrntation ! - Loop With PRMR
-... Loep witneut PRNR 1200 ioco - -
n i E
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% / g
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m soo- .'= c. s e e i l I H . .,/ l 400 - - I I'
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if if 18 1d id Time (Seconds) Figure 4.3 3 Steam Generator Pressure. Reference LONF t
?
i. r l l Steam Generator Water Level . E $5 . ., , .- i.>. 1
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t i i C . '. ' l .. , 1 1 10 100 le<C3 le+04 time (s) l Figura 4.3 4 Steam Generator Liquid Level. TRAC Sinvilation 1 l Loop Witt. PRMR
.... Loop witneet PRNR i
l 140000 ) I
- i20000 - .
i l ,i . g 100000 -,- i
- 1 - l
' >% 80000 -um - l 15 l A I 80000-. l g 40000 - - socco. ! ... ........ .
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l . . . .,. 0 , , l ' 10 id Id Id Id l Time (seconds) Figure 4.3-5 Steam Generator Liquid inventory. Reference LONF 1 I I l l 4-36 l I l i
f. l t I !' Reactor Power ! 1.1 . . . . . , . l > i i !.; ! i! las 1 :
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i l L I I i l 1 l t
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1 l Pressurizer Pressure J l 2.6e+03 ' .. . . ; -. it; t -
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! Figure 4.3 8 Pressurizer Pressure. TRAC Simulation l
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4-38 l l i I j
l Pressurizerlevel ! M i , ii i, , 5 I. i i ( !.
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l 10 - , . 10 100 le+03 le+04 i [ - time (s) I Figure 4.3-10 Pressurizer Level. TRAC Simulation. I
~
Presseriter Water Volume I
'= isoo .
E . c u 2m 8'00 -- -
.u -
e E 1200 - -
= '
s -
.S t o c o - -
m - L
-l 800 --
g go, ! id Id 1d Id Id Time (Seconds) Figure 4.311 Pressurizer Liquid Inventory. Reference LONF 4 39
1 l Turbine Line Mass Flow Rate 3e+03 ! t
- i. .
I til I
- i'. ;
-I l
; .: i :!' ! i n
t!, ! 4 ., i e
\
I t A ri- b: d-2.5e+03- ,t-- i-
^ ,
- 1,: i 0 *
!i :; I i 6 03- -
i -- - !, to- d : -- L- - + !-- -}- - - ;- t -- !- w i
- 1 1 ea : 1 f
** :,- ! i es
]
g 1.5e+03- - ' 4~- A -- -- M^ - - -i ,
- E i- !
, !ll k ,
- i.
l 2 :: - !! W 1e+03- + - +i t +1 . , - - i- - U r*- -
*+d -- ;- 4-I, : 1: 'ii i
{ l i , I' !' 500- ;
" rih t-- ![i" '
; !fth '
4 i i ; .! . lii ii
..lli
. ii:. 4 j'
ii i! l i ,i l ;ji- '
; i 0 , . -
1 10 100 le+03 le+04 I l time (S) q-l l Figure 4.3-12 Turbine Line Mass Flow Rate. TRAC Simulation Steam Generator Steam Flow !. 1.6e+03 - - - , .
;i ; :,
i 4 -
- i; ' i i,...
- - 1 3 t -
30-1 i- ~ - + ; - - G+; ; - 4~ ~ Hb - ;- i~ I.4e+03- '
, t t . i!! so-2 l m ) ' ;i.. '
t!!
- 1.2e+03- j- 1
, pi ,
J
- Ic+03- i- t>- -+-- -
'I [
l v . ! ,
- + ' , >: iin ' rit ;-
i. t sa . l e 800- } H ! ! E iji j :. t+!;;t i l 5 600- - '
'pi~'
i l;i -
-i ' !+ 14 '!-
l l 2 ti, ; i: i U! 1 b ca 400- l-i Ii-
+.t-i I ! < -!!: '- -
+ I*Eu -
I- !- E ! ii , .' 3 200- l '+b i i- , ii - i-0- - i
- ?
i' . i-
; U G *" **" ', .i. i
! i:j i 'ii; i i
-200 , , . -
1 10 100 le+03 le+04 time (S) Figure 4.313 Steam Generator Steam Flow. TRAC Simulat'en 4-40 u_________________________ . _ _ - . _ _ _ . . _ _
[ - f f I t [ I l l- ~ l l L PRHR Inlet Mass Flow Rate i 250 . . . ;.. ,; ., .. :- , . , : , ,' e ilt.; '
.. l1: ;; ; -
. l: !;
..5: .!:
.!. ;j}!. ,
( i z i :- lili
~
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, 2, :
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ri ...' - t
- g:i I : : . . : i ,'
- :2 +
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't H
+
F
!'((,
' ' f; : o - Ref.
- l:!. k: <pII
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t d. e ! l. ' i
. l'!.,t Ei 1 i- , ,i :- : i'l-{.
4
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. !?
- t 200- 1it pH-- it!+ty -e 4+7 .wit-'g ! !FH;7 -li :,j:tH4-4-t ;; -
~
l *
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.i! in li;:
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i. l
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.l.
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-{ .?
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- t. i l j.! '
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% il:-
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l - 150- .j i +k n.:i- r! ^ it' 4 6 i+- + m .. i0-;%l;- 4 ,1
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i r .. ! @ ;.. ! .:i'.. !j. 5
;i..i ;- - t ! ;:. .; >t ::
w 'i ;! : !'!:j l(!s.- j . lg !. - - : 5 ; 3 ;i ' i. ;
' ;i.t 3:
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g
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. ..-41:'..
1
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. i,
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i , . , . i, , .,c.. - i',
+
L : : n. . ! - i : , 34 C ,- .- 0 le+03 2e+03 3e+03 4e+03 Se+03 6e+03 l time (S) Figure 4.314 PRHR Inlet Mass Flow Rate l 4-41
l l l Powcf TI*"SI"""d in the PW 0'1 * ' . , i fuc 0.09- :tl-
~~"
i Decay H*" 1
. t
- Ret e 0.08- P ....
.. .. .r - . . . . . -
=
0.0'7- i . . . .
..4..........--1 .. .;
i
. i u ' ..
w 0.06- : g\-
. ~.
9 - , 3 . o 1,
+
i, b 0.05- :
\
i t" -- 6 1 g : .
\
.* 1
$ 0.04- i,
+ ...! . ),. --
o t
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\
', i,
., i
\ T 0.03-
';- ! . i. -
.o ' " i.
' t.
a .t s
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~
. ... ...;.~~ "'
s._
* - - -~
~ - -
0.01- ' , , , , , . . . " " " " '
...1$.._...m , * -
- ~ '
i C , , , , , O le+03 2e+03 3e+03 4e+03 Se+03 6e+03
- - time (s)
Figure 4.315 Power Transfer in PRHR 4 42 w______-__.
I I-l 1 l 4 I
. i l Steam Line MSIV Fraction I j 1.1 i: - , ;.
i ! ; i ,
! 3 ' I ! I ' '
$O.1 1 ;.m -
i! l:i
. 4 e l' }g . i t i!. 1 ? SC-2 j
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& ; : i : : it; O .9.......-...l....3...
. f.y... ; .
l !, . . . .........!... .... E j i ! .' :i t fi, i C i .i4..a.4.!..i! ; i l ! *= W
.......,.4.i. -
' ...i.. ! .Q .. i r :i: : . ! ; i '...
I i !! W . , . 3
- +,
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i
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[
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4 . , j i
- i
. I !! .. t ' ' ' ' I'
[ i :
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- 1. : .i :
. I ts t 0 . , , :;
1 10 100 le+03 le44 time (s) Figure 4.3-16 Steam Une MSN Fractxm l l Pump's AngularSpeed 200 . , , , : ,
! ; . , , ;i 'i i~ -
r
.l .
l-tr Lag la 2 t - t.
, . i. ..
_y- - _ _ _ _ _ _ _ _ _ , _ _ _ _ _ _
, g l ^ I ;; . : . ! i !-
I 150- - (';' 4- 4 M;I ;- -l- tes 2a m
- l e6 ::,! l . - ?i !.sg 2b 6 ; !! .
i
+ . .
- ii: ,
i 3 I
'I ! ! !
li. . l
---3--- +- -! '- ' ;3 i- t2<-
E100-l
- rc l 6 a
- :: . i ii l 3me l i
i i ' '.i C 50- +- r- e ~ ~ !* i. r
+- +- "
l- 4 ! !.i ' i i ' I
. i. , ...
f ili l 0 . h! , I 10 100 le+03 le44 l time (s) Figure 4.317 Pump's Angular Speed 4-43 t - _ - _ _ - _ _ -
i l 1 l l Core Makeup Tanks. Mass Flow Rates 60 , i 1 4 ! ,- i t I
- i>
Ii CMT-1 r -
. ! i
' { ..
cMT-2
- i- i- .
^ 50- 7-
!;1
(-- i if+ 3 -i-
- !I ! !
) ,'
(!! . t
' !! ! i .
40- -- i- :+i - ;--- ' l-ji: i
.e w l, i .
I N i i i i ! . ? ii ! M 30- - t -+rL4~ 'i -!i- 5!.t
!- ~+ 2 .
- F-k !
l i ! l i !' C> i
-i e
W i : 1 ; . e 3 ...p......,...;..
. < .. ... . .. ... . . . i. . .! . .i . L . . . . .i..j..j... ,.. ... l... .. .1. _
; i , ;; - :;
' ' 3 i 3
; I, ,i 2 10 I
. p. ...+.. ,
!ii; I!
i i* ; ;
-I I ! .i
, . .i i
i ,. i 0, . , . 10 100 le+03 te+04 I time (s) l l Figure 4.3-18 Core Makeup Tanks. Mass Flow Rate. TRAC Simulation l l
- 20 .
u 4c 100 - - 1 1 6
~
30 . I n O I l C ~
- 60 -
e 2 . . c . j- - k sn . I emens to - - N v -
~
0 , , . i d- Id 18 1d 18 Time (Seconds) l Figure 4.319 Core Makeup Tanks. Mass Flow Rate. Reference LONF 1 4 44 l _ _ _ - - - - - - - - 1
WESTINGHOUSE PROPR!ETARY CLASS 2 i t l Cold Legs Liquid Temperature 700 . s : i: !
!!' i li 2 12g la 650- -4 -- ' - -
L'i. ;- +- i us tb f g., ' ,i i .....:;..L . .. . f ., ..9...+. . . ; . .. 1 - ..
! ;i >
!i i teg 2a C
v 550- d +!- -l~ O"- w.;.:.d.c.,%.. ; c- {;a 2b
} 5 :- , t : I 8 500- ---- +
-t- ;-H +
- t r b +- J'" v'%-
-i- -
3 gm i
. ! ; [
i - : t I '
- 8 1
'i
. t
%4 . i 88 b
450- --
~~t-+"! ++! l
~--
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--H + i -
I i ' i i )
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)
400- - --- i- > + -- r +- t - t- -1r. - - r;' a
!' l l
{ I Ii - f . i .
' i:
+i- -+-+~
[s 350- - i-
- t-t . :
+--' i
- - -+
-- m -
i n-4e
! I I
..';... 4 . t f '.
3QQ.
........;. ..4...l........o...-....-..k.......... -
...A.......a......;.4.-
! i !! $
i + !! 5 Y! 250- --
; -+- ! E- - -i '
I't1 H- - ', 1
+L' "r :-
j .- i, > ;
. i : i. i. . s i
200 . , . i I 10 100 le+03 le+04 time (s) Figure 4.3-20 C.,id Leg Liquid Temperatures. TRAC Simulation l l Hot Legs Liquid Temperature 700 .
; i.,
I
! * - g
.j -
i i.
;.. ! r u""g l
{: ~ l , 'la 650-
- r
' * ^ i-us2 5 { b
-i 4 t a i 1 \ ,b. $b
}
l: i 6 . 1- ! 1
+
- A
-l ]
; i.' ! !
e !-.o ....... i o . T e -
.s, 550- ....p... 't t i :
.i; j;
. . i
' ~
g 9
- 6. ii: i, i i 4:
4,*j. ?P - o , a ,. & !: +* - -t .es 2 B '. 1 W t e . . H 450- - ,
, "i i it-ii-
'i i ? '
. i . - ;
a ! !
} i t ! !
i + i i- H - 400- ! t l i f i I t ' l 350, . . . > 10 100 le d le+04 I i time (S) Figure 4.3 21 Hot Leg Uquid Temperature. TRAC Simulation } 4-45 I
- - - . _ _ _ - _ - - . - _ . - _ - - . . - - - _ - _ . - - - - _ - - _ _ _ _ . _ - - _ _ . _ . _ _ .- - _ _ _ . - - _ _ - - - - - _ _ - _.____-----___.._--N
l I r Seturetiea (- ----Het Leg
--~ ~ Ceie Let i
700- I 1 550-~ - T 600 - {~~~~~ i
.a :
. " , . '=,s
\
$ 50- ,,..
3 .
. ss g 500 - - g %
~ s v -
*r s .*
a.
's * ,'
E : e'
- 450 : '
s " '
- s ,
400 -: s.." 350 e e i 10 td 18 to to i Time (Seconds) l i Figure 4.3-22 PRHR Legs (Loop 1). Liquid Temperatures. ReferenceLONF 5eturotien l
----wet Le,
----coonte, 700 m 650 - -
s F : . - 'i, - 1 o -..
- 500 - - ,
u - s u . 5: : ,' % . ' - 550 - . - g . . . E e
- af's s '
" 500 -' ','. , ,-'s
- g s 9 s e
, ' a * ..,,,
45g .; .... , e s s a s to 10 10 10 10 Time (Seconds) Figure 4.3 23 CMT Legs (Loop 2) Liquid Temperatures. Reference LONF 4 46 l
i 1 i 4 l ! l 1 Hot Legs Mass Flow Rate 1.2e+04 , i:.
- 1. le+04- lI ;
$8I l u2s le+04- !
4---T..;.. . u-ti t . ; 4.. 4 7. 4.p. ...!- g }.
;.. 5
. 1
+
- - - ^ - i 'i ' --- -
1 i &s w 8e+03- > : - ,. i
'J-S 7e+03- i! :- , t i!i '
i C5 1^ ~L-- i W 6e+03- -, + 4-i- - H -- ;- -
"- - :h g ii .
i Hi 1: i-o
===
Se+03- .!+ nt 1 . 1 I4W ..j .{. . 4.I.{3. .....p.....~...3..., ..J,.. . . . . . . . . - . _ ... j. . . ......L-Ull 4e43 . j . .[:
- I ; -tfI
'-t
--- t- 4-- - - - - -
3e+03- - -- tt t t- r-
~
2e+03- - rn, ! ri!- l ' !
- : ti :
.l- .i le+03- ,
lti . 4 t - !-
. ....a i ;;
.i O
10 100 te+03 le44 tinte (S) ; 1 Figure 4.3-24 Hot Leg Mass Row Rates. TRAC Simulation i I Loop with P9MR
--~~ Loop without PAM4 j l
12 se e A 3
'N .
M - 4: R 6- - c . MS N
.4- -
" i
~ !
.2- -
0 . , , s
- e. 2 s a 10 10 to 10 10 Tune (Seconds)
Figure 4.3 25 Hot Leg Mass Row Rates. Reference LONF l r 4-47 w____.__._ ___._.___m. _ _ . _ _ _ _ . . _ . _ . _ _ _ _ _ _ _ . . _ _ _ _ . J
l l l
- 4.3.2 Neutronic Benchmarklag l l
The neutronic bench marking of the core model was carried out by running a series of st .ndard Hot Zero Power (HZP) and Hot Full Power (HFP) scenarios. The objective was to evaluate the 'wo-dimensional normalized power maps for the steady state and SCRAMMED core with a stuck rod at location l K 2 [4.3-5]. Two runs with constant thermalhydraulic parameters were selected to represent the HZP and HFP states. In addition, results for full thermalhydraulic feedback, that is, with radial and axial temperature profiles of the fuel rods and coolan, where also obtained from the steady state.
)
i l l The results from the fixed thermalhydraulic conditions were used to compute SCRAM and Rod worths. These value were then compared with Reference data provided by Westinghouse (4.3-6], and the differences between fuel assembly norrnalized powers were used to assess the accuracy of the core and reflector models. The following table shows the K, values obtained for standard HZP and HFP conditions: HOT ZERO POWER [4.31] l Conditions , Fuel Temperature : 558.15 K (545 *F) Core Pressure : 15.1685 MPa (2200 psia) Coolant Density : 755.21 Kg/m* (47.15 lbm/ft*) O 558.15 K (545 *F) Boron Conc.: 1925.0 ppm K,
- All Rods Up
- 1.02204 SCRAM: 0.918201 Stuck Rod: 0.934288 l SCRAM Worth ( AK,/ K, %) : 10.15 %
Rod Worth : 1.574 % ! Fuel Assembly Normalized Max. Peak Power : 1.2836 (Ref.: 1.330) Stuck Rod Normalized Peak Power : 11.0753 I HOT FULL POWER [4.3-1] Conditions Fuel Temperature : 804.37 K (988.20 *F) Core Pressure : 15.1685 MPa (2200 psia) Coolant Density : 726.77 Kg/m* (45.37 lbmnt*) e 572.87 K (571.5 *F) [4.3 7] Boron Conc.: 1753.0 ppm 4-48 L__ _ . . _ . ._ _ _ _ _ _ _ _ _ _ . _ __ _ _ _ - _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ -
I K, All Rods Up : 1.01403 l SCRAM: 0.908895 Stuck Rod: 0.924013 i SCRAM Worth (A K ,/ K., %) : 10.51 % (Ref.: 9.68 %) l Rod Worth : 1.51 % (Ref.: 2.04 %) Fuel Assembly Norrnalized Max. Peak Power : 1.2817 Stuck Rod Normalized Peak Power : 10.4842 (Ref.: 11.987) The Steady State run with full thermelhydraulic feedback at Thermal Design Flow (TDF) conditions yields a K, = 1.004 for 1830 ppm boron concentration. This K, represents 400 pcm positive reactivity. The effect of this small reactivity on the power is negligible during transients. As observed in the LONF transient power plot (Fig. 4.3-6), the power increases less than 0.03% during the 10.0 seconds prior to the Loss of Feedwater event. The results of the rt.ns described above are presented in the two dimensional normalized power l l (NP) maps displayed below (Figs. 4.3-26 to 4.3 32). The maps show that the maximum differences between the reference normalized powers and the NEM values are toss than 6.7% for HFP conditions (Fig. 4.3-28). The values shown in the plot are the ratios (NPu - NPW /NP , The largest differences are observed in the penfery, close to the reflector region, j For full thermalhydraulic feedback (Fig. 4.3-30) the maximum differences are less than 7.9%. In this case, the discrepancies could be due to the three4imensional profiles (radial and axial) in fuel temperature and coolant density that TRAC feeds to the NEM model. The reference HFP results, however, are computed assuming homogeneous fuel temperature and coolant density conditions in the core. I It is important to note that the critical core average concentration for the Steady State conditions :
)
with full thermalhydraulic feedback is 1830 ppm. The value 1753 ppm was adopted to compare results for ! the standard HZP and HFP conditions, since the reference results were obtained for this core average concentration. I l I 4-49 l
l i l l t i l AP600 NEM Model. New Reflector ; 1 Reference HFP from Westinghouse M .# _ _.
- . 1.3 t
1.2 1.1 l I 0.9 1 10 o.: 0.7 0.6 0.5 I 0.4 0.3 l l 0.2 4 1
"' - 0.1 i I
0 l
, i .
g 1 10 16 l 1 2 D Normalized Power (NP) 0000 .0000 .0000 .0000 .0000 .0000 0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 0000 .0000
.5420 1160 9430 .9430 7160 .Stae .SS00 .0004 ,0000 .0000 ,0000 .0000 .0000 .0000 0000 .S$00 0000 .0000 0000 .7230 1 1100 9150 1 1920 1.1250 1 1250 1.1920 .9150 1.1990 .7230 .es00 .0000 .0000 0000 .0000 .1180 1.2000 1.0060 1.2200 .0010 1.!!60 1.2160 .9810 1.2106 1.0048 1.2800 1160 0000 .0000 0000 .53$0 1.1390 1.0140 1.1740 1.0410 1.3300 1.0060 1.0060 1.3300 1.0470 1.1740 1.0140 1,1510 .13Se .0000 9003 0110 0830 1.1900 . 0300 1.1100 9020 1.1930 1.1830 .9820 1.1100 1.0300 1.1900 .4030 .4150 .0000 i
l
.0009 1410 1.1400 .9110 1.2910 .9120 1.1210 .7350 1350 1.1220 .9710 1.3910 .9170 1.1400 1470 .0000 .0000 .8940 1.0750 1.1590 .9160 1.1670 1330 .5030 .5030 7330 1.1470 .9160 1.1990 1.0150 .0960 .0000 .0000 .8940 1.0150 1.1990 .9160 1 1610 1830 test .6030 1330 1.1670 .9160 1.1990 1.8790 .8940 .0000 .0000 9410 1.1400 .9110 1.2910 9120 1.1220 1390 .1350 1.1220 .9720 1.2910 .9110 1.1400 1410 .0000 .0080 .8150 .0430 1.1900 1.0300 1.1100 .9620 1.1030 1.1830 .9020 1.1100 1.0300 1.1900 .4830 8150 0000 .0000 .5350 1.1110 1.0140 1 1740 1.0a10 1.3,30,0 1.0040 1.0080 1.3300 1.04?0 1.1740 1.0140 1.1570 5350 .0000 000 .0000 .,100 1.2eu 1 ein 1.22 0 00 1.21 0 1.21 0 .9 10 1.2200 1. ten 1 2000 11a . ouc 0000 0000 .0006 .0000 1230 1 1190 9150 1 1920 1.1250 1 1250 1.1920 9150 1.1190 .1330 0000 0000 0000 0000 .0000 0000 .0000 1500 .0420 7140 .9430 9630 4160 8830 1900 .0000 .0000 0000 .9000 0000 .0000 .0000 .0000 0000 .0000 0000 .0000 0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 Figure 4.3 26 Reference Hot Full Power Map 4 50
1
- AP600 NEM Model. New Reflector Hot Full Power 16' _ _t_ 1 ' _i i ' i -
_ 1.2 1.1
= 1
= 0.9
=
0.8 0.7 0.6 1 l 0.3 l 1 I 0.4
=
. 0.3
. ' O.2 ;
0.1
=
1 0 1 i i i 1 10 16 2-D Normalized Power (NP) l
.0000 .0000 .0000 C000 .0000 .0000 0000 0000 .0006 .0000 .0000 .0600 .0000 .0000 .0000 .0000 0000 .0000 .0000 .0000 .5588 .0039 1985 .9036 .9036 1501 .8039 .3560 .0000 .0000 .0000 .0000
.0000 .0000 0000 1411 1.1441 .9399 1.1341 1.1156 1 1894 1.1341 .9399 1.1441 1411 .0000 .0000 .0000 0000 .0000 . 73 81 1. 3 S ?1 1.113 $ 1 3450 1. 0161 1. 2 049 1. 2069 1. 0161 1. 3410 1.113 5 1. 3STS .1387 .0000 .0000 0000 . 5414 1.1399 1.1143 1. 2384 1.10$ 4 1. 3 9 36 1. 03 44 1. 0346 1. 38 36 1.1956 1. 2164 1.1143 1. 2 399 .5474 .0000
.0000 .7816 .9139 1.2163 1.0929 1.1507 .9994 1.1313 1.1313 .9999 1.1607 1.0929 1.2163 .9138 7816 .0060 i .0000 .1339 1.0190 .95S1 1.3509 .9914 1.0684 1633 1433 1.0654 .9914 1.3$09 .9SS1 1.0190 ,1339 .0000 l 0000 .4495 1.0415 1.1541 9914 1.1013 1611 5004 1204 1611 1.101) .9916 1.1941 1.04?S .4699 .0000 0000 .0495 1.0419 1.1141 .9916 1.1011 1611 .5004 .5004 1611 1.1073 .9916 1.1141 1.0475 .3699 .0000
.0000 .1339 1.0790 .9151 1.3509 .9914 1 06S4 1633 1633 1.0654 .9914 1.3199 .9111 1.0790 .7339 .0000
.0000 7816 .9134 1.3163 1.0929 1.1507 9998 1 1813 1.1313 .9990 1.1501 1.0939 1.3163 .9113 .Tels .0000
.C649 .5014 1.1399 1.1143 1.2364 1 10$8 1 as te 1 03 44 1. 0 344 1 3836 1.1058 1. 3384 1.1143 1.1399 .5414 .0000
* .Ctet . u te flat 1.2 511 1.1135 1 3 490 1. 0181 1. 3065 1. 304l 1 0161 1.3 458 1,1135 1.3t?! 1381 .0000 .0000
.0000 .0000 . O ne 1441 1.1441 9319 1.1341 9 1411 .0006 .0000 .0000
.0000 . 004 _ One .0ne .n. on . 1.1114
. 90 1.1116 1.1347 .n399 n n36 ein 1.1441
. sin n00 n0 .n00 0000
. 00n . uG4 . .on One . nu 9000 un 0000 0000 un . nu .ent . n00 .One .n00 00n Figure 4.3 27 NEM TRAC Hot Full Power Map 4 51
AP600 NEM Model. New Reflector 1 l Hot Full Power. Comparison with Reference HFP Map 16 . . - - .. e 0.06
- Y, ' '
q ~ 1 5 L L 0.05 l m (- ~s rw.- .. . N a 4_, '1 . . i.. 7 0.04 l
' i w .cn ..a , n. r; .1 0.03 ;
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l-0.05
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[ t - 1 10 16 2-D Normaltzed Power Comparison ( (NP . NP.)/ NPu) i
.0000 0000 .0000 0000 .6000 0003 .0000 .0000 .0000 .0000 .0000 0600 .0000 .0000 0000 .0000 .0000 .0000 .0000 0000 .0160 .0453 .0234 .0417 .6411 .0226 .0453 . 0160 0000 .0006 .0000 .0000 ,0000 0000 .0000 .0259 .0394 .0213 .0141 .0004 .0004 .0541 0294 .0259 .0000 .0000 .00C0 0000 .0000
- 0200
. .0119 0244
- 0138 . 039$ .0410 .0010 . 0299 ..0313 .9134 - 8344 .0199 .0280 .0000 .0000 0004 . 0131 0234
- 0318 .0443 +.0542 0349 . 0181 .0105 .0349 ..etta . 9453 .0314 .0274 . 0232 .0004 0400 .0410 . 0337 . 0220
- 0411 . 0341 . 0181 0522 0133 .0181 . 0347 . 0411 0320 .0331 .0410 .0000
.0400 .0109 .0935
- 0419 .6311 . 0200 .0504 . 0304 . 0394 .0$04 .0104 .0311 .0415 .0535 0189 .0000
.0000 .0214 0016 .0043 0221 .0$12
- 0383 .0053 .0033 . 0343 .0513 .0221 0042 .0010 0214 .0000
.0000 Otte .0010 0043 . 0331 .0512 0303 .0052 .0053 . 0383 .0912 . 0121 .0042 .0070 .4274 .6000 .0000 .0149 .0135 - 6415 .0311 .0200 .0504 . 0384 . 0384 .0004 - 4200 .0311 . 6411 .0535 0109 .0000 0000 Sete .0331 .0330 a.0611
- 0341 . 0181 .0123 .0831 + 0181 . 0341 . 0411 . 0226 . 0331 6410 .0000
.9000 a.0333 .0234 .,0374 .0403 . 0543 .0349 .0195 .0101 0349 a.0163 . 0443 .0374 .4234 . 0233 .0000 "90 0164 .0179 0244 0134 - 0299 .0010 .0014 0295 .,0134 . 0244 tatt .0304 0000 .0000 0000 5000 ate 0000 . 0359 .8294 0312 0541 .0084 .0044 .6141 .0212 .0294 . 6159 .0000 .0000 .0000
.0000 *.0160 Ossa .0214 cent .0411 .0124 0453 . 0140 .0000 .0060 .0000 .0000 001 000 .0000 00 . .0 0 0000 .0000 00n 0a un . 0ut out . eue un .00u . nu . 00* 00u Figure 4.3 28 Companson NEM. TRAC vs. Reierence Hot Full Power Maps 4 52
AP600 NEM Model. New Reflector Steady State. FullT/H Feedback 16 .,.i- ,. - 3 . ., l.3 1.2 1.1 1 0.9 10 ' O.8 0.7 l 0.6
=
0.5 1
=
0.4 ? O.3
=
l 0.2
" 0.1 O
t g , , ,i l 10 16 2 D Normalized Power (NP)
.0000 .0000 .0000 .0000 .0000 .0000 0000 0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0004
.0000 0000 .0000 .0000 .5444 .ts00 1440 .4011 .3879 1443 .1005 .54s8 .0000 0000 .0000 .0000 0000 .0000 .0300 1241 1 litt 9231 1.1092 1,0904 1.0901 1.1096 .9222 1.1202 72$2 0000 .0000 .0000
.0000 .0000 7240 1.2334 1 0924 1,3457 1.0202 1.2131 3.2131 1.0205 1.3464 1.0936 1.2319 .t294 .0000 .0000
.0000 . 3 346 1 1109 1. 0962 1. 213 3 1.1142 1. 3049 1. 0 404 1. 04 64 1 J ot a 1.1190 1. 2113 1. 0 004 1.1134 .5399 .0000
.0090 .7719 9010 1.2233 1.10SJ 1.1134 1.0319 3.1910 1.1810 1 0211 1.1129 1.1043 1.2345 .9030 .TT38 .0000
.0000 .7351 1 0139 .94Se 1.2192 3.0171 1.0918 .1444 .1964 1.0910 1.0113 1.2194 .9643 1.0149 .7249 .0000 0000 .0623 1.0609 3 1903 1.0194 1.1419 9036 .1131 .5137 . ?t il 1.1420 1 0191 1.1164 1.0411 .0633 .0000
.0000 .0633 1.0816 1.1704 1.0194 1.1419 4037 5131 S$37 1830 1.1420 1.0197 1.1104 1.0404 .6634 .0000 0000 .?264 1.0141 .9462 1.2195 1.0172 1 0911 .7844 .?844 1.0974 1.0111 1.3793 .9610 1.0729 .t2S2 0000 0000 7131 .9029 1.2344 1.1941 1.1138 1 0231 1.1110 1.1909 1.0219 1 1924 1.1053 1.2334 .9011 1730 .0000 0000 $ 3 99 1.1135 1. 0903 1. 2113 1.1149 1. 305 2 1. 040 4 1. 0433 1. 304 9 1.1143 1. 2132 1. 0 983 1.1110 .5306 .0000 l
.0000 .0000 .?254 1 2316 1.0931 1 3461 1 0304 1.3137 1 2131 1.0302 1.2451 1.0038 1.2324 .7341 .0000 .0000 1 0000 .0000 ,9000 .9219 1.1191 7347 .0000 .0000 0000
. 00n .0000 .0000 . .1251 00n1.120,3
.Su .9321
. ,ut 1.1396 14u 1.0989 u,9 1 090,4 us 1 .2440 1891
.itu .sou .0000 .e009 .uu . nu
.no one . One . 6m .0000 . 0nD 00n un . net . Ou0 0ne un .uu .nu .uu . no ,. 1 1
l l l Figure 4.3-29 Steady State. Full Thermalhydraulic Feedback 4 53
l AP600 NEM Model. New Reflector I Full T/H Feedback. Comparison with Reference HFP Map 16 , ...g_.,, b. j '; , ^ 06
- ., ,i g, m
- k')
[). .,_ I J {Q g,, 0.04 10 @ g ao2 f!- Ms j;, g n; 6.94e-18 K W. ( E i U .. O 4'02 r a stb BB~ p 7 . . s r.' ' . .
; 0.04
~'
lu.. t
- l. - 4.o6 k-lb ' '
i I 1"- - ' i 1 1 10 16 2.D Normalized Power Comparison ( (NPu . NP )/ NPu)
.0000 .0000 0000 0000 0000 .0000 .0000 .0000 .0000 .0000 .0000 .0006 .0006 .0000 .0000 .0000 6000 .0000 .0000 00 tie 0040 .0631 .0409 .0140 .tiet .0412 .0641 006S 0000 .0000 .0000 .0000
.00Je .0000 .0000 .0029 0499 . 0016 .0691 .0234 .0236 0695 . 0013 .0$$$ . 0024 .0000 .0000 .0000
.0000 .0000 . 0103 .0310 . 0069 0149 . 0330 .0019 .0619 . 0334 . 0144 0061 ,0312 . 0005 .0000
.0000 0000 . 0092 .0316 . 0326 . 0369 . 0640 .0106 . 0342 . 0341 .0189 . 0442 . 0334 . 0205 .0390 0061 .0000 0000 .9901 0139 . 0560 . 0404 0000 .02*6 022$ . 0209 .0210 .0211 . 0404 . 0563 . 0133 . 6281 . 0205 .0920 .0000
.3113 0531 0009 . 0465 .6211 . 0472 . 0613 .0211 . 0444 .0091 . 0$32 .0$09 0292 0000
.0000 .0343 0125 - 0090 . 0441 .0219 . 0492 . 0213 0213 0493 .0214 . 0444 .0890 ,0134 .6353 .0000
.0000 .0385 .0135 . 0091 ..d441 .021$ . 0693 0213 0213 . 0693 .0214 . 0440 . 0090 .0124 .03e2 4000
.0000 0293 0509 . 0$32 .0091 . 0444 .0211 . 0412 . 0612 .0216 . 0465 .0048 . 0536 .4513 .0214 0000
.0000 .0529 0304 0280 . 0131 . 0562 . 0406 .0210 .0210 . 0400 0$41 . Ofte . 0290 . 0221 .0506 .0000
.0000 0041 .0394 . 0201 . 0134 . 0643 .0169 . 0343 . 0342 .0166 . 0649 . 0349 0221 .0315 . 0092 .0000 0000 .0000 *.0044 .0312 . 0041 . 0144 . 0334 .0019 .0019 . 0339 . 0110 . 0010 .0311 . 0163 . One .0000 0000 .0000 .0000 *.0024 .0109 . 0013 0695 02 .0 .0491 . 0019 .0000 .0000
.0499 . 0030 .0000
.nu .0000 .00n un . 00n . net . 04n .0,J6 03 .0,234 n .nu .un .ene . n00 .ene .0000 . One
. One .0000 . 0nt .nu .0000 . 0n D .00n .0000 .0ne . 00n . 00n . n00 . n00 . n00 .0000 00n Figure 4.3 30 Full Therma! hydraulic Feedbeck vs. Reference HFP 4 54
i I i I l l AP600 NEM Model. New Reflector l Hot Full Power. SCRAM with Stuck Rod l l 10 10 ' s l b -
~
1
*o -
7
~
6 ! g - 1 e s
.tl '
3 - 4 l C s l ' Z ' _&- 2
-n P. 16 16 y X l
f 2 D Normalized Power (NP) 0000 .0000 .0000 .0000 .0060 .0000 .0000 .0000 .0004 .0000 .0000 .0000 .0000 .0000 .0004 .0000
.0000 0000 0000 .0000 S 0181 1.3463 2 1234 2 1881 1.8202 1.1411 4993 .3409 .0000 ,0000 0000 0000 0000 .0000 .0040 1.5344 10.4842 S.0444 2.4812 2.1931 1.9052 1.0318 .4591 .4712 .4193 .0000 .0004 .0000
.0000 .0000 4.4321 0.3151 7.0903 3.1171 3.3145 1.4833 1.1858 .9421 .Sete .5441 .549J .3392 .000s .0000 0000 1,44S9 3.1094 4.5495 3.3874 3.0944 1.9249 1.4916 1.3415 .8043 .etu .4229 .4209 .2471 .1449 .0000
.0000 1 1094 8.9518 2.0140 3.4151 3.3449 1.1444 1.S130 1.2948 .9344 .4433 .4549 2401 .3324 .1113 0000
,0000 9952 1.04T2 1.2299 1.3904 1.5492 1.4973 .8431 7236 .5953 .5340 .3381 .2144 .134) .1351 .0000 1
6000 .9313 1.0452 .0187 1.9361 1.2379 7434 .2984 .2482 .4119 .4499 .2999 .1714 1798 .1414 .0000 l 0000 .4055 .4942 .4515 .0404 1.0144 .4324 .2314 .1918 .3412 .4076 .2441 .1545 .1444 .1319 .0000
.0000 .S244 .5011 .5134 .3899 .4904 4053 .3581 .3131 .2923 .3058 .3068 .1403 .1981 .1009 .0000
.0004 .24S9 .3434 .3373 .4535 .4951 .4114 .3899 .3539 .2832 .2499 .1852 .1114 .0931 .0594 .0000 i 0004 .1984 .3441 .3393 .2749 .3232 .2598 .2434 .2240 .1871 .1112 .1224 .1193 .0884 .0534 .0000
. 00. . On. 2in .24n .uG3 . u s.
. u u, .ine .lat .au, . ine .au .eue .ne . 000 l
.000. . een .. a.u uS .t a ul .itts .uu .1154 .lu . net .0ue .uu .uu .Out .0u2 .000. .Oue
! . On. . 0ne .nu .uu .0us .ute 10u .nu .0ue ..Su .04u . u0. e . 00n .eu0 l On. .au . nee . nee .uu .nu aco Ono .euu .u.uco un .0000 . 00u .. . 0n.a . uu .nu 1 i i Figure 4.3-31 Hot FuH Power SCRAM with Stuck Rod 4-55
I l l l t AP600 NEM Model. New Reflector Hot Zero Power. SCRAM with Stuck Rod 11 10 11.1 - 10 ' 9 j 6 8 g
*o 7
t . 6
.%- ~ s l 5 -
4 i b 3= 3 o . - l Z ~ 2 o
- 7. 16 16 rm ,
X Y . l l 2-D Normalized Power (NP) 0000 .0000 .0000 .4000 .0000 .0000 .0000 .0000 .0000 .04S0 .0000 .0000 0000 .0000 .0000 .0000
.0000 .0000 .0000 .0000 9.2439 3.3841 2.1154 2.2139 1.430S 1.1334 .4049 .3219 0000 .0000 .0000 0000 0000 .0000 .0040 7. 9443 11.07S3 5.3472 2.5310 3.3 055 1. 9030 1 ette .4324 .4441 .3913 .0000 .0000 .0000
.0009 .0000 4 8(t3 0.0307 1.4242 3.0332 3.32601.dets 1.1810 .9044 .9906 .5229 .5485 .3120 .0000 .0000 0000 1.4014 3.3247 4.744) 3.4049 3.1330 1.9009 1 4504 1.1947 .8390 .4410 .3094 .36$9 .2643 .1304 0000
.0000 1.1201 1.8141 3 0412 3.4060 2.3339 1.1215 1.4839 1.2324 .4597 .4310 .4157 .3J41 .1814 .1943 .0000
.0006 .9050 1.0544 1 3094 1.3414 1.5041 1.0914 1991 .6111 .Sese .4644 .3013 .1980 .13S? .1191 0000
.0000 .9149 1.0201 .it27 .9928 1.1790 .1110 2145 .22S3 .3899 .4109 .2641 .1997 .1693 .1299 .0006
.0000 1054 .8435 .6214 .0029 .9157 .Sitt .3013 .1101 .3034 .3594 .3331 .1331 .1449 .1344 .0000
.0000 .1943 .4148 .4407 .9483 .4384 .4413 .3194 .2150 2956 .2439 .1199 .1195 .0929 0010 .0000
.0000 .3301 .3173 .300? .4127 .4847 .Stal .3436 .3084 34e9 .3143 .1974 .0934 .0119 .0494 0000 s 4000 .1450 .2409 .3043 .2443 2474 .2364 3114 .1939 1390 .1497 .102S .'1075 .0134 .0449 0006
.0000 .0000 4121 .3344 .3399 .1543 .1450 .5109 .1994 .1061 .0445 .1434 .1234 0114 .0099 .0000 00)0 . 08* . 00n .1974 .1922 1314 .0995 .1315 .3151 0113 .4100 .0491 .0757 .0000 .0000 0000 000 .4600 .0000 0 .0030 .0904 .0844 0909 .0940 .ette .0433 .0410 0000 .0000 .0000 0000 i .00.00 . 00* . One . 000 on . nae Son nos 0000 0000 0000 . 00n .no . u 00 . 0ne .00e0 een Figure 4.3 32 Hot Zero Power. SCRAM with Stuck Rod
< 56 l
l 4.3.3 References 4.3 1 AP600 Loss of Normal Feedwater Transient Information Westinghouse Memos NTD-NSA-TA 127 and NTD-NSR&LA LEH 95437, dated March 29,1995 (Supplemented by Westinghouse Memo NTD-NSR&LA LEH 95-046, 'AP600 Boron Transient Calculations using TRAC PF1*, L.E. Hochreiter, Apnl 24,1995.). 4.3-2 Westinghouse Memo NSA-LEH-96-22, dated April 30,1996. 4.3-3 Simplified Passive Advanced Light Water Reactor Plant Program. AP600 Standard Analysis Report. Section 15.2.7, " Loss of Normal Feedwater Flow", Revision 5, dated February 29,1996. j 4.3-4 PSU TRAC-PF1 Code Effort: PRHR Data from the AP600 LONF Transient, Westinghouse Memo ! NSA-LEH 96-34, dated June 27,1996. 4.3-5 PSU TRAC PFt Code Ef' ort: Power Shapes, Peaking Factors, and 200 *F Minimum Boron Concentration, Westinghouse Memo NSA LEH-96-35, dated June 27,1996. . 4.3-6 Westinghouse Communication, Meeting on December 7,1995. 4.3-7 Westinghouse Memo NTD NSA TA-95-199, dated May 12,1995. l 4 57 ' - - - - - ~ ~ _ _ _ _ _ _
5 Dilution Transients 5.1 Standard Decay Heat Calculation Neutronic studies performed with the NEM Neutronic and Thermalhydraulic core model described in Section 5.4 have proven that the average core concentration required to yield a critical core under the SCRAM c.mditions assumed in the LONF transient (with a stuck rod), is much lower than the entical concentration during operation, even when the lowest core temperature reached during the LONF transient (see Fig. 51.2) is assumed for the calculations. This result is consistent with the large negative reactivity introduced by the SCRAM worth required to prevent recriticality, even with a cold core. Nevertheless, the possMity of local increases of power caused by small pockets of unborated coolant circulating through the core cannot completely be ruled out, especially when a stuck rod is assumed. For this reason, the LONF transient described in Section 4.2 was also used as a base case for studying the boron distribution in the AP600 primary system resulting from the natural circulation flow that the passive safety systems generatw in the event of a LONF transient. The PRHR-lRWST heat removal, and the CMT injectio'n generate thermal heads that move the flow in both legs of the primary aystem. There exists the concem that, during a LONF transient, pockets of stagnant coolant could form in some regions in the primary system. Such regions would remain at low boron concentrations relative'to the rest of the system in fact, the minimum concentration would be that , which produced criticality during operation, with all the control rods out. No physical mechanism has been I observed during the analysis of the results of the LONF transient TRAC simulation that would result in a coolant plug with a lower concentration than the critical one of 1830 ppm. Such mechanisms should introduce unborated water into the system or should lead to a reflux-reflooding type of process in the primary side of the steam generators. None of these mechanisms seem to be possible according to the results presented in Section 4.2. In particular, the reflux reflood scenario can only occur under a severe primary side depressurization. From Fig 5.1 1, it can be argued that with a minimum system pressure over 1800 psia, and a rapid system repressurization resulting from the reduction of CMT flow, the conditions for a reflux reflooding or low pressure condensation process are simply not met. The analysis had to focus, therefore, on identifying regions of the primary system that could contain stagnant pockets of cntical boron concentration, and that, under certain mechanisms could somehow be filled with unborated water. In order to address this issue, the flow in all the legs of the AP900 primary system was studied, as well as the boron concortrations predicted by TRAC. After a first run with the standard TRAC low order solute tracker, it was observed that, in all legs, cold and hot, the flow did not stop. Figures 5.13 and 5.14 51 l i I
show that after the pumps tripped, the flow in all the Isgs suffered a sharp fal; and then recovered; in Loop 1 because of the PRHR induced t stural circulation, and in Loop 2 because of the flow to the CMTs through the pressure balarte lines. In fact, the flow in Loop 2 is larger than that in Loop 1. For this reas'on, no stagnant regions appear in either loop's legs. The reason for using the low order solute tracker is based on the lack of sharp fronts and on the active and leng term convective transport, that does not require accurate tracking of well defined solute rich or poor regions. The possibility remained that the steam generators, ospecially, 'he one in Loop 1, would contain
- stagnant plugs. The steem generator in Loop 2 is not bypassed, and thus, the flow through it follows the !
s,ame partem as the flow in the cold and hot legs (see Fig. 5.1-6). The steam generator in Loop 1 is bypassed partly by the flow going to the PRHR, which provides the main driving head in the loop. However, part of the flow coming from the vessel through the hot leg is diverted into the steam penerator, and contributes to the increase of the pressurizer level, whose connection to the hot leg is located after the j PRHR connection. As; the flow slowly decreases in Loop 1, because of the diminishing heat transfer in the L 'PRHR (see Fig. 4.3-14 and 4.3-15), the flow in the steam generator also decreases. From the analysis above, it is expected that the boron distnbution in the primary system will present i a typical rising profile, resulting from the convective transport by the natural cin:ulation flow. The injection of highly borated water from the CMTs into the downcomer and in the vessel wit distribute the solute throughout the primary systerrr, since there appears to be no stagnant regions in the primary systcr 1 urder LONF conditions. The concentration inside the vessel at 4000 seconds, when the temperatures are lowest and the natural circulation flows reach a relatively constant valus, is homogeneously high. There are no pockets of low concentration coolant inside the vessel or downcomer, since the natural circulation flow actively distributes the solute by convective transport (see App. A). Figures 5.17 to 5.1 14 show how the concentration in the primary system increases almost linearly with time, to reach a plateau of maximum concentration at about 30C0 seconds. This linear increase, almost simultaneous at different locations within the same leg, is a sign that the transport is mamly convective, and that numerical diffusion plays a very small role, if any, in delving the solute distribution within the system. For this reason, as menboned above, this run was not repeated with the high order solute transport methods, since the expected results would be basically the same. Even in the steam generator of Loop 1, which has the towest flow rate in the pnmary system, the concentrations raise steadily to over 2250 ppm, well above the criticality concentration of 1800 ppm. This is obviously because of the mass flow rate observed in the hot leg after the PRHR connection, until about 3000 seconds. At this time, the natural circulation in the system had about 2400 seconds to carry highly borated coolant from the vessel to the steam generator in Loop 1, with mass flow rates of more than 100 lbm/s. 1 5-2
l l i I To complete the analysis, tables 5.1 1, 5.12 and 5.13 show the concentration in the prima;y side components at 4000 seconds. This time was chosen because the cold legs reached a minimum l temperature, and the legs convective mass flow rstes abo stabilized before small oscillations appeared. The system state at this time will also be used as initial conditions in order to perform the zero slug iterations for the standard decay heat case. From the tab!es, it is clear that the entire pri. nary system has a large boron concentration. The minimum concentration is 2333.35 ppm at the fluid cell connecting the Loop 1 steam generator U-tube with its outlet pienum. The concentration in the steam gencrator outbt l plenum is larger because the PRHR line injects flow coming directly from the hot leg in the outlet plenum. l In summary, the LONF transient does not show any stagnant regicns in the primary side. The boron from the CMTs injected into the dowxomer is thoroughly distributed throughout the system by the natural circulation flows appearing as a result of the actuation of the passive safety syctems. l l l l l l l l I i l I l l I I l S-3 L
l' i \ l 1 l Componcot # ComponentType Comments Cell # Concentration
'7 EC l-i i
i l Table 5.1 1 Boron Distribution in Loop 1 at 4000 s. TRAC LONF Transient Sinviation 54 --m._ . _ _ _ _ _ _ . _._ _ . . _ . . _ _ _
l 1 r l l Component # Component Type Comments Cell # Concentration j ' - t, C-i l 1 i l l l l' W i Table 5.1 1 Boron Distrtution in Loop 1 at 4000 s. TRAC LONF Transient Simulation (Cted.) 5-5 l l [ i L . _ _ _ _ _ . . _ . _.m_..___ _. ._ _ _ ...m...
l 1 i l i l i' l-i ! Component # Component Type Comments Cell # Concentration i ? C ' m R.s & L-l i 1 l l f i i- [ : J., Table 5.12 Boron Distribution in Loop 2 at 4000 s. TRAC LONF Transient Simulation 54 I I
t-l i i l l l i I i Component # component Type comments cell # Concenuation q., C-
~
c -- l l
\ h
- i l
1 i l i i i
)
l l l i 1 l I' i
,e s Table 5.12 Boron Distribution in Loop 2 at 4000 s. TRAC LONF Transient Simulation (Cted.)
l 57 t f ( i _ - - - . . - . - - _ ._._e.-~-_ - _ - - - _ . . . _ _ _ _ . _ . . _ . - - - - - _ _ . . - __ _ _ __ _ - . - . _ . _ . _ - _ . _ .__..-a
[ I I I i I i l l Core Average Pressure f 2.6e+03 , a g { . -r : I t , . t
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, g . .2 fj 1'.
- 8 5 < > i !
l 2 r i i i ^! ,'. 1 i 4- t r f' i- 1 A+03- - 4- -- -- -- -- -- - d.- - i !i ! , . i i f .1 !. . t ! I i 1.7e+03- -- r . f 1
,~r, i i r-i, r, i v~' -
i a
> , i
- - T - - : r7 - -
i ! . l ' ' f ! 8 f ! f i 1.6e+03 . , . , . 10 100 le+03 le+04 time (s) Figure 5.1 1 Core Average Precsure. TRAC Simulation Core AverageTemperature 700 . i AI 5 $ . { f. f ' I-
,, i. < s i,. .-! i. ; .,
t ;
, :. ,i; W
650- Fi '- et i i-Li i-
! h .
3
.lf
' l 4
~
h 1 i f
.i r
i
~
r f . .4 H- r *- 4-3, 550- . F t;
-i- :
1 b a : ;;! i
+ i '
i i l l ~. ! e * - - . - 3 e I f
' t !
) i' E : ; .., 'i .i ;
' i
& 2 8
ii - e
,_'= t-j
. .. 5 -
Vl " i j
! ,i >: .
- i i i ; i ti if i .
!: 1 i ; !i
~iti-
- 400- -i r.
!- ; 'r
;4
; r ;;;
f 1 1;
. , i i :
;i * ,t!' -
I { ! 350
. . . -1 L !
10 100 le43 le+04 time (s) Figure 5.12 Core Average Temperature. TRAC S'w retation t I 58 I
l l l Hot Legs Mass Flow Rate le+03 ,
=.
i - I. '
~
i Leg 1
! -'i ". --
l 900- --- --
-- - -~~-' M 1--" i t -
-1 i
14:2 1 i ; 800-
;- ' '- iI r- -
+-!-
2 '-- !
! I i
] 700-
- -* + - ;+! --\--
a i L C . I. , o
- g. . . . . . . . . .
. . . _ . . .;.. . a.. . 4..
._..i...;..,....
- ;2 gg ;
g 500- H - - ' - i- - +- EA.I -
-- - --~ -> -- - -
'i
' i k ! !
l 400- - -
+~j- ji' -'" itr; -- , - r" .
r i i" '-+-/. l - ..,s.t.i), -'" ---
- - ' - +-
Q 300- - -- TT> :.
. ee ,
i.. . . . . .,v-I 200- --
---4t-3 .
-3
'* - "'* -i - -
t- ."'- l i i ! I i I . "d. 1
---- L '. j',---I-+'- W --* -
I 100- -- s l l i ! i 0 . le+03 le+04 l 100 time (s) Figure 5.13 Hot Log Mass Flow Rate. TRAC Simulation Cold Legs Mass Flow Rate 500 . , ii !l 3 leg It. l . 3 I i
. leg Ib
-- e -- - 1- -- ..
l ^ 400-jI i I* l f , i i 2
! Leg 2b v
i i l g 3@.
. 1.. im
. . . . . . .1 .. .4.. ;
>t :
- t l
i n l ! i f ! E i iJ I ! j k 4- -'--
- l' R 200- - - -
E *1. i j ,, 'A T. m ,; m . n t !. l .
,... ...... 4 2 ioo. . . . - .
- l. . . .;. ... ?.... . ...,....
i ! i j i i i f !
! ! I O ,
100 le43 le+04 time (5) Figure 5.1-4 Cold Leg Mass Flow Rates. TRAC Simulation i i i I i-I 5-9 i
- _ - - _ _ - _ _ _ ~ - --' - - _ _ _ _ _ _ _ _ _ _ _ _ _ . _ ._
l i f-SG-1 Mass Flow Rate i 400 ' i . __ Inlet , i l ! i j 1 Top
^ 300- - ,- - -
j l ; i , ouuet
.a l C i .
l
.as 200-l J +
i , b ! !, i J 100- -
-r - - . . e. - .: ,
i
, r
.i ! ,
! i I Q.. . . . . . ............,...:... . . . . . . .
._ ,4.. , l
!t . I
; ! i l
i i !
~
--100 ,
100 le403 1e+04 titne (S) Figure 5.1-5 Steam Generator 1. Mass Flow Rate. TRAC Simulation i SG-2 Mass Flow Rate !
- 60C . , j lakt N TP
- ^ 500- .
t
,p
} ,
oucet l i ; .
~
400- - - -
--:--?- ;-
-l - - - -- -
es : ;,! , o 1 es j : eg 300- - -- - --- -- - I-
~
l > 2 :
% 200- - - -- -
E- 4- - - - - m 100- - i- -- i !' 1 1 C ,
~~ ,
le+04 l 100 le+03 thne (s) i Figure 5.16 Steam Generator 2. Mass Flow Rate. TRAC Simulation ! i l 5 10
l Hot Leg-1 Concentration 0.003 j j' i ! , _
! ! Reactor Side I l -
+ . . .. : .
\ O.00275- - '- - PHRH Conn. t I {! i { SG Conn. ng 0.0025- .
- j -
. ~[ ... ;
l t W ii l c ------~-L-'- -$ r ,^ - i l
.)0.00225- j i
i i l 18 i - l l Jg 0.002- - { t- 4 --+ -- t-- 4 '..l....._ l D ; : ; a - i; ~ o - p 0.00175- -
----+--L-+-- ?-,4' -- -- t-' . ?. -
l t i i j I O.0015 . , 100 te+03 le+04 time (S) Figure 5.17 Hot Leg-1. Boron Concentration. TRAC Simulation Hot Leg-2 Concentration 0.003 , , ! ; , } woulside i i , M*
;;p. 0.00275- j --[ f - !- ,
t- i- - ..- - M i '! ! ! so cons. W 4 ,
- & 0.0025- - --- -L- -- -
+ -- - - - -
~}--,-
- m , t i W
~
* + ! .
L-- ~~- ~=- .-- '- - g0.00225- --- ~r
-~-j- 7 ~ - - ---- -i- 1 i ens i es i '
be i l g e 0.002- ~ - - -
+: -i- -+- i r
l {- a r-u . t x
- a ; i l o : i y 0.00175- - -
F - .
+
t-i t ! i !
+ i* !
1 I ! 0.0015 . . 100 1e+03 le+04 time (s) Figure 5.18 Hot Leg 2 Boron Concentration. TRAC Simulation 5 11 a-_______--____--
SG- I Concentration 0.003 .
, j
. i -
a
; j so-t intet
^ 0.00275- .-i' '! i- ,
_ 50-1 rop
! j !
Oc - 50-1 Outlet E m 0.0025- - "-- r se-' 4' , J ' 30-10 Plenum oc ! I l l g v i i
' ..:! . ... .-. .j;-:.n --
.t l c 0.00225 --- 1. l~. u .;..' . -/.;/s .--, .
o
- c ; ,
.* y i .. .
l ce i , ,, .,,- ! ,. u ' .-
. I 1e 0.002- -- -
i- ? -+ ';.. . i/'. !- - p :-- - - : -- 1 u ,
'...t, .'.'r' >
- m. - r.it r ii-0.00175- - - - + ~' -++ L - <--- +~-
i i l I i ! ! i . i ! ! 0.0015 . , l 100 le+03 le+04 i l time (s) l l Figure 5.1-9 Steam Generator 1. Boron Concentration. TRAC Simulatim I 1 i I SG-2 Concentration l 0.003 , i . i - j i i 50-2 Inlet
^ i l 1
-i -i so-2 Top g 0.00275- -r- --
oC ; ; ; SG-2 Outlet I i ! 0.0025- !--; -- - - i- -
- i i ... ... s'a-2 O. Plenum i
i
! g! a Mv ! f** i !
, i ! l c 000225- - - - - - " , - - - - - * - - F--- b - ,.f4(--j----- :--H-j
.. . s.. -
"/*
, , / ! i 3
..f< i 1 G 0.E- -
+- i l i
i ;/f
'e.s.-- +- -
I -- f GA ; -
?
.' J.! i )}r :
1 OMW- ! -l l A- + - - - i I i '
. .- i l
l 0.0015 - 100 te+03 le+04 time (S) Figure 5.1 10 Steam Generator 2. Boron Concentration. TRAC Simulation i 5 12
t l I t Cold Leg-1a Concentration ! 0.003 . , ! ! ,! i i '
' Pump Side
; 1 !
-i +-
0.00275- - T I j- - - .- Middl* i , .. i oc ! g , j vene1 Side CG 0.002.5-oc
- o - -b- -
-- -- - -- - b- - v- . . +
r-W v I
+-v i
c0 00225- ------n-~- . r --- -+ + m-r--
.8 , i! !
2 i! ! i a 0.002= -e+-- - 1- - -;- l - -=- 8 ! I s: o ' i i. .i Q 0.00175-
--+
r, ; -h. -'! 1 g : I !~
, 0.0015 : . ',
100 le+03 le+04 time (s) Figure 5.111 Cold Leg 1 a. Boron Concentration. TRAC Simulation Cold I.cg-lb Concentradon 0.003 . . i ! t Pump Side 3 i .
^ 0.00275- 5-
*H- "
%Os i t
-t- --- -
Vessel Side Oc 0.0025- -
--' r +-y---'-
i Wv I 3
. t
.c c 0.00225-i
"--t
! t
- 1, - - - - - - - - -
en 1 - E ! ! !
---+
1e 0.002- - - - - - ---- 2
& r -- -
i !, v i e CD i - i y 0.00175- +- r *-+ - e T' [; + i i ! ! i i
! i i !i ! i 0.0015 - >
100 le+03 le+04 time (5) Figure 5.1 12 Cold Log 1 b. Boron Concentration. TRAC Simulation 5 13
r I i l i l l
- . \
I Cold Leg-2a Concentration ! l 0.003 , t _. i , !i Pump Side j. Mddle {0.00275- ;r > . -. ne i i i-i
! Venel side QQ 0.0025- - -
-+- -.
. .. i om W
v i i I c 0.00225- ~ ~ - - + - o j.rN+- - -- - ... . -.+.
*s i ! . !
I as > i -' w ! ; ,, , ! 0.002- J--. ;..-. -- l c an s
- [- '-
- -} e. - 1 i ;
O I 'i ; i a !
~
i ! 1 l
@ } } i Q 0.00175-
- - i F ! >-- r . b. -
i
, : i I ! i i . .
- f f
0.0015 , 100 le+03 le+04 time (s) l Figure 5.1-13 Cold Leg 2 a. Boron Concentration. TRAC Simulation i Cold Leg-2b Concentration O.003 . t 1 -
. r rump side t ..
i
- - Md*
[ 0.00275- ;
#8 .
venel side W. !
& 0.0025- --
+- ; ' i-- - --b- - -
no i i ;i ! . W v
!, t s
c 0.00225-
- - ~~
-- - - - t- i - - !
i
- ~ ~ - - - -
I,
'n !
I es t Q,@. . . . ....:,
...i..., {...-.. . . . . ,......e .
W . ! u i i a d 0.00175- - L - r i i 0.0015 . . 100 le+03 le+04 time (S) Figure 5.1 14 Cold Leg 2 b. Boron Concentration. TRAC Simulation 5 14 l
5.2 Low Decay Heat Calculation The results presented in Section 5.1 for the LONF transient showed that, for normal decay heat levels after SCRAM, the passive safety system would generate enough natural circulation flow to prevent any region in the primary system from becoming stagnant. As a result, the distnbution of boron within the primary system was fairly homogeneous. The possibility of very low decay heat levels after SCRAM is addressed in this section. The Low Decay Heat (LDH) LONF calculation assumes that the conditions in the core are such that the decay heat level is reduced to 1% of the standard ANS 79 decay heat curve used by the NEM mMel. The decey hest level was reduced by directly modsfying the code subroutine where its value is computed. The control system and the trip settings are the same as those used in the standard LONF transient described in Sections 4.3 and 5.1. Although the predicted activation of the main trips is sequentially similar to that of the full decay heat LONF transient, the timing is different. The lower power level generated in the core after SCRAM is the main reason for this behavior. As a result, the system temperatures and pressure quicidy drop to levels well below those observed in the standard LONF transier,t. Lors energy is stored in the system as dacay heat generates smaller thermal huds in the PRHR end the CMT pressure balance lines. This directly affects the natural circulation flows in the primary legs, which, as expected, are also smaller, and can lead to stagnant regions with low boron concentration in some of the primary side cornponents. The period of time before the SCRAM is common for both transients, standard and low decay heat. It is only after the control rods have been inserted, that the differences in system thermalhydraulic behavior appear. System temperature and pressure histories are clearty different. According to Figs. 5.2 4 and 5.2 5, core temperature decreases to about 395.0 K (- E51.0 *F), much lower than the rninimum temperature for the standard LONF transient, while the system pressure never again rises after the initial drop following the SCRAM, and steadily falls below 11.0 MPa (1600 psia). Since the system pressure remains relatively high throughout the transient, ths possibility of a reflux rolloodmg type of scenario can also be ruled out, as in the case of the starxiard LONF transics, Therefore, the only possible scenario that could yield low boron concentration pockets !s the flow stagnation in some regions of the primary system doe to the diminishing thermal heads as the energy stored in the coolant is released to the IRWST and the system cools down with cold coolant from the CMT injection. Another difference between the standard LONF and de low decay host transient is that all the actions that initiate natural circulation flow in the system occur earlier in the latter. The reason is that the i Low T-Cold signal is reached sooner because of the faster cooling of the primary system. From Fig. 5.2 7 and 5.2 4 it is clear that during the penod between SCRAM and the pump trip, the PRHR flow, driven by 5 15
- u. I
t 1 the pumps, extracts much of the stored energy in the system (very little of which is now decay heat). This large heat transfer contributes to the fast drop in system temperature and pressure. After the CMTs start l to inject cold coolant into the vessel downcomer, the drop in system temperature is even more pronounced. The rapid cooling of the system compared to the standard LONF trantient reducas appreciably the thermal heads that generate the natural circulation flows in the primary side. In fact, the effect of reduced heads can be seen lo Figs. 5.2-9 to 5 211, where the flows are smaller than the ones observed for the standard t LONF transient, especially in Loop 2. The plots show that the flow in this loop drops to alrnost zero at 1000 seconds, presenting a small rise during the penod of maximum CMT injection. A srnali negative mass flow rate in the cold legs, between the connection to the CMT lines and the vessel, can be seen in Fig. 5.210, which is not observed in the standard LONF transient. The negative flow indcates a ' sucking" effect by l the pressure balance lines obscured in the standard LONF by the relatively high positive flow coming from the hot leg through the steam generator in Loop 2. Figures 5.2 9 and 5.211 show that the flow in the hot and cold legs of Loop 1 is not stagnant. The j PRHR provides enough thennat head to drive the coolant from the vessel through the hot leg and the l PRHR piping to the steam generator outlet pienum. The fiow is then distnbuted to each of the two mid legs back to the reactor vessel. The effect in the boron concentration distribution is depicted in Figs. 5215, 5.2-17 and 5.218. They show an efficient convective transport of solute driving the concentration in Loop 1 ; close to the system mammum of 2660 ppm in the vessel as the transient progresses. The low concentration observed in Fig. 5.215 in the portion of the hot leg between the PRHR connection and the steam generator is due to the flow of voided coolant and condensate from an emptying pressurizer where some of the excess volume assumed at the beginning of the transient was unborated (see Fig. 5.2 6). The slow stagnation of the flow in this region (see Fig. 5.211) contributes also to the decrease of the boren i concentration after an initial rise up to 2000 ppm by 1600 seconds. This behavior reflects the fact that most of the natural circulation flow in Loop 1 is diverted to the PRHR piping and very Ettle of it goes to the steam generator. As a result, the flow in the stearn gensrator of Loop 1 follows a similar course to that in the Loop 2 steam generator. Stagnation conditions are reached at 3000 seconds in the steam generator of Loop 1 whereas the flow in the steam generator of Loop 2 reaches zero flow at about 1000 seconds (compare Figs. l 5.214 and 5.213). The boron distribution in Loop 1 steam generator is determmed by the stagnation process, and, as Fig. 5.2 21 shows, the concentration in the U tubes will not rise above 2000 ppm. The relatively slow decrease of the flow, however, provides sufficirent convective transport to inject enough boron and increase the concentration over the initial critical concentration of 1830 ppm along the entire tube l bundle before stagnation occurs. The concentration in the Loop 1 steam generator outlet plenum is much j larger than the one in the U tubes because of the flow from the PRHR piping being injected to the plenum. l This difference in concentration clearly shows the stagnation process in the Loop 1 steam generator. 5 16
1 1 The natural circulation flow in Loop 2 is smal!er than in loop 1, and also stops earlier, except for the section of the cold legs from the vessel to the connections with the CMT lines. The result is a faster stagnation of the flow in Loop 2 steam generator, and lower concentrations in the U4ube bundle. The cold legs of Loop 2, however, show a higher concentration distribution in the section from the vessel to the connections with the CMT lines, since the flow there is not stagnant, and the flow direction from the vessel toward the CMT lines carries highly borated coolant from the vessel upper plenum. In summary, the low decay heat scenario has the potential for flow stagnation in both loops, especially in Loop 2 and in the steam generator of Loop 1. Lower thermal driving heads because of the smaller energy content in the core can be assumed to be the most likely explanation for this flow pattom. A more detailed picture of the boron distribution in the primary side at 4500 seconds is shown in Tables 5.21 and 5.2 2. They list the boron concentrated in the primary side components. In addition, the concentration in the vessel and downcomer corps, displayed in App. A, is over 2000 ppm for all fluid cells up to the upper hood, where the minimum concentration is 2170 ppm. No pockets of low coolant l concentration were found neither in the downcomer nor in the vessel; the low values of 1830 ppm, correspond to cells with no volume and no flow area needed to complete the computational model, but playing no role in the calculations. Finally, it is important to justify the time selected to display the results discussed above. At 4500 seconds most of the natural circulation flows had reached a stable regime, and the boron concentrations will change very slowly from then on. This time was selected as the restart moment for the results presented in Section 5.3. l l 1 I I I l f l l 5 17
Component # Coroponent Type Comments Cell # Concentrauon v- ~ . q, y l 1 i i l i l 1 l l l L- . l Table 5.21 Boron Distributed in Loop 1 at 4500 s.1% Decay Heat J ! 5 18 I
l l l l l
%aent # Component Type Comments Cell # Concenuation I'
' Es i
I I I i l i I l l l i l l i l 3 l l L- w Table 5.21 Boeon Distribution in Loop 1 at 4500 s.1% Demy Heat (Cted.) i l 5 te l l
f l Component # ComponentType Comments Cell # Concentration . F ' RC e 1 1 i i 1 l 1 l I i i l l ;c. i 7 y Table 5.2-2 Boron Distribution in Loop 2 at 4500 s.1% Decay Heat 5 20 L________. . _ . . . _ __ _ _
1 l i
- l t
Component # ComponentType Commenu Cell # hem
-. ~'
Q., G - l 1 l i i
)
i I l ! i 1 l l I i i L I I f u Table 5.2 2 Boron Distribution in Loop 2 at 4500 s.1% Decay Heat 5-21
Reactor Power 1.1
, ;, );, ; , ,'
be i ij ji' ! ii (A j- * '* i
, i.. ;j .. .i i 1
.. }. .
1: I I 1
! i.
!!>- , ; h 8
- i 0.9- i-- ;- - t ~{+: +j tt- !
; , t
' ;!-lt
- '- ['
'c 4- -.
-l - -- .-
1 : .
} ' l! l 13 8 0.8-l '
N
! l -
! L !! !
- 3. -
I-! en . 3 ; t s
- 0.7- -
t- -- -
; ,- r e- -;-
,;3 -i-t 1
- it; ; 9"rt :
"ir I ..
.E - 0.6- ---;
i
-j -
4 p-
,. I.-[ l{-
i !! E c> o.5- -
.1
! ~ ' l U-Z
! i
) i .i,'!i !I w 0.4-
)
- -+ -
e- -! - ' .- o , I i!i i
-j- + i i
i i i r- +i : ; c 0.3- - 1- 7 i" i & i it tb o i } , i -
-l
*$ 0.2- - J -- - ' i j- ! - '. i se l1: t: !l t.. t; !'-} '
t i i
; r- -
i- - +'!F b u o,1 e
+ :
c o 3 ..', J'i ..
-l
+
i ' : i !!jr i; L, ! l 1 ij!. 0 . 10 100 le+03 le+04 time (s) Figure 5.21 Reactor Power.1% Decay Heat Pump's AngularSpeed
, g,, C-Lag la Lag Ib
^ ..
tes 2a Las 2b m. Cr) 6
.5 h
time (5) Figure 5.2 2 Pump's Angular Speed.1% Decay Heat 6 22
CMT Mass Flow Rates.1% Decay Heat 60 ,
^!
i 1
, CMT-1
,1 ,
m 50- m cMT-2 i . k
~
i i ei
- 40- :
i! V
+ +.- .-
a w o i . . i w ; i og 30- ' ' ..
. t k
- -- b
- - { 4- E--- I~^ t ; 7 - Si .
- r. -4 -t -
g I ij t - l i *
, j . i:
G ii 1* i '! m 20- o L' "Le+- - i, j
~---&.,
t i J- ;- ll 'll
=
E : l i; ' 'I ; 2 '
. ' ! ;j , i. i !!
10- -i 6i- -
?i-
.i r
- . --l r
.r - i i i, . , 1 I ,
s I ,f !; 4
-i i -c. i.
i '&
- +
! i 0 . , .
10 100 le+03 te+04 time (S) Figure 5.2 3 CMTs Mass Flow Rates.1% Decay Heat I Core Average Temperature.1% Decay Heat 650 . ., - t .
! i. : s , ' i i .3 , - i 1i 600- !! -
i a 3 i 550- - 3 t--
- r '-
a .i- : b v ; i, ; 1 i li ' : i
- i. :,
o 500- i ! ~ r:; : '
-'-- *,H 6 .
-} -
t : !: i- :t : g w
!! ! 2 6 450- i i+ i&- -
i? -
-i e
( f ! ,
- i. I E 400- -
- i ' - - ' ! 4-
- t -- - +'-
as i i , Em . i; . 350- -- r, " .
.,1 r - +' ',' t
-} *i1
; .! i; 300- - -
l, , i; . .i I .' j 4
.i 250 . . - . .
10 100 le+03 le+04 time (s) i Figure 5.2 4 Core Average Temperature.1% Decay Heat 1 5 23 L___________._____ - - - - - - - - - - - - - - - - - - -
i i I 1 , 1 l l 1 l i t Pressurizer Pressure.1% Decay Heat , 2.6e+03 , , ; l i ; :; - i-, ! 3 : i 2.4e+03-
!t .
-j 4 i-t i , i i , i : .
i .i
- t
< - , 3 ;-
i -l 2.2e+03-
-+ ++ ~+ b~i ' ; -- ' i-m i
' : i . :i. .
?!
SB -; i
'g 1 -
t i! j I' pgf3 .-..-.4...
'.3..' ;..Lp...-... ... i.... ' . d ; { 1.. . ..
is ,. . :.
& f
!l !, , i !!
t (. .j j l 1 . { !! ! 81.8e+03-2
- - - - U-~ + - ? ! 4 L--
i
-- & ~ , - !.+ -
-~ 4- rJM !-
i i!, ! ; t sp) g 6
' , .i t I
- i.
! t 8
i
] a i
g 6
},gg4Q3 ..-..i.... . . ..) .4. .- ..{... .. L . ' . ...y..{ ' ........?... ,....
.fi 5 . . . ; . ! it 1 i i k g,4e+03 .
.y.4-+.4++-
-!. . i ' . .. L L -. i. .-).- .L [+!; )! .f. 1 1 + 1 i ',
i: i. j e i : : : ! i t - i j 1.2e+03-
- f. 4- ', ei-I 1- i - i-i ;
1, . i, ! , i i: i i t' *
!i 1e+03 .
10 100 le+03 le+04 time (s) Figure 5.2-5 Pressurizer Pressure.1% Decay Heat F Pressurizer Level.1% Decay Heat 30 . . :. .
; 4 28- -i. . !+ ' . :? '
? i if
~
26- i 4. -
~4
]4 '
. . 4 .. ,
.J .. .i. .. . . . . j i 2 ! ; ,ii 2 22 . .;........., ....-.....yt.
.. {:.
t : :i i l 20- - - - -
'+-4 ++ - - - - --
^
r i; - - s. :-. 4$ }g. .
. 1
. . . . ..4......
~ i e
...l..',.4...........s... ..,.... j .. " !.
v- -
. i, ; 'it l
-v} $. 4- 4
- , t
- . ; v .: ...
\ i.
,t
, 3 t > 14- .
-t r '
- i. t . . -
o 1 3 +i t i ;4 l 4 12- - r' L 1- - i-- l 1 4 i . !i 10= ~~ '~ - - ' ~ ;-
-- - ,~ - +-
. .. .. .. ?. . . E. . . n > 1 <. n... . ..p. 3 . e.
i,
- g. .....4. . . . . . .-
..).. ,
..3. .
;} !
4- < -
..i . - - -
; - : i l '
I T 2-
. . m 4
- +
r : :- [t
- ia i l I l
l 0 . . . . 10 100 le+03 le+04 time (s) 1 Figure 5.2 6 Pressurizer Level.1% Decay Heat l 5 24
1 1 I l i l l l i l l Power Transfer in the PRHR.1% Decay Heat 0.1 , . I i 0.09- -- i
^ 0.08- - !- -
+- -
i g 0.07- , K w 1 i i I I v i ! w 0.06- r- - '-
+ -
e g t I ' o 1 i b 0.05- - +- -
'M , I E o.04- -
o Z T 0.03- i- < -- o c i 0.02- - 0.01- - - i 0 . . . . 0 le+03 2e+03 3e+03 4e+03 Se+03 Time (s) ! Figure 5.2-7 Power Transfer in the PRHR.1% Decay Heat i 5-25
i l 1 l PRHR Inlet Mass Flow Rate.1% Decay Heat 500 , , , ,
/ :
( - 45O. 3, E f s
- a. -
.. f .. ...q.... ....
- l t i I
m }$Q. .
.1-_.- ,_
an . i e 300- > i 7- ' w o i
$ 250-- '
r i- -
) i l C i !
, h 200- - T i
- 150- r
-t- -
i
. . . . . mi 50- - -- --- -
l l C , , , , 0 le+03 2e+03 3e+03 4e+03 Se+03 i time (S) i Figure 5.2 8 PRHR Inlet Mass Flow Rate 5-26
l l l l l l Cold legs 1 Mass Flow Rate.1% Decay Heat 3% , i ? - i
. t Pump Side is
. t 250- !- -i - i-I - -
^
r feuei side i. i
} } ..
4 , , Pump Side Ib 200- ~i. #- +- - O t i C ' I i
! i i Vesel Side Ib e ; 1: i
~N-150- ' '
- 1 :- -*- s - --
i l k 100-
.9 r
i 4 'I- ..:H ' I -- r- :- i ss. ., ; ; i 50- '- - I l j
+
f !. - I' - h - - 3 i l ; 0- *-
' [-
1 . ! n
.j i ) I :
- ! i a 1 3
-50 , .
100 le+03 le+04 time (s) l Figure 5.2 9 Cold Leg Mass Flow Rates.1% Decay Heat Cold Leg 2 Mass Flow Rate.1% Decay Heat 300 g , , , l ; i
+ !
j Pump Side 2a 250- ' m Vessel Side 2a
. . j .!
I i . ; I 200- - - J- -- .. ; . . .... Pump .'ide 2b 1 -l- -- - f ... i d i
='
Vessel Side 2b r.
'o 150-i.
j
- l. t -
- +-
4 i 4 -=-> i N i. i ! 1 i
?
! og - -- - - - - J'
)
100- --- i i \ .6
- b~ - t- '
----h- -
j
- - h--
E o 50-l \/\: t1,, r- ;-
= , i )
M e i : '. : j O. . . =
........;~......s,....?g..... ,, ; ,. . ;. . . . .
2 i . q . .;.' . . . .,, . .; . - i l 3 4
.. t i, ,
+. V...
L ~ -- i l . ! Ij- i 1
,' I ii ! i l- -100 , .
100 le+03 le+04 time (s) Figure 5.210 Cold Leg-2 Mass Flow Rates.1% Decay Heat 5 27 l I
Hot legs Mass Flow Rate.1% Decay Heat 500 . i i ._ 450- - L- -;- Before PRHR LI t, j - . m 400- ;- < l, L-
- After Pdzer L1 j 350- -- y , 7-I --
$ 300- --
- l- , -+ t
- 250- + '
a ' r-- >
! i '. ii4 g 200- - - - - - - - -
4-H- 4-4 9 - - - - .
-----4-- -----
) ! l 3 150- -
, + 'p. ] , +
F- -
; l b 100- -- + +-
- i '.: i,
+-
l l2 l I'h., i i 50- ~- r r+ r... ,- -u- ,- 1 1i i ll 0- --
'4' "".' -""~~~~ -
3 ; j ! j:l ~> : - l ! ! r >
~'
-100 100 led 3 ledd
- i. time (s)
Figure 5.2-11 Hot Log Mass Flow Rate Hot L:g-2 Mass Flow Rate.1% Decay Heat 500 . , . - i 4 __ 450- -
'- **^DS-#
5efore SG-2 m 400-
-+- 4--
-r-3=350- '
i- - - a ii i e 300- '~ b' I.
,t
. + '
e-
.o i i
f a 250- + ' i-
-i! i' g 200 _
r o i . E 150- - - - - - 4 i- - -- m
$ 100' t g 50- - -
i
- 1 ; ~7-
! 0- = l , ; l i t ! I
-50 .
100 1e+03 1e44 time (S) Figure 5.212 Hot Leg 2 Mass Flow Rate.1% Decay Heat 5 28 l i i t i
r--_ _ . - - _ _ _ _ _ _ _ _ _ _ _ - - 1
\
l l l i SG1 Mass Flow Rate.1% Decay Heat j 500 . . . l l !
- ( ji .
' - 1 L 450- - I- L i
~
** I l i i ! i --
A 4QQ. ..'h i i
- - .J.. l
. Top i~ 350- *
' -h -r- -
- - - - - U- --- 5*'
\
$ 300- - ---
i
--{, > ,
-p- .
3a 250- , l- "- --
'{' ~+l -
t i g 200- - - - - - - - - - - + E--- ;- r -
-r---.- -- -
p ! i ' ' i' 150- .
; 1 ! -
1 i i j g., .
; . . ...I....... .f... . .J . . . . - .
..l; +
, i 1 i -
?
$0- - - - -
T~- " rt- ----+-- ~ - - " - - r --- E '
+
i ll _ 0- '
+f- ,
i i
~ j- - i-i J;~-- h 4-i i
~d '
-100 . . . !
100 le+03 le+04 l time (S) Figure 5.213 Steam Generator 1 Mass Flow Rate.1% Decay Heat l I l SG2 Mass Flow Rue.1% Decay Heat ! l 500 . , , i , - ! 450- L a ! . - *' 1 i ! . 400- l- , , ! . Top i m j ._
+ ' ** t 350- -
+- -+ '
i
- I t.
h
- 3QQ. . . - . .
I.. ...h. l
..j....;.............,....A... ...-.....f...
\ i 3a 250- 4-v '
.i
! g 200- ---------- !- - - -;- - t ! - i o i- i - 150- !- ; -
, i,
% 100- -
i - i4 - -- .i - --
=
- M :
a $Q. ~~~ --. - ..s~ .. . L .4 & . ..- 2 0- - i r -- i 1-i l i i ! ! i
- 1- -
3 I ! ! 4
-100 ,
100 le+03 le+04 time (s) Figure 5.214 Steam Generator 2 Mass Flow Rate.1% Decay Heat 5 29
l Hot Leg-1 Concentration.1% Decay Heat 0.003 . ; . , :, . tt
- t
'+i i
.4- -
t
, Reactor Side
; , .! i l
g^0.00275- " -:-f ; -i-
- [{ ; .
De -;
. i
~
fRH Conn. A SG Conn.
. ! . . .i '
l.) . ! O.0025- ;--l- i'- > !^ .!r. - '-- Oc ii'! ! 1 ;- M
; Ji! ' - -
V . ! . ! ;:
.! I 1
, .i a ij
- ! i
;i g 0.00225- '---'---
O
. - r -+- ? 4i - i t-' i :
li- ----t--- m4 l-
' i j I >
e i
*J3 1 ; .
! . j g ,
.i ( i ! .; -
nw i
- i 1 j
* +-
m 0.002- j ,--- ""'2* ea u 3
-t--tj -r-[tif.
- j:
- 4 t
, - r ,;=Mi.
! , I.-
-r
! s.
a .! 3 .: il o ! 6 i . Q 0.00175- a. d- J ;li.,F 4 - , i- t
, - i t j l-
'..4.' -[ ,
i-
. - : i.
1 ;
; i ,, ..
I h ; 2
-,. i : : .i- - : i 3
i 1 r ei i
.e i, .
e 0.0015 4 10 100 le+03 1c+04 tirne (S) Figure 5.215 Hot Leg 1 Boron Concentration.1% Decay Heat Hot Leg-2 Concentration.1% Deca 3 Heat 0.003 , ; , i ' 2 ll ! !! Rawne Side
^ : :: !' i : 't Middle
$om0.0027- -
' i I- '
-+ !4 i+i - r- 4' '
'i- ..
' so conn.
hd
- i 5! . 2 i
Ngg n k i!!i lff it t I l 0 V 0.0024- :j11 j f ? !:f - -
-l - l
' i * ;j < i !!' i i !
. -* !4 i
E I i
! k ! '!
f
. 1 -. ,' !;
0 M 1- --
-} I ; f- ;-
;'--" t w
C j j;
} - h ...m M"*-...*W.av j && i i
W .
!!! I I :
g ! . :
. 1 Itj
- g Q,@ { g. ......! }.. .. j 4 4 ; .- ,
......r'...;......j....{... . . . .
9.. .. j . . . .. . --4 . Q . I 3 , I '
} i
->:i: . 3. iit !
- i 3
i :
. 7. : .
4
':3 l;!
f. 0.0015 , 10 100 le+03 le+04 time (S) l Figure 5.216 Hot Leg-2 Boron Concentration,1% Decay Heat I i s.ao i I l
I l Cold Leg-la Concentration.1% Decay Heat 0.003 . , 1. i
- , ... I i ! . '
i i i 1;; i , ,1 -
! '. Pw.np Side
, ! ) : ! !!
' i 4 I M.
{0.00275- j t l ;. Eiddle 00 if '
* .y!- ! , EeswJ Side i '!. <
; j!l !
Q,QQ-),j. .....{. ...j...... ,
, .. ;... .. .; . { } ..
' i
,y 60 !! '
W !
', i
, ' i i ii ' i' i I l i v ; ..: .
.i .
l
'-2i y g 0.00225- f :l.d -
~ '
1 em . ti ji
,L :~} ih
~.
i .4 l-l i et - i
!j i l i b
{ l 2 iif , t ! 0.002-tti,14f- 1-i - 'i 1! -[ - !- -...1 j
- 4) e '
i - e: 7: - : 1 h 4 h r: i
- l
! l I
o t ii <i
. 4
. t i ttl- .:t i
U 0.00175- t
-t -i! 't " j p i ii!
{ 1 I !! it i '! ' i;i Iii !! O,0015 '3
~
10 100 le+03 le+04 time (s) Figure 5.217 Cold Leg 1 a Mass Flow Rates.1% Decay Heat ; Cold Leg 1-b Concentration.1% Decay Heat 0.003- . . .,..
, . .i - ! , .
i.
. i _.
'.i
; j
. :i i i i ! Pup Side
! l i ..
C 0.00275- ' i Midd3' F ',s L t, h t. j oc - ! W ' venet sid.
% i i !!
~'
c !i sci 0.0025- - Fr - - - i -i ~ , me ! +'r '+i ' ' ~ t+l i i i Mv
; 1
- i !!'. ii. :
e 0.00225-o f 4 41i - ~ ~ " - -b - - - : '
- eq :
1
.i
- i, i
3
! ti !
6 . i a u 0.002- -;-- -r +- .~ r - { ;- 7 -
-e - ~~
u i
- s ii c ~ ,
.!i -
o . r .
- t!
. g 0.00175- !..'t-H+ i-l : 1 T
]- : i
.i
. -e ,
j i.. i
'l !te
! ; i . Eh ! f'
. j t
0.0015 . 10 100 le+03 le+04 time (5) Figure 5.218 Cold Leg 1 b Boron Concentration.1% Decay Heat r l 5 31
I Cold Leg-2a Concentration.1% Decay Heat 0.003 . i ; i ' i j ; j i Pump Side m i ! Conn. CMT 0.0027- - - - - - -
--- ; - : Hi * -i- -- .
Vewel Side j' 9.0024- - - -- - j, f - 3;*' I l i
'; . . - g ?
C 4- '< !
! . 1 s
',Ij , t' ! '
O.0021- -
-t , --
it- - ' ---'- L.
<* i' -i i !
t .* a C i -j !! - i
.e s . , t , f
- 2 ' .'d l
~ i ,
3 0.0018. - -- - -' -- i- - - - U ,
! j !
l t t i i t
.t- ! -
i i
' i i i 0.0015
~
~
100 te+03 le+04 time (s) Figure 5.2-19 Cold Leg 2-a Boron Concentration.1% Decay Heat i Cold Leg-2b Concentration.1% Decay Heat 0.003 ; ; . .
. ~ i . -
, ; i Pump Side
- t. ; Conn. CMT te 0.0027- --- -- -
+- r- '- -- -- -
[ Vessel Side d ' ! e CC no i, i. i. j/ g 0.0024- : i- -- - - ~- v t f- t.v f-i , i C I fi o i > r! g - i 1
..e t
. Q,QQ}}. ......&..-..... . . . . . . .
4A . ,.- .. . . . . , e.a c i
'.+
l .y ,..
- u ! .
- ;
i c - o 0.001Bi - - - -
- e- -
V ;- i t
! i J ! i 0.0015 .
100 le+03 le+04 time (s) Figure 5.2 20 Cold Leg 2-b Boron Concentration.1% Decay Heat 5 32
SG-1 Concentration.1% Decay Heat 0.003 1 ,
+ , !i, ; -
' ' i .
i i
, : i ,
l ; i ;} SG-l inlet
- i. j ; !. i-
..i : . 1; -
C0 + l ~i -h4 [F l '
, ;- 50-1 T9 5 .00275- - t.- * ; 1 -
.i i, 3:
i i
; ! !! i
...; i-i i: so-t outwa e
j .: t 1 - ,!
.j M
0.0025- + - -
- i-'7;
;--'! ! 4:iit ---
i
! /
t.<' --- i t EG-1 ON=
! i ' li
'W
! !'i!Ii ,'
l l }: 1 i i i {l !l ' I. ! , II / ( l! , a 0.00225- ~I t O a1 ---~!~~: +1!t j; ;
. 1 i
-t- j i 6-~ -4 A
!/
- +H + -
! ! i ti
; .: ; i ! - t -
he
; . ,/i (
- i i';i g 0.002- b - j-~*j- i ,d.. - ' ~' ,j ; i !
U g i
! j !!. .rI ,//: 1
'".. i, . N!i :
- - ;dr+ - + i! pM ..
J- {+ + - t 1 U 0.00175-7 ~'
- i4- b, . i j-4 1 , . i i 1 ; : .
i s , t i i t t
- -?
i ! i' i ! j1 0.0015 . >
~
10 100 le+03 le46 time (s) Figure 5.2-21 Steam Generator 1. Bomn Concentra%n.1% Decay Heat
- SG-2 eventration.1% Decay. Heat 0.003 . .
, i i it ! i -
j i :i, . i! ll - ( ii SG-2 !alet
. i . i i ; ,
@ 0.00275- L !~ so-2T ,
es> 7 :! i-+ 1
} !+- !'
I ii i. M I'ii 'i i !;! ;' ii ...
; < SG-2 Outlet 4
i ; .: : . .
! :j j i !!! ! ! **
0.0025- - !-+ ;+ - 7 +4- %'~- - ;t -r i sG-2 0.Pkam M I !. - W
;I i !
V i
,i
)' i -
i!
- -- H4-4 i - i - !
' : [;
E 0.00225-
- -- - - - - 2- i. - - - bi- -
C 1 i i
! : t
*3 ! l
' i
! i j!
05 ;* 6 . 4 i ! iI.i.**-....***...*==.4. : 5i j;
- : ,/',.*"-j 1
;j a 0.002- 4-e - . +-+- t + t - ?
- t "+ 't t es v
a
. I' i.i
! e e ,:- - .
. !j.
- . . .r. . e.
, _ . r. . . 4 i4. f . . . . .. . .. . .: . . . .< .
C :: l
! ! , i$.: , i t
t l
! t' y 0.00175-4 '
+~ -i + - -
", i l, l
- t. + - ".-
i , t ( ;
; i. y
! ! I I
{ !
- t. , ,
i . ,. 3.
! , ,i - -
il 4 . 4 i i ! '
- l 0.0015 .
. . . . - i 10 100 le+03 le+04 time (S)
Figure 5.2 22 Stearn Generator 2. Boron Concentration.1% Decay Heat L
- l. 5-33
__.__._______m..- _ - - - - - - - - - - - - - - - - " " - ' - - - ' - - - " - - - - - - - - - - - - " ' ' - - ' - - - - - - ' ' '
I
)
>- 5.3 Maximum Slug size Itcations The results discussed in Sect}ons 5.1 and 5.2 have shown that there is no mechanisms during the LONF transient, with standard or very low levels of decay heat, that can result in the accumulation of an L unborated plug of coolant in the primary system. The low decay heat run resulted in very low flows, that I led to stagnant regions in both loop. But, in both cases, the concentrations were above the critical i l concentration during operating conditions of 1830 ppm. I Nevertheless, the possibility still exists that by some mechanism not contemplated in the LONF l transient, an unborated plug of coo! ant could accumulate in the tract between the pump and the steam generator U-tube b:Jndle. Since the lowest natural circulation flow in case of non-design conditions for the operation of the passive safety systems (i.e. Iow decay heat) occurs in Loop 2, a boron dilution analysis was carried out by assuming the pump restart scenario with the plug of unborated coolant in Loop 2. Two possible scanarios have been addressed : 1 i L 1 the Direct Mixing can, where the two pumps of the loop where the unborated plug is located i (Loop 2) are restarted. l j 2 - the Backmixing case, where the two pumps of the loop without the unborated plug (Loop 1) are l restarted. ! , The analysis will study these two scenarios in order to calculate the size of the plug of unborated i cociant in Loop 2 that will yield a minimum boron concentration at any location in the core inlet region (level 3 of the TRAC vessel model) of 1200.0 ppm (5.31] for cold leg temperatures about 489 K (420 *F), and of 1310 ppm (5.3 2] for cold leg temperatures about 366 K (200 *F). This values are a conservative ! estimate for the minimum concentration allowed at any regon inside the core in order to prevent large local i L reactivity insertions that could lead to fuel damage. It covers both BOL and EOL conditions. 1 The initial conditions for these runs have been obtained from the TRAC-PF1 MOD 2 standard and low decay heat simulatiorm discussed above. Four input decks, two for each mixing case, were prepared containing the relevant components of the primary system whose boron concentration had to be changed dunng the iterations. Each of the two input decks for each mixing case a based on the standard and low decay heat runs ae;+id . Ini additen, the number of cats in the cold and hot legs where the high order j solute tracker was applied was doubled in order to achieve better resolution of the dilution fronts during their transport to the vessel. The vessel and downcomer noding schemes, however, were maintained, since they are close to the maximum number of cells that can be officently used in the present computations according to CPU and memory limitations. The new noding scheme is presented in table 5.21. 5-34
l I i ( The input conditions (temperatures, velocities, concentrations, etc.) for each of the components in l the four decks consopond to those of the system at 4000.0 seconds for the standard decay beat case, and at 4500.0 seconds for the low decay heat run. These times have been selected so that the system mass l. l flow rates were relatively stable (Iow decay heat run) and the cold leg and core temperatures reached minimum values for the transients. 1 The iterative process is based on the modification of the boron concentration in selected cells situated between the pump impellers and the stean generator in Leg 2. For the backmixing runs, the whole steam generator U tube in Loop 2 was assumed unborated, whereas, for the direct mixing case, ony the region between the pump irnpollers and the steam generator outlet plenuta was diluted. For this l particular case, additional cells were added to the outlet p'enum component (TEE 222) so that the volume l l of unborated coolant could be finely adjusted. By varying the volume of these additsnal cells, keeping the i total volume in the outlet plenum constarA a maximum plug size was obtained. The model is described in Section 3.1 (Fig. 3.17). l The pump restart sequence, obtained from Westinghouse [5.3-1) assumes that the pumps reach ! nominal speed in 5 seconds, with a 2 seconds delay between the restart c! purnp 2a and the restart of l pump 2b. A trip controlling the restart time was set to activate at 0.5 seconds into the transient. After the trip gives the start signal, a linear table of angular speed vs. time sets the impeller speed for each pump. The nominal angular speeds were taken as those computed in the steady state run resulting in nominal mass flow rates for TDF conditions in the cold legs. The values for each loop are : Loop 1 : 172.43 rd/s Loop 2 : 171.30 rd/s l l The runs for the direct rnixing cases were extended to 20 seconds, since it was observed that the i minimum concentration values at the core inlet are reached at about 9 seconds from the beginrdng of the transient. The backmixing cases were run up to 105 seconds for the standard decay heat model, and up to 150 seconds for the low decoy heat model. At these times, the rninimum conantration values in the core inlet have already been reached, and a rising trend is observed, t 5.3.1 Loop 2 Pump Reetart (Direct Mixing)
- The system initief conditions for each of the two cases analyzed were those at
l i 4000.0 seconds for the standard decay heat run 4500.0 seconds for the low decay heat run l l 5 35 1 i
l In both transients, the high order solute tracker was used in the one dimensional and the three-dimensional components. The iterative procedure consisted of varying the size of an unborated plug of l coolant situated in the region between the pump impellers and the steam generator outlet plenum in Loop l 2. Then several runs were rnade with different plug volumes in order to obtain the size of the plug that ! would yield a minimum core inlet concentration of 1200 ppm or 1310 ppm any location in the core intet, depending on the minimum cold leg temperatue as discussed above. For the standard decay heat run (StdDH) the results of three Iterations are presented below. Each one represents a certain volume of unborated water being injected into the vessel (there are 2 pump casings and two SG nonles in each loop) : Case 1 : Pump casing : I ' SG Nontes : Outlet Plenum : Total Volume :
] I Minimum Concentration : 1065 ppm Location : S-12 Case 2 : Pump casing :
SG Nozzles : Outlet Plenum : ; Total Volume : L
]
Nhirnum Concentration : 1150 ppm Location : S 12 s M Q., & Case 3 : Pump casing : SG Nozzles : Outlet Plenum :
, Total Volurr4 :
[ Minimum Concentration : 1197 ppm Location : S-12 L9 cation S-12 (sector 12) corresponds to the same azimuthallocation that Cold Lag 2a. The results shown above are deplayed in Fig. 5.3 3. The plug is clearty identifiable when passing through the core inlet in approximately one and a half seconds. Since the concentration throughout the primary system is almost homogeneous at the beginning of the transient, as shown in Section 5.1, after the sharp drop, the core inlet concentration rises rapidly to the initial value, as borated water from the rest of ( 5 36 I
Loop 2 is injected into the vessel immediatly following the unborated plug. The results above give a value of 3.2892 m* (116.57ft'). as the maximum volume size of an unborated plug of coolant in Loop 2 under post i.ONF conditions (with standard decay heat) which satisfies the 1200 ppm minimum requirement for i the direct mixing scenario, i l The results for three iterations are also presented below for the low decay heat runs, where the cold leg temperature , Case 1 : r -
%C Purnp casing :
! SG Nozzles : l Outlet Plenum : Total Volume :
]
Minimum Concentration : 1250 ppm l Location : S 12 i q 2, C-Case 2 : Pump casing : SG Nozzles : 1 ( Outlet Plenum : Total Volume : J [ Minimum Concentration : 1330 ppm t Locaton : S 12 ! p
~
[ Case 3 : Pump casing : SG Nozzles : Outlet Plenum : ' Total Volume : g ) i ' Minimum Concentration : 1307 ppm Locaten : S 12 As expected, the maximum volume of unborated coolant is smaller than the one predicted in the l . standard decay heat run. The reason can be found in the lower boron concentrabon of the stagnant coolant in the primary system legs, especially in the Loop 2 steam generator, at the beginning of the transient j because of the lower natural circulation flows discussed in Section 5.2. Fig. 5.3 4 shows the effect of this l as a longer time to recover the initial core inlet concentration after the plug has passed. The plot shows
. how, after the minimum concentration is roadwd, the build up to initial concentration in the vessel (-2660 ppm) is . slower than that observed h the standard decay heat run, since the concentration in Loop 2 is larger in the latter case. Once the initial relatively low concentration coolant of the steem generator and cold
, lege has Sowed through the vessel, the highly borated waler from the veneel upper pienum and upper head le pumped through the hot and cold legs of Loop 2, again into the vessel, cousing the concentration in the core inlet to rise again. 5 37
l Only the initial minimum concentration is important in both cases. Once the plug has passed through the vessel once, successive circulations are less severe because of additional mixing and the diversion of i part of the flow to the other leg. in order to interpret the results described Lbove, it is necessary to take into account that the cases discussed above have been computed under more severe conditions than those expected to occur in the actual system. For instance, no credit for mixing by the highly turbulent flow at the pumps' impellers has l l been assumed. In addition, the highty turbulent mixing as a result of the unborated jet from the cold leg impinging against the downcomer wall la not modeled, since no satisfactory model has been found that ; could simulate this process with a reasonable noding scheme within TRAC-PF1/ MOD 2 capabilities. Regarding the flow distribution in the downcomer, the probable, and expenmentally observed, flow splitting at the point of impact, cannot be successfully simulated by TRAC with the coarse models this code uses 1 when compared with more detailed flow analysis CFD codes, requiring meshing schemes of the order of tens of thousands of nodes. As a result, tis diluted plug is direc0y diverted downwards into the core, almost intact. In the actual system, the flow splitting would render a broken plug that would more easily be mixed and would probably result in a less severe transient. Fnally, the model used to simulate the vessel, b& sed on a LANL deck as described in Section 3, consists of two three dsnensional components connected by one dimensional pipes. This layout reduces the cross flow in the downcomer, thus reducing'the spread of any plug that may be injected in it. l In summary, the volumes obtained above represent a conservative estenate when compared to the ! i l physical mixing and dispersive meeturkms expected to occur during the pump restart scenario, which are 1 not included in the model used to track the unborated plug of coolant. From the neutronic point of view, Figs. 5.3 7 and 5.34 show that the core remains in a subcritical condition, which indicates that the core average concentration romans higher during the transient than that needed for enticality (see 5.4). j Finally, Figs. 5.3-5 and 5.34 show that the time lag between pump restarts contribute to the reduction of the severfty of the transient. The initial driving head of the flow in Cold Leg 2a from the
. restarted purnp establishes a reverse flow in Cold Log 2b before the pump in this leg starts. The reverse flow injects the unborated plug of this leg, and some of the borated coolant between the pump and the vessel, into the outlet plenum; under real condmons, this situation would generate an actwo mixing, in fact reducing the size of the final unborated plug being injected into the vessel through Cold Leg 2b. This result could point towards a restart strategy in case the presence of unborated coolant regions is detected in the
, loops. In contrast, simultaneous restart of both pumps would not yield such beneficial effects. I s.= l L_-_______----_--_ - - - _
, Pump Angular Speed. StdDH 200 ,
, ~~-
, tC-
, I i i _
I
} ;
- Pump la j i <
. . . i -
4... . .!. ., . . ,7. - .-.7.....-..m_.._.. . Mp ib jg. .
.... , . .. .. . j../ .1.
. ...i... ....i 4.....,.. .. 4... . . . . . .
^ j ,' '
j y' i i Pump 2e ( s. i [ [' i - i
- /
/ i Pump 2b v l !
i e :
/ ;
I ..j......... 57 j2Q
?
......,....a....../.
...p...-..
. . .; ... . . 4 . .. p.. . .. . ; . .. .i.......
! $ / / I + i i ! CL i
/
i i , i r/) - if / j : i 6 j/ / i ! ' a 80- -' :r - /- +- '- '
+- - - --
i i
= '-! / i ti r ;
E ll
~
c l .
; ./ .e , i :
dd 40- +/ e
-,n-8
/
i i i- - - i t-F- +--- - + - - - -- f } , -
/
e - ,/ 1 i i I i i i
? . l s !
e i t ;
~
0 . . l 4e+03 4.0le+03 4.02'e+03
- time (s)
Figure 5.31 Pump Angular Speed. Standard Decay Heat I b 1 n Pumn Anrular Speed. IDH , A@ j PumpIs Pumplb
^
Pump 2a Mg .. v P g 2b i
- Ch t
rt) 6
.5
- 4 i i I l
l 1 I i tirne (s) I Figure 5.3-2 Pump Angular Speed. Low Decay Heat i M i ! l i _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ]
I l i i l Core Minimum Inlet Concentration. Sector 12. StdDH 0.003 .
- i ! ! !' f. .. ..
l ! Cuel i ! ; m ,! , . ..
% +
Cue 2 7os0.0025- - - -
- + - - ;- - ' " ' ' --' ---
/, . u.
Cue 3 i _ \ 1200 ppm I {i oc > g 0.002- v 4-- -,- --,- 4....~. v i , a > o .
*"3 O 0.0015-
~4- . -+-
r
--4 - '- ' -
i +
..:--......:-..e.. . . .
i, c . e v _____+_,__-__ i i i : - L __ _ a, _ _t______j_______ - i i i E ; I ! l ;*.',' I ! - o 0.001' t-+ t- -~ 4 '- - - e -- O != ; ; i l' l i 0.0005 . , l l 4e+03 4.0le+03 4.02e+03 l time (S) l Figure 5.3 3 Mmimum Core inlet Concentration. Standard Decay Heat i i Core Minimum Inlet Concentration. Sector 12. LDH 0.003 . l I Case 1 i . t !
- C , i i j Case 2
> 0.0026- -
-'-- + -- - - +-
+ . -
-+- -
Da ! i Case 3 i
, j 1310 ppm 08 ..;. I Q,QQ22 .......... .. 4 ..&. ..- . . . . . . ......:-.
v i c i ! !
.I i
{ . w t - g 0.0018- - *-+ t ,
+- --- --+- --
l j----~~~ E o i i a 1 i 1 4 . 0.0014- - + - + - _ _ _. _ _ _ _+- ~: 1 - - - + - - - g , _ _ _ i _ _i. -' .., s ~_.....t.e - - -- - t.___--,____.-,r._ .
. . .i 0.001 .
4.5e+03 4.51e403 4.52e+03 time (s) Figure 5.3 4 Minimum Core inlet Concentration. Low Decay Heat 5 40
Mass Flow Rate at SG Nozzle Connection. StdDH 7e+03 i , r I ! ~ t -i e
; i ! i Imp 24 6e+03- + -- .
+
- .a . .
i .e L4op 2b i Se+03- - l -t- - - - - i -- . . -
....e ....
.a 1i i ; i
$ 4e+03- - :- - L 4- r - f $~ "-
,-.d.. ...; ..
& f . .. . . ... . .
, f ,
j
.i I
i 3e+03- l ~-- n
-++-.4-+- .. .c.- i_ d. _ .
i g ~i I t ,/ i t ;
~
i . l
}
2e+03- '-
!! -l i .
-.. .. .d... ! .. -... . .. , .._
! " i' A i i f; ; i , ; I le+03- --
-i--+ . /: 4' a. -
l l/ . i / i ; ; i 0- -frq"
;\
f
/ ' :
.r j
- 4. t ...,.........
i -
! \ t :/ i i .
; i N!'-
i
'A i ! I i i l
-1e+03 l ,
4e+03 4.01e+03 4.02e+03 time (S) Figure 5.3-5 Mass Flow Rate at SG-2 Nozzle Connection. Standard Decay Heat Mass Flow Rate at SG Nonle Connection. LDH 7e+03 . . i
! ! } Loop 2a r
6e+03-
-L +-
I
, IMP 2b i- t .
E
^
i Se+03- - -r - .
- - +- -~
-+ - - --
i ./i ! d5551 2 i it I
" r-1 ge+03 .. L - . - ..i 1. -.L- ....;._
-- + . -.
w o ;i i 1 l i l n > j , i pg l 3e+03 _ __ , _-. _. l
, _ s /-i . ..j. . _ _ _ _. j __ t_ 4___._
i N i / ' j { ! t j 2e 43-i 1 - 1 l 4
- ir ti- 3 i
i !
+, -- --
i l r i, i
! I ! i i
le+03- 3-+
-!r:-+- '- 4- =' - - - --
E '
.i
/ .
l,
- o. s l... , ... ... . ; .
*% i
- f
<' s ; / i :
.N! / j '
' * ! 1 N~ / t i }
_]e43 4.5e+03 4.51e+03 4.52e+03 time (s) Figure 5.3-6 Mass Flow Rate at SG-2 Nozzle Connecten. Low Decay Heat Run 5-41
1
}
i l
)
l Reactor Power. Standard Decay Heat 0.0143 . . l i ; e 4 i j 3 t i, i
*- y. + "t - "4 -
i 0.0143- " .
. r. - ~r :+ y-~ - + - -
N l l ! !
! ; 1 8 0.0143. i -- + -
l
- +
' - . - -i-- - : --
i i i
- f. - t i
---l i i i I .
0 .0143- - r +- -
*- -+- - - r-
- i, .
- +- - '~-
k
$ I ' ' '
i ! ! i --- '- - - - - -
.--+ ' r-t- -- --t' -i- -*-- --
l0.0143-l ! l g 0.0143- 4 F-6 +-o -- '
- l- +- ] p -f-
' .) 0.0143-
+-, -p L -"i - 7 " ---r - l --. I
-- i ---
W i ;
} i ?
M 0.0143- ~ * - + '
+--
r- -- w 1 i i
& I i i ! .
1 g 0.0143-8 t t l '
-; r -- ' ;- --+---
'- i -- -
l M 0 .0143- ~~ --- I ,. t,' -. ~- ---- - f ' i i !
. 4 : !' !
0.0143 . 1 4e+03 4.01e+03 4.02eM)3 time (s) Figure 5.3-7 Reactor Power. Standard Decay Heat Reactor Power. Low Decay Heat 0.000137- . i j *
+
..+. . 4. .. 4. , . .
...i.. . . . . . . .._..,. ,
e 3 l t i i
..r..... . . . .
(
. . . . . . . , . i i
S
. .. 4 . , ~ . . . . . ;
. . . . . . ,. .i. - ; . . .. .
! ! l 1 !.
..x...
.............. .9.. .. ... ..;. . ... . . s. . . . . . . . .....
i I
}
Q g }}]. . ... . . . . . ,
}
p . . . .
.y 9.. .... . . . . . ,
.............-t . . . . - . . . . . . . . . . . . . . . . . . . ,
....i...,.. ... . .... . . . , ..
j i i
) .
l l .
. , - ,-....+. ...........t... ...'.!. . . . .. . . . . .
l
.2
. . . . . . . . . . . . . .. . i... . .,. . . _ . .
.. . . . . , I . ..
w . . . . 4._......3.......i i. .. . :.. . ..: .............. i t e ;
; i 1 i ,
-- }' _ ; ..a .,v... L . . . .__ _ .
! I l 3: ; ,
.<_ ..4....
cp - i ; ; + g - .1- _..;.....-.....~.. . . . .i . . . . 4 1 0.000137- :--r "b rw -+--r- - - " -
! - i i 0.000137 .
4.5e+03 4.51e+03 4.52e+03 time (s) Figure 5.3-8 Reactor Power. Low Decay Heat 5-42 L_________________._.______.__ _ _ . _ - - -
5,3.2 Loop 1 Pump Restart (Backmixing) The backmixing runs were performed by restarting the two pumps in Loop 1. The restatt sequence was similar to that used for the direct mixing case, and the pumps in Loop 2 remained idle. Similariy to the
. direct mixing runs, two cases were analyzed, i.e., with standard and low decay heat conditions.
The results for both cases showed that the rninimum concentration in the core inlet was never lower ihan 1780 ppm for standard decay heat, and 1800 ppm for low decay heat, even when Loop 2 steam generator U-tube, plena and p* mp casings were assumed fun of unborated water This situation would correspond to the most severe case, where the stagnation observed in the low decay heat runs ( ec 5.2) was complete, and by some mechanism the entire water inventory in the U-tubes wm diluted to unborated conditions. Figures 6.3-11 and 5.3-12 show the boron concentration history for the locations in the core inlet of minimum concentration. These locations are sectors 16 and 10, situated at the same azimuthal sector as the Loop 1 Cold Leg a and b respectively. Although the volume of unborated water for the backmixing nJns is quite large 36.4629 rrf (1287.68 ft"), the transient is much less severe than the direct mixing case described nbove. The reason for this can be found in the flow pattem that develops in the primary system fogs after the restart d the pumps in Loop L
- 1. The flow in Loop 2 is reversed, and enters the vessel through the hot leg. There,4 mixes with a rnech larger flow coming from the core (see Fig. 5.313 and 5.314), and leaves the vessel through the Loop 1 hot leg nozz'e. The flow coming from the core is highly borated when compared to the coolant injected from '
I Loop 2, and, since the ratio of flows is altnost ten to one, the dilution of the coolant leaving the vessel 1 towards Loop 1 is relat!vely small. The result is that the coolant in Loop 1 piping is no longer a well defined unborated plug, as in the case of direct mixing, but a partially diluted coolant flow. This coolant enters the vossel again through the Loop 1 cold legs, and after fkung down the downcomer, finally enters the core. The result is a much slower decrease in boron concentration after an initial period when the urmven distribution of boron in the system, especially in the low decay heat case, causes some oscillatioris in the concentration.
?
Both figures clearty show the two second lag between the the restart times of pump 1a ared 1b at the beginning of the transient where the concentration changes in sector 10 follow those observed in sector i 16 by about 2 seconds (the lag time). The standard decay heat run presents an initial rise in boron concentration as a result of the movement of coolant from the upper downcomer, whose concentration is larger than that of the rest of the vessel because of the CMT infecten lines. In addK'on, an incease in the CMT injection flow from about g Kg/s to a mammum of 13 kg/s is also cbserved due to the movent of coolant in the downcamer caused by the restarted pumps. This action increases the content of highly bortled water in the downcomer, which ultimately ends up in the core inlet. After this initial amat increment, a drop in concentrated follows as the more diluted coolant stored in Loop 1 steam generator U-tube is 5-43
i l l l l iniscted into the vessel. This drop is not as pronounced as the one observed in the low decay heat case because the concentration in the U tube in the standard decay heat case is onY 200 or 300 ppm lower than l I the vessel concentration. The concentration nsts again as the coolant in loop 1, which carries high concentration water from the PRHR and the hot leg piping, is pumped into the vessel From this point on, the slow dilution in the vessel upper plenum as a result of the cross-flow rnochanism desenbod above, , lowers the core inlet concentratbn to a minimum of 1730 ppm at the locations shown in Fig. 5.313. Once this value is reached, the continuing movement of coc: ant in the pnmary system will eventually homogenize the concentration throughout the primary system. The evolution of the minimum com inlet concentration in the low. decay heat case follows a similar l pattom. The reason is that the flow distribution in the primary system is mainly dependent on the pumps' ! head after they restart and reach full speed. The differences in rninimum concentrations are due to the
)
j higher vessel concentration at the beginrdng of the transient (at 4500 seconds it is about 2660 ppm), and l to the lower concentration in the Loop 1 steam generator U tube, as a result of the faster stagnation process desentrd in Section 5.2. The initial drop in concentration, caused by the relatively low concentration U tube inventory, is consequently much larger. After the boron concentration nses again, the l dilution process is essentially the same as the one described for the standard decay heat model. In summary, the backmixing scenario provides a mecharusm for restatting the pumps under j conditons of high dilution in ene of the loops. The reverse flow mechanism established as a result of the l restart of the pumps in the loop which does not contain the unborated coolant, wil avoid the rapid injection of well defined unborated coolant pluga in the core, contrary to what was observed during the direct mixing scenario. This allows for a much larger margin for safety, in case highly diluted pockets of coolant are suspected somewhere in the pnmary system. 5.3.3 References , 5.3 1 P SU TRAC-PF1 Code Effort: Minimum Boron Concentration and RCP Start-up Time, Westinghouse Memo NSA-l.EH-9&25, dated May 17,1996. l 5.3-2 PSU TRAC PF1 Code Effort: Power Shapes, Pealdng Factors, and 200*F Minimum Boron Concentration, Westinghouse Memo NSA LEH 96-36, dated June 27,1996. 4 5 44 r L--____ --
r---------------------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Pump Angular Speed.StdDH { s 1
%(
Empla Pump lb h 2a v iNmp 2b 1 N i 18 4
)
time (s) Figure 5.3-9 Pump Angular Speed. Standard Decay Heat l Pump AngularSpeed.IDH , %D banp Ia 1 bPlb l T 5mp 2a v hmP 2h 1 k 4 time (8) ! Figure 5.3-10 Pump Angular Speed. Low Decay Heat 5 45 I i
l I Pump Angular Speed. StdDH 200 ,
- i i .
l } }: ! l h mpla Pumplb l-n gg. .. . L' i. . .. . i I;
+
l
. .j .. . . . , . . , , , , ,
g ! ! ! Pump 2a
" Pump 2d l; l ;
120- - I- ~- - -
+-...
. .-...l..-......... ... . . . .
I' i 1 I - W) l ; i be l 6
-n 80- '
1 *- - -L - - - - . L - .- - E a I I i . i' i
< 40-l I -+. +- -
i ! 4-~ - k ~.- - - -. .. .- - :. - - . . - . . . . - . - 1 I i ffI i i 0 . , de+03 4.le+03 4.12e+03 time (S) l Figure 5.3-9 Pump Angular Speed. Standard Decay Heat Pump Angular Speed. LDH 2% , ., . i ' i . Pump la 171- r; ; ; , Pumptb
. i 1 , .-
7a .
, . Pump 2a
%w i 143- ' t i , e t- - -.
l : i 1 Pump 2b 1 m *
. . I
.t s 114- : i -
U . i . 4' ca., 4 i 4 ! . i r/)
- j ;
l' 6 a 85.7-
!~
1
- i- . 1 g -
OD
- i a 57.1- '-
~ -
4 l 1 i l' 1 , j i . . 28.6- : r 4 i i- i, - ;'
! I i
! i l- i 2
O . 4.Se+03 4.6ed3 4.65c+03 time (s) Figure 5.310 ? ump Angular Speed. Low Decay Heat 5 45
1 4 l j Core Minimum Inlet Concentration. StdDH 0.003 1 i j .
! ., ! Sector 10 l .
i : ! I E
^ l 5 '
! ; I i . . ! betor 16 0.0027- - +-
' -l -+ - --
- l- -4 i- v- -
00 . f g . 2 ! ! ! i ! I ' i , !
; i -
- l r ! i Oc ! 3 g 0.0024- 1 -
+-- .
+- *-
1-+- :
~ -+- -
l ! ! l ! n , i i i i 4 i i l 0 ; i : :' : c . ! i'- i i i ! 5 0.0021- - -
-lt i 1,
i < w 1 1 i
~
- 4 i
, . , i. . I i , j , 4 i r* , - i g 1 f i C 0.M18- - '- - '<--l-- +- -
+ i --
Q ; l
! i
! i
! l i !
~
l 0.0015 . 4e+03 4.le+03 4.15e+03 time (S) i l l Figure 5.311 Minimum Core Inlet Concentration. Standard Decay Heat t 1 l '~ Core Minimum inlet Concentration. LDH 0.003 ,.
. , Sector 10 i
t, _.
^ >
> Sector 16
)as-0.0027- -
- i- -
--+- -
- +- --
x: i l W ' i i
~
Mas ! t I
+
Q,@f. ...g
.7 j. . l
. . . . . . . . . .>.... ...s...... ., .... l i
V - j . ; - e i I ' i l C {
'C 3 t i n 0.0021- -i
-- - - - - - - - 4 w i ? .
** 1 6 i c . .
e 0.0018- 4- '- - 4- o- -+---i---+--- - +- - U ! i i i i
- i. ,
I 0.0015 , 4.5e+03 4.6e+03 4.65e+03 time (s) Figure 5.312 Minimum Core inlet Concentration. Low Decay Heat 5-46
Mass Flow Rates in Vessel. StdDH 1.4e+04 , { i t . - i l Hot Leg i j-]g4Q(. i i ! . HM Leg 2 t i I .. Ie+04- .; .p z .;.z .. ,. ... r.. .. w .. .r we. n . .. w. cr.. u .. .. ..
. . -- Con: Outlet
@ i
.e ge+03 .
; s.- . . . - . .
i
'. -[ .
i geg3 l.__._..- ._
.~,.. _ ,, ... 4 _ ~ . . . - . _ _ . - ~ . _ . . -
j k ' i i ! i i g 4, o3 ,
...j _..
q...
.. i... .
I E u o3 ..... I ..._.._....
...!.........._._.-.7.. . . _
i l Q. k. [ .. .f. . d .. .! + d i
.Y- . . .
1 ' .i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....i...........................j.r... 1 3 t 4e+03 4.le+03 4.12e+03 ' tittle (S) i Figure 5.313 Mass Flow Rates in Vessel. Standard Decay Heat Mass Flow Rates in Vessel. LDH 1.4e+04 , . i .
- j. ! i ! '
j I , , j HM ieg l l.2e44 - F
%2
'f~ ' '-
j t A 3 .
'.~'i
;.......+..r....y.....,.
.,. .. - .. .. .. .2 .. .,. ..
.. .. .,..... .;..~ ... . .. .. .. .. ,, .. ., .. .--
8
%o,,
g,44 . i...-.-.. ... . m -
' { ! !
I 1 i C -i u b O3- -
-l
~~E -
' --- ~ ~ - i~'- " ~ h '
"" '~
- * !, i i
I - . n' i
. .i .
! 6e+03- : " F -~ ? r' ~-~
' - t- '-
i- ' ^ ~ - " ' '~^ ^ ' '3.' ~ y , . i de+03- *"
- 7- ----- ~j "" '"~ ~'
, " ;~ ~" ~ ""~~ "~ .
i i ! ! - 2e+03- -I- 2 - ' ,
" ~ ~2 "~ ~-
E s ! i
- I i !.
...J
- i. !. !
i i "h" "
,.....-...~e.-...,......._. ...... . . . . . . . . . . . . . . . . . . . . . . . . . ., . . . . . . . . . . .
-2e43 -
4.5e+03 4.6e+03 4.65e+03 time (S)
^
Figure 5.314 Mass Flow Rates in' Vessel. Low Decay Heat l 5 47 i l j
5.4 Possibility of Recriticality during a LONF Transient A study of the possibility of recriticality under LONF conditions was carried out based on the predicted system response to the transient (see 5.1). The basic model for the analysis was the neutronic model desenbed in Section 3.2. All the rods are assumed to be inserted, except for the stuck rod at location K-2. The results were based on the analysis of the core under the following conddions: . Fuel Temperature : 558.15 K ( 545 "F) Core Pressure : 15.5132 MPa (2250 psia) Neutronic State : SCRAM with Stuck Rod ! Boron Concentration: 1830 ppm These conditions are kept constant for all the runs and represent Hot Zero Power conditions (HZP). Boron concentration and coolant temperature will be varied in order to study the dependence of K,, on these parameters. 5.4.1 Correction of Critical K,, The benchmark of the neutronic modelin Steady State conditions described in 4.3.2 showed a slight discrepancy between the results produced by the NEM module and the reference results from Westinghouse. Such differences meant that the core used in this study somehow was less reactive, since both SCRAM and Stuck Rod worths are larger that those from the reference results. In order to extend the results of the recriticality analysis to reflect the reference worths, a corrected value for the critical K., was computed based on the additional negative reactivity predicted by the NEM model when uompared to the reference core. The reference values at HZP are : (worth is defined as (1.0-()/1.0, where 1.0 id the critical K.,). Reference Stuck Rod Worth : 0.0204 Reference SCRAM Worth : 0.0968 (% = 0.9032) SCRAM with Stuck Rod Worth; 0.0764 (K,,p 0.9236) The calculated values at HZP are : HZP Stuck Rod Worth : 0.015738 SCRAM Worth : 0.10150 (K,, = 0.8985) SCRAM with Stuck Rod Worth: 0.08576 (K,,, = 0.91423) 5-48
l The additional negative reactivity that the NEM model used in this report introduces with respect to j the reference core is : K.,,y - K,m = 936.2 pcm in the results for minimum coolant temperature and minimum boron concentration two values for critical K, have been used, i.e., K,=1.0, which represents the NEM core as is, and the corrected value to account for the excess negative reactMty of the NEM model with respect to the reference core : K.,, = 1.0 - (K,y - K,y) = 0.900638 ;
- The value of K., will yleid more conservative results that are equivalent to those that would have been obtained had the NEM core had the same SCRAM and Stuck Rad worths as the Reference core.
l 5.4.2 Analysis of Minimum Core Average Concentration for Recriticality Table 5.41 shows the dependence of Keff on coolant temperature for the range of values expected during a LONF transient. The results plotted in Fig. S.41 give a close to linear relationship for the interval of temperatures expected in a LONF transient. The relationship is not completely linear, because the l positive reactivity insertion resulting from the increase of coolant density as it cools, is not linear. At high l temperatures the small variation of coolant density for a given temperature cha.9 si larger than at lower temperatures. Nevertheless, a linear regression analysis based on the curve : K, (TCoolant)= m
- TCoolant + b gives, for the values in table 5.41, the following parameters:
m = 0.0002 b = 1.0157 l Correlation Coefficient = -0.9941 ( -1.0 means perfectly linear) i K,(TCoolant)= 0.0002
- TCoolant + 1.0f 57 The linear interpolation is conservative with respect to the reacthnty insertton. From Fig. 5.41, it is I
clear that a linear fitting based on the points shown in Table 5.41 (which is the one used for the remainder of the analysis) will yield a higher K, as the coolant temperature decreases than the K, based on the actual change in coolant denetty. 5-49 L____________.____________ . _ _ _ _ ._ .-
7.-...._. l I l The extrapolation based on the linear fitting predicts a coolant temperature of 102.88 K to achieve criticality under the conditions described above, and 162.24 K for the corrected K,. TMs is obviously impossible, since the minimum temperature the core can be at is room temperature of about 300 K. The result means that with the core SCRAMMED and 1830 ppm boron, even when there is one stuck rod, there will be no retum to criticality if the concentration in the system is the same or larger than the one in the core j- (1830 ppm). Although the possibility of recriticality under LONF conditions seems to be of no concem, there still l remains the scenario where the core could become partially unborated, lowering its average concentration l to a value such that a recriticality scenario would be possible. In order to address this question, an l investigation of the minimum average core boron concentration that yields a critical core was carried out l for the range of coolant temperatures expected during a LONF transient. The fuel temperature and core l pressure were kept the same as those used for HZP conditions. Table 5.4-2 shows K, as a function of coolant temperature and core average concentration. A similar linear analysis to that made for the dependence between K, and cooient temperature has been done for the boron concentration at different temperatures. The parameters of the linear fittings are displayed in Table 5.4-3. The corrt.lation coefficients are very close to 1.0, which indicates an almost-perfect linear
. dependency of K, on the boron concentration for the range of coolant temperatures expected during a LONF transient (see Fig. 5.4-2).
The minimum temperature used in the analysis is 490 K (422.3 *F), which is lower that the minimum core temperature predicted by TRAC and the Reference LONF transent (see Secten 4.3.1). The values of K, for 490 K were extrapolated from the calculated values for five different temperatures by following , a linear fitting as described above. The results will be, therefore, conservative; that is, the actual core at 490 K will be less reactive than the results presented in Table 5.4 2 suggest. The reason for the using linear interpolation is that, at this low temperature with a stuck rod. the peak power at the stuck rod location is too large and the NEM method has difficulty trying to converge to a meaningful solution, in order to obtain the core average concentration that yields a critical core at every temperature in Table 5.4 2, a linser interpolated was again used. Table 5.4 3 and Fig. 5.4 2 show an almost perfect linear dependency. The results are shown at the bottom of Table 5.4 2 for K,=1 and for the corrected K,,,,, value. The row labelled Keff, shows the actual value computed by NEM with the predicted citical boron concentration as a benchmark for the interpolator procedure. As the results show, the minimum core average concentrations that produce recriticality are less than the operating equilibrium concentration of 1830 ppm, for the range of temperatures expected in a LONF 5 50 ! 1
l l 1 transient. This means that only in those accidents where a mechanism for dilution of the coolant below the
)
l equilibrium boron concentration can be found, should concern exist far the potential for recriticality. As ; l i shown in Sections 4 and 5, the LONF transient does not meet such criterium. ' l [ f I i l l l 5-51 l u__________._..___.__._____..______. _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ __ _ _ __
i i I l l I 0.9400 1 1 0.9390 - 1 0 9380 - -.. i 0 9370 - ! i r 0.9360 - - -- Y 0.9350 - ! W l 0.9340 - - - ......--. 7 - - -- 7-- .
..-_.g.._
0 9330 - - - - - --j . - - l 0.9120- -- .L~ .t- +. . . . . . - 0.9310 --- . - - J -- . . 0.9300 490.00 500.00 510.00 520.00 530.00 540.00 550.00 560.00 Coolant Temperatun (K) Figure 5.41 Keff vs. Coolant Temperature Keff.vs BorasConcestretles s i ce < Contant Terma 1.c:0 -+- $34 K x - m- 545 K l000- m,,s - . nsK
.,U ' 4.. X $30 K
.., -m- 500 K f C 9to I 'k; .490 K 0 940 < 4:. '. .-. ..
N..; - l q. i 0 980 N.,. . e 0 920 500 700 130 1100 1300 1500 4700 8900 Beren Caessetensten M l. Figurc 5.4 2 Kolf vs. Boron Concentration 5-51
l , Keff as a Function of Coolant Ternperature l Core Conditions : l Fuel Temperature : 558.15 K (545 F) Core Pressure : 15.5132 MPa (2250 psia) SCRAMMED Reactor with Stuck Rod Boron Concentration : 1830 ppm Coolant T. (K) Keff 500.00 0.939080 530.00 0.935188 1 535.00 0.934404 { 545.00 0.932693 550.00 0.931748 j 558.15 0.930074 l Table 5.4-1 Keff as a Function of Coolant Ternperature Keff as a Function of Coolant Ternperature and Boron Concentration Coolant Tensperature (K) ppm 553.15 545.00 535.00 530.00 500 00 490.00 1830 0 9301 0.9327 0.9344 0.9352 0.9391 .f] ) 1600 0 9431 0.9463 0.9483 0.9493 0.9540 N i I400 1200 0 9549 0.9670 0.9545 0.9711 0.9609 0.9738 0 9619 0.9750 0.9675 Dh 0.9814 ;, , d 900 0 9854 0.9906 0.9939 0.9953 1.0030 :t 700 0.9989 1.0043 1 0079 1.0096 1.0182 f.ht7 M Wik Crideal Boroe Concemtsuon l 668.96 755.31 808 39 831.95 946.15 3;.#93nid.',l Kaft , l 1.0010 1.0005 1.0001 1.0000 0.9996 l l Corrected Critical Boron Concentration l 822 60 902.95 952 25 974.12 1079.76 m ai121.112 . <l l Table 5.4 2 Keff as a Function of Coolant Ternperature and Boron Concentra: ion 5 52
i l l l t l Keff Criticality : 1.0000 Keff Corrected : 0.990638 1 Linear Approshnaden Kett vs. Coeinst Temp. 1 ppm m b Corr. Coefficient I 1830 -0.00015 1.01554 4 99339 I 1600 0.00018 1.04649 0.99M7 1400 -0.00021 1.074M -0.99415 1200 -0.00024 1.10368 0.99464 j 900 0.00029 1.84965 -0.99519 700 -0.00033 1.18266 -0.99548 i l
)
i j l T Cootaat m b Corr. Coefraient 558.15 0.0001 1.04076 -0.99969 545.00 -0.0001 104790 -0.99969 535.00 -0.0001 1.05261 -0.99967 530.00 0.0001 1.05478 -0.99967 l 500.00 00001 1.06630 -0.99963 490.00 0 0001 1.07135 -0.99963 l l Table 5.4 3 Linear Approximation Coefficients 5 53 l t
6 Conclusions The othectve of the stucy presented in this report was the analysis of boron dilution transients in the AP600 system. The strategy was based on the identification of stagnation regions in the primary side when the safety systems were operating under nominal conditions (standard decay heat) and under very low thermal heads (Iow decay heat). The LONF transient, without loss of offsite power, was selected as the baseline calculation that would activate the PRHR and the CMT systems, providing natural circulation thermal heads to move the flow in the primary legs. It was found that in natural circulation, flows coveloping under thermal heads for normal decay heat conditions were high enough to preclude the formation of stagnant pockets. The resulting convective transport of boron throughout the system, raised the concentration everywhere above the minimum critical concentration for operabng conditions. In partcular, the concentration in the vessel lower plenum was much , larger than this minimum value, because the coolant is moved by the natural circulation flow, and no stagnation is observed there. Low decay heet levels, however, would slowly lead to stagnation of the flow in Loop 2 and in the Loop 1 steam generator. Nevertheless, the results for this simulation showed that the flows developed in the PRHR pgung and the CMTs' Pressure Balance Lines would distribute the boron from the CMTs throughout the vessel. No pockets of stagnant coolant were found in the vessel. Moreover, the decaying flows in the r loop legs were high enough to distribute some of the highly borated water from the CMTs throughout the system, so that the boron concentration in the steam generators and cold legs was larger than the critical concentration. From this result, it is clear that, even if the natural circulation flows are small and decay to zero, the final boron concentrabon in the stagnant regions will be equal or larger than the concentration that yielded a critical core under normal operating conditions. Another important finding from the two simulations of the LONF transient was the lack of a physical mechanism that could produce clean plugs of coolant in the primary system. The relatively high system pressures in both cases, precluded the occurrence of reflux condensation type of flows in the steam generators. This result indcates that for transients were no large depressurization is expected, the passive safety systems will activate and maintain a certain level of coolant circulebon, and there does not seem to exist any physical mechanism that could produce clean pockets of stagnant coolant in the primary system. There remamed, however, the possatulity that by some mechanism not related to the normal transient evoluton, a clean plug of coolant would appear in the primary piping. In order to cover this scenario, and to determine the maximum size that such unborated plug of coolant could have before damage to the fuel happened, a series of pump restart transients were run similar to the Finnish Scenario. 64 (
The results from these analyses showed that there was in fact a maximum plug size for the direct injection of unborated coolant into the vessel. The size of the plug was larger for the normal decay heat runs because of the larger boron concentration in the Loop 2 steam generator (the loop whose pumps were restarted), thari in the low decay heat simulation. The plug sizes can be also used as a maximum value for the generation of clean pockets under different conditions (e.g. tube rupture, reflux-reflooding, maintenance error, pump seal leakage, etc.). Nevertheless, none of these mechanisms would produce a well defined clean plug like the one assumed in the calculations, since the unborated water would mix in the steam generator outlet plenum, resulting in a smaller clean plug for an equivalent volume of unborated water. In this sense, the predicted size of the plugs can be considered as a conservative value. Finally, it was observed that a sequential pump restart, where one pump lags the other, would produce a less severe transient because of the reverse flow in the lagging pump injects the unborated plug in the pump casing I and steam generator nozzle into the outlet plenum. There, the clean water mixes with the borated coolant, and the resulting plug is no longer a clean one. This effect would not appear if both pumps were simultaneously restarted. The backmixing runs tiled to test the effect of the restart of the pumps in the opposite loop to where the clean ooolant plugs might have formed. The results showed that the volume of clean coolant was in fact quite large. The entire primary side of the steam generator in the opposite loop could be completely unborated, and the dilution process would be slow enough, that the minimum concentration in the core inlet would be larger than the minimum value of 1200 ppm or 1310 ppm (the minimum that would not result in fuel damage). This was observed for both, the standard decay heat and the low decay heat cases Therefore, a procedure for restarting the purnps in case dilution in one of tha loops is suspected, could j entail the activation of the pumps in the opposite loop, so that the slow dilution process discussed above, , would prevent the injection of well defined clean plugs as observed when the purnpa in the loop containing the unborated plugs were restarted. Finally, the neutronic analysis of the minimum core awrage concentration required to drive the core into a critical state predicted a value well beyond the critical concentration for operating conditions. This result indmates the need for large dilutions of the entire core, if rectibcality is to appear under the conditions discussed in Section 5.4. Therefore, the possibility for core recriticality is subtected to the formation of large unborated pockets of coolant in the pnmary side.; in partcular, since the backmodng has proven to be quite effective in limiting the severity of the dilution, the only scenario that seems plausible would be a large deboration in the loop where the pumps are to be restarted, followed by the pump restart process in the I 1 same loop. Such an scenario could be averted by detection of the dilubon (the large size of the plug would make it relatively easy), and the restarting of the other loop's pumps. j j I 62
l Therefore, the most severe case appears to be the formation of relatively small and difficult to detect clean pockets by some physical mechanism, and the subsequent pump restart in the same loop. The results I discussed above give conservative estimates of plug sizes that could result in fuel damage because of a sudden local reactivity injection in the path of the clean plug through the core. This assumes a minimum I concentration value of 1200 ppm or 1310 ppm (local concentration) is adopted as a bounding criterium for j BOL and EOL conditions. i i t l l i i I l I l I I 63 l l l i ( L___________ . _ _ _ _ _ _ _ _ _ _ _ _ _ I
1 ! I Appendix A. Vessel Boron Distribution for LONF transient (Standard and Low Decay Heat) ! l i A.1 S'andard Decay Heat 1 sepse 44,64 1 00000 ( u 0 ee u - 4000.9 430 a. use . e. . .12t m e. ~ se un. sie.e . . 4. 11 e o i1 1 IStet 64444 1 0 0 1 1 . .. 4 not sees ve.ee 1 0 . ! i:1 ..... 44.. iii 000 0 l
*svel. 1 date eene l 3.3291448-03 3.530442s 03 3.5313418 03 2.5336358 03 2.532070s-03 3.9310423-03 2.S312248-03 .2.9303568-43 t 2.5391025-03 3.8393418-43 3.928923s.03 2.$38439s-03 2.5310545-03 3.5301378-03 2.5341305-03 2.5289118-03 3.5204S33 03 3.5304338-93 2.521s03s.e3 3.$27150s.03 2.s299448 0J 2.5313415-03 2.latiles-03 3.128240s-03 1.836000s-0J 1.034960s 43 1.8300005 03 1.836000s-03 1.8300008 03 1.030000s.43 1.430000s.03 1.830000s.03 level 2 data sene 1 2.534159sa43 3.5344438-03 2.5406908-03 2.5414998 03 3.5437995 43 3.5414345-43 2.540444s.43 2.13 s??Ss-03 ~
2.9349598-03 1.5311348-83 3.9308368-83 3.1403348 43 3.543ttis.e3 3.539931s.e3 3. 53 03498-e 3 3.Satitts-83 j 2.5359548 03 3.5344418-03 3.S31842s 03 3.1393918 03 2.5430903 03 3.5369943-03 3.5313ee8 03 2.5342198-83 3.$383598 03 2.5365988-03 3.llt3006-03 3.5389048-03 2.544126s-43 2.9384918 03 3.5310113-03 2.s353433-03 level 3 date came 2.938tt28-03 3.5337338-03 2.9405848-03 2.54148s8 03 3.$43111s-03 3.5413098-03 3.54043cs-03 3.5341598-03 3.536510s.03 3.9311148 43 3.9380058 03 2.S4823SE-03 2.943605s.03 3.5398958 03 2.5343398 43 3.93t14cs-03 3.5349918-03 3.134430s+03 2.5313113 03 3.531600s 43 3.5316093 03 3.5354418-03 2.9354148 9) 3.5355513 03 1.4300005 43 1.8300003 03 3.eJ06008-43 1.4300005 43 1.9300005 03 1.0304048-03 1.030000s-03 1.83000ts 43 level 4 data eene 2.536ttss=03 3.9387248 03 3.1404408-03 3.9414113 43 3.8433123 03 3.1412??S 03 2.1403138-03 3.934444s-03 3.S364 Sis-03 1.5311118 03 3.9344358-03 2.5402148 43 2.9431504 03 3.9396068 03 3.5303188-03 2.5311938-83 3.5353128 03 3.9J47008 93 3.13?S958 03 3.53??435-43 3.5311408-03 2.5354640-03 2.llstats-03 3.5350518-03 1.430600s 93 1.8304408-43 1.4300004 03 1.8380005-03 4.0300005-03 1.8340605-03 1.4366000-03 1.8300008 93 level 9 data eene 3.Satt?3S-43 3.5301138 03 3.1403 Sos.03 2. $ 413 3 Se-43 3.S430918 93 3.541301s.03 2.1401338-03 3.938543s-03 3.5344496 43 3.93tt368-03 2.5344348-03 2.5403003-43 2.6430493 03 3.1390118-03 3.5303478-43 3.lJ13243-03 3.5394048-el 3.9349568 03 3.$311998-03 3.53?t13s.03 3.131stts e3 3.5341013 03 3.534640s 43 2.134130s-43 1.8300908-03 1.0306098-03 1.030000s-03 1.4300048 83 1.4300605 43 1.0300005-03 1.8304048 43 1.0300005 03 level 4 date eene 2.$341108-03 3.9346943-03 2.1402418-03 2.5413915-83 3.5434195-03 3.5411498 03 3.$404418-43 3.S364Sas-03 [ 2.S341118 03 3.9311448 03 2.1364448-03 3.5441948 03 3.542$92s.03 3.8396398-03 3.536314s-43 2.S313608 03 3.5354418 05 3.5371140-03 3.9319198 03 3.1386418 03 3.S319918 03 3.9343073 43 3.1342518-43 2.5363t38 03 1.8304008 93 1.4304098-03 1.830000s el 3.03 000s.03 3.8304408 03 1.8366668-43 1.430040s 43 1.8300006-03 A1 w-____-_-________-__-___
i 3+ vel 1 esta come 3.8341408 63 2.5304728-03 2.S4021ST'03 2.5412948-03 3.1430092 03 3 $411443-0's 2.939999s 03 3.6303815 03 i-l 2.5345358-03 2.531119s-43 2.9381138 03 2.640311s-03 3.543993s-03 2.5398958-03 2.S343108-03 2.53?3218 43 i' i 3.1340438r03 2.931311s 03 2.938141s-03 2.538140s 03 2.3340948 03 2.lJ64006 03 2.5364608-03 3.5365s3s.03 1.430000s-03 1.430000s 03 1.0300005-03 1.5300003 03 1.830000s 03 1.830000s-03 1.830000s-03 1 830000s 03 level 8 date ! came I 2.8341238-03 2.$304458-43 2.Se#18?s 03 3.5413112-03 2.843050s-03 2.5412195 03 2.$399968-03 1.5303298-03 2.5356435-93 2.9379043-43 2.5301158-03 2.540240s-03 2.943431s-03 3.1399128-03 2.S363538 03 2.631370s-0J 3.934353s 03 3.5375408-03 2.3383808-03 2.5308778-03 2.538199s 03 2.S34427s 03 2.534415s-03 2.534941s-03 1.0300005-e3 1.030440s-03 1.430000s-03 1.0300003-03 3.030000E-03 1.830060s-03 1.030000s-03 1.030000s 03 newet 9 esta i I cens ! 2.5347078-0J 2.5304108-03 3.540179s-03 2.541350s 03 3.543112s-03 2.5413tes 03 2.8400135-03 2.9382918 03 l j 3.5345435-03 2.531040s 03 2.$34644a 03 1.54032La 03 3.543044s-03 2.5399998 03 3.539411s-03 2.SJ1432s-03 l 2.5343798 03 3.9376414-03 2.5304108 03 2.S343738-03 2.9342828 63 3.934?S68-43 2.534414s-03 2.534913s-03
- 1. 3 0048-03 1.030. 0. .3 .. 300.es-.3 i.83 000s-.3 1..i00 0.-43 1. 3 0.es-03 1. 300..s-03 1. 30000s.03 i
level 10 data eene 2.934494s 03 2.938581s e3 3.5441418 83 2.9413764-03 3.5431535-03 2.541331s 03 2.5404258-43 2.1352115-43 2.5343395 43 2.537051s-43 3.1380918-03 3.l403415 03 3.942112s-03 2.539184s-03 3.8344208 03 3.531444s-03 3.534441s-83 2.33???3s 03 2.538489s 03 3.3384428-03 3.5303578-03 2.8348965 83 3.5349538-03 2.S310348-43 1.430000s-83 '. 936000s-03 1.8J00008-43 1.030006e-03 1.030060s 03 1.8360000-43 1.3300006-03 1.830600s-43 level 11 data came 3.8346037 43 3.5344048 03 2.93Pe148-03 3.5411438-03 3.54393?s 03 3.$41J138 03 3.S391438 03 1.5360008 93 l 2.5344498-03 3.5316418 43 2.5306478-03 2.$40304s 43 2.9419308-43 2.5396438-03 2.5364118-43 2.137644s-43 ; l 2. 3,232.-0, 2.53,,0.s.03 3.53 5108-.3 3.83...... 3 3.13. 46s-03 2. 3 4 4. 03 3.i3,,i38 03 2.ll,413s-03 1.0300000 03 1.8340006-03 1.8J00006.e3 1. 83 0 Dees-43 1.439000s-03 1.830460s-03 1.8304408-03 1.030060s-03 level 12 data cone 3.5344948 e) 3 5304108-03 3.S39480s-43 2.5408228-03 3.9414Sts-03 3.5409014-03 3.9394198 03 3.9379348-03 1.5344938-03 2.531893s-03 3.534e99s-03 3.1403ste-03 2.54144es-03 2.940s398-83 2.539493s-03 3.937504s-03 3.5310715 03 3.5371998-03 3.538143s-03 3.5391198-03 3.53D4340 63 3.9395318-43 3.5382348 03 3.9375928 03 ! 1.5300ees 03 s.si00eos-el 1.e3eeoos 03 1.slooses e3 1.slooee's e3 1.eseeees-e3 1.e30eoes-s3 1 s30 eses e3 level 13 data s ene 3.53402SS-03 2.6303148 93 3.$393138-93 3.940331s 43 3.5411018 03 2.9ta3148 03 3.9393355-03 2.S37933s-03 3.5349458 03 3.9319913 63 3.5309448 03 3.1401038-43 2.1413138 03 2.5400els-03 3.lletets-03 3.531414s-03 l 2.$313298 03 3.5310445-43 3.5364198 03 3.lJ964SS-43 3.5644498 63 2.5394148-e3 1.S385648 03 3.5370540-03 !: 1.8344000-43 1.8346405-63 1.0300045 03 1.0306408-93 4.0500005-03 1.830060s-03 1.8304000-03 1 830000s-01 l level 14 esta e sas 2.1314476 43 3.9319115 03 3.5309858 03 2.539933s-03 3.5400098 93 2.93993?e-03 3.5390748-03 2.5342134-03 3.5315508-03 3.9310138-03 2.1300836-43 3.5399L35-03 3.540406e 03 3.5391028-43 3.1364308-03 3.9319218 03 3.9317998 03 3.5379728-03 2.538?438-03 3.539441s 03 2.5399248-93 3.$393438 43 2.5304415-63 3.9308098 53 1.0300000-03 8.036e005-03 1.0300006-e3 3.0306040 63 1.0306400-e3 1.0300008-63 1.43000e8-03 1.4300o48-03 level il date eene 2.4441198-03 2.4424918 03 3.4423445 e3 3.4433545 03 2.4444138-43 3.4414475 43 3.451131s 03 1.44tt338 03 2,4413440 03 3.4361490 83 3.4374478 03 3.43S9918 93 1.4399S18-03 3.446SE3s 03 3.451131s 03 3.4413425 03 f 1 r ! A2 L_______________________._____ _ _ _ _ _ _ _
i l I i f l 2.441999s-03 2.4JS4448-03 2.4304548 03 2.4344tas 03 1.4404378 03 2.445311s 03 2.413649s 03 2.4442303 43 1.8300004-03 1.030000s.0J 1.834800s 03 1.8300003 03 1.410000s 03 1.8300003-03 1.03D0003-03 1.8300005-03 l 1evet 15 esta 1 i eene 2.400?lts 03 2.4021318-03 2,3993248 03 2.40044ts.03 2.6000018-03 2.3972338 0J 2.3940455-03 2.39tates-03 2.4034045-03 2.4047248-63 2.4338948-03 2.4084STS 03 3.401224t-03 2.397390s.03 2.4039198-03 2.194244s 03 2.4132tes.03 2.42394?s.03 2.4125638 03 2.421233s.63 2.4184218 03 2.409490s.03 2.4127033 33 2.4051848 03 2.4119995 03 2.421022s-03 2.4154903 03 1.414132s 03 2.4130135-03 2.4012415 03 2.401930r-03 2.40$321s.03 I i level 17 data rene 2.218152s-03 2.2131438 03 2.2144448-03 3.32$4068 03 2.J3454 s.03 2.2249258 03 2.241704s-03 2.2254443 83 2.2249408 83 2.239944s-03 2.2418445 03 2.261894s=63 2.2378?38 03 2.243177s-03 2.2170928-03 2.291331s-03 I 2.304906s.03 2.304710s-03 J.305$118-43 2.30440ts-03 2.2st403s 43 3.3052295 03 2.311414s-03 2.3044438 03 1.430000s 0J 1.0300003-03 1.830000s-03 1.430000s-03 1.830000s 43 1.830000s.03 1.g300003-03 1.430000s 03 1 80004 17111 32222 00C00 11 0 0 1 tLas e 4000.094309 s. t Lee st es a .127117 a, nummer tLas stepe e 4844 20 0 1 68648 1 22222 0 0 1 0 8 ? $20$ downcomes vessel 2 0 0 111 98066 1 22222 00000 level 1 est a come 1.8300005-03 1.430000s-03 1.030400s 03 1.330000s.03 1.8300003 03 1.8300003-03 1.030400s-01 1.030000s-03 1.8300005-63 1.430000s 03 1.4306098 03 1. 83 D4003 43 2.136020s.03 2.934133s-03 2.S3413ts-03 2.9348743-03 2.S312348 03 2.1383498-03 2.9441313 03 2.531931s-03 2.134097s.03 2.534544s.03 3.534263s-03 2.534160s-03 novel 3 data j eens 1.4300003 43 1.030000s-03 1.0300005-03 1.0300005 03 3.8300003-03 1.4300003-03 1.8300005-03 1.030000s 01 1.830$005 03 1.830060s-03 1.030000s-03 1.8304003-03 2.5354458 03 2.13 541 LS-43 2.5394415 43 2.535833s 03 2.$350048 03 2.134902s.03 2.5441348 03 2.934445s-03 2.53S843s.83 2.9314578 03 2.5395595 83 3.935429s 03 level 3 data eene 3.03000es 03 1010000s e3 1.s30e00s e3 1.83000*s.03 1.03es00s-e3 1.esteots-03 1.s30000s-e3 1.s3000es 03 l l 1.s30000s-03 1.e300ees.03 1.e3:000s-el 1.s30000s.s3 2.sassass-e3 2.13s4 ?r.4; 3.s3ssees-03 2.13533ts.03 2.5343518-03 2.5347298 43 2.1441345-03 3.93Sc20s 03 2.5349938 43 2.934032s.03 3.535390s.03 2.5313?ts 03 ie.ei 4 <a y emne 1.6340ees.83 1.830000s 03 1.430000s 03 1.430000s.43 1.030600s.03 1.93Deees.43 1.430000s.03 1.8300005 03 1.4360008-43 1.8390ees-03 1.430000s-03 1 830000s.03 2.1333448-03 8.1331875 03 2.5334908-03 2.S134925 03 2.933666s.03 2.533190s.03 2.54413ts.03 3.534521s-03 3.5341728-03 2.5343648 03 2.5343898-03 2.533812s.03 L eve l 5 asse tone 1.430000s-03 1.030040s-03 1 830000s.03 1.830000s.43 1. 8 3000Ds.03 1. 8364 Des-03 1.0300098-03 1.830000s-03 1.030000s-03 1.830000s.03 1.8300005-03 1.030400s-03 3.5241013 03 2.5349248-03 2.5241818 03 1.52?t31s-03 2.5204938 93 2.533020s.03 2.544936s.63 2.134$498-03 3.5340128-03 2.521316s.03 2.1303008 63 2.524839s 03 level 4 data cone 1 880000s 03 1 8300005 03 1.8300008 63 1.830000s.03 1.830000s-03 1 8304048 83 1.838600s-03 1.330000s 03 1 8300003-03 1 830000s-03 1 830000s.83 1.430000s 03 2.1346478 93 3.131405s.03 3.5253918 63 2.525419s 03 A3
l 1 i 2.3362438-03 2.534439s-03 2.54S4098 03 2.5353C18-03 2.S2510SS-03 2.535318s-03 2.5231193-03 3.525211s 03 l' level 1 data eens 1.8300003-03 1.830000s-03 1.030000s 03 LO30000s 03 1.830000s 03 1.8300003-03 1.430000s 63 1.830000s 03 1.830000s-03 1.630000s-03 1.435000s-03 1.8300003-03 2.93441Ss-03 2.124tsSt 03 3.535514s 03 2 S25150s-03 2.53S$918-03 2.531094s-03 2.S406943-03 2.539130s 03 2 5264028-03 2.52S190s-03 2.125393s-43 2.525443s-03 Level s data eens
- 1. 4 3 0f#003- 0J 1.830000s-03 1.0300003-03 1.030080s-03 1.430000s-03 1.430000s 03 1.8380003-03 1.030000s.03 4 1.0380008 83 1.5300003-03 1.830000s-03 1.830000s-03 2.524680s+03 2.5254413 03 2.525659s 03 2.5305513 03 3.9360088 03 2.S40541s-03 2.3149118 03 2.S49446s 03 2.S310998-03 2.130913s 03 2.52SS31s-03 2.52S5333 03 i level 9 dets j
4 cene 1.8300003 83 1.830020s-03 1.0300005 03 1.8300205-33 1.3300003 03 1.0300003 03 1.030s00s-03 1.0300095-03 ! 1.8300005 03 1.0300000-03 1.9300000-03 1.8300003-03 2.5244S18 03 3.8256935 83 2.S25141s-03 2.9414438-03 [. 2,SSS190s-03 2.540460s 03 3.940140s-03 3.340$sts 03 2.S$56015-03 2.5415490-03 3.525482s 03 2.825992s-03 level 10 data sena 1.4300005-03 1.030000s-03 1.8300003 03 1.8300005-03 1.830000s-03 1.0300005-03 1.830000s-03 1.830000s 03 1.4300005-03 1.8300005-03 1.8300005-03 1.430000s*03 2.524224s-03 2.525113s-03 2.5260453-03 2.6043368 03 2.9908338 03 2.5180Sle 03 2.96048Ss 03 2.S??9698-63 2.5910425 03 2.4043438-03 2.5240113-03 2.S256458-03 l 1evel 11 date seat 1.430000s 03 1.330000s 03 1.4300005-03 1.4300003-03 1.0300003 03 1.830000s-03 1.0300005-03 1.8300003 03 1.0300003-01 1.830000s-03 1.4300005-03 1.8300005-03 2.5231235 03 2.53S600s 03 2.1342168 03 2.5939358-03 2.94S1908-63 2.5454398-03 2.SS02938 03 2.5463115-03 2.546210s-03 2.6930058-03 2.5342498 03 2.82S1348 03 levet 13 desa eene 1.8300005-03 1.830000s-03 1.8300005-03 8.830000s-01 1.4300003-03 1.538000s 03 1.430000s-03 1.8300000-03 i
)
' 1 1.039000s-03 1.8300003-03 1.830000s-03 1.030000s*03 3.533Sles-03 2.93S833s 03 2.8290218 03 2.5360913-03 ; 2.5394968 03 2.9384438-03 2.S391035 03 2.S304448-03 2.539930s-03 2.S303438-03 3.5216338-03 3.5251548 03 level 13 data came 1.0300004-03 1.830000s-03 1.0300004 03 1.030000s-03 1.030000s 03 1.9300006-03 1.9300003 03 1.430000s 03 1.830000s 03 1.0300006-03 1.4300000 03 1.8300006 03 2.533313s-03 2.1210558 03 2.S$11198-03 3.S311438-03 2.5360188-03 2.538S998 03 2.5391598-03 2.5386See 03 2.5349018-03 2.5304918 03 2.5304308 03 2.52S1028-03 Level 14 data eene 3.g300003 03 1.8300000-08 1.4300005-03 1.930000s-03 1.0300038 03 1.8300000-03 1.4300006-03 1 830000s-03 1.0300003 03 1.8300005-03 1.8J00003-03 1.830000s 03 2.4019305-03 2.S2434se.03 3.5309638 43 2.5323908-03 I 3.5318118-03 2.9321648-03 2.9202248-03 2.5311428-03 2.S301194-03 2.S316018 03 2.8303908-03 2.5359048 03 I A-4 l a-_________-_-_-_______ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - __ _ _ _ _ _ - _ . _ _ _ _ _ _ . _ . _ _ _ _ _ _ __ _. . _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _
l l [ I A.2 Low Decay Heat I j 1 a.n mu 1 0. m lG 11 e 94 tiaie a 4500.460333 e. time step e .500009 s. i' L nummer ttme essee = 3331 11 0 0 l- 1 86804 64664 1 0 0 1 6 s4 -6 3104 core vessel 1 0 0 [ 111 scend uses I. 111 0000o
..... ................ ......... ................. ....... .. ....... =........,...........-.... ......
level 1 date j eone ' i 3.648839s-03 3.64501Sbc3 3.6430338-03 3.665031s.03 3.4453198 03 3. 665014>03 3.662070s CA 3 66SO438 04 i 3.64$0683-03 3.665034bO3 3.665439s-03 3.6449518-03 3.6413363-03 3.445132s 03 3. 66 $nos-03 3.648046be3 l= i L 3,6490443 03 3.4666415-43 3.8650098-03 3.6444193 43 3.648310s-03 3. 665160be) 3.6450418-03 3.665010s-03 i l l 1.4300005-03 1.830000s.43 3.6300008-03 1.6306448 03 1.430440s-03 1.830400s 03 1.630600s.03 1.6M000s-03 level 3 data -
.some 3.64S11Ss-C3 3.8481348.e3 3.6650413 03 3.4649313-43 2.645119s-03 3.643153s-03 3.6653313 03 3.643336s-03 3.46S143s.03 2.645063s-03 3.444914s-03 3.644400s-03 3.645334s-03 3.6453114 03 3.665133s-03 3.66$1513-03 I 3.441149s.03 3.66Se us-03 3.644090s.23 3.6641198-03 3.6483648-03 3.4413918 43 3.6611335-03 3.6451368-03 i
3.4651668 03 3.44S4118 03 3.664?)64 83 3.6448438-63 3.6654133-03 3.6453038-03 3.64531es.03 3.6651S?s-03 level 3 date sono 3.6433998 03 3.6493S68 c3 3.6433415-43 3.64S1$48 43 3.645334s-03 3.66S3648 03 3.6416138-43 3.645661s.43 l 3.665310s.03 3.665211s-03 3.64S101s-03 3.6650440-43 3.6451438-63 3.6651138 03 3.44519?s.03 3.66S3093-03 3.6655348 03 3.643399s.03 3.4431648 03 3.665139s-03 3.4451315-43 3.645106s 03 3.64$3??g-63 3.4653948 03 i 1..ams-u 1..nu .u 1. nam.n 1.u00.a.n 1.u..os.u 1.u.ms-u 1.ucem.u i.num.u l ! level 4 date ! cane l' 3.661999s-03 3.46500es 03 3.4654048 03 3.64Sl01s-43 1.4494tts.63 3.669940s.03 3.4643418-03 3.466119s 03 1 3.6696348 43 3.669536s.01 3.5613363 03 3.8883318 43 3.6654798-03 3.6458398-03 3.64S8335-03 3.6659098 03 3.66S1393-03 3.6438648 43 3.6453Jos-03 3.66l1998-93 3.6451438-43 3.6493558 43 3.6454308-03 3.645160s 43 1.3300606-03 3. 63H90s.03 1.8J00005 03 4.030000s-03 1.430000s.83 3.8390440-03 1.430000s 83 1.4306005 03 lows 1 5 esta sene 3.4644SDs-03 3.8643998.e3 3.6440765-93 3.4499118-03 3.6643198 03 3.466164s.03 3.6446348-03 3.6661318-03 3.4663395 03 3.6690990 43 3.64$490s.63 3.64Seles-03 3.64600$s-93 3.4661138-03 3.6643135 03 3.6644468 03 3.6619348 43 3.449S260 43 3.6433998 03 3.6413168-03 3.6413338-03 3.66t3845-43 3.64n5688 03 3.669964s.03 1.830800s.43 3.6390008 93 1.8380098-03 1.6300068 03 1.836000s-83 3.83000e8 03 1.6300006-03 1.s30000s-93 level 4 date e sees 2.644930s.43 3.6666348.e3 3.6666198-03 3.6664898 03 P.4461448-03 3.6411648-43 3.4613015 03 3.64?1735-03 t 3.6441318 03 3.464304s 03 3.664100s.03 3.66setes.e3 3.4644sas-43 3.4464738 43 3.4441188-03 3.444931s.03 3.6641498 03 3.6454553-03 3.6433143-43 3.6413668-43 3.64995M-03 3.6485668 43 3.445603s 03 3.6663298 03 l L 1.u0ms.u 1. nems-u 1.unm-u 1.u.e.cs.u 1.umn-u 1.unm.u 1. news-u 1. unne.n 1swel ? esta cone 3.641380s-03 3.6413 He-83 3.6413356 03 3.6410H s-03 3.e41360s.03 3.6411398.e3 3.647654s-03 3. 641159> 03 3 6410138 03 3.4661173-03 3.6445138-03 1.464540s-03 3.4640018-83 3. Ht1J 9s-93 3.6411038-93 3.6413648-63 3.664353s.03 3.645193s 0J 3.6414u s 03 3.66S(tSs-03 3.44Ss438 03 3.6451948 03 3.6460438-83 3.6444668 03 l A5 f f j t
1.433460s-43 1.8300048 03 1.836600s 03 1. 4300fes-e3 1.0300048-03 1.5366005-03 1.030000s-83 1.8300048-43 Level e esta emne 3.6419645 43 3.6460638-03 3.4419168-83 3.4617648-03 3.461144s-43 3.6479888-62 3.6640313-43 3.661947s 03 3.6473558-03 3.64130S8 63 3.6649950-43 3.461995s-03 3.6613148 e3 3.4675248-03 3.6614005-43 3.6671678-03 3.6449368 03 3.4499338-03 3.669563s-43 3.649400s 43 3.664155s-e) 3.646011s 03 3.4443958-03 3.464494s-03 !- 1.6300008-03' 1.4390048-03 1.830000s e3 1.030000s-03 1.030000s 03 3.030000s-e3 1.s30000s-03 1.g30000s 03 level 9 Gata some 3.660404s 43 3.6664448-03 3.668500s-43 1.46444S8-03 3.6401948 03 3.6403638-03 3.640344s-03 3.464336s e3 j 2.459406J-03 2.4679175-03 3.4661538 03 3.66??31s.43 i.660776s 03 3.6476418-e3 1.6601333 03 3.4679038 03 2.6444968 43 3.664010s-03 3.64S6148-03 3.445713s-43 3,666471s-03 2.6463398-e3 3.6645438-63 3.666896s-03 1.8300048-03 1.4304068-43 1.035800s 03 1.430000s 03 1.33000es-63 1,g30000s-03 1.03000og.e3 1.230000t-03
, e3 ,e ..
eene 3.6680148-03 3.4484180 03 3.6664498-43 3.644038s 43 3.6480065-03 3.44030es-03 3.664003s-03 3.6443618-03 l 3.699496s 43 3.6463648-03 3.6443048-43 3.6469948-43 3.666634s-43 3.6449568 03 3.6407128-43 3.4644418-03 3.6633138-03 3.4643598-e3 3.6434445-43 3.6444495-03 3.64373Ss-03 3.6449500-43 3.643100s 03 3.664416s-03 3.43DD000-03 1.0304003-e3 1.8300003 03 1.0300004-03 1.8360000-03 1.436000s 03 1.4300Dee-03 1.0300008-93 level && data eene 3.6445008-43 3.4414838 03 3.6649058-03 3.6479068 03 3.665445s-03 3.6813998 03 3.664346a 03 3.6640398-43 3.4$94994-e3 3.445tfee-63 3.6403068-03 3.4643540-03 3.6400608-03 3. 66415 3e-63 3.660440s 03 3.645>008-43 l i 2.659330s-03 3.ee30418-03 3.4596348 03 3.6433564-03 3.6tet048 03 3.6s33618-03 3.6997498-43 3.4431198-43 1.8300005 03 1.8300003-43 1.4304408 03 1.0300000-43 1.0344443 03 1.8300008 e3 1.430440s 08 1.6364006-03 I level 13 data omne 3.664141s eJ 3.66?444s-03 3.5499548-63 3.641140s 63 3.6461113-03 3.6664108-43 3.6645135 03 3.644775s 03 l 3.6633015 e3 3.64S5368-63 3.6431668 e3 3.6640448-03 3.6444488-43 3.6495918 03 3.461955s-03 3.6451935-03 3.6617698-03 3.643666s.63 3.6404348-43 3.6426438 43 3.643954s-43 3.441910s 03 3.6400428-03 3.643416s.03 1.4390060-e3 1.430000s.63 1.8300005-03 1.4300000 43 1.4300000-03 1.030000e 03 1.030006s-43 1.436000s-43 towel 13 data cons 2.659491s-03 3.6999948-03 3.6394338 03 3.695485E-63 3.8510198-03 3.66943f8-63 3.6171548 03 3.6S46108-03 3.4599318 63 3.6994498-03 3.69ttpos-43 3.494t338-03 3.6444148-03 3.6564108-03 3.6S?)33s-03 3.659313s 03 3.41196SB e3 3.4953038 43 3.653000s-es 2.64e9368 03 S.Cel4548 03 3.6464546 03 3.4511838-03 3.4549138-63 3.4300005 03 1.0360000-e3 1.8344006-03 1.4300606-03 1.8300408-43 1.030000s-03 1.030000sA3 1.0s0000s 03 l 1rvet le data cone 3.6130418 03 3.646D118-43 3.4393999 03 3.636389s 03 3.4451105-03 3.644530s 43 3.64403es-03 3.656414s-03 3.653S018-43 3.454s448-43 3.6691568 93 1.64t63SS 03 3.6414198-43 3.6904e18 el 2.6S04468-03 3.654 sees.63
. 3.6636405-43 3.8606498-03 3.6496048 83 3.tet94ts-03 3.441035s-43 3.64tl31s e3 3.6444138-03 3.4503590 63 l 1.4300408-03 1.830000s-43 1.6344008 43 8.030004s 63 1.430Dett 83 1.electos 03 1.e36000e-03 1.830000s 43 level 15 esta 1
esos 3.3494550 03 3.3916948 03 3.3117138 03 3.3176438-03 1.3153118-03 3.3603098-43 3.3643418-03 3.3054428 03 3.3197178-03 3.41431D8-63 1.3964393-03 1.4403015 43 3.3464368-43 3.4644858 03 3.3035198 03 3,4115398-03 l 3.3933968-03 3. 41D64 Ls-43 3.3917415-03 3. es 34068-43 3.3Dete30 04 3.4414108-03 3.Sete198 93 3.401D018 03 1.4300008-43 1.0360008 43 1.030000s 03 1.4300008-43 1.0344008-s3 1.0304406-03 1.8344045 03 1.0340005 03 novel 16 este eene 3.3916438 03 3.3910345-43 3.3939393 03 3.396?las-03 3.3934340 03 1.3046tts-03 3.3915468 43 3.3096435-03
/kHO 1
u________________________._________ _ _ . . _ _ _ _ _ _ ._ __ __. _ _ _ _ _ _ _ _ _ .
l l i l 3.336S198-03 2.3356912 03 3.3230938 03 3.339957s 03 3.3144441 03 3.33906?t-03 2.3110943-03 3.3353113-03 2.3849648-03 3.340074E 03 3.364114s.03 2.3839308-03 3.3931S43-03 3.3437818-03 2.310633s 03 3.306902t 03 ' l 2.379347s-0J 3.3408918-03 3.3151708 03 3.3496438-03 3.3644735-03 3.3804482-03 3.3101913 03 3.394?135-03 level 11 date I sene l 3.164312s 03 3.14'8618-03 2.14001st-03 2.1101943 03 3.1701048-03 3.1482038-03 2.144899E 03 3.166570s-01 t 3.3000393 08 3.a333338 03 3.30344Js-03 2.3311008-83 2.2061348-03 3.3306?nt 03 3.30313341 3.330$005-01 i 3.313444E.03 3.384010s-03 3.2781412 03 3.2715S30-03 3.3630ses-03 3.2145495-03 3.214153s 03 2.363203u-03 i
. 9,0000.-., 1. !
3 0... 03 1.4,0000s-0, 1..,00 0.-03 s..,0000s-.3 3..,0 00s.0, 1. 3 000s. 3 1..,.00.. 0,
....................... ......................................................... I i
1 06408 71177 ' 1 33333 00000 11 0 $ 9 time e 4500.466333 e, time step e .500000 e. nasbee time etape e 2331 30 0 1 48000 1 13323 0 0 3 0 8 7 8308 dowacemet vesset 3 0 0 l til 80000 ? 33322 00000 level 1 deta came I 1.8300003-01 1.430000s-03 1.4300004 03 1.430000s-03 1.0348*$s-03 1.4300003 03 1.830000a-03 1.830000s.07 1.0300005-03 1.0300005-03 1.439600s 03 1.43D000a 03 3.441105s.03 3.6449355-03 3.464129s-03 3.644459s-63 ; 3.8644338 03 3.6444018-03 3.4484468-03 3.44$4848 03 3.4413598-03 3.6453685 03 3.46$2855-03 3.6451978 03 level 3 esta esos 1.430000s.03 1.3300005-03 1.830600s.03 1.4360005-03 1.0300003-03 1.830060s-03 1. 03 D0003-03 1.830000s.03 1.030000E-03 1.830000s.03 1.830000s-03 1.830000s.03 2.441024s-03 3.64444S8 03 3.4441158 03 2.6444738-03 1.6446331 03 3.6645300-03 3.4494644-03 3.665443s a3 3.6411558-03 3.4654938 03 3.6453418 03 3.445160s.03 level 3 esta tone 1.4308088 03 1.8300008 03 1.830000s.03 1.830000s-03 t .330040 s.03 1.3300002-03 1 830000E-03 1.430000E 03 1.8300004 03 1 8300005-03 1.330000s.03 1.4306064 03 3.6634318 03 3.8549128-03 3.64444s5-03 3.6448068-03 3.6647098 03 3.s443993 03 3.4694984-03 3.5660048 03 3.6451308-03 3.6415448-03 3.441343s-03 2.6451715-03 level 4 data eene 1.83D0002-03 1 830000s 03 4.830600s-03 1.8300003 03 1.0300008 43 1.430000s.03 1.030600s-03 1.836000s 03 8.0300002-03 1.036000s.03 1.4300005 03 1.430000s-03 3.44506St.03 3.4649018-03 3.445018s 83 3.645134s 03 3.6450848 03 3.6443845-03 3.4691308 03 3.4441448-03 3.6457308 03 3.4664938-03 3.649335s 03 3 e451378 03 leven 5 esta cone 1.8300005 03 1.830060s-03 1.030000s 03 1.0300000-03 1.0360004 03 1.8300006 03 1.8300004-03 1.8300008-03 1.4300005-03 1.0360005-03 1.830000s 03 1.8300005 03 3.6611118 03 3.4410418 03 3.68$138s.03 3.4461118 03 3.643446s-03 3.6448938-03 3.4689308 03 3.664416s-03 3.4694364 03 3.649432s-03 3.641316s-03 3.465314s-03 level 4 data tone 1.8300003 03 1. 03 D660s.43 1.4300005 03 1.836000s-03 1.8300000 03 1.4360068-03 1.030600s.03 1.6360002-03 1.0300008 03 1.930000s 03 1.830000s 03 1.4300005-03 3.449181s-03 3.64S1548 03 3.445164s 03 3.6493018-03 3.4490098-03 3.4640448 03 3.6494948-63 3.644360s 03 3.4415368 03 3.645381s-03 3.445310s 08 3.4482468 03 leven ? esta come 1.8300006-03 1.8360005 03 1.8360008 83 1.810000s.03 1.830060s.03 1.4300000-03 1.8364 Des 03 1.8300003 03 1.830000s-03 1.8300008 03 1.8300005-03 S.030600s 03 3.4413358-03 3.641347s-03 3.4453538-03 3.4463768 03 A.7 L______
I l l l l 2.4e19623 43 2.6434$93-03 2.4494158 13 2.64446ss 03 2.5684498-03 2.4693998 03 2 6413223 03 2.445291s-03 level 8 date sons l 1.6390000 83 1.0300008-03 1.6300005-03 1.8300006-03 1.4300003-03 1.8300005 03 1.0300003-03 1.4306003 43 l 1.4300003-43 l
- 1. tJ 00005-03 1.e30000s.43 1.4300003-03 2.6452188-03 2.86S311s-03 2.4st321s-03 2.44s4478-43 1 2.4112413 43 2.6810S$3 03 2.645179s-43 2.4614325 03 2.6654185 03 2.6433618-03 2.445343s-03 2.645336s-03 level 9 date eens 1.8300005 03 1.030000s-03 1.930000E 03 1.330000s-03 1. e 3 0000s-03 1.4300003-03 1.830000s-03 1.4300008 83 l
1.830000s-03 1.8300005-03 1.430000s-03 1.e30000s-03 2.6653248-03 3.63430ss 03 2.4947068 e3 2 st414Ss 03 I 2.4419593-03 2.6560435-03 2.444399s-43 2.s49090s 03 2.6403318-03 2.6444105-43 2.4309343-63 2.43239's 03 1 level 10 data cone 1.5300008-43 1.0300043-03 1.0300003-03 1. e 3 0000s-03 8.8300003-03 1.830000 -03 1.430000s 03 1.430 Coot 03 1.8300698-03 1.eJ0000s 43 1.8300005-03 1.0300005-03 2.647040s-93 2.4234345-03 2.4296818 03 2.1541315 03 2.90133e3-03 2.6244598-03 2.4438938 03 2.6543003-03 2.1343438-43 2.7199668 03 2.6316218-03 2.604349s 03 level 11 data sene 1.030000s-03 1.e30000s-03 1.830000s-03 1.e300003-03 1.830000s-03 1.430000s-03 1.830000s-83 1.030000s-03 1.830000s=03 1.0300003-03 1.8300003-03 1.8300005 03 ".ses 30$s-03 3.40341es-43 2.402916s 43 3.4410858 03 { 2.599149s-43 2.5992035-03 2.6311658 03 3.01.*15s 43 2.612610s-03 3.083190s-03 2.631154B-03 2. 4044$08-03 level 12 data cens 1.430400s-03 1.8300005-03 1.4300008-43 1.030000s-03 1.4300005 03 1.430000s=43 1.e300005-03 1.0300443-43 1.03tf00s-03 1.0304005-03 1.030000s-43 1.830000s 03 2.6454225-03 2.8904998-03 2.6001988-03 2.5001248-43
- 2. Set 9948 03 2.5994905-03 2.8315438 03 2.412202s 43 2.6131946 93 2.613450s-03 2.613610s 03 2.604945s-03 level 13 dass eene 1.030000s-03 1.830000s-03 1.830000s-03 1.030000s-03 1.030000s-03 1.83090es 43 1.830000s 03 1.a30000s-03 1.83c000s-03 1.e30*005 03 1.030000s-03 1.8300005-03 2.446603s-03 2.S990458-03 2.S$29313-03 2.192225s-03 2.999337B-63 2.6227013-03 2.631747s-03 2.4293428-03 2.4202218-03 2.4293415 03 2.613521s-03 2.6062015 03 Level 14 data cens 1 830000s 03 1.0300048 03 1.430040s-03 1.8300003 03 1.830000s-03 1.e30000s-03 1.830090s-43 1.038000s-03 1.0300003 03 1.4308003-43 1.030040s-03 1.830000s-03 2.4154073-43 2.3916458 03 2.415116s-03 2.4251048-03 2.1249288 03 2.42302S3-83 3.415011s 03 2.4226093-03 2.63e117s.03 2.424230s-43 2.4154t13-03 2.390110s-03 l
{ l A8
i , Appendix B. Evaluation of TRAC-PF1/ MOD 2 AP600 Model. (by Greg Hill) The steady state conditions from the TRAC PF1 runs performed by Penn State, which model the AP600 NSSS, are presented below with comparisons to several E generated values. These comparisons serve as a means to " benchmark' the initialization of the TRAC-PF1/ AP600 model. It should be noted that this ' benchmark
- la not intended as a formal
- verification and validation" of the AP600 model in TRAC-PF1 code. This comparison, in conjunction with a " transient benchmark" to be documented later in a PSU report, will demonstrate that the TRAC-PF1 model is performing " reasonable" calculation 9. It is important to note that the output from this AP600 modelin the TRAC PF1 code will .rg be used for design-basis transients.
Qgg Reactivity Conditions-Keff=1.004 1830 ppm Boron 102% Power Good agreement; per Reference 1, for equilibrium cycle, 24 month cycle conditions, the design has 1753 ppm at hot full power (HFP), no Xenon and 1925 ppm at hot zero power (HZP), no Xenon. CoreNessel Pressure Qmg Qgtg1 Pressurizer Pressure : m h Lower Plenum Pavg.: Core inlet Pressure: Core Outlet Pressure: Upper Plenum Pavg.: Core Pressure Drop :
'- u Following the first review of these pressure values, it appeared that there was a discrepancy.
However, additional and more detailed information was requested from PSU. Reference 4 provided more detailed pressure drop information. The Reference 4 reactor fgre notes identifies the differential pressure from the cold-leg to the ggnozzles ) psi,a[which is very close to the value presented in Reference f The small difference can be attributed to the 2 data being generated using a thermal oesign flow of 204,000 gpm, whereas the TRAC-PF1 runs have modeled an RCS flow rate of 73.28 Mlbm/hr, or -189,800 gpm".
- Vessel flow in gpm, based on inlet conditions; p[529*F,2220 psia] = 48.137 bm4f 73.28 x 10' lbm/hr * (1 hr20 min) (7.481 gal 4f) (1 ff/48.137 bm) = 189,800 gpm B1
G2f.t fl2E B.RIE Core inlet mir: 8540.0 Kg/s 67.78 Mibrn/h Core Outlet mir: 8540.0 Kg/s 67.78 Mlbm/h A core flow of 67.78 x 10' lbm/hr matches the value given in Reference 1 for 10% Steam Generator Plugging. l QErg and yqAgg! Temperatures: l l Lower Plenum Tavg.: 548.9 K 528.59 'F l Core Inlet Tavg.: 549.0 K 528.53 'F Core Outlet Tavg.: 591.1 K 604.31 "F l Temp. Rise in Core : 42.1 K 75.78 'F Upper Plenum Tavg.: 589.5 K 601.43 "F The average of the Lower plenum and Upper Plenum Tavg values is 565.01*F. Reference 6 defined l that the runs were to be pedormed at a Tavg of 561.25'F. The average of the lower and upper plenum temperature values predicted by TRAC-PF1 does not include the cooling effect of core bypass flow, thus the vessel average temperature is slightly lower than this value. The Reference 1 core outlet i temperature for the 10% SG plugging case is 605.1*F, compared to the 604.31'F value given above; ( this shows good agreement. Reference 1 give' 74.7'F for a full power core AT value. This TRAC-f41 run is performed at 102% ! powet '5us it stanc ivason that the core AT will be slightly higher. A linear approximation yields a cue AT of 76.194 J 4.7'F
- 1.02 = 78.19*F). This demonstrates that the value calculated t*/ TRAC-PF1 is reasonable.
I h Flow Ratgg Hot Log A mir : 4616.0 Kg/s 36.64 Mlbm/h Hot Log 8 mir : 4616.0 Kg/s 36.64 Mibnh Cold Leg A1 mir : 2308.0 Kg/s 18.32 Mlbm/h Cold Leg A2 mir : 2308.0 Kg/s 18.32 MibmM Cold Leg 81 mir : 2308.0 Kg/s 18.32 Mlbm/h Cold Leg B2 mir : 2308.0 Kg/s 18.32 MibmM Ref arence 1 gives a vessel flow of 73.27 x 10' lbmMr. The sum of the two hot leg flow rates, or the B2
l four cold leg flow rates gives 73.28 x 10' lbm/hr, which shows very good agreement. Furthermore, a check of the TRAC-PF1 calculated bypass flow is: l 1 - (67.78 / 73.28) = 7.5055%, 1 which agrees well with the Reference 1'and 2 values of 7.5% for the core bypass flow.Lqsg ! , Tomoeratures: 1 Hot Leg A Tliq. : 588.6 K 599.81 'F Hot Leg B Tlig. : 588.6 K 599.81 *F l Cold Leg A1 Tliq.: 548.9 K 528.59 'F Cold Leg A2 Tliq.: 548.9 K 528.59 'F l Cold Leg B1 Tliq.: 548.9 'K 528.59 'F l Cold Leg B2 Tliq.: 548.9 K 528.59 *F l The Reference 1 value for T hot is 600.0*F, and the cold leg value is 530.4*F, both of these value I show that the TRAC predicted values are in good agreement. S.tgam Generator Parameters: l Steam Generator 1 : I i Boiler inlet mir: 1864.0 Kg/s 14.79 Mlbm/h Liquid Level: 14.31 m 46.95 ft Feedwater Flow- 540.8 Kg/s 4.29 MlbrWh Steam Flow: 540.7 Kg/s 4.29 Mlbmh Steam Line Press.: 5.301 MPa 768.85 psia l S. Side Total Water Mass : 54487.19 Kg 120123.7 lbm t i l Steam Generator 2 : Boiler inlet mir: 1865.0 Kg/s 14.80 MibmM Liquid Level: 14.31 m 46.95 ft l Feedwater Flow: 542.4 Kg/s 4.30 MibmM Steam Flow: 542.9 Kg/s 4.30 MlbmM i Steam Line Press.: 5.301 MPa 768.85 pela S. Side Total Water Mass : 54701.06 Kg 120595.19 lbm The Reference 5 NOTitVMP and GENF predicted steam pressures are 771.7 and 772.7 psia, resMd;, whch agree well with the TRAC value abow. The Reference 5 predicted steam and feed flow rates of 4.31 Mlbmhr (1197.19 lbrWeec
- 3600 sechr) have good agreement with the TRAC values above.
The GENF predicted secondary side water mass is 121235 bm per steam generator (see page 29 of B-3
Reference 5), which is reasonably close to the TRAC-PF1 values given above. The TRAC PF1 predicted circulation ratio, (the ratio of the boiler inlet flow to the header steam flow, is 3.45. This value falls between those given on page 29 of Reference 5, which are 3.62 and 3.30 for NOTRUMP and GENF, respectively. Reference 7 specified that a SG level of 76% NRS was to be to be modeled. The liquid level given above corresponds to 563.4 inches above the tubesheet. Using linear interpolation between the two data l points below gives a level 76.4% NRS, which is very good. 554' - > 72.5% NRS (GENF data on page 29 of Refarence 5) 530' -> 62.5% NRS (GENF data on page 30 of Reference 5). I References
- 1. NTD-NSR&LA LEH 95-009, 'AP600 Kinetics information to Penn State," 3/6/95.
- 2. MSE RAEA 240, " Revised THRIVE Data Packages for AP600 Plant Changes.' 9/26/94 (attachment 18 of CN TA 94-204, Revision 0).
- 3. RCS-M3-001, 'AP600 Power Capability Parameters," 9/2W94.
- 4. Letter frorn Dr. Gordon E. RobMson (PSU) to Gregory J. Hill, 12/12/95 {provie loss coefficient and pressure drop data for the AP600 core, as predicted by PSU's TRAC-PF1 mod).
- 5. CN TA-92137, Revision 0, ' A75 Steam Generator NOTRUMP Steady State initialization," 9/21/92.
- 6. NTD-NSR&LA-LEH-95-046, 'AP600 Boron Transient Calculations using TRAC-PF1,* 4/24/95 (input provided by NTD NSA TA 95-156).
- 7. NTO-NSA TA 95127,* AP600 Boron Transient Calculations By PSU Using TRAC-PF1: Loss of Normal Foodwater Transient Infonnation,' 3/29/95.
I f I s-4
L LOFTRAN Gede Dancnntion LOFTRAN is a dignal computer code developed to simulate behavior in a multi-loop pressurized water reactor system. The code simulates a multi-loop system by modelmg the reactor core and vessel, hot and l t cold leg piping, steam generator (tube and shell sides), pressurizer, and reactor coolant pumps (RCPs), with up to four reactor coolant loops. The pressunzer heaters, spray, and safety valves are Woo considered
' in the computer code. Point model neutron kinetics, and reactivity effects of the moderator, fuel, boron, and rods are included. The secondary side of the steam generator utilizes a homogermous, saturated mixture for the tr' ornal transierds and a water level correlation for indication and control. The reactor i
l protechon system is simulated to include, but not lirruled to reactor trips on high neutron flux, ' cvertemperature AT, high and now pressurizer pressure, low flow, and high pressurizer level. Control systems are also simulated including rod control, steem dump, feedwater control, and pressunzer level and pressure control. The emergency core coolmg system, including the accumulators, is also modeled. i LOFTRAN is a versatile program which is sulted for both accident evaluation and control studies as well as parameter sizing. The code has an extensive history of use in portorming design and licensing. basis non loss-of coolart accident (non-LOCA) analyses and has been reviewed and approved for use in l non-LOCA analyses by the NRC. i j The AP600 is an advanced two loop pressurized water reactor design, which includes many features that differ fmm previous PWR designs that use the LOFTRAN code for desigtFbasis transient analyses. ; Among the new AP600 features are passive safeguards systems, canned RCPs, twin reactor coolant ! systsm (RCS) cold legs per RCS loop, and an automatic RCS depressurization system. The LOFTRAN code has been modified to allow the simulation of the passive residual heat removal (PRHR) system, core ! makeup tanks (CMT) ed a====*=d protection system logic. LOFTRAN is further discussed in References ! a and b.
)
References t'
- a. Burnett, T. W. T., 'LOFTRAN Code Description," WCAP 7907 P A (Proprietary) and WCAP 7907 A l (Non-Proprietary), Apr51g84. i L
- b. 'AP600 LOFTRAN AP and LOFTTR2 AP Fme! Verthcallon and Valdeten Report,' WCAP 14307, June i 1995.
I \ l l ! S6 L _ __ _ ______ --_ ____ - _ _
Appendix C. Input Docks The input decks used for the analysis discussed in this report are displayed in this appendix. They are : - 1.- NEM AP600 Core Model
- 2. Staady State input Deck 3.- First Restart Deck (CMT Model) 4.- Second Restart Deck (PRHR IRWST) and LONF specific controllers 5.- Direct Mixing Decks : 5.a - Standard Decay Heat 5.b Low Decay Heat 6.- Backmixing Decks : 6.a - Standard Decay Heat 6.b Low Decay Heat l
l l l l l O I
. C1 -
l l l l The input decks in Appendix C contain information that is proprietary to Westinghouse and have been submitted under separate cover i l l t l l l l l I j
i Appendix D. High Order Solute Trackers in System Codes l l l l l D1 l w____-____________
l HIGH ORDER NUMERICAL MODELING OF SOLUTE TRANSPORT IN SYSTEM CODES l First Annual Report Captember 1995 l = ..- l i l l l Prepared by : Rafael Macian and John H. Mahaffy NuclearEngineering Department The Pennsylvania State University
. . . . . . . . . . . . . . . . ....~ .. - .- . . . - . .
I l l i
- a i
T ABLE OF CONTENTS l 1. ! INTRODUCTION 11 i t . l ! 1
- 2. JUSTIFICATION OF THE USE OF HIGH ORDER SOLUTE TRACKING METHODS IN SYSTEM CODES. The Study Of Boron Dilution Transients 2-1 2.1 Reactivity Induced Accidents.. . . . . . . 2-2 j
2.1.1 Reactivity Induced Accidents in. General Review. . .. . . . .22 2.1.2 Local Dilution Transients.. . . .. . .. . . .. . . . .2-4
- 3. THE TRACKING OF SCALAR FIELDS BY SYSTEM CODES. THE UPWIND DIFFERENCING SCHEME 3-1 l
3.1 Numerical Diffusion in The Tracking Of Scalar Fields By System Codes. ne Solute Tracking Algorithm in TRAC-PFI/ MOD 2.. . . . . ...... . . 31 3.2 The Upwind Numerical Scheme.. . . . . . . . .. . . . . . . . . . . . . . . ..3-2 I
- 4. HIGH ORDER METHODS. A BIBLIOGRAPHICAL REVIEW 4-1 4.1 Finite-Difference Methods For Hyperbolic Conservation Laws.. . .. . . . 4- 1 1
- 5. THE IMPLEMENTATION OF A HIGH-ORDER SOLITI'E TRACKER IN SYSTEM CODES 5-1 5.1 General Considerations . . . . . . . . . . . . . . . . . . . . . .
;;5-1 5.2 Implementation of Explicit High-Order Schemes in Implicit or Semi Implicit Codes.... .. ..52
- 6. ONE DIME.NSIONAL SOLUTE TRACKING 6-1 6.1 ne ULTIMATE-QUICKEST Methodology. Justification for its use in System Codes .61 6.2 The One. dimensional QUICKEST Algorithm ; .. . . . ... . . . . . . .. . 6-4 6.2.1 Basic Description .. . . . .. . . . . . . . . . . . . . . . . . . .6-4 6.2.2 Application of QUICKEST to System Codes .. . . . . .. . .. .6-7 6.2.3 The Tee Component.. .. . . . . . . . . . . . . . . . .6-14
- 7. THE ULTIMATE LIMITER 71 7.1 Description of the ULTIMATE Flux Limiter.. .. . . . . . ...71 7.2 Application of ULTIMATE to System Codes... ... . . . . ..s....... .. .. .. .73
- 8. MULTIDIMENSIONAL SOLUTE TRACKING 8-1 8.1 SMOLARKIEWICZ's Method. Basic Description.. .. . . . . . . . . . . . . . . . . . . . ..81 8.2 Justificasics for the Applicauon to the Multidimensional Solute Tracking in System Codes . .84 8.3 Applicanons to a Dree Dimensional System Code... .. ..... . .. . . . . . . . .8-6
- 9. IMPLEMENTATION OF THE SOLtJTE TRACKING ALGORITHMS INTO TRAC.PFl/ MOD 2. 9-1 9.1 Summary of the Procedure. . 9- 1 l .. . . . . . . . . . . . . . . . . . . . . .
l 9.2 One Dimensional Tracker . . . .. .. ..... . . ..._.....................................9-3 1 9 2.1 Test Case 1. . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . . ... 9 3 9.2.2 Test Case 2... . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . .97 9.2.3 Test Case 3.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 12 9.2.4 Conclusions m. .. . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 14 9.3 Multidimensional Tracker ... . .. . . .. . . . . . . . . .. . . . . . . . . . .. ..9-15 9 3.1 Test Case I . . . . . .. . .. . 9 15 l ! i
i I l l i i 9.3.2 Conclusions. .. . .. . . . . . . 9 24
- 10. CONCLUSIONS AND FUTURE WORK 10-1 f
l Appendix A A1 j i l ! l l l l l l l l l l , i 1 l 1 l I l I i l l l l l l l l l l l I l l
I TABLE OF FIGURES l Figure 5-1 Layout of the Implementation of the Explicit Solute Tracking Algonthm.. .5-2 Figure 5-2 Explicit Solute Tracking Algorithm.. . .. . . .53 Figure 5 3 Time Steps Used in' Solute Tracking . . .5-4 . Figure 6-1 Schematic of Main Variables used by QUICKEST.. .6-5 Figure 6-2 Scheme of Main Vanables used to Apply QUICKEST to System Codes . . 6-13 Figure 6-3 Scheme for the Variables.. . . . . . 6-14 Figure 6-4 Junction Cell Scheme.. ... . . . .. . . . . . .6-15 Figure 6-5 TEE Flow Configurations used to Compute Junction Cell Faces' Curvature Terms. . 6 16 Figure 71 Schematic of Main Variables Used in the ULTIMA ~E Formulation.. . 7-4 Figure 8-1. Scheme used in Averaging Procedure.. . . . . . . .8-6 Figure 9-1 Case I and 2 Component Layout... .. . . . . .93 Figure 9-2 Case 1. Solute Step Injection. Original vs. New ID Tracker... . . . . .. .9-5 Figure 9 3 Case 1. Dilute Step Injection. Original vs. New Tracker.. . . . . . .95 Figure 9-4 Case 1. Solute Step Injection. New Tracker with Physical Diffusion . . ..9-6 Figure 9-5 Case 2 Dilute Step Injection. New Tracker with Physical Diffusion. . . . .. .. . .. . 9 6 Figure 9 6 Case 2. Solute Square Wave. Old vs. New Tracker... .. . .. ..99 Figure 9 7 Case 2. Dilute Square Wave. New vs. Original Tracker. ..9-9 Figure 9-8 Case 2. Solute Square Wave . New Tracker with Physical Diffusion . .9-10 Figure 9-9 Case 2. Dilute Square Wave. New Tracker with Physical Diffusion . 9 10 Figure 9 10 Case 2. Solute Square Wave. Courant Number Study. . - 9 11 Figure 911 Case 2. Solute Square Wave. Courant Number = 1. . .9-11 Figure 912. Case 3 Component Layout.. . . . . . . .. . . . .. . .... . . . . 9 12 Figure 9 13 Case 3. Solute Square Wave. New vs. Original Tracker.... . . . . . . . 9 13 Figure 9 14. Multidimensional Test Problem Schematics.. . .. . . . . 9 15 Figure 915 Multidimensional Test Problem. Interpolated Concentration Plots. 25 seconds.. . 9 18 Figure 9-16 Multidimensional Test Problem. Surface Concentration Plots. 25 seconds.. .. . .. ... 9 19 Figure 9 17 Multidimensional Test Problem. Interpolated Concentration Plots.150 seconds... . ..9 20 Figure 9-18 Multidimensional Test Problem. Surface Concentration Plots.150 seconds.. .9-21 Figure 9 19 Multidimensional Test Problem. Interpolated Concentration Plots. 300 seconds.. .9 22 Figure 9 20 Multidimensional Test Problem. Surface Concentration Plots. 300 seconds.. . .9-23 6 0
.alGR*
e u__._. ._.___.___ _
l { l
- 1. INTRODUCTION l
I l Recent interest on reactivity induced accidents, in panicular those related to boron dilution inside -i i l the core, has prompted a series of studies focused on the accurate modeling of the boron field inside the vessel. It is widely recognized that the relatively low accuracy shown by current state of the an System Codes when tracking a solute field being transported by the flow, is a major obstacle to perform detailed boron dilution analyses. Herefore, many researchers have opted for the simulation of the solute field inside the vessel by using complex CFD codes. They certainly give a good picture of the concentra. ion distnbution l inside the core, but at the cost of very large number of computational cells. Moreovet, due to the size of the problems, they tend to eliminate the whole primary system, substituting it by boundary conditions applied to the vessel inlet and outlet nozzles. This is a major and arguable simplification when the events resulting l from a sudden nse in power may affect the flow in the whole primary system (i.e. pressure waves) or when I l the mechanism that inserts a dilute coolant plug into the vessel may directly depend on complex flow l 0 ! interactions amongst the primary side components. In addition, recent advances in neutronics modeling have produced System Codes able to describe the interaction between the core neutronic behavior and the thermal-hydraulic conditions inside the vessel in a three-dimensional and fully transient way. In order to I make proper use of such detailed analysis of the core power history during transients where boron concentration plays a decisive role in controlling core reactivity, a good description of the boron field inside i the core, and of its transport inside the primary system, is clearly desired. After the ideas presented above, it is clear that improving the ability of System Codes to accurately l desenbe the transport of solute through the pnmary system is of interest for a wide variery of safety studies. In this line of work, this report desenbes a methodology developed to implement high order numerical methods to desenbe the transport of scalar tields in one and multidimensional components. This ! methodology is based on two high order numerical schemes selected after the review of possible candidates from the wide variety of numerical schemes available. De methodology has been implemented in TRAC. PFl/ MOD 2, a complex System Code in order to test its applicability to the accurate tracking of solute. De choice of TRAC PF1/ MOD 2 stems from the fact that it is a three-dimensional code, able to describe i complex multidimensional flow pattems inside the vessel. In addition, the version of the code used in this work contains a three-dimensional transient neutronics module that can be used in conjunction with the ! cnhanced solute tracker to perform detailed boron dilution or shutdown analyses. I De study discussed in this report consists of an initial review of the current research on reactivity induced accidents in order to establish the need for accurate solute tracking in System Codes. A brief introduction to the problems that current codes face when desenbing solute transport is then introduced. Afier some of the solutions to these problems are desenbed, two methods are selected and reformulated and expanded in order to implement them in System Codes. Finally, the results for simple test problems l l1
[ I analyzed with the implementation of the selected methods into TRAC PFl/ MOD 2 is presented and discussed. The report concludes with general conclusions and the proposal for additional work to be l performed in the future. t f I2
l 2. JUSTIFICATION OF THE USE OF HIGH ORDER SOLUTE TRACKING METHODS IN SYSTEM CODES. The Study Of Boron Dilution Transients l The core of an operating nuclear reactor is a dynamic system whose physical properties vary with time. The effect of such variations is reDected in the change of the core multiplication factor, k. whose value l determines if the reactor is subcritical, entical or superentical. Successful operation at full power dunng the core cycle lifetime requires the ability to place the core in a critical state as the fuel is depleted and Ossion f products accumulate. To compensate for these phenomena and for other mechanisms that diminish the core j intrinsic multiplication (Doppler effect, void formation, etc.), all reactors are loaded with more fuel than the i required to achieve initial criticality. This action introduces a large amount of positive reactivity (excess ! reactivity) which should suffice to allow the core to reach a critical state throughout its cycle lifetime. ! Obviously, a larger amount of nes;ative reactivity (which decreases k) has to be provided to control the reactor power level by counterbalancing the excess eeavity introduced in the initial fuel load. This negadve reactivity is implemented in the form of strong neutron absorbers that can be inserted or withdrawn j from the core as required, thus modifying the neutron population. available for fission, and ultimately,. 6 l modifying the value of the multiplication factor k. 1 By controlling the negadve reactivity the operator can bring the reactor into any of the three previously mentioned states at will. Modifice. tion of the amount of negadve reactivity present in the reactor at any tirre allows the operator to: ) l (a) exactly compensate for the excess reactivity, yielding a critical reactor with a stable power level. (b) increase the power level by decreasing the connot reactivity so that it is slightly smaller than the excess rescuvity, resulting in a supercritical reactor. (c) decrease the power level or snot down the rea:: tor by increasing the negative control reactivity l over the excess reactivity, which drives the core into a subcritical state. l ! I it is important to nocce that the excess reactivity in the core is not a fixed value dunng the core l; I' lifeume. It slowly decreases as the fuel depletes and fission products build-up. It also depends strongly on the reactor conditions at a given time (moderator density, fuel tempeinture, etc.). Therefore, a given amount of l control reactivity, sufficient to keep the core stable in a critical or suberitical state may not be enough if the
]
core conditions change. This change could either increase the core exceas reactivity or decrease the control ! reactivity, to a point where supercriticality is reached, and the cete suffers a power excursion with the potential for fuel damage. Such a situation is known as a Reacovity Induced Accident (RIA). j i l 21
i 1 2.1 ReactivityInduced Accidents I l l l 2.1.1 Reactivity Induced Accidents in. General Review. l j Reactivity Induced Accidents have been a concern since the early days of nuclear power. As ( discussed previously, if the delicate balance that prevents the reactor from becoming supercritical is brcken, the resulung power excursion can lead to severe core darnsge. l These accidents have been traditionally part of the required safety analysis of every nuclear power plant. The results of such analysis must show that the accidents result in acceptable consequences if the operating license is to be granted. For Light Water Ret.ctors (LWR), RIAs are related to changes in the moderator / coolant density and to the reduction of the control reactivity to a level that it can no longer balance the excess reactivity present at a given time. This last event can be sudden, i.e., control rod ejection, or grzJual, i.e. slow boron dilution. Table 2-1 shows PWR and BWR's RIA initiators currently part of the required safety analysis, together with the core parameter whose modification leads to the net increase in core reactivity. A certain number of other events that can result in a RIA are not traditiorudly analyzed because of the low probabilities assigned to them. They have, however, the potencial for causing unacceptable consequences. Two of the most severe accidents in nuclear power hittory, the SL 1 expenmental reactor in 1%1 and the Chemobyl disaster in 1986, are proof of the potential destructiveness of such events. In particular, the Chemobyl accident showed that relatively large reactivity insertions in a short period of time could cause severe fuel damage; a fact not fully appreciated previously. It was in the aftermath of Cherr.6yl, that the Intemational Atomic Energy Agency (IAEA) held two technical committee meetings in 1987 and 1989 to review potential rescuvity accidents. Most of the studies reassessed previous!y identified events, and new Probabilistic Risk Analyses (PRA) were performed to quantify their potential nsks, and to help select those accidents requinng more detailed analysis. In addiuon, new sequences of events wre recognized and a particular category of accident, the Boron Dilution Accident, was studied under a new light. In 1990, a report to the NRC [1] by Diamond et al. at the Brookhaven National Lab (BNL) reviewed m detail a large number of potential RIAs expected in both PWR and BWR icactors. 'the study quantified the probabilities of each of them and classified them accordingly. The screening enteria for the classification were based on the expected damage to the core and on the estirnated frequencies of the events. The consequences ure considered acceptable if they met the currer.t NRC acceptance criteria, and unacceptable if they led to slow core melt or rapid fuel damage (fuel fragmentacon and rapid change in core geometry). Fuel damage was conservatively assurned to happen when the energy transfer to the fuel at any core ! locanon was in excess of 1.172 MJ/Kg (280 cal /g) dunng a tirne interval cf the order of I second (this is i } considerably lower than that estimated in the Chemobyl accident) [2]. i 22
j
~
I l t Table 21. Most Common RIAs in LWR. Initiators and Effect on Reactivity l l l PWR Reacovity Events . . Consequences increase in heat ternoval by secondary system Increase in moderator density Uncontrolled control assembly bank withdrawal Sudden reduction of neutron absorpuon l Stanup of an inactive RCP in an idle loop Injecuon of cold moderator into the core inadvenent boron diluuon of the core Slow reduccon of neutron absorgion Single control rod withdrawal at power Sudden reducuon of neutron absorpuon j Control rod ejecuon Sudden reduccon of neutron absorpoon l 4 BWR Reacuvity Events l Overpressunzacon by MSIV closure Increase in moderator density Core coolant tempenture reducuons increase in moderator density Control rod withdrawal enor Sudden reduccon of neucon absorpoon increase in core coolant flow rare increase in moderasur densary Free fall of control rod Sudden reduccon of neutron absorpoon Regarding the event frequencies (measured in (Reactor Year)^'), three categories were established. 4 Events with frequencies larger than 10 /RY that led to core damage were to be reponed as part of the 4 indmdual Plant Examination Program. For the range 10 /RY to 10 /RY the event may be of interest if it led to rapid fuel damage. Finally, events whose frepsy was less than 10 /RY were considered too unitkely to warrant further study. The report evaluated ten types of RIAs for PWRs (Westinghouse plant) ed seven for BWRs (BWR-4). The results showed that only two BWR accident sequences had the potenual for causing rapid fuel damage
.with a tugh probability (first categoryy. The first one, a refueling accident was resolved by changing technical l
specifications. For the second one, the flushing of boron during an ATWS because of uncontrolled ADS l l acuvauon and injection of LP!S unborased water, there are not detailed deterministic calculation to fully understand core behavior to this day, 9 23
1 The remainder RIAs yielded a low probability of occurrence, and the authors regarded them as not requiring immediate consideration. Nevertheless, they also acknowledged that, in some of the sequences, a j plug of dilute water could possibly pass through the core generating a power excursion which might result in fuel damage. The authors did not perform, however, any thermal-hydraulic or neutronic analysis but indicated , the necessity for such studies to be carried out. In addition to those concerns, there are also two other factors that may render some of the inidally discarded RIA's as threatening to the plant safety. First, human error plays an important role in the development of some of the accident sequences, but the quantification of human error probabilides is less that satisfactory. l The authors made sensitivity analyses and found that when human error probability was increased one order of magnitude, those sequences that required human intervention to complete or involved maintenance failures, 4 yielded frequencies over the threshold 10 /RY. Those kinds of human errors are not rare, especially in the ; case of steam generator maintenance. For instance, Jacobson [2] reports that from a scanning of the Nuclear l Power Experience (NPE) reports from 1970-1989, five maintenance errors that produced Reactor Coolant ! System (RCS) dilution were found. Second, as discussed also by Jacobson, the RIAs related with boron I dilution have traditionally assumed (as [1] does) that as the flow of diluted water is added, it mixes instantaneously with the whole RCS volume. The resulting transient is driven by a slowly changing boron j concentration, which results in an almost linear increase in reactivity. Although the increase is slow, if l unchecked, it can lead to core melt. l Several authors [2), [3), (4) have put forward a new approach L7 this kind of dilution scenario, and opted for a more realisde consideradon of the mixing process. The old assumption of instantaneous mixing in i the whole RCS results in an homogeneous boron field, which affects the core uniformly, and, therefore, is not sensitive to thermal hydraulic changes in the RCS flow. Some important boron dilution transients cannot be reahstically analyzed under such assumpdons. The boron field they generate inside the core is heterogeneous, l because the truxing of the diluted slugs of coolant flowing towards the core is not complete. Initial analyses of such scenanos have shown that the potential exists for fast reactivity increases when such dilute slugs flow l through the core. They can lead to fuel damage depending on the concentration, extension, form, etc. of the plug. This means that the accident evolution depends on the instant flow situation in the RCS, and, in particular, on the distribution of the boron field inside the core [2] .in summary, the detailed study of this kind of event requires new approaches and analytical tools which can resolve the coupled thermal-hydraulic and neutronic response of the core, and can accurately model mixing and transport processes of the dilute plug. 2.1.2 1.ocal Dilution Transients Because of the special characteristic of the excess reactivity control in PWRs, the potential for boron diludon accidents is always present. For instance, as mentioned before, the slow inadvenent dilution caused by the rnalfunedon of the Chenucal Control System (CVCS) is a design-basis event which cust sansfy stnct accepu,nce entena. l 2-4
l Amongst the beyond design-basis reactivity accidents discussed above, several of them deal with dilution events. For instance, seven of the of the beyond design-basis RIAs desenbed in the BNL repon [1] were boron dilution events. Namely. l - addition of diluted accumulator water during refueling, l i addition of diluted RWST water during shutdown, l - inadvenent boron dilution at shutdown, startup of Reactor Coolant Pumps (RCP) after improper dilution,
. LOCA with diluted Emergency Core Coolant System (ECCS) water, LOCA with diluted sump water suction.
LOCA/SGTR with secondary side diluting the primary inventory. i l Diamond et al. [4] classified them in three groups according to how they cause the power to raise: I ! (1) Slow power excursion as a result of uncontrolled dilution in which the boron concentration in the i core changes homogeneously and slowly, but steadily. De volume of unborated water has to be large to induce a significant change in the RCS boron concentration. De power, in this case, l raises almost linearly as the dilution in the core increases. i l l i (2) Accumulation of diluted water in the lower plenum. his requires that the RCPs be off. If the l level of dilute water reaches the lower core, it can increase the power production there. This will t j initiate a natural circulation flow which will draw more of the liquid into the core, thus increasing ! the multiplication factor. De core can eventually be driven into a supercritical configuration. In the absence of fast thermal hydraulic feedback, this process is an autocatalytic power excursion that can produce severe core damage if the natural circulation flow is fast enough. (3) Fast power excursion caused by a slug of diluted water flowing rapidly through the core. De plug disrupts the homogeneous boron field in the core, and creates zones with low boron content which l l can experience a sudden power outburst. This type of event is different from the other two in that l it has the potential for causing catastrophic fuel damage, rather than slow fuel melt ng. Current inearest by the NRC, and most of the IAEA members engaged in R1A studies, is focused on the third type of events because of its severe consequences ney are known as Local Boron Dilution Transients (because they do not a5ect the entire RCS, as traditionally assumed) or Rapid Boron Dilution events (because the dilute water plug is carried through the core by a fast transport mechanism, i.e. the initiation of the RCPs). Two basic requiremen:s have to be fulfilled to generate a local dilution transient:
- A boron free or highly diluted mass of coolant has to accumulate in some region of the RCS dunng a penod when there is minimal circulation, so that the water can collect in one place. The reactor 1 25 L __ _ ____ _ _ _ _ _ _ _ _ _ _ - _ _ _
l ! coolant pumps have to be off, as in the case of a shutdoms or the period immediately follomng a reactor trip. It is imponant to realize that in a shutdown situation, the control rod banks are already ! inserted and, therefore, no extra control reactivity r* mains to control a positive reactisity inscruon in the core. Although thermal-hydraulic and Doppler feedback would surely limit the damage, its quantific1 tion remains to be assessed. A mecharusm that can transpon the dilute slug from its onginal formation place in the RCS into the vessel and through the core. Recent studies [2] [3], [5]have identified two main mechanisms for this I l process: RCP start and two-phase natural circulation. The mechanism of accumulation of diluted coolant is what characterizes the accident and pnmanly determines its probability. The BNL study identified several of them that assumed the reactor in shutdown conditions, that is, when the flow through the RCS was negligible. Jacobson analyzed in detail these events adding a new one, already identified in previous studies made by the Swedish State Power Board (SSPB). It consisted in the restan of one of the RCP after a dilute water plug had formed in the loop seal because of steam generator maintenance errors. He also noted that the risk for small volumes of clear water being introduced in the RCS because of such errors is reladvely high. Hyvarinen (3), idenufied a second mechanism occurring under accident conditions: the reflux / boiler condensation, which may accumulate boron free coolant in the loop seals. The author concluded, from l experimental knowledge of natural circulation phenomena as well as Small Break LOCAs (SBLOCA), that ! there exist an inherent mechanism for boron dilution in the P.CP loop seals whenever the reflux / boiler condensation mechanism occurs, where a minimum boron-he coolant volume of 3 m' collecting in each loop, even if mixing enhancement from the ECCS injecuon was accounted for. This process, together with a high probability of natural circulation flow initiated during the pnmary side refill (which moves the dilute plug into the core), leads to a sigruficant reactivity accident risk. The event can occur even if the SBLOCA is mitigated according to the currently accepted practice. Such a situation is especially dangerous, since any possible ! reenticality would happen during the process of mitigation of an accident. sornething which is not acceptable i from a safety point of view. Finally Hyvarinen pointed out the panicular characterisdes of this type of dilution event, where the process is driven merely by thermal hydraulic mechanisms. Therefote, the quantification of the nsk associated to this type of events would require deuuled descripuon of the thermal hydraulic system response under SBLOCA (or any other transient resulting in reflux / boiler circulation). The author suggested six points to be addressed by future research efforts. They include amongst others: strnulation of the dilute plug movement and mixing process in its vav to the core. , 1
- determination of the reactivity response of the core, boroe, concentradon that results in recriticality l 1
i or prompt enticality, energy accumulated in the fuel, and study beyond the inidal power peak. He i also suggested the study of the possible chimney oscillations in the downcomer / core system. l I l 26 j
1 I l
- analysis of the local enticality effects in an asymmetne distnbution of boron m the core. For example,in the case that not all the loops hase been diluted. This is related to the event studied by
)
l Jacobson, where, due to the restart of only one of the RCP, the flow inside the vessel is eminently asymmetric, resulting in a heterogeneous boron field. Diamond (4] idenufied another scenario wfuch occurs at the end of the shutdown, when the plant is being brought back to enucality. The deboration process is done when the RCS is at hot, pressunzed i conditions, and the shutdown banks are withdrawn. After a Loss of off-site power, the reactor is tnpped. If emergency power starts the charging pumps, they can pump low boron content water into the RCS, which will collect as a dilute slug at the bottom of the Reactor Pressure Vessel (RPV). If off-site power is recovered and the operator restarts the RCPs to continue with the reactor startup, the slug will be sent through the core probably causing fuel damage. Diamond reports that this event was studied in Europe with conservative l assumptions, and a relatively high frequency for core darnage was found. j Finally, other sequences have been identified by French and Swedish workers which could lead to the necessary conditions for causing a Local Dilution Transient. Some of them have prompted hardware changes or modifications of operation procedures to preclude the formation of dilute plugs. l As a results of the concerns outlined above, several studies about the core neutronic response during local dilution transients have been performed lately. One of the fint anempts, made by Hedlund [6] employed a l static core analysis program (POLCA). His results, reported by Jacobson, showed that a relatively small amount of boron free water (2.4 m') could add significant reactivity to a core loaded with fresh fuel (in the range of 10-17%), and could bring the core to prompt entical for an initially assumed shutdown margin of 4E j This study also showed that the distribution of boron in the core had a large impact in the amount of reactivity . added. For instance, the largest reactivity insertion resulted when the bulk of the water plug flowed through the highest ennched fuel elements. The analysis did not take into account, however, the probable mixing of the l RCS boron with the boron free slug during its transport to the core, which is clearly a conservative assumption. Also conservatively, it did not simulate the thermal-hydraulic response of the pnmary system, nor did it i modelled the transient conditions that a rise in power would undoubtedly generate in the thermal-hydraulic l behavior of the core. Nevertheless, the volume of boron-free water was regarded as small since other scenanos were idenufied winch yielded larger boron free water volumes. In this respect, a more refined study was made by Jacobson on Ringhals 2 (Westinghouse 800 MWe PWR) using 1RAC-PFI with point kinetics (5). The size of the largest expected boron-free water plus was obtained from an analysis of possible sources of unborated water into the RCS. A maximurn value of 14 m' was found as a result of erroneous seal injection from the reactor make up system, and 40 m' in case of natural ctreulauon onset with one of the loops initially stagnant and depleted of boron. The results depended greatly on the truual core boron concentrauon. The aether observed recriticality with 40 m8 , and an irutial core boron concentrsuon of 850 ppm. although the total energy deposition in the fuel did not led to fuel damage. Review 27
i of the results by a panel of experts, the author said, suggested that they may suffer from numencal diffusion. f which smoothed the boron profile and resulted in a less severe transient. Moreover, the point kinetics model, based on core average parameters could not account for the effect of a heterogeneous boron field in the core. > Finally, the author acknowledged that, since the model did not simulate the whole system, the effect of the , pressure evolution in the thermal-hydraulic system response and neutronic feedback was not properly considered. Diamond et ars results on the Loss of off-site power event analysis discussed above, included also a (. l boron mixing model to calculate the degree of mixing resulting from natural circulation dunng the l accumulation time. They carried out several analyses with three PWR plants adopting conservative conditions I that would result in a conservative scenario. The static neutronic calculations showed that the possibility of I l catastrophic fuel damage depended on the initial shutdown margin, the Doppler feedback and the distribution i of the slug in the core, but it could not be ruled out. As they pointed out, after the initial power excursion, the power may remain high until the slug has flowed out of the core; but even then, the final boron concentration may be low enough so that, if the shutdown margin were small or the Doppler effect were not large enough, fuel damage could occur in some regions of the core. It is imponant to mention that no real transient analysis was done in this study. Oosterkamp et al (7) reported a more refined study where they tracked the boron field with a panicle (- tracking algorithm that, together with a turbulent k t model described the dismbuuon of the boron field in the 3 f core with time by using the code FLUENT, The transient analyzed was a RCP start with 10 m' and 15 m of boron-free water being transported into the core. Only the vessel was modelled, and only the hydraulic i characterisdes of the system were computed to track the boron field and feed the concentration distnbution into a neutronics code. No credit was given for thermal-hydraulic or Doppler feedback, nor for the pnmary system l behavior irifluence in the transient evolution. The results showed that criticality could be achieved with boron-free plugs of volumes about 15 m' for an initial concentradon of 2200 ppm, and that the most acdve turbulent mixing between the vessel inlet and the core barrel was mainly responsible for the necessity of such large volumes to reach entical condiuons. Finally, the study of Jacobson (2) on the potential for prompt criticality aher a the restart of a RCP in a boron depleted loop evaluased two different local dilution scenarios specifically tadored to a typical Swedish l PWR plant In order to track the baron field, the author used a hydraulo: code (PHOENICS) able to track the f boron dispersion by a panicle tracking algonthm, where the turtmlent dispersion was accounted for by a simple eddy viscosity model with a constant value. The neutroeuc calculadon was a samedy stase one petformed with SD4UI. ATE 3. The borop concentrahon field was input and a 4, obtained for different points in time. The results of the two scenanos, a loss of'off site power during start-up aher refueling (similar to that of Diamond's in (4] and the dilution at cold sht.tdown due to errors commiend dunng sisam generator maintenance, showed ! i that none of them could cause prompt enticality. However, the condinons of the analysis, as the author said, ; were specific to the type of plant analyzed, and in other plants may vary, in panicular, for the " loss of off site l 1 t 1 b 2-8
- _ _ _ - - _ - _ _ _ _ _ _ - - - _ _ - _ _ _ _ _ _ _ _ _ _ = - _ _ _ _ _ _ - - _. _
! I l I l 1 ! l l l I I j power during start-up" case, he recognized that in some plants the free boron water volume could be much 1 l larger posing a serious risk of recriticality. In the same study, Jacobson evaluated the actual capability of available thermal hydraulic codes, and 1 concluded that the best approhch to analyzing the consequences of a local dilution transient would be to I l simulate mth 2ng single computer program the total system behavior, because such a complete analysis could l simulate the impact of the power escalation on the fuel and RCS integrity. He proposed that such a code should have the following capabilities:
- a three-dimensional transient flow analysis capability.
ability to model complex system interactions. l boron tracking algodthm not affected by numerical diffusion. ;
- three-dimensional transient core model which can handle the thermal-hydraulic feedback from the moderator and the Doppler feedback from the fuel, and that is able to simulate the fast power excursion that a prompt enticality situation would produce.
At the time of Jacobson's work there was not such a tool, but the current version of TRAC-PFIMOD2 v5.4 together with the three-dimensional NEM neutronics method satisfied all those chteria except the accurate boron tracking capability. Similar requirements were also suggested in Diamond's study, and would offer the possibility to make real transient analysis of the core power evolution and of coupling this with the whole system response. Moreover, scenarios like those described by Hyvarinen, where the mechanism of transport is purely dependent on the thermal-hydraulic conditions at every instant in the primary system could be analyzed with such a tool. Even in the case of pump driven scenarios, like those studied by Jacobson and Diamond, a more detailed j understandmg could be gained by incorporating whole system interaction and neutronics feedback into the j analysis. For instance, scenarios with larger boron-free water plugs that result in a prompt critical state could turn up to be self limiting because of fast negative reactivity feedbacks resulting from Doppler or thermal- ! hydraulic feedback not taken into account in any of the studies discussed above. Finally, autocatalytic power excursions hke those suggested by Diamond (see above), also mentioned by Jacobson in his conclusions, and studied by Finnish workers can only be attempted if feedback mechanisms and whole system interactions are included in the analysis. The obpective of this work is to study the requirements that the implementadon of a high order l tracking method in a System Code would entail. After the major problems have been identified and solved, the pracucal implementation of two of these methods in TRAC PFIMOD2 v5.4 is presented. L__________--- - 2'9
l l I l i l j l i i
- 1. Diamond, D.. J. et al., ' Reactivity Accidents. A Reassessment of the Design Basis Event', Brookhaven !
l N.trional Laboratory, NUREG/CR 5368. January 1990. j
-1
- 2. Jacobson. S., Risk Evaluation of Local Dilution Transients in Pressurized Water Reactors. Ph.D.
Thesis. Linkoping University. I
- 3. Hyvarinen, J., 'An Inherent Boron Dilution Mechanism in Pressurized Water Reactors', Finnish Center l for Radiation and Nuclear Safety (STUK),1992. l l
l 4.' Diamond, D., et al., ' Probability and Consequences of Rapid Boron Dilution in a PWR', NUREG/CR- i 5819,1992.
]
- 5. Jacobson, S., ' Reactivity Transients after a Pump Start in a Boron Diluted Loop *, ANS Transactiorr.
Vol. 61,1990 Annual Meting, Nashville, Tennessee, US A, June 1990. i ! 6. Hedlund, T.. 'PWR Boron Dilution in a Cold Shutdown Reactor *, Swedish State Power Board Internal l Report, K3S-TH/KM 3489, December 1992. ! 7. Oosterkamp, K. P., 'k c Modeling of Deboration Transient in a PWR', Presentation at ANS/ ENS ; l International Meeting, November 1992. l \ l l l l l I l 1 i l l 2 10 o---_ _
I. l i
\
I
- 3. THE TRACKING OF SCALAR FIELDS BY SYSTEM CODES.THE UPWIND DIFFERENCING SCHEME ;
3.1 Numerical Diffusio'n in The Tracking Of Scalar Fields By System Codes. The ' Solute Tracking Algorithm in TRAC-PF1/ MOD 2.
- Several System Codes, i e. TRAC-PFl[1] TRAC-BFl[2), RELAP5[3), CATHARE(4), include
. the capability of tracking a soluble field, usually a neutron poison, to simulate the negative reacuvity l
l insertion resuldng from the poison flowing through the core, ne solute is treated as a separate field modeled by a single hyperbolic transport equation in which molecular and turbulent diffusions are neglected. ( As an example TRAC-PFl/ MOD 2 desenbes the scalar field by solving the following j multidimensional convecove transport equadon: 3 ((1-et)$ pr ) + V((1-a)$ p, uj ) = S at , (Eq. 31) where et is the coolant void fracdon, e is the solute mass concentration, p, is the liquid density, si is the liquid i velocity field (averaged at the cell faces, and S is a solute source term. All variables at space and time l dependent. j TRAC-PFI solves (Eq. 3 1) at the end of the time step in a post pass operation after the velocity field l has been obtained [51, so that its soludon does not directly affect the general soludon procedure. I As wuh all the convective terms in the TRAC PFI's conservadon equations, the convecdve term of (Eo. 3 1) is explicidy differences on a staggered grid with upwmd donor-cell spadal differencing [6), while the drr.e gradient is t'ested implicitly. According to Rider [7), this method is quite stable, but suffers from j numerical diffusion due to its first-order spatial accuracy. Ride.t recosmzes that the use of this method to solve l the conservadon equations may be acceptable in many applicadons, since most of the uncenainnes in such system codes reside in the two phase closure reladonships. But, in cases where the detailed desenption of the spatial and temporal disenbuuon of the solute field is required, the method is less than satisfactory. An example can be found in shusdown studies where fast transport and diludon of soluble poison into the core, artificially enhanced by the numencal diffusion, may render non conservadve results from a safety point of view. In general, any transient that requires accurale traciung of a heterogenous solute field within the vessel will be adversely affected by excessive numerical diffusion-In addinon to the shoncomings reponed above, the solute transport equation in TRAC PFI, as in most system codes, does not desenbe any mixing effect in the solute field caused by the turt>ulence in the main flow. As reponed in [8] one of the factors believed to reduced the seventy of the transients with large boron-free water plugs is the turbulent nuung that takes place at the vessel inlet. Moreover, in situadons where a 31
l l ,. diluted coolant plug is accumulating in the lower plenum, an effective mixing between the water already in the t l vessel and the incoming dilute plug can substantially reduce the reactivity insertion. l f The implementation of any physical diffusion mechanism in the solute equation requires the reduction, and if possible elimination, of the numerical diffusion associated with the upwind differencing scheme. In [9], Rhode . at al. reported that it is well known that a portion of the discrepancies with measure.nents of many turbulence models may lay m false numerical diffusion, which can overpower the very effect under investigation. Sinular i ! comments can be found elsewhere in the literature. It is clear from the ideas expressed above that the description of the spatial and temporal evolution of the boron field in the vessel, which requires the implementation of a mechanism capable of simulating physical turbulent diffusion, should be affected by as little nuraerical artificial numerical diffusion as possible. 3.2 The Upwind Numerical Scheme The upwind numerical scheme, also known as donor-cell differencing, is a widely used method to numerically solve the conservation equations describing the advection of scalar or vector fields. Its popularity lays in its robustness and the property that it produces positive definite solutions, which is very ~ important to guarantee the stability of the solution of systems of conservation equations. L Methods based on central space discretization (i.e. second-order central differences), do not distinguish upstream from downstream, and the physical propagation of perturbations (i.e. solute fronts) is L not inherent to the numerical method. In regions of smooth behavior of the flow variables, these methods j can be applied with any order of accrue without any oscillatory behavior; but they generate oscillations in I the vicinity of discontinuities (10). Additional artificial diffusive terms have to be added to these schemes in 1 l order to damp the oscillations, thus affecting the accuracy of the original method. Upwind schemes try to overcome the oscillatory behavior by introducing the physical properties of f' , the flow equations into the discretization process. In particular, the application of these methods to the l l- solution of scalar transport equations is based on the sign of the convective velocity, which contains physical information about the actual flow direction. His parameter controls the form of the scheme, by )
. providing, in fact, the asymmemc character that mimics the actual downsusam physical transport process of the scalar. A: cording to [10), methods based on upwind weighted schetnes can represent discontinuities better than centered schemes of similar order of accuracy that use artificial viscosity terms to dissipate the oscillauons near discontinuities.
he properties of robustness and relative good accuracy near discontinuities have made this class of methods widely used in CFD and System Codes. De ability to accurately resolve discontinuities, however, is directly dependent on the order of the scheme. In this sense, a large number of codes have implemented first order upwind, which, although able to resolve sharp gradients better than centered method combined with artificial dissipation (i.e. Laa.Friedrichs) of similar order of accuracy, is itself' M
l l affected by artificial numerical diffusion. This diffusive character may rener these codes unsuitable to track sharp gradients of scalar quantities with the degree of accuracy required for cert.:in applicativ :.
. The diffusive character of the first-order upwind differencing scheme (hereafter referred simply as upwind) becomes clear when a truncation error analysis is made on the time and space discretized transport ,
egi'.ation. According to (11] for a fully implicit time integration on a staggered mesh and constant velocity, the one dimensional advection equation, (Eq. 3-1), becomes: p"I I- p7., = F-c( i p"I . p7Idi uff.'g )- F, g( p"Jji, p"J',uf,*)g ) l (Eq. 3 2) where p"lI =(1-a,"+3 )$,"*' p f,f' , and the functions F,.,4 and F,.,a represent the numerical fluxes across cell faces i+in and i in respectively. The value of the fluxed in the upwind scheme is given by : , l F,.o( p"]', p7J1,ufjg i )= , (pl]! i (ufjg + ufjg )+ p"J' (ufjg - ufjgl)) (Eq. 3-3) and F, g( plllg , p *j',uf,*)g ) = (p*;' (ufje + uf,f)g )+ p";]n (uf,f}g - uf,,*)g )) . l (Eq. 3-4) for positive velocity field. The truncadon error analysis, involving the Taylor expansion of the scalar densities about ( x, t..,, yields an equation of the form : n+\ n+n
=
2'3 p, i
& x (p, u,)l*"*' +0x ' O.5(lugl A x + a t us ,
Bt ,
&x ,
(Eq. 3-5) where the second term in the r.h.s. represents a diffusive transport. This equation approximates with second-order accuracy the following advecdon-diffusion p.d.e[12] i~ 3 p,' aBtp, =&x & (p, su )+ &'K g 2&g &x ,, (Eq. 3-6) which physically represents a convection-diffusion tras. sport of the scalar p, with a diffusion coefficient, Kw. given by[1I):
~
Kg = 0.5( lug lo x + u[ A t). l . (Eq. 3 7) For a esplicit nme integradon, the truncation error analysis around (x, tJ yields a similar equation to (Eq. 3 5), but for the time level a instead of n+1. The diffusion coefficient in this case is given by (12): K4 = 0.5( lug la.r - u? as), ($q.3-8) l 3-3
1 l l l From the above analysis, it is clear that the upwind scheme will always produce a diffusive ! solution in the case of implicit time differencing, whose magnitude will grow with both increasing dme step snd cell sizes. The explicit approach, however, has the potential for cancelling the effect of K., when the l combination of time step, cell size and velocity is such that the r.h.s. of (Eq. 3 8) becomes zero. His case is equivalent to a Courant number equal to one, which would result in a perfect cell center to cell center convective solution. This satisfactory but nonrealistic situation is only attainable in simple test problems. I when the three responsible parameters mentioned above can be easily set to the adequate values. De application of explicit upwind to a system code, where the velocity field may be divergent and unsteady, the ! cell sizes are not equal, and the time step size is constramed by the necessity to achieve an stable solution of the conservation equations that describe the system, cannot guarantee a unity Courant number in all cells. Therefore, the use of explicit upwind to track solute field in synem codes will always result in non-physical diffusive solution, similarly to the implicit scheme. i Nevertheless, the diffusion that the explicit upwind scheme introduces in the convecuve transport l l solution can be at least reduced with the appropriate selection of a large Courant number for the computational cells. De maximum value of these Courant numbers will always be limited by the need to ! maintain the Courant Friedrich Lax (CFL) stability criterion in each cell, limiting the maximum Courant l number to be less or equal than one in all cells. Within this limit, however, the value of the cells' Courant numbers can be set as large as possible his approach is based on the explicit upwind's important property that the value of K., diminishes with increasing time step size; thus, achieving a high code speed would, in l effect, reduce the numerical diffusion. t ne implicit upwind shows a worse behavior regarding the time step size-diffusion dependency. As noted above, the coeficient Kg cannot be eliminated by any combination of time step size and cell sizes, since the affects from each one of them add to each other. In fact, increasing the time step size, will increase the diffusion introduced by the method in the numerical solution. His is also true for the semi-implicit variation of the scheme as repoted in (11). Derefore, codes that use this approach will show an inherent l' diffusive behavior that will grow as the code selects larger and larger time steps; a common feature of fully. L implicit unconditionally stable codes not affected by the CFL stability condition. f 1 i 1 j i 3-4 l w________ - _ _ . _ l
I
- 1. Schnurr, N. M., et al., ' TRAC PFl/ MOD 2 Theory manual', Los Alamos National Laboratory unpublished Report LA-12031 M, US Nuclear Regulatory Commission Report NUREG/CR-5673 (1992). .
Borkowski, J. A., (Ed.) et al., ' TRAC BFl: An advanced best. estimate computer program for bwr l ' accident analysis', Idaho National Engineering Laboratory Report EGG 2626 US Nuclear Regulatory Commission Report NUREG/CR-4356 (1992).
- 3. Allison, C., (Ed.) et al., 'RELAP5/ MOD 3 Code Manual *, US Nuclear Regulatory Commission Report j NUREG/CR-5535 (1990).
4 Barre, F., Parent, M., Brun, B., ' Advanced Numerical Methods for Thermalhydraulics', CSNI Specialist Meeting on Transient Two-Phase Flow, Aix-en-Provence, France (1992). l- 5. Mahaffy, J. H., 'A Stablility Enhancing Two-Step Method for Fluid Flow Calculations', Journal of l Computational Physics, 46, 326 (l 985).
- 6. Liles, D. R., and Reed W. H., Journal of Compuntional Physics,26,77 (1978).
7 Rider. W J., 'High-Order Solute Tracking in Two Phase Thermal Hydraulics', 4th International Symposium on CFD, Davis, CA, September 1991. j 8. Oosterkamp, K. P., 'k-e Modeling Of Deboration Transient in a PWR', Presented at the ANS/ ENS International Meeting, November 1982.
- 9. Rhode, D. L. And Stowers, S. T., 'Combustor Air Flow Prediction Capability Comparing Several Turbulence Models', Journal of Propulsion, S,242 (1986).
- 10. Hirsch, C., Numerical Computation of Intemal and Extema! Flows, Vol. 2, Wiley and Sons, Chichester (1990).
! 11. Mahaffy, J. H., 'Numenes of Codes: Stability, diffusion and convergence', Nuclear Engineering and Design. 145 (1993). l 12. Smolarkievicz, P. K., *A Simple Positive Definite Advection Scheme with Small Implicit Diffusion'. Monthly Weather Review,3. March 1983. l l l l l 35
l
- 1. Spore, J. W., et al., ' TRAC PFl/ MOD 2 Theory Manual', LA 12031 M Vol.1, NUREG/CR 5673 (1993) l 2. TRAC.BFI Theory Manual -
l l 3. RELAPS Theory Manual ! l
- 4. CATHARE Theory Manual 1
- 5. Mahaffy, J. H., Journal of Computa:ional Physiscs 46, 326 (l985). l l
- 6. Liles, D. R., and Reed, W. H., Journal of Computational Physics,26,77 (1978).
l 7 Rider, W. J., 'High-Order Solute Tracking in Two-Phase ' Thermal Hydraulics', 4th International Symposium on CFD, Davis, CA, September 1991.
- 8. Oosterkamp, K. P., 'k e Modeling od Deboration Transient in a PWR', Presented at the ANS/ ENS l International Meeting, November 1982.
- 9. Rhode, D. L. And Stowers, S T., 'Combustor Air Flow Prediction Capability Comparing Several I Turbulenee Models*, Journal of Propulsion,5,242 (1986).
l 10. Hirsch, C., Numerical Computation of Internal and External Flows, Vol. 2, Wiley and Sons, Chichester ! (1990).
- f. 11. Mahaffy, J. H., ' Numerics of Codes: Stability, diffusion and convergence *, Nuclear Engineering and Design, 145 (1993).
- 12. Smolarkievicz, P. K., 'A Simple Positive Definite Advection Scheme with Small Implicit Diffusion'.
Monthly Weather Review,3, March 1983. l r. 35
! l l l 4. HIGH ORDER METHODS. A BIBLIOGRAPHICAL REVIEW l 4.1 Finite-Difference Methods For Hyperbolic Conservation Laws As discussed in the Section 3, the modeling of the transpon of solute by means of local conservative l methods, that is, based on average concentrations at discrete location of the Ocw field (i.e. cell centers), requires the numerical solution of a hyperbolic conservation law for the concentration of solute. Other approaches for the tracking of solute fields based on Lagrangian-like panicle tracking will not be considered here, since its application to System Codes is not deemed very effective in terms of computational efficiency; especially for long transient simulation (see [1], [2]). Such methods are generally based on stochastic I l approaches requiring the tracking of large ensembles of " concentration particles" in order to be statistically l accurate; this would require too much computation time when applied to transient simulations, since the calculation should be performed every time step to account for the dynamic character ot'the flow field being l simulated. ! Most current System Codes make use of the local approach by integrating the transport equation in time and space over computational cells, control volumes, into which the fluid field is meshed. Unfortunately, there are difficulties associated with the numerical solution of this type of equations by this approach, especially when discontinuous solutions are expected (3) (i.e. solute fronts). Methods based on l simple finite-difference approximations can yield wrong results when such discontinuities are present (4). l Several methods are available to solve hyperbolic conservation laws (e.g. finite-element (5], spectral l viscosity methods (6), front tracking methods (7), etc.), but, since the purpose of this review is to find suitable methods to improve the actual methodology in System Codes, only the finite-difference schemes ! used by these codes will be addressed. l The basic equation for the convective transport of an scalar with no source in one-dimensional space can be written in conservative form as: l i be(A t) B F(6(x t))
+ = 0, I Bt &x l
l (Eq. 4 1) where the function f($(xt)) represents the nurnerical flux of $(At) across the surfaces limiting the control volume where the equation is applied. If f($) = u, the velocity field, then the equation is linear and can be rewntten as: 96(x t) 96(s t) = 0,
+u Bt Bx (Eq. 4-2) 4-1
l l When developing numerical rnethods for this type of equations the time and space region where
$(At)is defmed is discretized with interval sizes at and & respectively. An approximate solution. C,", is then l
computed at point x, = i h, and at time t,= n At. The accuracy of such solution depends directly of the
- numerical method used to obtain it. ,
De time discreuzation is usually first-order, that is, the partial time derivative is approumated by:
&#(x t) @l*I- @l Br at (Eq. 4 3) l I
which results from a first-order truncation of the Taylor series expansion about @,". It is primanly the spatial differencmg approximatica of the convective term in (Eq. 4-2) what confers a method its properties of consistency, convergence and stability, and its ability to track sharp discontinuities. Most of the fmite difference approximations of die convective term are based on a Taylor series expansion about $" , where terms of high order are dropped in order to approximate the spatial gradient of Wst). According to the lowest order of the terms dropped the methods are known as first (drop second order and higher) second (drop third and higher), etc. Such procedure introduces the so ca!!ed truncation error of the scheme. As shown in Section 3, the truncadon error of the first order approximation results in an additional diffusive term in the r.h.s of (Eq. 4-2) whose associated diffusion coefficient depends, in general, on the grid size &, time the step size At and the convective coefficient, u (8]. This non-physical diffusion causes the smoothing of sharp discontinuities in the WAt) field. Second order schemes do not show a serious smoothing effect, but they usually yield oscillatory behavior near discontinuities (3), [4]. Amongst first-order methods, two of the most widely used are the Lax Friednchs' [9), and the basic l Upwind. De first one is based on the central difference approximation, where the spatial gradient is approximated by a central difference formulation (yielding for equally spaced mesh and constant velocity):
#l*' = el / Cr(#l,, ef.;},
(Eq. 4-4) where Cr = u at / As is the Courant number. This method is unconditionally unstable (3), and Lax and Friedrichs modified it by replacing 4,' by the average 1/2 (4,,' + @*,.,) but it remained first order accurate l and, hence, affected by large numencal diffusion, As previously mentioned, the-most widely used scheme in System Codes is the Upwind donor cell differocing; also a first-order accurate scheme. It transports information f in the direcuon of the flow, indicated by the sign of u, since the spatial gradient of War)is approximated by a backward,if u>0, or a forward differencing scheme,if u<0. De final form of the theme is : el*' = el Ctf@l-el.;) uf u > 0, el*' = @l - Criel.g- @l) . sf u < 0 .
** a 42
(Eq. 4 5) Both first order methods described above are stable for ICri < 1 (the CFL condition mentioned in Section 3), and consistent with the conservation law [4], but they suffer from severe numerical diffusion because of their first-order character, which results in poor resolution of sharp discontinuities. In order to overcome this disadvantage, second-order accurate methods have been developed based on third-order truncation approximations to the Taylor series expansion: 4(x, t + ht) = #(x, t) a t u 0 'O Bx
+ bar 22 u + O( A g3) ,
2 Ox2 (Eq. 4-6) Lax Wendroffs method [10], retains the first three terms of(Eq. 4-6) and uses central differencing for the spadal derivatives. ~Ihe resulting scheme is, for u > 0: 1 1 2 4l+1 = @l 3 Cr(@l ,-@l} + -Cr (@l,; 26l + @l.,), (Eq. 4-7) which is stable for ICr i < 1, and consistent with the conservation law. Another widely used second-order method, introduced by Beam and Warming (11), uses a one-sided approximation to the derivatives in (Eq. 4-6). For u>0, the scheme has the form: 1 4l*l = @l 1 Cr (3 #l 4 ef,, + @l.2) C 2 + 3 r (#l 2 6l.; + @l.2) , (Eq. 4-8) stable for 0 < 1 Cr l < 2 and also consistent with the conservation law (Eq. 4-1). l The major problem with cell centered second or higher-order differencing schernes, as those presented above, is their ter:dency to show oscillatory behavior before and/or after discontinuities [3]. Obviously, tids is of great concern when implementing them in a finite-difference based code in order to ! resolve sharp gradients, because the elimination of the smearing of discononuities would be substituted by ) unstable solutions, whose ampliede and frequency depend on flow and numwie parameters and order of the approx.imation (12). In complex System Codes, where such parameters vary frequently as the system evolves dunng a tra.uient, the use of numencal methods that can lead to instabilities should be avoided if possible. For this reason it was decided to search for other methods that could provide good resolution in discontinuities, but would also show no oscillatory behavior in their vicinity. A bnef review of alternative methods is presented next from (4). More sophisucated numerical schemes to resolve sharp discontinuities than those discussed above, have been developed in recent years. Two l of the most trnportant fanulies .ve the Goudonov-type and the High Resolution methods. 43
The basic Goudonov-type method obtains a numerical soludon that is piecevase constant in each mesh cell /x,.ia, x,.,4) at time t = n At. The cell interfaces separate constant states. @, and 4,,, , at t.. The time evolution of the solution from t, to t.., is obtained from the solution of the Riemann problem: l ip"(x,In) = 4,* , x e [xt.v2, x +y1) . a (Eq. 4-9) 8 5l(x, t) BF(5l(x. t)) dI
+
dx
= 0' l (Eq. 4-10) with l '
*? 1 *C 1?+ c e, (x,1) = <
\
*?+1 1 > x?+ n l
l (Eq. 411) The new piecewise constant approximadons are obtained by averaging the exact Riemann solution over each respective cell. The basic Goudonov method is, thus, a first-order spatial approximat2on because of 1 the constant assumption of $(x,t)in each cell. Since the exact solution of the Riemann problem is expensive to obtain, several approximate Riemann solvers have been proposed (e.g., the Goudonov type schemes by Osher [13) and Roe (14)) to be applied to the basic numerical method desenbed above. As shown in [4], both methods are first-order, however, since the discontinuides are smeared out. Thus, they are not suitable for the accurate tracking of solute fronts. High resolution rnethods, are in general, second-order accurate in regions where the solution is smooth, and give oscillation free results around discondnuities. These schemes satisfy a convergence criterion known u Total Varianon Diminishing (TVD), which mathemancally assures that for a given time, t.. the total vanadon of the numerical soludon: Total Variation iTv') = l#*.; 4*I, (Eq. 412) l will be bounded in the spatial domain, and that, as time advances, the value of the total vanadon of the soludon, IV" , will decreass 'he effect is the suppression of oscillations near discondnuides. The most used high resolution schemes which satisfy the TVD condition are the Flux Limiter methods [15),[16). They incorporate some form of limiter for the numencal flux, F,.,4. The definition of numerical flux stems from the form in wtuch a conservative numencal method can always be expressed. For a (2k + /)-point finite difference method, with two time levels, a conservative numerical method can be written as: 1 4-4
- . _ _ _ _ _ _ _ _ _ _ _ _ - _}}