Coupled 3-D kinetics thermal-hydraulic analysis of Hot Zero Power main steam line breaks using RETRAN and STAR codes

Nuclear Engineed.ng ELSEVIER

Nuclear Engineering and Design 146 (1994) 439-450

D gn

Coupled 3-D kinetics thermal-hydraulic analysis of Hot Zero Power main steam line breaks using RETRAN and STAR codes M a d e l i n e A n n e Feltus * Pennsylvania State University, 231 Sackett Bldg., University Park, PA 16802, USA

Abstract

The Main Steam Line Break (MSLB) at End of Life (EOL), Hot Zero Power (HZP) conditions accident was analyzed using a fully time-dependent coupled thermal-hydraulic (T/H) and neutronics method, and compared against conservative Final Safety Analysis Report (FSAR) results, which predict a return-to-power. The development and improvement of coupled neutronics/T/H analysis techniques provide many advantages including the capability to evaluate the impact of modeling assumptions made in previous reactor kinetics and T / H calculations. The coupled STAR kinetics and RETRAN T / H technique developed here provides a means to evaluate the quasi-static, point kinetics approximation against a fully time-dependent, three-dimensionai approach. Using the state-of-the-art 3-D STAR reactor kinetics code with the RETRAN reactor coolant system (RCS) T / H code in a best-estimate approach, it is now possible to evaluate the impact on safety margins imposed by conservative FSAR MSLB assumptions. The method presented shows how the time-dependent 3-D STAR nodal code model was used directly with core inlet conditions determined by RETRAN for a Westinghouse PWR. The S T A R / R E T R A N results clearly demonstrate that a return-to-power is NOT predicted when a 3-D thermal-hydraulically coupled time-dependent kinetics approach is used. This study shows that: (a) quasi-static and point kinetics methods are not able to describe severe PWR asymmetric transient phenomena adequately; and (b) fully coupled, 3-D time-dependent analysis methods should be used for PWR reactor transients instead. By coupling the RCS response in terms of updated core inlet conditions with 3-D time-dependent core kinetics response, in a tandem manner, the core power and T / H RCS conditions are forced to be self-consistent during the entire event, when non-equilibrium conditions exist.

1. Introduction The Main Steam Line Break (MSLB) at End of Life (EOL) Hot Zero Power (HZP) conditions

* Correspondence to: M.A. Feltus, Assistant Professor, Pennsylvania State University, 231 Saekett Bldg., University Park, PA 16802, USA; tel. (814) 865-1341, fax (814) 865-8499.

has become increasingly important in PWR reload analysis. With the increased burnup from 12 to 18 or even 24 month cycles, the MSLB HZP becomes more prohibitive at EOL conditions since: (a) the delayed neutron fraction,/3, is potentially smaller [1,6] resulting in a smaller prompt critical margin (p =/3); and (b) lower reactor coolant system (RCS) temperatures may be needed for fuel cycle coastdown.

0029-5493/94/$07.00 © 1994 Elsevier Science B.V. All fights reserved SSDI 0029-5493(93)E0249-J

440

M.A. Feltus/Nuclear Engineering and Design 146 (1994) 439-450

The MSLB HZP postulates that a main steam line breaks completely at the exit nozzle of a single steam generator [1]. A break upstream of the venturi nozzle causes simultaneous blowdown of all four steam generators via the main steam mixing header. Eventually, flow out of the three intact generators is terminated by closure of isolation valves. The generator with the broken pipe continues to release steam, causing a very rapid asymmetric cooldown and depressurization of the RCS. The MSLB is most severe at HZP EOL conditions [1] where the coolant and fuel start at the same temperature, 557 K, and where all control rods have been inserted into the core, except one standby safety control rod bank. The Doppler effect, both isothermal and Power Defect [1,6] causes an effective reactivity insertion as the RCS temperature is rapidly decreased. For conservatism, the control rod with the largest reactivity worth is assumed to fail stuck out [1]. In licensing studies, the MSLB at EOL I-IZP typically is assessed using quasi-static or point reactor kinetics methods that produce very conservative returnto-power predictions [1]. The improvement of coupled T / H and reactor kinetics analysis techniques provides many advantages, including the capability to evaluate the impact of modeling assumptions made previously in FSAR design basis calculations. With the advances in state-of-the-art computer technology, especially in tandem and parallel processing with PC hardware, the evaluation of conservative assumptions made in such earlier methodology becomes practical. Using the 3-D STAR 1 [2] reactor kinetics code with the RETRAN 2 [3] code in a time-dependent best-estimate approach, it is now possible to evaluate the impact of conservative FSAR-type assumptions on available margins

i The STAR code [2] has been developed jointly by NUS and several utilities. The author would like to express appreciation to NUS and C.L. Hoxie for their assistance with the STAR code. STAR is available now from Yankee Atomic Electric Company, Bolton, MA, and includes COBRA, VIPRE and WIGL models. 2 RETRAN [3] is an EPRI code available to EPRI member utilities.

in terms of DNBR, shutdown requirements, and boron injection via safety injection systems. This analysis demonstrates how to consistently couple RETRAN RCS T / H dynamics results as inlet flow conditions for the STAR neutronics code for the asymmetric MSLB event. The tandem S T A R / R E T R A N technique: (a) gives a means to evaluate quasi-static and point kinetics approximations against a fully 3-D time-dependent approach; and (b) demonstrates how to couple the core kinetics and entire RCS T / H response rigorously.

2. Methodology The methodology used in this study shows how the time-dependent, 3-D reactor kinetics STAR nodal code was directly coupled with the RETRAN RCS T / H code, in a tandem, iterative approach for the MSLB at HZP EOL conditions. This tandem, predictive-corrective method was also applied to three other PWR transients starting at full power conditions: Loss of Feedwater Anticipated Transient Without Scram (ATWS), and a Total Loss of Reactor Coolant System (RCS) Flow with a Scram, and Station Blackout ATWS events [6,7,8]. STAR [2] is based on the QUANDRY Analytic Nodal Method (ANM) and calculates the 3-D time-dependent, coupled T / H kinetics response. STAR uses a coarse spatial mesh, standard finite difference technique, and standard flux, fission source, and fully-implicit temporal iterations. A nonlinear iteration is used outside of the standard techniques to correct the coarse-mesh finite differences and force the coarse-mesh finite difference (CMFD) solution to match the higher order QUANDRY ANM solution. The advantages of STAR [2,6] are: (a) it is systematic and reliable since in the limit of a fine mesh, the CMFD discontinuity factors approach unity and STAR converges to the exact solution of the diffusion equation; (b) no "tuning" of results from finite difference codes, e.g., PDQ-7, is needed; and (c) STAR uses a true two- versus one-and-a-half group solution. STAR was executed: (a) quasi-statically using RETRAN T / H conditions at each "snapshot" in time, and (b)

M.4. Feltus~Nuclear Engineering and Design 146 (1994) 439-450

~70 OI >

V

~40 0-

2

iso .80 O. ~7 H

47O 0

..... o'oo .2. . . . o'oo .2. . . . ' . . . . ".... ". . . . o'. . . . o'oo ,o'oo TIME

SINCE

START

OF

ACCIOENT,

SEC.

Fig. 1. Main steam line break inlet temperatures.

time-dependently, using inlet RCS T / H conditions generated by RETRAN. Benchmarked RETRAN results [4,5,6], based on point kinetics [3], are used as core inlet conditions for the STAR time-dependent T / H input. Cold leg T / H responses (pressure, temperature, flow) for the broken and intact loops are used as core inlet conditions, using a totally mixed condition (inlet temperature set equal to average of all loop inlet temperatures), or a zero mixing case, where the coldest (broken) loop fluid enters the quarter core with the stuck-out rod, and the remaining 3 / 4 core use T / H inlet conditions of the intact loops. Fig. 1 shows the inlet temperature conditions generated by RETRAN used in this analysis, which were benchmarked against the FSAR [1,4,5,6]. The STAR global power level is calculated directly from 3-D nodal power distributions without any quasi-static or cross section collapsing approximations. This tandem predictive-corrective method converges consistently for PWR transients with large changes in T / H conditions [6,7,8]. The STAR global power is used directly as a power forcing function for the RETRAN T / H response. The method for using RETRAN and STAR is described by these steps: (1) Previous benchmark RETRAN results [4,5], based on a point kinetics approach, are used as first approximations for the inlet boundary conditions for the STAR time-dependent T / H input file, STARTH, and for quasi-static inlet conditions.

441

(2) STAR is executed in two ways: (a) quasi-statically using RETRAN pressure, temperature and flow at a particular point in the transient; and (b) time-dependently using the STARTH inlet boundary condition file generated by RETRAN. These inlet boundary conditions produce overall STAR core power levels different from the RETRAN point kinetics code. This STAR power is then used as a forcing function in RETRAN. (3) Steps 1 and 2 are repeated tandemly until the resultant STAR power and RETRAN T / H responses converge to an acceptable error level, less than 1%, for all time steps during the transient. This assures consistency between the T / H and neutronic phenomena [6,7,8]. Note that the STAR global power level truly provides a 3-D, time-dependent, core power response that is coupled with the entire RCS loop T / H dynamics. This STAR global power represents the core kinetics response without using any quasi-static approximation or lower-dimensional collapsing. It is not necessary to use STAR outlet T / H boundary conditions or to re-calculate power using RETRAN point kinetics parameters since the STAR global power level consistently incorporates three-dimensional and time-dependent local nodal power information. This approach ensures that the complete system transient response is integrated back into core inlet boundary conditions for the full accident duration. Otherwise, the differences in the core power level would result in different core outlet fluid conditions, and therefore, result in inconsistent subsequent inlet boundary conditions. This technique is used iteratively to determine a self-consistent set of overall system and core power response. By correcting the global power in this consistent manner, the T / H boundary conditions become self-limiting and converge quickly. This tandem S T A R / R E T R A N technique converges rapidly to produce a best-estimate, consistently coupled, 3-D time-dependent methodology. This coupled method has also been demonstrated for PWR transients at full power, with and without scram, where 3-D power levels are dependent on RCS dynamics [6,7,8].

442

M.4. Feltus/Nuclear Engineering and Design 146 (1994) 439-450

This tandem predictive-corrective approach demonstrates that a truly parallel process not only is feasible, but could be more efficient than a total integration of the STAR core neutronics code within the RETRAN code [6]. Only the global power level and the inlet T / H boundary conditions need to be passed between STAR and a system dynamics code if they are executed in parallel.

3. Model description Rather than using simplified RCS and core models, both the theory and methodology were applied practically by using realistic models that closely represent an actual four-loop Westinghouse PWR plant [6]. The STAR core model used in this study models a full three-dimensional PWR core in detail [6]. It has a full 193 assemblies, each assembly modeled as a separate square node in the radial direction and 12 axial nodes, with the baffle/ reflector region modeled explicitly. This baffle/ reflector region uses one node on the flat face of the baffle and four water/baffle nodes at the inner jagged edge of the baffle, where there is large neutron reflection. Such modeling of the baffle/reflector provides proper boundary conditions for realistically handling the nodal interfaces. Older methods use boundary conditions with fixed albedos based on the flux going to zero in the reflector. No albedo approximations are used in this STAR model. By using an explicit baffle/reflector model, it was found [6] that the albedo changes during MSLB transients since RCS flux and T / H conditions change. The use of a single-valued albedo, determined a pr/or/ by quasi-static methods, biases the peripheral assembly power production. The STAR core physics and kinetics model is based on full 3-D fuel cycle depletion [6] to EOL conditions for a Westinghouse Cycle 1 core design starting from BOL [1]. Benchmark calculations were made to demonstrate that the STAR core model matches an actual core [1,6] closely from BOL to EOL depletion and at Hot Full Power and HZP conditions. The STAR code [2]

allows for cross section data to be input as functionalized input for each fuel type in terms of boron concentration, burnup, temperature, xenon and samarium levels, relative moderator density, and complete and partial control rod insertion CT arrays, based on the standard SIMULATE [9] SIGDAT method tables in DAT and TABK files. A complete set of DAT and TABK files for eight fuel types and the baffle/reflector region was used to approximate the typical PWR core [6,9]. The STAR code was modified [6] to have both scram rod reactivity and control boron perturbations during different time spans for flexible core physics modeling, needed for the MSLB event, which has an early (2-4 seconds) scram and later (after 30 seconds) boron injection. The control rod "curtain" effect is modeled using total rod bank worths for MSLB EOL HZP transient. Resuits are described here for a "heterogeneous" scram model, where the scram rod curtain effects are seen as the rods drop down through the core, and a "homogeneous" scram model where all axial nodes are equally rodded at the same time. Since the MSLB is at HZP, all banks are inserted except a required shutdown bank, which is totally withdrawn at the beginning. Modeling scram effects in 3-D yields effectively higher scram worths during transients at intermediate insertions, which serve to shut the core down faster, reducing the severity of the accident. The fraction of total control rod absorption was determined by eigenvalue searches, based on referenced scram rod worths, so that the proper control rod worths can be used during a transient as a function of scram time and axial position. The assumption is made that all assemblies are effectively and uniformly rodded when all the rods are inserted. Also, the CT value that best matches the change in total reactivity worth is used to normalize the CT array input. These CT values were used to find nodal reactivity perturbations for modeling the control rod scram in the MSLB event. The analysis uses a heterogeneous scram model, where the scram rod curtain effects are seen as the rods drop down through the core, versus a homogeneous scram model where all axial nodes are equally rodded at the same time step. The effects of uniform and cur-

M.'I. Feitus ~Nuclear Engineering and Design 146 0994) 439-450

tain rod effects were given in detail previously [6]. Point kinetics approximations inherently assume that the scram is felt uniformly throughout the core, and therefore reflect a homogeneous scram modelling assumption. In order to ensure self-consistency, sensitivity studies [6] were performed with the STAR model. STAR has T / H options such as: (a) a WIGL [2] model that allows for no crossflow conditions, and (b) a COBRA based routine [2] to handle crossflow if boiling occurs. The STAR T / H WIGL parameters were benchmarked with RETRAN T / H results. STAR [2] can use either uniform, plenum-averaged or varied, assemblyunique inlet boundary conditions. Since STAR models time-dependent neutronic phenomena, STAR needs input data for perturbations in the values for the neutronics data. The neutronics input includes two group velocities and six delayed neutron group data [2,6]. The RETRAN code [3] has been used [4,5] to model the Indian Point 3 plant, a WestinghOuse 3025 MWth four-loop PWR with Model 44 steam generators. This RETRAN model has been used for complex transients that require detailed modeling of the RCS, such as asymmetric loop behavior, loss of reactor coolant flow, main steam line breaks with varied break sizes and feedwater flow conditions, loss of feedwater or electric load, and several ATWS events [4-8]. The RETRAN model used in this study is a four-loop plant which resembles the IP3 plant, but is based on bestestimate versus "worst case" FSAR-type licensing assumptions, using the RETRAN-02 MOD003 version options. The base RETRAN model [4,5] has a 2 loops that (a) lumps three intact RCS loops into one lumped loop, and (b) has a single loop that stands alone so that symmetric and asymmetric transients can be easily modeled. The pressurizer can be moved to either loop. Finer nodalization is used in the steam generator tubes with RETRAN local conditions heat transfer option [3,5]. The break friction losses are set to zero to maximize blowdown and system cooldown during the MSLB. By using an asymmetric RETRAN model, cold leg temperature effects in the broken and intact loops can be differentiated, and different mixing models can be investigated.

443

A detailed boron injection model using RETRAN control blocks [3] is required [4,5,6] because proper modeling of the dependence of safety injection flow rate and core boron concentration on time-dependent RCS T / H conditions is important for the MSLB scenario. The RETRAN model was: (a) first benchmarked against IP3 MSLB HZP results and was extended to address possible continuous feedwater flow addition concerns, [4,5] and (b) was used as part of an evaluation to determine whether RCS T / H behavior during multiple steam generator blowdown due to an auxiliary feedwater steam line break would necessitate plant modifications [5].

4. Discussion and results

Both LOFTRAN [1] and RETRAN [3] use complete lower plenum mixing and predict a return-to-power using point kinetics MSLB analysis, with point kinetics coefficients. Point kinetics parameters are developed with Doppler reactivity weighting to account for asymmetric and localized reactivity effects during the scram with the stuck-out rod. The STAR model, based on full 3-D fuel cycle depletion [6] to EOL conditions, did not produce a return-to-power for any of the cases analyzed. S T A R / R E T R A N results for: (a) the heterogeneous vs. homogeneous scram model, (b) the asymmetric vs. symmetric inlet T / H conditions, and (c) various stuck-out rod cases are described in greater detail below in terms of time-dependent axial and radial power distributions. By using an explicit, detailed baffle/reflector region model, it was also found [6] that the neutron reflection (albedo) changes as flux and T / H conditions change in the core and in the vessel downcomer. The use of a fixed single-valued albedo, determined a priori by quasi-static methods, biases the amount of power produced in the peripheral nodes. Various parametric studies [6] show that the STAR results were well-bounded. Several sensitivity studies were used to evaluate different aspects of MSLB events:

444

M.A. Feltus /Nuclear Engineeringand Design 146 (1994) 439-450

Table 1 STAR time-dependent 3-D results for MSLB symmetric inlet temperature cases Time (s)

STAR normalized power level, 3-D time-dependent heterogeneous, all rods 66 in

Peak node power at [X,Y,Z]

STAR normalized power level, 3-D time-dependent, heterogeneous one stuck-out rod

Peak node power at [X,Y,Z]

2

0.7781

2.136 [5,5,6]

0.7807

2.133 [5,5,6]

2.4 3

0.4453 0.1315

3.2 3.4

0.0826 0.0549

3.6 4

0.0407 0.0332

5 10

0.0297 0.0210

20 50 75

0.0104 0.0042 0.0022

0.4480 0.1335

3.099 [5,5,6]

3.092 [5,5,6]

0.0843 0.0560

2.486 [5,5,3]

2.528 [5,5,3]

0.0420 0.0344 [5,5,6] 0.0297 0.0219

2.340 [5,5,61 1.982 [5,5,61

2.349

0.0109 0.0104 0.0023

Table 2 STAR time-dependent 3-D results for MSLB asymmetric inlet temperature cases Time (s)

STAR power level 3-D, full core time-dependent, heterogeneous, all rods go in

2.0

0.9865

2.4 3.0

0.9723 0.4947

3.2 3.4

0.2629 0.1264

3.6 4.0

0.0641 0.0383

5.0 10.0

0.0323 0.0184

20.0 50.0 75.0

0.0104 0.0021 0.0022

Peak node, assembly power at

[13,13,Z] axial Z 8.56, Z 3.499

= 4

9.74, Z = 3 3.250 10.36, Z = 3 3.097 8.58, Z = 4 3.504 8.61, Z = 4 3.517 8.84, Z = 4

STAR power level 3-D, full core time-dependent, heterogeneous, one rod stuck 0.9865 0.9723 0.4995 0.2661 0.1285 0.0655 0.0393 0.0332 0.0189 0.0107 0.0221 0.0023

[13,13,Z]

Power, 1/4 core 4 stuck rods, Tavg

axial Z

s~flmnet~

Peak node, assembly power at

8.56, Z 3.499

= 4

9.763, Z = 3 3.333 10.69, Z = 3 3.36 10.39, Z = 4 4.247 10.45, Z = 4 4.27 10.64, Z = 4

0.7897 0.4480 0.1335 0.0843 0.0560 0.0420 0.3442 0.0278 0.0180 0.0109 0.0044 0.0024

M.A. Feltus~Nuclear Engineering and Design 146 (1994) 439-450

(1) The RETRAN model was used to produce symmetric and asymmetric core inlet conditions for the asymmetric MSLB event, where one steam generator is broken and blows down rapidly. The asymmetric case assumed that the colder fluid did not mix in the RCS lower plenum, a zero-mixing case, so that 1 / 4 core has the broken T / H conditions, and remaining 3 / 4 core has the intact loop inlet conditions. The symmetric case assumes that the lower plenum inlet fluid is totally mixed at an inlet temperature averaged for all 4 loops. Figure 1 shows the inlet temperature responses used. (2) A heterogeneous scram model was used to model the control rod curtain effect as rods pass through the core. This was compared with a homogeneous model that assumed all

445

the 3-D nodes experienced the same rod reactivity worth simultaneously. (3) Four symmetrically stuck-out rods were assumed for the symmetric MSLB with symmetric core inlet conditions case. (4) To yield an even more severe MSLB scenario, one asymmetric case assumed that other nearest-neighbor assemblies also had stuckout rods. (5) Other cases assume larger CT worths and nearest-neighbor assemblies have stuck-out control rods. These demonstrate the effect of assuming control rod worths at values higher than FSAR values and how important a certain core region is neutronieally. When fully time-dependent STAR results were compared with quasi-static STAR sensitivity cases [6], it was revealed that the location of the highest

Time

(s) 2 3 3.4 4 75

0.9223 0.8881 0.8544 0.8411 0.7103

POWER sec sec sec

sec sec 1.0728 1.1084 1.1487 1.1746 1.2690

0.6238 0.6457 0.6695 0.6825 0.7602

1.2674 1.3389 1.4347 1.5210 1.5587

1.1934 1.2344 1.2775 1.3091 1.3647

0.8752 0.8979 0.9222 0.9354 1.0124

1.0258 1.0221 1.0193 1.0199 0.9734

1.2136 1.2280 1.2491 1.2680 1.2513

1.0364 1.0454 1.0545 1.0606 1.0556

1.0287 1.0419 1.0539 1.0583 1.1130

0.5847 0.5963 0.6079 0.6124 0.6743

0.9626 0.9420 0.9205 0.9073 0.8520

1.1357 1.1203 1.1040 1.0938 1.0470

1.0152 1.0051 0.0027 0.9844 0.9414

1.1845 1.1813 1.1750 1.1686 1.1598

0.9642 0.9641 0.9600 0.9536 0.9690

0.7633 0.7728 0.7813 0.7828 0.8501

0.9314 0.9072 0.8837 0.8696 0.8249

1.0861 1.0622 1.0386 1.0241 0.9791

0.9761 0.9512 0.9292 0.9151 0.8658

1.1494 1.1328 1.1136 1.0999 1.0657

1.0266 1.0150 0.9991 0.9863 0.9648

1.1517 1.1501 1.1445 1.1359 1.1710

0.8096 0.8179 0.8252 0.8256 0.9003

1.0620 1.0305 1.0004 0.9864 0.8954

0.9415 0.9130 0.8840 0.8699 0.7754

1.1078 1.0796 1.0502 1.0355 0.9379

0.9963 0.9729 0.9463 0.9321 0.8420

1.1884 1.1701 1.1475 1.1348 1.0650

1.0088 0.9981 0.9828 0.9728 0.9377

0.8196 0.8220 0.8230 0.8230 0.8488

Fig. 2. Symmetric MSLB STAR results for scram with one stuck-out rod.

446

M.A. Feltus/Nuclear Engineering and Design 146 (1994) 439-450

power assembly and node was predicted incorrectly by the quasi-static approach, for both the homogeneous and heterogeneous scram model, especially during and shortly after the scram interval, when the transient neutronic effects are strongest. The STAR quasi-static MSLB results for averaged core inlet conditions show that a return-to-power was improbable, since there was a large decrease in static eigenvalves. Moreover, the effect of how delayed neutrons would minimize flux perturbations were not observed in the static STAR results. The stuck-out rod was assumed to be in the highest power producing node {5,5} in the radial plane. Table 1 gives the STAR time-dependent 3-D results for the symmetric MSLB case, for the heterogeneous curtain scram model, both for an all-rods-in case and for one stuck-out rod, which is equivalent to four rods symmetrically stuck out. The total normalized power is not changed significantly, but the peak power in the {5,5} node is different during the scram. Power

vs.

Time

2 3 3.4 4 i0 75

The STAR time-dependent results using heterogeneous scram model for the asymmetric core inlet temperature distribution are shown on Table 2. Whether the control rod is stuck-out at the highest power assembly {13,13,Z} or is inserted, the overall STAR power level for the entire core is not changed much; however, the local power is higher if the rod is stuck out in that node. The total core power for the symmetric MSLB with four symmetrical stuck-out rods, given in Table 1, is also shown on Table 2 for comparison. The difference between using symmetric and asymmetric inlet boundary conditions is shown on Table 2. Fig. 2 shows the radial power distribution for the symmetric MSLB with one stuck-out control rod as a function of time. The importance of the stuck-out rod is limited to its nearest neighboring assemblies. Figs. 3 and 4 show the S T A R / RETRAN results [6] for the cases with and without one stuck-out rod using the heterogeneous scram model and asymmetric core inlet T / H

at sec sec sec sec sec sec

C/L

Y=I3

1.1768 1.1817 1.7330 1.6885 1.6737 1.6000

3.3730 3.0116 2.8967 3.4123 3.4399 3.5499

3.2268 2.8918 2.8044 3.3467 3.3873 3.5902

3.0973 2.8739 2.7163 3.0303 3.0322 3.0111

3.4956 3.2513 3.0975 3.5037 3.5171 3.5751

2.4263 3.1744 3.0431 3.4825 3.4825 3.6262

2.4266 2.3655 2.2265 2.3361 2.3250 2.2580

2.9871 2.9152 2.7573 2.9410 2.9394 2.9250

2.5881 2.4858 2.4000 2.5642 2.5637 2.5617

AT

45 DEGREES

X=I3

Fig. 3. AsymmetricMSI~ STAR resultswithall rodsinserted.

M.,4. Feltus ~Nuclear Engineering and Design 146 (1994) 439-450

conditions. The effect of the stuck-out rod is to raise the power in surrounding assemblies, and only slightly in the cold quadrant. A return-to-power is NOT predicted with asymmetric core inlet T / H conditions by STAR, using a full core model, even with a single stuckout rod in the coldest quadrant. This lack of return-to-power was also produced by further sensitivity cases using asymmetric inlet conditions assuming: (a) a stuck-out rod in each of the four quadrants, at the {5,5} symmetric locations; (b) BOL kinetics parameters, i.e., different delayed neutron constants and neutron velocities and lifetimes; and (c) different stuck-out rod worths (CT) within the Westinghouse PWR design range [1,6]. The stuck-out rod worths assumed for the MSLB cases varied from the nominal HZP EOL worth of 0.521 for the CT STAR array [6] to twice and three times that value. The nominal value was based on a -7.56% change in reactivity given in the FSAR [1]. Thus, the nominal stuck-

Power

vs.

Time

2 3 3.4 4 I0 75

out rod worth was 7.56% p, based on the integral worth for all-rods-in versus all-rods-out. The sensitivity cases that used two to three times this value represented extreme conservatisms, since the actual single rod worth of a PWR is limited. Specific results [6] for the H_ZP EOL MSLB analysis with asymmetric and symmetric RETRAN inlet conditions are delineated below: (1) A return-to-power is NOT predicted in a HZP EOL MSLB event when a fully asymmetric, thermal-hydraulically coupled, threedimensional, time-dependent kinetics method is used, versus a point reactor kinetics approximation. The return-to-power is not predicted by either: (a) a symmetric quarter core model with four stuck-out rods, or (b) the asymmetric MSLB event with a single stuckout rod in the coldest region. (2) The three-dimensional time-dependent STAR method yields different and much smaller global power levels than RETRAN point ki-

at sec sec sec sec sec sec C/L

Y=I3

1.7684 1.8200 1.7358 1.6817 1.6076 1.5942

447

3.3732 3.0551 3.0185 3.7023 3.7360 3.8440

3.2268 2.9270 2.8962 3.5400 3.5866 3.7881

3.0973 3.4987 2.9081 3.3328 2.8162 3.3603 3.2745 4.2467 3.2813 4.2732 3.2561 ,4.3584

3.4264 3.2181 3.1648 3.7701 3.8014 3.9186

2.4266 2.3839 2.2773 2.4475 2.4400 2.3690

2.5881 2.5589 2.4605 2.6910 2.6947 2.6891

2.9872 2.9496 2.8574 3.1858 3.1891 3.1705

AT

45

DEGREES

X=13

Fig. 4. Asymmetric MSLB STAR results with one stuck-out rod.

448

M.4. Feltus/Nuclear Engineering and Design 146 0994) 439-450

netics and STAR quasi-static results. The RETRAN point kinetics method, where large Doppler weighting (flux squared) and homogeneous scram worths are assumed, yields a return-to-power because time-dependent 3-D T / H and neutronic conditions are not fed back explicitly. (3) MSLB STAR results show that albedos change during the MSLB transient [6], because the vessel downcomer T / H conditions and boron concentration change. Using either single- or fixed-valued albedos based on initial steady state quasi-static conditions will lead to erroneous results. (4) The STAR core physics model yielded moderator temperature coefficient (MTC) values that are within the range of expected MTC values for similar plants, as shown on Table 3. This means these STAR MSLB results are representative of the kind of MSLB responses that would be calculated for actual PWRs.

(5) The nodal power levels increase greatly between the complete insertion case and the one stuck-out rod case in the highest powered assembly with the stuck-out rod. The shift in the axial power distribution, combined with the effects of the stuck-out rod in the highest powered assembly, may lead to DNBR limit concerns, since the MSLB event causes RCS depressurization. (6) A quasi-static approach assumes thermal-hydraulic and neutronic equilibrium, so that no delayed neutron effects are determined. The time-dependent MSLB cases show how delayed neutrons affect the kinetics response. The all-rods-in axial flux distributions are similar to the initial all-rods-out power shape; however, the flux is slightly increased at the bottom because of the colder inlet temperatures. The MSLB event is strongly dependent on the moderator temperature feedback effects as the

Table 3 Moderator temperature coefficient comparisons for reference Westinghouse four-loop PWRs and the STAR E O L HZP core physics model Plant name

Reference ([6], biblio.)

MTC value ( p c m / F )

Comments

Indian Point 3

(N4)

-30.6

FSAR MSLB Ref. value

Indian Point 3

(N4)

- 28.

FSAR E O L Cycle 1

Indian Point 3

(N4)

- 30.

FSAR E O L Cycle 4

Indian Point 3

(N4)

- 38.

FSAR E O L Cycle 6

Salem 1

(P4)

- 35.

FSAR MSLB Ref. value

Salem 2

(P4)

- 32.

FSAR MSLB Ref. value

RESSAR

(W5)

- 37.2

RESSAR MSLB Ref. value

STAR core model

-

-35.

Based on reactivity difference between HFP @ 2250 psia, 573 F and HZP @ 1000 psia and 542 F.

STAR core model

-

- 32.9

Based on reactivity difference between HZP @ 1000 psia from 450 to 500 F.

M.,I. Feltus~Nuclear Engineering and Design 146 (1994) 439--450

RCS cools down rapidly. The absence of a predicted return-to-power led to further comparisons between the STAR core model moderator temperature coefficient (MTC) value and that of other reference Westinghouse PWRs [6]. The STAR kinetics model used in this study produces MTC values that are well within the MTC range exhibited by similar four-loop PWRs, as shown on Table 3. This means these STAR MSLB resuits are representative of the kind of MSLB responses that would be calculated for actual PWRs. The results of this coupled S T A R / R E T R A N technique conclusively demonstrate [6] that NO return-to-power is predicted in a four-loop Westinghouse H Z P EOL MSLB event when a fully asymmetric, thermal-hydraulically coupled, three-dimensional, time-dependent kinetics method is used, rather than 3-D quasi-static or point reactor kinetics approximations. Other methodologies have been recently presented for PWR MSLB analysis [10]; however, these generally involve simplifications compared to the method presented here. Agee [10] presents three MSLB analyses: (a) a RETRAN reactor coolant system model using a point kinetics model; (b) a stand-alone A R R O T T A / V I P R E [10] model using RETRAN flow conditions, without continuous RCS feedback; and (c) a quasistatic STAR physics model used to generate quasi-static weighting factors for RETRAN point kinetics system feedback. A.F. Dias [10, p. 2.1-7] suggests that a tandem RETRAN and ARR O ' [ T A / V I P R E execution would provide an inexpensive MSLB analysis on the IBM RISC/6000 environment. The results presented here and in the earlier thesis research [6] demonstrate that a tandem methodology that includes the entire RCS is rigorous, feasible, and inexpensive.

5. Conclusions and summary

The asymmetric time-dependent coupled S T A R / R E T R A N MSLB at HZP EOL conditions analyses show that using a quasi-static or a point kinetics approach will lead to erroneous

449

results. Quasi-static and point kinetics approximations may yield: (a) over-prediction in the global power for the MSLB event, and (b) an incorrectly predicted return-to-power. A returnto-power is not predicted by: (a) a symmetric quarter core model with four stuck-out rods; (b) the asymmetric MSLB transient, with a single stuck-out rod in the coldest quadrant; or (c) sensitivity cases using larger rod worths. The STAR sensitivity cases show conclusively that NO return-to-power is predicted in a HZP EOL MSLB event when a fully asymmetric, thermal-hydraulically coupled, three-dimensional, time-dependent kinetics method is used, rather than quasi-static or point reactor kinetics approximations. No return-to-power is predicted even with various assumptions about stuck-out control rod positions and core inlet mixing conditions. In contrast, the point kinetics approach predicts a return to criticality with a substantial power increase [1]. The tandem S T A R / R E T R A N method described in this study provides an efficient way and inexpensive (STAR was executed on an IBMbased 386 PC, with some tandem RETRAN executions) means to evaluate quasi-static and point reactor kinetics approach against a time-dependent, three-dimensional approach that couples the core power and RCS-loop T / H responses together. The STAR global power level is calculated directly from the three-dimensional nodal power distribution without using any quasi-static approximation or lower-dimensional cross section collapsing techniques or reactivity coefficients. The STAR global power is used directly in the system T / H response. This coupled S T A R / RETRAN method converges consistently for PWR transients that yield large changes in T / H conditions. This tandem method demonstrates the feasibility of using parallel-processing to calculate the core and global system response simultaneously. The research [6] provides the technical and phenomenological basis for properly integrating analytic nodal methods (STAR) with system dynamics codes (RETRAN). In view of the ready availability and economic feasibility of using a more rigorous method, such as the S T A R /

450

M.A. Feltus~Nuclear Engineering and Design 146 (1994) 439-450

RETRAN method presented here 3, there seems to be no excuse for further attempts at applying: (a) point kinetics methods that require spatial parameter collapsing, or (b) quasi-static approaches that require temporal flux shape assumptions to analyze PWR safety during postulated transients. 6. References [1] New York Power Authority, Final Safety Analysis Report - Indian Point Unit 3, Chapters 3, 4, and 14 (1987 Revision). [2] C.L. Hoxie, STAR: Space and Time Analysis of Reactors, STAR Version 4, Level 1, MOd 1, Gaithersburg, MD, NUS Corporation (June 1987). [3] J.H. McFadden et al., RETRAN-02: a program for transient thermal-hydraulic analysis of complex fluid flow systems, Palo Alto, CA, Electric Power Research Institute, EPRI NP-1850-CCM, Computer Code Manual (May 1981). [4] Madeline A. Feltus, Thermal-hydraulic analysis of main steam line breaks with continuous feedwater addition, in:

3 Other codes have been developed for coupled 3D T / H and kinetics analyses, e.g., ARROTTA, RAMONA-3B, and TRAC-G. Some of these are not publicly released, nor useful for PWRs, or model only in-vessel effects, without complete RCS dynamics. STAR was already available and benchmarked [2,6] when the initial research was performed in 1987-1989 [6,7,8].

Proc. ANS Meeting on Anticipated and Abnormal Plant Transients in Light Water Reactors, Jackson, WY, September 1983 (Plenum Press, New York, 1984), pp. 843-856. [5] Madeline A. Feltus, RETRAN analysis of multiple steam generator blowdown due to an auxiliary feedwater steam line break, in: Trans. ANS 13th Conference on Reactor Operating Experience, International Meeting on Nuclear Power Operation, Chicago, IL, August 1987; TANSAO 54, Suppl. 1 (1987) 1-196. [6] Madeline A. Feltus, Evaluation of nodal reactor physics methods for quasi-static and time-dependent coupled neutronic thermal-hydraulic analysis of pressurized water reactor transients, Ph.D. diss., New York, Columbia University (May 1990). [7] Madeline A. Feltus, Three-dimensional time-dependent PWR transient analysis using the tandemly-coupled STAR/MCPWR and RETRAN methodology, in: Proc. ANS International Topical Meeting on Advances in Mathematics, Computations and Reactor Physics, Pittsburgh, PA, April 28-May 2, 1991, Volume 4 (1991). [8] M a d e l i n e A . Feltus, Three-dimensional time-dependent STAR reactor kinetics analyses coupled with RETRAN and MCPWR system response, ANS 1989 Winter Meeting, San Francisco, CA, November 1989; TANSAO 60, pp. 771-775, in: Thermal-Hydraulics Proceedings (1989), pp. 327-335. [9] D.M. Vet Plank, SIMULATE-E: a nodal core analysis program for light water reactors, Palo Alto, CA, Electric Power Research Institute, EPRI NP-2792-CMM, Computer Code Manual (March 1983). [10] L.J. Agee, Stearnline break analysis methodologies, Simulation of PWR steam line break accidents, Electric Power Research Institute, Palo Alto, CA, TR-100521 (April 1992).