Three-Dimensional Kinetics Analysis of Large LMFBR Cores With<Br

NEACRP-A- 66+-

THREE-DIMENSIONAL KINETICS ANALYSIS OF LARGE LMFBR CORES WITH THERMAL HYDRAULIC FEEDBACK

Y. Oka, N. Tada*, M. Konomura**, S. Kondo and S. An***

Nuclear Engineering Research Laboratory, Faculty of Engineering, University of Tokyo

Tokai-mura, Ibaraki 319-11, JAPAN

September 1984

present address: * Toyo Engineering Corp. Higashi Funabashi 6-12-10, Funabashi City, Chiba 213, JAPAN ** Power Reactor and Nuclear Fuel Development Corp. Oa~rai Engineering Center, Oarai-cho, Ibaraki 311-13, JAPAN xxx Tokai University Tomigaya 2-28-4, Shibuya-ku, Tokyo 151, JAPAN

063900.0 ', Abstract,

Transient behavior of LMFBRs due to withdrawal of a control rod was analysed by the two-dimensional FXZ-TH code and three-dimensional IBIS. Both calculations agreed well with each other for the transient due to central control rod withdrawal. The analysis oft the behavior against peripheral control rod withdrawal showed that the two-dimensional calculation in R-Z geometry gave 30 % higher fuel temperature rise at 1 second after the initiation. Overpower transient due to withdrawal of a control rod in 1000 MWe homogeneous, radial heterogeneous and axial heterogeneous LMFBR cores were analysed by IBIS. The earliest scram was triggered in the axial heterogeneous core and the coolant temperature rise was the smallest. In the case that the scram was not triggered, the fuel temperature reached the melting point before coolant boiling or cladmelting. The largest power increase was observed in the homogeneous cores. The time to reach the fuel melting point was the largest in the axial heterogeneous core due to the small reactivity insertion rate in.the axial blanket.

1. Introduction

In the evaluation of large, dilute and'in particular heterogeneous liquid metal fast breeder reactor (LMFBR) performance for the purposes of design, optimization and safety analysis, space-time kinetic calculations are needed. Two-dimensional space- time kinetics calculation code, FX2-TH made feasible.an evaluation of the impor of spatial effects in the calculation of operational fast reactor transients. KU Analysis of local perturbations, however, requires essentially three-dimensional calculation. For example, withdrawal of an asymmetric ccintrol rod cannot be modeled by neither two-dimensional R-Z nor triangular geometry. A three-dimensional (hexagonal- Z) nuclear reactor kinetics code IBIS was developed by us for large fast breeder reactor trz+sient analysis. 13,41' The code takes into account feedback effects from changes in both the average fuel and coolant temperatures. Sodium boiling feedback can also be considered in the code, while FX2-TH assumes no bo' Detailed description of IBIS is given in other documents. [ 3yyg tI',",,'yt :"s=yrye;;y reviewed as follows: The code is designed for transient analysis of a fast breeder reactor in hexagonal-Z geometry. The source-free, time-dependent, multi-energy group diffusion equations are used to describe the neutronic behavior of the core. The equations are solved by using the quasi-static method. The point kinetics equations is solved for an ampli- tude function with periodic recalculation of the space- and time-dependent multigroup shape function. Nine-point difference approximation to neutron transport is used to solve shape function equation in hexagonal geometry. Successive over-relaxhtion method (SOR) is used for an accerelation of the calculation. The neutronic solutions are based on a three group cross section set. In the present study the cross sections are collapsed from JARRI fast 25 group set. The purpose of thermal-hydraulic calculation of IBIS is to reasonably predict the initiation time and the propagationof sodium voiding, and to obtain the temperature distribution of fuel pellet. The fuel heat transport model employs a solutionof the heat conductibn equation in an one- dimensional(radia1) fuel pellet, gap, clad and coolant configuration. Axial and angular conduction of heat are thought to be relatively unimportant for the class of problems under consideration with IBIS. The channel is divided into axial segments (up to 20), and the temperature calculations are made for each of the sections in succession following the direction of coolant flow. Some assumptions are also iu- eluded in the thermal analysis: 1. Behavior of one-subassembly can be represented by the single fuel pinaudits associated coolant model. 2. The geometry does not change and the fuel does not expand. 3. No heat transport occurs between subassemblies. 4. The pressure changewhichis induced by sodiumvoiding in a subassembly has uo effect on another subassembly. Two different models are used for simulating boiling expulsion. A slip-flow two-phase model is used for the initial portion and up to short time after flow reversal when resonably large void fraction exists. Since the slip-flow model is less meaningful from a physical standpoint when vaporvoid fraction is approaching 1.0 and coolant is being expelled from both ends of the channel, a switch is then made to a simple slug model to continue the voiding calculation. Throughout all the coolant-dynamics calculations, the coolant channel geometry is assumed to remain intact. The calculated temporary and spatial void distribution is then used to obtain the coolant-voiding component of feedback reactivity. a 2.Conpaxison of 2-D and 3-D kinetics

Au overpower transient due to the withdrawal of a single control rod was analysed by FX2-TH (two-dimensional) and by-IBIS (three-dimensional). The results are compared in chapter 2.1 for central control rod withdrawal of a homogeneous LMFBR and in chapter 2.2 for peripheral control rod withdrawal. The core coufigu- rations are shown inFig. I. The reactor power is 500 MW thermal and active core size is 1 n high and 1.85 m in diameter. The core characteristics are summarised in Table I. The values are similar to the parameters of Super Pheuix 1, but the radial blanket assemblies are replaced by the stainless steel reflectors for the simplicity of calculation. Only one control rod is located in the core at the position C or P in Fig. 1. All others are fuel assemblies with axial blanket regions. Both R-Z and triangular geometry were used for FX2-TN analysis. Equivalent radius was used for the R-Z model in order that the volume should be the sane as that of the Hexagonal-Z model. The transverse buckling for triangular geometry analysis was determ'ned by using the two-dimensional diffusion calculation code, APOLLO in R-Z geometry. &I

a 2.1 Withdrawal of a central control rod Enrichment of the core and the B4C volume fraction of the central control rod were determined from the results of steady state calculations by using FX2-TH code in R-Z geometry under the following condition : (1) The effective multiplication factor (keff ) should be unity at full insertion of the rod (2) The worth of the rod should be about one dollar. The enrichment of the Pu02 fuel was 15.69 % and the B4C volume fraction in the control rod was 0.562 X. Steady state of the reactor was analysed by IBIS and FX2-TH (triangular geometry). The results are compared in Table II. Values of keff agree rather well with each other. Thus the diffusion calculation routine of IBIS is verified. The radial temperature distributions in the core are compared in Fig. 2. The central control rod was fully inserted. R-Z geometry was used for FX2-TH the calculation. Both coolant and fuel temperature distributions agree very well. The result shows that the steady state thermal and hydraulic calculation of IBIS is valid. Radial reactor power distributions also agree well with each other. Transient behavior due CO withdrawal of the central control rod was analysed by FXZ-TH and IBIS. The rate of the withdrawal was 100 cm/set. The net reactivity, taking into account thermal and hydraulic feedback effects, for this rate of insertion is shown in Fig. 3 as a function of time. The fuel temperature increase in the hottest subassembly during the transient is displayed in Fig. 4. The net reactivity and the temperature increase predicted by IBIS agrees well with that of FXZ-TH in R-Z geometry. Thus we think that IBIS is also valid for fast breeder reactor transient analysis with reactivity feedback effect. The slight difference of net reactivity which is observed in Fig. 3 is due to difference in the rod geometry in hexagonal-z and R-Z approximation. The slight difference may also be due to the numerical error of the calculation. The prediction of FXZ-TH calculation in triangular geometry fails, because axial movement of the control rod cannot be well simulated by the constant decrease of B4C concentration in the rod. Abrupt decrease of net reactivity is observed,at 1.0 set since there is no axial blanket region in the triangular model.

2.2 Withdrawal of a peripheral control rod

Comparison of two-dimensional calculation by FX2-TH and three-dimensional calcu- lationby IBIS was also made in the analysis of an overpower transient due to asymmetric reactivity insertion by a peripheral control rod. The core configuration for the analysis is the same as shown in Fig; 1, but the only one control rod locates at the peripheral position'"P". AC first enrichment of the core and B4C volume fraction of the control rod were determined from steady state calculation in the same way as in chapter 2.1. The effective multiplication factors with full-in and full out of the control rod are shown in:~the left column of table III. The difference in L effective multiplication factors or the control rod worth differs with one another. Both FX2-TH calculations had approximations: The peripheral control rod was represented by a ring-shape in the R-Z geometry and axial temperature distribution was neglected in the triangular geometry. This proved to bias the results. To mitigate this bias, in the following analysis different fuel enrichment and B4C volume fraction, normalized to give equal control rod worth were used in the two dimensional and the three dimensional calculations. The results are summarized in Table III. An overpower transient due to the withdrawal of the peripheral control rod was calculated by FX2-TH and IBIS. The rate of the withdrawal was also 100 cm/set. The time response of the net reactivity is shown in Fig. 5. The figure shows that the asymmetric reactivity transient cannot be predicted by the two-dimensional calculation. The fuel temperacure change of the subassembly adjacent to the withdrawn rod (position "A" in Fig. 1)is shown in Fig. 6. The local reactor conditions such as the fuel temperature need to be predicted by using three dimensional calculation.

3. Three-bensional transient behavior of large homogeneous, radial heterogeneous and axial heterogeneous cores

The three-dimensional code, IBIS was used to study the neutronic behavior with thermal hydraulic feedback of 1000 MWe homogeneous and heterogeneous cores subject to the same withdrawal rate of a control rod. The configurations of the 1000 MWe cores for the analysis are shown inFig. 7. Only one row of radial shield subassemblies was included in the calculational models due to the limitation of the computer storage. The design characteristics of the cores are summarized in Table IV. Initial outlet coolant temperature'distributions of the cores were calculated by

,.06390004 IBIS. The control rod to be withdrawn was determined for each cores so that it located in the hottest coolant region and had high reactivity worth. The positions of the rods are also indicated in Fig. 7. The reactivityworth values of the rods were estimated by steady state calculation and given in Table V. The withdrawal rate of the rods was determined to be 30 cm/set from the table so that the reactivity insertion rate was about 0.5 dollorfsec. First, transient behavior with scram was analysed. The scram was set to be triggered at 20 % overpower and all the backup control rod began to be inserted after 200 msec. The insertion rate of the rod was also 30 cm/set. The reactor power and the average coolant temperature in the hottest channel are presented as a function of time in Fig. 8. The time response of the reactor power is similar to that of the reactivity., The scram is triggered earlier in the axial heterogeneous core. The initial reactivity insertion rate of the core is high due to the flatness of the importance in the axial direction. The reactor powers of the homogeneous and the radial heterogeneous cores change very closely with time until the scram is triggered. After the scram the reactivity insertion rate in the radial heterogeneous core is higher than that of the homogeneous core, because the worth of the backup rods is high. Then the increase in the maximum coolant temperature of the radial heterogeneous cores is lower than that of the homogeneous one. The values of the coolant temperature increase themselves are very small and the maximum coolant temperatures are wellbelowthe coolant boiling point. These results shows that the l cores suffer no damage if the scram is successful. Secondly, transient behavior without scram was analysed. The rate of the control rod withdrawal is also 30 cm/set. Time responses of net reactivity are shown in Fig. 9. The reactivity of the axial heterogeneous core is initially high and becomes low afterwards. Then the reactivity reaches maximum somewhat later than those of another cores. The difference in the net reactivity between the different core configurations results in differences in the time response of the reactor powers. The changes of the reactor power, the av.erage fuel temperature and the average coolant temperaturein,the hottest channel are shown in Fig. 10 to Fig. 12 for the ' homogeneous, 'the radial heterogeneous and the axial heterogeneous cores. The fuel temperature of the axial heterogeneous core reaches the melting point latest as shown in Table VI. The maximum value of the reactor power is the lowest in the radial heterogeneous core, but the time to reach the maximum is the earliest. The transient behavior of the axial heterogeneous core is slow and mild due to the small reactivity insertion rate in the internal blanket region. Contour maps of total flux are shown in Fig. 13 to 15 for the three different core configurations. Three dimensional analysis gives us very clear view of the transient behavior of the large LMFBR cores.

Conclusions

1. The transient due to the withdrawal of a peripheral control rod even in a homogeneous LMFBR core requires three-dimensional space-time analysis. 2. Three-dimensional kinetic analysis of 1000 MWe homogeneous, radial heterogeneous and axial heterogeneous cores subject to the fast withdrawal of a fully inserted control rod at the rate of 30 cm/set showed that:

(1) The rises in fuel and coolant temperatures were very small for the reactivity insertion with scram at 120 % overpower. (2) When the scram failed, the fuel temperature reached the melting point before coolant boiling or clad melting. The largest increase in power was observed in the homogeneous core. The radial heterogeneous core showed the smallest increase in power due to the internal blanket. The axial heterogeneous core also showed smaller increase in power. The time to reach the fuel melting point was the largest in the axial heterogeneous cores due to the small reactivity insertion rate in the internal blanket.

The authors express their thanks to K. Shirakata for valuable discussions.

R. A. Shober, T. A. Daly and D.R.Ferguson, "FX2-TH, A two-dimensional nuclear a 1.reactor kinetics code with thermal and hybraulic feedback", ANL-78-97, Argonne National Laboratory.(1978).

2. S. F. Su, Y. Orechwa and H. Henryson II, "Neutronic space-time effects with thermal-hybraulic feedback in large homogeneous and heterogeneous liquid metal fast breeder reactors", Nucl. Technol. 52, 370 (1981).

3. M. Konomura, Y.Oka and S. An, "IBIS: Three dimensional nuclear kinetics code, Version I", UTNL-R-0153, Nuclear Engineering Research Laboratory, University of Tokyo (1983).

4. M. Konomura et al., submitted to J. Nucl. Sci. Technol.

5. K. Ikawa et al., "APOLLO" JABRI-M-5886 (1974).

06390006 Table I Core characteristics

Power, me 500 Active core size (HXD), m 1 x 1.85 assembly pitch. cm 17.86

volume ratio 38.0/28.5/33.5 (f"el/structure/coolantl

Fuel demity, % T.D. 85.0

Composition ratio, % 63/22/12/3

(~39P"/~"P"/'~'Pu/"zPu~

Pin/Pellet diamater. cm 0.850/0.702

Cladding thickness, m 0.702(type 316S.S.l

Na coolant temperature 38OE.40 (inlet/outletl. 'C

.._

Table II Pu enrichment in.the core and 84C volume fraction of the central control rod for the transient overpower calculation

Pu02 enrici-ment 15.69 % BqC volume traction in the control rod 0.562 %

Code FXZ-TH FX2-TH IBIS Geometry R-8 Triangular Hex.-8 k,ff(full in) 1.00038 1.00717 1.00453 EeffuO-31 3.53077 3.50752 3.55376

Table III PU enrichment of the core and B4C volume fraction of the peripheral control rod for the transient overpower calculation

preliminary final I I code FX2-TH FXZ-TH IBIS IBIS FXZ-TH FXZ-TH

geometry R-8 -- Hex.-8 sex.-8 R-8 --

Pu Enrichment 15.62 $ 15.62 % 15.77 $ 15.54 $

BqC Vol. Fraction 1.183 % 1.46 $ 0.945 $ 1.706 $

mu up 1.00365 1.91501 1.00939 1.00939 1.00944 1.00946 Xeff Full I" 1.00000 1.00969 1.00635 1.00596 1.00605 1.00607

Rod Worth IS1 1.03 1.48 0.842 0.950 0.950 0.949 Table IV Characteristics of 1000 "We LMFBR cm%5

Power, me (MWI 1000 (2480) 1000 (2480) 1000 12480) Core size. cm (8x01 100 x 325 100 x 331 100 x 323 Axial blanket length. cm 35/35 35,35 ‘IO/40 Radial blanket thickness. cm CTI.40 ea.40 ca.40 Assembly pitch, mm 145.4 145.5 163.0 Volume ratio, 8 38.6/37.1/24.3 38.6/37.1/24.3 38.4/37.4/24.2 dri"er (blanket, (54.3/25.6/20.1) (47.5/30.4/22.1) (50.8/X3.4/20.8) Fuel density, %l'D 94.5 94.5 94.5 r~9P”/‘~~PU/“‘PU/‘~ZPUI $ 58/24/14/4 58/24/14/4 5;/:;<194<4 r150,*11" 0.3/99.7 0.3/99.7 . . Pu enrichment 11.4(in)14.4(out) 16.3 15.3 Pellet radius. mm 6.44 6.44 6.44 Clad o.r./thickness, mm 7.uo.4 7.4,0.4 7.4,0.4 NO. pins. core (blanket1 217(91) 217(169) 23,7(127) ??a coolant inlet/outlet 658/803 658,803 658/803 temperature, I(

Table V Reactivity worth of the control rods

Homoqe"eo"s Radial Axial heteroqenwus heterogeneous

full up 1.00393 0.99732 1.00098 k eff full in 0.99878 0.99237 0.99620

Rod worth, $ 1.46 1.42 1.38

Table VI Summary of transient response of the 1000 me cores

Homogeneous Radial Axial heteroqeneous heterogeneous

Max. reactivity, S 0.549 0.503 0.491 time to reach, set 2.39 2.39 2.90

Max. power, w4t 9174 7524 8331 time to reach, set 2.87 2.65 2.94

Time to reach fuel 3.23 3.54 4.15 reltirq~rab.lre,sec - FX2-TH

(a) R-Z model.

I I I , I _ 0 I.0 aiatanoe from Core cen,ra ,m,

- FX2-TH(R-21

I b) Hexagonal - 7. model. - FXZ-TH (R-Z1 --- FXZ-TH (Triangulari o IBIS (Hex.-21

I I I I I - FX2-TH (R-Z1 2co- -o- FX 2-TH CR-21 --- FX2 -TH (Trianqular 1 % me A FX2-TH (Triangular),’ c) -c--IBIS (Hex.-2) ,’ 1

I I I t 0 1.1 Time (sea) Tlma(see) Withdrown’ rod

odial blanket

@I Main control rod @ Main contml rod @ Backup contml rod Withdmwn md Mari -WI

I .\ 0 1.0 Time (seci .

Ioooo- - Homo. - -.- Rcdidl helero. --- Axial hetero.

a .z ‘Z :: c?z - Homogenous -- Rodiol Hetero. , ----- Axial Hetero. aov I 0 2.0 4.0 Time , set Time Eec)

3500 - - Homo. -- Radial hetero. -- Axial hereto. “3aoa-

Time , set A -A section A -A section A -A section

I- I- -l I-- -i A A A A A

Et - B section tj - Et section B - B section

063900 13 A -A section A -A seclion A -A section I I

7 -4 I-- A-- I-A A b A

E - B section 8 -B section B

A -A section A -A section A’ - A section

r--WIthdrawn Rod

I-- 7 I-- I- 3 A A A A A

B - B section B - B section Et - B section .

COMPUTERCODE ABSTRACT

1. NAME AND TITLE OF CODE IBIS (VersionI.2): A Threft) -dimensional nuclear reactor kinetics calculation code AUXILIARY ROUTINES PAINTV An output processing routine for drawing some contour maps of neutron flux or material temperature in an arbitrary section either horizontal or vertical INFORMATIONS In this version of IB only JAERI fast 25- group neutron cross section set 'i% can be read. It is collapsed to 3 groups and used for calculation 2. CONTRIBUTORS Version I.1 Mamoru KONOMURA, Yoshiaki OKA and Shigehiro AN Nuclear Engineering Research Laboratory, Faculty of Engineering, University of Tokyo Version I.2 Nobuo TADA Nuclear Engineering Research Laboratory, Faculty of Engineering, University of Tokyo 3. CODING LANGUAGEAND COMPUTER FORTRAN 77 ; HITAC M-200H 4. NATURE OF PROBLEMSOLVED The IBIS code performs steady state and kinetics calculations based on a three-dimensional nuclear diffusion kinetics with thermal hydraulic feedback It can calculate the following values in Hexagonal-Z geometry of a fast breeder reactor core through the progress of transient (1) Net reactivity (2) Total and groupwise delayed neutron fraction (3) Groupwise delayed neutron precursor concentration (4) Total power and ener'gy (5) Space dependent neutron flux in each energy group (6) Space dependent temperature of each material (7) Maximum temperature of each material and its location 5. METHODOF SOLUTIONS The quasi-static method is adopted to solve a three- ional nuclear diffusion kinetics. The method refers to $y?8. Shape function equation is solved with the treatment which is used as in CITATION (din:;; ;;;EfyecIgeB?~ ) . One-dimensional thermo-hydraul' s is solved with the model similar to that given in SASlA (8. Sodium boiling can be taken into account. 6. RESTRICTIONS and LIMITATIONS The number of neutron energy group is fixed to be 3

063800.16 .

groups in the present version of the code. TYPICAL RUNNING TIME The sample problem included in the code package required about 15 minutes CPU time for the steady state calculation and about 34 minutes for the 1-set transient calculation by HITAC M-200H with integrated array processor (IAP)

8. COMPUTERHARDWARE REQUIREMENTS IBIS has been implemented on the HITAC M-200H computer at the computex centre, University of Tokyo. The core requirement for the calculation of the sample problem that the number of diagonal sub-assemblies of the core hexagon is 33., is 6500KB. Maximum number of auxiliary storage requirements, in addition to the standard input output devices, are 29 devices and minimum size of them are 21000KB. COMPUTERSOFTWARE REQUIREMENTS a 9. The IBIS code is written in FORTRAN 77 (fixed style). The subroutine CLOCK is called to sample CPU time, which should be substituted for an appropriate system subroutine in another system. The auxiliary routine PAINTV is written in FORTRAN 77 (free style). utilizes some subroutine of the SCD graphics system offered by National Center for Atomos- pheric Research, USA

10. REFERENCES 1. M. Konomura, et al., "IBIS: Three Dimensional Nuclear Reactor kinetics Code (version I)", UTNL-R-0153, Nuclear Engineering Research Laboratory, University of Tokyo, (1983). 2. i. Hasegawa, et al., "JAERI-fast 70 group Structure Constants Utility Programme System : J'-FAST-70U", JAERI-M-5381, (1973). 3. D. A. Meneley, et al., "Fast-Reactor Kinetics - The QXl Code", ANL-7769, (1971). 4. T. B. Fowler, et al., "Nuclear Reactor Core Analysis Code : CITATION", ORNL-TM-2496, Rev. 2, (1969). 5. T. Suzuki, "Development Study on Computer Program HONEYCOMBfor Analysing Detailed Nuclear Characteristics of Fast Breeder Reactor Core", JAERI-M-6677 (In Japanese), (1976). 6. J. C. Carter, et al., "SASlA, A Computer Code for the Analysis of Fast-Reactor Power and Flow Transients", ANL-7607, (1970). 7. McArthur, G. R. ed., "An Introduction to the SCD Graphics System", NCAR-TN/16l+lA, (1981). "The System Plot Package", NCAR-TN/162+lA, (1981). "The SCD Graphics Utilities", NCAR-TN/166+1A, (1981). 8. M. Konomura et al., "Development of three dimensional space dependent kinetics code, IBIS and analysis of transient behavior of homogeneous and hetergeneous LMFBR cores" submitted to J. Nucl. Sci. Technol. 9. N. Tada and Y. Oka et al., "Three dimensional kinetics analysis of large LMFBR cores with thermal hydraulic feedback" presented atANS Topical Meeting on Reactor Physics and Shielding, September 17-19, 1984, Chicago.

COBTEblTS OF PROGW PACEAGE 1. IBIS.FORT F&RAN source of the IBIS code 2. IBIS.CNTL JCL data for the IBIS code 3. INPUT.OATA Input data for the sample problem 4. RESTART-DATA Input data for the restart run 5. OUTPUT.OATA SYSPRINT output for the sample problem 6. FLUX-DATA Output data of neutron flux (unit 16) 7. TEMPERAT.OATA Output data of material temperature (unit 17) 8. PAINTV.FORT FORTRAN source of the PAINTV routine 9. PAINTV.CNTL JCL data for the PAINTV routine 10. PAINTV.DATA output data for the PAINTV routine, which will be processed to draw some contour maps in use of VERSATEC elec- trostatic plotter