Int. J. Nuclear Energy Science and Technology, Vol. X, No. Y, XXXX
Validation of 3D kinetics code ‘TRIKIN’ using OECD PWR core transient benchmark R.P. Jain and K. Obaidurrahman* Atomic Energy Regulatory Board, Anushaktinagar, Niyamak Bhavan, Mumbai – 400094, India Email:
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[email protected] *Corresponding author Abstract: A space-time kinetics code, ‘TRIKIN’, was developed and validated to analyse vast array of transient problem involving reactivity and power distribution anomalies in VVER reactors. Neutronics model of TRIKIN is based on centre mesh finite difference approach for solving space- and timedependent neutron flux in a 3D core whereas thermal hydraulics model is based on fuel pin simulation and employs a semi-implicit scheme for numerical solution. The code was validated against a series of rod ejection accidents with different levels of reactivity feedback. With likely induction of square lattice Pressurised Water Reactors (PWRs) in India, capabilities of TRIKIN code have been extended to analyse space-time kinetics related problems in this geometry. Newly added features of TRIKIN have been validated against an NEA rod withdrawal accident benchmark problem at Hot Zero Power (HZP) state. It has been demonstrated that TRIKIN results are in agreement with benchmark results. Keywords: TRIKIN; space-time kinetics; reactor kinetics; rod withdrawal accident; reactivity initiated transients. Reference to this paper should be made as follows: Jain, R.P. and Obaidurrahman, K. (XXXX) ‘Validation of 3D kinetics code ‘TRIKIN’ using OECD PWR core transient benchmark’, Int. J. Nuclear Energy Science and Technology, Vol. X, No. Y, pp.xxx–xxx. Biographical notes: R.P. Jain, a science post graduate, has a long working experience with Bhabha Atomic Research Centre (BARC), Mumbai, India spanning over four decades. During his career at BARC, he has been actively involved in development of many computer codes for lattice and core physics analysis of Indian reactors. Since 2007, after retiring from BARC, he has worked as expert consultant for IIT Bombay and Atomic Energy Regulatory Board, Mumbai to develop space-time kinetics code for large LWRs. He has notable contribution in the development of present AERB space-time kinetics code TRIKIN. K. Obaidurrahman, a doctorate in Mechanical Engineering from IIT Bombay, Mumbai, India, is working with Atomic Energy Regulatory Board (AERB), Mumbai, India since 2006. He is working in the area core dynamics studies in large LWRs. He has been extensively involved in development and validation of AERB space-time kinetics code TRIKIN since its inception. He has developed a novel scheme to couple core 3D kinetics and thermal hydraulics computations. His area of research is core dynamics, spatial instability and control aspects of new generation reactors.
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R.P. Jain and K. Obaidurrahman
1
Introduction
In depth safety evaluation of nuclear reactors has led to the development of a large number of computer codes in the area of core physics, neutron kinetics, thermal hydraulics and structural dynamics disciplines. Conventionally, these physical phenomena were simulated independently without any common connections. Such simulations led significant opaqueness in understanding of many problems of reactor dynamics which involve strong interaction between these physics disciplines. In the new era of strong computing resources, addressing interconnection between the different physical disciplines has become quite feasible. Advanced methods of reactor safety analysis emphasise on multiphysics interactions between two or more different physics disciplines. This provides a basis to have better insights into reactor dynamics studies. Simulation of neutron kinetics using coupled 3D space-time kinetics and core thermal hydraulics is an important step in this direction for best estimate analysis of large LWRs particularly for the analysis of transients involving reactivity and power distribution anomalies. Consistent with this objective, many computer codes like DYN3D, PARCS, NEM etc. have been developed or upgraded during past decade. On the same line a new computer code, TRIKIN (Obaidurrahman et al., 2010) was developed for spatial kinetics studies of VVER reactors. The code has been validated against a series of AER benchmark problems (Kereszturi and Telbisz, 1992; Grundmann and Rodhe, 1993; Kyrki-Rajamäki and Kaloinen, 1994) in VVER reactors. Code was subsequently used (Obaidurrahman and Doshi, 2011) for spatial instability studies in few advanced Pressurised Water Reactors (PWRs). With inevitable expansion of nuclear power programme in India, western type large sized PWRs are likely to be introduced shortly. This necessitates an identical coupled 3D kinetics expertise for square lattice PWR. Consistent with this objective capabilities of TRIKIN have been extended to analyse spatial kinetics related problems in square lattice geometry. Neutron flux spatial calculations are based on centre mesh finite difference approach. Core thermal hydraulics is based on fuel pin simulation model. Newly developed square geometry space-time model has been validated against NEA/OECD PWR core transient benchmark problems (Fraikin and Finnemann, 1993) which involve uncontrolled withdrawal of control rod bank in Hot Zero Power (HZP) state. These benchmarks have been analysed by many researchers (Asaka et al., 2000; Ziabletsev and Ivanov, 2000; Aoki et al., 2007) in order to validate their code systems. In the present paper, TRIKIN results of the above said benchmark problem have been compared with 3D kinetics code, PANTHER (Kuijper, 1995; Fraikin, 1997). In this paper Section 2 gives a brief description of the features of spatial kinetics code ‘TRIKIN’. The NEA/OECD PWR core transient benchmark problem specifications are described in Section 3. Specific TRIKIN model used in simulation of NEA/OECD PWR core and comparison of steady state benchmark results with reference solutions are presented in Section 4. Results of the transient part of the benchmark problems are compared and discussed in Section 5.
2
Spatial kinetics code ‘TRIKIN’
TRIKIN is a 3D space-time kinetics code with thermal hydraulics feedback. The spaceand time-dependent group fluxes are factored, adopting Improved Quasi-Static (IQS) approximation, into a space-dependent shape functions and time-dependent amplitude
Validation of 3D kinetics code ‘TRIKIN’ function. Shape function calculations are done by solving multi-group diffusion equation using centre mesh finite difference method (Jagannathan et al., 2006). Initially the programme was developed and validated for hexagonal/triangular geometry. It has now been modified to handle square geometry. Solution procedure involves finer subdivision of fuel assemblies. Neutron flux is assumed to be uniform in the every fine mesh. During space discretisation, radial pitch of hexagons/triangles/squares is required to be same for fuel as well as non-fuel regions. Figure 1
Computational flow chart of space –time kinetics code TRIKIN Start Read all input data Steady state NEUTRONICS Calculations Make reactor critical, Calculate initial reactivity, precursor concentration and point kinetics parameters Steady state thermal hydraulic Calculations Amplitude =1.0, Time = 0
Time=time + dt
New group cross sections due to change in rod position/boron level /feedback parameters Update point kinetics parameters Point Kinetics Solution between time ti-1 and ti at micro intervals
Update precursor concentrations Thermal Feedbacks
New Shape calculations
No
Shape converged?
Yes Transient thermal hydraulic Calculations between time ti-1 and ti
Evaluate Safety Parameters like MDNBR, Fuel enthalpy
Print Results
Yes Stop
Time ≥ Total time?
No
R.P. Jain and K. Obaidurrahman A symmetric part of the core can be simulated using reflective or rotational symmetry. Provision has been made available to eliminate bulky reflector regions from the computational domain by using an appropriate albedo boundary condition. Kinetics equations are solved by a modified Generalised Runge-Kutta (GRK) method (Sanchez, 1989) which is easy to implement algorithm and provides results with sufficient accuracy for most of the kinetics applications. The method allows modification of finer time step size while solving point kinetics equations. The core thermal hydraulics is modelled by 1D fuel pin simulation approach in which radial fuel heat conduction and axial coolant transport equations are solved. Coolant transport mass, momentum and energy conservation equations are solved using semi-implicit computational schemes. An approximate model is available for rapid evaluation of void fraction under phase change situation without solving detailed two phase equations. The coolant flow is modelled by defining a number of (user defined) T-H channels within the core and some hot channels with a given power peaking factors. There is no limit on number of T-H channels. Number of thermal hydraulic nodes in coolant equations can be different from number of neutronic nodes. The code has a provision to employ a power weighted scheme to calculate feedback parameters to all fuel assemblies belonging to a particular T-H channel (Obaidurrahman, 2011). Computational scheme used in TRIKIN are shown in Figure 1.
3
NEA/OECD 3D PWR core benchmarks
TRIKIN has been previously validated against as series of AER benchmarks and it was found that TRIKIN results show excellent match with other international code systems. Newly added capability of TRIKIN to analyse spatial kinetics problems of square geometry PWRs has been validated against an NEA/OECD PWR benchmark problem. The problem is analysis of uncontrolled withdrawal of control rods accident at zero power. Details and specification of the benchmark are given in the following sections.
3.1 Core geometry The radial and axial geometry of the reactor core (1/8th part) is shown in Figure 2. Radially, the core is divided into 157 cells, 21.606 21.606 cm, each corresponding to one fuel assembly (FA), and 64 reflector cells (shaded area) of the same size. Axially the reactor core is divided into four sections, bottom and top reflectors of thickness 30 cm each and the active core sections of thickness 7.7 cm and 359.6 cm, respectively. Radial arrangement of control assemblies (CAs) is also shown in Figure 2. Each CA comprises of absorber length of 362.159 cm and a header section of unspecified length. The axial layout in the presence and absence of CA is also depicted in Figure 2. There are total of 48 CAs in the core which are grouped into five banks named as A, B, C, D and S. Required material composition maps, macroscopic cross sections and their derivative with respect to feedback parameters, boron and various type of CAs, kinetics parameters and thermal hydraulics data have been provided in the benchmark specifications (Fraikin and Finnemann, 1993). Important characteristic data about the PWR core, being analysed in this benchmark, are reproduced in Table 1.
Validation of 3D kinetics code ‘TRIKIN’ Figure 2
NEA/OECD PWR benchmark – radial and axial core geometry and CA banks
Table 1
General core data of NEA/OECD PWR benchmark
Nominal core thermal power Number of fuel assemblies (FAs)
2775 MW 157
Active core height
367.3 cm
Fuel assembly pitch
21.606 cm
Geometry:
17 17
Number of fuel rods per FA
264
Number of guide tubes per FA
25
Fuel rod pitch
12.655 mm
Pellet diameter
8.239 mm
Clad diameter(outside)
9.517 mm
Clad wall thickness
0.571 mm
Coolant inlet temperature Core pressure Net mass flow through core (constant)
286°C 155 Bar 12893 kg/s
3.2 Problem description Benchmark is a transient problem, which is initiated by uncontrolled withdrawal of a bank(s) of control assemblies (CAs) from an initial core at HZP state. Initial power of the reactor is given as 0.2775 mW. The moderator inlet conditions viz. mass flow, pressure, temperature and boron concentration are held constant during the transients. CA banks move up with a constant speed of 72 steps per minute (1.94 cm/s) during withdrawal. Scram signal is generated when the fission power reaches 35% of nominal reactor power.
R.P. Jain and K. Obaidurrahman CAs start moving down after a delay of 0.6 s. All CAs participate in scram with a constant speed of 228 steps in 2.2 s. Transients have to be analysed till 10 s after calculated initiation of the scram. There are four combinations of CAs withdrawn as described below. Case A: Initial CA positions are – initially banks A, B, C and S fully withdrawn and bank D fully inserted. Transient is initiated by withdrawing CA bank D. Case B: Initial CA positions are – initially banks A, B, C and D fully inserted and bank S fully withdrawn. Transient is initiated by withdrawing CA banks B and C. Case C: Case C is identical to case B, except that the heat transfer coefficient between cladding and water is set to a constant value (30,000 W/m2/C). Case D: initial CA positions are same as in case B. Transient is initiated by withdrawing peripheral CA banks A and B.
4
TRIKIN model for NEA/OECD PWR core benchmarks
All the cases mentioned above have 1/8th core symmetry therefore TRIKIN calculations have been performed using 1/8th symmetric part of the PWR core as shown in Figure 2. TRIKIN modules handling, assignment of macroscopic cross section and their derivatives, thermo-mechanical properties of fuel, clad and air gap and kinetics parameters were modified to suit the requirement of benchmark specifications. Effect of control absorber/header section in the top reflector meshes has been simulated. However, change in macroscopic fission and nu-fission (f and f) cross section was set to 0 in reflector region. Axially 60 meshes have been considered, six meshes (6 5 cm) each in bottom and top reflector regions and 48 (1 7.7 cm + 47 7.651 cm) in active core. It has been observed that for reasonably accurate spatial kinetic calculations using FDM scheme a subdivision of 24 meshes per FA is adequate enough (Obaidurrahman et al., 2010). Based on this experience, 25 radial meshes per fuel/reflector cell have been considered for analysis present benchmark. Heat conduction in fuel has been simulated by taking eight meshes in fuel pellet and two meshes in clad. Axially, one thermal hydraulics node per neutronic node has been considered for solving heat conduction and coolant equations for each T-H channel. Only one average T-H channel has been considered in these simulations. The code TRIKIN has no built in procedure for fixing the macro-time steps for flux shape calculations. User defined macro-time steps are used. However within a single macro-time step, the kinetics equations are solved by taking finer steps which are calculated using an adaptive time step control recipe, which works reasonably well for most of the applications. The finer time step of size prompt neutron life time is taken to start with and subsequently time steps are evaluated by the programme. A user defined time step ( 0.01 s) is used for solving time-dependent heat conduction and thermal hydraulics equations.
4.1 Comparison of steady state results Initial state for cases B/C/D is identical, steady state critical boron concentration (CB) and relative power factors at selected locations only for cases A and B are presented here.
Validation of 3D kinetics code ‘TRIKIN’ TRIKIN results along with finer results from PANTHER code are compared in Table 2. It can be observed from the table that CB values calculated by TRIKIN are higher than the reference (PANTHER) values. The reactivity worth of CAs is lower by 1.9% for cases A and B and is higher by 1.7% for case D. Relative power peak factors compare within 1% with reference results of the code PANTHER. Detailed radial power distribution for case A is compared in Figure 3. Though the relative power peak factors are within 1% in core region, but they deviate up to 3.5% in reflector regions. Steady state solutions of the two problems were obtained with relatively finer space grid to understand the effect of finer mesh size on the critical boron concentration and rod worths. The CB with finer division per cell is plotted in Figure 4. It is observed that even with 225 meshes per cell, the CB predicted by TRIKIN is higher by 5 ppm compared to PANTHER value which is clearly due to finite difference method used in TRIKIN. Figure 3
Comparison of relative radial power distribution at initial state – case A
Figure 4
Critical boron concentration as a function of finer divisions of cells – case A (see online version for colours)
R.P. Jain and K. Obaidurrahman Table 2
Comparison of results – steady state conditions
Item of comparison
Case – A
Case – B/C/D
TRIKIN
PANTHER
TRIKIN
PANTHER
Critical boron concentration(ppm)
1291.1
1262.7
818.4
793.6
Moving CA(s) and worth of full length CAs (mk)
D 13.73
D 14.00
B and C 37.30 A and B 32.55
B and C 38.00 A and B 32.00
Axial power peak factor
1.527
1.513
1.520
1.507
Radial power peak factor
1.234
1.242
1.892
1.912
Overall 3D power peak factor
1.871
1.880
2.881
2.886
Radial peak factor at z = 108.7 cm
1.525
1.542
2.358
2.377
Radial peak factor at z = 318.7 cm
0.803
0.811
1.238
1.245
5
Comparison of results of the transients and summary
Reactivity as a function of transient time for cases A, B and D are plotted in Figure 5. Fission power is compared in Figures 6–8 for the three cases. Results of case C were found to be identical with that of case B and they are not presented here. Some important parameters at the time of maximum fission power are summarised in Table 3. Few interesting observations of TRIKIN results are described in the following sections. Figure 5
Reactivity as a function of time for PWR benchmarks – TRIKIN results (see online version for colours)
Validation of 3D kinetics code ‘TRIKIN’ Table 3
Results of transients at the time of maximum fission power
Item of comparison
Case – A
Case – B
Case – D
TRIKIN
PANTHER
TRIKIN
PANTHER
TRIKIN
PANTHER
Time of maximum fission power(s)
80.73
82.14
35.07
34.30
39.23
39.40
Maximum fission power (fraction)
0.364
0.3556
1.20
1.348
0.912
0.9685
Core average coolant exit temperature(°C)
295.0
295.3
294.4
290.5
291.6
290.0
Core average Doppler temperature(°C)
348.5
358.7
323.6
315.2
318.4
312.6
Axial power peak
1.966
1.985
2.580
2.437
2.533
2.325
Radial power peak
1.183
1.195
1.724
1.751
1.692
1.715
Overall 3D power peak
2.339
2.395
4.174
3.967
3.836
3.718
Radial power peak at z = 108.7 cm
2.339
2.395
3.029
3.053
3.100
3.120
Radial power peak at z = 318.7 cm
0.292
0.272
0.299
0.322
0.305
0.330
5.1 Case A It can be seen from Figure 5 that reactivity insertion rate for case A is much slower as compared to other cases. Rise in reactivity is arrested by feedback effects and it starts decreasing. Reactivity remains slightly below prompt critical throughout the transient. Fission power rise for case A (Figure 6) follows the reactivity to start with. When reactivity starts decreasing the power rise is slowed down due to feedbacks. Fission power reaches a maximum in 0.6 s (till CA continues to move out) after generation of scram signal. From Figure 6 it can be seen that compared to PANTHER results time of initial power surge in TRIKIN comes about 2 s later and power rise is smaller. Until this time no significant feedback comes into play. It is felt this delay in power surge is due to under prediction of CA worth by about 2% (static). Beyond this time rise in fission power for TRIKIN is faster because the fuel temperatures estimated in TRIKIN are lower (by 3%) compared to PANTHER values. It can be seen from Table 3 that core average Doppler temperature at the time of maximum fission power predicted by TRIKIN is lower by 10°C. Maximum fission power reached in the transient as calculated by TRIKIN is higher by 2.4% and coolant temperature at this time is lower by 0.3°C. Deviation in temperatures can be attributed to the difference in engineering correlations and heat transfer model used in different codes. This deviation has also been observed significantly while comparing results of same benchmark with other code like PANBOX, QUABOX, etc. (Fraikin, 1997). In all if benchmark strictly suggests use of specific engineering correlations, then such minor discrepancies could be avoided. The fall in fission power when all CAs start moving down due to scram is identical to PANTHER solutions. As for relative power fractions at the time of maximum fission power, TRIKIN values in general are in agreement with PANTHER values.
R.P. Jain and K. Obaidurrahman Figure 6
Comparison of relative fission power for PWR benchmark case A (see online version for colours)
5.2 Case B and D It can be seen from Figure 5 that reactivity insertion rate for cases B and D, where two CA banks are moving, is very fast. As a result fission power increase in cases B and D is also very fast. Reactivity goes beyond prompt critical level and fission power (Figures 7 and 8) increases much beyond scram level in the next time step immediately after generation of scram signal. Feedback effect plays very insignificant role till the sudden power surge as no significant rise in temperatures has occurred. It can be seen from Table 3 that core average Doppler temperature at the time of maximum fission power predicted by TRIKIN is higher by about 6–8°C. This higher temperature leads to better negative reactivity feedback and results in a lower peak fission power, by 11% and 6% for the two cases. Due to small under-prediction of reactivity in case B results in a late power peak in TRIKIN. Reverse is observed in case D where a minor over estimation of reactivity results in an earlier power peak. This is an interesting observation of reactor kinetics problems near prompt criticality. This difference has also been observed in other solutions also (Fraikin and Finnemann, 1993). Exit coolant temperatures at the time of power peak are also higher compared to PANTHER values. The fall in relative fission power after scram is more in TRIKIN simulation (below 0.2) compared to PANTHER results (close to 0.5). This deviation can be attributed to the time step size and corresponding reactivity values after scram. As for relative power fractions at the time of maximum fission power, TRIKIN values in general are in good agreement with PANTHER values.
5.3 Summary Capabilities of TRIKIN space-time kinetics code have been successfully extended for the analysis of square lattice PWRs. Square lattice space-time kinetics model of TRIKIN has been validated by analysing a well-known international core transient benchmarks.
Validation of 3D kinetics code ‘TRIKIN’ Results have been compared with PANTHER reference solutions. It has been observed that the steady state and transient results of TRIKIN code are in agreement with reference results. This additional validation of TRIKIN coupled space-time model has provided significant confidence in space-time kinetics modelling of square lattice PWRs. The work can be extended to the coupling of present TRIKIN core dynamics code with any system thermal hydraulics code for the best estimate plant dynamic analysis. Figure 7
Comparison of relative fission power for PWR benchmark case B (see online version for colours)
Figure 8
Comparison of relative fission power for PWR benchmark case D (see online version for colours)
R.P. Jain and K. Obaidurrahman
Acknowledgements Authors express their sincere gratitude to Dr. V. Jagannathan, BARC and Shri A. Ramkrishnan, AERB, for many useful discussions. Support and motivation provided by Shri R. Bhattacharya director ITSD, AERB, to carry out this activity is gratefully acknowledged.
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