COUPLED BWR CALCULATIONS with the NUMERICAL NUCLEAR REACTOR SOFTWARE SYSTEM

Transcription

1 Supercomputing in Nuclear Applications (M&C + SNA 2007) Monterey, California, April 15-19, 2007, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2007) COUPLED BWR CALCULATIONS with the NUMERICAL NUCLEAR REACTOR SOFTWARE SYSTEM T. Sofu, J. W. Thomas, D. P. Weber, and W.D. Pointer Argonne National Laboratory 9700 S. Cass Ave, Argonne, Illinois tsofu@anl.gov; jthomas@anl.gov; dpweber@anl.gov; dpointer@anl.gov T. J. Downar Department of Nuclear Engineering Purdue University 400 Central Drive West Lafayette, IN downar@ecn.purdue.edu ABSTRACT The Numerical Nuclear Reactor (NNR) is a software suite for integrated high-fidelity reactor core simulations including neutronic and thermal-hydraulic feedback. Using solution modules with formulations to reflect the multi-dimensional nature of the system, NNR offers a comprehensive core modeling capability with pin-by-pin representation of fuel assemblies and coolant channels. Originally developed for pressurized water reactors, the NNR analysis capabilities have recently been extended for boiling water reactor (BWR) applications as part of EPRI Fuel Reliability Program. The neutronics methodology is extended to treat non-periodic structure of BWR fuel assemblies, and a new Eulerian two-phase CFD boiling heat transfer model has been integrated with the software system. This paper summarizes the experience with, and results of, the first-of-akind coupled calculations as demonstration of a fully-integrated, high-fidelity simulation capability for assessment of margin to crud-induced failure from fuel-duty perspective. Key Words: BWR simulation, coupled calculations, Eulerian boiling model for CFD. 1. INTRODUCTION The software system known as Numerical Nuclear Reactor (NNR) provides the first example of next-generation simulation tools for design and analysis of a light-water reactor (LWR) core based on high-fidelity, first-principles based calculations.[1,2,3] NNR is capable of performing integrated neutronic and thermal-hydraulic analysis for a reactor core at an unprecedented scale and the level of fidelity. With NNR, a whole-core LWR simulation with pin-by-pin representation of the fuel assemblies is feasible using sub-pin level thermal feedback and explicit representation of individual coolant channels based on CFD techniques. Initial development of the software system was performed through DOE s International Nuclear Energy Research Initiative (INERI) via bilateral agreement between the U.S. and the Republic of Corresponding author

2 T. Sofu et al. Korea. As a product of collaborations between ANL, KAERI, Purdue University, and Seoul National University, a new direct whole-core transport code, DeCART, was developed based on method of characteristics to generate sub-pin level flux distributions,[4] and the computational fluid dynamics (CFD) methods were used for flow and heat transfer in the core.[5] Unlike the conventional multi-step approach which involves geometric homogenizations and few-group condensation for a nodal diffusion method, the NNR employs a one-step bottom-up approach in which the neutronics module performs an efficient multigroup whole core neutron transport simulation directly with explicit geometric representation of the fuel pins. DeCART employs a 3-D coarse mesh finite difference approach for the global flux solution with higher-order 2-D solutions provided by the method of characteristics applied to several (10-30) axial planes. The analysis capabilities of NNR has recently been extended for boiling water reactor (BWR) applications under a jointly funded DOE and EPRI program on fuel reliability.[6] The methodology of the neutronics module, DeCART, is extended to treat non-periodic structure of BWR fuel assemblies [7]. The NNR approach is based on the use of computational fluid dynamics techniques for simulation of flow and heat transfer in fuel rod bundle configurations. As a more mechanistic approach with reduced reliance on empiricism, CFD offers a capability to capture important feedback effects between the first-principles based models on a consistent scale. However, development of an accurate two-phase boiling model that is valid under the various boiling regimes typically found in BWRs is an active research area. Starting with the standard Eulerian multiphase flow capability of STAR-CD[8] based on bubbly flow topology (which is expected to be suitable mostly for the subcooled part of a coolant channel), the boiling model development roadmap included a second generation extended boiling framework to simulate the annular mist flow and transition topologies to treat high void fraction flow regimes. Continued validation of the extended CFD based boiling models against prototypic data, including experiments and other computational methods, is an ongoing effort. [9,10] 2. COUPLED CALCULATIONS with EULERIAN TWO-PHASE BOILING MODEL The potential of new NNR analysis capabilities has so far been demonstrated for a 3 3 multi-pin problem and an Atrium-10-like BWR fuel assembly model Results for a 3 3 Pin Model The initial demonstration calculations have been performed for a symmetric arrangement of 3 3 multi-pin configuration with 5 UO 2 pins, 3 mixed oxide (MOX) pins, and a central guide tube shown in Figure 1. The neutronics model includes a total of 11,000 flat-source regions; rays are spaced 0.02 cm apart with 8 azimuthal and 4 polar angles per octant. The CFD model includes 150,000 computational cells and models the water inside the guide tube as a non-convective region with no flow. The geometry is similar to that of a PWR, except that the fuel is shortened to 2 m. In addition to illustrating the capabilities and convergence characteristics of the coupled neutronic and thermal-hydraulic analyses with two-phase boiling, this model provides an assessment of impact of subcooled nucleate boiling on local power density and pin temperatures under PWR conditions. 2/15

3 Coupled BWR Calculations with the Numerical Nuclear Reactor (NNR) Figure 1. DeCART grid (left) and the CFD mesh (right) for 3 3 multi-pin model. Three pins on the north-east corner are MOX fuel pins. Both single- and two-phase calculations have been performed for this model. The NNR calculations are generally completed in two stages: (1) standalone CFD solutions with an assumed pin power distribution, and (2) coupled calculations using thermal and density feedback from CFD module. Table I summarizes the computational time required for the single phase and two phase cases of the initial standalone CFD solutions on four ANL jazz [11] cluster compute nodes. Table I. Computational requirements with the 3 3 multi-pin model for standalone CFD solutions to initialize coupled calculations. Standalone CFD for 3x3 multi-pin Number of Memory/ Node Elapsed time per iteration Total time model on two processors iterations (MB) (sec) (min) Single-phase Two-phase In this particular case, the two phase calculation converged fast than the single phase calculation. This appears to be an artifact of the small size of the model and the relatively low void; the twophase flow calculations for BWR assemblies converge far more slowly. The two-phase calculation required nearly 40% more time per iteration than the single phase case and requires 55% more memory. Starting from these standalone CFD solutions, coupled calculations were performed for both the single- and two-phase cases. These coupled calculations were performed using four compute nodes for CFD, four compute nodes for neutronics, and one compute node for the interface module. Each DeCART node required 190 MB of memory. STAR-CD required 100 MB for the single-phase calculation and 268 MB for the two-phase calculation. Table II summarizes the computation time required with the 3 3 multi-pin model for coupled calculations. DeCART 3/15

4 T. Sofu et al. obtains updated temperature and density distributions each time the largest STAR-CD residual is reduced one order of magnitude. Then DeCART performs 4 MOC transport sweeps and transfers the new power distribution to STAR-CD. Thus, the number of DeCART transport sweeps is 4 times the number of data exchanges printed in Table II. These data exchanges between DeCART and STAR-CD continue until the convergence criteria in each code are satisfied, and until the power distribution obtained from DeCART stops changing significantly from consecutive data exchanges. The latter criterion on the power distribution was the last to be satisfied in both calculations. Table II. Computational requirements for 3 3 multi-pin model for coupled calculations. Coupled calculations for 3x3 multipin STAR-CD Data Elapsed time (minutes) model on eight processors Iterations Exchanges CFD Total Single-phase Two-phase In the case of single-phase calculations, the computational burden for the coupled phase is 40% more expensive than that of the STAR-CD initialization calculation. The coupled portion of the two-phase calculation is nearly 5 times more expensive than the initialization process, and nearly 4 times more expensive than the single-phase case. There are two reasons for this. First, two more data exchanges are required, which indicates tighter coupling between the STAR-CD and DeCART modules due to void reactivity feedback. The global criterion on power distribution is plotted in Figure 2. Note that this figure shows additional data exchanges that were performed beyond the necessary convergence criterion. Second, significantly more STAR-CD iterations were required between data exchanges in the two-phase case. In both the single- and two-phase cases, the residual associated with the pressure Poisson equation was the last to reach the criterion of This residual is plotted for both cases in Figure 2, and the iterations where a data exchange occurred are marked with data points. Often, particularly in the two-phase case, the updated DeCART power distribution causes a spike in the residual. In the single-phase case, a data exchange occurs at iteration 40 where the pressure residual is below 10-3, and another occurs at iteration 223 where the residual is below In the two-phase case, the corresponding data exchanges occur 355 iterations apart, at iterations 252 and 607, indicating that this equation is somewhat less stable in the two-phase case. It should be noted, however, that the default STAR-CD convergence criterion is 10-3, which is attained much faster in both cases. In practice, this tightened criterion helps achieve a tight convergence on the change in power distribution, but these criteria may be relaxed for practical applications. With 1 m/s nominal flow rate and 543 K inlet temperature, the expected exit temperature for 200 W/cm 3 average power density is only 595 K, measurably below the 610 K saturation temperature at 15 MPa. Although this translates to zero exit quality under equilibrium conditions, the coupled model predicts void fractions as high as 12% at 2/3 the core height near the MOX pin surfaces. While most of the bubbles condense in the surrounding subcooled liquid, some are rapidly entrained through the core with the bulk flow and reach the outlet plane at the top of the fuel rods as can be seen in Figure 3. Note the difference in scales in this figure. 4/15

5 Coupled BWR Calculations with the Numerical Nuclear Reactor (NNR) Figure 2. Relative change in power density distribution during coupled calculations (top) and evolution of Pressure Poisson equation residual during coupled calculations (bottom). Figure 3. Contour plots for void fraction at 2/3 core height (left) and at the outlet (right). 5/15

6 T. Sofu et al. The results indicate that the presence of localized subcooled boiling has a noticeable influence on the flow field and the calculated temperatures. A comparison of the liquid-phase velocity magnitude for the single-phase and two-phase solutions is shown in Figure 4. Figure 4. Comparison of liquid velocity (m/s) for single-phase (left) and two-phase (right) solutions on a horizontal plane at 2/3 core height. Because of the void reactivity feedback and improved heat transfer due to higher flow rate and subcooled boiling around the MOX pins, the power density in upper half of the assembly is somewhat suppressed in the two-phase case. As a result, the fuel temperatures for single and two-phase solutions are measurably different. To quantify this difference, a cell-by-cell comparison of the fuel temperatures for single-phase and two-phase solutions at 2/3 core height is provided in Figure 5. The difference, as high as 25 K near the fuel-cladding interface of the MOX pins, highlights the importance of proper treatment of azimuthal variations in power density combined with localized subcooled boiling. Figure 5. Difference between single- and two-phase solutions for fuel temperatures (K) at 2/3 core height. 6/15

7 Coupled BWR Calculations with the Numerical Nuclear Reactor (NNR) 2.2. Results for an Assembly Model The coupled calculations are also performed for an Atrium-10 type fuel assembly as shown in Figure 6. The 2-D configuration is obtained from the uranium-fueled option in a BWR MOX specification [12]. This model was simply extruded axially to generate this 3-D model. The model contains 91 fuel pins with an off-center coolant channel in a 10x10 configuration, as well as the canister that envelopes the bundle. Eight of fuel pins are partial-length rods; the active fuel has a height that is 60% of that of the full-length rods and occupies the lower portion of the lattice. Different colored pins in Figure 6 indicate different fuel enrichments. The other model details include 2 m/s nominal flow rate at the inlet with 552K inlet temperature (saturation temperature is 564K), and an assembly power of 5.75 MW. The BWR assembly model includes 170,000 DeCART regions and 3.2 million CFD cells. The Atrium10 assembly problem presented new challenges for coupled DeCART/STAR-CD calculations. In past models, such as the 3x3 pin model, the STAR-CD mesh was required to be a subset of the DeCART spatial mesh such that each CFD cell falls within a DeCART region. In the Atrium10 assembly model, some of the CFD cells are shared by two DeCART regions as seen in Figure 7. To accommodate such situations, the coupling software was extended to permit CFD cells to be shared between two adjacent DeCART regions, permitting a many to many mapping for certain special cases The second challenge is the greater computational burden associated with the CFD solution of the two-fluid equations at high void fractions. The convergence of two-phase models at high void is much slower than at low voids. In the early part of the coupled calculations as many as 2000 iterations are required to establish the initial void profile in each coolant channel, and near the end perhaps iterations are required per data exchange cycle. Such expensive calculations motivate the development of a more flexible file input/output based coupling, rather than the socket transfer based coupling performed in the past. Having the temperature, density, and power distributions available in files permits the user to monitor the STAR-CD calculation and invoke a data exchange manually. Because the computational burden associated with DeCART is significantly smaller for assembly size problems, a complete DeCART solution is performed at each data exchange cycle rather than performing only a few MOC sweeps as was the case for the 3x3 model. During the coupled calculations, intermediate DeCART calculations were performed without interrupting STAR-CD solutions to evaluate the change in k eff and power distribution as an indication of whether or not the CFD solution is changing in a way that is important to the neutronics field. As an example, the eigenvalue and power distributions are compared at each intermediate step between the 2971 st and 3321 st iterations in Table III. The reactivity difference between iterations 3271 and 3321 was only 5 pcm, the maximum change in power distribution was less than 0.1% of the average power density, and the RMS error was less than 1%. Thus updating the power distribution in the CFD calculation is reasonable at this point, and most likely significantly sooner than this is permissible. 7/15

8 T. Sofu et al. Figure 6. Grid structure of the fuel assembly for the DeCART (top) and STAR-CD (bottom) models. 8/15

9 Coupled BWR Calculations with the Numerical Nuclear Reactor (NNR) Figure 7. STAR-CD (black) and DeCART (red) spatial mesh for a typical fuel pin, with shared cells highlighted in green. Table III. Comparisons of intermediate DeCART calculations during the second data exchange. Max Q / ρ Max Q Q avg RMS Iteration (pcm) (W/cm 3 ) (%) (%) k eff The global convergence criterion was similar to the criterion for updating the power distribution, i.e. the power distribution and k eff were compared at consecutive data exchange cycles. These parameters are given in Table IV for each of the nine DeCART solutions during the coupled Atrium 10 calculation. As can be seen from this table, the initial guess for the thermofluid field was quite far from the converged solution, as indicated by the 1700 pcm correction at the second data exchange. The evolution of the pressure residual in the CFD calculation, again the slowest to converge, is given in Figure 8. The figure shows sudden increases in the pressure residual whenever a DeCART update occurs. Note that some data was lost between data exchanges, thus there are gaps in the figure. 9/15

10 T. Sofu et al. Table IV. Global convergence of neutronics field in Atrium10 calculations. Max Data Exchange Cycle ρ (pcm) Max Q (W/cm 3 ) Q / Q avg (%) RMS (%) k eff Figure 8. Evolution of Pressure Poisson equation residual during coupled calculations. Detailed distributions of neutron flux and thermofluid properties are available from the coupled DeCART/STAR-CD solution. The void fraction distribution at 5 axial levels is plotted in Figure 9. In the lower portion of the assembly, the void remains near the wall where it is generated. As the flow develops, bubbles move to the center of the flow channels and peak void fractions are located in the center of high-powered channels at the outlet. Sample results for the power density, void fraction, fuel temperature, liquid phase temperature, and velocity magnitudes of both phases are given in Figure 10. The color scales in these figures are based on the global maximum and minimum values. Note that the power is bottom-peaked, such that the average power in the midplane is lower than the peak values. The location of the eleven gadolinium pins is also evident from the power profile, as is the effect of increased moderation along the 10/15

11 Coupled BWR Calculations with the Numerical Nuclear Reactor (NNR) periphery of the assembly and near the off-center water channel. Note that the saturation temperature is 564K, which is dark-orange in the liquid phase temperature plot, and that there is nearly 4K liquid phase superheat in some locations as the liquid droplets get entrained with the saturated steam as the carrying phase. The difference between the liquid and gas phase velocities is on average 2 m/s, and is higher near the center of flow channels. The results of the coupled calculations reveal significant differences in power density for peripheral pins near the assembly can as well as water channels in comparison to the interior fuel pins with identical composition. Furthermore, for those peripheral pins the power density has a strong azimuthal asymmetry with more power generated in part of those pins facing the water channel and assembly can. This is particularly important since it is fairly consistent with the crud formation patterns observed in some BWRs experiencing fuel failures.[13] In addition to the CFD cell-wise quantities shown in Figs 9 and 10, STAR-CD is capable of calculating wall quantities, such as the heat flux at the clad-fluid interface as shown in Figure 11 for a corner pin. The capability to predict such azimuthally asymmetric heat flux and steaming rate distributions on the individual pin surfaces in an assembly is crucial to enhance quantification of margin to crud-induced fuel failure from fuel-duty perspective as part of the EPRI Fuel Reliability Program. 3. CONCLUSIONS The analysis capabilities of NNR software system has recently been extended for boiling water reactor (BWR) applications under a jointly funded DOE and EPRI program on fuel reliability. As a product of collaborations between ANL, Purdue University, and CD-adapco Inc., the methodology of the neutronics module, DeCART, is extended to treat non-periodic structure of BWR fuel assemblies by removing the pin-cell symmetry assumption and introducing an assembly-level modular ray-tracing algorithm. Also, the new Eulerian two-phase boiling model of the thermo-fluid analysis module, STAR-CD, has been integrated with software system. The results initial coupled calculations illustrate the ability of the BWR version of the NNR to produce converged, coupled solutions to predict detailed local results within the context of larger scale coupled calculations. The calculated variations in the pin power density reflect on the coolant and fuel temperature, and the results highlights the importance of modeling geometric inhomogeneities. The verification and benchmarking of the BWR version of the neutronics module, experimental validation of the two-phase flow boiling model, and application of the NNR to address the operational and design issues for BWRs is an ongoing effort. ACKNOWLEDGMENTS This work was completed under the auspices of the U.S. Department of Energy Office of Nuclear Energy as part of the Nuclear Energy Plant Optimization program and the Electric Power Research Institute as part of the Fuel Reliability Program. The submitted manuscript has been created by the University of Chicago as Operator of Argonne National Laboratory ( Argonne ) under contract No. W ENG-38 with the U.S. Department of Energy. 11/15

12 T. Sofu et al. Figure 9. Void fraction at (a) 1/5, (b) 2/5, (c) 3/5, (d) 4/5 core height, and (e) the top of fuel. 12/15

13 Coupled BWR Calculations with the Numerical Nuclear Reactor (NNR) Power Density (W/cm 3 ) Void Fraction Fuel Temperature (K) Liquid Phase Temperature (K) Liquid Phase Velocity Magnitude (m/s) Gas Phase Velocity Magnitude (m/s) Figure 10. Coupled calculation results at the midplane. 13/15

14 T. Sofu et al. Figure 11. Wall heat flux distribution (W/cm 2 ) at the cladding-fluid interface of the pin in the northwest corner of the assembly. REFERENCES 1. D.P. Weber, et al. High Fidelity LWR Analysis with the Numerical Nuclear Reactor, pending publication, Nuclear Science and Engineering (2007). 2. T. Sofu et al., Development of a Comprehensive Modeling Capability Based on Rigorous Treatment of Multi-Physics Phenomena Influencing Reactor Core Design, Proceedings of 2004 International Congress on Advances in Nuclear Power Plants (ICAPP 04), Pittsburgh, Pennsylvania, USA, June (2004). 3. D. P. Weber et al., The Numerical Nuclear Reactor A High Fidelity, Integrated Neutronic, Thermal-Hydraulic and Thermo-Mechanical Code, Proceedings of Intl. Mtg. on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Palais des Papes, Avignon, France, September (2005). 4. H. G.. Joo et al., Methods and Performance of a Three-Dimensional Whole-Core Transport Code DeCART, Proceedings of PHYSOR-2004, Chicago, Illinois, USA, April (2004). 5. T. Sofu, T. H. Chun, W. K. In, Evaluation of Turbulence Models for Flow and Heat Transfer in Fuel Rod Bundle Geometries, Proceedings of PHYSOR-2004, Chicago, Illinois, USA, April (2004). 6. D. P. Weber et al., Extension of Integrated Neutronic and Thermal-Hydraulic Analysis Capabilities of the Numerical Nuclear Reactor Software System for BWR Applications, Proceedings of PHYSOR-2006, Vancouver, BC, Canada, Septemebr (2006). 7. J.W. Thomas, et al, Assembly Based Modular Ray Tracing and CMFD Acceleration for BWR Cores with Different Fuel Lattices, Proceedings of ICAPP 2006, Reno, Nevada, USA, June 4-8 (2006). 14/15

15 Coupled BWR Calculations with the Numerical Nuclear Reactor (NNR) 8. STAR-CD CFD Software, Version 3.27, Melville, New York (2006). 9. A. Tentner, S. Lo, A. Ioilev, M. Samigulin, V. Ustinenko, Computational Fluid Dynamics Modeling of Two-Phase Flow in a Boiling Water Reactor Fuel Assembly, Proceedings of Math. and Computation, Supercomputing, Reactor Physics, Nuclear and Biological Applications, Palais des Papes, Avignon, France, September (2005). 10. A. M. Tentner et al., Advances in Computational Fluid Dynamics Modeling of Two Phase Flow in a Boiling Water Reactor Fuel Assembly, Proceedings of International Conference on Nuclear Engineering (ICONE-14), Miami, Florida, USA, July (2006). 11. ANL LCRC Computing Cluster: Physics of Plutonium Fuels, BWR MOX Benchmark, Specification and Results. Nuclear Science Committee, Working Party on the Physics of Plutonium Fuels and Innovative Fuel Cycles, Volume VII. Nuclear Energy Agency/Organization for Economic Cooperation and Development. Jan E. J. Ruzauskas and D. L. Smith, Fuel Failures During Cycle 11 at River Bend, Proceedings of the International Meeting on LWR Fuel Performance, Orlando, Florida, September (2004). 15/15