March 12, 2013

Fig. 1: Simulation and Modeling of Nuclear Fuel
Performance (Source:
Wikimedia
Commons) |

Computational Fluid Dynamics or CFD is a method to solve the governing equations of fluid flow like the Navier Stokes equations numerically. The governing equations for fluid flow are complex higher order PDEs and are generally very difficult to solve analytically. Generally CFD solution involves three stages: Pre-processing, solving and post processing. Pre-processing involves setting up of the problem under consideration. This involves making a model of the equipment, meshing which discretizing the geometrical domain into smaller parts or cells and setting boundary conditions. The cell size and distribution and boundary condition assignment are key components because they determine the accuracy and nature of the final solution. Solver is a CFD code which is either written specifically for the problem or a general purpose flow solver can be used. For problems in nuclear physics however, one deals with one or a combination of complex phenomena and many a times demands customized designing of codes. The results obtained are plotted on a colour coded graph or indicated on the geometry in the post processing stage.

One of the main advantages of CFD is that phenomena which are either not reproducible or are extremely costly to evaluate experimentally can be simulated at a much lower cost with reasonable accuracy. The main areas in nuclear industry where CFD is used are (1) fluid engineering, (2) reactor safety, (3) thermal and hydraulic design, (4) boiling and heat transfer, (5) steam generation, (6) drop fuel testing, and (7) spent fuel processing.

Some of the famous CFD codes applied in the nuclear industry are

**MCNP:**The Monte Carlo N-Particle Transport Code uses Monte Carlo methods in probability and predictions to simulate particle collisions, movements and interactions for proton, neutrons, electrons etc. Examples of application include fission and fusion reaction simulation, accelerator target design, detector design, radiation shielding. [1]**PARCS:**This code is used for spatial kinetics which encompasses a wide range of phenomena from neutron transport to generation and decay of neutron precursors. Spatial Kinetics involves solution of Eigenvalue problems and solving time dependent neutron transport equations. [2]**CASMO-5:**This involves codes used to model lattice physics in PWR and BWR fuels. [3]**TRACE:**TRACE is used to model thermal hydraulic phenomena in 2D and 3D space. It is a finite difference method solver for multidimensional flow modeling and 2D heat conduction which can handle different coolant types and two-phase flows. [4]**RELAPS:**The Reactor Excursion and Leak Analysis Program code involves transient analysis of system in of PWR and BWR. It only has thermal hydraulic analysis in 1D, however is very popularly used.

Apart from these, commercial codes from ANSYS like CFX and FLUENT and STAR-CD are also used. One can also write a customized script inside the commercial packages to define and solve specific problems.

CFD simulation results were checked against experimental findings for a Boiling Water Reactor (BWR). A special analysis module was added in the commercial CFD software STAR-CD to model the two phase heat transfer phenomenon which involves generation of vapour and interaction of vapour at heated metal surfaces with liquid coolant. The heat transfer modeling for multiphase flow is a critical problem which is still under research in the field of CFD. The code was used to calculate void fractions, temperature and velocity fields in pipes. This was checked against the experimental results from an extensive literature survey available for similar problem. One of the test cases for void fraction, velocity and temperature fields in pipe flow under atmospheric pressure is tested against experimentally measured values. There two results were in agreement with each other. [5]

CFD analysis is used to monitor thermal fatigue in nuclear pipework. The thermal fatigue in pipe material is as a result of mixing of hot and cold fluids. Regular thermal fluctuations are well documented and can be dealt with using proper plant regulation and instrumentation. However when there are high frequency fluctuations for example as in turbulent mixing, normal plant thermocouple instrumentation is insufficient. To predict the impact of turbulent mixing of fluids and the resulting temperature distribution in the pipe material, combined CFD and FEM algorithms are used. The CFD package used is FLUENT and the scheme used is second order implicit time- advancing non iterative. Large Eddy Simulation (LES) was used with PISO pressure volume coupling algorithm along with convective modeling using second order upwind scheme. The CFD and FEM solvers are coupled and the temperature data from CFD results is used as an input to the FEM solvers. The FEM solvers use this data to calculate the thermal stresses. This stress analysis is then used to design the reactor using the ASME Boiler and pressure vessel code. [6]

© Chaitali Dalvi. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

[1] R. A. Forster *et al.*, "MCNP Capabilities
for Nuclear Well Logging Calculations," IEEE Trans. Nucl. Sci.
**37**, 1378 (1990).

[2] T. Kozlowski *et al.*, "Consistent
Comparison of the Codes RELAP5/PARCS and TRAC-M/PARCS for the OECD MSLB
Coupled Code Benchmark," Nucl. Technol. **146**, 15 (2004).

[3] J. Rhodes, K. Smith and D. Lee, "CASMO-5 Development and Applications," Studsvik Scandpower Inc., 10 Sep 06.

[4] W. Jaeger, V. H. S. Espinoza and W. Lischke,
"Safety Related Investigations of the VVER-1000 Reactor Type by the
Coupled Code System TRACE/PARCS," J. Power Energy Sys. **2**, 648
(2008).

[5] V. Ustinenko *et al.*, "Validation of CFD-BWR, a
New Two-Phase Computational Fluid Dynamics Model For Boiling Water
Reactor Analysis," Nucl. Eng. Design **238**, 660 (2008).

[6] M. H. C. Hannink and F. J. Blom, "Numerical
Methods for the Prediction of Thermal Fatigue Due to Turbulent Mixing,"
Nucl. Eng. Des. **241**, 681 (2011).