# Reactor Simulation

Funded under US DOE Nuclear Energy Research Initiative for Consortia, DE-PS07-07ID14812

## Research Personnel

**Rensselaer Polytechnic Institute** Michael Z. Podowski, Project Director, ** **Steven P. Antal, Kenneth Jansen, ** **Li (Emily) Liu

**Stony Brook University** James Glimm, Roman Samulyak

**Columbia** **University** **David Keyes**

**Brookhaven National Laboratory** (funding will by provided directly by DOE, and is not included in the current budget for the university partners) Lap Cheng, ** **Roman Samulyak

## Project Description

The overall purpose of this collaboration is to deploy advanced simulation capabilities for next generation reactor systems utilizing newly available, high-performance computing facilities. The goals are 1) to develop and deploy high-performance computing tools for coupled thermal-hydraulic, neutronic, and materials multi-scale simulations of the sodium fast reactor (SFR) and 2) apply the new computational methodology to study reactor fuel and core transient response under beyond-design and accident conditions.

The work will encompass a broad spectrum of issues that are critical for developing next-generation reactors. Deliverables will include multi-physics, multi-scale computational modeling capabilities to investigate the impact of long-term thermal and mechanical loads and high-burnup fuel on reactor safety and accident mitigation strategies. The consortium will address three major groups of problems: 1) development of new simulation capabilities for state-of-the-art computer codes (FronTier, PHASTA, and NPHASE) coupled with MD-type analysis, 2) development of advanced numerical solvers for massive parallel computing, and 3) deployment of a multiple-code computational platform for the Blue Gene supercomputer simulations of SFR fuel performance during accidents.

Researchers will use the simulation codes to study fuel performance, including molecular-scale fission product release from ceramic fuel material, local core degradation, and fission product/fuel particle transport and release in the reactor core. Since no single computer code or technology level can be expected to cover such a broad range of design and operation issues during the reactor�s lifetime, it is anticipated that the proposed suite of tools will dramatically improve the accuracy and efficiency of reactor simulations. This, in turn, will significantly reduce conservative design and safety margins that are inherently associated with current reactor engineering methods.

Schematic of fuel degradation and transport in SFR during fuel rod failure accidents.

The NPHASE, PHASTA and FronTier codes are well suited to form the basis of a multidimensional, multifield and multiscale simulation capability. The NPHASE code is robust finite volume solver for the simulation of ensemble averaged time-dependent two-phase flows. PHASTA is a finite element, time-accurate computer code using single phase and level-set tracking methods. FronTier is a multiphysics code for the simulation of multiphase / free surface flows based on the explicit tracking of material interfaces. To enhance and optimize the performance of these three codes on massively parallel supercomputers, state-of-the-art multilevel solvers software for nonlinear partial differential equations will be used, developed at Columbia University.

## ITAPS related software

### FronTier Code

FronTier, a multiphysics code for the simulation of multiphase / free surface flows based on the method of front tracking has been developed at Stony Brook University in collaboration with BNL and LANL. Front tracking is a numerical method in which surfaces of discontinuity are given explicit computational degrees of freedom, supplementing the continuous solution values at regular grid points. FronTier has been tested on multi-material, multi-physics problems using massively parallel supercomputers, and used for simulations of turbulent fluid mixing, design of liquid mercury targets for future advances accelerators, pellet fuelling of thermonuclear fusion reactors, and astrophysical studies.

The FronTier research will be focused in the following major directions:

- The development of new capabilities of the FronTier code to enable simulations of the fuel rod failure during severe accidents in Liquid Metal Fast Rectors. New phase transition models for the fuel melting and vaporization will be developed as well as models for the formation and evolution of cracks in the solid fuel cladding. FronTier will simulate the creation of a melt volume within the fuel rod, release of volatile fission products and the subsequent rise in melt volume pressure, growth of the melt volume, the clad failure and debris ejection into the coolant channel.

- The modeling and simulations of the injection of fission products from the failed fuel rod into liquid coolant and the injection of liquid coolant into the inside of fuel elements. The interface with the NPHASE and PHASTA codes will also be developed for the data exchange purpose.

- FronTier will provide new closure models for multiphase systems and benchmark with existing averaged models of NPHASE through direct numerical simulations at microscale.

- The development of geometrical interface tracking capabilities to NPHASE and PHASTA codes, and the multiple code platform. Explicit interface tracking will increase capabilities of NPHASE and PHASTA to simulate complex multiphase flows. We will leverage the development of the geometrical front tracking package FronTier-Lite within the SciDAC ITAPS collaboration, and provide interfaces for its use in both single and coupled code simulations.

### Massively Parallel Anisotropic Mesh Adaptivity Enables PHASTA Code

PHASTA is a parallel, hierarchic (higher order accurate from 2nd-5th order accurate depending on function choice), adaptive, stabilized (finite element) transient analysis flow solver (both incompressible and compressible) that has been developed at RPI. This approach has been shown by Karanam et al. [2007], Whiting at al. [2003], Whiting and Jansen [2001] and Jansen [1999] to be an effective tool for bridging a broad range of length scales in turbulent (RANS, LES, DES, DNS) flows. PHASTA (and its predecessor ENSA) was the first unstructured grid LES code [Jansen, 1993; Jansen, 1994; and Jansen, 1999] and has been applied to turbulent flows ranging from validation benchmarks (channel flow, decay of isotropic turbulence) to complex flows (airfoils at maximum lift, flow over a cavity, near lip jet engine flows and fin-tube heat exchangers). It has also developed advanced anisotropic adaptive algorithms [Sahni et al., 2006,2007; Mueller et al., 2005; Shephard et al., 2005] and the most advanced LES/DES models [Hughes et al. 2000, Martinez and Jansen, 2000, 2003, 2004, 2005a and 2005b]. Note that DES, LES, and DNS are computationally intensive even for single phase flows. We have recently [Nagrath et al., 2006; Nagrath et al., 2005] extended this capability to two phase flows where we use the level set method to track the boundary between two immiscible fluids (either compressible where we captured new instabilities in sonoluminescence or incompressible where we studied bubble coalescence and two-phase turbulence including ongoing studies of turbulent annular flow and water jet air entrainment). Making simulations this complex grid independent, while ambitious, is reasonable with available computational resources due the efficient use of anisotropically adapted unstructured grids and highly scalable performance on massively parallel computers (the code has shown perfect scaling out to 32k IBM Blue Gene processors (largest available for testing)). An example of PHASTA�s current two-phase flow modeling is shown in the figure below where an annular flow (blue is liquid, red is gas, 30 degree sector is modeled) is initiated with an unstable wave which grows, breaks and forms droplets (surface shown is the phase interface which is colored by local speed).

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### References

Hughes, T.J.R., Mazzei, L., and Jansen, K.E., 2000, �Large-Eddy Simulation and the Variational Multiscale Method,� *Computing and Visualization in Science*, 3, 47-59.

Jansen, K.E., 1999, �A stabilized finite element method for computing turbulence,� *Computer Methods in Applied Mechanics and Engineering*, 174, 299-317**.**

Jansen, K.E., 1993, �Unstructured Grid Large Eddy Simulations of Wall Bounded Flows�, *Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford University,* 151.

Jansen, K.E., 1994, �Unstructured Grid Large Eddy Simulations of Flow Over an Airfoil�, *Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford University,* 161-.

Jansen, K.E., Johan, Z., Hughes, T.J.R., 1993, �Implementation of a One-Equation Turbulence Model within A Stabilized Finite Element Formulation of a Symmetric Advective-Diffusive System,� *Computational Methods in Applied Mechanics and Engineering,* **105,** 405-.

Karanam, A.K., Jansen, K.E. and Whiting, C.H., 2007, �Geometry based pre-processor for parallel fluid dynamic simulations�, *Engineering with Computers* (in press).

Mueller, J., Sahni, O., Jansen, K.E., Shephard, M.S. and Taylor, C.A., 2005, �Anisotropic Adaptive Finite Element Method for Modeling Blood Flow�, *Computer Methods in Biomechanics and Biomedical Engineering,** * **8**, n5, pp 295-305.

Nagrath, S, Jansen, K.E. , Lahey, R.T. and Akhatov, I. , 2006, �Hydrodynamic Simulation of Air Bubble Implosion Using a FEM based Level Set Approach�, *Journal of Computational Physics,* **215**, pp 98-132.

Nagrath,S. , Jansen, K.E. , and Lahey, R.T. , 2005,�Three Dimensional Simulation of Incompressible Two Phase Flows Using a Stabilized Finite Element Method and the Level Set Approach�, *Computer Methods in Applied Mechanics and Engineering,* **194**, n 42-44, 4565-4587.

Sahni, O., Mueller, J., Jansen, K.E., Shephard, M.S. and Taylor, C.A., 2006, �Efficient Anisotropic Adaptive Discretization of the Cardiovascular System�, *Computer Methods in Applied Mechanics and Engineering*, **195**, n41-43, pp 5634-5655.

Sahni, O., Jansen, K.E., Shephard, M.S., Taylor, C.A., and Beall, M.W., 2007, �Adaptive Boundary Layer Meshing for Viscous Flow Simulations�, *Engineering with Computers*, accepted.

Shephard, M.S., Flaherty, J.E., Jansen, K.E., Li, X., Luo, X., Chevaugeon, N., Remacle, J.F., Beall, M.W., and O�Bara, R.M., 2005, �Adaptive Mesh Generation for Curved Domains�, *Journal of Applied Numerical Math,* **52,** 251-271.

Tejada-Martinez, A.E. and Jansen, K.E., 2005, �A parameter-free dynamic subgrid-scale model for large-eddy simulation�, *Computer Methods in Applied Mechanics and Engineering,* **194**, No. 9, 1225-1248.

Tejada-Martinez, A.E. and Jansen, K.E., 2004, �A Dynamic Smagorinsky Model with a Dynamic Filter Width Ratio�, *Physics of Fluids*, **16**, 2514-2528.

Tejada-Martinez, A.E. and Jansen, K.E., 2005, �On the Interaction Between Dynamic Model Dissipation and Numerical Dissipation Due to Streamline Upwind/Petrov-Galerkin Stabilization�, *Computer Methods in Applied Mechanics and Engineering*, **194**, n9-11, 1225-1248.

Tejada-Martinez, A.E. and Jansen, K.E., 2003, �Spatial Test Filters for Dynamic Model LES with Finite Elements�, *Communications in Numerical Methods in Engineering*, 19, 3, 205-213.

Whiting, C.H. and Jansen, K.E., 2001, �A Stabilized Finite Element Formulation For The Incompressible Navier-Stokes Equations Using A Hierarchical Basis,� *International Journal of Numerical Methods in Fluids,* 35, 93-116.

Whiting, C.H, Jansen, K.E. and Dey, S., 2003, �Hierarchical Basis for Stabilized Finite Element Methods for Compressible Flows,� *Computer Methods in Applied Mechanics and Engineering*, 192, 5167-5185.

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