## Science and Technology

### Analysis of Two-Dimensional Lattice Physics

CASL is developing the Virtual Environment for Reactor Applications (VERA) as a key capability to support the analysis of the CASL Challenge Problems. VERA will include a range of physics modeling capabilities necessary to model reactors, including neutronics, thermal hydraulics, fuel performance, and coolant chemistry. Lattice physics analyses, utilizing the newly-developed Michigan lattice physics neutronics capability in MPACT 1.0, are important to CASL for several reasons:

- The nuclear power industry regularly performs 2D lattice calculations. The ability of VERA to perform these types of calculations is critical.
- The Advanced Modeling Applications Focus Area has defined the VERA requirements for 2D lattice capability as part of the Core Physics Benchmark Progression Problems.
- Several of the neutronics methods planned for VERA include a spatially hybrid approach to the 3D neutron transport solution, combining solutions of 2D slices of the core coupled to some form of axial solution (i.e. 2D/1D or 2D/3D). Therefore, testing the performance of the 2D lattice features is critical to understanding how the coupled 2D and 3D solution methodology will perform.

Numerical validation of the lattice physics capability in MPACT (and its associated multi-group cross section library) is achieved by comparison of many lattice eigenvalues and normalized fission rate densities to solutions generated by two independent continuous energy (CE) Monte Carlo particle transport codes, KENO-VI and MCNP5. In addition, an analysis of a 2D 3x3 multi-assembly problem is performed and the control rod reactivity worth is also evaluated. In each of these cases MPACT is shown to provide solutions that are in excellent agreement with the reference solutions.

In addition to CE Monte Carlo results, comparisons are also made to the Westinghouse lattice physics code PARAGON. PARAGON is part of the Westinghouse in-house core physics suite that is qualified and routinely employed for the analysis of commercial PWRs. It relies on an extensive validation basis and comparison against measurements of US and world-wide PWRs and critical experiments, and is representative of the current industry state-of-the-art lattice physics tools. Comparisons between the results from PARAGON and MPACT also demonstrate that MPACT is performing very well.

After application and testing of MPACT v1.0 on many lattice physics problems, encompassing a wide range of fuel temperatures, integral and discrete burnable absorbers, control rods, and a multi-assembly controlled configuration, it is evident that MPACT has a strong capability for solving these types of problems. Figure 1 displays the eigenvalue agreement between MPACT and the CE Monte Carlo codes, and Figure 2 provides the relative pin power differences between MPACT and CE KENO-VI for the controlled 2D 3x3 sample problem.

**Figure 1: MPACT Eigenvalue Differences with B-VII Cross Sections**

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**Figure 2: Problem 4-2D (3x3) ENDF/B-VII Controlled Pin Power Differences between MPACT and CE KENO-VI**

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