Modern nuclear reactor safety codes require the ability to solve detailed coupled neutronicthermal fluids problems. For larger cores, this implies fully coupled 3-D spatial dynamics with appropriate feedback models that can provide enough resolution to accurately compute core heat generation and removal during steady and unsteady conditions. The reactor analysis code PRONGHORN is being coupled to RELAP-7 as a first step to extend RELAP's current capabilities. This report details the mathematical models, the type of coupling, and the testing that will be used to produce an integrated system. RELAP-7 is a MOOSE-based application that solves the continuity, momentum, and energy equations in 1-D for a compressible fluid. The pipe and joint capabilities enable it to model parts of the power conversion unit. The PRONGHORN application, also developed on the MOOSE infrastructure, solves the coupled equations that define the neutron diffusion, fluid flow, and heat transfer in a 3-D core model.

SUMMARYProgress toward collaboration between the SHARP and MOOSE computational frameworks has been demonstrated through sharing of mesh generation and ensuring mesh compatibility of both tools with MeshKit. MeshKit was used to build a three-dimensional, full-core very high temperature reactor (VHTR) geometry with 120-degree symmetry, which was used to solve a neutron diffusion critical eigenvalue problem in PRONGHORN. PRONGHORN is an application of MOOSE that is capable of solving coupled neutron diffusion, heat conduction, and homogenized flow problems. The results were compared to a solution found on a 120-degree, reflected, three-dimensional VHTR mesh geometry generated by PRONGHORN. The ability to exchange compatible mesh geometries between the two codes is instrumental for future collaboration and interoperability. The results were found to be in good agreement between the two meshes, thus demonstrating the compatibility of the SHARP and MOOSE frameworks. This outcome makes future collaboration possible.

An accurate and computationally efficient two-or three-dimensional (2-D or 3-D) neutron diffusion model will be needed to develop, compute safety parameters, and analyze the fuel cycle of a prismatic very high temperature reactor design under the Next Generation Nuclear Plant. To meet this need, an analytical Nodal Green's function method for the transverse integrated neutron diffusion equation was developed in 2-D and 3-D hexagonal geometry. This scheme is incorporated into the algorithm of the HEXPEDITE, a code first developed by Fitzpatrick and Ougouag. HEXPEDITE neglects discontinuous terms that arise in the transverse leakage because of the transverse integration procedure application to hexagonal geometry, and cannot account for the localized effects of burnable poisons across nodal boundaries. The test code being developed for this document accounts for these terms by maintaining a strict inventory of neutrons by using the nodal balance equation as a constraint of the neutron flux equation. The method developed in this report is intended to restore neutron conservation and increase the accuracy and fidelity of the code by adding the effect of the discontinuous terms to the transverse integrated flux solution. This is achieved through the use of the Nodal Green's function method to the complete equation resulting from the transverse integration procedure. The result is a rigorous semi-analytical solution. The new treatment of the burnable applies a similar approach, but with singular terms of pre-computed strength, based on blackness theory. vi vii ACKNOWLEDGEMENTS

Modern nuclear reactor safety codes require the ability to solve detailed coupled neutronics and thermal fluids problems. For larger cores, this implies fully coupled higher dimensionality spatial dynamics with appropriate feedback models that can provide enough resolution to accurately compute core heat generation and removal during steady and unsteady conditions. In this work, the reactor analysis code PRONGHORN is coupled to RELAP-7 as a first step to extend RELAPs current capabilities. This report details the mathematical models, the type of coupling, and the testing results from the integrated system. RELAP-7 is a MOOSE-based application that solves the continuity, momentum, and energy equations in 1-D for a compressible fluid. The pipe and joint capabilities enable it to model parts of the power conversion unit. The PRONGHORN application, also developed on the MOOSE infrastructure, solves the coupled equations that define the neutron diffusion, fluid flow, and heat transfer in a full core model. The two systems are loosely coupled to simplify the transition towards a more complex infrastructure. The integration is tested on a simplified version of the OECD/NEA MHTGR-350 Coupled Neutronics-Thermal Fluids benchmark model.