Jerome Solberg

An arbitrary Lagrangian–Eulerian discretization of MHD on 3D unstructured grids

Abstract We present an arbitrary Lagrangian–Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion , and Eulerian advection . The resistive magnetic induction equation is discretized using a compatible mixed finite element method with a second order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a second order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence-free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.

High-Fidelity Simulation of Flow-Induced Vibrations in Helical Steam Generators for Small Modular Reactors

Abstract Flow-induced vibration (FIV) is a widespread problem in energy systems as they rely on fluid movement for energy conversion. Vibrating structures may be damaged as fatigue or wear occur. Given the importance of reliable components in the nuclear industry, FIV has long been a major concern in the safety and operation of nuclear reactors. In particular, nuclear fuel rods and steam generators have been known to suffer from FIV and related failures. In this paper we discuss the use of the computational fluid dynamics code Nek5000 coupled to the structural code Diablo to simulate the flow in helical coil heat exchangers and associated FIV. In particular, one-way coupled calculations are performed, where pressure and tractions data are loaded into the structural model. The main focus of this paper is on validation of this capability. Fluid-only Nek5000 large eddy simulations are first compared against dedicated high-resolution experiments. Then, one-way coupled calculations are performed with Nek5000 and Diablo for two data sets that provide FIV data for validation. These calculations were aimed at simulating available legacy FIV experiments in helical steam generators in the turbulent buffeting regime. In this regime one-way coupling is judged sufficient since the pressure loads do not cause substantial displacements. It is also the most common source of vibration in helical steam generators at the low flows expected in integral pressurized water reactors. We discuss validation of two-way coupled experiments and benchmarks toward the simulation of fluid elastic instability. We briefly discuss the application of these methods to grid-to-rod fretting.

Multi-Physics Demonstration Problem with the SHARP Reactor Simulation Toolkit

This report describes to employ SHARP to perform a first-of-a-kind analysis of the core radial expansion phenomenon in an SFR. This effort required significant advances in the framework Multi-Physics Demonstration Problem with the SHARP Reactor Simulation Toolkit used to drive the coupled simulations, manipulate the mesh in response to the deformation of the geometry, and generate the necessary modified mesh files. Furthermore, the model geometry is fairly complex, and consistent mesh generation for the three physics modules required significant effort. Fully-integrated simulations of a 7-assembly mini-core test problem have been performed, and the results are presented here. Physics models of a full-core model of the Advanced Burner Test Reactor have also been developed for each of the three physics modules. Standalone results of each of the three physics modules for the ABTR are presented here, which provides a demonstration of the feasibility of the fully-integrated simulation.

Full Core Multiphysics Simulation with Offline Mesh Deformation

In this report, building on previous reports issued in FY13 we describe our continued efforts to integrate thermal/hydraulics, neutronics, and structural mechanics modeling codes to perform coupled analysis of a representative fast sodium-cooled reactor core. The focus of the present report is a full core simulation with off-line mesh deformation.

Accomplishments and Challenges in Code Development for Parallel and Multimechanics Simulations

The Methods Development Group at Lawrence Livermore National Laboratory has historically developed and supported software for engineering simulations, with a focus on nonlinear structural mechanics and heat transfer. The quality, quantity and complexity of engineering analyses have continued to increase over time as advances in chip speed and multiprocessing computers have empowered this simulation software. As such, the evolution of simulation software has seen a greater focus on multimechanics and the incorporation of more sophisticated algorithms to improve accuracy, robustness and usability. This paper will give an overview of the latest code technologies developed by the Methods Development group in the areas of large deformation transient analysis and implicit coupled codes. Applications were run on the state of the art hardware available at the national laboratories.