Proper Orthogonal Decomposition Based Reduced Order Modeling of the Very High Temperature Reactor Lower Plenum Hydrodynamics

Abstract

The feasibility of reduced order modeling for turbulent flows using Proper Orthogonal Decomposition (POD) based Surrogate modeling and Galerkin Projection is demonstrated for use in the hydrodynamic modeling of the Very High Temperature Reactor (VHTR) lower plenum. The lower plenum of the Helium-cooled VHTR consists of vertical cylinder arrays subjected to turbulent jetting and cross-flow. Unsteady Reynolds-Averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) simulations are used to acquire an ensemble of possible solution fields for flow around a circular cylinder in an open domain. Numerical results are validated to prior published literature. From the resultant data ensemble are extracted the coherent structures to create an optimal basis. POD is used to extract the coherent structures as this technique has been demonstrated to provide a basis of a chosen dimension such that the average L2-error is minimized for the best approximation of the basis to the data ensemble. The resultant optimal basis is used to construct accurate reduced order models. The computational effectiveness and insights revealed by this reduced order modeling approach are discussed for both the Surrogate modeling approach and Galerkin Projection.

Neural network closures for nonlinear model order reduction

“…Fig. (8) shows the performance of the Fourier-GP-ROM and POD-GP-ROM methods against the Fourier-ANN-ROM and POD-ANN-ROM approaches for the first five modes. The true projections are also shown for the purpose of comparison.…”

“…The choice of the transformation aids the user in the identification of sparseness and thus allows them to obtain a dense (but low dimensional) representation of the same governing law. Among the large variety of reduced order modeling strategies, proper orthogonal decomposition (POD) has emerged as a popular technique for the study of dynamical systems [3,6,8]. With respect to terminology, POD is also referred to as the Karhunen-Loéve expansion [54], principal component analysis [41] or the empirical orthogonal function [55].…”