GENERALIZED FLOW FIELD SHAPE OPTIMIZATION WITH SNAPSHOT POD

Abstract

This paper presents optimal design using Shape Optimization Problem considering Snapshot Proper Orthogonal Decomposition (Snapshot POD) which is the same algorithm as Prinary Component Analysis (PCA) and is able to decompose time dependent flow into time average and time fluctuation parts. The method suppresses time periodic flows driven only by the non-stationary boundary condition at a sufficiently low Reynolds number. For shape optimization, the eigenvalue in Snapshot POD is defined as a cost function. The main problems are Reynolds Average Navier-Stokes problem and eigenvalue problem of Snapshot POD. An objective functional is described using Lagrange multipliers and finite element method. Two-dimensional cavity flow with a disk-shaped isolated body is adopted for an initial domain. The non-stationary boundary condition is defined on the top boundary and non-slip boundary condition for side and bottom boundaries and for the disk boundary. For numerical demonstration in Newtonian fluid and Non-Newtonian fluid, the disk boundary is used as the design boundary. Using H ¹ gradient method for domain deformation, all triangles over a mesh are deformed as the cost function decreases.