Optimal Design for Suppressing Time Fluctuation Part of Two-Dimensional Jet in Crossflow

Abstract

This paper proposes a shape optimisation method for suppressing a time fluctuation part of the two-dimensional jet-in-cross flow. Previously, the author has formulated a shape optimisation problem for suppressing transient fluids using Snapshot proper orthogonal decomposition (POD). This study extends it to a two-dimensional jet-in-cross flow. For this purpose, the eigenvalues of Snapshot POD are integrated to a cost function, where the constraint functions are the nonstationary Navier–Stokes equation and the eigenvalue equation of Snapshot POD. An objective functional is described using Lagrange multipliers and the finite element method as the sum of the cost and constraint functions. To verify the proposed optimisation strategy, using the gradient method for domain deformation, all triangles over a mesh are deformed, which causes the cost function to decrease. Finally, the eigenvalues of Snapshot POD in the initial and optimal domains are compared.