Eigenmode optimization of a contraction channel based on stability analysis

Abstract

This work studies flow control in a channel flow with a sudden geometry contraction. Optimization investigations have been carried out aiming at minimizing the amplification rate of the most unstable mode, to keep the symmetric flow topology in the contraction channel. In this framework, the DLR-TAU code is employed to obtain the compressible base flow solution, from which the critical Reynolds numbers for the bifurcations have been found. A first-discretize-then-linearize approach was used, taking advantage of the linear Jacobian matrix implementation present in the DLR-TAU code for stability analysis, from which the eigenmodes responsible for the bifurcations are obtained. A geometry parametrized representation, an FFD mesh deformation program and a dynamically updated RBF surrogate model are developed to drive the optimization investigation. In this investigation, geometry configurations with negative amplification rates have been obtained, making the eigenmodes stable. The potential of the method is illustrated by the increase of critical Reynolds number of bifurcation.