Direct Numerical Simulation Code Validation for Compressible Shear Flows Using Linear Stability Theory

Abstract

In order to simulate compressible shear flow stability and aeroacoustic problems, a numerical code must be able to capture how a baseflow behaves when submitted to small disturbances. If the disturbances are amplified, the flow is unstable. The linear stability theory (LST) provides a framework to obtain information about the growth rate in relation to the excitation frequency for a given baseflow. A linear direct numerical simulation (DNS) should capture the same growth rate as the LST, providing a severe test for the code. In the present study, DNS simulations of a two-dimensional compressible mixing layer and of a two-dimensional compressible plane jet are performed. Disturbances are introduced at the domain inflow and spatial growth rates obtained with a DNS code are compared with growth rates obtained from LST analyses, for each baseflow, in order to verify and validate the DNS code. The good comparison between DNS simulations and LST results indicates that the code is able to simulate compressible flow problems and it is possible to use it to perform numerical simulation of instability and aeroacoustic problems.