Favre-Averaged Nonlinear Harmonic Method for Compressible Periodic Flows

Abstract

The treatment of compressible flows subject to periodic disturbances of finite amplitude with nonlinear harmonic (NLH) methods requires a careful choice of averaging procedures and variable sets to average. A judicious choice of averaging procedure for the unsteady Navier–Stokes equations and its associated variable set is one that preserves certain properties of the flow of particular interest and also leads to a simple formulation of the equations governing the time-mean flow. This paper studies the time-averaged Navier–Stokes equations with different averaging procedure and variable set, and presents a new formulation of the NLH method based on Favre averaging of the primitive variable set. The resulting formulation of the time-averaged Navier–Stokes equations has exactly the same form as the steady base flow plus contributions from deterministic fluxes and stresses. Favre averages of the primitive variables preserve the time average of the conserved flow variables. From a practical point of view, this can minimize the modifications to the baseline solver to implement the NLH method. The details of the method are presented, and the method is validated from a two-dimensional transonic diffuser to compressors in subsonic and transonic flow regimes. A good agreement with the unsteady simulations using time marching is observed for all cases.