Nonparallel stability analysis of compressible boundary layer using 3-D PSE

Abstract

The receptivity, stability and transition mechanisms of hypersonic flows over 3-D bodies have been the focus of recent research efforts. 2-D and 3-D DNS (Direct Numerical Simulation) have been used as a primary tool in attacking the problems. However, to fully address the problems, less costly methods are desirable to provide independent checks and theoretical interpretations of the numerical results. 3-D PSE (Parabolized Stability Equations), a 3-D extension of the 2-D linear PSE, derived from the full compressible Navier-Stokes disturbance equations in generalized coordinates, have been developed as a cost effective alternative to DNS in solving the problems. Specifically, 3-D PSE intend to account for spanwise variations of basic flow as well as the wavenumbers and shape functions of the disturbances which are ignored in 2-D PSE. Along with 3-D DNS to provide the receptivity solutions, 3-D PSE may serve as a very practical tool in understanding the 3-D stability and transition mechanisms for compressible flows. The formulations and numerical methodology are presented for 2-D and 3-D PSE. At the testing stage, 2-D and 3-D linear PSE are validated with previous 2-D linear PSE results for supersonic flows over flat plate.