Application of the reduced Navier-Stokes methodology to flow stability of Falkner-Skan class flows

This investigation ascertains the ability of the reduced Navier-Stokes (RNS ) methodology to model linear flow stability. This is accomplished through development and investigation of two reduced forms of the Orr-Sommerfeld eq uation and of a second order RNS direct numerical simulation (DNS). The sta bility of five Falkner-Skan flows (beta = 1.0, 0.2, 0.0, -0.1, and -0.1988) is investigated for these modified forms of the Orr-Sommerfeld equation (O SE). Neutral stability curves are numerically generated and compared for th ree forms of the OSE, viz. full Navier-Stokes equations, two-dimensional; t hin-layer Navier-Stokes equations which exclude only axial diffusion, and t wo-dimensional reduced Navier-Stokes equations which exclude all axial diff usion, as well as all diffusion in the normal momentum equation. Effects of a deferred corrector to include these terms are also investigated. Results of the computations demonstrate that the reduced forms of the OSE are cons istent with the full OSE. With confirmation that the reduced Navier-Stokes equations contain the information required to properly model flow stability , development of a new class of asymptotic theories, stability methods, and approaches to direct numerical simulations, based on the RNS methodology, becomes feasible. Results from full DNS calculations using the RNS equation s demonstrate the proper characteristics for disturbance growth and decay o f the velocity disturbances. Velocity disturbance profiles are also of the required shape and magnitude. (C) 1999 Elsevier Science Ltd. All rights res erved.