APPLICATION OF THE REDUCED NAVIER-STOKES METHODOLOGY TO FLOW STABILITY OF FALKNER-SKAN CLASS FLOWS

摘要

This investigation ascertains the ability of the Reduced Navier-Stokes (RNS) methodology to model linear flow stability. The stability of five Falkner-Skan flows (3 = 1.0, 0.2, 0.0, -0.1, and -.1988) is investigated for modified forms of the Orr-Sommerfeld Equation (OSE). Neutral stability curves are numerically generated and compared for three forms of the OSE. The three OSE equation forms are based on the full Navier-Stokes equations, the 2-D Thin-Layer Navier-Stokes equations which exclude only axial derivatives in the viscous terms, and the 2-D Reduced Navier-Stokes equations which exclude the axial derivatives and the V{sub}(yy) derivative in the viscous terms. Results of the computations demonstrate that the reduced forms of the OSE are consistent with the full OSE. Having confirmed 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 are feasible. DNS calculations using the RNS equations are currently in progress. Preliminary results appear to demonstrate proper characteristics in disturbance growth and decay of the velocity disturbances. Velocity disturbances profiles also appear to be of proper shape and magnitude.