Elliptic Length Scales in Laminar, Two-Dimensional Supersonic Flows

Abstract : A similarity approach to characterizing the influence of shocks and compression ramps on flat plate flows is presented. New correlations for laminar compressive interactions on two-dimensional compression ramps and shock impingements for adiabatic walls have been developed that utilize a universal form which is enabled by the discovery of a new similarity parameter of the Navier-Stokes equations. These new correlations have been developed for two-dimensional, laminar adiabatic wall flows over compression ramps and flows with shock impingements. The new correlations are derived from existing numerical data and incorporate the new similarity parameter for the Navier-Stokes equations that represents the ratio of pressure forces to viscous forces. The new correlations are in excellent agreement with previously published experimental and numerical data. By utilizing the correlations, known freestream conditions, and empirical relations for the undisturbed boundary layer thickness, it is possible to determine a priori estimates for the streamwise length of the region influenced by a shock impinging on a flat plate or a region influenced by a flat plate / compression ramp juncture.