Nonlinear Stability of Liquid Film Adjacent to a Viscous Supersonic Stream,

摘要

The nonlinear stability of a liquid film adjacent to a viscous supersonic gas stream is investigated. The gas is assumed to exert a mean shear stress at the liquid/gas interface which in turn establishes a linear mean velocity profile in the liquid. The shear and pressure perturbations exerted by the gas on the liquid are calculated by taking into account the gas viscosity and mean velocity profile. The problem is formulated within the long wave approximation and solutions are obtained for small but finite amplitudes and for small and moderate liquid Reynolds number. The predicted wavenumbers are found to be in good agreement with those observed over wedge and cone shaped models in laminar supersonic wind tunnels. The analysis is incapable of predicting the observed amplitudes,wave speeds and frequencies. (Author)