Unsteady Compressible Laminar Boundary-Layer Flow within a Moving Expansion Wave

Abstract

Numerical solutions for the unsteady compressible laminar boundary-layer flow developed within a centered expansion wave are obtained for two wall thermal conditions, isothermal and adiabatic. The Howarth's transformation, similarity transformation via one-parameter groups, and then series expansion are employed for the solutions. The solutions are of second-order accuracy and are shown to improve over the Hall's zero-order solution for the temperature distribution in the boundary layer. It is shown that both velocity and temperature boundary layer grow rapidly behind the expansion wavefront but attenuate further downstream. If the wall temperature is held at the undisturbed temperature, the heat transfer occurs from the wall to the expanding gas. The rate of heat transfer increases from the wavefront to approximately £ = 0.35 behind the wave where maximum heat transfer is observed. The isothermal wall temperature is found to be higher than the adiabatic wall temperature by a factor (1 + 0.335£).