Transient laminar compressible boundary layers over a permeable circular cone near a plane of symmetry

Abstract

The transient laminar compressible boundary layer over a circular cone at an angle of attack near a plane of symmetry in hypersonic flow has been investigated. The case of the boundary layer near the windward and leeward planes has been considered. The effect of suction is included in the analysis which plays an important role in obtaining unique solution. We have examined the situation where the flow is steady at time t = 0 and at time t > 0, the total enthalpy at the wall is suddenly increased and subsequently maintained at that value. This imports unsteadiness in the flow field. The effects of the variable fluid properties, non-unity Prandtl number and viscous dissipation are considered. By suitable transformations, the coupled nonlinear parabolic partial differential equations with three independent variables governing the flow have been reduced to partial differential equations with two independent variables. The resulting partial differential equations have been solved by using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been carried out from the initial steady state to the final steady state. It is found that in a small time interval immediately after the start of the impulsive motion, the direction of the heat transfer changes. The surface shear stresses in the streamwise and cross-wise directions and the surface heat transfer, in general, increase with time and attain final steady state values rather quickly (i.e., spin-up time is small). The total enthalpy at the wall strongly affects the surface shear stresses in the streamwise and cross-flow directions and the surface heat transfer, the suction strongly affects the surface shear stress in the streamwise direction and the surface heat transfer, and the cross-flow parameter strongly affects only the cross-flow surface shear stress.