Three-Dimensional Heat-Transfer and Ablation Disturbances in High-speed Flows

Abstract

A unified theory of steady-state disturbances in compressible laminar or turbulent boundary-layers and their interaction with the adjacent surface material is developed on the basis of a small perturbation approach. Fourier transformation is used to treat both periodic and nonperiodic disturbances within a common framework. The important effect of the highly nonuniform flow across the boundary-layer is taken into account, as are the effects of surface heat and mass transfer, lateral pressure gradient, and upstream influenc in the disturbance field. Three illustrative applications to the prediction of pressure, skin-friction, and heat-transfer disturbances are given including comparisons with experiment: the boundary-layer along a wavy structural skin with heat transfer, ablation surface cross-hatching, and flow past a rear-facing step or suction gap. Nomenclature= constant pressure, specific heat = step height = basic flow and perturbation total enthalpy, respectively = thermal conductivity = upstream influence distance , = basic flow and perturbation surface mass loss rates, respectively = Mach number = surface injection Mach number = basic flow and perturbation pressures, respectively = basic flow and perturbation surface heat-transfer rates, respectively = basic flow and perturbation absolute static temperatures, respectively = perturbation velocity components in x, y, z coordinate directions = basic undisturbed boundary layer in x-direction = coordinate normal to surface = sonic height in boundary-layer profile T w » T w = boundary-layer thickness = viscous disturbance sublayer thickness = turbulent eddy kinematic viscosity = wavy surface wavelength = laminar coefficients of dynamic and kinematic viscosity, respectively = basic flow density = coordinate resolved perpendicular to a chosen reference direction = basic flow and perturbation wall shear stress, respectively Subscripts e = edge of boundary layer n = component resolved in ^-direction o = basic undisturbed flow s = state within solid surface w = flow conditions at the wall surface