Simulation of Lees-Dorodnitsyn hypersonic laminar boundary layers with temperature-dependent properties

Abstract

The Lees-Dorodnitsyn (L-D) boundary layer equations for 2D, laminar hypersonic boundary layer flows and an assumption of an isentropic external flow are used to represent both flows over a flat plate with an external pressure gradient and also curved geometries for which the Thin Shear Layer assumptions are still valid. This work expands on previous work to explore both similarity and non-similarity solutions for high-temperature hypersonic flows using a uniform and compact computational stencil. This thesis also explores the impact of treating high-temperature effects present in hypersonic flows, namely, treating air as a thermally perfect gas with temperature-variable properties. The ability to solve these flows computationally using 2nd order finite difference methods is evaluated as are various models for viscosity, specific heat, and thermal conductivity. Methodology for solving the external flow properties in the transformed L-D computational domain is also discussed. It is found that the L-D equations evaluated using the "box" computational stencil are an apt means for evaluating hypersonic boundary layer flows. This thesis also provides initial insight into the accuracy of three air thermal conductivity models for constructing a temperature-variable Prandtl number.