A robust computational approach to Lees–Dorodnitsyn laminar hypersonic boundary layers with temperature-dependent properties

Abstract

The Lees–Dorodnitsyn (L–D) boundary layer equations for two-dimensional, non-reactive, laminar, hypersonic, boundary layer flows, and an assumption of an isentropic external flow are examined. They are applied to various geometries for which the Thin Shear Layer assumptions are valid. This study expands on previous work to develop a novel and robust methodology for computing high-temperature hypersonic flows using a uniform and compact computational stencil implemented through a computational tool, the Bulk-property Boundary Layer (BuBL) solver. In particular, we explore 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 second-order finite difference methods is evaluated as are various models for viscosity, Prandtl number, and specific heat. The methodology for solving the external flow properties in the transformed L–D computational domain is also discussed. It is shown that the L–D equations evaluated using the “box” computational stencil are an effective means for evaluating laminar hypersonic boundary layer flows. Solutions for displacement and momentum thicknesses, skin friction, and Stanton number variations are obtained as a function of Prandtl number, specific heat model, and Mach number. Verification and validation measures are performed for the code. Excellent agreement is found in comparisons between BuBL and other computational fluid dynamics and experimental results, thus demonstrating the utility of the proposed methodology.