Three-dimensional laminar boundary layers with large cross-flow

Abstract

The paper is concerned with the detailed formulation and evaluation of a previously proposed physical model and method of analysis for three-dimensional hypersonic laminar boundary layers. In this approach, the boundary layer is subdivided into two (inner and outer) regions characterized by widely different momentum fluxes per unit area. The subdivision leads to considerable simplifications in the statements of the inner and outer equations and in the determination of the associated solutions. An over-all description of the flow is obtained by matching the two solutions. The heuristic model and method of analysis are corroborated by comparing their predictions with those of numerical solutions of the complete boundary-layer equations. The family of self-preserving flows near a plane of symmetry is used as test problem. The two-layer model yields closed-form results for velocity and enthalpy profiles as well as for skin friction and wall heat transfer, in good agreement with the exact predictions. The application of the model to general three-dimensional flows is discussed in the context of this comparison and of the salient features of the analysis; interalia, the extension to moderate Mach number flows is indicated.