A Method of Solving the Three-Dimensional Laminar Boundary-Layer Equations with Application to a Lifting Reentry Body

摘要

The general three-dimensional laminar compressible boundary-layer equations, written in terms of streamline coordinates, are reduced to a sequence of two-dimensional equations by means of a systematic perturbation procedure. The perturbation parameter is related to the inviscid streamline curvature and the lowest (zeroth-order) equations are identical with the small crossflow equations of Hayes. In addition, the equations for the first-order terms are given explicitly both in terms of physical and transformed (Lees-Levy) variables. Two alternate finite difference methods (for physical and transformed variables respectively) are developed to solve the zeroth as well as the first-order equations exactly. Local similarity methods are also considered for comparison. A variety of boundary conditions are possible including the case for which the heat and mass-transfer rates are coupled through an energy balance. The methods were applied to the problem of boundary-layer flow on a blunted cone at angle-of-attack. The results show that the crossflow often becomes rather large near the wall. The first-order corrections to the enthalpy and tangential velocity in the boundary layer are nevertheless small. (Author)