Analytical Study of Laminar Boundary Layers near Blunted Bodies

Abstract

In high-speed flows, blunt body elements having an irregular shape due to which gas dynamic parameters undergo significant changes are, as a rule, the most thermally loaded parts. In this respect, a quick evaluation of the thermal load on blunt bodies is important. Laminar boundary-layer equations given in special coordinates in a constant axisymmetric flow of a compressible perfect gas are considered. The adhesion condition is accepted as a boundary condition on the wall and it is assumed that the speed and temperature on the boundary correspond to the values of the external flow. The Pohlhausen method introduces the concepts of the displacement thickness and momentum thickness, finds relations between these values and the boundary-layer thickness, and derives a differential equation to determine the boundary-layer form parameter such that all other characteristics of the boundary layer are determined via it. The Pohlhausen method is modified in order to simplify the calculation by excluding the differential equations from it. Similarly to the velocity, a special function including the enthalpy and dimensionless kinetic parameter to be determined is introduced as a biquadratic polynomial. The boundary conditions on the wall and on the border of the boundary layer are used to determine the polynomial coefficients. The kinetic parameter is defined in different ways for bodies of various shapes. We provide the results of applying the proposed method for the calculation of heat flux that have been analyzed numerically (in various papers) in complete systems of Navier-Stokes and Prandtl equations. The comparison of the results shows the efficiency of the proposed method.