Analytical study of laminar boundary layer near blunted bodies

V. N. Bulgakov ; V. P. Kotenev ; Iu. S. Ozhgibisova

Matematičeskoe modelirovanie, Tome 31 (2019) no. 6, pp. 82-94

Résumé

In high-speed flow, blunt body elements having an irregular shape due to which gas dynamic parameters undergo considerable changes are, as a rule, the most thermally loaded parts. In this connection, quick evaluation of thermal loading on blunt bodies is important. Laminar boundary layer equations given in special coordinates in the constant axisymmetric flow of a compressible perfect gas are considered. The «adhesion» condition is accepted as a boundary condition on the wall, and equality of speed and temperature to the corresponding values of the external flow is accepted on the border. In the Pohlhausen's method, concepts of displacement thickness and momentum thickness are introduced, relations between these values and the boundary layer thickness are established, and a differential equation is derived to define the boundary layer form-parameter using which other characteristics of the boundary layer are identified. The Pohlhausen's method is modified in order to simplify the calculation, excluding from it the differential equations. Similar to velocity, a special function which includes enthalpy and dimensionless «kinetic» parameter to be determined is introduced as a biquadratic polynom. Boundary conditions on the wall and on the border of the boundary layer are used to determine the polynom coefficients. The kinetic parameter is defined in a different way for bodies of various shapes. Application results of the proposed method for calculation of thermal flows which numerical analysis is also given in number of papers within full systems of Navier–Stokes and Prandtl equations. Comparison of the results shows efficiency of the proposed method.

Détail

Keywords: boundary layer, viscosity, Pohlhausen method, supersonic flow, heat transfer, sonic point.