Numerical study of the skin friction on a spheroid at incidence

This paper is concerned with a numerical solution of the three-dimensional, incompressible, steady laminar flowfield about a prolate spheroid at incidence. The governing equations were simplified by neglecting the streamwise diffusion terms to yield the so-called parabolized Navier-Stokes equations. The number of equations and the number of dependent variables are identical to those of the full Navier Stokes equations (although the mathematical character of the equations becomes simpler). Therefore, the equations are valid in separated regions whereas the parabolic boundary-layer equations are not. The three-dimensional case was solved using a curvilinear orthogonal coordinate system and primitive variables. An efficient numerical method particularly suitable to the parabolized Navier-Stokes equations was used. The paper concentrates on the distribution of the skin-friction lines for two test cases. In the first test case, the axes ratio of the spheroid was 4:1, with incidence of 6 deg and a Reynolds number (based on half the major axis) of 10⁶. In the second case the axes ratio was 6:1, with incidence of 10 deg and a Reynolds number of 0.8.10⁶. Favorable agreement with experimental results was obtained in the laminar regions. Some properties of the flowfield near the body are discussed on the basis of the pattern of the skin-friction lines and the shape of the separation lines. Yet no definite conclusions on the flow pattern in the separated region can be drawn from the skin-friction results alone.