Three-dimensional boundary layer near the plane of symmetry of a spheroid at incidence

1970 ◽  
Vol 43 (1) ◽  
pp. 187-209 ◽  
Author(s):  
K. C. Wang

This paper presents incompressible laminar boundary-layer results on both the leeside and windside of a prolate spheroid. The results are obtained by an implicit finite difference method of the Crank–Nicolson type. Particular attention has been given to the determination of separation and of embedded streamwise vortices. No restriction on the angle of attack or the thickness ratio is imposed, nor are there invoked any of the common assumptions such as similarity, conical flow and others. The results suggest an embedded vortex region existing between the regular boundary-layer region and the separated region. At higher angle of attack, the vortex region becomes so thick that it itself may be more appropriately called ‘separated’ also. The latter possibility leads to questions of applicability for existing theories on three-dimensional separation.

This work examines the stability of viscous, incompressible flow along a streamwise corner, often called the corner boundary-layer problem. The semi-infinite boundary value problem satisfied by small-amplitude disturbances in the ‘blending boundary layer’ region is obtained. The mean secondary flow induced by the corner exhibits a flow reversal in this region. Uniformly valid ‘first approximations’ to solutions of the governing differ­ential equations are derived. Uniformity at infinity is achieved by a suitable choice of the large parameter and use of an appropriate Langer variable. Approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two-dimensional boundary layer profiles.


1991 ◽  
Vol 113 (2) ◽  
pp. 228-239 ◽  
Author(s):  
Tzuyin Wu ◽  
Shan-Fu Shen

Recent interest in unsteady separation and separated flows brings up the need of an accurate and efficient computational scheme for general unsteady three-dimensional boundary-layer flows. Resolution of the singular behavior at separation is a delicate problem. The task is further complicated by the geometrical singularity and the nonstationary stagnation point. The present paper proposes a numerical scheme to sidestep these difficulties. At the first stage of development, the simpler problem of the symmetry-plane solution of the laminar boundary-layer over an impulsively-started prolate spheroid is calculated. Results show that the present Eulerian calculation satisfactorily captures the singular behavior of the boundary layer when separation is approached. Comparison with Xu and Wang’s recent results and those for the two-dimensional elliptic cylinder calculated by the Lagrangian method are also made. Discussions of the results for unsteady separation at zero, small and large incidences are presented.


1971 ◽  
Vol 48 (2) ◽  
pp. 397-404 ◽  
Author(s):  
K. C. Wang

The zones of influence and dependence for three-dimensional boundary-layer equations first studied by Raetz are re-examined from the viewpoint of the subcharacteristics. It is shown that in contrast, the zones of influence and dependence for a totally hyperbolic system are determined by the characteristics; for the present parabolic system of three-dimensional boundary-layer equations, the zones are determined by the characteristics and subcharacteristics. The same idea should be applicable to more general systems of equations of similar type.


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