層流境界層方程式の解について(應用力學)

概要

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Owing to the mathematical difficulties, the exact solutions of the laminar boundary layer equations are possible only when the velocity outside the layer, U, is given by a simple function of the distance along the surface, x. In such cases, the boundary layer equations are reduced to the ordinary differential equations by the transformation of the variables and these equations are solved by the numerical integration. In this paper, it is found that the boundary layer equations can be reduced to the ordinary differential equations if, and only if, x(dM_1/dx) is expressed as a polynomial o.f the parameter M_1=(x/U)(dU/dx), or M_1 as that of x. Several examples of U appropriate to this condition are presented. Especially, in the case U=U_0x exp (-x), namely the Falkner's flow, the transformation of the equation is developed. According to the results of solutions for several cases, it seems that it is very difficult to find sole parameter which determines the velocity distributions across the layer, uniquely.
宇宙航空研究開発機構の論文
1950-01-20