層流境界層方程式の解法について

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An approximate method for solving the equations for steady, two dimenional boundary layer by using Mises transformation is presented. Chapter 1 deals with incompressible fluid. As is shown by Mises and Karman-Millikan, equation of motion for the boundary layer is written : [numerical formula] where v is kinematic viscosity, z=(u_1^2 - u^2 )/2 (u_1 : outside velocity), z_0=z(ψ=0)=u_1^2/2, [numerical formula] and ψ is stream function defined by [numerical formula], [numerical formula]. Now, 1-z/z_0 in the right side can be expanded in power series of ψ if we take as z Karman-Millikan's outer solution. The essential point of the present method lies in taking only the first term as an approximation. Then using instead of φ a new variable which is a function of φ, we can obtain z in an integral form containing the distribution of the outside velocity in the integrand. Several numerical examples show that the accuracy of the method is satisfactory. In Chapter 2, compressible fluid with Prandtl number 1 is considered, for the case without surface heat transfer. By proper modifications in the definitions of φ, ψ and z, the method of the first chapter is also available for this case. Similarity between compressible and incompressible case is discussed. (Received May 2, 1951)
宇宙航空研究開発機構の論文
1951-08-20