A New Multifold Series General Solution of the Steady, Laminar Boundary Layers : 3rd Report, Extension of the Solution to the Case of Not Smoothly joining Mainstream-Velocities

Abstract

In the preceding reports, a new theory of multifold series expansion for the steady, laminar boundary layers has been presented. The solution is given in a series of the multi-parameters which involve respectively different order derivatives of the characteristic function β(ξ)=(2ξ/U.)(dU./dξ), so that the theory covers an extremely wide range of mainstream velocity distributions. The only problem remaining unsolved is the case of the mainstream U(x) which is described by a function of class C^k(∞>k≥E; 0), that is, the case when the derivative d^k+1 U (x)/dx^k+1 indicates a discontinuity at some x-position. The present paper extends the solution to this problem by replacing the original singular characteristic function with a smooth function which is substantially equivalent to the original one for determining the boundary layer flow characteristics. The theory can be applied widely and gives good result even for a very difficult problem, for example, such as a flow containing separation and reattachment.