The Calculation of Steady Laminar Boundary Layer Flows by a Power-Series Method

Abstract

A power series method of calculating the two-dimensional flow in the boundary layer of an incompressible fluid is presented. First, a general method of series solution, which is a generalization of H. Gortler's series and retains the desirable features of his method that the first term of the series satisfies the outer flow boundary condition, is given. Then a practical method of calculation, a particular case of the general method, in which the independent variables are geometrical coordinates, is explained in detail. Coefficients of the new series are universal functions and can be expressed in terms of the known universal functions of the Blasius' series or the Gort1er's series. Thus numerical calculation of the boundary layer by the present method is easy to perform. Skin friction on a circular cylinder in the stream is calculated by the writer's series and the rapidity of convergence is examined. It gives a good approximation to the solution even when only two terms of the series are used, thus proving it suitable for the use in practical calculations.