Unsteady Boundary Layers : (4th Report, Calculation of Boundary Layer around a Body with Arbitrary Shape by Use of a Series Expansion Method)

Abstract

A method of calculating unsteady laminar boundary layers is presented. Two-dimensional flow of an incompressible fluid is assumed. The case of an oscillating outer flow, about a time-mean value, with a small amplitude and at relatively low frequency, is considered. By the use of a power series expansion method, the boundary layer around a body with an arbitrary shape and with a wedge-shaped nose of arbitrary angle, can be calculated. The solution is obtained as a linear combination of a set of universal functions. Velocity fluctuations in the boundary layer, of second order in magnitude, are taken into account. The time-mean velocity at a point in the boundary layer shifts as the amplitude of outside flow oscillation is increased. At the same time, the second harmonic fluctuation is produced. The method of calculation is applied to the boundary layer of a circular cylinder, and it is found that the influence of the second order velocity change is rather small, even at the outside velocity fluctuation 0.5 times the mean velocity.