Analysis of Unsteady Laminar Boundary Layer Flow by an Integral Method

Abstract

An approximate integral method of analysis is developed for unsteady laminar boundary layer flows. The case of a flat plate in a free stream with small harmonic velocity oscillations about a steady mean is used to formulate the method. Results are compared with the available experimental data. The essence of the method is to: First obtain asymptotic solutions for limiting cases of the flow under consideration. Then, assume velocity profiles with sufficient generality to include the asymptotic solutions. The profile form functions are determined by applying integral relations (velocity weighted averages of the momentum equation) and compatibility conditions (normal derivatives of the momentum equation evaluated at the boundary). As an example of the method, the second-order mean flow correction is determined for oscillating flow over a flat plate.