A Two Parameter Family of Laminar Boundary Layer Profiles on Swept Wings

Abstract

The simple one parameter family of velocity profiles generated by the Falkner-SkanCooke equations does not provide accurate representations of those occurring on swept wings. Stability calculations based on such velocity profiles do not therefore provide accurate estimates of ‘N-Factors’ for transition prediction. Velocity profiles based on the one parameter similarity family ignore small terms arising from local deviations from the power law free-stream velocity. A two-parameter formulation that enables the solutions to approximately cater for these weak deviations from similarity is proposed. Examples of the two-parameter profile family are evaluated and displayed. These will then be incorporated in the ‘Rapid-Solver’ scheme already used to predict ‘N-Factors’ for two-dimensional compressible boundary layers. Nomenclature δ = boundary layer thickness 1 δ = displacement thickness of the boundary layer in a direction normal to the leading edge 2 δ = displacement thickness of the cross-flow boundary layer θ = momentum thickness of the boundary layer normal to the leading edge H = shape factor θ δ 1 D = 1 2 1 / ) ( δ δ δ −