Laminar separation bubbles in two and three dimensional incompressible flow.

Abstract

A theoretical and experimental study is made of the closed 'bubbles` of separated flow formed when a laminar boundary layer separates from an aerofoil surface and, after undergoing transition to turbulence, subsequently re-attaches. Attention is mainly confined to the so-called 'short' type of bubble, which is distinguished from the 'long' type by its relatively slight overall effect upon the pressure distribution. In Part I, a semi-empirical theory for the prediction of the growth and bursting of two-dimensional short bubbles is developed. The existing data concerning short bubbles are re-examined, with particular emphasis upon the conditions governing re-attachment. A criterion for the determination of turbulent re-attachment is proposed, and approximate quadrature methods developed for the calculation of the momentum thickness in the separated region. These results, together with am empirical formula for the determination of the position of transition, are combined with a simplified model of the pressure distritbution in the bubble region to predict the re-attachment position. It is found that, for a given imposed pressure distribution, there exists a Reynolds number at separation below which re-attachment is impossible. This is associated with the phenomenon of short bubble bursting. The predictions of the theory are in reasonable quantitative agreement with experiment. Part II deals with bubbles in three-dimensional flow. Experiments are described in which separation bubbles were produced using an apparatus closely simulating conditions near the leading-edge of a swept wing of infinite span. Measurements of surface pressure, mean velocity and turbulence level are presented, from which it is deduced that the bubble structure is similar to that of two-dimensional bubbles, apart from the existence of cross-flows in the shear-layer and a strong spanwise flow in the reverse-flow vortex. An extension of the two-dimensional bursting theory by means of the independence principle is in reasonable agreement with measured bursting parameters.