Modelling turbulent spots in swept boundary layers

Abstract

A computational technique is presented for determining the fully 3-d viscid unsteady perturbation to a non-developing laminar swept boundary layer. For zero pressure gradient, unswept boundary layers, the perturbation method reveals a strongly three dimensional flow within the turbulent spot and its associated calmed region which is very similar to that observed in experiments and full DNS calculations. The perturbation method cannot predict turbulent motion but nevertheless provides a simple yet accurate means of studying and understanding the development of turbulent spot geometry. The most influential flow feature is the horseshoe vortex observed in the fluctuation velocity field, which is responsible for delivering the fluid found in the calmed region between its trailing legs. The upwards flow around the outer periphery of the vortex is also responsible for delivering low momentum fluid to the spot, but additional high momentum fluid also enters the spot from its rear through the downward sweeping motion of fluid between the vortex legs. The effect of an adverse streamwise pressure gradient is to increase the size of the spot and calmed region whereas a favourable pressure gradient has the opposite effect. When sweep is introduced to the boundary layer the spot is skewed for all non-zero pressure gradients, but the changes in size of the spot and calmed region due to pressure gradient are reduced. For favourable pressure gradients the skew increases monotonically with sweep, but this is not the case for adverse pressure gradients where the effect of sweep is more complex.