Prediction of turbulent spot growth rates

Abstract

A computational technique is presented for determining the fully 3-d viscid unsteady perturbation to a non-developing steady boundary layer flow. Streamlines through the perturbed region depict a strong hairpin vortex which bounds the calmed region. The nose of the hairpin projects into the rear of the turbulent spot. The streamlines show that the hairpin is responsible for mixing low momentum fluid forward of the hairpin with high momentum fluid from the rear and ejecting this fluid forward into the spot. The movement of the extremities of the spot and the calmed region are used to determine the trailing and leading edge celerities, the spot spreading angle and the propagation rate for Re e = 50 to 1000 and λ =-9 to 12. The spot growth is significantly suppressed at Re e below 200. Strong favourable pressure gradients also lead to a modest suppression in growth rate, but adverse pressure gradients increase growth rates substantially. New correlations for the celerities, spot spreading half angle and propagation parameter are formulated. These improve on previous correlations by including the effect of Reynolds number as well as pressure gradient.