Prediction of boundary layer transition on a flat plate subject to surface waviness

The current understanding of the boundary layer transition is reviewed briefly. The effects of leading edge geometry, inlet turbulence, and surface waviness, on boundary layer transition on a flat plate are predicted using a commercial computational fluid dynamics (CFD) code, STAR-CCM+ which incorporates the gamma - R-theta correlation model. The investigations on surface waviness were focused on sinusoidal waves with the ratios of wave amplitude to wavelength h/L-w and wave amplitude to boundary layer displacement thickness h/delta* in the range 0.0025-0.015 and 0.3-2.8, respectively. It is recommended that in wind tunnel testing/CFD analysis of boundary layer transition, a leading edge aspect ratio of 12 is maintained to avoid significant effect of leading edge geometry. The predictions for the effect of surface waviness on transition for multiple waves, using gamma - R-theta model, agree well with those using the stability theory. New correlations for the effect of waviness on transition Reynolds number are proposed. The correlations combine the effects of upstream boundary layer displacement thickness, wave height, and wavelength (h* or h**). It is recommended that a value of h* < 2 or h** < 0.03 is maintained on aircraft surfaces to avoid any significant effect of waviness on drag. The variation of transition Reynolds number with h* for a surface with waviness is of the same order to that on a surface with a forward facing step, but significantly smaller when compared with a surface with a backward facing step (BFS). A value of h* < 0.5 is recommended for a BFS to avoid significant effect on transition.