Evolution of the Favorable Pressure Gradient Turbulent Boundary Layer Towards a Quasi-Laminar State (Invited)

Abstract

The development of a favorable pressure gradient (FPG) turbulent boundary layer that undergoes quasilaminarization is studied by means of equilibrium similarity of the equations of motion and considering experimental data. Traditionally, favorable pressure gradients have been characterized using the acceleration parameter, K = U2 1 dU1 dx . It is shown that this parameter does not suce as a condition to predict quasilaminarization. The pressure parameter, given by = U1 d dx dU1 dx , is found to possess distinct values which are dependent on the o w conditions. Two quadrants are found to describe FPG o ws: Quadrant I describes turbulent FPG o ws and Quadrant II describes quasi-laminar o ws. Experimental measurements of the o w eld and the skin friction obtained by Warnack and Fernholz [2] are used as well as other experiments. Furthermore, a reduction of the component of the Reynolds stress is observed due to the imposed pressure gradient. The shape of the prole remains the same until a quasi-laminar state is reached where the prole no longer shows high values of the stress close to the wall. At this point, a pressure parameter, , value of 0.47 is reached. The component is entirely killed by the external pressure gradient impending quasi-laminarization. The Reynolds shear stress component, , survives due to the contribution of the streamwise component. The skin friction suddenly decreases due to the imposed pressure gradient. A percent in reduction of 57 % and a value for the pressure parameter of 0.47 is matched when this phenomenon occurs. The production term is nearly zero for very strong favorable pressure gradient o ws. The turbulent boundary layer subject to FPG is found to reach a quasi-laminar state but never reaches a fully laminar state.