Abstract
This paper numerically investigates the energy expenditure of the co-flow wall jet for separation control by analyzing the widely studied NASA hump with 2D unsteady Reynolds averaged Navier-Stokes equations. Co-flow wall jet is shown to be effective in both adverse and favorable pressure gradients, but is more efficient in adverse pressure gradients due to lower velocity, lower entropy increase, and more enhanced mixing. An energy-efficient way to devise a co-flow wall jet flow control is two-fold: 1) place the injection near the separation onset point at a slightly downstream location; 2) place the suction slot further downstream with sufficiently long distance in adverse pressure gradient region for a thorough mixing and energy transfer. The vanishing of the counter-clockwise wall jet vorticity appears to indicate a sufficient mixing distance. In that case, the injection plays the dominant role. The suction makes a small contribution with a weak coupling effect, but primarily serves as the flow source for the mass conservation of the zero-net-mass-flux flow control, which is essential to be energy efficient. The co-flow wall jet is also compared with the injection-only and suction-only flow controls, which are effective if the slots are placed at the desirable position slightly downstream of the separation onset point. But if they are not placed near the separation onset locations, the co-flow wall jet is much more efficient and effective than the injection-only or suction-only flow controls due to the coupling effect between the injection and suction.