Adjoint-based sensitivity analysis for airfoil flow control aiming at lift-to-drag ratio improvement

Sensitivities of drag and lift to body force and blowing/suction are investigated based on a continuous adjoint method through Reynolds-averaged Navier–Stokes simulation (RANS). For a Clark-Y airfoil, changes in the drag, the lift, and the lift-to-drag ratio are found to be caused by different mechanisms depending on the type and locations of control input. Improvement in the lift-to-drag ratio by body forces is achieved by both pressure drag reduction and pressure lift enhancement. The effective angle for blowing/suction is nearly normal to the surface, and blowing around the leading edge and blowing/suction on the lower/upper surface near the trailing edge improve the lift-to-drag ratio effectively. Investigation on the control amplitude reveals that the present sensitivity analysis is valid when the blowing/suction velocity is less than 1% of the freestream velocity. The sensitivities are observed to be slightly weakened by decreasing the Reynolds number due to the difference in the baseline drag and lift coefficients, whereas the higher angle of attack is found to raise the sensitivities. Finally, the similar sensitivity analysis is performed also for NACA4412 and NACA0012, and it is found that slight differences in the shape result in substantial differences in the sensitivities.