An Inverse Design Method for Airfoils Based on Pressure Gradient Distribution

Abstract

An airfoil inverse design method is proposed by using the pressure gradient distribution as the design target. The adjoint method is used to compute the derivatives of the design target. A combination of the weighted drag coefficient and the target dimensionless pressure gradient is applied as the optimization objective, while the lift coefficient is considered as a constraint. The advantage of this method is that the designer can sketch a rough expectation of the pressure distribution pattern rather than a precise pressure coefficient under a certain lift coefficient and Mach number, which can greatly reduce the design iteration in the initial stage of the design process. Multiple solutions can be obtained under different objective weights. The feasibility of the method is validated by a supercritical airfoil and a supercritical natural laminar flow airfoil, which are designed based on the target pressure gradients on the airfoils. Eight supercritical airfoils are designed under different upper surface pressure gradients. The drag creep and drag divergence characteristics of the airfoils are numerically tested. The shockfree airfoil demonstrates poor performance because of a high suction peak and the double-shock phenomenon. The adverse pressure gradient on the upper surface before the shockwave needs to be less than 0.2 to maintain both good drag creep and drag divergence characteristics.