An exact inverse method for subsonic flows

Abstract

Abstract. A new inverse method for aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed in a natural way, i.e., as a function of arclength of the as yet unknown body. This inverse problem is shown to be mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this nonlinear problem determines the airfoil, free stream Mach number Moo and the upstream flow direction 6^. The existence of a solution to a given pressure distribution is discussed. The method is easy to implement and extremely efficient. We present a series of results for which comparisons are made with the known airfoils. This method will be extended to design supercritical airfoils in the future.1. Introduction. The inverse problem in the context of aerodynamics is the determination of an airfoil that will generate a given pressure distribution. This problem has been considered important for decades because many desirable features of the flowfield, such as delay of separation and laminar-turbulent transition, can be achieved by proper prescription of the pressure distribution along the surface of the as yet unknown body (Stratford [33,34,35]). The point of separation of zero skin friction is related to the specified pressure distribution (see Stratford [33,34] and references therein) and a flow with zero skin friction throughout its region of pressure rise is expected to achieve any specified pressure rise in the shortest possible distance with least possible energy loss (Stratford [35]). In aerodynamics these flow features are highly desirable and can be realized in practice since a suitable pressure distribution can be specified to avoid the undesirable flow features and an airfoil can be generated that will have this pressure distribution along its body. This paper addresses this problem of generating an airfoil from a given pressure distribution and proposes a new and extremely efficient method of solution to this problem.