ABSTRACT: This paper concerns a numerical optimization method for designing airfoils based on adjoint method. The goal of present work is to reduce the compressibility drag or pitching moment of transonic airfoils without compromising on the lift coefficient. A new cost function based on this requirement is defined and the corresponding adjoint equations are discussed in details. At the end, by demonstrating some numerical results, we show that this technique is capable of converging to the optimum design point corresponding to the initial geometry of the airfoil.

ABSTRACT: This paper concerns a new coupled free wake-CFD method for proper calculation of aerodynamic loads on a two bladed helicopter rotor in hovering flight. Loading is computed by solving the three dimensional Euler equations in a rotating coordinate system. However, since direct simulation of the tip vortices and wake requires a very fine grid, the rotor's wake effects are modeled by a free wake approach and included into the CFD calculation by a transpiration boundary condition at the rotor surface. An influence coefficient solution method is used to find the rotor's wake shape, being steady in a rotating frame. Euler equations are also considered in the form of absolute flow variables and solved by a multi grid Jameson's finite-volume method. The accuracy of the proposed method is illustrated by comparing numerical results to the available experimental results for the pressure distribution on a blade of a model helicopter rotor at different tip Mach numbers.