Noise reduction in car aerodynamics using a surrogate objective function and the continuous adjoint method with wall functions

The purpose of this paper is twofold. In the first part, the continuous adjoint formulation for field integral objective functions used in steady-state, incompressible aerodynamic optimization is developed. The formulation includes the full differentiation of the Spalart-Allmaras turbulence model based on wall functions. In the second part, the developed adjoint method is used for optimizing the side mirror shape of a passenger car, using volumetric B-Splines as the parameterization tool. Based on industrial experience, an appropriate, though approximate, objective function to be minimized is expressed by the integral of the squared turbulent viscosity over a volume residing next to the driver's window. It should be stressed that if the commonly used “frozen turbulence” assumption was made, by skipping the differentiation of the turbulence model, the adjoint method would not have been able to provide any kind of sensitivity derivatives, since this objective function depends exclusively upon the turbulent viscosity.