Response Surface Techniques for Diffuser Shape Optimization

Abstract

The design of incompressible diffusers for maximum pressure recovery is used to demonstrate the utility of response surface approximations for design optimization of flow devices. Two examples involving two and five design variables are treated, with the diffuser wall shapes described by polynomials and B-splines. In both cases monotonicity conditions drastically reduce the design space. In this irregularly shaped space, a pool of designs is selected by a D-optimality criterion and analyzed by a finite volume computational fluid dynamics (CFD) code. Quadratic polynomial response surfaces are then fitted to the pressure recovery coefficients. To improve the prediction accuracy, uncertain regressor terms and possible outlier design points are excluded based on statistical tests. A standard optimization algorithm is used to find the optimal diffuser design from the response surface approximations. The optimum diffusers exhibit minimal flow separation and yield similar wall shapes for the two parameterizations. A main asset of the response surface optimization approach lies in the smoothing of noisy response functions. Therefore, the issue of numerical noise in CFD results based on the use of two different analysis codes is addressed