Optimisation of structured grid spacing parameters for separated flow simulation using mathematical optimisation

This paper describes the use of computational fluid dynamics (CFD) and mathematical optimisation techniques to minimise the error in predicting the recirculation zone for a separated flow topology. Grid spacing parameters are varied in the optimisation process. The accuracy of separated flow solutions is known to be dependent on the grid resolution and clustering. Although general guidelines have been developed for grid generation of separated flow topologies, the flow solutions using the resulting grids often under-predict features like recirculation zones. This study addresses this aspect by providing an automatic tool for optimising the grid for solution accuracy. This approach has until recently been too expensive, but is becoming more viable with ever-increasing computer power. A two-dimensional sinusoidal hill is used as an example of a separated flow topology. The CFD simulation employs the commercial CFD solver STAR-CD to solve the Reynolds-Averaged Navier–Stokes equations with the RNG k– turbulence model. CFD solution time is drastically reduced by making use of initial field restarts. The optimisation is carried out by means of Snyman's DYNAMIC-Q method, which is specifically designed to handle constrained problems where the objective or constraint functions are expensive to evaluate. Six design variables (grid spacing parameters) are considered in this study. The results indicate that the re-attachment point of the recirculation zone is predicted to within 1% of the specified experimental value in four optimisation iterations and therefore represents a cost-effective way to determine grids based on solution accuracy.