Multi-objective optimisation of the model parameters for the realisable k-ε turbulence model

Abstract

The broad family of k-e turbulence models is very often used in engineering computational fluid dynamics (CFD). All these models contain semi-empirical parameters that have been determined based on idealised flows. However, it is important to recall that the model parameters are not universal and not even necessarily constant. Consequently, a large span of model parameters can be found in the scientific literature. The objective of the present study is to determine optimised but generally applicable model parameters for the prediction of turbulent quantities for the realisable k-e model. Four canonic flow configurations are considered simultaneously in the optimisation: channel flow, flow over a backward-facing step, jet flow, and flow over a periodic hill. The optimisation problem thus involves several concurrent objectives that must be fulfilled simultaneously. The obtained optimised model parameters do not differ tremendously from the standard recommended values. Nevertheless, for all the configurations the optimised model delivers better, or at least equally good results compared with experimental measurements. Therefore, employing the model parameter values proposed in this work is recommended, since a slightly improved prediction is obtained at no additional numerical cost.