LEARNING RANS MODEL PARAMETERS FROM LES USING BAYESIAN INFERENCE

We propose a formal mathematical approach to assimilate LES data into values of RANS model parameters combined with some prior knowledge of the expected RANS parameter values. This is achieved using Bayesian inference to determine parameter values that maximize their posterior probability and is known as maximum a posteriori (MAP) estimation. We apply this approach to a premixed turbulent methane-air round jet flame using unburnt mixture equivalence ratio and bulk flow velocity as design parameters. The k-e model is used for turbulence closure and the eddy dissipation concept (EDC) model is used to model combustion. Three dimesional LES data for six design cases are computed and upto three of these are used for MAP estimation. The likelihood of RANS solutions is evaluated using flow field statistics from LES at training data points. The results show significant improvement in agreement between LES and RANS solutions, computed using MAP estimate parameters for species mass fraction and temperature fields at design points not in the training set. Marginal improvement is observed for velocity fields. This is most likely due to the absence of production terms in the RANS model that capture the three-dimensional nature of the flow being modelled. The marginal likelihood of the RANS model when assimilating both k- e and EDC model parameters is significantly higher than the case that leaves out the EDC model parameters. This suggests that the former approach is more likely to yield reliable RANS parameters. These results demonstrate the viability of MAP estimation as a means to improving the reliability of turbulent reacting flow RANS simulations for engineering design and optimization applications.