Improved Data Assimilation for Hypersonic Machine-Learned Turbulence Modeling

Recently, machine learning methodologies have demonstrated the ability to substantially improve Reynolds-averaged Navier-Stokes (RANS) computational models. The current work applies Data Assimilation and Field Inversion (DAFI) to train a Neural Network (NN) to learn two parameters, g^(1) and Pr_t, for closure of the k-ω SST turbulence model. The NN learns a mapping between scalar invariants in the flowfield and g^(1) and Pr_t fields, which embeds Galilean invariance into the turbulence model. The NN model is trained separately on two different cases to produce two different turbulence models. The first case uses Direct Numerical Simulation (DNS) data for Mach 5.86 flow over a flat plate. The second cases uses experimental data for Mach 7.11 flow over a 20° cylinder flare. The trained NN models were used to predict Mach 11 flow over a cone flare. Both models demonstrated improvement over the baseline k-ω SST model. The model trained on the cylinder flare predicts flow in the recirculation zone of the cone flare much better than either the k-ω SST model or the model trained on the flat plate data.