Model identification in reactor-based combustion closures using sparse symbolic regression

In Large Eddy Simulations (LES) of combustion, the accuracy of predictions might be heavily affected by deficiencies in traditional/simplified closure models, especially when employed to simulate non-conventional fuels and combustion regimes. The increasing availability of data from experiments and higher-fidelity numerical simulations offers attractive opportunities for improving combustion models with data-driven techniques. In this work, we focus on sub-grid turbulence-chemistry interactions with the Partially Stirred Reactor (PaSR) model and its associated cell reacting fraction sub-model. We combine machine learning and sparsity-promoting techniques to improve the predictive capabilities of PaSR by discovering new functional forms of the cell reacting fraction sub-model from data. The obtained models are parsimonious models that balance accuracy with model complexity to avoid over-fitting. We employ the proposed model identification approach on data from a Direct Numerical Simulation (DNS) of a three-dimensional non-premixed n-heptane/air jet flame. As a result, we single out the most plausible model form of the cell reacting fraction, expressed as a function of the local Damköhler number. Then, the capability of the model to generalize properly to new, previously unseen data is tested. The results demonstrate the ability of the machine learning approaches to infer robust corrections for turbulence-chemistry reactor-based combustion models.