Data-Based Progress Variable Dissipation Rate Modeling for Turbulent Premixed Combustion

Manifold-based turbulent combustion models substantially reduce computational cost by projecting the thermochemical state onto a lower-dimensional space and reconstructing the state from a set of manifold equations. Closure of the one-dimensional premixed manifold equations in progress variable requires a profile for the progress variable dissipation rate with respect to the progress variable. In LES, the filtered progress variable dissipation rate can be obtained by convoluting this model profile against a presumed subfilter PDF. These profiles are typically ad hoc and derived analytically with crude assumptions, and the resulting thermochemical state can be sensitive to these profiles. In this work, deep neural networks (DNN) are leveraged to model both the filtered progress variable dissipation rate and its profile. The particular focus of this work is the role of the selection of model inputs and the pre-processing of these inputs using simple physical principles. Consideration of the progress variable source term as a model input for the filtered progress variable dissipation rate, for instance, is shown to substantially reduce model error. The data-based models are assessed using a priori analysis of a DNS database of a turbulent premixed jet flame.