Data-based modeling of instantaneous dissipation rate profiles in multi-modal turbulent combustion

Computational modeling approaches must be developed to more accurately and efficiently characterize multi-modal turbulent combustion. The computational cost of turbulent combustion modeling can be reduced considerably by projecting the thermochemical state onto a low-dimensional manifold, but, in traditional approaches, a single manifold coordinate of mixture fraction or progress variable limits model applicability to a single combustion 'mode.' While new approaches with two manifold coordinates (mixture fraction and generalized progress variable) can describe multi-modal combustion, more dissipation rates appear in the manifold equations as coefficients. These dissipation rates vary with mixture fraction and generalized progress variable and must be modeled. This work leverages DNS data of a temporally evolving n-dodecane jet flame to extract instantaneous dissipation rate profiles and interpolate their values in unaccessed regions of manifold space via Gaussian process regression (GPR). A deep neural network (DNN) is then trained to predict the instantaneous profiles as a function of coarse-grained data to provide model closure for the manifold equations, resulting in a hybrid physics-derived and data-derived model applicable to multi-modal combustion.