Data-based instantaneous conditional progress variable dissipation rate modeling for turbulent premixed combustion

Manifold-based turbulent combustion modeling reduces computational cost considerably by projecting the thermochemical state onto a lower-dimensional space of a few manifold variables and reconstructing the state from a set of manifold equations. In turbulent premixed combustion, a one-dimensional space is defined by the progress variable, and the progress variable dissipation rate appears as a parameter in the resulting one-dimensional manifold equations. Closure of the manifold equations requires a model for the dependence of this dissipation rate on the progress variable. Existing models for these profiles are often ad hoc, derived analytically with crude assumptions, and assumed to be spatially and temporally 'universal' - yet the resulting thermochemical state can be sensitive to these profiles. To evaluate the assumptions in traditional models, instantaneous conditional progress variable dissipation rate profiles are extracted from DNS databases of turbulent premixed jet flames. At low Karlovitz number, the instantaneous conditional progress variable dissipation rate profiles exhibit some variance but are relatively well-characterized by a 'universal' model. However, a large variance in the instantaneous conditional progress variable dissipation rate profiles is observed at high Karlovitz number, indicating the form of the conditional dissipation rate is certainly not 'universal'. To capture this variation at high Karlovitz number, a data-based model for the instantaneous conditional progress variable dissipation rate profiles is generated, and the resulting model predictions demonstrate excellent agreement with profiles extracted from DNS and far less error than 'universal' models. The sensitivity of the solutions of the one-dimensional premixed manifold equations to the dissipation rate profile is demonstrated a priori, and the error associated with the observed variance in the instantaneous conditional progress variable dissipation rate profiles (i.e., relative to the DNS mean) indicates that an instantaneous modeling approach is necessary. A variable importance study is conducted, and the conditional velocity gradient is identified as the critical quantity that characterizes the observed variance in the instantaneous conditional progress variable dissipation rate profiles, providing further motivation for a data-based modeling approach.