Neural network-augmented eddy viscosity closures for turbulent premixed jet flames

Abstract

Extending gradient-type turbulence closures to turbulent premixed flames is challenging due to the significant influence of combustion heat release. We incorporate a deep neural network (DNN) into Reynolds-averaged Navier–Stokes (RANS) models for the turbulent viscosity and thermal conductivity as nonlinear functions of the local flow state and thermochemical gradients. Our models are optimized over the RANS partial differential equations (PDEs) using an adjoint-based data assimilation procedure. Because we directly target the RANS solution, as opposed to the unclosed terms, successfully trained models are guaranteed to improve the in-sample accuracy of the DNN-augmented RANS predictions. We demonstrate the learned closures for in- and out-of-sample a posteriori RANS predictions of compressible, premixed, turbulent jet flames with turbulent Damköhler numbers spanning the gradient- and counter-gradient transport regimes. The DNN-augmented RANS predictions have one to two orders of magnitude lower spatiotemporal mean-squared error than those using a baseline $k$–$ϵ$ model, even for Damköhler numbers far from those used for training. This demonstrates the accuracy, stability, and generalizability of the PDE-constrained modeling approach for turbulent jet flames over this relatively wide Damköhler number range.

Novelty and Significance Statement

We develop a deep learning turbulence closure method for RANS calculations of turbulent premixed flames. The closure method embeds an untrained neural network into the RANS equations and then optimizes it over the flow solution using an adjoint-based technique. Novelty: This is the first application of solver-embedded deep learning to turbulent premixed jet flames. Significance: The method is a new, general-purpose closure-modeling framework for turbulent flames. For the present turbulent premixed jet flames, the method significantly reduces the error of a posteriori RANS predictions. The trained models generalize this improved accuracy across a wide range of Damköhler numbers, even in combustion regimes that are far out-of-sample from those used to train a particular model, which is not typical of deep learning closures.