Deep Residual Networks for Flamelet/progress Variable Tabulation with Application to a Piloted Flame with Inhomogeneous Inlet

ABSTRACT

In this work, a deep neural network is presented which is trained on flamelet/progress variable (FPV) tables and validated in a combustion large eddy simulation (LES) of the Sydney/Sandia flame with inhomogeneous inlets. Using data scaling and transformation techniques, as well as novel network architectures as the residual skip connection we are able to store all combustion relevant quantities in one single network, thus reducing effectively the memory footprint compared to the FPV tables, while keeping data retrieval times similar to table interpolation. The accuracy of the deep neural networks (DNN) is compared to its FPV counterpart and achieves excellent agreement. The DNN is also able to accurately predict the stiff progress variable source term ${\tilde{\dot{\omega }}}_{PV}$ in the thin reaction zone. Finally, the DNN thermochemistry representation is validated in combustion simulations of a 2D laminar premixed flame and a 3D LES of the Sydney/Sandia piloted jet flame with inhomogeneous inlet. The DNN results are in very good agreement with the conventional tabulated FPV simulations and show a promising way to efficiently reduce the storage size of high dimensional pretabulated thermochemical state space in reactive flow simulations.

Abbreviations: ANN: Artificial neural network; API: Application programming interface; CFD: Computational fluid dynamics; CFL: Courant-Friedrichs-Lewy; CPU: Central processing unit; DL: Deep learning; DNN: Deep neural network; FGM: Flamelet generated manifold; FLOPS: Floating point operation per second; FPV: Flamelet/progress variable; GPU: Graphics processing unit; HPC: High-performance computing; ILDM: Intrinsic low-dimensional manifold; LES: Large eddy simulation; MAE: Mean absolute error; MPI: Message passing interface; MSE: Mean squared error; PDF: Probability density function; SGS: Subgrid scale; SOM: Self-organizing map; TCI: Turbulence–chemistry interaction.

KEYWORDS:

• Deep learning
• neural networks
• FPV
• mixed-mode combustion
• LES

Acknowledgments

The financial support from Deutsche Forschungs Gesellschaft is gratefully acknowledged.

Notes

¹ $http://www.me.berkeley.edu/gri\mathrm{\_}mech/$

² www.tensorflow.org

³ This does also apply to inference on CPUs.

Additional information

Funding

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through grant no. 319178666 and SFB/TRR40.