Hydrogen reaction rate modeling based on convolutional neural network for large eddy simulation

TL;DR

Lean hydrogen LES modeling faces severe subfilter-scale challenges due to rapid H2 diffusion and thermodiffusive instabilities. The authors train a convolutional neural network, inspired by U-net, to map 3D LES fields $\widetilde{c}$ and $\widetilde{\\phi}$ to the filtered burning rate $\overline{\dot{\omega}}$, using a DNS-derived dataset across five equivalence ratios and three filtering scales. The model achieves high accuracy on unseen test data (NMAE ~5%), generalizes to new filter sizes and equivalence ratios, and outperforms a standard filtered tabulated-chemistry approach, particularly in very lean flames. This data-driven closure offers a promising pathway to accurate, carbon-free hydrogen combustion simulations and motivates further integration of ML closures into LES workflows for turbulent reacting flows.

Abstract

This paper establishes a data-driven modeling framework for lean Hydrogen (H2)-air reaction rates for the Large Eddy Simulation (LES) of turbulent reactive flows. This is particularly challenging since H2 molecules diffuse much faster than heat, leading to large variations in burning rates, thermodiffusive instabilities at the subfilter scale, and complex turbulence-chemistry interactions. Our data-driven approach leverages a Convolutional Neural Network (CNN), trained to approximate filtered burning rates from emulated LES data. First, five different lean premixed turbulent H2-air flame Direct Numerical Simulations (DNSs) are computed each with a unique global equivalence ratio. Second, DNS snapshots are filtered and downsampled to emulate LES data. Third, a CNN is trained to approximate the filtered burning rates as a function of LES scalar quantities: progress variable, local equivalence ratio and flame thickening due to filtering. Finally, the performances of the CNN model are assessed on test solutions never seen during training. The model retrieves burning rates with very high accuracy. It is also tested on two filter and downsampling parameters and two global equivalence ratios between those used during training. For these interpolation cases, the model approximates burning rates with low error even though the cases were not included in the training dataset. This a priori study shows that the proposed data-driven machine learning framework is able to address the challenge of modeling lean premixed H2-air burning rates. It paves the way for a new modeling paradigm for the simulation of carbon-free hydrogen combustion systems.

Figures (9)

• Figure 1: U-net type architecture used in the present work. Each black box corresponds to a multi-channel feature map. The number of channels is denoted on top of the box. The input sample has three channels: $\widetilde{c}$, $\widetilde{\phi}$ and $\delta_L^0/\delta_L^1$. The ratio $\delta_L^0/\delta_L^1$ is the inverse of the laminar flame thickening due to filtering (Section \ref{['sec:filtering']}). The original size of the cubic sample is $\mathrm{N^3}$. It is then reduced to $\mathrm{(N/2)^3}$ and $\mathrm{(N/4)^3}$ during the contracting path before to go back to the original size during the expansive path. Gray boxes represent copied feature maps. The arrows denote the different operations
• Figure 2: Diagram of the slot burner configuration used to generate the DNS database. The flame is depicted by an iso-surface at a progress variable $c=0.5$ colored by $\dot{\omega}=-\dot{\omega}_\mathrm{H_2}$. The dimensions of the domain are annotated on the right. The length $L_x$ is adapted to the length of the turbulent flame brush, which is function of the global equivalence ratio $\phi_g$
• Figure 3: Diagram of the strategy used to generate data and train the CNN. $\delta_L^0/\delta_L^1$ is the inverse of the laminar flame thickening due to filtering (Section \ref{['sec:filtering']}). $\widetilde{\phi}$ is calculated from $\widetilde{\xi}$ using Eq. (\ref{['eq:phi_tilde']})
• Figure 4: Left: Evolution of the RMSE during training, evaluated over the training dataset (red circles) and the validation dataset (blue squares). Black solid lines are moving averages of the RMSE. The black circle shows the lowest RMSE over the validation dataset. The model parameters at this specific epoch are selected. Right: Normalized mean absolute error over the testing solutions (Eq. (\ref{['eq:NMAE']})) for the different equivalence ratios and LES parameters used for building the training dataset. Error bars show first and third quartiles of the data points
• Figure 5: Scatter plots with 2D histograms: CNN-modeled burning rate $\overline{\dot{\omega}}^{\mathrm{NN}}$ versus ground-truth filtered burning rate $\overline{\dot{\omega}}^{\ast}$. Individual values are normalized by the maximum burning rate in the datasets. The points used for the histograms have a progress variable $c$: $0.05\leq c \leq 0.95$. Histogram values below the colour scale are transparent. Gray dashed line indicates $x=y$ (i.e. zero error). Each column corresponds to a global equivalence ratio. Each row corresponds to a set of LES parameters (filtering and downsampling). Data are collected from the testing solutions