Source-linked AI summary
Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates
C. J. Lapeyre, A. Misdariis, N. Cazard, D. Veynante, T. Poinsot
TL;DR
The paper addresses sub-grid-scale contributions in premixed turbulent combustion using a mixed models/data approach. It uses a U-Net-inspired CNN to predict sub-grid-scale flame-surface-density wrinkling, with excellent agreement in a test case and better performance than classical models, while noting limited variability in the covered wrinkling values.
Problem
Determining the sub-grid-scale contribution in combustion motivates a mixed models/data approach.
Method
A U-Net-inspired convolutional neural network predicts sub-grid-scale flame-surface-density wrinkling.
Results
The CNN shows excellent agreement in a test case and significantly outperforms the comparison models.
Takeaways & Limitations
The approach can generalize to a different test case than the training set.
Takeaways & Limitations
The covered wrinkling values are not absolute, and more variability should be introduced in the dataset to confirm broader generalization.
Abstract
from arXiv · showhide
This work presents a new approach for premixed turbulent combustion modeling based on convolutional neural networks (CNN). We first propose a framework to reformulate the problem of subgrid flame surface density estimation as a machine learning task. Data needed to train the CNN is produced by direct numerical simulations (DNS) of a premixed turbulent flame stabilized in a slot-burner configuration. A CNN inspired from a U-Net architecture is designed and trained on the DNS fields to estimate sub-grid scale wrinkling. It is then tested on an unsteady turbulent flame where the mean inlet velocity is increased for a short time and the flame must react to a varying turbulent incoming flow. The CNN is found to efficiently extract the topological nature of the flame and predict subgrid scale wrinkling, outperforming classical algebraic models. This method can be seen as a data-driven extension of dynamic formulations, where topological information was extracted in a hand-designed fashion.
1. Introduction
The introduction motivates CNNs as a data-driven approach to estimating unresolved flame wrinkling in premixed turbulent combustion, where subgrid flame–turbulence interactions make reaction-rate closure difficult. The paper reformulates this estimation as supervised learning and evaluates a deep CNN against classical models.
- Data-driven methods are especially promising for closure subproblems involving simple assumptions and known flow topology, although they remain approximations despite available deterministic equations.
- Subgrid interactions between flames and turbulent scales strongly affect flame behavior, making filtered reaction-rate closure a longstanding combustion challenge.
- Unresolved flame-surface wrinkling is central to models based on flame surface area in both RANS and LES.
- Dynamic procedures suggest that extracting topological information can improve model accuracy, motivating CNNs as a natural extension that automatically aggregates multi-scale information.
- The paper proposes a deep CNN model for the subgrid reaction-rate contribution in premixed turbulent flames and tests it against classical models after DNS-based training.
- The evaluation freezes the trained network, applies it to new fields, compares accuracy with classical models, and discusses challenges specific to learning-based evaluation.
2. Theoretical modeling
The theoretical framework recasts flame-surface-density estimation as learning a field from spatially organized progress-variable data. Unlike local algebraic closures, the CNN uses convolutions to extract topology and construct subgrid quantities from surrounding flow information.
- Flame surface density models: In LES, spatial filtering removes unresolved turbulence scales, so filtered flame surfaces cannot generally provide the total flame surface needed for reaction-rate modeling.
- Flame surface density models: The framework limits the study to perfectly premixed adiabatic combustion and defines a progress variable c from unburnt and burnt-gas temperatures.
- Flame surface density models: Classical models represent unresolved wrinkling through a factor comparing total and resolved generalized flame surfaces, with alternatives based on fractal, multifractal, or dynamically determined parameters.
- Machine-learning reformulation: The machine-learning formulation maps local input fields to a matching output field of flame surface density, using DNS data where both c and Σ are known for supervised training.
- Machine-learning reformulation: A trained model is frozen and executed in an LES setting where the progress variable c is available but the flame surface density Σ is not.
- Machine-learning reformulation: Spatial convolutions reconstruct relevant information from cubes of adjacent mesh nodes, allowing the CNN to use surrounding topology rather than only pointwise local variables.
3. Building the training database
The training database uses DNS of premixed turbulent flames to generate filtered, downsampled inputs and normalized subgrid flame-surface-density targets on a coarser LES mesh.
- DNS simulations: Two DNS simulations of methane–air slot-burner flames provide the instantaneous fields used to generate c and ∇c data.The simulations use simplified two-step chemistry and a compressible Navier–Stokes solver.
- DNS simulations: The computational domain contains 512 cells in x and 256 cells in y and z, with periodic transverse boundaries and a double-tanh inlet profile.The inlet contains a fresh central flow surrounded by slower burnt-gas coflow.
- DNS simulations: DNS1 and DNS2 are steady-state simulations run for 14 ms, with the first 4 ms discarded and fields saved every 0.2 ms.The resulting datasets each span 10 ms and provide changing flame shapes for training.
- Dataset construction: Fine DNS fields are Gaussian-filtered and sampled on an LES mesh eight times coarser in every direction to form network inputs and targets.The filter width is tied to the maximum gradient of a one-dimensional laminar flame.
- Dataset construction: The input progress variable c is normalized from fresh-gas value 0 to burnt-flow value 1, while Σ is normalized by its laminar maximum.Normalized target values above 1 indicate unresolved flame surface caused by subgrid wrinkling.
4. Training the CNN to perform FSD estimation
The CNN reformulates full-field subgrid flame-surface-density estimation as a three-dimensional regression task, using a U-Net-inspired architecture trained on filtered DNS data.
- Problem formulation: The network maps a full 3D scalar field c(X), X ∈ R^n3, to an output field of the same dimension for pointwise Σ estimation.This preserves spatial locality while producing the complete field in a single inference.
- Network architecture: The U-Net-inspired CNN uses downsampling and upsampling paths with skip connections and is adapted from classification to regression.The final activation is changed to ReLU to prevent negative outputs.
- Network architecture: The network contains 1,414,145 trainable parameters.Its architecture comprises 13 layers and uses three-dimensional convolutions.
- Training data: DNS1 and DNS2 supply training and validation data, while a separate DNS3 simulation provides a testing distribution with different turbulent conditions.This split tests whether the network learns features that generalize beyond the training distribution.
- Training procedure: The network converges in approximately 150 epochs, requiring 20 minutes on an Nvidia Tesla V100 GPU.A validation set is used to monitor error and detect overfitting before final testing.
5. Using the CNN to evaluate subgrid scale wrinkling
The trained CNN is evaluated on an unsteady DNS3 flame after a temporary inlet-velocity increase, where it predicts subgrid wrinkling accurately and outperforms algebraic models.
- CNN inference: The CNN performs full-field inference in one pass because its fully convolutional structure accepts 3D fields of arbitrary size.For a 64 × 32 × 32 field, inference takes 12 ms and avoids overlapping inference regions.
- DNS3 test case: The flame surface continues increasing until approximately snapshot 9 after the inlet flow returns to its initial value, then recovers near snapshot 23.Snapshots after 15 are excluded because the later state shows no significant difference and is less challenging.
- Comparison with algebraic models: The CNN predicts total flame surface with very high accuracy compared with the algebraic models of Charlette et al. and the fractal model.The fractal model overestimates near the inlet, while the Charlette model underpredicts downstream.
- Comparison with algebraic models: The CNN uses large-scale flow topology to identify that the inlet flame is not yet wrinkled, where the algebraic models assume an equilibrium relation.This produces accurate inlet predictions despite turbulence being present before it has wrinkled the flame front.
6. Conclusions
A U-Net-inspired CNN predicts sub-grid scale flame surface density and wrinkling from turbulent-combustion data, matching DNS well on an underresolved test flame and outperforming algebraic models. Its learned topological representation extends dynamic formulations without hand-designed feature extraction, while broader generalization remains a challenge.
- Approach: A U-Net-inspired CNN was used to predict sub-grid scale flame surface density for a premixed turbulent flame.The approach targets flame wrinkling in turbulent-combustion modeling.
- Results: The CNN showed excellent agreement with the DNS baseline for an underresolved flame on a mesh typical of large eddy simulation.This test evaluates prediction on a flame represented at lower resolution than the DNS reference.
- Results: Algebraic models from the literature significantly underperformed compared with the CNN.The comparison supports the CNN’s advantage on the reported test case.
- Interpretation: Including topological information improved unresolved flame-wrinkling accuracy, consistent with earlier dynamic formulations.The CNN extracted this information automatically rather than through hand-designed processing.
- Generalization: The network demonstrated good accuracy and capacity to generalize to a different test case than the training set.The authors describe this as evidence of learned prediction beyond the original training setup.
- Limitations: The method’s broader generalization is limited because the studied wrinkling values are not comprehensive and require greater variability in the dataset.Future work is intended to expand generalization across new configurations and flame regimes.
Funding
The research received no specific grant from public, commercial, or not-for-profit funding agencies.
- No specific grant supported the research.
- The funding statement covers public funding agencies.
- The funding statement also covers commercial and not-for-profit sectors.