Assessment of tabulated-chemistry models for lean premixed strained hydrogen flames with low-dimensional manifolds

TL;DR

The study addresses the challenge of accurately modeling lean premixed hydrogen flames with differential diffusion using tabulated-chemistry approaches in LES. It systematically compares 1D fixed-strain, 2D unstretched, and 2D fixed-strain-with-varying-equivalence-ratio flamelet manifolds against DNS-based a priori data, employing beta-FDF and F-TACLES closures, plus a laminar-based correction for unstretched manifolds. Key findings show strong limitations of unstretched flamelet manifolds, while strained flamelets—especially fixed-strain with varying equivalence ratio—achieve significantly better predictions of consumption speed and local reaction rates across grid resolutions; a simple correction derived from laminar data further improves turbulent predictions for coarse grids. The work provides strain-selection guidelines and correction strategies that preserve memory efficiency, enabling more reliable, diffusion-aware LES of practical hydrogen combustion systems.

Abstract

This study presents a comprehensive a priori analysis of tabulated-chemistry models for both laminar and turbulent lean premixed hydrogen flames in strained counterflow configuration. Particular focus is drawn on differential and preferential diffusion effects and the synergistic interaction of thermodiffusive instabilities and turbulence that existing models struggle to capture. Through detailed assessment of various modelling approaches at unfiltered and filtered grids, we identify significant limitations in traditional unstretched flamelet manifolds, particularly their strong filter dependence and systematic reaction rate mispredictions. To address these challenges, we introduce and evaluate novel strained flamelet approaches, including: (1) a one-dimensional manifold constructed from a single strained flamelet that provides computationally efficient and reliable consumption speed predictions at coarser grids, and (2) a two-dimensional manifold combining fixed strain with varying equivalence ratio that demonstrates improved performance in predicting the local reaction rates across multiple grid resolutions. Additionally, we develop a correction methodology derived from laminar simulations that significantly improves consumption speed predictions of unstretched flamelet manifolds in turbulent settings. Unlike previous works, our solutions maintain computational efficiency without increasing manifold dimensionality, keeping memory costs unchanged. These advancements provide guidance for developing reliable LES models that properly account for differential and preferential diffusion and strain effects in practical hydrogen combustion systems.

Figures (11)

• Figure 1: Sketch of the two-dimensional laminar reactants-to-products counterflow setup, showing the flame solution at $a=706.85$ s$^{-1}$porcarelli2025stability. The flame front is identified by the contour of hydrogen source term $\dot{\omega}_{\rm H_2}$, and super-adiabatic temperatures are visible in the region of super-unity temperature progress variable $\Theta$.
• Figure 2: Cross-section sketch at the mid cutting plane of the three-dimensional turbulent counterflow setup at a sample timestep, showing a snapshot of the flame solution at $a=2000$ s$^{-1}$fathi2025strain. The flame front is identified by the contour of hydrogen source term $\dot{\omega}_{\rm H_2}$, and super-adiabatic temperatures are visible in the region of super-unity temperature progress variable $\Theta$.
• Figure 3: Ratio of modelled versus DNS consumption speed for the first three cases (a) and cases four to nine (b) of Table \ref{['tab:cases']}, for increasing filter widths.
• Figure 4: Relative error of the H$_2$ source term $\dot{\omega}_{\rm H_2}$ over the resolved grid and with increased filter width obtained with the 2DU-type manifolds. The filtered fields are reconstructed with the $\beta$-FDF (a) and with the F-TACLES (b) subgrid models.
• Figure 5: Snapshots at $t=t_1$ (first row) and $t=t_2$ (second row) of H$_2$ source term at the mid-plane of the a5000T simulation over the unfiltered field and with increasing filter width.