Investigation of Differential Diffusion and Strain Coupling in Large Eddy Simulations of Hydrogen-Air Flames

Large Eddy Simulations with flamelet-based thermochemistry are used to investigate the behaviour of a premixed hydrogen-air flame stabilised by a bluff-body. Validation against experimental data is carried out first to demonstrate the model’s ability to predict both velocity field and flame structure. The capability of the model in predicting differential diffusion effects is then assessed, in particular regarding the coupling between differential diffusion, tangential strain and curvature, and their effect on mixture fraction redistribution and reaction rate variation. Results indicate that unstretched flamelet thermochemistry is capable of capturing the increase in mixture fraction caused by positive resolved strain, as well as negative variations of mixture fraction due to negative curvature. Furthermore, the model is observed to mimic the effects of negative Markstein length to a certain extent, so that positive tangential strain causes reaction rate increase. The interplay between resolved stretch and preferential diffusion is also shown to lead to a shorter flame length which is in better agreement with experimental observations as compared to simulations under unity Lewis number assumption. These findings highlight that the macroscopic effects of differential diffusion and stretch on the premixed hydrogen flame, characterised by significant strain levels, can be predicted using a flamelet-based approach and without recurring to strained flamelets database, which implies important simplifications in the combustion modelling of turbulent hydrogen-premixed flames and offers valuable insights for the design of novel combustors.

💡 Research Summary

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This paper investigates the interplay of differential diffusion, strain, and curvature in a premixed hydrogen‑air flame stabilized by a bluff‑body, using large‑eddy simulations (LES) coupled with a flamelet‑based thermochemistry model. The authors first validate the LES framework against experimental particle‑image‑velocimetry (PIV) and OH* chemiluminescence data obtained from the NTNU unconstrained bluff‑body burner (equivalence ratio φ = 0.4, atmospheric pressure, 25 °C). Validation shows that the LES predicts the mean velocity field and flame position within 5 % of the measurements, and that incorporating differential diffusion yields a flame length that matches the experiment, whereas a unity‑Lewis‑number assumption over‑predicts the length.

The combustion model relies on a database of one‑dimensional, unstretched premixed flamelets spanning a range of equivalence ratios. Two controlling scalars are used: a progress variable c based on water mass fraction and Bilger’s mixture fraction z. Their filtered (Favre‑averaged) values (˜c, ˜z) and sub‑grid variances (!ρ²c, !ρ²z) are solved through transport equations. A presumed filtered density function (FDF) assumes the joint PDF of c and z to be the product of two Beta distributions, whose shape parameters are linked to the resolved gradients and sub‑grid variances. Reaction rates are obtained by integrating the 1‑D flamelet rate φ̇c(c,z) over this joint PDF.

Differential diffusion is introduced at the flamelet generation stage by computing mixture‑averaged diffusion coefficients for each species from binary diffusion data. In the LES, two cases are compared: (i) unity Lewis number for all species (Leₖ = 1) and (ii) species‑specific diffusion (Leₖ ≠ 1). The latter captures preferential diffusion of hydrogen, which leads to a redistribution of the mixture fraction and a shortening of the flame.

Key physical findings are: (1) Positive resolved tangential strain increases the filtered mixture fraction z, which in turn raises the filtered reaction rate φ̇c. This mimics the effect of a negative Markstein length, even though the flamelet library contains only unstretched flames. (2) Negative curvature (flame front concave toward the fresh gases) reduces z and suppresses the reaction rate, consistent with curvature‑induced dilution. (3) The combined influence of strain and curvature on z and φ̇c is captured without resorting to strained flamelet databases, provided that the LES resolves the dominant strain rates.

The study demonstrates that a flamelet‑based LES with a presumed FDF closure can reproduce macroscopic differential‑diffusion effects and strain‑curvature coupling in hydrogen‑rich premixed flames. This approach offers a substantial simplification compared with databases of strained flamelets, while still delivering accurate predictions of flame length, structure, and response to strain. Limitations include the moderate strain rates examined (≈10⁴ s⁻¹); higher strain regimes may require explicit strained flamelet data. Additionally, the model employs an empirical scalar dissipation parameter β_c to account for curvature and diffusion effects, suggesting a need for dynamic closure models. Future work should extend the methodology to multi‑component fuels, higher pressures, and more extreme strain environments. Overall, the paper provides valuable insight for the design of low‑emission hydrogen combustors and establishes a practical LES‑flamelet framework that balances computational efficiency with fidelity to differential‑diffusion physics.