Regime-general turbulence–chemistry interaction closures for large-eddy simulation of premixed turbulent combustion

Large eddy simulation (LES) of premixed turbulent combustion filters out the thin flame front, so the filtered chemical source terms must be closed by subgrid models. A comparison study of flamelet and finite-rate-chemistry LES closures (Fureby, AIAA Paper 2007-1413, 2007) showed that each existing closure family carries regime-specific assumptions whose validity is tied to the local Karlovitz and Damköhler numbers, and the AIAA LES Working Group survey co-authored by the same author (Georgiadis, Rizzetta and Fureby, AIAA Journal 48, 2010; NASA/TM-2009-215616) identifies advances in subgrid modeling for reacting-flow simulations as a necessary future research direction. The surviving open core is a subgrid turbulence–chemistry interaction closure for premixed combustion whose validity is not confined to a single regime but extends from the flamelet regime through thin-reaction-zone and broken-reaction-zone regimes, together with the supporting aspects that a regime-general solution must address consistently: treatment of subgrid scalar statistics, affordable yet demonstrably accurate chemistry, and principled local selection or hybridization between flamelet- and finite-rate-type closures. As of 2022–2025 the literature still treats these aspects as active, unresolved modeling challenges: filtered chemical source term modeling is still described as a fundamental challenge for LES of reacting flows in 2025, and the extreme-turbulence regime physics that a general closure must cover is itself under revision.

Background

In large eddy simulation (LES), the large turbulent scales are resolved on the computational grid while the effect of the small (subgrid) scales is modeled; for reacting flows this means the species transport equations are spatially filtered, producing filtered reaction rates that depend on the unresolved subgrid distribution of temperature and species. Because chemical reaction rates follow strongly nonlinear, temperature-sensitive Arrhenius kinetics (rates that rise steeply with temperature), the filtered reaction rate cannot be recomputed from filtered (grid-averaged) quantities — this is the turbulence–chemistry interaction (TCI) closure problem, the central open problem of combustion LES.

For premixed combustion (fuel and oxidizer mixed before ignition, so the flame propagates as a front characterized by the unstretched laminar flame speed $S_u^0$ and thickness $\delta_u^0$), the standard map of operating conditions is the Borghi–Peters regime diagram, parametrized by the Damköhler number $Da$ (large-scale turbulent time over chemical time) and the Karlovitz number $Ka$ (chemical time over Kolmogorov, i.e. smallest turbulent-eddy, time). In the flamelet regime ($Ka\ll 1$) turbulence only wrinkles an internally intact thin flame; for $Ka\gtrsim 1$ Kolmogorov eddies penetrate the flame preheat zone (thin-reaction-zone regime) and for sufficiently large $Ka$ penetrate the reaction zone itself (broken-reaction-zone or distributed regime), so the thin-front picture underlying flamelet models fails. Practical devices (gas-turbine combustors, afterburners, ramjets/scramjets) locally span all of these regimes in a single flow, so a closure valid only in one regime cannot serve as a single predictive tool. Recent experiments and direct numerical simulation (DNS, which resolves all turbulence and chemistry scales without subgrid models) reviewed by Driscoll et al. (2020) show that under extreme turbulence preheat layers broaden while thin reaction layers survive to $Ka$ far above the classical flamelet-breakdown limit, so even the regime boundaries a general closure must cover remain under revision.

The main closure families are: flamelet models, which assume the turbulent flame is an ensemble of locally one-dimensional laminar flamelets — including flame-surface-density and wrinkling-factor models (the wrinkled flame area is corrected by flame-wrinkling factors) and flamelet/progress-variable tabulation (thermochemistry precomputed and tabulated against a reaction progress variable); thickened-flame models (TFM/ATF), which artificially thicken the flame so it resolves on the grid and correct the lost subgrid wrinkling with an efficiency function; and finite-rate-chemistry models, which solve filtered species equations with a reaction mechanism and model the subgrid TCI through presumed probability density functions (presumed-PDF, requiring modeled subgrid scalar variances), the eddy-dissipation concept (EDC, which assumes reaction occurs only in the fine turbulent structures), or the partially stirred reactor model (PaSR, in which each cell reacts only in a fraction of its volume determined from the ratio of a mixing time to a chemical time). Detailed chemical mechanisms are too expensive for LES, so reduced mechanisms are used, trading accuracy for cost; they must reproduce $S_u^0$, $\delta_u^0$, the adiabatic flame temperature $T_{ad}$, and intermediate species such as CO. Because each family carries regime-specific assumptions, hybrid and adaptive-selection approaches have also been explored: hybrid flamelet/finite-rate-chemistry approaches that place computationally expensive transported-FDF finite-rate Lagrangian particles only at dynamically selected locations, with flamelet chemistry elsewhere (Rieth, Chen, Menon and Kempf, 2019); adaptive scalar transport that groups the scalar state between a fully transported and a flamelet-manifold representation according to drift-difference and strain-sensitivity criteria (Zhao, Huang and Zhou, 2025); and the Pareto-efficient combustion framework, whose manifold drift term quantifies the local model-form uncertainty of flamelet-type closures as a basis for local model selection (Wu, Ma, Jaravel and Ihme, 2017). Each of these is a particular switching or grouping heuristic rather than a closure demonstrated to be regime-general across the Karlovitz- and Damköhler-number range.

The source paper, Fureby, "Comparison of Flamelet and Finite Rate Chemistry LES for Premixed Turbulent Combustion" (AIAA Paper 2007-1413, 45th AIAA Aerospace Sciences Meeting, 2007), compared flamelet and finite-rate LES closures for a bluff-body-stabilized premixed propane/air flame, classified closures into infinite/finite-rate-chemistry and flamelet families, and employed a local Karlovitz number defined from the chemical and Kolmogorov time scales. Citing papers record that it found the PaSR closure appropriate over a wide range of problems (with validity dependent on subgrid mixing intensity in the regime considered) and that intermediate species such as CO were underpredicted with the chemistry used. Georgiadis, Rizzetta and Fureby (AIAA Journal 48, 2010; NASA/TM-2009-215616) describe modeling of the filtered reaction rates — the subgrid turbulence–chemistry interaction — as an outstanding modeling challenge, and state that advances in subgrid modeling for reacting-flow simulations are necessary.

Problem Statement

Formulate a subgrid turbulence–chemistry interaction (TCI) closure for the filtered chemical source terms in LES of premixed turbulent combustion that meets the following core objective: a single predictive LES combustion capability spanning the turbulence–chemistry regime range — from the flamelet regime ($Ka\ll 1$) through thin-reaction-zone ($Ka\sim 1$) and broken-reaction-zone (large $Ka$) conditions — rather than a patchwork of regime-limited models. Fureby (AIAA Paper 2007-1413) documented the regime-dependent validity of existing closure families, and Georgiadis, Rizzetta and Fureby (AIAA Journal 48, 2010; NASA/TM-2009-215616) identify advances in subgrid modeling for reacting-flow simulations as a future research need.

1. Regime generality (core objective): the closure is applicable across the range of local turbulence–chemistry regimes encountered in premixed combustion — from flamelet conditions (Karlovitz number $Ka\ll 1$) through thin-reaction-zone and broken-reaction-zone conditions (large $Ka$), for varying Damköhler number $Da$ — so that its validity is not confined to a single regime or to the regime-specific limits of existing closure families.

A regime-general solution must also address the following supporting aspects consistently:

2. Subgrid scalar statistics: it consistently treats the subgrid scalar variances and their influence on the strongly nonlinear, temperature-sensitive filtered reaction rates.
3. Affordable, accurate chemistry: it is compatible with chemical mechanisms that remain computationally tractable in LES while demonstrably reproducing laminar flame speed $S_u^0$, flame thickness $\delta_u^0$, adiabatic flame temperature $T_{ad}$, and intermediate-species prediction (e.g., CO).
4. Principled closure selection: where multiple closures are combined, the local selection or blending between flamelet-type and finite-rate-type closures follows stated local criteria rather than case-by-case user prescription, and the resulting model's validity is not confined to the regime-specific limits of the constituent closures.

Items 2–4 are to be addressed consistently with the regime-generality of the core objective in item 1: item 3 may be met by an existing reduced mechanism that satisfies the stated accuracy targets, and item 4 applies only where closures are combined.

References

1. Christer Fureby, "Comparison of Flamelet and Finite Rate Chemistry LES for Premixed Turbulent Combustion", AIAA Paper 2007-1413, 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV (2007), DOI 10.2514/6.2007-1413, https://doi.org/10.2514/6.2007-1413
2. Christer Fureby, "Large eddy simulation modelling of combustion for propulsion applications", Philosophical Transactions of the Royal Society A 367, 2957–2969 (2009), DOI 10.1098/rsta.2008.0271, https://doi.org/10.1098/rsta.2008.0271
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