In the MILD (Moderate or Intense Low-oxygen Dilution) combustion regime, reactions proceed in a hot, diluted, distributed reaction-zone mode in which classical turbulence-chemistry interaction closures lose their supporting assumptions. The source study (De and Dongre, Flow, Turbulence and Combustion 94:439-478, 2015) assessed steady-flamelet, Eddy Dissipation Concept (EDC), transported PDF (LPDF), and multi-environment PDF (MEPDF) closures on the Delft-jet-in-hot-coflow (DJHC-I, fuel-jet Reynolds number Re=4100) and Adelaide JHC (HM1-HM3, CH4/H2 fuel jet, Re=10000) benchmark flames and found that, while mean velocity, temperature, and major species are captured reasonably, all closures fail on the minor species CO and OH and their RMS fields; it further identified six unresolved modeling obstacles: the unknown origin of the CO/OH failure, MEPDF ill-conditioning and realizability violations, LPDF Monte-Carlo statistical/bias errors, the absence of a general micro-mixing model prescription for MILD, unstandardized inlet scalar-fluctuation boundary conditions, and the lack of any principled (non-tuned) parametrization of the EDC fine-structure constants at low Damköhler number. A decade of follow-up work has partially advanced individual obstacles - a generalised EDC with Reynolds- and Damköhler-dependent parameters (Lewandowski et al., 2020), LES/TPDF evidence that resolved molecular diffusion rather than the micro-mixing model controls accuracy (Zhou et al., 2020), and laminar-flow evidence that OH itself is in non-equilibrium under differential transport (Nourani Najafi et al., 2021) - but no closure has been demonstrated to predict CO and OH mean and RMS profiles across both burner families without case-specific tuning. The problem, whose common objective is predictive, model-agnostic simulation of mean and radical fields in MILD JHC flames, remains open.

Background

MILD (Moderate or Intense Low-oxygen Dilution) combustion is a low-NOx combustion technology in which fuel burns in a hot, oxygen-diluted environment produced by strong internal exhaust-gas recirculation, so that the flame front is suppressed and reactions occur in a distributed, low-temperature-rise mode. Laboratory surrogates of this regime are the jet-in-hot-coflow (JHC) burners: the Delft DJHC burner (in the source study, the DJHC-I flame: a Dutch-natural-gas fuel jet, modeled as 81% CH4, 4% C2H6 and 15% N2, issuing into a hot coflow containing 7.6% O2 by mass, at fuel-jet Reynolds number 4100) and the Adelaide JHC burner with its HM1, HM2, HM3 flames (a methane-hydrogen fuel jet at fuel-jet Reynolds number 10000, with coflow oxygen of 3%, 6%, and 9% by mass), both of which serve as the standard modeling benchmarks with published measurements; as documented in the source study, the DJHC database provides velocity, temperature, and turbulent quantities but no species data, while the Adelaide JHC database includes species measurements.

Turbulence-chemistry interaction (TCI) closures describe how sub-grid or sub-filter turbulent fluctuations couple with finite-rate chemistry. The source study compares four RANS-based closures: (i) the steady-flamelet presumed-shape PDF approach, which presumes the joint statistics of a conserved scalar (mixture fraction) and models chemistry by a family of steady counterflow flamelets - it fails here because the single-mixture-fraction, adiabatic, steady assumptions break down in a diluted hot coflow; (ii) the Eddy Dissipation Concept (EDC), which partitions each computational cell into a 'fine structure' region where chemistry occurs as a perfectly stirred reactor and a surrounding region where only mixing occurs, with the reacting fraction and residence time set by two model constants derived originally for high Reynolds and Damköhler number conditions; (iii) the Lagrangian transported probability density function (LPDF) method, which transports the one-point joint composition PDF with stochastic particles and therefore treats finite-rate chemistry exactly, requiring only a micro-mixing (molecular-diffusion) closure - candidates being IEM (interaction by exchange with the mean), CD (coalescence-dispersion, which pairs randomly selected particles), and EMST (Euclidean minimum spanning tree mixing, which mixes only composition-space neighbors and hence enforces localness); and (iv) the multi-environment Eulerian PDF (MEPDF) method, a deterministic moment-type approximation of the PDF by a weighted sum of delta functions in composition space.

The Damköhler number Da\mathrm{Da} (ratio of turbulent time scale to chemical time scale) is a key regime parameter: in MILD combustion chemistry is comparatively slow and the local Da\mathrm{Da} of the fine structures is low, which invalidates the assumptions under which the standard EDC constants were derived. The study finds that mean axial velocity and turbulent kinetic energy agree with measurements, that temperature is over-predicted downstream by EDC and PDF models on the DJHC flame, that LPDF and EDC capture major species on the Adelaide flames reasonably, but that all models show major discrepancies for the minor species CO and OH and their RMS profiles, improving somewhat as coflow oxygen (hence Da\mathrm{Da}) increases. The paper also documents: MEPDF source-term ill-conditioning and realizability violations for multi-component systems (traced to Jaishree and Haworth, 2012); LPDF statistical and bias errors associated with notional particles and Monte-Carlo solution; the sensitivity of transported-PDF results to including inlet temperature fluctuations in the boundary conditions (a sensitivity first established for MILD conditions by Ihme and See, 2011); and the empirical fact that increasing the EDC chemical-time-scale constant improves MILD predictions without any principled derivation. The minor radicals CO and OH matter practically - CO for emissions and OH as the flame-structure marker - and theoretically, because their prediction is a stringent test of whether a closure correctly represents the competition among turbulent mixing, molecular (and differential) diffusion, and finite-rate chemistry in distributed reaction zones.

Problem Statement

Achieve predictive, model-agnostic simulation of MILD jet-in-hot-coflow flames, in the sense defined and benchmarked by De and Dongre (2015): a turbulence-chemistry interaction closure (or family of closures with a common, non-case-specific parametrization) that, without per-flame tuning of closure constants, quantitatively predicts, on the standard public jet-in-hot-coflow (JHC) benchmark flames (the Delft DJHC-I flame at fuel-jet Reynolds number Re=4100 and the Adelaide HM1, HM2, HM3 flames at Re=10000, spanning 3-9% coflow oxygen by mass), the mean and RMS profiles of the quantities measured on each flame: temperature on both burner families, and the major species (CH4, H2, O2, H2O, CO2) and - the discriminating test - the minor species CO and OH on the Adelaide flames, since (as in the source study) the DJHC database provides velocity, temperature, and turbulent quantities but no species data. The source study documented six modeling obstacles in this regime, which jointly serve this single objective: (1) determine the origin of the persistent CO and OH (mean and RMS) misprediction among micro-mixing closure, chemical mechanism, turbulence parametrization, molecular/differential diffusion, and inlet data inadequacy; (2) remedy or replace the multi-environment PDF (MEPDF) formulation (ill-conditioned source terms, realizability violations for multi-component systems, ambiguous boundary-condition specification) if that route is to be viable for JHC flames; (3) quantify and control transported-PDF numerical errors (Monte-Carlo statistical and bias errors, particle-tracking and particle-density consistency); (4) establish a principled prescription for micro-mixing model selection in the MILD regime, including its interaction with detailed chemistry and differential diffusion; (5) establish a physically consistent, standardized method for prescribing inlet scalar-fluctuation boundary conditions for JHC burners; and (6) provide a first-principles (or at least mechanistic, non-tuned) parametrization of the Eddy Dissipation Concept (EDC) fine-structure constants valid at the low Damköhler numbers of MILD combustion. The six obstacles above are the modeling subgoals of this single objective; the objective requires a turbulence-chemistry interaction closure, or a family of closures with a common non-case-specific parametrization, whose resulting simulation capability quantitatively predicts the fields measured on each benchmark flame - including the CO and OH mean and RMS profiles on the Adelaide flames - without case-specific adjustment.

References

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