MILD Combustion: Low-oxygen Dilution Regime

• MILD combustion is a turbulent regime characterized by preheated, highly diluted reactants that create broad, low-intensity reaction zones.
• It enhances thermal efficiency and minimizes NOₓ emissions by moderating reaction rates and reducing peak temperatures in industrial applications.
• Advanced modeling employs turbulence–chemistry interaction methods such as EDC, PDF approaches, and machine learning-enhanced closures for predictive accuracy.

Moderate or Intense Low-oxygen Dilution (MILD) combustion is a turbulent combustion regime characterized by preheated, highly diluted reactants resulting in distributed, low-intensity reaction zones and suppressed pollutant formation. Distinguished from conventional flames by the absence of localized luminous fronts and the presence of extended, kinetically regulated reaction regions, MILD combustion operates under conditions of elevated reactant temperature (typically $T > 1100\,\mathrm{K}$), low oxygen concentrations (${\lesssim}10\%$ by volume), and extensive recirculation of flue gases or hot products. These properties yield high thermal efficiency, low NOₓ emissions, and robust flame stability, with significant relevance for industrial furnaces and next-generation clean combustion systems (Xiao et al., 4 Jan 2026, De et al., 2021, Yang et al., 22 Sep 2025).

1. Defining Criteria and Physical Chemistry of MILD Combustion

MILD combustion arises when incoming reactant streams are sufficiently preheated and highly diluted, such that local auto-ignition occurs well above the temperature at which a classical ignition front would form, but volumetric reaction rates remain moderated due to dilution by inert products (CO₂, H₂O, N₂) (Xiao et al., 4 Jan 2026, Dongre et al., 2021). Canonical criteria include:

• Preheat temperature $T_\mathrm{obs} \gtrsim 1100\,\mathrm{K}$ (with some DNS studies employing $T_u = 1500\,\mathrm{K}$) (Xiao et al., 4 Jan 2026, Yang et al., 22 Sep 2025).
• Oxidizer dilution to $3$–$10$ vol % O₂ (further reduction—below 2%—marks the “intense” subregime) (Yang et al., 22 Sep 2025, Dongre et al., 2021).
• Distributed, non-luminous reaction zones with a broad thermal thickness ($\delta_\mathrm{th}^{\mathrm{st}} \sim$1.6–3 mm depending on regime) (Yang et al., 22 Sep 2025).

The chemical characteristic is a suppression of local maxima in heat release, driven by both the reduced O₂ concentration and enhanced radical pool—particularly OH and H₂O—which moderate chain-branching rates. Arrhenius-type finite-rate chemistry is essential; for species $\alpha$,

$$\dot{\omega}_\alpha = W_\alpha (\nu_\alpha' - \nu_\alpha'') k(T) \left[ \prod_j C_j^{\nu_j''} - \frac{1}{K_{eq}} \prod_j C_j^{\nu_j'} \right],$$

with $k(T)$ governed by $A T^n \exp(-E/(RT))$. Radical-driven pathways, slow global reaction rates, and strong coupling between mixing and chemical timescales are observed features (Xiao et al., 4 Jan 2026, De et al., 2021). The thick reaction zone leads to a broader spatial distribution of heat release, a lower peak temperature, and decreased pollutant (NOₓ) formation (Xiao et al., 4 Jan 2026, Dongre et al., 2021).

2. Experimental Configurations and Canonical Burners

MILD combustion has been systematically investigated in laboratory-scale configurations such as the Delft Jet-in-Hot-Coflow (DJHC) and Adelaide Jet-in-Hot-Coflow (JHC) burners (De et al., 2021, Xiao et al., 4 Jan 2026). These configurations are characterized by:

• Central methane or methane-hydrogen jets (diameter 4–4.5 mm) surrounded by annular hot coflow tubes (inner diameter ≈82 mm) (Dongre et al., 2021).
• Hot coflow compositions: oxidizer mole fractions $X_{O_2}$ of 3–11% balanced by CO₂, H₂O, or N₂, with coflow temperatures up to $T_\mathrm{coflow} \approx 1400\,\mathrm{K}$ (Dongre et al., 2021, De et al., 2021).
• Reynolds numbers ranging from $Re = 4100$ to $Re = 23{,}000$, enabling both well-mixed and high-turbulence regimes (Dongre et al., 2021, Xiao et al., 4 Jan 2026).
• Diagnostic access to centerline and radial velocity, mixture fraction, species, and temperature profiles via LDA, CARS, Raman, and LIF (Bhaya et al., 2021).

These setups allow detailed validation of modeling strategies, including both velocity/mixing statistics and chemical scalars (Dongre et al., 2021, Bhaya et al., 2021, De et al., 2021).

3. Governing Equations and Combustion Modeling Approaches

MILD combustion necessitates simulation frameworks that resolve strong turbulence–chemistry interactions and finite-rate chemical kinetics. Governing equations for mass, momentum, enthalpy, and species transport, amended for turbulent flow (e.g., RANS or LES operators), are standard (Xiao et al., 4 Jan 2026, Bhaya et al., 2021): $$\begin{align*} \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho\mathbf{u}) &= 0 \ \frac{\partial (\rho\mathbf{u})}{\partial t} + \nabla \cdot(\rho\mathbf{u}\mathbf{u}) &= -\nabla p + \nabla \cdot [\mu_{eff} (\nabla\mathbf{u} + (\nabla\mathbf{u})^T ) ] + \rho\mathbf{g} \ \frac{\partial (\rho Y_\alpha)}{\partial t} + \nabla \cdot (\rho\mathbf{u}Y_\alpha) &= \nabla \cdot (\rho D_{eff} \nabla Y_\alpha) + \dot{\omega}_\alpha \end{align*}$$ with $\mu_{eff}$ and $D_{eff}$ incorporating both molecular and modeled turbulent diffusion.

Reactive closure approaches include:

• Eddy Dissipation Concept (EDC): The mean rate of production couples turbulent mixing and chemical kinetics through the fine-structure residence time $\tau = C_2 (k/\epsilon)^{1/2}$ and structure size $\gamma = C_1 (k/\epsilon)^{-1/3}$ (De et al., 2021).
• Probability Density Function (PDF) Methods: Both Lagrangian (LPDF) and Multi-Environment Eulerian (MEPDF) PDFs are used to model scalar mixing and finite-rate chemistry, with closures for molecular micro-mixing such as IEM, EMST, or CD (De et al., 2021, Dongre et al., 2021, Bhaya et al., 2021).
• Presumed-shape PDF and Flamelet Models: Beta-PDF and flamelet tabulations are common but may inadequately resolve the distributed reaction and high scalar variance characteristic of MILD regimes (Yang et al., 22 Sep 2025).

Direct Numerical Simulation (DNS) data for MILD flames have been utilized for both model training and a priori validation. Example methane–air DNS conditions include $T_u = 1500\,\mathrm{K}$, $X_{O_2}^{max} = 0.035$–$0.020$, $Re_T ≈ 96$, grid spacing $Δx ≈ 20\,\mu m$ (Yang et al., 22 Sep 2025).

4. Model Performance, Sensitivity, and Comparison

A major theme in MILD combustion modeling is sensitivity to both turbulence and micro-mixing models. Key findings include:

• EDC models with default constants systematically ignite too early, over-predicting temperature and under-predicting flame lift-off. Corrective action—such as increasing the mixing constant $C_2$ or reducing $C_1$—aligns ignition and temperature fields with experimental values (De et al., 2021, De et al., 2021). For example, increasing $C_2$ from 0.4082 to 3.0 can delay reaction rates by a factor of seven.
• PDF-based models (especially LPDF-EMST and MEPDF-IEM): LPDF-EMST offers local-mixing fidelity, reproducing the distributed nature of the reaction zone and capturing mean and RMS fluctuations of major species and temperature. MEPDF, while avoiding particle noise, can show realizability and boundedness issues under extreme dilution. Both approaches underpredict lift-off due to over-rapid mixing when using non-local micro-mixing (IEM) closures (De et al., 2021, Dongre et al., 2021).
• Machine learning enhanced closures: JPResUnet demonstrates substantial improvement over analytic β-PDFs and fully connected ANNs, accurately predicting sub-grid joint PDFs and low-pass filtered reaction rates across moderate and intense regimes. For a multi-regime LES, high-resolution JPResUnet-LUTs reduce radial temperature error by 20–30% compared to β-PDF LUTs (Yang et al., 22 Sep 2025).

Typical model comparisons are summarized below:

Burner/Regime	Approach	T_pred - T_exp	Lift-off Δx	Species/Variance Capture
DJHC, Re=4100, 7.6% O₂	EDC (default)	+22%	-43 mm	Major/RMS: Mean $\uparrow$, RMS $\uparrow$ (over); poor lift-off
	LPDF-EMST	+10%	-45 mm	Improved RMS, early ignition
Adelaide JHC, 3–9% O₂	EDC	<+5% (peak T)		Major species: matched, radicals poor
	LPDF-EMST	-7 to -22%		CO/H₂O profile accuracy $\uparrow$ for EMST
Large eddy simulation (LES)	JPResUnet-LUT	-20–30% error vs exp	Corrected RMS peak	Recovers sub-grid bimodality, accurate $c$–$Z$ correlation

A plausible implication is that tailored micro-mixing models or data-driven sub-grid closures are critical for predictive fidelity in MILD simulations (Yang et al., 22 Sep 2025).

5. Emission, Flame Stability, and Validation Metrics

Quantified benefits of MILD combustion include:

• Peak flame temperature reduction: Experimental and simulation results show 8–21% lower $T_{max}$ than conventional flames (e.g., $T_{max} \sim 1,740\,\mathrm{K}$, baseline $>2,200\,\mathrm{K}$) (Xiao et al., 4 Jan 2026).
• NOₓ emissions: Simulated NOₓ is typically $18$ ppm (40% less than initial, which is itself low compared to standard diffusion flames) (Xiao et al., 4 Jan 2026).
• Reaction zone broadening: The width of the zone containing $10$–$90$% of total heat release increases significantly (e.g., $\Delta x_{90}$ from $15$ mm up to $25$ mm after optimization) (Xiao et al., 4 Jan 2026).
• Flame stability: The index $$S = \frac{\int \dot{Q}\, dx}{\mathrm{max}(\dot{Q})}$$ increases, indicating more distributed heat release and flame robustness (e.g., $S$ rising from $0.45$ to $0.60$, a 33% enhancement) (Xiao et al., 4 Jan 2026).
• Lift-off height: Systematically decreases with increasing Reynolds number, indicative of faster turbulent mixing and delayed ignition with decreased local stoichiometry (Bhaya et al., 2021).

Model–experiment agreement is further quantified by RMS error in filtered reaction rates (e.g., $RMSE \sim 0.09$ for JPResUnet vs $0.16$ for β-PDF) and Jensen–Shannon divergence in sub-grid PDFs ($JSD <0.03$ for JPResUnet) (Yang et al., 22 Sep 2025).

6. Computational and Algorithmic Considerations

Simulations employ both structured and non-uniform grids (typical mesh: $200 \times 50$ for 2D RANS, $2.8$M cells for LES), with boundary conditions drawn from experiment or prior simulation (preheated inlets, prescribed turbulence intensity). Solver settings include pseudo-steady PIMPLE or SIMPLE loops, k–$\epsilon$ or realizable k–$\epsilon$ turbulence models, and time-step convergence to residuals $<1 \times 10^{-6}$ (Xiao et al., 4 Jan 2026, Dongre et al., 2021). Micro-mixing closure constants and inlet fluctuation prescription are proven to be crucial; e.g., adjusting $C_{1\epsilon}$ in k-$\epsilon$ or ensuring $\geq 30$ LPDF particles per cell to reduce bias (De et al., 2021).

Machine learning integration, as in the JPResUnet workflow, leverages in-situ adaptive tabulation (ISAT) and high-resolution look-up tables (LUTs), with demonstrated gains in sub-grid accuracy and a posteriori LES temperature fields (Yang et al., 22 Sep 2025).

7. Challenges, Limitations, and Future Directions

Persistent challenges in MILD combustion research include:

• Overprediction of temperature or underprediction of lift-off, especially by EDC or nonlocal-mixing PDF models (De et al., 2021, Dongre et al., 2021).
• Inadequate radical species (OH, CO) prediction in both EDC and transported-PDF closures, particularly under conditions of extreme dilution or in the presence of H₂ (De et al., 2021, Dongre et al., 2021).
• Sensitivity of Eulerian PDF methods (MEPDF) to the number of environments and realizability constraints at high-dilution, suggesting extensions to more than two environments or improved cross-moment closures (Dongre et al., 2021).
• Need for non-local micro-mixing closures (EMST, IECM) and improved treatment of differential diffusion—especially for accurately simulating flames with significant H₂ content (Yang et al., 22 Sep 2025, Dongre et al., 2021).

Advances with machine learning (e.g., JPResUnet) demonstrate promise in directly mapping analytic PDF representations to DNS-resolved closures, with gains in reaction-rate accuracy and computational tractability. Ongoing developments include on-the-fly GPU inference, multi-fuel/pressure generalization, and incorporation of joint scalar copulas (Yang et al., 22 Sep 2025).

A plausible implication is that continued hybridization of physics-based and data-driven closures, supported by high-fidelity DNS and rigorous validation, will play a central role in predictive MILD combustion modeling for engineering-scale applications.