Large eddy simulation of turbulent swirl-stabilized flames using the front propagation formulation: impact of the resolved flame thickness

This study extends the front propagation formulation combustion model to large eddy simulation of swirl-stabilized turbulent premixed flames by incorporating non-adiabatic effects and improved sub-filter flame speed estimation, demonstrating that accurately resolving flame thickness is critical for capturing vortical stretching-induced flame pockets and secondary temperature peaks in the TECFLAM burner.

The Gist

The Big Picture: Simulating a Fire in a Whirlwind

Imagine you are trying to predict how a campfire behaves when a strong wind blows through it in a circle (a swirl). This is exactly what happens inside modern jet engines and gas turbines. They use swirling air to keep the flame stable and efficient.

Scientists use supercomputers to simulate this process, a method called Large Eddy Simulation (LES). Think of this like watching a movie of the fire. However, computers aren't fast enough to see every single tiny spark and air molecule. They have to "zoom out" and only see the big, swirling movements, while guessing what the tiny details are doing.

The problem? When you zoom out too much, the computer gets confused. It thinks the fire is spreading where it shouldn't, or it misses important details about how the fire burns. This paper introduces a new way to fix that confusion, specifically for swirling flames.

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The Problem: The "Blurry Fire" Issue

Imagine looking at a sharp, crisp flame through a foggy window.

• The Reality: The flame has a very thin, sharp edge where the fuel turns into heat.
• The Computer's View: Because the computer's "grid" (its way of measuring space) is too coarse, it sees a thick, blurry smudge instead of a sharp line.

When the computer sees this blurry smudge, it makes a mistake: it thinks the fire is burning slower and spreading wider than it actually is. It's like trying to drive a car while looking through a dirty windshield; you might swerve into the wrong lane.

The Solution: The "Front Propagation" Fix

The authors improved a mathematical tool called the Front Propagation Formulation (FPF).

Think of the flame not as a solid block of fire, but as a moving front, like a line of people marching.

• Old Way: The computer just guessed how fast the line moved based on the blurry view.
• New Way: The FPF method acts like a smart traffic controller. Even if the computer can't see the individual people (the tiny chemical reactions), it knows the rules of how the line should tighten up and move fast. It forces the "blurry smudge" to behave like a sharp, real flame.

The Secret Ingredient: "Chemical Steepening"

Here is the most important discovery in the paper.

In a real fire, the chemical reactions act like a magnet that pulls the flame edges together, keeping them thin and sharp. The authors call this "chemical steepening."

• Scenario A (The Good Simulation): The computer includes this "magnet." It realizes, "Hey, even though my grid is big, the chemistry is pulling this flame tight." The result? The flame stays thin, interacts correctly with the swirling air, and behaves like the real experiment.
• Scenario B (The Bad Simulation): The computer ignores the "magnet." It lets the flame get thick and floppy. Because the flame is too thick, it drifts away from the swirling air currents. It misses a crucial interaction, and the simulation fails to predict a specific phenomenon.

The "Flame Pockets" Mystery

The researchers were studying a specific swirl burner (the TECFLAM burner). In real experiments, they noticed something weird: Secondary Temperature Peaks.

Imagine the main fire is a big wave. Sometimes, little bubbles of fire get ripped off the main wave, float away into the outer edge of the swirl, and burn there for a moment. These are called "flame pockets." They cause a second, smaller spike in temperature.

• What the Good Simulation Did: Because it kept the flame thin and sharp (thanks to the "magnet"), it correctly predicted that the swirling air would stretch the flame, tear off these little pockets, and trap them in the outer edge. It matched the real experiment perfectly.
• What the Bad Simulation Did: Because it let the flame get too thick, the flame drifted away from the swirling air. The air couldn't grab the flame to tear off a pocket. The simulation saw a smooth, boring flame and completely missed the secondary temperature peaks.

The Takeaway

This paper teaches us a vital lesson for simulating fire in engines:

It's not just about how big your computer grid is; it's about how well you model the "tightening" force of the chemistry.

If you ignore the fact that chemistry tries to keep the flame thin, your simulation will think the flame is too thick and lazy. It will miss the exciting, chaotic interactions (like the flame pockets) that actually happen in real engines. By fixing how they modeled this "tightening," the authors made their computer simulations much more accurate, helping engineers design cleaner, more efficient engines.

Technical Summary

1. Problem Statement

Premixed swirl combustion is critical for modern gas turbines and aero-engines due to its high efficiency and low emissions. However, simulating these flows using Large Eddy Simulation (LES) presents significant challenges:

• Grid Resolution vs. Flame Thickness: In practical LES, grid sizes are often comparable to or larger than the laminar flame thickness. This leads to "under-resolved" flames where the reaction zone is not fully captured.
• Spurious Propagation: Under-resolved flames often suffer from inaccurate total reaction rate predictions and spurious (artificial) flame propagation.
• Complex Physics: Swirl-stabilized flames involve strong interactions between turbulence and vortices, fuel stratification, and non-adiabatic effects (heat loss). Existing models often struggle to capture the interplay between resolved flame thickness and sub-filter turbulence, particularly regarding the "chemical steepening" effect where reactions thin the flame front against turbulent diffusion.
• Gap in Knowledge: While the Front Propagation Formulation (FPF) has been tested on canonical flames (e.g., Bunsen, jet), its application to complex, stratified, non-adiabatic swirl flames and the specific impact of the resolved flame thickness on flame dynamics remain unexplored.

2. Methodology

The authors extended the Front Propagation Formulation (FPF) model for LES and applied it to the TECFLAM swirl-stabilized burner (a well-documented experimental case).

• Governing Equations: The simulation solves filtered continuity, momentum, and transport equations for three scalars: progress variable ($c$), mixture fraction ($Z$), and total enthalpy ($h_t$) to account for non-adiabatic conditions.
• Extended FPF Model:
  • Reaction Source Term: Modeled as the product of unburned density, sub-filter flame speed, and a regularized Dirac delta function ($\psi$). This eliminates spurious propagation errors.
  • Flame Structure Function ($\psi$): Defined by parameters $\alpha$ and $\gamma$. The exponent $\gamma$ is crucial as it controls the chemical steepening effect (thinning of the flame due to reactions).
  • Non-Adiabatic Effects: A library for laminar flame speed ($S_L$) and thickness ($l_F$) was constructed using 1D simulations with varying heat loss factors, allowing the model to retrieve local values based on enthalpy and equivalence ratio.
  • Sub-filter Flame Speed: An improved estimation of the sub-filter flame speed ($S_{c,t}$) was implemented. It addresses the inconsistency where sub-filter turbulence parameters are typically defined for unburned flow but applied within the heat-releasing flame brush. The authors corrected this by extending values from the unburned side along the surface normal.
• Numerical Setup:
  • Solver: Finite difference scheme on a non-uniform staggered grid in cylindrical coordinates.
  • Discretization: Second-order central scheme for momentum; fifth-order WENO for scalar transport to handle steep gradients.
  • Case Study: TECFLAM burner, $Re = 10,000$, Swirl number = 0.75, Equivalence ratio = 0.833.
  • Comparative Simulations: Two cases were run to isolate the effect of resolved flame thickness:
    1. $\gamma = 2.5$: Physics-based model including chemical steepening (thinning).
    2. $\gamma = 1.0$: Control case where chemical steepening is neglected (flame thickens artificially due to diffusion).

3. Key Contributions

1. Model Extension: Successfully extended the FPF method to handle fuel stratification and non-adiabatic heat loss in complex swirl-stabilized combustion, a configuration previously untested with this model.
2. Inconsistency Resolution: Proposed a novel method to resolve the inconsistency in sub-filter flame speed estimation caused by heat-release effects on local turbulence, improving the accuracy of flame propagation prediction.
3. Mechanism Discovery: Identified the physical mechanism behind secondary temperature peaks in the outer shear layer as the formation and trapping of isolated flame pockets (or peninsulas) caused by the stretching of the flame front by large-scale vortical structures.
4. Critical Role of Resolved Flame Thickness: Demonstrated that the resolved flame thickness is a decisive factor in LES fidelity. If chemical steepening is not modeled (leading to an over-predicted flame thickness), the flame detaches from the shear layer, failing to capture critical flame-vortex interactions.

4. Results

• Validation: The extended FPF model showed excellent agreement with experimental data for mean and RMS velocities, mixture fractions, and temperatures. It successfully captured the central recirculation zone and the dual-peak structures in velocity fluctuations.
• Impact of $\gamma$ (Resolved Flame Thickness):
  • $\gamma = 2.5$ (Steepening included): The flame remained thin and highly wrinkled. The simulation successfully captured the interaction between the flame and outer shear layer vortices. This led to the formation of flame pockets (isolated hot gas regions) trapped in the low-velocity outer shear layer, reproducing the secondary temperature peaks observed in experiments.
  • $\gamma = 1.0$ (Steepening neglected): The resolved flame thickness was over-predicted (thicker). This caused the flame brush to detach from the outer shear layer. Consequently, the large-scale vortices could not stretch the flame to form pockets. The simulation failed to capture the secondary temperature peaks and under-predicted the total flame consumption rate.
• Physical Mechanism: The study revealed that secondary temperature peaks are not just statistical noise but are caused by specific flame-vortex interactions where rotating eddies in the outer shear layer stretch the flame front, creating isolated pockets that are transported and trapped. This mechanism is only captured when the resolved flame thickness is physically accurate.

5. Significance

This work highlights a critical, often overlooked aspect of LES for turbulent combustion: the importance of accurately modeling the resolved flame thickness.

• Model Fidelity: It proves that simply using the filter size as the characteristic length scale for sub-filter modeling is insufficient if the chemical steepening effects (which thin the flame) are not properly represented.
• Prediction Capability: Accurate prediction of complex flame dynamics, such as flame pocket formation and secondary temperature peaks, is strictly dependent on the balance between turbulent diffusion and chemical thinning.
• Design Implications: For the design of next-generation clean propulsion systems, relying on models that over-predict flame thickness can lead to incorrect predictions of flame stability, pollutant formation (NOx), and heat release distribution. The extended FPF method offers a robust framework to address these issues in complex, realistic combustors.