A Novel Approach for Direct Measurement of the Stretch Factor in Laminar Premixed Hydrogen-Air Flames Affected by Thermodiffusive Instabilities

This study introduces a novel OH-PLIF-based experimental method to directly measure the stretch factor in laminar premixed hydrogen-air flames, revealing how thermodiffusive instabilities increase flame consumption speed and cause the stretch factor to decrease monotonically as the equivalence ratio increases.

The Gist

The Big Picture: Catching Fire in a "Wrinkly" State

Imagine you are trying to understand how a campfire burns. Usually, we think of fire as a smooth, steady sheet of flame. But when you burn hydrogen (the fuel used in this study) mixed with air, the fire doesn't always behave nicely. Because hydrogen is so light and moves quickly, the flame can suddenly get "wrinkly," forming tiny, chaotic bubbles and fingers. Scientists call this thermodiffusive instability.

The big question the researchers wanted to answer is: How much faster does the fire burn when it gets wrinkly compared to when it is smooth?

To figure this out, they invented a clever new way to measure a specific number called the "Stretch Factor" ($I_0$). Think of this factor as a "speed multiplier." If the factor is 1.2, the wrinkly fire is burning 20% faster than a smooth one.

The Experiment: The "V-Shaped" Fire Slide

Instead of using a standard Bunsen burner (which looks like a candle flame), the team built a special setup that creates a V-shaped flame.

1. The Anchor: They held a tiny ceramic rod (like a very thin pencil) in a stream of hydrogen and air.
2. The Smooth Start: Right next to the rod, the flame is calm and smooth. It looks like a sleek, blue slide. This is the "Stable Branch."
3. The Wrinkly Turn: As the flame travels further away from the rod, something dramatic happens. It suddenly snaps into a chaotic, wrinkly state. It looks like crumpled paper or a crinkled potato chip. This is the "Unstable Branch."

The Analogy: Imagine a river flowing smoothly over a flat rock (the rod). Right next to the rock, the water is calm. But a little further downstream, the water hits a hidden reef and suddenly turns into white-water rapids with lots of splashing and turbulence.

How They Measured the Speed

The researchers used a high-speed camera with a special laser (OH-PLIF) to take pictures of the flame. They didn't need to measure the speed of the gas directly; they used geometry, which is like solving a puzzle using angles.

• The Angle Trick:
  • The Smooth Part of the flame leans back at a gentle angle.
  • The Wrinkly Part leans back at a much steeper angle.
  • Why? Because the wrinkly fire is burning faster, it pushes back against the wind more aggressively, forcing the flame to stand up straighter.
  • By measuring the difference in these angles, they could calculate how much faster the wrinkly fire is moving compared to the smooth fire.

The "Surface Area" Problem

Here is the tricky part. A wrinkly fire isn't just faster; it also has more surface area.

• Analogy: Imagine a smooth sheet of paper (the smooth flame). Now, crumple that same sheet of paper into a ball (the wrinkly flame). The ball takes up the same space, but if you tried to unfold it, it would be much longer and have more "edge" for the fire to eat.
• Because the wrinkly flame has more surface area, it consumes fuel faster. The researchers had to measure how much "wrinkled" the flame got to separate the speed increase caused by geometry from the speed increase caused by chemistry.

The Results: What Did They Find?

They tested different mixtures of hydrogen and air (some very lean, some slightly richer).

1. Leaner Mixtures = More Wrinkles: When the mixture had less fuel (leaner), the fire got much more wrinkly and chaotic.
2. The Speed Multiplier ($I_0$):
   • In the leanest mixtures, the "Stretch Factor" was high (around 1.1 to 1.3). This means the wrinkly fire was burning significantly faster than the smooth one.
   • As they added more fuel (making the mixture richer), the fire became smoother, and the "Stretch Factor" dropped closer to 1.0 (meaning the wrinkly and smooth fires burned at similar speeds).

Why Does This Matter?

This research is like finding a new rulebook for how hydrogen fires behave.

• Safety: Hydrogen is being used more in cars and power plants. If a fire suddenly gets "wrinkly" and speeds up, it can cause flashback (where the fire runs backward into the fuel tank) or damage walls.
• Better Models: Engineers use computer simulations to design engines. This paper gives them a new, accurate way to check if their computer models are right. They found that their new experimental method matches well with complex computer simulations, giving them confidence that they are on the right track.

Summary in One Sentence

The researchers built a special "V-shaped" hydrogen flame that naturally splits into a smooth part and a wrinkly part, allowing them to measure exactly how much faster and more chaotic the fire gets when it becomes unstable, providing crucial data for making hydrogen energy safer and more efficient.

Technical Summary

1. Problem Statement

Hydrogen (H₂) is a critical energy carrier for decarbonization, particularly when used in lean premixed combustion to reduce NOₓ emissions. However, lean hydrogen flames possess a Lewis number less than unity, making them highly susceptible to thermodiffusive instabilities (TDIs). These instabilities cause the flame front to develop cellular and finger-like structures, increasing the local flame speed and surface area.

While TDIs are known to enhance global flame consumption speed ($S_c$), quantifying this effect is challenging. The stretch factor ($I_0$), defined as the ratio of the normalised flame consumption speed to the laminar flame speed ($S_c/S_L$), is a key parameter for modeling these effects.

• Current Limitations: Existing methods to determine $I_0$ often rely on computationally expensive 3D simulations or indirect experimental measurements (e.g., in spherical flames or jet burners) where configuration-induced effects (curvature, interactions) complicate the isolation of intrinsic TDIs. Direct experimental measurement of $I_0$ in laminar hydrogen flames remains scarce.

2. Methodology

The authors propose a novel experimental and numerical approach using a rod-anchored V-shaped flame configuration.

Experimental Setup

• Configuration: A laminar premixed H₂/air flame is stabilized on a 1 mm ceramic rod in a laminar flow. The setup creates a V-flame with two distinct regimes along the flow direction:
  1. Stable Branch (Upstream): A smooth, quasi-stable flame front with a defined inclination angle ($\theta_s$).
  2. TD-Unstable Branch (Downstream): A region where the flame abruptly transitions to a highly wrinkled, cellular structure due to TDIs, characterized by a steeper inclination angle ($\theta_u$).
• Diagnostics: OH Planar Laser-Induced Fluorescence (OH-PLIF) is used to visualize the flame front. 200 single-shot images are averaged to determine mean structures, while instantaneous images capture wrinkling.
• Data Processing:
  • Transition Detection: The onset of TDIs is identified by fitting two linear segments to the mean flame front and finding the intersection point that minimizes the Root-Mean-Square Error (RMSE).
  • Flame Speed Ratio: The ratio of burning velocities ($S_u/S_s$) is derived geometrically from the inclination angles: $S_u/S_s = \sin(\theta_u) / \sin(\theta_s)$.
  • Surface Area Enhancement: Three distinct image processing strategies ("f-canny," "f-otsu," and "f-otsuCanny") are employed to calculate the ratio of the wrinkled flame contour length ($A$) to the smooth reference length ($A_0$).
  • Stretch Factor Calculation: $I_0$ is estimated using the relation: $I_0 \approx (S_u/S_s) \times (A_0/A)$.

Numerical Setup

• Simulation: 2D numerical simulations were performed using the CONVERGE solver with detailed chemistry (Burke mechanism) and adaptive mesh refinement (down to 25 µm).
• Validation: The simulations replicate the experimental geometry and boundary conditions. They utilize the progress variable ($Y_c$) to define flame fronts, allowing for a direct comparison with experimental OH-PLIF data and providing a "ground truth" for the thermochemical state.

3. Key Contributions

1. Novel Measurement Technique: Introduction of a method to directly estimate the stretch factor ($I_0$) in laminar flames by exploiting the natural transition from a stable to a TD-unstable regime within a single V-flame, eliminating the need for complex curvature corrections found in spherical or jet flames.
2. Decoupling of Effects: The configuration allows TDIs to develop largely independently of external perturbations, isolating the intrinsic instability mechanisms from configuration-induced dynamics.
3. Multi-Method Robustness: The application of three different flame front detection algorithms to quantify surface area ($A/A_0$) provides a robust assessment of measurement uncertainty.
4. Experimental-Numerical Synergy: The study validates the experimental methodology against 2D simulations, confirming that the observed transition behavior and trends are physically consistent.

4. Key Results

• Flame Regime Transition: Both experiments and simulations confirmed a clear transition from a smooth upstream branch to a wrinkled downstream branch. The onset location of TDIs moves closer to the anchor rod as the equivalence ratio ($\phi$) increases.
• Flame Speed and Angle: The TD-unstable branch exhibits a steeper inclination angle ($\theta_u$) than the stable branch ($\theta_s$), indicating a higher effective flame consumption speed.
• Trends in $I_0$:
  • The ratio of burning velocities ($S_u/S_s$) decreases monotonically as the equivalence ratio increases (from $\phi=0.35$ to $0.4$).
  • The surface area ratio ($A/A_0$) remains relatively constant across the tested equivalence ratios.
  • Consequently, the calculated stretch factor $I_0$ decreases monotonically with increasing equivalence ratio.
    • At $\phi = 0.35$, $I_0 \approx 1.1 - 1.3$.
    • At $\phi = 0.4$, $I_0 \approx 0.8 - 0.9$.
• Validation: The experimental $I_0$ trends align well with theoretical predictions and empirical models derived from 2D and 3D simulations of freely propagating flames.
• Discrepancies: Minor differences in magnitude between experimental, numerical, and model results are attributed to:
  • Variations in flame front definition criteria (e.g., OH vs. H₂ mass fraction).
  • 3D effects present in experiments but absent in 2D simulations.
  • Uncertainties in surface area estimation.

5. Significance

This work provides a valuable experimental benchmark for the development and validation of numerical models for hydrogen combustion.

• Model Validation: The derived $I_0$ values offer critical data for validating empirical models used in Large Eddy Simulations (LES) and Reynolds-Averaged Navier-Stokes (RANS) models, particularly for lean hydrogen flames prone to instabilities.
• Safety and Design: Understanding the enhancement of flame speed due to TDIs is crucial for predicting flame flashback and flame-wall interactions in industrial hydrogen burners and internal combustion engines.
• Methodological Advancement: The proposed V-flame approach offers a simpler, more direct route to characterizing intrinsic flame instabilities compared to traditional methods, facilitating future parametric studies in hydrogen combustion.