Acoustic radiation of thermodiffusively unstable turbulent lean premixed hydrogen-air flames

This study utilizes Direct Numerical Simulations to demonstrate that thermodiffusive instabilities in turbulent lean premixed hydrogen-air flames significantly enhance low-frequency combustion noise by altering heat release fluctuations and flame surface dynamics through the coupled action of turbulence and flame stretch, distinguishing their acoustic behavior from stable methane flames.

The Gist

The Big Picture: Why Hydrogen Fire is Noisier (and Different)

Imagine you are trying to build a cleaner, greener future for airplanes and power plants. The plan is to switch from burning natural gas (methane) to burning hydrogen. Hydrogen is great because it only produces water when it burns, but it has a tricky personality.

This paper is like a detective story where scientists use super-powerful computer simulations (like a high-tech wind tunnel) to figure out exactly how hydrogen flames behave compared to methane flames, specifically focusing on noise.

Why does noise matter? Because in jet engines, loud, chaotic noise can shake the engine apart or trigger dangerous vibrations. The researchers wanted to know: If we switch to hydrogen, will the engine get louder, and what kind of noise will it make?

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The Main Characters

1. The Methane Flame (The Steady Old Guard):
   Think of a methane flame like a calm, predictable marching band. It moves in a straight line, keeps its rhythm, and doesn't get too excited. It's "thermodiffusively stable," which is a fancy way of saying its heat and fuel mix together perfectly without causing chaos.

2. The Hydrogen Flames (The Energetic Dancers):
   Hydrogen flames are like a group of energetic dancers who can't stand still. Because hydrogen is so light and moves so fast, it creates a phenomenon called thermodiffusive instability.

   • The Analogy: Imagine trying to walk through a crowd while holding a balloon. If you move too fast, the balloon (the flame) starts to wobble, stretch, and twist on its own. Hydrogen flames do this naturally. They wrinkle, fold, and stretch themselves into complex shapes even without wind pushing them.

The Experiment: Three Races

The scientists set up three different "races" to see how these flames behave:

• Race A (Methane): A standard methane flame moving at a medium speed.
• Race B (Hydrogen Fast): A hydrogen flame moving very fast, designed to have the same overall "length" as the methane flame.
• Race C (Hydrogen Slow): A hydrogen flame moving at the same speed as the methane flame, just to see what happens when they are side-by-side.

The Discovery: How the Noise is Made

The paper found two main ways these flames make noise, and hydrogen changes both of them.

1. The "Squeaky Hinge" Effect (Direct Noise)

In a normal methane flame, the noise mostly comes from the tip of the flame snapping off small pockets of unburnt gas. It's like a door hinge that squeaks loudly when it snaps shut quickly. This creates a lot of high-pitched, sharp noise.

In the hydrogen flames, the "wrinkling" (thermodiffusive instability) changes the game:

• The Analogy: Instead of a door snapping shut, imagine a rubber sheet being stretched and pulled. The hydrogen flame stretches so much that it doesn't snap off those little pockets as violently.
• The Result: The hydrogen flames make less high-pitched noise (the sharp squeaks disappear). However, because the flame is stretching and wriggling so much, it creates more low-frequency rumbling (like a deep bass drum).
• Why it matters: Hydrogen engines might be less "hissy" but more "rumbling."

2. The "Whirlpool" Effect (Indirect Noise)

When hot gas shoots out of a flame into cold air, it creates a shear layer (a boundary where fast hot gas rubs against slow cold air). This boundary is unstable and creates swirls, like a whirlpool in a river.

• The Methane Flame: The boundary is smooth. The whirlpools are big and lazy.
• The Hydrogen Flame: Because hydrogen burns so hot and creates gases that are much lighter and move faster, the boundary becomes very choppy.
• The Analogy: Imagine pouring honey (methane) into water versus pouring boiling water (hydrogen) into cold water. The boiling water creates tiny, frantic bubbles and swirls immediately.
• The Result: The hydrogen flames create stronger, more chaotic swirls right at the edge of the flame. These swirls generate their own sound waves, adding to the overall noise, especially at low frequencies.

The "Stretch Factor" Theory

The scientists also developed a new math formula to predict this noise.

• Old Theory: "The louder the flame surface changes size, the louder the noise."
• New Theory: "The louder the flame surface changes size AND the more it gets stretched by its own instability, the louder the noise."

They found that for hydrogen, the "stretch" is a huge amplifier. It's like pulling a rubber band; the more you stretch it, the more energy is stored, and the louder it snaps back. This stretch factor explains why hydrogen flames are so noisy at low frequencies.

The Conclusion: What Does This Mean for the Future?

If we switch to hydrogen engines, we can't just copy the noise rules from natural gas engines.

1. The Sound Profile Changes: Hydrogen engines will likely be quieter at high pitches (less "hiss") but louder at low pitches (more "rumble").
2. The Instability is Key: The weird, wrinkling nature of hydrogen flames (thermodiffusive instability) is the main culprit. It makes the flame surface dance, which creates deep, low-frequency noise.
3. Design Implications: Engineers designing hydrogen engines need to account for these deep rumbles and the chaotic swirls at the flame's edge. They can't just assume the noise will behave like a methane engine.

In a nutshell: Hydrogen flames are like a hyperactive child who can't sit still. They don't just burn; they dance, stretch, and wiggle. This dancing creates a deep, low-frequency roar rather than the sharp crackle of a methane flame. Understanding this "dance" is crucial for building quiet, safe, and efficient hydrogen-powered planes and power plants.

Technical Summary

1. Problem Statement

The transition to hydrogen ($H_2$) as a fuel for gas turbines in aviation and power generation is critical for reducing carbon emissions. However, lean premixed hydrogen combustion introduces unique challenges due to thermodiffusive (TD) effects. Unlike hydrocarbon flames (e.g., methane), lean hydrogen-air mixtures have a Lewis number ($Le$) significantly less than 1. This leads to:

• TD Instabilities: Intrinsic cellular structures and enhanced flame wrinkling.
• Stretch Sensitivity: The flame speed becomes highly sensitive to stretch (accelerating under positive stretch), altering flame dynamics.
• Combustion Noise: There is a lack of understanding regarding how these TD instabilities interact with turbulence to generate direct (from heat release rate fluctuations) and indirect (from entropy/vorticity acceleration) combustion noise. Previous studies were limited to 1-D/2-D laminar cases or hydrocarbon flames, leaving the 3-D turbulent $H_2$ acoustic mechanisms unclear.

2. Methodology

The study employs Direct Numerical Simulations (DNS) to investigate the acoustic radiation of turbulent slot jet flames in an open ambient environment.

• Numerical Solver: The explicit massively parallel compressible multi-species Navier–Stokes solver AVBP was used.
• Chemistry:
  • $H_2$: San Diego mechanism (9 species, 21 reactions).
  • $CH_4$: Semi-global two-step mechanism (6 species).
• Flame Configurations: Three cases were simulated to isolate the effects of TD instability and flow velocity:
  1. M10 (Reference): Stoichiometric ($\phi=1.0$) Methane-Air flame, $U_B = 10$ m/s. (Thermodiffusively stable, $Le \approx 1$).
  2. H25: Lean ($\phi=0.45$) Hydrogen-Air flame, $U_B = 25$ m/s. (Designed to match the turbulent flame brush length of M10).
  3. H10: Lean ($\phi=0.45$) Hydrogen-Air flame, $U_B = 10$ m/s. (Matches the bulk velocity of M10 to isolate Reynolds number effects).
• Domain & Resolution: A 3-D slot jet configuration with coflows. Grid resolution was $\Delta x \le 100$ $\mu$m in the flame region (ensuring 7–10 points across the flame front), resulting in grids of 165–210 million cells.
• Analysis Tools:
  • Spectral analysis of Heat Release Rate (HRR) and pressure.
  • Spectral Proper Orthogonal Decomposition (SPOD) to identify coherent structures in the pressure field.
  • A novel theoretical framework extending classical flamelet theory to include stretch effects.

3. Key Contributions

The paper makes three primary theoretical and methodological contributions:

1. Extended Flamelet Theory for TD-Unstable Flames:
   The authors propose and validate a generalized acoustic radiation model. While classical theory relates far-field pressure ($p'$) to the time derivative of the flame surface area ($dA_T/dt$), this work introduces the stretch factor ($I_0$).

   • Equation: $p' \propto S_L^0 \frac{d(I_0 A_T)}{dt}$.
   • Significance: This framework successfully predicts acoustic radiation for $Le < 1$ flames, showing that noise is modulated by the stretch factor, which amplifies sound generation in unstable flames.

2. Mechanism of Noise Generation in $H_2$:
   The study identifies that TD instabilities shift the noise generation mechanism. Unlike hydrocarbon flames where flame annihilation (destruction of pockets at the tip) dominates high-frequency noise, $H_2$ flames exhibit a dominance of flame surface generation due to positive stretch. This suppresses high-frequency annihilation events.

3. Indirect Noise via Shear Layer Instabilities:
   The research demonstrates that non-equidiffusion in $H_2$ alters the density field in the burnt gases, intensifying Kelvin-Helmholtz (K-H) shear layer instabilities at the interface between combustion products and ambient air. This generates coherent wavepackets that contribute to low-frequency noise and persist to higher frequencies than in $CH_4$ flames.

4. Key Results

A. Flame Dynamics and Stretch

• Flame Surface: $H_2$ flames exhibit highly corrugated fronts with pronounced local HRR fluctuations. The stretch factor $I_0$ is significantly higher for $H_2$ ($I_0 \approx 1.7 - 2.0$) compared to $CH_4$ ($I_0 \approx 1$).
• Stretch Balance: In $CH_4$, negative curvature (flame tip annihilation) dominates, driving high-frequency noise. In $H_2$, positive curvature (surface generation) is enhanced by TD instabilities, reducing the relative importance of annihilation.
• HRR Spectra: $H_2$ flames show stronger low-frequency HRR fluctuations but a steeper roll-off at high frequencies compared to $CH_4$. The cut-off Strouhal number ($St_c$) is higher for $H_2$, indicating a broader range of unstable scales.

B. Acoustic Radiation Characteristics

• Spectral Shift: $H_2$ flames radiate more strongly at low frequencies (near the acoustic peak) but exhibit a steeper high-frequency decay ($\alpha \approx 4.5$ for $H_2$ vs. $\alpha \approx 2.9$ for $CH_4$).
• Directivity: While $CH_4$ noise is dominated by the flame tip, $H_2$ noise shows significant contributions from the outer shear layer.
• Validation: The proposed theoretical model (Eq. 3.7/3.8) accurately reconstructs the pressure fluctuations for $H_2$ flames (correlation coefficient $r_c > 0.9$), whereas the classical model underestimates the noise.

C. Modal Analysis (SPOD)

• Low Frequencies ($St \approx 0.15$): $H_2$ flames display strong, spatially extended wavepackets associated with K-H instability in the outer shear layer. These structures are more pronounced than in $CH_4$ due to stronger density gradients caused by non-equidiffusion.
• High Frequencies: The noise is dominated by the turbulent flame brush itself, with no coherent shear layer structures, confirming that the spectral differences are driven by HRR dynamics.

5. Significance

This work provides a fundamental understanding of why lean hydrogen flames behave acoustically differently from traditional hydrocarbon flames.

• Design Implications: The findings suggest that hydrogen combustion systems may be more prone to low-frequency thermoacoustic instabilities due to enhanced shear layer dynamics and low-frequency HRR fluctuations.
• Noise Prediction: The validated theoretical framework allows for more accurate prediction of combustion noise in $H_2$ engines without requiring full DNS, by accounting for the stretch factor $I_0$.
• Mechanism Clarification: It resolves the paradox of why $H_2$ flames (which have higher burning rates) do not necessarily produce more high-frequency noise; instead, the TD stabilization of small scales suppresses the high-frequency "crackling" noise associated with flame pocket annihilation.

In conclusion, thermodiffusive effects in hydrogen flames fundamentally alter both direct noise (via modified flame surface dynamics and HRR spectra) and indirect noise (via intensified shear layer instabilities), necessitating a re-evaluation of noise control strategies for hydrogen-fueled gas turbines.