Thermoacoustic Response of Aligned & Staggered H₂ Micromix Twin-Injector Flames
Does it matter how you arrange the injectors?
Hydrogen micromix combustors put thousands of tiny flames in an annulus. Geometry forces some of them out of line. I ran a large eddy simulation campaign to find out whether that offset changes how the flames respond to acoustic pressure waves, the mechanism behind combustion instability.
It does, but not in the way you would guess. Staggering does not change when the flame responds. It changes how spread out that response is.
Compressible LES at 14 bar, five-tone forcing from 335 to 4087 Hz, run in STAR-CCM+ with MATLAB post-processing.
One large flame becomes thousands of small ones
Hydrogen burns hotter and faster than kerosene, so a conventional combustor cannot simply be refuelled. The micromix architecture answers this by replacing one large flame with thousands of millimetre-scale diffusion flames, which cuts NOx by keeping residence time short. The unanswered question is what that array does acoustically. If the flames release heat in step with a pressure wave, the wave grows, and combustors destroy themselves this way.
Packing thousands of injectors into an annulus means adjacent rows do not line up. Whether that offset matters had not been tested at resolved fidelity for a twin-injector pair. That is the gap this work addresses.
Aligned, then offset
Two domains, one signal, one defensible measurement
Built two computational domains identical except for the circumferential offset, forced both with the same acoustic signal, and measured the flame transfer function — the complex ratio of heat release fluctuation to velocity fluctuation. Everything downstream of that is signal processing, and most of the work went into making the signal processing defensible.
Steady screening cannot see the arrangement
Four accepted ways of extracting a flame delay from the same steady field disagree by a factor of sixteen. Only the forced, resolved measurement settles it.
| marker | aligned τ (ms) | staggered τ (ms) |
|---|---|---|
| MLFS — maximum laminar flame speed | 0.0109 | 0.0128 |
| FB — fresh vs burnt gases | 0.0173 | 0.0094 |
| NHRR — normalised heat release rate | 0.0781 | 0.0774 |
| MGT — maximum gradient of temperature | 0.1782 | 0.1634 |
The response, and its uncertainty
Both arrangements share one response shape, and its zero-frequency limit vanishes — which follows analytically from the fixed-fuel boundary rather than from anything about the flame. Turning the uncertainty bands off is the demonstration: without them the difference looks decisive, with them it does not.
| f (Hz) | gain A | gain S | ε_A % | ε_S % |
|---|---|---|---|---|
| 335 | 0.033 | 0.037 | 51.7 | 59.8 |
| 469 | 0.070 | 0.097 | 26.6 | 25.2 |
| 1139 | 0.128 | 0.129 | 35.1 | 28.6 |
| 2479 | 0.217 | 0.189 | 15.6 | 20.7 |
| 4087 | 0.300 | 0.260 | 32.8 | 34.2 |
Why a wider spread tilts the curve
A flame does not respond after one delay. It responds after a distribution of them. Fix the mean of that distribution and widen its spread, and the gain curve pivots down at the high-frequency end while the low end barely moves.
Where the heat release sits
The arrangement redistributes the response across frequency without moving its characteristic timing. The mean reaction field shows the same thing: the centre of heat release moves 0.047 mm while its streamwise spread widens ten times as much.
The forcing signal
Five tones on bins {5, 7, 17, 37, 61} × 66.9882 Hz — every tone completes a whole number of cycles in the 14.93 ms record and leaks into no other bin. Untick a tone to see the waveform rebuild without it.
What this does not show
One operating point. Five tones at finite amplitude, so this is an approximate transfer function and not an asymptotically linear one. The configuration difference is smaller than the measurement bound at every tone under one of the two reference definitions, so the result is a consistent tendency rather than a resolved difference. The zero-frequency result is conditional on an imposed stiff fuel boundary. A real engine fuel system has impedance this model does not carry.
Under the hood of the simulation
The full numerical setup behind the micromix study — expandable for readers who want the methodology.
Geometry & domain
Twin-injector micromix configurations, identical except for the circumferential offset, with tank domain and discrete fuel-injection holes.
Software & solver
Siemens STAR-CCM+ (v19.04). Compressible Large-Eddy Simulation with finite-rate chemistry at 14 bar.
Combustion models compared
Flamelet Generated Manifold (FGM) vs Complex Chemistry (CC), evaluated on flame structure, temperature fields, and NOx prediction.
Validation & operating conditions
Validated against the HESTIA experimental dataset (Cambridge atmospheric JICF configuration), with awareness of the DLR 7 bar intermediate dataset.
Meshing challenges solved
Prism-layer meshing on sharp 90° edges — Boundary March Angle tuning, feature-edge marking, layer reduction at concave corners, cell-count optimisation. Trimmed-mesh asymmetry in the fuel-hole tunnels resolved with cylindrical volumetric controls aligned to anchor points.
Where this research goes next
The directions I want to pursue at doctoral level: intrinsic thermoacoustic instabilities (ITAs) in lean premixed hydrogen flames, flame transfer functions and acoustic–flame coupling, Large Eddy Simulation of high-pressure hydrogen combustion, and NOx prediction for next-generation combustors. Working familiarity with the CERFACS toolchain — AVBP, AVSP, and the TFLES method — and grounded in Poinsot and Veynante, Theoretical and Numerical Combustion.