⚡ electrical engineering

Simulation of a Reacting Hydrogen Jet in Air Cross-Flow: Analysis of Inter-jet Spacing Impact in Gas Turbine Design

This study employs highly resolved simulations to evaluate the impact of injector spacing on a reacting hydrogen jet in a hot air cross-flow, revealing that intermediate-to-wide spacing (approximately eight diameters) offers the optimal design trade-off by balancing unburnt hydrogen throughput, wall heat transfer, and flow stability.

Original authors: Kaku E. Eduku, Gustaaf Jacobs, Pavel P. Popov

Published 2026-07-02

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CC BY 4.0

Original authors: Kaku E. Eduku, Gustaaf Jacobs, Pavel P. Popov

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to mix a cup of hot tea with a stream of cold milk. If you pour the milk in a single, steady stream, it might just sink to the bottom or swirl around without mixing well. But what if you had a row of tiny straws, all shooting milk into the tea at once? That's essentially what this paper is about, but instead of tea and milk, it's hydrogen fuel and hot air inside a gas turbine engine.

The researchers from San Diego State University wanted to figure out the perfect distance between these tiny fuel "straws" (injectors) to make the engine run efficiently and safely. They used powerful computer simulations to watch how the fuel behaves when it's shot into a fast-moving stream of hot air.

Here is the breakdown of their findings using simple analogies:

The Setup: The "Traffic Jam" of Fuel

The team simulated a row of hydrogen jets shooting into hot air. They tested five different distances between the jets, ranging from very close together (2 "diameters" apart) to far apart (10 "diameters" apart).

Think of the jets like cars entering a highway.

Close Spacing (2 diameters): This is like a traffic jam. The cars (fuel jets) are so close that they block each other. This creates a "blockage" effect that speeds up the air flowing between the cars.
Wide Spacing (10 diameters): This is like cars on an open highway. They have plenty of room to move, but they are also more sensitive to small bumps or changes in the road.

The Problem: The "Traffic Jam" Effect

When the jets are packed too tightly (the 2-diameter case), the fuel jets crowd the air stream. This forces the air to squeeze through the gaps, making it move faster right next to the fuel.

The Consequence: Because the air is moving so fast, it sweeps the hydrogen fuel downstream before it has a chance to burn completely. It's like trying to light a match in a strong wind; the flame gets blown away before it can catch.
The Result: More unburnt fuel escapes the engine (waste), and the heat gets concentrated in a smaller, hotter spot near the walls, which could damage the engine.

The Problem: The "Wobbly Wake" Effect

When the jets are spaced far apart (the 10-diameter case), the fuel has more room to breathe. However, the researchers found a different problem.

The Consequence: The area behind the jet (the "wake") becomes unstable. If you give the system a tiny nudge (like a sudden change in ignition), the flame doesn't just settle back down; it starts to wobble side-to-side and stays that way.
The Result: The flame becomes "sensitive" and unpredictable, which isn't ideal for a steady-running engine.

The Sweet Spot: The "Goldilocks" Zone

The researchers tested the middle ground and found a "sweet spot" at 8 diameters apart.

Why it works: At this distance, the jets aren't crowded enough to create a traffic jam that blows the fuel away, but they aren't so far apart that the flame becomes wobbly and unstable.
The Result: This spacing burned the most fuel efficiently, kept the heat spread out evenly (so it didn't overheat the engine walls), and didn't leave a lot of unburnt fuel escaping.

The Bottom Line

The paper concludes that for retrofitting gas turbines to run on hydrogen, you shouldn't just pack the fuel injectors as tightly as possible.

Too close: You get a traffic jam that blows the fuel away and overheats the walls.
Too far: You get a wobbly, unstable flame.
Just right (8 diameters): You get the best balance of burning fuel efficiently and keeping the engine cool and stable.

The study confirms that the distance between fuel injectors is a critical design knob that engineers can turn to make hydrogen engines safer and more efficient.

Technical Summary: Simulation of a Reacting Hydrogen Jet in Air Cross-Flow: Analysis of Inter-jet Spacing Impact in Gas Turbine Design

Problem Statement and Motivation
Hydrogen is increasingly pursued as a low-carbon fuel for gas turbines, particularly for retrofitting existing natural gas infrastructure. However, hydrogen combustion presents distinct challenges compared to hydrocarbon fuels, including high burning velocity, strong molecular diffusivity, and elevated adiabatic flame temperatures, which exacerbate risks of flashback, flame instability, and excessive wall thermal loading. Consequently, modern strategies emphasize injector-scale mixing and flame placement, specifically through "micromix" combustion concepts.

While the "jet in cross-flow" (JICF) is a canonical configuration for studying fuel injection, practical combustors utilize arrays of injectors rather than isolated jets. Previous literature has established that injector spacing influences mixing and penetration in confined cross-flows. However, a gap remains in isolating the specific impact of inter-jet spacing on performance metrics within a hydrogen-fueled micromix combustor setting. This study addresses that gap by investigating how inter-jet spacing modifies flow organization, mixing-chemistry interactions, and design-relevant performance metrics in a turbulent reacting hydrogen jet.

Methodology
The authors conducted highly resolved numerical simulations of a reacting hydrogen jet issuing into a hot air cross-flow. The study utilized the PlasCom2 CFD code, which employs a high-order finite-difference discretization on overset, curvilinear coordinates. The simulations solved the compressible Navier-Stokes equations coupled with species transport and energy equations, using a reduced 9-species, 12-reaction hydrogen-air mechanism. No Reynolds-averaged turbulence model or explicit subgrid closure was employed; instead, the simulations relied on resolving unsteady velocity and scalar fields directly.

Configuration: A 1.27 mm diameter hydrogen jet ($Re = 2,610$, $Ma = 0.16$) injected into a hot air cross-flow ( $T = 700$ K, $U = 85.66$ m/s, $Ma = 0.17$) at 1 atm. The momentum flux ratio was $J = 1.13$ .
Boundary Conditions: Periodic spanwise boundary conditions were used to model an inline injector row. The spanwise domain width was varied to serve as a controlled surrogate for changing inter-jet spacing ( $l_{sp}$ ).
Parametric Study: Five spacing cases were simulated, ranging from $2D$ to $10D$ (where $D$ is the jet diameter), with $6D$ serving as the baseline.
Mesh Strategy: A two-stage mesh approach was employed. An initialization mesh ( $G_I$ ) developed the bulk reacting flow, followed by interpolation to a highly refined production mesh ( $G_P$ ) for collecting time-averaged statistics.
Quantities of Interest (QIs): Three design-oriented metrics were analyzed within the primary analysis region ( $x/D \le 12$ $x / D \leq 12$ ):
1. Downstream unburnt hydrogen throughput: Normalized mass flow ratio of unburnt hydrogen at the exit.
2. Wall heat transfer rate: Area-averaged heat flux to the combustor wall.
3. Bulk temperature concentration: A metric ( $\|T\|_2 / \|T\|_1$ ) reflecting the spatial localization of high-temperature regions.

Key Results and Findings

Flow Organization and Blockage Effects:
Inter-jet spacing significantly modulates the coherence of vortical structures. Narrow spacing ( $2D$ ) leads to a compact, coherent vortical field that persists further downstream. In contrast, wider spacing allows for earlier breakdown of coherent structures.
Crucially, spacing acts as a control on the local cross-flow velocity. Narrow spacing creates a blockage effect, accelerating the near-field cross-flow velocity by approximately 15% compared to the free-stream. This acceleration reduces the local jet-to-cross-flow velocity ratio ( $R_l$ ). Conversely, wider spacing reduces this blockage, allowing the cross-flow to remain closer to free-stream conditions.
Impact on Combustion and Mixing:
- Unburnt Hydrogen: The narrowest spacing ( $2D$ ) resulted in the highest unburnt hydrogen throughput (approximately 16% higher than the next case). The blockage-induced acceleration convects fuel downstream more rapidly, reducing residence time for consumption within the control volume.
- Wall Heat Transfer: Narrow spacing ( $2D$ and $4D$ ) generally increased near-wall thermal loading. The minimum time-averaged wall heat transfer was observed at $8D$ .
- Temperature Distribution: Narrow spacing promoted a more concentrated thermal field (higher bulk temperature concentration metric), while wider spacing yielded a more diffuse distribution.
Sensitivity to Perturbations:
The study analyzed the system's response to the removal of an ignition aid (a transient disturbance). While narrow spacing suppressed lateral deflections, intermediate-to-wide spacing ( $6D$ and $10D$ ) exhibited increased sensitivity. Specifically, these cases developed a sustained, persistent spanwise offset (lateral bias) in the near-wall wake following the disturbance. This behavior is linked to the modified local velocity ratio, which places the flow in a regime where antisymmetric wake modes are unstable.
Optimal Spacing Trade-off:
The performance landscape is non-monotonic. The narrowest spacing ( $2D$ ) was unfavorable due to high unburnt fuel, high wall heat transfer, and concentrated thermal fields. The widest spacing ( $10D$ ) reintroduced penalties regarding unburnt fuel and wall heat transfer while introducing high sensitivity to perturbations.
The study identifies $8D$ spacing as the optimal compromise. This configuration minimized both downstream unburnt hydrogen throughput and wall heat transfer while maintaining a low bulk temperature concentration metric.

Significance and Claims
The paper claims to isolate and interpret the specific role of inter-jet spacing in a turbulent reacting hydrogen jet, a variable often embedded within broader burner concepts. The primary contribution is the identification of two simultaneous mechanisms by which spacing alters performance:

Transport Control: Narrow spacing increases blockage, accelerating the cross-flow and reducing the local velocity ratio, which delays fuel consumption and increases unburnt throughput.
Wake Receptivity: Wider spacing increases sensitivity to perturbations, leading to persistent lateral wake deflections.

The authors conclude that for hydrogen retrofit applications utilizing micromix injectors, intermediate-to-wide spacing (specifically near $8D$ ) offers the best trade-off between minimizing unburnt fuel, managing wall thermal loading, and maintaining flow stability against transient disturbances. The study validates a two-stage mesh strategy as a practical approach for resolving these complex thermochemical interactions while managing computational costs.

The Setup: The "Traffic Jam" of Fuel

The Problem: The "Traffic Jam" Effect

The Problem: The "Wobbly Wake" Effect

The Sweet Spot: The "Goldilocks" Zone

The Bottom Line

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