Investigation of Mist and Air Film Cooling in a Two-Phase Rotating Detonation Combustor with Liquid Kerosene

This numerical study demonstrates that kerosene-based mist film cooling, particularly when combined with air, offers superior thermal protection for rotating detonation combustors compared to conventional air cooling by forming a more persistent near-wall layer with enhanced heat removal through phase change and improved resistance to detonation wave interaction.

The Gist

Imagine you are trying to keep a metal pot from melting while you are cooking a firestorm inside it. That is essentially the challenge engineers face with Rotating Detonation Combustors (RDCs). These are futuristic engines that create a continuous, spinning ring of fire (a detonation wave) to generate power. They are incredibly efficient and compact, but the heat they produce is so intense that it threatens to melt the engine walls themselves.

To stop the engine from melting, engineers need a "shield." This paper investigates three different ways to build that shield using a computer simulation, comparing them to see which one works best.

Here is the breakdown of their findings, explained with some everyday analogies:

1. The Problem: The "Firestorm"

Inside the engine, a shockwave of fire spins around at supersonic speeds. It's like a tornado made of pure heat. If you just let it hit the metal wall, the wall would fail instantly. You need to put a barrier between the fire and the wall.

2. The Three Shield Strategies

Strategy A: The "Air Blanket" (Conventional Air Film Cooling)

This is the traditional method. Imagine blowing a steady stream of cool air through tiny holes in the wall to create a thin, protective blanket of air between the fire and the metal.

• The Catch: It's a delicate balance.
  • Too little air: The firestorm punches through the blanket, hitting the wall (like a weak umbrella in a hurricane).
  • Too much air: The force of the air blowing out is so strong that the spinning firestorm pushes it away, breaking the blanket and creating turbulence. It's like trying to hold a beach towel against a gale; if you grip it too hard, the wind rips it out of your hands.
• The Result: There is a "Goldilocks zone" (a medium amount of air) where this works best. Too little or too much makes it fail.

Strategy B: The "Mist Spray" (Kerosene Droplet Cooling)

Instead of just air, this method sprays tiny droplets of liquid fuel (kerosene) through the holes.

• The Magic Trick: Think of this like sweating. When your body sweats, the water evaporates and takes heat away from your skin. Similarly, when these kerosene droplets hit the hot wall, they evaporate. This phase change (liquid to gas) absorbs a massive amount of heat, acting like a super-charged cooling system.
• The Advantage: Unlike the air blanket, which can be blown away, these liquid droplets are heavier. They have "momentum" (inertia), so they stick to the wall better, even when the firestorm hits them. They form a more persistent, sticky shield that is harder to break.
• The Size Matters: The size of the droplets is crucial.
  • Too big: They are like big raindrops; they take too long to evaporate and don't cool the wall immediately.
  • Too small: They evaporate too fast or burn up right at the hole.
  • Just right: Medium-sized droplets offer the best balance of sticking to the wall and absorbing heat.

Strategy C: The "Hybrid Shield" (Mist + Air)

This combines the two: a mix of cool air and a small amount of kerosene mist.

• The Result: This was the winner. The air provides a steady base layer, while the kerosene droplets add that extra "sweat" cooling power. It cools the wall down faster after the firestorm passes and is more stable than using air alone. It's like wearing a raincoat (air) but also having a cooling gel pack (mist) underneath.

3. The "Burning" Question

A major concern was: If we spray fuel (kerosene) near the wall, won't it catch fire and make the wall hotter?

• The Finding: Yes, a little bit of the kerosene does burn, but it happens in a very specific, controlled way. It burns in a "banded" strip away from the most critical parts of the wall. The heat released by this small burn is far less than the massive amount of heat removed by the evaporation of the droplets. It's a net win: the cooling effect is much stronger than the heating effect.

4. The Big Picture Conclusion

The study concludes that while blowing air works okay if you get the pressure just right, spraying kerosene mist is a much tougher, more reliable shield. It sticks better, absorbs more heat, and handles the violent spinning firestorm without falling apart.

In simple terms:
If you are trying to protect a wall from a spinning fire tornado:

• Air is like a flimsy sheet of paper; it works if the wind is gentle, but rips easily.
• Kerosene Mist is like a heavy, wet towel; it clings to the wall and absorbs the heat, even when the wind is wild.
• The Mix is the ultimate protection, using the best of both worlds to keep the engine cool enough to run for a long time.

This research suggests that future engines using liquid fuel (like kerosene) can use their own fuel as a cooling agent, making them more efficient and durable without needing extra, heavy cooling systems.

Technical Summary

1. Problem Statement

Rotating Detonation Combustors (RDCs) offer high energy release efficiency and compact structures for aerospace and ground power applications. However, the intense heat flux and extreme temperatures generated by rotating detonation waves (RDWs) pose severe challenges to combustor wall thermal protection.

• Limitations of Current Methods: Existing studies primarily focus on gaseous fuels and gaseous coolants (air/nitrogen). In practical liquid-fuel RDCs (e.g., rocket-based or air-breathing systems), dedicated cooling air supplies are often unavailable or diverting inlet air degrades propulsion performance.
• Research Gap: There is a lack of investigation into using liquid fuels (specifically kerosene) as coolants via mist film cooling. While mist cooling (injecting fine droplets) is known to enhance heat removal via phase change in gas turbines, its application in the unsteady, high-pressure environment of a two-phase RDC with liquid kerosene has not been reported.

2. Methodology

The study employs a numerical approach using ANSYS Fluent to simulate unsteady Reynolds-averaged Navier–Stokes (URANS) equations.

• Physical Model: A 36 mm outer diameter, 30 mm inner diameter RDC with four rows of film cooling holes (0.6 mm diameter) on the outer wall.
• Numerical Setup:
  • Turbulence & Chemistry: Realizable $k-\epsilon$ model with a finite-rate chemistry model. A simplified two-step mechanism for kerosene-air combustion is used.
  • Multiphase Flow: The Discrete Phase Model (DPM) tracks kerosene droplets, accounting for drag, convective heat transfer, and diffusion-controlled vaporization.
  • Boundary Conditions: Mainstream air/kerosene inlet (1200 K, 0.62 kg/s); pressure outlet (1 atm); adiabatic walls.
• Validation: The numerical framework was validated against flat-plate film cooling experimental data (Huo et al.) and previous RDC detonation flow simulations. The model successfully captured cooling effectiveness trends and velocity profiles, though it slightly overpredicted mist cooling benefits compared to experiments.
• Simulation Cases:
  • Air Film Cooling: Blowing ratios ($M$) of 0.5, 1.0, 2.0, and 3.0.
  • Kerosene Mist Cooling: $M$ from 0.5 to 3.0; droplet diameters of 10, 20, and 50 $\mu$m.
  • Combined Mist/Air Cooling: $M=1.0$ with 10% kerosene mass fraction in the coolant stream.

3. Key Contributions

1. Feasibility of Kerosene Mist Cooling: Demonstrated that liquid kerosene can serve as an effective coolant in RDCs, leveraging both latent heat of vaporization and heat capacity without requiring external cooling air.
2. Mechanism Analysis: Revealed the distinct interaction mechanisms between mist films and rotating detonation waves, specifically how droplet inertia and phase change delay film separation compared to gaseous coolants.
3. Optimization of Parameters: Identified optimal blowing ratios and droplet sizes that balance thermal protection with mainstream flow preservation (total pressure loss).
4. Combustion Interaction: Analyzed the chemical behavior of kerosene mist near the wall, showing that while partial combustion occurs, the net thermal load is reduced due to the dominance of evaporative cooling.

4. Key Results

A. Air Film Cooling Performance

• Blowing Ratio Sensitivity: Air cooling exhibits a narrow optimal range ($M = 1.0 - 2.0$).
  • Low $M$ (0.5): Insufficient momentum leads to reverse penetration of hot gases into cooling holes and poor film coverage.
  • High $M$ (3.0): Excessive injection causes the coolant to accumulate and be blown away by the detonation wave, leading to film separation and degraded cooling.
• Thermal Impact: Moderate blowing ratios reduce peak wall temperatures, but the cooling film is highly susceptible to the unsteady pressure fluctuations of the RDW.

B. Kerosene Mist Cooling Performance

• Superior Robustness: Unlike air, kerosene mist cooling shows a monotonic increase in low-temperature coverage as the blowing ratio increases (up to $M=3.0$). The droplets' inertia and wall-adhering behavior prevent film separation even at high injection rates.
• Cooling Mechanism: The phase change (evaporation) absorbs significant latent heat, creating a persistent near-wall cooling layer that resists the high-temperature mainstream.
• Trade-off: While cooling improves with higher $M$, total pressure loss increases (from ~13.8% at $M=0.5$ to 16.6% at $M=3.0$).
• Droplet Size:
  • Small (10 $\mu$m): Evaporates too quickly, potentially reacting near the injection point.
  • Large (50 $\mu$m): Evaporates too slowly, failing to provide immediate cooling downstream of the holes.
  • Optimal (20 $\mu$m): Provides the best balance between evaporation rate and film continuity.

C. Combined Mist/Air Cooling

• Synergistic Effect: Injecting a small mass fraction (10%) of kerosene droplets into an optimal air film ($M=1.0$) significantly accelerates wall temperature recovery.
• Performance: Compared to pure air cooling, the combined scheme reduces the time to cool the wall to near-ambient levels by ~10% near the detonation wave head and ~50% at mid-wave height.
• Stability: The droplets act as a buffer, maintaining film integrity against flow disturbances better than air alone.

D. Combustion Characteristics

• Partial Combustion: Kerosene droplets partially evaporate and react near the wall, producing CO and H$_2$O but suppressing the formation of CO$_2$ due to oxygen depletion and local cooling.
• Net Benefit: Despite the localized heat release from partial combustion, the cooling effect of evaporation and the protective film layer far outweighs the thermal load, resulting in a net reduction in wall temperature.

5. Significance

• Engineering Application: This study validates a practical thermal protection strategy for liquid-fuel RDCs where dedicated cooling air is unavailable. It suggests that the fuel itself can be utilized for cooling, simplifying system design.
• Design Guidelines: The findings provide specific design parameters (e.g., $M=1.0-2.0$, droplet size $\approx 20 \mu$m) for optimizing film cooling in rotating detonation environments.
• Thermal Management: The combined mist/air strategy offers a pathway to enhance cooling efficiency without the severe pressure penalties associated with high-mass-flow air injection, addressing a critical bottleneck in RDC engineering.
• Future Work: The authors highlight the need for experimental validation under realistic detonation conditions and high-fidelity simulations to further refine the understanding of unsteady mist-detonation interactions.