Effect of Carbon Black and Aluminum Additives on Combustion Instability in Paraffin/GOX Hybrid Rockets: Experiments and a Classification Framework

Technical Summary: Effect of Carbon Black and Aluminum Additives on Combustion Instability in Paraffin/GOX Hybrid Rockets

Problem Statement
Hybrid rocket engines offer inherent safety and throttling capabilities due to the physical separation of fuel and oxidizer. However, their widespread adoption is constrained by two primary issues: low fuel regression rates and combustion instabilities that often accompany performance-enhancing additives. While strategies such as using paraffin-based fuels or adding metallic powders (e.g., aluminum) can improve regression rates, they frequently introduce unpredictable flame dynamics and pressure oscillations. These instabilities range from low-frequency "chugging" to high-frequency acoustic modes, potentially leading to catastrophic failure. The specific challenge addressed in this work is the lack of a unified understanding of how different additives affect the trade-off between regression rate performance and combustion stability in paraffin/gaseous oxygen (GOX) systems.

Methodology
The study employed a systematic experimental campaign involving 31 firings of a laboratory-scale hybrid rocket motor (30 mm inner diameter, 50 mm fuel grain length) using gaseous oxygen. Three distinct paraffin-based fuel formulations were tested under identical nominal conditions, with burn durations varied (4 s, 6 s, and 7.5 s) to achieve a wide range of oxidizer mass fluxes (28–71 kg/m²·s):

1. PC: Paraffin doped with 1 wt% carbon black.
2. PA: Paraffin doped with 14 wt% conventional micron-aluminum.
3. PAA: Paraffin doped with 14 wt% activated nano-aluminum (chemically treated to remove surface impurities).

Data Acquisition and Analysis:

• Regression Rate: Calculated via the time-averaged mass loss method, with uncertainty propagation estimated at ±5%.
• Stability Analysis: Chamber pressure was sampled at 1 kHz. Power Spectral Densities (PSD) were computed using Welch's method to identify instability modes.
• Statistical Framework: A Two One-Sided Test (TOST) with a ±10% equivalence margin was used to determine if regression rate differences were practically significant.
• Classification Framework: An ensemble classifier (decision trees) trained on the experimental dataset was used to categorize instability signatures into three classes: Stable, Low-Frequency Instability (LFI)-dominant, and Intermediate-Frequency Instability (IFI)-dominant.

Key Contributions

1. Decoupling of Performance and Stability: The study demonstrates that regression rate and combustion stability can be decoupled in paraffin/GOX systems. While additives significantly altered stability signatures, they did not produce statistically distinct differences in regression rates.
2. Classification of Instability Mechanisms: The authors propose a hierarchical classification framework distinguishing between Low-Frequency Instabilities (LFI, 5–20 Hz, driven by thermal lag/boundary layer coupling), Feed-System Coupled Bulk Modes (80–250 Hz), and Secondary High-Frequency Peaks (250–450 Hz).
3. Additive-Specific Stability Signatures: The paper provides a detailed comparative analysis of how carbon black, micron-aluminum, and activated nano-aluminum uniquely influence the pressure oscillation spectrum.
4. Data-Driven Tool: A machine learning-based classification tool was developed and cross-validated to automatically identify instability categories from pressure data.

Results

• Regression Rates: The TOST equivalence test confirmed that the regression rates of PC, PA, and PAA are practically equivalent within a ±10% margin. All fuels followed a power-law relationship ($\dot{r} = aG^n$) with exponents ($n$) ranging from 0.55 to 0.61, significantly lower than the classical turbulent boundary layer value of 0.8, consistent with droplet entrainment mechanisms.
• Combustion Stability:
  • PC (Carbon Black): Burned in a stable manner. The spectrum showed no significant peaks in the LFI band (5–20 Hz) and only weak residual modes (<2% amplitude), confirming the damping effect of carbon black.
  • PA (Micron-Aluminum): Exhibited coupled LFI-bulk mode instability. Distinct peaks were observed at 5.3 Hz (LFI), 237.3 Hz (bulk feed-system mode), and a coherent secondary peak at 254.2 Hz. The amplitude of oscillations reached ~8%.
  • PAA (Activated Nano-Aluminum): Showed an intermediate stability behavior. While it exhibited LFI (5.9 Hz) and a bulk mode (227.7 Hz), its secondary peak appeared at a higher frequency (414.5 Hz) and was decoupled from the lower-frequency oscillations.
• Classification Performance: The ensemble classifier achieved 90.3% accuracy (28/31 runs) in distinguishing between stable, LFI-dominant, and IFI-dominant cases on the training dataset, though the authors note that independent validation is required.

Significance and Claims
The paper claims that its primary significance lies in quantifying the performance-stability trade-off and demonstrating that performance enhancement (via additives) does not necessarily dictate a specific stability outcome, as the regression rates remained equivalent despite vastly different instability profiles.

The authors modestly conclude that:

• Carbon black offers a stable alternative with equivalent regression performance to metallized fuels, making it suitable for stability-critical applications.
• Micron-aluminum introduces coupled instabilities that may require active control or structural mitigation.
• Activated nano-aluminum presents a potential compromise, retaining the bulk mode instability but shifting secondary peaks to higher, decoupled frequencies, which may be less damaging.
• The physical mechanism behind the shift in secondary peak frequencies (from 254 Hz in PA to 414 Hz in PAA) remains unclear and warrants further study, potentially involving high-speed imaging and single-particle combustion analysis.

The study is limited to laboratory-scale tests with fixed additive loadings and a sampling rate insufficient to resolve high-frequency chamber acoustic modes (>2400 Hz). The proposed classification framework is presented as an exploratory tool requiring external validation before predictive use.