Decoupled regression rate and stability characteristics of carbon-black and aluminum-doped paraffin fuels for hybrid rocket engines

Abstract Hybrid rocket engines offer inherent safety and throttling by separating fuel and oxidizer, yet their wider use is hindered by low fuel regression rates and by combustion instabilities that frequently accompany performance-enhancing additives. In this paper, an experimental and analytical framework is presented that decouples these two issues. Instability mechanisms are classified into low-frequency (LFI), intermediate-frequency (IFI), and feed-system coupled modes. A systematic experimental campaign of 31 firings was conducted on paraffin-based fuels doped with carbon black (PC, 1 wt\%), conventional micron-aluminum (PA, 14 wt\%), and activated nano-aluminum (PAA, 14 wt\%), all burned with gaseous oxygen. A two one‑sided test (TOST) equivalence procedure with a $\pm10\%$ margin confirmed that the regression rates of the three fuels are practically equivalent. In contrast, the stability signatures differ fundamentally: PC burns in a stable manner; PA exhibits coupled LFI‑bulk mode instability with a secondary peak at 254 Hz; PAA shows LFI and a bulk mode together with a decoupled higher‑frequency peak at 414 Hz. The physical mechanism for this shift remains unclear and warrants further study. A data‑driven classification framework using an ensemble classifier, trained and cross‑validated on the present dataset, achieved 90\% accuracy across instability categories, though independent validation is needed. The results quantify the performance–stability trade-off and demonstrate the utility of the proposed analysis approach.