On Quantifying Energy Conversion Processes in Rotating Detonation Combustors

Rotating detonation combustors (RDCs) are an emerging pressure gain combustion technology that offers the potential for higher thermodynamic efficiency than conventional deflagrative combustors. While prior work has largely focused on demonstrating positive pressure gain, achieving high combustion efficiency is equally critical for enabling RDCs to serve as viable replacements in propulsion and power generation systems. However, direct measurements of combustion efficiency remain limited due to short test durations, extreme spatiotemporal gradients, and the inadequacy of conventional diagnostic techniques. Furthermore, existing measurements have relied on proxy definitions that are not derived from first principles and therefore cannot be directly incorporated into conservation-based models.

This dissertation addresses these challenges through the development of two complementary methods for quantifying combustion efficiency based on conserved quantities. Both methods were demonstrated in a H₂-air axial-air-inlet (AAI) RDC with a nominal outer diameter of 154 mm and a channel gap width of 7.6 mm. The inlet-to-channel and exit-to-channel area ratios are A₃.₁/A₃.₂ = 0.22 and A₈/A₃.₂ = 0.50, respectively. Data was acquired over a range of equivalence ratios Φ = 0.55–1.4 and air mass flow rates ṁ = 150–400 g/s.

The first method is derived from a chemical balance model and quantifies the remaining fuel mass at the exit of the combustor from H₂O mole fraction measurements obtained using a MHz-rate scanned-wavelength-modulation spectroscopy sensor developed in this work. The sensor measures temperature and H₂O partial pressure with average uncertainties of 7.4% and 15.5%, respectively, and the 1 MHz measurement rate provides sufficient temporal resolution to resolve the unsteady RDC flowfield. Application of this method yields combustion efficiencies of 50–65% with uncertainties of 14–16% and reveals a clear inverse relationship between combustion efficiency and equivalence ratio.

The second method is derived from a quasi-one-dimensional analysis and quantifies the amount of chemical energy released as heat from widely available thrust stand measurements, making it broadly applicable in configurations where optical diagnostics are unavailable. This approach enables simultaneous evaluation of thrust, pressure gain, and combustion efficiency. Application of this method yields combustion efficiencies of 40–70% with uncertainties of 15–30% and shows that combustion efficiency increases with CJ-normalized detonation wave speed, decreases with equivalence ratio, and exhibits no consistent dependence on combustor length.

To provide further physical insight, measured combustion efficiencies are coupled with a reduced-order model to partition the total heat release into detonative and deflagrative contributions. The results show that the heat released across the detonation wave increases quadratically with wave speed. Specifically, detonation waves with D/Dcᴊ < 0.6 consume less than 20% of the fuel supplied to the combustor, with nearly all heat release occurring through deflagrative processes at D/Dcᴊ ≈ 0.5, while detonation waves with D/Dcᴊ ≈ 0.8 consume 40–50% of the fuel supplied to the combustor. The analysis also identified a pathway by which parasitic deflagration increases the detonation wave speed while reducing the pressure ratio toward unity. Therefore, although results indicate that increasing D/Dcᴊ improves combustion efficiency, inlet designs must achieve this while suppressing parasitic deflagration to preserve pressure gain.

Overall, this dissertation establishes a framework for quantifying combustion efficiency in RDCs using methods grounded in conserved quantities and provides new insight into the underlying energy conversion processes governing their performance.

Recommended citation: Guerrero, Jose. "On Quantifying Energy Conversion Processes in Rotating Detonation Combustors," Ph.D. thesis, University of Michigan, 2026. https://doi.org/10.7302/dspace/29603
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