Statistical analysis of liquid detonation wave structure

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Abstract
Liquid-fueled detonation has attracted considerable interest due to the high volumetric energy density of liquid fuels. In the present work, detonation wave propagation in n-dodecane droplets was investigated through two-dimensional simulations. The dispersed droplets were tracked based on the Lagrangian framework, while the continuous phase was solved in an Eulerian way. The Pilch–Erdman model was applied to account for droplet breakup. A detailed reaction mechanism was used for n-dodecane combustion. Three cases with different liquid equivalence ratios and oxygen mass fractions were considered. The simulation results of the detonation cell width were generally consistent with those of the experiment, with quantitative deviations of approximately 10%–40%. The droplet size distribution and breakup behavior were analyzed. It was shown that droplet breakup is the most pronounced behind the Mach stem. Three types of fuel droplets were identified behind the detonation front, i.e., droplets just shocked by the detonation front, shocked droplets progressively relaxing toward equilibrium with the surrounding gas, and small droplets associated with localized intense transverse detonations. Two distinct peaks were observed in the probability density functions of droplet diameter. In the case with low oxygen concentrations, a higher probability of smaller droplet diameters is identified. The liquid equivalence ratio has only a minor effect on the droplet diameter distribution. The statistical analysis of the leading front was conducted to characterize the detonation front dynamics. The leading front showed significant velocity deficits in all cases. It was found that the most probable velocities of the leading front decrease with increasing mass loading ratios. The joint probability density function of the detonation speed and the induction length was also examined, and a negative correlation between the two quantities was observed. Droplet breakup and evaporation significantly lengthen the induction zone to approximately 2–4 times that of the corresponding purely gaseous detonation.
Funding Information
  • National Natural Science Foundation of China (U2441282)
  • Fundamental Research Funds for the Central Universities (K20250106)

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