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Theory and computations have established that thermodynamic gradients createdby hot spots in reactive gas mixtures can lead to spontaneous detonationinitiation. However, the current laminar theory of the temperature-gradientmechanism for detonation initiation is restricted to idealized physicalconfigurations. Thus, it only predicts conditions for the onset of detonationsin quiescent gases, where an isolated hot spot is formed on a timescale shorterthan the chemical and acoustic timescales of the gas. In this work, we extendthe laminar temperature-gradient mechanism into a statistical model forpredicting the detonability of an autoignitive gas experiencing compressibleisotropic turbulence fluctuations. Compressible turbulence forms non-monotonictemperature fields with tightly-spaced local minima and maxima that evolve overa range of timescales, including those much larger than chemical and acoustictimescales. We examine the utility of the adapted statistical model throughdirect numerical simulations of compressible isotropic turbulence in premixedhydrogen-air reactants for a range of conditions. We find strong, but notconclusive, evidence that the model can predict the degree of detonability inan autoignitive gas due to turbulence-induced thermodynamic gradients.

Detonation initiation by compressible turbulence thermodynamic fluctuations