Spontaneous Detonation Initiation in Compressible Isotropic Turbulence

Theory and computations have shown that local hot spots in highly compressible turbulent reactive mixtures can lead to spontaneous detonation initiation. However, present theory and models are restricted to single hot spots that i) are well-separated from other local maxima in temperature; ii) are formed on timescales comparable to, or shorter than, the chemical induction and acoustic crossing times of the hot spot; and iii) evolve freely in a gas with zero initial velocity fluctuations. In this talk, by contrast, we examine detonation initiation in non-monotonic temperature fields with local maxima that are tightly spaced and evolve over a range of timescales, from an outer scale comparable to the mean induction time to a much shorter inner diffusive timescale. We perform a series of direct numerical simulations of homogeneous isotropic turbulence in reactive gas mixtures that sweep over a range turbulent Mach numbers and test both a thermally-regulated single-step Arrhenius reaction mechanism and a chain-branching-regulated detailed hydrogen-air mechanism. Although we find some evidence of spontaneous detonation initiation due to compressible turbulence, distributions of temperature-gradient magnitudes and wave propagation speeds are inconsistent with previous theory.