Stochastic and spectra contents of detonation initiated by compressible turbulent thermodynamic fluctuations

A canonical system that contains the basic elements of detonation initiated by compressible turbulence thermodynamic fluctuations was proposed by Towery et al. [“Detonation initiation by compressible turbulence thermodynamic fluctuations,” Combust. Flame 213, 172–183 (2020)] and successfully tested using direct numerical simulation (DNS). In the present study, the DNS dataset is used to assess the applicability of a few compressible turbulence theories to the problem of detonation and to investigate some statistical aspects of the problem and the spectra of the turbulence kinetic energy (TKE) and reactive scalar fields within the context of detonating and deflagrating compressible flows. It has been found that scaling of the dilatational and solenoidal components of compressible turbulence as reported in the literature does not apply to the case of detonation or deflagration. Also, the detonating cases were found to have significantly lower Karlovitz numbers compared to the nondetonating ones and to conform to the Bray–Moss–Libby premixed combustion (bimodal probability density function) model for intense turbulence and large Damkhöler number. The nondetonating cases show distributed pdfs. The stronger combustion in the detonating cases shows effects on the spectra of the TKE and reactive scalars, particularly when the wavenumber is scaled with the Kolmogorov length and the Schmidt number.