Role of the Induction Zone on Turbulence-Detonation Interaction

This paper presents an in-depth analysis on the weak turbulence detonation linear interaction problem. The emphasis is on scaling and resonance issues due to the presence of structural scales that are intrinsic to the post-shock heat release region. Natural frequencies are determined as eigenvalues of the non-forced interaction inviscid problem. Influence of detonation parameters on the set of natural frequencies and concomitant effects on the one dimensional power spectra are analyzed. Scaling effects associated with the ratios between longitudinal turbulence length scale and the detonation induction scale are discussed. Acoustic and entropy far-field disturbance patterns are analyzed separately. Analysis of the parameter space reveals a strong link between detonation overdrive and acoustic attenuation. The damping is correlated with the sub-critical nature of the characteristic solutions for high overdrives. High activation energy detonations support resonant interaction with finer turbulence. The range of natural wave numbers increases with the heat release. Entropy patterns of the temperature and density are more strongly affected by resonance than those of the longitudinal velocity. This outcome highlights the thermal nature of the interaction in the induction region. For detonation conditions on the stability boundary, a larger overdrive supports a weaker resonant peak in both the temperature and longitudinal velocity spectra.