Space-time correlations and the Taylor hypothesis behind forced detonations

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The competition between the intrinsic motion of detonation and convected disturbance is analyzed computationally by both performing a dynamic mode decomposition analysis and obtaining the space-time correlations. The dynamic modes are considerably affected by the presence of pre-shock forcing, while the space-time correlations are weakly affected by the convected turbulence. The triple point motion dominates the space-time correlations and manifests itself with a shift of the ellipsis towards the shock front. Rotating detonation engines (RDE) feature a non-uniform preshock field as a consequence of the filling process. The interface between mixed products from a previous wave and the fresh mixture supports a shear layer that impinges on the wave front as shown in Fig. 1. Such an interaction between convected vorticity and the detonation wave defines non-ideal propagating waves and is of practical importance because non-ideal detonations are characterized by a wave speed deficit and hot spots. 1 The effect of non-ideal preshock conditions on the performance of RDE is not known. In the previous work 2,3 we have shown that turbulence–detonation interaction can be analyzed from two points of view. First, the coupling between the exothermic structure of the detonation wave and the convected vorticity can be described in terms of the ratio between half reaction distance and Taylor microscale N ≡ L1/2/�0, and leads to selective amplification of wave amplitudes in Fourier space. Second, the analysis of the interaction between convected preshock perturbation and self-excited structures points to the importance of freestream entropic fluctuations in changing the postshock statistics. The present paper analyzes the interaction between preshock vorticity and the front in terms of space-time correlations. The primary objective of the research is to understand the space-time coupling between lead shock and convected entropy and acoustic waves, thus space-time propagation of structures. This effort will lead to the development and validation of sub-grid models for the postshock field. He et al. 4 analyzed isotropic flows and correlated the accuracy of large eddy simulation (LES) models to the prediction of both energy spectra and sweeping velocity. For shear (convectively unstable) flows, He and Zhang 5 proposed an elliptic model for time-space correlations that compounds information from both convective (i.e. associated with the Taylor hypothesis) and random sweeping velocity (i.e. associated with homogeneous turbulence with zero mean). In a recent work 3 we have shown that a detonation wave is an absolutely rather than convectively unstable system and its receptivity to postshock perturbations extends several half-reaction distances behind the lead front. The present paper aims to validate and extend elliptic models to the chemically reactive, self-excited post-detonation flow by determining contour of space-time cross correlations under entropic and vortical forcing. The focus is on the existence of a unique convection velocity, its scaling with the Chapman-Joguet (CJ) speed and the contribution of intrinsic scales. Crosscorrelations are evaluated based on large scale three-dimensional Navier-Stokes simulations carried out with a high resolution WENO scheme. Correlation results at different distances from the lead shock are presented.