Wave-packets in a reacting, imperfectly-expanded supersonic jet

Abstract

The present work focuses on the large coherent structures of a turbulent, reacting and imperfectly-expanded supersonic jet. These have been extracted from a Large Eddy Simulation (LES) including chemical reactions by Spectral Proper Orthogonal Decomposition (SPOD). While SPOD is now a standard tool for non-reactive flows, very few studies have dealt with reactive jets. The article shows that the pressure and axial velocity fields exhibit coherent wave-packets with a well-defined wavelength and amplitude envelope. The shock/recompression cells have a strong effect on the amplitude of the wave-packet, but a weak effect on the wavelength. The temperature field exhibits a lower self-coherence and exhibits small scale structures upstream, generated within the mixing layer, and an irregular pattern of larger structures downstream in agreement with Prasad and Morris (2020) [65]. A high-energy coherent structure has been observed at a Strouhal number of St=0.4 (normalized by the jet diameter and the jet exit velocity), which appears to result from a mutual reinforcement between the main shear layer instability and the vortex shedding from the normal shock. An attempt is made to model the wave-packets using the parabolized stability equations (PSE) about the mean flow, ignoring the chemical reactions. The PSE solution fails to model the temperature fluctuations, but shows rather good agreement with the leading SPOD modes of pressure and axial velocity downstream. This reveals that the flame impacts the pressure and velocity wave-packets in a weak manner: the coherent structures in the pressure and velocity field are generated by hydrodynamic convective instability, without being significantly altered by the reactive nature of the flow.