Linear dynamical model of overexpanded supersonic jet resonances
Creators: name:  V. JAUNET 
name:   G. LEHNASCH 
name:   E. GONCALVES 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: PROPULSION PHYSICS
NOZZLE
TURBOPUMPS

description: Unsteady side loads, observed in supersonic nozzles operating in over-expanded regimes, have received a lot of atten- tion in the research community since the pioneering work of Schmucker (1973). There seem to be a consensus on the origin of these undesirable side-forces. Steady off-axis loads are attributed to asymmetric separation of the flow due to uneven combustion or nozzle fabrication issues Schmucker (1973). On the other, and this is the main topic of this study, unsteady side-loads are still a very active topic of research. The thrust optimized contoured (TOC) nozzle profiles obtained by Rao (1958) and Rao (1961) suffer from a dramatic increase of side forces encountered during the startup phase. This was related to a rapid change in flow configura- tion with increasing nozzle pressure ratio (NPR): the Free Shock Separation (FSS) regime gives way to the Restricted Shock Separation (RSS) regime (Frey and Hagemann, 1999, Hagemann et al., 2000). This lead researcher to develop modern nozzle profiles to avoid the switch to RSS regime Frey et al. (2017), Stark and Genin (2017). These new nozzle hence only show FSS regimes but are still subject to side loads whenever utilized in over-expanded conditions. In these regimes, unsteady forces are most often associated with intrinsic unsteadiness of the shock system and of the separation line, both of them exhibiting random broadband low-frequency motions. As shown by Jaunet et al. (2017), tonal behavior can also be encountered at very specific NPRs in truncated ideal contour (TIC) nozzle in FSS regime. This behavior has also been observed in other studies (see amongst others Baars et al. (2012), Martelli et al. (2020)) and its origins attributed to either a transonic resonance mechanism (Zaman et al., 2002) or a long-range resonance scenario (Jaunet et al., 2017, Martelli et al., 2020). It has been shown that the wall pressure signature of this organised, resonating, jet motion is responsible for some of the nozzle side-loads, but it is the response of the shock system to the solicitations of this organised motions, that seem to create most of the wall pressure signature associated with the side-forces Bakulu et al. (2021). Hence, exploring the origins of these resonances is of importance is what motivates the current study. Due to the presence of a strong shock wave in the jet core, the mean flow exiting nozzles C-D nozzles in over-expanded conditions is made of a supersonic annular jet surrounding a lower, subsonic, velocity core. Therefore, in this study, we will explore the dynamics of a supersonic annular jet using linear stability analysis. Effects of the shear-layer thick- nesses, relative positions in the jet core as well as nozzle pressure ratios on the dynamics of the jet will be computed and discussed in order to provide explanations, and to model the occurrence of resonances in such flows.