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A weakly nonlinear analysis for pressure generation in shock vorticity interaction
Journal
AIAA AVIATION 2022 Forum
Date Issued
2022-01-01
Author(s)
Thakare, Pranav
Sinha, Krishnendu
Nair, Vineeth
Abstract
Shock–turbulence interaction is an important phenomenon occurring in various engineering applications. Linear interaction analysis (LIA) theory is used to investigate shock-turbulence interaction theoretically. Flow fluctuations are assumed to be linear and inviscid in LIA, and nonlinear effects in the flow are neglected, which limit its application to low amplitudes of shock upstream vorticity fluctuations. This paper presents a weakly nonlinear analysis (WNLA) to extend the LIA application limit to larger amplitudes of upstream disturbances. Specifically, we investigate the generation of nonlinear pressure fluctuations arising immediately downstream of the shock because of the interaction of two–dimensional vorticity wave with the shock. The shock deformation and variations in fluctuating mass flux across the shock are the most significant physical mechanisms responsible for the observed nonlinear effects in shock downstream pressure fluctuations. The predictions from WNLA compare well with results from high-fidelity numerical simulations, and the numerical data collapsed to a single curve when scaled by second-order effects in pressure fluctuations obtained theoretically, thus validating WNLA. Finally, we identify a bound for the applicability of LIA for calculating the downstream pressure field. We find that the range of upstream amplitudes of vorticity wave for which LIA is sufficiently accurate is a function of the shock Mach number and the incidence angle of the shock upstream vorticity fluctuations. These findings strongly suggest that limit of validity of LIA is different for various turbulence quantities of interest (vorticity, pressure, Reynolds stress, etc.) as the physical mechanisms themselves are distinct. This disparity is a potential reason why there exist no universal criteria for the operating bounds of LIA in the literature.