viscous and nonequilibrium effects on kelvin–helmholtz instabilities

Abstract

The Kelvin-Helmholtz instability (KHI) is a shear-driven hydrodynamic instability observedacross a wide range of flow regimes, from astrophysical phenomena to oceanic currents. In high-speed flows, KHI plays a critical role in shock–wave/boundary–layer interactions, mixing layers, jet dynamics, laminar–to–turbulent transition, and combustion processes such as those occurring in scramjet engines. In the hypersonic regime, thermal-nonequilibrium effects must be taken into account to accurately model the flow. To this end, a new, less dissipative density-based hypersonic solver, HAVAFoam, is developed to benchmark thermal- nonequilibrium effects on KHI. In particular, high-fidelity approximate Riemann solvers with the numerical schemes of HLL, HLLC, and AUSM+ are implemented in HAVAFoam. Thorough validation and verification studies were performed to ensure that findings are independent of any numerical parameters. Direct numerical simulations were carried out, and the analysis reveals that AUSM+ exhibited the least numerical dissipation when compared with Kraichnan-Batchelor-Leith (KBL) theory, showing very good agreement with inviscid solutions reported in the literature. In this thesis work, for the first time, the impact of viscous and thermal nonequi- librium (TNE) effects on KHI with varying pressure fields to simulate a wide spectrum of flow conditions is reported. Incorporating viscosity with different degrees of nonequilib- rium and comparisons with inviscid nondimensional counterparts enable the quantification of its influence through the vorticity thickness, the growth of disturbances, and the degree of nonequilibrium intensity. At a low pressure of 40 Pa, the large kinematic viscosity at- tenuates the shear-layer instability, especially in the linear regime. At moderate pressures, 500 Pa, it was demonstrated that coupling is observed between TNE effects and shear-driven instability wherein TNE effects propagated within the shear layers and vortex cores. At high pressure, the TNE intensity was observed to increase with TNE ratios. It is noteworthy that with increasing TNE ratio, the resulting cat-eye cores and KHI billows become larger and more elevated. These findings demonstrate the capability of the in-house HAVAFoam solver to accurately model hypersonic reacting flows, encompassing not only theoretical confined cases but also laminar–to–turbulent transition in three-dimensional external flows.