Effect of Inhomogeneity and Unsteadiness on the Stability of High-Speed Shear Flows
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In hypersonic flows, turbulence critically influences mass and momentum transport, mixing, heat transfer and acoustic noise generation. In contrast to incompressible flow, in high speed flows pressure is a true thermodynamic variable and flowthermodynamic interactions render the investigations extremely challenging. Most studies to date have been performed on steady, uniform or homogeneous shear flows leading to important insight on the flow physics. In most real world applications,flows of practical importance will exhibit unsteadiness and strong inhomogeneity. To date, investigations of unsteadiness and inhomogeneity in high-speed flows are rare. The goal of this dissertation is to study and understand these non-ideal effects when pertinent to shear flows. Towards this goal, we perform three distinct studies: (a) examination of time reversal characteristics of linear inviscid mass, momentum, energy and state equation in compressible flows; (b) Linear analysis (RDT) of compressibility effects on instabilities in temporally periodic (unsteady) homogeneous shear flow; and (c) Numerical investigation of small perturbation evolution in compressible Kolmogorov (inhomogeneous) shear flow. The first study shows that even with the additional governing equations required in the high-speed regime, the inviscid flow field is still reversible. This justifies the use of temporal periodicity to investigate the effect of unsteadiness. The second study presents a detailed analysis of the pressure equation in temporally periodic homogeneous shear flow. The analysis and numerical results show unsteady uniform shear exhibits two stages of evolution due to the changing behavior of pressure. These stages are analogous to the first two stages of evolution established in steady shear. The third stage seen in steady shear is not achieved by periodic shear flow. The final study shows that the evolution of small perturbations in spatially periodic Kolmogorov flow is influenced by: i) the initial compressibility parameter, M_(g0), ii) the initial perturbation orientation, and iii) the stream normal location. Ultimately, the final study supports the postulate that all shear flows exhibit perturbation stability boundary classifications seen in homogeneous shear flows. The findings of this research further our understanding of the effects of unsteadiness and inhomogeneity in realistic flows, which will aid in the development of improved computational tools.
Bertsch, Rebecca Lynne (2014). Effect of Inhomogeneity and Unsteadiness on the Stability of High-Speed Shear Flows. Doctoral dissertation, Texas A & M University. Available electronically from