There has been a continuous effort to unveil the physics of hypersonic flows both experimentally and numerically, in order to achieve an efficient hypersonic vehicle design. With the advent of the high speed computers, a lot of focus has been given on research pertaining to numerical approach to understand this physics. The features of such flows are quite different from those of subsonic, transonic and supersonic ones and thus normal CFD methodologies fail to capture the high speed flows efficiently. Such calculations are made even more challenging by the presence of nonequilibrium thermodynamic and chemical effects. Thus further research in the field of nonequilibrium thermodynamics is required for the accurate prediction of such high enthalpy flows. The objective of this thesis is to develop improved computational tools for hypersonic aerodynamics accounting for non-equilibrium effects. A survey of the fundamental theory and mathematical modeling pertaining to modeling high temperature flow physics is presented. The computational approaches and numerical methods pertaining to high speed flows are discussed. In the first part of this work, the fundamental theory and mathematical modeling pertaining to modeling high temperature flow physics is presented. Continuum based approach (Navier Stokes) and Boltzmann equation based approach (Gas Kinetic) are discussed. It is shown mathematically that unlike the most popular continuum based methods, Gas Kinetic method presented in this work satisfies the entropy condition. In the second part of this work, the computational approaches and numerical methods pertaining to high speed flows is discussed. In the continuum methods, the Steger Warming schemes and Roe’s scheme are discussed. The kinetic approach discussed is the Boltzmann equation with Bhatnagar Gross Krook (BGK) collision operator. In the third part, the results from new computational fluid dynamics code developed are presented. A range of validation and verification test cases are presented. A comparison of the two common reconstruction techniques: Green Gauss gradient method and MUSCL scheme are discussed. Two of the most common failings of continuum based methods: excessive numerical dissipation and carbuncle phenomenon techniques, are investigated. It is found that for the blunt body problem, Boltzmann BGK method is free of these failings.

This thesis investigates fundamental flows of resistive magnetohydrodynamics (MHD) by a new numerical tool based on the gas-kinetic method. The motivation for this work stems from the need to analyze the mechanisms of plasma detachment in the exhaust plume of the magnetoplasma rocket known as VASIMRR. This rocket has great potential for reducing the travel time for deep space exploration missions. However, it is very difficult to investigate detachment in ground-based experiments because this large-scale device can fully function only in a vacuum. This difficulty makes computational analysis and modeling an important part of the design and testing process. A parallelized Boltzmann-BGK continuum flow solver is expanded to include resistive MHD physics. This new code is validated against known solutions to MHD channel flows and new results are presented for simulations of a laminar round jet subject to a constant applied magnetic field as well as the diverging magnetic field of a current loop. Additionally, a parametric map is presented that outlines appropriate conditions required when using a fluid model for magnetic nozzle flows. The work of this thesis serves as an introductory step to developing a robust numerical ow solver capable of simulating magnetic nozzle flows and other plasmas that cannot be easily replicated in ground facilities.

In this thesis, gas-kinetic methods for inviscid and viscous flow simulations are developed. Initially, the finite volume gas-kinetic methods are investigated for 1-D flows as a preliminary study and are discussed in detail from theoretical and numerical points of view. The preliminary results show that the gas-kinetic methods do not produce any unphysical flow phenomena. Especially the Gas-Kinetic BGK method, which takes into account the particle collisions, predicts compressible flows accurately. The Gas-Kinetic BGK method is then extended for the solution of 2-D and 3-D inviscid and viscous flows on unstructured/hybrid grids. The computations are performed in parallel. Various inviscid and viscous test cases are considered and it is shown that the Gas-Kinetic BGK method predicts both inviscid and viscous flow fields accurately. The implementation of hybrid grids for viscous flows reduces the overall number of grid cells while enabling the resolution of boundary layers. The parallel computations significantly improve the computation time of the Gas-Kinetic BGK method which, in turn, enable the method for the computation of practical aerodynamic flow problems.

Despite significant advancements in the understanding of fluid flows, combustion and material technologies, hypersonic flight still presents numerous technological challenges. In hypersonic vehicles turbulence is critical in controlling heat generation in the boundary layer, mixing inside the combustor, generation of acoustic noise, and mass flow in the intake. The study of turbulence in highly compressible flows is challenging compared to incompressible due to a drastic change in the behavior of pressure and a relaxation of the incompressibility constraint. In addition fluid flow inside a flight vehicle is complicated by wall-effects, heat generation and complex boundary conditions. Homogeneous shear flow contains most of the relevant physics of boundary and mixing layers without the aforementioned complicating effects. In this work we aim to understand and characterize the role of pressure, velocity-pressure interaction, velocity-thermodynamics interaction in the late-stage transition-to-turbulence regime in a high speed shear dominated flow by studying the evolution of perturbations in in a high Mach number homogeneous shear flow. We use a modal-analysis based approach towards understanding the statistical behavior of turbulence. Individual Fourier waves constituting the initial flow field are studied in isolation and in combination to understand collective statistical behavior. We demonstrate proof of concept of novel acoustic based strategies for controlling the onset of turbulence. Towards this goal we perform direct numerical simulations (DNS) in three studies: (a) development and evaluation of gas kinetic based numerical tool for DNS of compressible turbulence, and perform detailed evaluation of the efficacy of different interpolation schemes in capturing solenoidal and dilatational quantities, (b) modal investigation in the behavior of pressure and isolation of linear, non-linear, inertial and pressure actions, and (c) modal investigation in the possible acoustic based control strategies in homogeneously sheared compressible flows. The findings help to understand the manifestation of the effects of compressibility on transition and turbulence via the velocity-pressure interactions and the action of individual waves. The present study helps towards the design of control mechanisms for compressible turbulence and the development of physically consistent pressure strain correlation models.