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Title: Multiphysics computational modelling of high-speed partially-rarefied flows
Author: Colonia, Simone
ISNI:       0000 0004 6058 2882
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2015
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Hypersonic flows of practical importance often involve flow fields having continuum and rarefied regions. It is well known that Boltzmann equation based methods can provide more physically accurate results in flows having rarefied and non-equilibrium regions than continuum flow models. However, these methods are extremely computational expensive in near-equilibrium regions, which prohibits their application to practical problems with complex geometries and large domains where continuum and rarefied regions coexist. On the other hand, Navier-Stokes (or Euler) based methods are computationally efficient in simulating a wide variety of flow problems, but the use of continuum theories for the flow problems involving rarefied gas or very small length scales produces inaccurate results due to the breakdown of the continuum assumption and occurrence of strong thermal non-equilibrium. A practical approach for solving flow fields having continuum to rarefied regions is to develop numerical methods combining approaches able to compute the continuum regime and/or the rarefied (or thermal non-equilibrium) regime. The aim of this thesis is to investigate and develop new methods for the calculation of hypersonic flow fields that contain both continuum and rarefied flow regions. The first part of the work is dedicated to the continuum regime. Among the different numerical inviscid flux functions available in the literature, the AUSM-family has been shown to be capable of solving to a good accuracy flow fields at a wide range of Mach regime including high-speed flows. For this reason an implicit formulation of the AUSM+ and AUSM+up schemes, with a Jacobian defined fully analytically, has been implemented in the Helicopter Multi-Block CFD code (HMB2), developed at the University of Liverpool, to predict continuum high-speed flow. The original form of the schemes lead to the presence of different branches in the computational algorithm for the Jacobian since do not guarantee the fluxes to be continuously differenciable functions of the primitive variables. Thus, a novel formulation of the AUSM+ and AUSM+up schemes is proposed in chapter 2. Here, a blending is introduced by means of parametric sigmoidal functions at the points of discontinuity in the schemes formulations. Predictions for wide range of test cases obtained employing the proposed formulation are compared with results available in the literature in chapter 3 to show that the reliability of the schemes has been preserved in the proposed formulation. Later on, the work focuses on partially-rarefied high-speed flows. At the University of Liverpool, this kind of flows are simulated using the hybrid approach available in the Multi-Physics Code (MΦC) where a discrete velocity method for kinetic Boltzmann equations is coupled with a traditional Navier-Stokes solver. Firstly, the discrete velocity method has been improved with the implementation of kinetic models for diatomic gases in the framework. A validation of the correctness of the implemented models is discussed in chapter 6. However, employing a discrete velocity method in hybrid simulation leads to high computational and memory cost. In this context, gas-kinetic schemes have been identified by the author, in the related literature, as efficient approaches, relative to discrete velocity methods, capable of modelling complex gas flows with moderate rarefaction effects but with significant thermal non-equilibrium. Thus, two gas-kinetic schemes, analytically defined on the basis of the Chapman-Enskog expansion of non-dimensional Shakhov and Rykov models, have been proposed in chapter 5. Compared with similar gas-kinetic schemes available in the literature, the presented schemes differ in the approach employed to evaluate the terms of Chapman-Enskog solutions and in the kinetic models used as mathematical foundations of the schemes. In chapters 6 and 7 the scheme is tested for various cases and Mach numbers, including complex 3D flows, proving to be a viable way to improve the performance of hybrid simulations, maintaining an acceptable level of reliability, if used in place of more complex methods for weakly rarefied flows. Finally, chapter 8 includes a summary of the findings as well as suggestions for future works.
Supervisor: Steijl, R. ; Barakos, G. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral