Predictive accuracy of the previously developed coupled code for the solution of the time-dependent Navier-Stokes equations in conjunction with the radiative transfer equation was first assessed by applying it to the prediction of thermally radiating, hydrodynamically developed laminar pipe flow for which the numerical solution had been reported in the literature. The effect of radiation on flow and temperature fields was demonstrated for different values of conduction to radiation ratio. It was found that the steady-state temperature predictions of the code agree well with the benchmark solution. In an attempt to test the predictive accuracy of the coupled code for turbulent radiating flows, it was applied to fully developed turbulent flow of a hot gas through a relatively cold pipe and the results were compared with the numerical solution available in the literature. The code was found to mimic the reported steady-state temperature profiles well. Having validated the predictive accuracy of the coupled code for steady, laminar/turbulent, radiating pipe flows, the performance of the code for transient radiating flows was tested by applying it to a test problem involving laminar/turbulent flow of carbon dioxide through a circular pipe for the simulation of simultaneous hydrodynamic and thermal development. The transient solutions for temperature, velocity and radiative energy source term fields were found to demonstrate the physically expected trends. In order to improve the performance of the code, a parallel algorithm of the code was developed and tested against sequential code for speed up and efficiency. It was found that the same results are obtained with a reasonably high speed-up and efficiency.

The Direct Simulation Monte Carlo method is a computational tool for modelling rarefied flows. The Macroscopic Chemistry Method was developed to simplify the modelling of dissociation and recombination reactions in DSMC. The ability to understand and predict the behaviour of chemically reacting, rarefied flows is a critical aspect in the development of high altitude, high speed bodies such as re-entry craft, high altitude aircraft, space transport vehicles and missiles. Computational methods are an invaluable source of information when experimental techniques are difficult, costly or time-consuming. However, traditional methods of modelling chemical kinetics using DSMC suffer from a number of drawbacks. The Macroscopic Chemistry Method overcomes a number of these problems, but has previously only been applied to simulations of a single diatomic gas. The Macroscopic Chemistry Method (MCM) is extended to consider multiple species and multiple reaction sets, thermal non-equilibrium effects, trace species modelling, unsteady flows, vibrational state specific chemistry, electronic excitation, relaxation and ionization and coupled nonequilibrium radiation emission. The Macroscopic Method is described as a general DSMC modelling philosophy rather than as a single formulated method. That is, the flexibility and utility of the method are shown through examples of applying a macroscopic approach to a number of problems, and by highlighting instances where a macroscopic approach is useful or even necessary. The problems investigated include reservoir relaxation calculations, 1-D shock, expansion and shock-expansion calculations, two-dimensional flows over a vertical step and through a cavity, and axis-symmetric flow about a sphere. The studies demonstrate that although MCM may often present a simplified approach as compared to traditional 'non-macroscopic' methods, it does not necessarily lead to more approximate solutions. On the contrary, the ability of macroscopic methods to combine different models of physical processes with the most recent (verified) data means that they are particularly suited to simulate high altitude, rarefied flows. It is also shown that, like any model approach, the validity of the approximations employed must be justified for a particular problem. In general, macroscopic methods of varying complexity and accuracy may be implemented to model a specific physical process. Adoption of the Macroscopic Chemistry Method in DSMC has the potential to enhance the modelling of chemical kinetics, charged-particle effects and radiation in rarefied hypersonic flows. This capability may be attributed to the simplicity and flexibility which the macroscopic approach affords over methods which seek to avoid the use of collective information. Macroscopic methods have already been employed to model weakly ionized flows. Their further application to model chemical kinetics and other processes would be useful for modelling and understanding the behaviour of objects in rarefied hypersonic flow-fields.

A non-iterative pressure based algorithm which consists of splitting the solution of momentum energy and species equations into a sequence of predictor-corrector stages was developed for the simulation of transient reacting radiating flows. A semi-discrete approach called the Method of Lines (MOL) which enables implicit time-integration at all splitting stages was used for the solution of conservation equations. The solution of elliptic pressure equation for the determination of pressure field was performed by a multi-grid solver (MUDPACK package). Radiation calculations were carried out by coupling previously developed gray and non-gray radiation models with the algorithm. A first order (global) reaction mechanism was employed to account for the chemistry. The predictions of the algorithm for the following test cases: i) non-isothermal turbulent pipe flow and ii) laminar methane-air diffusion flame / were benchmarked against experimental data and numerical solutions available in the literature and the capability of the code to predict transient solutions was demonstrated on these test cases. Favorable agreements were obtained for both test cases. The effect of radiation and non-gray treatment of the radiative properties were investigated on the second test case. It was found that incorporation of radiation has significant effect on Temeprature and velocity fields but its effect is limited in species predictions. Executions with both radiation models revealed that the non-gray radiation model considered in the present study produces similar results with the gray model at a considerably higher computational cost. The algorithm developed was found to be an efficient and versatile tool for the timedependent simulation of different flow scenarios constitutes the initial steps towards the computation of transient turbulent combustion.

Ce travail de thèse porte sur l'extension et l'analyse d'un solveur volumes finis eulérien, co-localisé avec capture d'interfaces pour la simulation des écoulements multi-matériaux non miscibles. Les extensions proposées s'inscrivent dans la volonté d'élaborer un outil de simulation multi-physiques. Dans le cadre de ce mémoire, le caractère multi-physiques recouvre les champs que nous allons détailler. Nous traitons le cas des écoulements radiatifs modélisés par un système à deux températures qui couple les phénomènes purement hydrodynamiques aux phénomènes radiatifs. Nous proposons un solveur permettant la prise en compte des effets de tension superficielle à l'interface entre deux fluides. Nous développons un solveur implicite permettant la simulation précise d'écoulements faisant intervenir de faibles nombres de Mach par le biais d'une méthode de renormalisation de la diffusion numérique. Enfin, les effets tri-dimensionnels sont considérés ainsi que la possibilité d'étendre le schéma de base aux écoulements à un nombre quelconque de matériaux. A chaque étape, les solveurs développés sont validés sur des cas-tests. / This work is devoted to the extension of a eulerian cell-centered finite volume scheme with interfaces capturing for the simulation of multimaterial fluid flows. Our purpose is to develop a simulation tool which could be able to handle multi-physics problems in the following sense. We address the case of radiating flows, modeled by a two temperature system of equations where the hydrodynamics are coupled to radiation transport. We address a numerical scheme for taking surface tension forces into account. An implicit scheme is proposed to handle low Mach number fluid flows by means of a renormalization of the numerical diffusion. Eventually, the scheme is extended to three-dimensional flows and to multimaterial flows, that is with an arbitrary number of materials. At each step, numerical simulations validate our schemes.