The work presented in this thesis studies acoustic perturbations in slowly varying pipes. The slow variation is introduced in the form of a small parameter ${\epsilon}$ and through this in turn gives rise to a slow axial scale $X$ such that $X = {\epsilon}x$ where $x$ is the normal axial coordinate. This allows an asymptotic approach and the WKB method is used to solve the subsequent mathematical problems. The first deals with the existence of a trapped mode in a hard-walled pipe of varying radius conveying fluid. For the derived leading order propagating mode solution, its amplitude becomes singular at transition points $X_{t}$ and $X_{t'}$ where $X_{t} > 0$ and $X_{t'} < 0$ and thus is unable to propagate past these points. Because of the break down in the solution, this leads to the theory that in the neighbourhood of these points there exists a boundary layer in which the original assumption about having slow variation does not hold. By first seeking the thickness of the layer, valid solutions can then be derived and then matched to the outer solutions in order to produce a uniform solution which holds for the entire axial domain. Once this is achieved, it is then used to derive trapped mode solutions. In this case, the theory used is that of two single turning points which are then combined to obtain the full solution. It is illustrated through consideration of examples and the dependence on ${\epsilon}$ is also shown through various plots. This problem will be considered for a symmetric and asymmetric duct and for differing duct parameters. Problems may arise when the two turning points lie close together and so we seek to improve on the method used by deriving a solution to trapped modes encompassing both turning points, which will be proposed together with some illustrations in order to justify its use and reliability. Next, the case of mode propagations on a thin elastic shell of varying radius conveying fluid is studied. The acoustic solutions of a straight shell in vacuo are first briefly reviewed and then built up by the addition of radius variation and the presence of a stationary fluid. The work presented first outlines the analysis for wave propagation in a slowly-varying thin elastic shell in vacuo. It is found that the shell and the fluid terms are coupled through the fluid pressure term, which is added to the equation governing the radial shell displacements since the pressure is assumed to affect radial motion only. Once the newly corrected equation for the radial shell displacements has been obtained, together with the axial and azimuthal displacements equations, this new system of governing equations is then separated into leading order ${\epsilon}^{0}$ and first order ${\epsilon}^{1}$ systems. In order to simplify the calculations, only the zeroth azimuthal order $m = 0$ will be studied here. With this simplification, a notable result is that the solutions of the torsional motion is decoupled from the axial and radial solutions. Once the dispersion equation is extracted from the leading order system, it can be seen that the axial and radial solutions are in fact coupled. The solution to the in vacuo with varying radius problem is first briefly presented and it is then followed by the solution to the fluid inclusion problem with varying radius, which makes up the main part of this section. The solution is studied for various frequencies and at various points along the shell. In addition, the axial and radial components of the first three modes are examined along with their amplitudes and energy distributions. Finally, mean flow is added and the same analysis is carried out, paying particular attention to the differences which arise in comparison to the stationary flow case.

L’objectif de cette étude est de modéliser et de simuler numériquement des phénomènes d’interaction fluide-structure dans un cadre compressible pour des écoulements non-visqueux. La modélisation proposée repose sur une formulation monolithique du couplage fluide-structure en considérant une unique équation permettant de résoudre simultanément le mouvement du fluide et du solide. Un terme supplémentaire dans l’équation de quantité de mouvement traduit la présence de l’obstacle dans l’écoulement. La contribution de ce terme de pénalisation est étudiée à travers l’analogie avec une formulation variationnelle et un intérêt est porté à la rigueur physique, mathématique et numérique de l’unification des deux milieux, en particulier à l’interface. L’approche numérique correspond à une méthode à pas fractionnaire, en tout point identique aux méthodes de prédiction correction utilisées en incompressible. Quelques résultats numériques clôturent ce travail et permettent de préciser les conditions d’application de ce modèle d’interaction fluide-structure en régime compressible. / This study deals with the modeling and simulation of fluid-structure interactions in a compressible framework for inviscid flows. A monolithic approach has been chosen for treating the coupling between the fluid and the solid through a single equation that solves the motion of both simultaniously. An additionnal term in the momentum equation allows to take into account the obstacle in the flow. A weak formulation is derived from previous similar works that confirms the unification problem is mathematically well-posed, especially on the interface. The numerical procedure relies on a time-splitting method similar to prediction-correction methods for incompressible flows. Some numerical examples illustrate this work and allows to conclude on the feasibility of this fluid-structure interaction model for compressible flows.

Accurate measurement of turbine engine compressor inlet total temperature is paramount for controlling engine speed and pressure ratio. Various methods exist for measuring compressor inlet total temperature on turbojet engines with hydromechanical control. One method involves the use of an ejector-diffuser system (eductor) to pull air from the engine inlet in order to measure the incoming total temperature. Analysis of historical test data has revealed that the inlet temperature measurement can be biased at certain flight conditions causing engine mis-scheduling and off-nominal engine operation. This bias is characterized primarily by adverse heat transfer effects and secondly by poor flow quality in the eductor tubing. Alternate eductor system configurations have been proposed to mitigate temperature bias. A one-dimensional engineering model of the eductor system was developed to facilitate the analysis of baseline and alternate eductor configurations. The model is calibrated with results from Computational Fluid Dynamics and validated with ground test data. The validated model is used to quantify the performance of several eductor configurations throughout the range of expected operating conditions and to quantify the amount of compressor inlet temperature measurement bias mitigation each configuration provides.

Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This document discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this document the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant.

To quantify primary side aerosol retention, an Eulerian/Lagrangian approach was used to investigate aerosol transport in a compressible, turbulent, adiabatic, internal, wall-bounded flow. The ARTIST experimental project (Phase I) served as the physical model replicated for numerical simulation. Realizable k-ε and standard k-ω turbulence models were selected from the computational fluid dynamics (CFD) code, FLUENT, to provide the Eulerian description of the gaseous phase. Flow field simulation results exhibited: a) onset of weak secondary flow accelerated at bend entrance towards the inner wall; b) flow separation zone development on the convex wall that persisted from the point of onset; c) centrifugal force concentrated high velocity flow in the direction of the concave wall; d) formation of vortices throughout the flow domain resulted from rotational (Dean-type) flow; e) weakened secondary flow assisted the formation of twin vortices in the outflow cross section; and f) perturbations induced by the bend influenced flow recovery several pipe diameters upstream of the bend. These observations were consistent with those of previous investigators. The Lagrangian discrete random walk model, with and without turbulent dispersion, simulated the dispersed phase behavior, incorrectly. Accurate deposition predictions in wall-bounded flow require modification of the Eddy Impaction Model (EIM). Thus, to circumvent shortcomings of the EIM, the Lagrangian time scale was changed to a wall function and the root-mean-square (RMS) fluctuating velocities were modified to account for the strong anisotropic nature of flow in the immediate vicinity of the wall (boundary layer). Subsequent computed trajectories suggest a precision that ranges from 0.1% to 0.7%, statistical sampling error. The aerodynamic mass median diameter (AMMD) at the inlet (5.5 μm) was consistent with the ARTIST experimental findings. The geometric standard deviation (GSD) varied depending on the scenario evaluated but ranged from 1.61 to 3.2. At the outlet, the computed AMMD (1.9 μm) had GSD between 1.12 and 2.76. Decontamination factors (DF), computed based on deposition from trajectory calculations, were just over 3.5 for the bend and 4.4 at the outlet. Computed DFs were consistent with expert elicitation cited in NUREG-1150 for aerosol retention in steam generators.

The jet-in-crossflow problem has been extensively studied, mainly because of its applications in film cooling and injector designs. It has been established that in low-speed flows, pulsing the jet significantly enhances mixing and jet penetration. This work investigates the effects of pulsing on mixing and jet trajectory in high speed (compressible) flow, using Large Eddy Simulation. Jets with different density ratios, velocity ratios and momentum ratios are pulsed from an injector into a crossflow. Density ratios used are 0.55 (CH4/air), 1.0 (air/air) and 1.5 (CO2/air). Results are compared with the low speed cases studied in the past and then analyzed for high speed scaling. The simulations show that the lower density jet develops faster than a higher density jet. This results in more jet spread for the lower density jet. Scaling for jet spread and the decay of centerline jet concentration for these cases are established, and variable density scaling law is developed and used to predict jet penetration in the far field. In most non-premixed combustor systems, the fuel and air being mixed are at different initial temperatures and densities. To account for these effects, heated jets at temperatures equal to 540K and 3000K have been run. It has been observed that, in addition to the lower density of heated jets, the higher kinematic viscosity effects the jet penetration. This effect has been included and validated in the scaling law for the heated jet trajectory.

This study presents an improved ghost-cell immersed boundary approach to represent a solid body in compressible flow simulations. In contrast to the commonly used approaches, in the present work ghost cells are mirrored through the boundary described using a level-set method to farther image points, incorporating a higher-order extra/interpolation scheme for the ghost cell values. In addition, a shock sensor is in- troduced to deal with image points near the discontinuities in the flow field. Adaptive mesh refinement (AMR) is used to improve the representation of the geometry efficiently. The improved ghost-cell method is validated against five test cases: (a) double Mach reflections on a ramp, (b) supersonic flows in a wind tunnel with a forward- facing step, (c) supersonic flows over a circular cylinder, (d) smooth Prandtl-Meyer expansion flows, and (e) steady shock-induced combustion over a wedge. It is demonstrated that the improved ghost-cell method can reach the accuracy of second order in L1 norm and higher than first order in L∞ norm. Direct comparisons against the cut-cell method demonstrate that the improved ghost-cell method is almost equally accurate with better efficiency for boundary representation in high-fidelity compressible flow simulations. Implementation of the improved ghost-cell method in reacting Euler flows further validates its general applicability for compressible flow simulations.

[pt] Neste trabalho é apresentado o estudo da interação entre um jato supersônico e uma superfície plana, com o objetivo de analisar o comportamento do campo de velocidade, pressão e temperatura do escoamento. Este estudo encontra sua motivação no processo de descamação térmica de rochas duras, a qual pode resultar da iteração entre um jato a alta pressão e temperatura e a rocha. Este processo, que pode ser útil na perfuração de rochas duras e profundas, ocorre devido ao acúmulo de tensões térmicas na rocha, o qual pode acarretar sua fratura. Este tipo de processo também envolve diversos mecanismos aerodinâmicos e termodinâmicos, que são isoladamente fenômenos abertos. No desenvolvimento deste trabalho o escoamento foi modelado pelas equações de Navier - Stokes bidimensionais para uma mistura de gases perfeitos em um sistema de coordenadas cilíndrico. O modelo considerado para descrever o transporte turbulento é o modelo de uma equação de Spalart - Allmaras, o qual envolve a solução de uma equação diferencial para a viscosidade turbulenta. Estas equações são resolvidas utilizando-se uma metodologia de volumes finitos adaptada a escoamentos compressíveis. A descrição dos escoamentos transientes obtidos necessitou de diversas modificações ao código computacional existente. Estas modificações trataram, em particular, das condições de contorno, que utilizam a noção de características, e do modelo de turbulência. A estrutura do escoamento resultante da interação entre o jato supersônico e a parede é estudada, avaliando-se a influência (i) da distância entre a saída do jato e a parede, (ii) da razão de pressões entre o jato e o ambiente. Além disso, é examinada a evolução transiente do escoamento. Os resultados obtidos são analisados com vista a obter as melhores condições aerodinâmicas para o processo de descamação térmica. / [en] I in this work a study of the interaction between a supersonic jet and a planar surface is presented, with the aim to analyze the behavior of the velocity, pressure and temperature flowfield. This study finds its motivation in the process of thermal spallation of hard rocks, which may result from the interaction between a high pressure and high temperature jet and the rock. This process, that can be used in the drilling of hard and deep rocks, occurs due to the accumulation of thermal stresses in the rock, which can cause its fracture. This type of process also involves several aerodynamic and thermodynamic mechanisms, which are still open phenomena. In the development of this work the flow was modeled by the two-dimensional Navier-Stokes equation for a mixture of perfect gases in a cylindrical coordinates system. The model considered to describe the turbulent transport is the one equation of Spalart - Allmaras model, which involves the solution of a differential equation for the turbulent viscosity. These equations are solved using a finite volumes methodology which is adapted to compressible flows. The description of the obtained transient flow required several modifications in the existing computational code. These modifications involved, in particular, the choice of boundary conditions, that use the notion of characteristics, and the turbulence model. The structure of the flow resulting from the interaction between the supersonic jet and the wall is studied. In particular, are examined the influence (i) the distance between the jet and wall, (II) of the pressures ratio between the jet and the environment. Moreover, the transient evolution of the flow is examined. The obtained results are examined to determine the best aerodynamic conditions for the process of thermal spallation to occur.

After the end of the NASA space shuttle programme, there has been resurgence of interest in developing a single stage-to-orbit spacecraft. The key technology to realize this dream is the airbreathing scramjet engine. The scramjet concept has been around for decades, but much work is still needed in order to eliminate the remaining obstacles to develop a practical working prototype of the engine. Many such obstacles are related to the inlet which functions as the main compression unit for the engine. Typically, a high speed inlet is designed to function properly in a single flight condition. Such an inlet would experience adverse flow conditions related to various shock-shock interactions, viscous effects, shock-boundary layer interactions, and many other flow phenomena at off-design conditions. The traditional mechanism to mitigate the adverse flow conditions is by varying the inlet geometry at off-design conditions. There are still gaps in understanding the behaviour of inlets at off-design conditions and the effectiveness of variable geometry as inlet flow control. This is partly due to complex flow diagnostics setup, which limits the type, quantity and quality of information that can be extracted from the inlet flow. The first objective of this thesis was to develop a global inlet measurement system that can provide an abundance of information on inlet flow. The pressure sensitive paint method was employed together with other methods to provide comprehensive understanding on inlet flow characteristics. Calculation of Mach number at the isolator exit using the isolator sidewall pressure map was successfully demonstrated. The measurement of Mach number at the isolator exit has allowed for performance of the inlet to be calculated without the need for intrusive flow diagnostics tools used by previous researchers. The global measurement system was then employed to investigate the characteristics of the scramjet inlet operating at various off-design conditions. Complex shock structures were observed at the inlet cowl entrance as the angle-of-attack was increased. The relationship of flow quality and inlet performance was examined and discussed. General improvements on the inlet performance were obtained if the size of separation on the compression ramp was reduced. The inlet was also observed to perform poorly when compression shocks impinged on the inner cowl surface. Cowl deflections were demonstrated to be effective in controlling the internal flow of the inlet and improving its performance. An exploratory study on the role of micro-vortex generators to control boundary layer separation on scramjet inlets has been included as well. Strategies for optimizing an inlet at off-design conditions were analysed, and it was found that any variable geometry combination must maintain high throat-to-freestream Mach number ratio in order to preserve high inlet performance.

We investigate the Richtmyer-Meshkov instability (RMI) that occurs when an incident shock impulsively accelerates the interface between two different fluids. RMI is important in many technological applications such as Inertial Confinement Fusion (ICF) and astrophysical phenomena such as supernovae. We consider RMI in the presence of the magnetic field in converging geometry through both simulations and analytical means in the framework of ideal magnetohydrodynamics (MHD). In this thesis, we perform linear stability analyses via simulations in the cylindrical geometry, which is of relevance to ICF. In converging geometry, RMI is usually followed by the Rayleigh-Taylor instability (RTI). We show that the presence of a magnetic field suppresses the instabilities. We study the influence of the strength of the magnetic field, perturbation wavenumbers and other relevant parameters on the evolution of the RM and RT instabilities. First, we perform linear stability simulations for a single interface between two different fluids in which the magnetic field is normal to the direction of the average motion of the density interface. The suppression of the instabilities is most evident for large wavenumbers and relatively strong magnetic fields strengths. The mechanism of suppression is the transport of vorticity away from the density interface by two Alfv ́en fronts. Second, we examine the case of an azimuthal magnetic field at the density interface. The most evident suppression of the instability at the interface is for large wavenumbers and relatively strong magnetic fields strengths. After the shock interacts with the interface, the emerging vorticity breaks up into waves traveling parallel and anti-parallel to the magnetic field. The interference as these waves propagate with alternating phase causing the perturbation growth rate of the interface to oscillate in time. Finally, we propose incompressible models for MHD RMI in the presence of normal or azimuthal magnetic field. The linearized equations are solved numerically using inverse Laplace transform. The incompressible models show that the magnetic field suppresses the RMI, and the mechanism of this suppression depends on the orientation of the initially applied magnetic field. The incompressible model agrees reasonably well with compressible linear simulations.