This work represents the initial steps in a wider project that aims to map out the sensitive areas in fuel injectors and combustion chambers. Direct numerical simulation (DNS) using a Low-Mach-number formulation of the Navier–Stokes equations is used to calculate direct-linear and adjoint global modes for axisymmetric low-density jets and lifted jet diffusion flames. The adjoint global modes provide a map of the most sensitive locations to open-loop external forcing and heating. For the jet flows considered here, the most sensitive region is at the inlet of the domain. The sensitivity of the global-mode eigenvalues to force feedback and to heat and drag from a hot-wire is found using a general structural sensitivity framework. Force feedback can occur from a sensor-actuator in the flow or as a mechanism that drives global instability. For the lifted flames, the most sensitive areas lie between the inlet and flame base. In this region the jet is absolutely unstable, but the close proximity of the flame suppresses the global instability seen in the non-reacting case. The lifted flame is therefore particularly sensitive to outside disturbances in the non-reacting zone. The DNS results are compared to a local analysis. The most absolutely unstable region for all the flows considered is at the inlet, with the wavemaker slightly downstream of the inlet. For lifted flames, the region of largest sensitivity to force feedback is near to the location of the wavemaker, but for the non-reacting jet this region is downstream of the wavemaker and outside of the pocket of absolute instability near the inlet. Analysing the sensitivity of reacting and non-reacting variable-density shear flows using the low-Mach-number approximation has up until now not been done. By including reaction, a large forward step has been taken in applying these techniques to real fuel injectors.

This dissertation deals with instabilities of thin liquid films up to entrainment of drops. Four types of instabilities have been classified depending on the type of structure and process on the liquid film surface: two-dimensional slow waves, two-dimensional fast waves, three-dimensional waves, solitary waves and entrainment of drops from the film surface. This thesis analyzes the physical principles of instabilities and deals with the mathematical formulation of the problem. Shear and pressure forces acting on the surface of the liquid film are identified as the cause of instabilities. Mathematical models for predicting instabilities are demonstrated using approaches based on solving the Orr-Sommerfeld equation and the equations of motion in integral form. Models of shear and pressure forces acting on the surface of the film and selected models of film thickness are presented. The work is focused on the prediction of the initiation of two-dimensional waves using the integral approach. Shear stress and pressure forces acting on the liquid film surface have been modeled using the simulation of air flow over a solid surface. Finally, criteria for drop entrainment are presented with their dependence on air velocity and film thickness.

Pressure swirl atomizers are commonly used in IC, aero-engines, and liquid propellant rocket combustion. Understanding the atomization process is important in order to enhance vaporization, mitigate soot formation, design of combustion chambers, and improve overall combustion efficiency. This work utilizes non-invasive techniques such as ultra -speed imaging, and Phase Doppler Particle Anemometry (PDPA) in order to investigate the cascade atomization process of pressure-swirl atomizers by examining swirling liquid film dynamics and the localized droplet characteristics of the resulting hollow cone spray. Specifically, experiments were conducted to examine these effects for three different nozzles with orifice diameters .3mm, .5mm, and .97mm. The ultra-speed imaging allowed for both visualization and interface tracking of the swirling conical film which emanated from each nozzle. Moreover, this allowed for the measurement of the radial fluctuations, film length, cone angle and maximum wavelength. Radial fluctuations are found to be maximum near the breakup or rupture of a swirling film. Film length decreases as Reynolds number increases. Cone angle increases until a critical Reynolds number is reached, beyond which it remains constant. A new approach to analyze the temporally unstable waves was developed and compared with the measured maximum wavelengths. The new approach incorporates the attenuation of a film thickness, as the radius of a conical film expands, with the classical dispersion relationship for an inviscid moving liquid film. This approach produces a new long wave solution which accurately matches the measured maximum wavelength swirling conical films generated from nozzles with the smallest orifice diameter. For the nozzle with the largest orifice diameter, the new long wave solution provides the upper bound limit, while the long wave solution for a constant film thickness provides the lower bound limit. These results indicate that temporal instability is the dominating mechanism which generates long Kelvin Helmholtz waves on the surface of a swirling liquid film. The PDPA was used to measure droplet size and velocity in both the near field and far field of the spray. For a constant Reynolds number, an increase in orifice diameter is shown to increase the overall diameter distribution of the spray. In addition, it was found that the probability of breakup, near the axis, decreases for the largest orifice diameter. This is in agreement with the cascading nature of atomization.

Ce travail s’inscrit dans le cadre de la prévision des oscillations de pression interne des moteurs à propergol solide. Il consiste à étudier la transition laminaire-turbulent de l’écoulement interne,modélisé par celui dans un conduit cylindrique à paroi débitante, et son lien avec l’instabilité naturelle de cet écoulement, le Vortex Shedding Pariétal (VSP). La démarche s’est organisée en trois temps. Des mesures antérieures sur un montage gaz froid, reproduisant l’écoulement modèle,sont analysées afin de mettre en évidence la transition laminaire-turbulent. Cette transition est ensuite imposée dans des simulations URANS afin de permettre l’étude de son influence sur les modes VSP. Enfin, une approche LES est mise en place pour simuler le développement de la transition dans les conditions de l’expérience ; dans ce but, une stratégie de perturbation spatiale de l’écoulement est utilisée. Cette étude met en avant quatre résultats principaux. La transition laminaire-turbulent découle de l’amplification spatiale des modes VSP. La simulation de ce processus met en évidence une forte influence de la perturbation numérique ajoutée à l’écoulement. D’autre part, les simulations URANS montrent que la transition réduit l’amplification des modes VSP et les oscillations de pression interne résultantes. Le rôle de la transition dans l’absence d’oscillations de pression lorsque le domaine a un grand rapport d’aspect, jusqu’alors supposé dans la littérature,est ainsi confirmé. Une particularité importante de cette transition est qu’elle dépend de la position radiale, l’écoulement étant turbulent près de la paroi débitante et laminaire au cœur. / The present work is related to the prediction of oscillations in solid rocket motors inner flow. It consists in a study of the laminar-turbulent transition of the motor’s inner flow, which is represented by a cylindrical injection-driven flow, and the relation between this phenomenon and the natural instability named Parietal Vortex Shedding (PVS). Three aspects have been analyzed.First of all, previous cold-gas experiments – reproducing the injection driven flow – are analyzed in order to highlight the transition laminar-turbulent transition. This transition is then imposedin URANS simulations to enable a study of its influence on the PVS modes. Finally, Large Eddy Simulations are performed to simulate the laminar-turbulent process. A strategy based on spatial steady disturbances is used to ease this process. The mains conclusions of this work are the following ones. The laminar-turbulent transition is a consequence of the spatial amplification of PVS modes. Simulations of this process highlight a strong influence of the injected numerical disturbances. The URANS simulations show that this transition reduces the amplification of PVSmodes, and the resulting pressure oscillations levels. These results confirm the role of the transitionin the absence of pressure oscillations when the motor cavity is long. A distinctive feature ofthis transition is its dependence on the radial position, which leads to the coexistence of a laminar region in the channel core and a turbulent region near the injecting wall at a given axial position.

Magnetohydrodynamic instabilities are responsible for geo- and astrophysical phenomena such as reversals of the geomagnetic field, sunspots, solar flares, and accretion disk dynamics. Two particular types of these instabilities were experimentally investigated in rotating spherical and cylindrical apparatus using the eutectic alloy GaInSn as a working fluid. The spherical apparatus, Hydromagnetic Experiment with Differentially Gyrating sphEres HOlding GaInSn (HEDGEHOG), was used to investigate the magnetised spherical Couette (MSC) flow for a range of the imposed axial magnetic field corresponding to Hartmann numbers of 0 to 40 and for a Reynolds number of 1000. A wave with an azimuthal wavenumber of 2 was observed at a Hartmann number of 0, which changed its azimuthal wavenumber to 3 at Hartmann numbers of 5 and 10. For Hartmann numbers between 10 and 22.5, the experimental flow displayed no temporal dependence, since the MSC flow was in its base state. In the remainder of the investigated range of Hartmann numbers, rotating waves with azimuthal wavenumbers of 2, 3, and 4 manifested, with some dependence on whether the Hartmann numbers were fixed or continuously varied. For the magnetised Taylor-Couette (MTC) flow investigated using the Potsdam ROssendorf Magnetic InStability Experiment (PROMISE), thermal convection was found to influence the azimuthal magnetorotational instability (AMRI) in two major ways. Firstly, it reduced the critical Hartmann number required for the onset of AMRI. Secondly, it broke the symmetry of the AMRI travelling waves so that they either travelled upwards or downwards depending on the direction of the radial heat flux.

Une étude numérique de la dynamique d'ondes internes de gravité en fluide stablement stratifié est menée. On décrit un algorithme pseudo-spectral<br />parallèle permettant d'intégrer les équations de Navier-Stokes sur une machine paralèele. En deux dimensions d'espace, on analyse la dynamique d'un<br />champ d'ondes internes propagatives, d'amplitude modérée et initialement plan et monochromatique. Le champ d'ondes est instable et déferle. Le déferlement produit une turbulence de petites échelles spatiales influencées par la stratification. L'étude<br />est étendue au cas tridimensionnel, plus réaliste. En trois dimensions, on étudie le même champ d'ondes internes, que l'on perturbe par un bruit infinitésimal ondulatoire tridimensionnel, mais on considère des ondes statiquement stables et<br />instables (grandes amplitudes). On montre que le déferlement d'une onde interne est un processus intrinsèquement tridimensionnel, y compris pour les ondes de faible amplitude. La tridimensionalisation du champ d'ondes s'opère dans les zones de l'espace où le champ de densité devient statiquement instable. L'effondrement gravitationnel d'une zone est de structure transverse au plan de propagation de l'onde. Les effets de la turbulence des petites échelles sur la production de la composante non propagatrice de l'écoulement, le mode de vorticité potentielle et la production d'un écoulement moyen, permet de conclure que seule une petite proportion de l'énergie mécanique initiale est convertie sous ses deux formes, la majeure partie étant dissipée par la dissipation visqueuse et conduction thermique. On reconsidère le mode de vorticiée potentielle par une approche Hamiltonienne non-canonique du fluide parfait stratifié. La dérivation d'un système de dynamique modifiée permet d'étudier la relaxation d'un écoulement stratifié, conservant sa vorticité potentielle et sa densité, vers un état stationnaire d'énergie minimale, correspondant au mode de vorticité potentielle.