LLean premixed combustion systems, attractive for low NOx performance, are inherently susceptible to thermo-acoustic instabilities - the interaction between unsteady heat release and excited acoustic wave effects. In the present work, a hybrid, coupled Large Eddy Simulation (LES) CFD approach is described, combining the computational efficiency of incompressible reacting LES with acoustic wave effects captured via an acoustic network model. A flamelet approach with an algebraic Flame Surface Density (FSD) combustion model was used. The ORACLES experiments - a perfectly premixed flame stabilised in a 3D sudden expansion - are used for validation. Simulations of the inert flow agree very well with experimental data, reproducing the measured amplitude and distribution of turbulent fluctuations as well as capturing the asymmetric mean flow. With reaction the measured data exhibit a plane wave acoustic mode at 50Hz. The influence of this plane wave must be incorporated into the LES calculation. Thus, a new approach to sensitise the incompressible LES CFD to acoustic waves is adopted. First an acoustic network model of the experimental geometry is analysed to predict the amplitude of the 50Hz mode just before the flame zone. This is then used to introduce a coherent plane wave at the LES inlet plane at the appropriate amplitude, unlike previous LES studies, which have adopted a "guess and adjust" approach. Incompressible LES predictions of this forced flow then show good agreement with measurements of mean and turbulent velocity, as well as for flame shape, with a considerable improvement relative to unforced simulations. To capitalise on the unsteady flame dynamics provided by LES, simulations with varying forcing amplitude were conducted and analysed. Amplitude dependent Flame Transfer Functions (FTFs) were extracted and fed into an acoustic network model. This allowed prediction of the stable/unstable nature of the flame at each forcing amplitude. An amplitude at which the flame changed from unstable to stable would be an indication that this coupled approach was capable of predicting a limit cycle behaviour. With the current simple FSD combustion model almost all cases studied showed a stable flame. Predictions showed considerable sensitivity to the value chosen for the combustion model parameter but specially to the acoustic geometric configuration and boundary conditions assumed showing evidence of limit cycle behaviour for some combinations. Nevertheless, further work is required to improve both combustion model and the accuracy of acoustic configuration and boundary condition specification.

Core-collapse supernovae are some of the most energetic events in the Universe, they herald the birth of neutron stars and black holes, are a major site for nucleosynthesis, influence galactic hydrodynamics, and trigger further star formation. As such, it is important to understand the mechanism of explosion. Moreover, observations imply that asymmetries are, in the least, a feature of the mechanism, and theory suggests that multi-dimensional hydrodynamics may be crucial for successful explosions. In this dissertation, we present theoretical investigations into the multi-dimensional nature of the supernova mechanism. It had been suggested that nuclear reactions might excite non-radial g-modes (the ε-mechanism) in the cores of progenitors, leading to asymmetric explosions. We calculate the eigenmodes for a large suite of progenitors including excitation by nuclear reactions and damping by neutrino and acoustic losses. Without exception, we find unstable g-modes for each progenitor. However, the timescales for growth are at least an order of magnitude longer than the time until collapse. Thus, the ε-mechanism does not provide appreciable amplification of non-radial modes before the core undergoes collapse. Regardless, neutrino-driven convection, the standing accretion shock instability, and other instabilities during the explosion provide ample asymmetry. To adequately simulate these, we have developed a new hydrodynamics code, BETHE-hydro that uses the Arbitrary Lagrangian-Eulerian (ALE) approach, includes rotational terms, solves Poisson’s equation for gravity on arbitrary grids, and conserves energy and momentum in its basic implementation. By using time dependent arbitrary grids that can adapt to the numerical challenges of the problem, this code offers unique flexibility in simulating astrophysical phenomena. Finally, we use BETHE-hydro to investigate the conditions and criteria for supernova explosions by the neutrino mechanism. We find that a critical luminosity/ mass-accretion-rate condition distinguishes non-exploding from exploding models in hydrodynamic 1D and 2D simulations. Importantly, the critical luminosity for 2D simulations is found to be ∼70% of the critical luminosity for 1D simulations. We identify the specifics ofmulti-dimensional hydrodynamic simulations that enable explosions at lower neutrino luminosities in 2D and discuss how these results might foreshadow successful explosions by eventual 3D radiation-hydrodynamic simulations.

This thesis deals with the dependence of the linear spatial growth rate of the cross-field ion acoustic instability on various plasma parameters. A kinetic theory model, with elastic and inelastic ion-neutral collisions included, is presented and used to conduct a numerical survey of the instability. The growth rate is computed as a function of distance into the plasma, taking into account the attenuation of the ion beam by charge exchange collisions. Further calculations show the variation in growth rate as a function of the following quantities: electron and ion beam temperature, electron density, beam velocity, background ion temperature, magnetic field, the angle between magnetic field direction and wave vector and the finite width of the plasma. The instability was observed in a double plasma device where an ion beam was passed through a background of stationary magnetized electrons. The magnetic field was sufficiently weak to allow approximately rectilinear ion motion. The growth rate of the wave was studied using interferometer techniques. It was identified by the dispersion relation as the cross-field ion acoustic wave propagating as the slow mode of the beam. It was found that the background ions play an important role in determining the phase velocity. Experimental data of the growth rate dependence on wave number, beam velocity and magnetic field strength were found to be well described by the theoretical model. The growth rate dependence of magnetic field direction on plasma width was furthermore found to be in qualitative agreement with the model. / Thesis (M.Sc.)-University of Natal, Durban, 1990.

This thesis investigates several aspects of stratified flow over isolated topography in ocean, lake, and atmospheric settings. Three major sub-topics are addressed: steady, inviscid internal waves trapped over topography in a pycnocline stratification, topographically generated internal waves and their interaction with the viscous bottom boundary layer, and flow over large-scale crater topography in the atmosphere. The first topic examines the conditions that lead to very large internal waves trapped over topography in a fluid with a pycnocline stratification. This type of stratification is connected to ocean or lake settings. The steady-state Euler equations of motion are used to derive a single partial differential equation for the isopycnal displacement in supercritical flows under two conditions: a vertically varying background current under the Boussinesq approximation and a constant background current under non-Boussinesq conditions. A numerical method is developed to solve these equations for an efficient exploration of parameter space. Very large waves are found over depression topography when the background flow speed is close to a limiting value. Variations in the background current are examined, as well as comparisons between Boussinesq and non-Boussinesq results. The second topic aims to extend the above subject by considering unsteady, viscous flows. Once again, supercritical flow over topography in a pycnocline stratification generates internal waves. These internal waves interact with the viscous bottom boundary layer to produce bottom boundary instabilities. The three-dimensional aspects of these instabilities are studied under changes in viscosity. The boundary layer instabilities have important implications for sediment transport in the coastal oceans or lakes. Lastly, the final topic is motivated by the connection between dust streaks on the Martian surface and crater topography. Flow over a large 100-km diameter crater is examined with numerical simulations conducted using the Weather Research and Forecasting model. Modifications to the stratification and topography are applied. It is found that a large hydraulic structure of amplitude comparable to the crater depth forms in many cases. This structure may have important implications for dust transport in the atmosphere. In addition, Martian atmospheric parameters are used to study the flow properties under Mars-like conditions.

Abstract available in PDF file. / Thesis (Ph.D.)-University of Natal, 1979.

Doctor of Philosophy / We investigate the linear growth and vertical structure of the magnetorotational instability (MRI) in weakly ionised, stratified accretion discs. The magnetic field is initially vertical and perturbations have vertical wavevectors only. Solutions are obtained at representative radial locations from the central protostar for different choices of the initial magnetic field strength, sources of ionisation, disc structure and configuration of the conductivity tensor. The MRI is active over a wide range of magnetic field strengths and fluid conditions in low conductivity discs. For the minimum-mass solar nebula model, incorporating cosmic ray and x-ray ionisation and assuming that charges are carried by ions and electrons only, perturbations grow at 1 AU for B < 8G. For a significant subset of these strengths (200mG < B < 5 G), the growth rate is of order the ideal MHD rate (0.75 Omega). Hall conductivity modifies the structure and growth rate of global unstable modes at 1 AU for all magnetic field strengths that support MRI. As a result, at this radius, modes obtained with a full conductivity tensor grow faster and are active over a more extended cross-section of the disc, than perturbations in the ambipolar diffusion limit. For relatively strong fields (e.g. B > 200 mG), ambipolar diffusion alters the envelope shapes of the unstable modes, which peak at an intermediate height, instead of being mostly flat as modes in the Hall limit are in this region of parameter space. Similarly, when cosmic rays are assumed to be excluded from the disc by the winds emitted by the magnetically active protostar, unstable modes grow at this radius for B < 2 G. For strong fields, perturbations exhibit a kink at the height where x-ray ionisation becomes active. Finally, for R = 5 AU (10 AU), unstable modes exist for B < 800 mG (B < 250 mG) and the maximum growth rate is close to the ideal-MHD rate for 20 mG < B < 500 mG (2 mG < B < 50 mG). Similarly, perturbations incorporating Hall conductivity have a higher wavenumber and grow faster than solutions in the ambipolar diffusion limit for B < 100 mG (B < 10 mG). Unstable modes grow even at the midplane for B > 100 mG (B ~ 1 mG), but for weaker fields, a small dead region exists. When a population of 0.1 um grains is assumed to be present, perturbations grow at 10 AU for B < 10 mG. We estimate that the figure for R = 1 AU would be of order 400 mG. We conclude that, despite the low magnetic coupling, the magnetic field is dynamically important for a large range of fluid conditions and field strengths in protostellar discs. An example of such magnetic activity is the generation of MRI unstable modes, which are supported at 1 AU for field strengths up to a few gauss. Hall diffusion largely determines the structure and growth rate of these perturbations for all studied radii. At radii of order 1 AU, in particular, it is crucial to incorporate the full conductivity tensor in the analysis of this instability, and more generally, in studies of the dynamics of astrophysical discs.

Thesis (M. S.)--Nuclear and Radiological Engineering, Georgia Institute of Technology, 2006. / Dr. Cassiano de Oliveira, Committee Member ; Dr. John Mandrekas, Committee Member ; Dr. Weston M. Stacey, Committee Chair. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (p. 116-121).

Abstract The present thesis investigates the dynamics of wave structures in dense planetary rings by employing hydrodynamic models, along with local N-body simulations of the particulate ring flow. The focus is on the large-scale satellite induced spiral density waves as well as on the free short-scale waves generated by the viscous overstability in Saturn's A and B rings. An analytic weakly nonlinear model is derived by using perturbation theory based on multi-scale methods to compute the damping behavior of nonlinear spiral density waves in a planetary ring subject to viscous overstability. In order to study the complex spatio-temporal evolution of these wave structures, numerical schemes are developed to integrate the hydrodynamical equations in time on large radial domains, taking into account collective self-gravity forces of the ring material, as well as the forcing by an external satellite. The required numerical stability and accuracy is achieved by applying Flux-Vector-Splitting methods aligned with advanced shock-capturing techniques. The free short-scale overstable waves are also investigated with local N-body simulations of the sheared ring flow. In particular, the influence of collective self-gravity between the ring particles as well as the periodic forcing due to a nearby Lindblad resonance on the overstable wave pattern is considered. The linear stability criterion for spiral density waves in Saturn’s rings is found to be identical to the condition for the onset of spontaneous viscous overstability in the limit of long wavelengths and agrees with the stability criterion for density waves derived by Borderies et al. within the streamline formalism. The derived nonlinear damping behavior of density waves can be very different from what has previously been thought. The role of collective self-gravity on the nonlinear evolution of short-scale overstable waves is determined, reconciling the partly contradicting results of previous studies. It is shown that collective self-gravity plays an important role in setting the length-scale on which the nonlinear overstable waves saturate in a planetary ring. A co-existence of spiral density waves and short-scale overstable waves is modeled in terms of one-dimensional large-scale hydrodynamical integrations. Due to the restriction to one space dimension, certain terms in the hydrodynamical equations that arise from the spiral shape of a density wave need to be approximated based on the weakly nonlinear model. These integrations reveal that density waves and spontaneous viscous overstability undergo complex interactions. In particular it is found that, depending on the relative magnitude of the two wave structures, the presence of short-scale overstable waves can lead to a damping of an overstable density wave and vice versa, density waves can suppress overstability. The effect of a density wave on the viscous overstability is also studied in terms of a simplified axisymmetric model of a ring perturbed by a nearby Lindblad resonance. A linear hydrodynamic stability analysis and local N-body simulations of this model system conform the corresponding results of the large-scale hydrodynamical integrations.

Les instabilités thermo-acoustiques résultent de l'interaction entre les oscillations de pression acoustique et les fluctuations du taux de dégagement de chaleur de la flamme. Ces instabilités de combustion sont particulièrement préoccupantes en raison de leur fréquence dans les turbines à gaz modernes et à faible émission. Leurs principaux effets indésirables sont une réduction du temps de fonctionnement du moteur en raison des oscillations de grandes amplitudes ainsi que de fortes vibrations à l'intérieur de la chambre de combustion. La simulation numérique est maintenant devenue une approche clé pour comprendre et prédire ces instabilités dans la phase de conception industrielle. Cependant, la prédiction de ce phénomène reste difficile en raison de sa complexité; cela se confirme lorsque les paramètres physiques du processus de modélisation sont incertains, ce qui est pratiquement toujours le cas pour des systèmes réels.Introduire la quantification des incertitudes pour la thermo-acoustique est le seul moyen d'étudier et de contrôler la stabilité des chambres de combustion qui fonctionnent dans des conditions réalistes; c'est l'objectif de cette thèse.Dans un premier temps, une chambre de combustion académique (avec un seul injecteur et une seule flamme) ainsi que deux chambres de moteurs d'hélicoptère (avec N injecteurs et des flammes) sont étudiés. Les calculs basés sur un solveur de Helmholtz et un outil quasi-analytique de bas ordre fournissent des estimations appropriées de la fréquence et des structures modales pour chaque géométrie. L'analyse suggère que la réponse de la flamme aux perturbations acoustiques joue un rôle prédominant dans la dynamique de la chambre de combustion. Ainsi, la prise en compte des incertitudes liées à la représentation de la flamme apparaît comme une étape nécessaire vers une analyse robuste de la stabilité du système.Dans un second temps, la notion de facteur de risque, c'est-à-dire la probabilité pour un mode thermo-acoustique d'être instable, est introduite afin de fournir une description plus générale du système que la classification classique et binaire (stable / instable). Les approches de modélisation de Monte Carlo et de modèle de substitution sont associées pour effectuer une analyse de quantification d'incertitudes de la chambre de combustion académique avec deux paramètres incertains (amplitude et temps de réponse de la flamme). On montre que l'utilisation de modèles de substitution algébriques réduit drastiquement le nombre de calculs initiales, donc la charge de calcul, tout en fournissant des estimations précises du facteur de risque modal. Pour traiter les problèmes multidimensionnel tels que les deux moteurs d'hélicoptère, une stratégie visant à réduire le nombre de paramètres incertains est introduite. La méthode <<Active Subspace>> combinée à une approche de changement de variables a permis d'identifier trois directions dominantes (au lieu des N paramètres incertains initiaux) qui suffisent à décrire la dynamique des deux systèmes industriels. Dès lors que ces paramètres dominants sont associés à des modèles de substitution appropriés, cela permet de réaliser efficacement une analyse de quantification des incertitudes de systèmes thermo-acoustiques complexes.Finalement, on examine la perspective d'utiliser la méthode adjointe pour analyser la sensibilité des systèmes thermo-acoustiques représentés par des solveurs 3D de Helmholtz. Les résultats obtenus sur des cas tests 2D et 3D sont prometteurs et suggèrent d'explorer davantage le potentiel de cette méthode dans le cas de problèmes thermo-acoustiques encore plus complexes. / Thermoacoustic instabilities result from the interaction between acoustic pressure oscillations and flame heat release rate fluctuations. These combustion instabilities are of particular concern due to their frequent occurrence in modern, low emission gas turbine engines. Their major undesirable consequence is a reduced time of operation due to large amplitude oscillations of the flame position and structural vibrations within the combustor. Computational Fluid Dynamics (CFD) has now become one a key approach to understand and predict these instabilities at industrial readiness level. Still, predicting this phenomenon remains difficult due to modelling and computational challenges; this is even more true when physical parameters of the modelling process are uncertain, which is always the case in practical situations. Introducing Uncertainty Quantification for thermoacoustics is the only way to study and control the stability of gas turbine combustors operated under realistic conditions; this is the objective of this work.First, a laboratory-scale combustor (with only one injector and flame) as well as two industrial helicopter engines (with N injectors and flames) are investigated. Calculations based on a Helmholtz solver and quasi analytical low order tool provide suitable estimates of the frequency and modal structures for each geometry. The analysis suggests that the flame response to acoustic perturbations plays the predominant role in the dynamics of the combustor. Accounting for the uncertainties of the flame representation is thus identified as a key step towards a robust stability analysis.Second, the notion of Risk Factor, that is to say the probability for a particular thermoacoustic mode to be unstable, is introduced in order to provide a more general description of the system than the classical binary (stable/unstable) classification. Monte Carlo and surrogate modelling approaches are then combined to perform an uncertainty quantification analysis of the laboratory-scale combustor with two uncertain parameters (amplitude and time delay of the flame response). It is shown that the use of algebraic surrogate models reduces drastically the number of state computations, thus the computational load, while providing accurate estimates of the modal risk factor. To deal with the curse of dimensionality, a strategy to reduce the number of uncertain parameters is further introduced in order to properly handle the two industrial helicopter engines. The active subspace algorithm used together with a change of variables allows identifying three dominant directions (instead of N initial uncertain parameters) which are sufficient to describe the dynamics of the industrial systems. Combined with appropriate surrogate models construction, this allows to conduct computationally efficient uncertainty quantification analysis of complex thermoacoustic systems.Third, the perspective of using adjoint method for the sensitivity analysis of thermoacoustic systems represented by 3D Helmholtz solvers is examined. The results obtained for 2D and 3D test cases are promising and suggest to further explore the potential of this method on even more complex thermoacoustic problems.