This work is concerned with the fluid dynamic processes and the associated loss of acoustic energy produced by circular apertures within noise absorbing perforated walls. Although applicable to a wide range of engineering applications particular emphasis in this work is placed on the use of such features within a gas turbine combustion system. The primary aim for noise absorbers in gas turbine combustion systems is the elimination of thermo-acoustic instabilities, which are characterised by rapidly rising pressure amplitudes which are potentially damaging to the combustion system components. By increasing the amount of acoustic energy being absorbed the occurrence of thermo-acoustic instabilities can be avoided. The fundamental acoustic characteristics relating to linear acoustic absorption are presented. It is shown that changes in orifice geometry, in terms of gas turbine combustion system representative length-to-diameter ratios, result in changes in the measured Rayleigh Conductivity. Furthermore in the linear regime the maximum possible acoustic energy absorption for a given cooling mass flow budget of a conventional combustor wall will be identified. An investigation into current Rayleigh Conductivity and aperture impedance (1D) modelling techniques are assessed and the ranges of validity for these modelling techniques will be identified. Moreover possible improvements to the modelling techniques are discussed. Within a gas turbine system absorption can also occur in the non-linear operating regime. Hence the influence of the orifice geometry upon the optimum non-linear acoustic absorption is also investigated. Furthermore the performance of non-linear acoustic absorption modelling techniques is evaluated against the conducted measurements. As the amplitudes within the combustion system increase the acoustic absorption will transition from the linear to the non-linear regime. This is important for the design of absorbers or cooling geometries for gas turbine combustion systems as the propensity for hot gas ingestion increases. Hence the relevant parameters and phenomena are investigated during the transition process from linear to non-linear acoustic absorption. The unsteady velocity field during linear and non-linear acoustic absorption is captured using particle image velocimetry. A novel analysis technique is developed which enables the identification of the unsteady flow field associated with the acoustic absorption. In this way an investigation into the relevant mechanisms within the unsteady flow fields to describe the acoustic absorption behaviour of the investigated orifice plates is conducted. This methodology will also help in the development and optimisation of future damping systems and provide validation for more sophisticated 3D numerical modelling methods. Finally a set of design tools developed during this work will be discussed which enable a comprehensive preliminary design of non-resonant and resonant acoustic absorbers with multiple perforated liners within a gas turbine combustion system. The tool set is applied to assess the impact of the gas turbine combustion system space envelope, complex swirling flow fields and the propensity to hot gas ingestion in the preliminary design stages.

Dans un moteur à propergol solide, des instabilités thermoacoustiques auto-entretenues, induites par le couplage de la dynamique de la combustion des gouttes d’aluminium, libérées par la combustion du propergol, avec le champ acoustique peuvent induire des oscillations de pression.L’analyse menée tout au long de ce manuscrit repose sur un ensemble d’hypothèses simplificatrices: (i) la réponse de la combustion de gouttes d’aluminium aux perturbations acoustiques est contrôlée par l’écoulement local autour de la goutte, (ii) le processus de combustion peut être supposé quasi stationnaire pour la gamme de fréquences et les amplitudes acoustiques étudiées et (iii) la combustion de l’aluminium est brusquement arrêtée lorsque le diamètre de la goutte d’aluminium diminue en dessous d’un diamètre résiduel.L’instabilité thermoacoustique est étudiée au moyen de simulations numériques de l’écoulement dans un moteur générique et d’analyses théoriques. Le diamètre résiduel des gouttes d’aluminium après la combustion, l’amplitude de la perturbation acoustique et la durée de la combustion des gouttes d’aluminium figurent parmi les principaux paramètres modifiant l’instabilité. En outre, trois comportements de réponse de la combustion à l’acoustique sont identifiés : un comportement linéaire pour les faibles niveaux de pression acoustique puis un comportement quadratique (faiblement non-linéaire) et enfin un comportement fortement non-linéaire quand l’amplitude des oscillations augmente.Ensuite, deux aspects importants de la réponse des gouttes d’aluminium sont identifiés. Ils sont associés aux oscillations de la durée du temps de combustion des gouttes, identifiables à la frontière du nuage de gouttes, et aux fluctuations du taux d’évaporation contrôlées par la convection de l’écoulement gazeux autour de chaque goutte. Tenant compte de ces dynamiques,des expressions analytiques sont obtenues permettant de reproduire avec précision les résultats numériques des simulations de l’écoulement. Quatre nombres sans dimension qui régissent la dynamique de ces instabilités sont également identifiés. Inspiré de l’analyse théorique précédente, un modèle numérique d’ordre réduit faiblement non linéaire est finalement développé pour prédire des cycles limites. / In a solid rocket motor, self-sustained thermo-acoustic instabilities, induced by the coupling of the combustion dynamics of aluminum droplets released by the burning propellant with the acoustic field can induce pressure oscillations.The analysis conducted throughout this manuscript relies thus on a set of simplifying hypothesis by assuming (i) that the response of the combustion of aluminum droplets to acoustic perturbations is controlled by the oscillating drag exerted by the local flow around the droplet, (ii) that this unsteady combustion process can be assumed quasi-steady for the range of frequencies and acoustic amplitudes studied and (iii) that aluminum combustion is abruptly quenched when the aluminum droplet diameter falls below a residual diameter.The thermo-acoustic instability is studied first by numerical flow simulations in a generic solid rocket motor and theoretical analyses. The post-combustion residual diameter of the aluminum particles, the amplitude of acoustic perturbation and the lifetime of the burning aluminum droplets are among the main parameters altering the instability. Also, three combustion response behaviors to acoustics are identified : a linear behavior for small acoustic pressure levels followed by a quadratic behavior then a highly non-linear behavior when the pressure amplitude increases in the motor chamber. Moreover, two important features of the response of aluminum droplets are identified. They are associated to oscillations of the droplet lifetime at the boundary of the droplet cloud and to fluctuations of the droplet evaporation rate, controlled by convection. The dynamics of the droplets highly depends on gas and droplet velocity fields and on droplet diameter. Taking these features into account, yields analytical expressions that allow to reproduce with accuracy the numerical results from the flow simulations. Four dimension less numbers are then identified. They govern the dynamics of these instabilities. Inspired from the previous theoretical analysis, a weakly nonlinear low-order numerical model is finally developed to predict limit cycles.

Dans la première partie de cette thèse de doctorat une méthodologie est présentée qui permet de prédire les niveaux de suies produits dans des flammes laminaires monodimensionnelles, ou un modèle semi-empirique de suies est utilisé en combinaison avec une chimie complexe et un solveur radiatif détaillé. La méthodologie est appliquée au calcul de suies dans une série de flammes de diffusion à contre-courant d'éthylène/air. Plusieurs modèles d'oxydation de suies sont testés et les constantes du modèle sont ajustées afin de retrouver un meilleur accord avec les expériences. L'effet des pertes thermiques radiatives sur la formation de suies et la structure des flammes est évalué. Finalement, la performance du modèle de suies est évalué sur des flammes prémélangées monodimensionnelles, ou une expression alternative du terme de croissance de surface est proposée pour reproduire les résultats expérimentaux. Dans la deuxième partie de cette thèse, des outils de Simulation aux Grandes Échelles (SGE) et d'analyse acoustique sont appliqués à la prédiction des oscillations de cycle limite (OCL) d'une instabilité thermo-acoustique qui apparaît dans un brûleur académique partiellement prémélangé de méthane/air à pression atmosphérique. La SGE prédit bien l'apparition et le développement des OCL est un bon accord est trouvé entre simulations et expériences en termes d'amplitude et fréquence des OCL. La simulation permet de révéler certains aspects clés responsables du comportement instable de la flamme. Ensuite, une analyse préliminaire de la quantification des incertitudes est fait, ou l'effet des paramètres tels que l'impédance des entrées, le degré de raffinement du maillage ou les pertes thermiques sur les caractéristiques des OCL est évalué. Aussi, la SGE prédit bien la dépendance de la stabilité de la flamme du point d'opération et de la géométrie du brûleur / In the first part of the present PhD. thesis a methodology is presented that allows to predict the soot produced in one-dimensional academic flames, where a semi-empirical soot model is used in combination with a complex chemistry and a detailed radiation solver. The methodology is applied to the computation of soot in a set of ethylene/air counterflow diffusion flames. Several oxidation models are tested and the constants of the model were adjusted to retrieve the experimental results. Also, the effect of radiative losses on soot formation and the flame structure is evaluated. Finally, the performance of the soot model is evaluated on 1D premixed flames, where an alternative expression for the surface growth term is proposed to better reproduce the experimental findings. In the second part of the thesis, Large-Eddy Simulation (LES) and acoustic analysis tools are applied to the prediction of limit cycle oscillations (LCO) of a thermo-acoustic instability appearing in a partially premixed methane/air academic burner operating at atmospheric pressure. The LES captures well the appearance and development of the LCO and a good agreement is found between simulations and experiments in terms of amplitude and frequency of the LCO. Some light is shed on the mechanisms leading to the existence of such instability. Then, a preliminar uncertainty quantification (UQ) analysis is performed, where the effect on the features of the LCO of several computational parameters such as the inlets impedances, mesh refinement or heat losses is assessed. Also, the LES captures well the flame stability behaviour dependence on the operating point and the burner geometry

For an engine running at a constant speed, both exhaust and intake processes are periodic in nature. This inspires the muffler designer to go for the much easier and faster frequency domain modeling. But analogous to electrical filter, as per Thevenin’s theorem, the acoustic filter or muffler requires prior knowledge of the load-independent source characteristics (acoustic pressure and internal impedance), corresponding to the open circuit voltage and internal impedance of an electrical source. Studies have shown that it is not feasible to evaluate these source characteristics making use of either the direct measurement method or the indirect evaluation method. Hence, prediction of the radiated exhaust or intake noise has been subject to trial and error. Making use of the fact that pressure perturbation in a duct is a superposition of the forward moving wave and the reflected wave, a simple hybrid approach has been proposed making use of an interrelationship between progressive wave variables of the linear acoustic theory and Riemann variables of the method of characteristics. Neglecting the effect of nonlinearities, reflection of the forward moving wave has been duly incorporated at the exhaust valve. The reflection co-efficient of the system downstream of the exhaust valve has been calculated by means of the transfer matrix method at each of the several harmonics of the engine firing frequency. This simplified approach can predict exhaust noise with or without muffler for a naturally aspirated, single cylinder engine. However, this proves to be inadequate in predicting the exhaust noise of multi-cylinder engines. Thus, estimation of radiated noise has met only limited success in this approach. Strictly speaking, unique source characteristics do not exist for an IC engine because of the associated non-linearity of the time-varying source. Yet, a designer would like to know the un-muffled noise level in order to assess the required insertion loss of a suitable muffler. As far as the analysis and design of a muffler is concerned, the linear frequency-domain analysis by means of the transfer matrix approach is most convenient and time saving. Therefore, from a practical point of view, it is very desirable to be able to evaluate source characteristics, even if grossly approximate. If somehow it were possible to parameterize the source characteristics of an engine in terms of basic engine parameters, then it would be possible to evaluate the un-muffled noise before a design is taken up as a first approximation. This aspect has been investigated in detail in this work. A finite-volume CFD (one dimensional) model has been used in conjunction with the two-load or multi-load method to evaluate the source characteristics at a point just downstream of the exhaust manifold for the exhaust system, and upstream of the air filter (dirty side) in the case of the intake system. These source characteristics have been extracted from the pressure time history calculated at that point using the electro-acoustic analogy. Systematic parametric studies have yielded approximate empirical expressions for the source characteristics of an engine in terms of the basic engine parameters like engine RPM, capacity (swept volume or displacement), air-fuel ratio, and the number of cylinders. The effect of other parameters has been found to be relatively insignificant. Unlike exhaust noise, the intake system noise of an automobile cannot be measured because of the proximity of the engine at the point of measurement. Besides, the intake side is associated with turbocharger (booster), intercooler, cooling fan, etc., which will make the measurement of the intake noise erroneous. From the noise radiation point of view, intake noise used to be considered to be a minor source of noise as compared to the exhaust noise. Therefore, very little has been done or reported on prediction of the intake noise as compared to the exhaust noise. But nowadays, with efficient exhaust mufflers, the un-muffled intake noise has become a contributing factor to the passenger compartment noise level as a luxury decisive factor. Therefore, in this investigation both the intake and the exhaust side source characteristics have been found out for the compression ignition as well as the spark ignition engines. Besides, in the case of compression ignition engines, typical turbocharged as well as naturally aspirated engines have been considered. One of the inputs to the time-domain simulation is the intake valve and exhaust valve lift histories as functions of crank angle. It is very cumbersome and time-consuming to measure and feed these data into the program. Sometimes, this data is not available or cannot be determined easily. So, a generalized formula for the valve lift has been developed by observing the valve lift curves of various engines. The maximum exhaust valve lift has been expressed as a function of the swept volume of the cylinder. This formulation is not intended for designing a cam profile; it is for the purpose of determining approximate thermodynamic quantities to help a muffler designer for an initial estimation. It has also been observed during the investigation that from the acoustic point of view, sometimes it is better to open the exhaust valve a little earlier, but very slowly and smoothly, and keep it open for a longer time. Although the exact source characteristics for an automobile engine cannot be determined precisely, yet the values of source characteristics calculated using this methodology have been shown to be reasonably good for approximate prediction of the un-muffled noise as well as insertion loss of a given muffler. The resultant empirical expressions for the source characteristics enable the potential user to make use of the frequency-domain cum-transfer matrix approach throughout; the time consuming time-domain simulation of the engine exhaust source is no longer necessary. Predictions of the un-muffled sound pressure level of automotive engines have been corroborated against measured values as the well as the full scale time-domain predictions making use of a finite-volume software.

The efficient and enhanced mixing of heat and incoming reactants is achieved in modern gas turbine systems by employing swirling flows. This is realized by a low velocity region (internal recirculation zone -IRZ) zone resulting from vortex breakdown phenomenon. Besides, IRZ acts as effective flame holder/stabilization mode. Double concentric swirling jet is employed in plethora of industrial applications such as heat exchange, spray drying and combustion. As such, understanding essential features of vortex breakdown induced IRZ and its acoustic response in swirling flow/flame is important in thermo-acoustic instability studies. The key results of the present experimental investigation are discussed in four parts. In the first part, primary transition (sub-critical states) from a pre-vortex breakdown (Pre-VB) flow reversal to a fully-developed central toroidal recirculation zone (CTRZ) in a non-reacting, double-concentric swirling jet configuration is discussed when the swirl number is varied in the range 0.592 S 0.801. This transition proceeds with the formation of two intermediate, critical flow regimes. First, a partially-penetrated vortex breakdown bubble (VBB) is formed that indicates the first occurrence of an enclosed structure resulting in an opposed flow stagnation region. Second, a metastable transition structure is formed that marks the collapse of inner mixing vortices. In this study, the time-averaged topological changes in the coherent recirculation structures are discussed based on the non-dimensional modified Rossby number (Rom) which appears to describe the spreading of the zone of swirl influence in different flow regimes. The second part describes a secondary transition from an open-bubble type axisymmetric vortex breakdown (sub-critical states) to partially-open bubble mode (super-critical states) through an intermediate, critical regime of conical sheet formation for flow modes Rom ≤ 1 is discussed when the swirl number (S) is increased beyond 0.801. In the third part, amplitude dependent acoustic response of above mentioned sub and supercritical flow states is discussed. It was observed that the global acoustic response of the sub-critical VB states was fundamentally different from their corresponding super-critical modes. In particular, with a stepwise increase in excitation amplitude till a critical value, the sub-critical VB topology moved downstream and radially outward. Beyond a critical magnitude, the VB bubble transited back upstream and finally underwent radial shrinkage at the threshold excitation amplitude. On the other hand, the topology of the super-critical VB state continuously moved downstream and radially outwards and finally widened/fanned-out at threshold amplitude. In the final part, transition in time-averaged flame global flame structure is reported as a function of geometric swirl number. In particular, with a stepwise increase in swirl intensity, primary transition is depicted as a transformation from zero-swirl straight jet flame to lifted flame with blue base and finally to swirling seated flame. Further, a secondary transition is reported which consists of transformation from swirling seated flame to swirling flame with a conical tailpiece and finally to highly-swirled near blowout ultra-lean flame. For this purpose, CH* chemiluminescence imaging and 2D PIV in meridional planes were employed. Three baseline fuel flow rates through the central fuel injection pipe were considered. For each of the fuel flow cases (Ref), six different co-airflow rate settings (Rea) were employed. The geometric swirl number (SG) was increased in steps from zero till blowout for a particular fuel and co-airflow setting. A regime map (SG vs Rea) depicting different regions of flame stabilization were then drawn for each fuel flow case. The secondary transformation is explained on the basis of physical significance of Rom.