One of the limiting factors for improved performance of the spark ignited internal combustion engine is the phenomenon of knock. The present investigation makes a survey of the available models for auto-ignition for introduction into an existing phenomenological combustion model. A mathematical model of knock, based on a degenerate branched chain mechanism for the prediction of autoignition delay time, was considered and introduced into the combustion model. Experiments were carried out on a single cylinder variable compression ratio engine to validate the model. The interaction of acoustic waves with unsteady combustion leading to unstable combustion and thus triggering knock is considered. This work examines the relationship between the variation in the power of the frequency component corresponding to the natural frequency of the combustion chamber, and the occurrence of knock. A model based on the relaxation oscillation phenomenon is developed to calculate the oscillating frequency of the flame front. This model was developed on the basis that the gas contents of the combustion chamber in an internal combustion engine can be considered as a 'lumped parameter' spring mass damper system. Analysis of the frequency spectrum of flame ionization data show a favourable comparison with the predictions from the model, thus, opening the possibility of future work on correlating the acoustic instability in the combustion chamber to knock in spark ignition engines.

Physical mechanism for high frequency instability in cryogenic engines at low hydrogen injection temperature has been a subject of debate for long time. Experimental and early developmental studies revealed no instabilities and it was only much later when liquid hydrogen at lower initial temperature (~50 to 100 K) was injected into the combustion chamber that instabilities were detected. From the compilations of the experimental data related to the instability of cryogenic engines by Hulka and Hutt, it was found that the instability was strongly connected to the temperature of hydrogen. Experiments conducted with hydrogen temperature ramping from a higher value to lower values indicated that the temperatures in excess of 90 K favor stability under most practical operating conditions. Even though this has been known for over forty years, there has been no clear and simple explanation for this. Many physical mechanisms have been hypothesized to explain how temperature ramping causes instability, but all appear to have limited range of applicability. Current understanding of cryogenic engine combustion instability has been achieved through a combination of experimental investigation and approximate analytical models as well as CFD tools. Various researchers have tried to link the low hydrogen injection temperature combustion instability phenomena with various potential mechanisms for combustion instability. They involve coupling of combustion acoustics with atomization, vaporization, mixing, chemical kinetics or any combination of these processes. Various studies related to the effect of recess, injector hydrodynamics, acoustic damping of gas liquid scheme injectors and effect of drop size distribution on the stability characteristics of cryogenic engines were compiled in the thesis. Several researchers examined fuel droplet vaporization as the rate controlling mechanism. Recently a new method for the evaluation of stability characteristics of the engine using model chamber were proposed by Russians and this is based on mixing as the rate controlling mechanism. Pros and cons of this method were discussed. Some people examined the combustion instability of rocket engines based on chemistry dynamics. A considerable amount of analytical and numerical studies were carried out by various researchers for finding out the cause of combustion instability. Because of the limitations of their analysis, they could not successfully explain the cause of combustion instability at low hydrogen injection temperature. A compilation of previous numerical studies were carried out. A number of researchers have applied CFD in the study of combustion instabilities in liquid propellant rocket engines. In the present thesis, a theoretical model has been developed based on the vaporization of droplets to predict the stability characteristics of the engine. The proposed concept focuses on three dimensional simulation of combustion instability for giving some meaningful explanations for the experimental work presented in the literature. In the present study the pressure wave corresponding to the transverse modes were superimposed on a three dimensional steady state operating conditions. Steady state parameters were obtained from the three dimensional combustion modeling. The conservation equations for mass, momentum and energy are non dimensionalized for facilitating the order of magnitude analysis. In order to do the stability analysis, variables are represented as the sum of their steady values and deviation from the steady state. A harmonic time dependence is assumed for the perturbations. For the transverse mode of oscillations independent variables of the zeroth order equations are r and θ only and the dependant variables are not functions of the axial distance. The axial dependence comes only through the first order equations. In this analysis, the wave motion in the combustion chamber is assumed to be linear, confining the nonlinearity to the vaporization process only. The reason behind making this assumption is that the vaporization process is the major mechanism driving the instability. Vaporization histories of liquid oxygen drops in a combustor with superimposed transverse oscillations were computed and stability characteristics of the engine were estimated. The stability characteristics of the engine are accessed from the solutions of first order equations. Effects of various parameters like droplet diameter, hydrogen injection temperature and hydrogen injection area on the stability characteristics of cryogenic engines are studied. A comparison of predicted and published experimental results was made which showed general agreement between experiment and computation. The present study and experimental results show clearly that hydrogen injection velocity is the critical parameter for instability rather than hydrogen injection temperature. What has happened in actual experiments when hydrogen injection temperature is varied is an effective alteration of the injection velocity that leads to the situation of instability. For higher relative velocity between hydrogen and liquid oxygen, the response of the vaporization rate in the presence of pressure wave is minimum compared to lower relative velocity. Due to this cryogenic engines will go to unstable mode at lower relative velocity.

This thesis describes the development, verification, and validation of a three dimensional time domain thermoacoustic solver. The purpose of the solver is to predict the frequencies, modeshapes, linear growth rates, and limit cycle amplitudes for combustion instability modes in gas turbine combustion chambers. The linearized Euler equations with nonlinear heat release source terms are solved using the finite volume method. The treatment of mean density gradients was found to be vital to the success of frequency and modeshape predictions due to the sharp density gradients that occur across deflagration waves. In order to treat mean density gradients with physical fidelity, a non-conservative finite volume method based on the wave propagation approach to the Riemann problem is applied. For modelling unsteady heat release, user input flexibility is maximized using a virtual class hierarchy within the OpenFOAM C++ library. Unsteady heat release based on time lag models are demonstrated. The solver gives accurate solutions compared with analytical methods for one-dimensional cases involving mean density gradients, cross-sectional area changes, uniform mean flow, arbitrary impedance boundary conditions, and unsteady heat release in a one-dimensional Rijke tube. The solver predicted resonant frequencies within 1% of the analytical solution for these verification cases, with the dominant component of the error coming from the finite time interval over which the simulation is performed. The linear iii growth rates predicted by the solver for the Rijke tube verification were within 5% of the theoretical values, provided that numerical dissipation effects were controlled. Finally, the solver is then used to predict the frequencies and limit cycle amplitudes for two lab scale experiments in which detailed acoustics data are available for comparison. For experiments at the University of Melbourne, an empirical flame describing function was provided. The present simulation code predicted a limit cycle of 0.21 times the mean pressure, which was in close agreement with the estimate of 0.25 from the experimental data. The experiments at Purdue University do not yet have an empirical flame model, so a general vortex-shedding model is proposed on physical grounds. It is shown that the coefficients of the model can be tuned to match the limit cycle amplitude of the 2L mode from the experiment with the same accuracy as the Melbourne case. The code did not predict the excitation of the 4L mode, therefore it is concluded that the vortex-shedding model is not sufficient and must be supplemented with additional heat release models to capture the entirety of the physics for this experiment.

Lean-premixed combustion has the advantage of low emissions for modern gas turbines, but it is susceptible to thermoacoustic instabilities, which can result in large amplitude pressure oscillations in the combustion chamber. The thermoacoustic limit cycle is generated by the unsteady heat release dynamics coupled to the combustor acoustics. In this dissertation, we focused on reduced-order modeling of the dynamics of a laminar premixed flame. From first principles of combustion dynamics, a physically-based, reduced-order, nonlinear model was developed based on the proper orthogonal decomposition technique and generalized Galerkin method. In addition, the describing function for the flame was measured experimentally and used to identify an empirical nonlinear flame model. Furthermore, a linear acoustic model was developed and identified for the Rijke tube experiment. Closed-loop thermoacoustic modeling using the first principles flame model coupled to the linear acoustics successfully reproduced the linear instability and predicted the thermoacoustic limit cycle amplitude. With the measured experimental flame data and the modeled linear acoustics, the describing function technique was applied for limit cycle analysis. The thermoacoustic limit cycle amplitude was predicted with reasonable accuracy, and the closed-loop model also predicted the performance for a phase shift controller. Some problems found in the predictions for high heat release cases were documented. / Ph. D.

Increasingly stringent emissions regulations have led combustion system designers to look for more environmentally combustion strategies. For gas turbine combustion, one promising technology is lean premixed combustion, which results in lower flame temperatures and therefore the possibility of significantly reduced nitric oxide emissions. While lean premixed combustion offers reduced environmental impacts, it has been observed to experience increased possibility of the occurrence of combustion instabilities, which may damage hardware and reduce efficiency. Thermoacoustic combustion instabilities occur when oscillations in the combustor acoustics and oscillations in the flame heat release rate form a closed feedback loop, through one of two possible mechanisms. The first is direct coupling which occurs due to the mean mass flow oscillations induced by the acoustic velocity. Secondly, the acoustics may couple with the flame due to acoustic interactions with fuel/air mixing, resulting in an oscillating equivalence ratio. Only velocity coupling was considered in this study. The methodology used in this study is analysis of instabilities through linear systems theory, requiring knowledge of the individual transfer functions making up the closed-loop system. Methods already exist by which combustor acoustics may be found. However, significant gaps still remain in knowledge of the nature of flame dynamics. Prior knowledge in literature about the flame transfer function suggests that the flame behaves as a low-pass filter, with cutoff frequency on the order of hundreds of hertz. Nondimensionalization of the frequency by flame length scales has been observed to result in a convenient scaling for the flame transfer function, suggesting that the flame dynamics may be dominated by spatial effects. This work was proposed in two parts to extend and apply the body of knowledge on flame dynamics. The phase one goal of this study was to further understand this relationship between the flame heat release rate dynamics and the dynamics of the reaction zone size. The second goal of this work was to apply this flame transfer function knowledge to predictions of instability, validated against measurements in an unstable combustor. Both of these goals meet an existing practical need, providing a design tool for prediction of potential thermoacoustic instabilities in a combustor at the design stage.Measurements of the flame transfer function were made in a swirl-stabilized, lean-premixed combustor. The novel portion of these measurements was the inclusion of spatial resolution of the heat release rate dynamics. By using a speaker, a sine dwell excitation to the velocity was introduced over the range of 10-400Hz. Measurements were then made of the input (inlet velocity) and output (heat release rate, or flame size) resulting in the flame transfer function. The spatial dynamics measurement was approached through several measures of the flame size: the volume and offset distance to the center of the heat release. Each was obtained from deconvoluted, phase averaged images of the flame, referenced to the speaker excitation signal. The results of these measurements showed that the spatial dynamics for each of these three measures were virtually identical to the heat release rate dynamics. This suggests a quite important result, namely that the flame heat release rate dynamics are completely determined by the dynamics of the flame structure. Therefore, prediction of flow structure interaction with the flame distribution is crucial to predict the dynamics of the flame. These spatially resolved transfer function measurements were used in conjunction with the linear closed-loop model to make predictions of instability. These predictions were made by applying the Bode stability criterion to the open-loop system transfer function. This criterion states that instabilities may occur at frequencies where the heat release rate and acoustic oscillations occur in phase and the system gain has a value greater than unity. Performing this analysis on the combined system transfer function yielded results that agreed quite well with actual instability measurements made in the combustor. Closed-loop predictions identified two possible modes for instability, both of which were observed experimentally. One mode resulted from an acoustic peak around 160 Hz, and occurred at lean equivalence ratios. A second mode occurred at lower frequencies (100-150 Hz) and was associated with the increase in flame transfer function gain at increasing equivalence ratios. These are some of the first successful predictions of combustion instability based on linear systems theory. When multiple modes were predicted, it was assumed that if non-linear effects were to be considered, the lower frequency mode would become the dominant mode at these operating conditions due to its higher gain margin. Also of note is that in the practical system, high frequency oscillations are observed, but not predicted, associated with harmonics of the low frequency mode due to the linear nature of the predictions. While these non-linear effects are not captured, the linear predictive capability is thought to be most important, as from a practical perspective, instabilities should be avoided altogether. The primary findings of this study have significant applications to modeling and prediction of combustion dynamics. The classic heat release rate flame transfer function was observed to coincide almost exactly with the flame size transfer functions. The time scales observed in these transfer functions correspond to convective length scales in the combustor, suggesting a fluid mechanical basis of the heat release rate response. Additionally, linear systems theory predictions of instability based on the measured flame transfer functions were proved capable of capturing the stability of the actual combustor with a reasonable degree of accuracy. These predictions should have considerable application to design level avoidance of combustion instability in practical systems. / Ph. D.

Combustion instabilities (thermo-acoustic pressure oscillations) have been recognised for some time as a problem limiting the development of low emissions (e.g., lean burn) gas turbine combustion systems, particularly for aviation propulsion applications. Recently, significant research efforts have been focused on acoustic damping for suppression of combustion instability. Most of this work has either been experimental or based on linear acoustic theory. The last 3-5 years has seen application of density based CFD methods to this problem, but no attempts to use pressure-based CFD methods which are much more commonly used in combustion predictions. The goal of the present work is therefore to develop a pressure-based CFD algorithm in order to predict accurately acoustic propagation and acoustic damping processes, as relevant to gas turbine combustors. The developed computational algorithm described in this thesis is based on the classical pressure-correction approach, which was modified to allow fluid density variation as a function of pressure in order to simulate acoustic phenomena, which are fundamentally compressible in nature. The fact that the overall flow Mach number of relevance was likely to be low ( mildly compressible flow) also influenced the chosen methodology. For accurate capture of acoustic wave propagation at minimum grid resolution and avoiding excessive numerical smearing/dispersion, a fifth order accurate Weighted Essentially Non-Oscillatory scheme (WENO) was introduced. Characteristic-based boundary conditions were incorporated to enable accurate representation of acoustic excitation (e.g. via a loudspeaker or siren) as well as enable precise evaluation of acoustic reflection and transmission coefficients. The new methodology was first validated against simple (1D and 2D) but well proven test cases for wave propagation and demonstrated low numerical diffusion/dispersion. The proper incorporation of Characteristic-based boundary conditions was validated by comparison against classical linear acoustic analysis of acoustic and entropy waves in quasi-1D variable area duct flows. The developed method was then applied to the prediction of experimental measurements of the acoustic absorption coefficient for a single round orifice flow. Excellent agreement with experimental data was obtained in both linear and non-linear regimes. Analysis of predicted flow fields both with and without bias flow showed that non-linear acoustic behavior occurred when flow reversal begins inside the orifice. Finally, the method was applied to study acoustic excitation of combustor external aerodynamics using a pre-diffuser/dump diffuser geometry previously studied experimentally at Loughborough University and showed the significance of boundary conditions and shear layer instability to produce a sustained pressure fluctuation in the external aerodynamics.

The ability of a propulsion system is very crucial for the capability of a missile or a rocket system. Unlike liquid propellant rocket motors, the only control mechanism of the thrust value is the propellant geometry in solid propellant rocket motors. When the operation of solid propellant rocket motor has started, it cannot be stopped anymore. For this main reason the advance of dual pulse motor technology has started. The aim of this study is to investigate the geometrical effects of design parameters on the flow behavior of a dual pulse solid propellant rocket motor by using commercial Computational Fluid Dynamics (CFD) methods. For the CFD analysis, a generic dual pulse rocket motor model is constituted. Within this model, initially four different geometry alternatives of Pulse Separation Device (PSD) are analyzed. To begin PSD analyses, mesh sensitivity analyses are performed on one PSD geometry alternative. By defined grid size, the analyses of PSD geometry alternatives are performed. Computed results were compared in terms of flow behavior (flow streamlines, velocity distribution, turbulent kinetic energy&hellip / etc.) with each other. With the selected PSD geometry alternative the effects of L/D ratio (Length/Diameter ratio) of first pulse chamber, Achamb/APSD ratio (Chamber area/PSD opening area) and APSD/Ath ratio (PSD opening area/Throat area) on the flow behavior is investigated. Flow analyses are performed by simulating the unsteady flow of second pulse operation. With the performed analyses, it is aimed to identify generic geometric definitions for a dual pulse rocket motor.

Air pollution regulations have driven modern power generation systems to move from diffusion to premixed combustion. However, these premixed combustion systems are prone to combustion instability, causing high fluctuations in pressure and temperature. This results in shortening of component life, system failure, or even catastrophic disasters. A large number of studies have been performed to understand and quantify the onset of combustion instability and the limit cycle amplitude. However, much work remains due to the complexity of the process associated with flow dynamics and chemistry. This thesis focuses on identifying, quantifying and predicting mechanisms of flame response subject to disturbances. A promising tool for predicting combustion instability is a flame transfer function. The flame transfer function is obtained by integrating unsteady heat release over the combustor domain. Thus, the better understanding of spatio-temporal characteristics of flame is required to better predict the flame transfer function. The spatio-temporal flame response is analyzed by the flame kinematic equation, so called G-equation. The flame is assumed to be a thin interface separating products and reactant, and the interface is governed by the local flow and the flame propagation. Much of the efforts were done to the flame response subject to the harmonic velocity disturbance. A key assumption allowing for analytic solutions is that the velocity is prescribed. For the mathematical tools, small perturbation theory, Hopf-Lax formula and numerical simulation were used. Solutions indicated that the flame response can be divided into three regions, referred to here as the near-field, mid-field, and farfield. In each regime, analytical expressions were derived, and those results were compared with numerical and experimental data. In the near field, it was shown that the flame response grows linearly with the normal component of the velocity disturbance. In the mid field, the flame response shows peaks in gain, and the axial location of these peaks can be predicted by the interference pattern by two characteristic waves. Lastly, in the far field where the flame response decreases, three mechanisms are studied; they are kinematic restoration, flame stretch, and turbulent flow effects. For each mechanism, key parameters are identified and their relative significances are compared.

Combustion instability plagues the combustion community in a wide range of applications. This un-solved problem is especially prevalent and expensive in aerospace propulsion and ground power generation. The challenges associated with understanding and predicting combustion instability lie in the flame response to the acoustic field. One of the more complicated flame response mechanisms is the velocity coupled flame response, where the flame responds dynamically to the acoustic velocity as well as the vortically induced velocity field excited by the acoustics. This vortically induced, or hydrodynamic, velocity field holds critical importance to the flame response but is computationally expensive to predict, often requiring high fidelity CFD computations. Furthermore, its behavior can be a strong function of the numerous flow parameters that change over the operability map of a combustor. This research focuses on a nominally two dimensional bluff body combustor, which has rich hydrodynamic stability behavior with a manageable number of stability parameters. The work focuses first on experimentally characterizing the dynamical flow and flame behavior. Next, the research shifts focus toward hydrodynamic stability theory, using it to explain the physical phenomena observed in the experimental work. Additionally, the hydrodynamic stability work shows how the use of simple, model analysis can identify the important stability parameters and elucidate their governing physical roles. Finally, the research explores the forced response of the flow and flame while systematically varying the underlying hydrodynamic stability characteristics. In the case of longitudinal combustion instability of highly preheated bluff body combustors, it shows that conditions where an acoustic mode frequency equals the hydrodynamic global mode frequency are not especially dangerous from a combustion instability standpoint, and may actually have a reduced heat release response. This demonstrates the very non-intuitive role that the natural hydrodynamic flow stability plays in the forced heat release response of the flame. For the fluid mechanics community, this work contributes to the detailed understanding of both unforced and forced bluff body combustor dynamics, and shows how each is influenced by the underlying hydrodynamics. In particular, it emphasizes the role of the density-shear layer offset, and shows how its extreme sensitivity leads to complicated flow dynamics. For the flow-combustor community as a whole, the work reviews a pre-existing method to obtain the important flow stability parameters, and demonstrates a novel way to link those parameters to the governing flow physics. For the combustion instability community, this thesis emphasizes the importance of the hydrodynamic stability characteristics of the flow, and concludes by offering a paradigm for consideration of the hydrodynamics in a combustion instability problem.

In this study, experimental investigation of solid propellant combustion instability using an end burning T-Burner setup is performed. For this purpose, a T-Burner setup is designed, analyzed, constructed and tested with all its sub components. T-Burner setup constructed is mainly composed of a base part, a control panel and the T-Burner itself. Combustion chamber, pressure stabilization mechanism, pressurization system, measurement instruments and data acquisition systems form the T-Burner. Pressure stabilization mechanism is utilized in two different alternatives, first of which is by the use of nitrogen gas and a small surge tank with a cavitating venturi. This is a brand new approach for this kind of system. The second alternative is the use of a choked nozzle for pressure stabilization. Resonance frequencies of the system with the two different pressure stabilization mechanisms are experimentally evaluated. Helmholtz frequency of the T-burner constructed is calculated and no Helmholtz instability is observed in the system. Constructed T-Burner setup is operated for a specific solid propellant. System worked successfully and pressure data are obtained. Pressure data revealed oscillatory behaviour. Decay and growth rates of pressure oscillations are used for the calculation of pressure response of the propellant tested. By the use of this T-Burner comparison of the behavior of different propellants can be performed. It can be used as a test device for measuring quantitatively the response of a burning propellant to unsteady motions.