Proper orthogonal decomposition analysis of a turbulent swirling self-excited premixed flame

Thermoacoustic oscillations constitute a serious threat to the integrity of combustion systems. The goal of the present work is to determine the effect of the equivalence ratio (φ), inlet flow velocity (U), and burner geometry on the characteristics of the self-excited oscillations and to reveal the dominant mechanisms. It also focuses on the data post-processing aiming at extracting information about the dynamics that are not captured through classical ensemble-averaging, and hence the Proper Orthogonal Decomposition technique is used. Experiments were conducted with a fully-premixed air/methane flame stabilized on a conical bluff body. Self-excited acoustic instabilities were induced by extending the length of the combustion chamber downstream of the bluff body. The flame was visualised using OH* chemiluminescence and OH PLIF at 5 kHz. Proper Orthogonal Decomposition (POD) and Fast Fourier Transform analysis were conducted on the imaging data. A strong effect of the chamber length was found, which primarily drove the generation of acoustic oscillation and flame-vortex interaction. Significant differences in the flame roll-up were found when either the burner geometry or the equivalence ratio was altered. Changes were detected in the frequency of oscillations, which showed a general trend to increase with φ and U and decrease with the length of the duct. Analysis of the POD modes allowed an estimate of the convection speed of the flame structures associated with the dominant frequency and it was found that this convection speed was about 1.5 U for most conditions studied

Mixing Snapshots and Fast Time Integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity proble

Mixing snapshots and fast time integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin system (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC intervals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computational effort is associated with the snapshots calculation in the first INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be constructed adapting the snapshots calculated in other runs to drastically reduce the size of the first INC interval and thus the involved computational cost. The strategy is successfully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

Reduced order modeling of some fluid flows of industrial interest

Some basic ideas are presented for the construction of robust, computationally efficient reduced order models amenable to be used in industrial environments, combined with somewhat rough computational fluid dynamics solvers. These ideas result from a critical review of the basic principles of proper orthogonal decomposition-based reduced order modeling of both steady and unsteady fluid flows. In particular, the extent to which some artifacts of the computational fluid dynamics solvers can be ignored is addressed, which opens up the possibility of obtaining quite flexible reduced order models. The methods are illustrated with the steady aerodynamic flow around a horizontal tail plane of a commercial aircraft in transonic conditions, and the unsteady lid-driven cavity problem. In both cases, the approximations are fairly good, thus reducing the computational cost by a significant factor

Assessing the Effect of Variable Ambient Temperature on the Self-ignition of a Reaction-diffusion System Employing a Reduced Order Modelling Methodology

The system under study in this work is a self-igniting pile of solid material. To predict and understand the effect of steep changes of the state variables on such systems, a reaction-diffusion model is employed. These systems can exhibit complex oscillatory behaviour, and changes in ambient conditions over time may strongly impact the inherent oscillations. To simulate the unsteady evolution of the pile, both a classical numerical technique (method of lines) and a reduced order approach are employed in combination with a stiff ODE solver. To account for circadian fluctuations in temperature, time-variable boundary conditions are assumed upon formulating the problem. The reduced order model is introduced in view of understanding if an approximated formulation characterized by a much lower number of state variables can accurately predict the complex behaviour of the system even in the case of sudden, steep variations of the values of the state variables due to the phenomenon of self-ignition, intensified here by variable boundary conditions. The selected case studies have the goal of exploring the effect of stockpile properties on the self-ignition phenomenon. Numerical solutions show the anticipated coupling between the system intrinsic dynamics and the oscillating temperature imposed at the boundary. All of the analysed cases are accurately replicated by the reduced order model

A method to generate computationally efficient reduced order models

A new method is presented to generate reduced order models (ROMs) in Fluid Dynamics problems. The method is based on the expansion of the flow variables on a Proper Orthogonal Decomposition (POD) basis, calculated from a limited number of snapshots, which are obtained via Computational Fluid Dynamics (CFD). Then, the POD-mode amplitudes are calculated as minimizers of a properly defined overall residual of the equations and boundary conditions. The residual can be calculated using only a limited number of points in the flow field, which can be scattered either all over the whole computational domain or over a smaller projection window. This means that the process is both computationally efficient (reconstructed flow fields require less than 1% of the time needed to compute a full CFD solution) and flexible (the projection window can avoid regions of large localized CFD errors). Also, various definitions of the residual are briefly discussed, along with the number and distribution of snapshots, the number of retained modes, and the effect of CFD errors, to conclude that the method is numerically robust. This is because the results are largely insensitive to the definition of the residual, to CFD errors, and to the CFD method itself, which may contain artificial stabilizing terms. Thus, the method is amenable for practical engineering applications

EXPERIMENTAL INVESTIGATION OF THE RESPONSE OF FLAMES WITH DIFFERENT DEGREES OF PREMIXEDNESS TO ACOUSTIC OSCILLATIONS

This thesis describes an experimental investigation of the response of lean turbulent swirling flames with different degrees of premixedness (i.e. different mixture patterns) to acoustic forcing using the same burner configuration and varying only the fuel injection strategy. Special emphasis was placed on the amplitude dependence of their response. Also, the behaviour of self-excited fully premixed flames was examined. kHz OH* chemiluminescence was used to study qualitatively the heat release response of the flames, while kHz OH Planar Laser Induced Fluorescence (PLIF) was employed to understand the response of the flame structure and the behaviour of the various parts of the flame. The Proper Orthogonal Decomposition (POD) method was used to extract the dominant structures of the flame and their periodicity. In the first part of the thesis, self-excited oscillations were induced by extending the length of the duct downstream of the bluff body. It was found that the longer the duct length and the higher the equivalence ratio, the stronger the self-excited oscillations were, with the effect of duct length being much stronger. The dominant frequencies of the system were found to increase with equivalence ratio and bulk velocity and decrease with duct length. For some conditions, three simultaneous periodic motions were observed, where the third motion oscillated at a frequency equal to the difference of the other two frequencies. A novel application of the POD method was proposed to estimate the convection velocity from the most dominant reaction zone structures detected by OH* chemiluminescence imaging. For a range of conditions, the convection velocity was found to be in the range of 1.4-1.7 bulk flow velocities at the inlet of the combustor. In the second part, the response of fully premixed, non-premixed with radial fuel injection (NPR) and axial fuel injection (NPA) flames was investigated and compared. All systems exhibited a nonlinear response to acoustic forcing. The highest response was observed by the NPR flame, followed by the fully premixed and the non-premixed with axial fuel injection flame. The proximity of forced flames to blow-off was found to be critical in their heat release response, as close to blow-off the flame response was significantly lower than that farther from blow-off. In the NPR and NPA systems, it was shown that the acoustic forcing reduced the stability of the flame and the stability decreased with the increase in forcing amplitude. In the fully premixed system, the flame area modulations constituted an important mechanism of the system, while in the NPR system both flame area and equivalence ratio modulations were important mechanisms of the heat release modulations. The quantification of the local response of the various parts of the flame at the forcing frequency showed that the ratio (OH fluctuation at 160 Hz to the total variance of OH) was greater in the inner shear layer region than in the other parts in the case of NPR and NPA flames. In fully premixed flames, greater values were observed in large regions on the downstream side of the flame than those in the ISL region close to the bluff body. The ratio of the convection velocity to the bulk velocity was estimated to be 0.54 for the NPR flame, while it was found to be unity for the respective fully premixed flame. In the last part of the thesis, the response of ethanol spray flames to acoustic oscillations was investigated. The nonlinear response was very low, which was reduced closer to blow-off. The ratio was the highest in the spray outer cone region, downstream of the annular air passage, while values were very low in the inner cone region, downstream of the bluff body. Unlike NPR and fully premixed flames, in case of spray and NPA systems, it was found that forcing did not affect greatly the flame structure. The understanding of the nonlinear response of flames with different degrees of premixedness in a configuration relevant to industrial systems contributes to the development of reliable flame response models and lean-burn devices, because the degree of premixedness affects greatly the flame response. Also, the understanding of the behaviour of forced spray flames is of great interest for industrial applications, contributing to the development of thermoacoustic models for liquid fuelled combustors. Finally, the estimation of the convection velocity is of importance in the modelling of self-excited flames and flame response models, since the convection velocity affects the flame response significantly