We experimentally study the nonlinear dynamics of a self-excited thermoacoustic system subjected to acoustic forcing. Our aim is to relate these dynamics to the behavior of universal model oscillators subjected to external forcing.The self-excited system under study consists of a swirl-stabilized turbulent premixed flame (equivalence ratio of 0.8 and thermal power of 13.6 kW) enclosed in a quartz tube with an open-ended exit. We acoustically force this system at different amplitudes and frequencies, and measure its response with pressure transducers and OH * chemiluminescence from the flame. By analyzing the data with the power spectral density and the Poincaré map, we find a range of nonlinear dynamics, including (i) a shifting of the self-excited frequency towards or away from the forcing frequency as the forcing amplitude increases; (ii) an accompanying transition from periodicity to two-frequency quasiperiodicity; and (iii) an eventual suppression of the self-excited amplitude, indicating synchronization of the self-excited mode with the forced mode. By further analyzing the data with the Hilbert transform, we find evidence of phase trapping, a partially synchronous state characterized by frequency locking without phase locking.All of these dynamics can be found in universal model oscillators subjected to external forcing. This suggests that such oscillators can be used to accurately represent thermoacoustically self-excited combusting systems subjected to similar forcing. It also suggests that the analytical solutions to such oscillators can be used to guide the reduction and analysis of experimental or numerical data obtained from real thermoacoustic systems, and to identify effective methods for open-loop control of their dynamics.

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SUMMARYThe objective of this work is to investigate the effects of boundary conditions on the combustion characteristic of combustible items in a room. A series of full-scale experiments were carried out in the ISO 9705 fire test room with an upholstered chair at four typical locations, i.e. at the middle of side wall, at the center of the room with the seat toward the door, at the center of the room with the seat toward inside of the room, at the room corner, respectively. Ignition was achieved through a BS No.7 wooden crib at the geometric center of the seat surface for each test. Besides the heat release rate (HRR), four thermocouple trees were placed around the chair to monitor detailed temperature distributions during the combustion process of an upholstered chair. The results indicated that the boundary conditions had some effects on the combustion behavior of a chair in a room. It was shown that there were clearly two main peak HRRs for the cases of a chair being clung to the side wall or at the corner. However, there was only one main peak HRR when the chair was placed at the center of the room, either outwards or inwards. In addition, the results of the two cases of chairs being at the center indicate that the maximum HRR (about 829 kW) for the chair seat toward the door was relatively larger than the maximum HRR (about 641 kW) for the chair seat toward inside of the room. It was suggested that the special complex structure of a chair was also a considerable factor for the effect of boundary conditions on the combustion behavior of a chair in an enclosure. Furthermore, the measured temperature distributions around the chair also illustrated the effects of boundary condition on the combustion behavior of a chair in a room. It was suggested that although HRR was one of the most important fire parameters, HRR mainly represented the comprehensive fire behavior of a combustible item. In order to develop more suitable room fire dynamic models, more detailed information such as the surrounding temperature distributions measured by the thermocouple trees are useful.

The gradient of local equivalence ratio in reacting mixtures significantly affects the flame structure and their corresponding response to acoustic velocity perturbations. We study the effect of acoustic velocity fluctuations on flames created by two co-annular, swirling streams with different equivalence ratios to simulate the effects of pilot-mains split. The flames are stabilized both by a bluff body and by swirl. The flame responses were measured via chemiluminescence as a function of frequency, in the linear perturbation range. A linearized version of the G-equation model is employed to describe the flame dynamics, combined with effects of axial and azimuthal velocity perturbations downstream of the swirlers. The model accounts for the phase shift between the main acoustic and swirler vortical perturbations, which propagate at different speeds. The very different flame structures generated by different fuel splits lead to different flame responses. Models based on time delay of vortical disturbances are able to capture the behaviour reasonably well for the case of outer fuel enrichment, but offer limited agreement for the case of the inner enriched flame, particularly under higher mean equivalence ratios.

One of the key elements in the prediction of thermoacoustic oscillations is the determination of the acoustic response of flames as an element in an acoustic network, in the form of a flame describing function (FDF). In order to obtain a response, flames often have to be confined into a system with its own acoustic response. Separating the pure flame response and that of the system can be complicated by the non-linear effects that the flame can have on the overall system response. In this paper, we investigate whether it is possible to obtain a flame response via the usual methods of dynamic chemiluminescence and pressure measurements, starting from an unforced system with incipient self-excitations at a given frequency f s , in the form of a stabilized flame at atmospheric pressure with a 700 mm tube as a combustor. The flame is forced at discrete frequencies from 20 to 400 Hz, away from the self-excitation, and the response of the flame is measured using OH * chemiluminescence. This response was compared to a flame response measured in a short tube with no other excitations.The results show that both the gain and phase can be entirely dominated by the behavior of the self-excitation, so that in general it is not possible to extract reliable gain and phase information as if the forced and selfexcited modes acted independently and linearly. Although the gain in this particular case was not significantly affected, the phase information of the original flame became dominated by the triggered self-excitation.Boundary conditions and systems used for flame acoustic forcing therefore need to be carefully controlled whenever there is a possibility of self-excitation.

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The local equivalence ratio distribution in a flame affects its shape and response under velocity perturbations. The forced heat release response of stratified lean-premixed flames to acoustic velocity fluctuations are investigated via chemiluminescence measurements and spatial Fourier transfer analysis. A laboratory scale burner and its boundary conditions were designed to generate high-amplitude acoustic velocity fluctuations in flames. These flames are subject to inlet radial equivalence ratio distributions created via a split annular fuel delivery system outfitted with a swirling stabilizer. Simultaneous measurements on the oscillations of inlet velocity and heat release rate were carried out via a two-microphone technique, and OH* chemiluminescence. The measurements show that, for a given mean total power and equivalence ratio (ϕg = 0.60), the flame responses vary significantly depending on forcing frequency, equivalence ratio split and velocity fluctuation amplitude, showing significant non-linearities with respect to forcing amplitude and stratification ratio. Furthermore, the spatial Fourier transfer analysis shows the underlying changes in the rate of heat release, including the direction and speed of the perturbation within the flame.