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The problem of combustion instabilities has existed since the early 1940s, when they were observed during the development of solid and liquid rocket engines. While various engineering solutions have served well in these fields, the problem is revisited in modern gas-turbine engines. The purpose of this work is to provide experimental measurements o...
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A laboratory-scale two-stage swirling burner fueled with dodecane is studied experimentally with the help of high speed (20 kHz) spray PIV and chemiluminescence imaging. For a lean operating point at 73 kW, fuel staging is changed and a hysteresis cycle is highlighted. The flame is first lifted from the injector exit plane and exhibits a strong the...
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... (Since his work was accomplished at Caltech, I am of course utterly unbiased.) His apparatus (see also Pun[8]) is sketched inFigure 2. Mounted horizontally, the tube, originally designed and constructed by Dylan Hixon, a research student at Caltech for one year, and then improved by Pun before it was finally completed by Matveev. The power to the electrical heater was controllable accurately, so the speed of flow through the tube was variable at will. ...
A matter of increasing interest is finding the best way to integrate the use of powerful computational facilities with the traditional practices of analysis and related disciplines. This is largely a problem in research and development, rather than fabrication of machines, or even development of codes. There is little question that modern manufacturing, for example, cannot be accomplished competitively without computing machinery - in fact, the more the merrier. However, there is a fairly widespread sense that in areas depending on the development and applications of new ideas, and perhaps especially in education, the general emphasis has been skewed too much to rely excessively on computers.
This paper has been prepared partly to make the point with examples taken from the author's experiences with unsteady combustion. My claim here is that in many cases, analytical methods (necessarily approximate) offer a path often initially preferable to that presented by numerical methods, which in the cases at hand, mean computational fluid mechanics. The first simple example treated here is the Rijke tube, well known primarily for two reasons: The physical behavior is easy to produce, and for which data may be relatively easily collected; and the necessary analysis seems quite simple, at first glance. Some recently published experimental results will be cited, with an approximate theory based on the known differential equations for one-dimensional motions.
The next section is a brief historical summary of Galerkin's method, followed by several sections summarizing the manner in which it may be combined with a perturbation/iteration method to give an effective approximate method. The general approach has been widely used to analyze practical problems of combustion instabilities arising in development of operational systems. Thus a large part of the paper is a review of previously published material, but with considerable clarifications of points that have caused some confusion.
The paper ends with a brief discussion answering a serious criticism, of the method, nearly fifteen years old. The basis for the criticism, arising from solution to a relatively simple problem, is shown to be a result of an omission of a term that arises when the average density in a flow changes abruptly. Presently, there is no known problem of combustion instability for which the kind of analysis discussed here is not applicable. The formalism is general; much effort is generally required to apply the analysis to a particular problem.
A particularly significant point, not elaborated here, is the inextricable dependence on expansion of the equations and their boundary conditions, in two small parameters, measures of the steady and unsteady flows. Whether or not those Mach numbers are actually ‘small’ in fact, is really beside the point. Work out applications of the method as if they were! Then maybe to get more accurate results, resort to some form of CFD. It is a huge practical point that the approach taken and advocated here cannot be expected to give precise results, but however accurate they may be, they will be obtained with relative ease and will always be instructive. In any case, the expansions must be carried out carefully with faithful attention to the rules of systematic procedures. Otherwise, inadvertent errors may arise from inclusion or exclusion of contributions.
I state without proof or further examples that the general method discussed here has been quite well and widely tested for practical systems much more complex than those normally studied in the laboratory. Every case has shown encouraging results. Thus the lifetimes of approximate analyses developed before computing resources became commonplace seem to be very long indeed.
... In the middle to late 1990s, laser-based methods became available to investigate the time and spatial characteristics of distributed combustion processes. Building on early works [42, 43] , a program was initiated at Caltech to measure the frequency response of §ames at atmospheric pressure. There were two principal methods available at that time: (i) passively observed chemiluminescence and (ii) planar laser induced §uorescence (PLIF). ...
... The great advantage of PLIF, which is far more di©cult to use and requires relatively expensive special equipment and data processing, is that it o¨ers unmatched opportunities for spatial and temporal resolution. For extended explanatory coverage, see two Ph.D. dissertations [43, 44] as well as several published papers. Sketches of the apparatus used for the two di¨erent sorts of experiments are given in Fig. 15. ...
Active control of combustion was proposed by Bollay [1]. Following that
idea, Tsien [2] worked out an analysis of controlling low-frequency
oscillations in a liquid rocket but no successful experimental results
followed. More than thirty years passed before the first laboratory
demonstrations were performed at Cambridge University. Interest grew
rapidly in the 1990s due to potentially wonderful applications to
practical combustion systems including liquid and solid rockets, gas
turbines, and thrust augmentors. Dreams have not materialized: There are
presently no operational control systems, despite considerable efforts,
and examples of partially controlled phenomena. Only one practical
installation for control of oscillations has been documented, for a
large Siemens machine [3]. Its use has been rendered unnecessary by
further experimental work leading to development of successful passive
control with modifications of hardware [4]. The purpose of this paper is
to examine briefly some of the reasons that active control of combustion
has failed to become the panacea widely anticipated two decades ago. The
authors' view is that the subject is far from exhausted, but rather
requires carefully planned research to understand the basis of
successful applications.
... In-flame measurements have progressed from UF (Dyer and Crosley 1982) to OH PUF (Cadou et al. 1991; McManus et al. 1995; and Shih et al. 1996), to NO PUF (), and HCO (Najm et al. 1998). Still, little work has been reported applying temporally and spatially resolved PUF imaging to acoustically active systems (Pun 2001; Pun et al. 2002; Ratner el at. 2002) and no systematic comparison of the relative benefits of the various techniques has been reported. ...
... Detailed descriptions of the experimental configuration, measurement methodologies, and data analysis procedures can be found in Pun (2001, and Ratner et al. (2002). The description here will be limited to the general system parameters. ...
Various techniques have been employed by investigators to measure the response of flames to unsteady changes, but there has been no systematic study of the relative benefits and drawbacks of these competing techniques. The goal of this work is to characterize the performance of two different measurement techniques applied in three ways and to examine the differing insights they offer for the response of a flame in a periodic acoustic field. The burner configuration consists of a jet flame in a partial enclosure that stabilizes the flame approximately 8 cm above the jet exit. This burner is installed in an acoustic chamber that has actively-controlled, frequency-selectable, acoustic forcing. Flame response data for different frequencies obtained with chemiluminescence, OR PLIF, and NO PLIF measurement techniques is the basis for this work. Analysis of the data shows the complexity of the measurement required to achieve a given level of understanding of the flame's behavior. The usefulness of these techniques in flame response measurements individually and taken in combination is discussed, with examples.
... Since radiation may also be absorbed, the final intensity at observation point does not in general represent only the activity of species produced in chemical reactions. Consequently, as we have shown (Ratner or Pun? et al. 2001) seriously misleading results are often obtained. Nevertheless, the method was the first to provide results for combustion dynamics (seeTable 1) and has given useful contribution to understanding combustion instabilities. ...
... A more generalized body of work is required to provide industry with guidelines that will be useful in designing stable combustion systems. Chen et al. (1993) (300 Hz, 400 Hz) " Cadou et al. (1998) (360 Hz, 420 Hz) Results obtained in the continuing program at Caltech have been reported by Pun (2001); Pun et al. (2000 Pun et al. ( ,2002 and Ratner et al. (2000 a, b, c). The test section, shown inFigure 5 consists of three major components: the acoustic driving system; the acoustic cavity; and the burner section. ...
Transient behavior of combustion systems has long been a subject of both fundamental and practical concerns. Extreme cases of very rapid changes include the ignition of reacting mixtures and detonation. At the other extreme is a wide range of quasi-steady changes of behavior, for example adjustments of the operating point of a combustion chamber. Between the limiting cases of 'infinitely fast' and 'infinitesimally slow' lie important fundamental problems of time-dependent behavior and a wide array
of practical applications. Among the latter are combustion instabilities and their active control, a primary motivation for the work reported in this paper. Owing to the
complicated chemistry, chemical kinetics and flow dynamics of actual combustion systems, numerical simulations of their behavior remains in a relatively primitive state.
Even as that situation continually improves, it is an essential part of the field that methods of measuring true dynamical behavior be developed to provide results having both fine spatial resolution and accuracy in time. This paper is a progress report of recent research
carried out in the Jet Propulsion Center of the California Institute of Technology.
... decreases (Figure 1-2). However, flames tend to be unstable near the lean limit, and their coupling with combustor acoustics may result in combustion instability. This is a major problem and an active research topic in modern gas turbine industry (Correa 1998). Another problem associated with acoustically unstable combustors is the intensive noise. Pun (2001) describes the unstable gas flares aimed at burning landfill gas, produced by decomposing material in LA county waste fields (Figure 1-3). When this system operates at the burning capacity exceeding 50% from the maximally possible, a loud, low-frequency rumbling is generated, unacceptable to people living near this facility. The tones ex ...
Thermoacoustic instability can appear in thermal devices when unsteady heat release is coupled with pressure perturbations. This effect results in excitation of eigen acoustic modes of the system. These instabilities are important in various technical applications, for instance, in rocket motors and thermoacoustic engines. A Rijke tube, representing a resonator with a mean flow and a concentrated heat source, is a convenient system for studying the fundamental physics of thermoacoustic instabilities. At certain values of the main system parameters, a loud sound is generated through a process similar to that in real-world devices prone to thermoacoustic instability. Rijke devices have been extensively employed for research purposes. The current work is intended to overcome the serious deficiencies of previous investigations with regard to estimating experimental errors and the influence of parameter variation on the results. Also, part of the objective here is to account for temperature field non-uniformity and to interpret nonlinear phenomena. The major goals of this study are to deliver accurate experimental results for the transition to instability and the scope and nature of the excited regimes, and to develop a theory that explains and predicts the effects observed. An electrically heated, horizontally oriented, Rijke tube is used for the experimental study of transition to instability. The stability boundary is quantified as a function of major system parameters with measured uncertainties for the data collected. Hysteresis in the stability boundary is observed for certain operating regimes of the Rijke tube. An innovative theory is developed for modeling the Rijke oscillations. First, linear theory, incorporating thermal analysis that accurately determines the properties of the modes responsible for the transition to instability, is used to predict the stability boundary. Then, a nonlinear extension of the theory is derived by introducing a hypothesis for a special form of the nonlinear heat transfer function. This nonlinear modeling is shown to predict the hysteresis phenomenon and the limit cycles observed during the tests. A new, reduced-order modeling approach for combustion instabilities in systems with vortex shedding is derived using the developed analytical framework. A hypothesis for the vortex detachment criterion is introduced, and a kicked oscillator model is applied to produce nonlinear results characteristic for unstable combustion systems. The experimental system and the mathematical model, developed in this work for the Rijke tube, are recommended for preliminary design and analysis of real-world thermal devices, where thermoacoustic instability is a concern.
The goal of this work is to characterize the excited states of a thermoacoustic system with mean flow. The properties of excited regimes are determined by the balance between thermoacoustic energy transformation and acoustic losses. In many systems, the sound intensity is not sufficient for nonlinear acoustic losses to be a major factor in defining nonlinear saturation of thermoacoustic instability. It is the nonlinearity of the heat transfer process that is responsible for limit-cycle stabilization of linearly unstable acoustic modes and for the appearance of higher harmonics. In the present study, both a nonlinear theory based on energy consideration and a model for the nonlinear convective heat transfer in unsteady flow are developed. Experimental data are obtained for the excited regimes of operation of an electric Rijke tube. Model results for hysteresis in the transition between stable and excited states and for limit-cycle parameters are compared with test data.
A horizontal Rijke tube with an electric heat source is a system convenient for studying the fundamental principles of thermoacoustic instabilities both experimentally and theoretically. Given the long history of the device, there is a surprising lack of accurate data defining its behavior. In this work, the main system parameters are varied in a quasi-steady fashion in order to find stability boundaries accurately. The chief purposes of this study are to obtain precise values of the system parameters at the transition to instability with specified uncertainties and to determine how well the experimental results can be explained with existing theory. Measurement errors are reported, and the influence of experimental procedures on the results is discussed. A form of hysteresis effect at stability boundaries has been observed. Mathematical modelling is based on a thermal analysis determining the temperature of the heater and the temperature field in the air inside the tube, which, consequently, affects acoustical mode shapes. Solutions of the linearized wave equation for a non-uniform medium, including losses and a heat source term, determine the stability properties of the eigen modes. Calculated results are compared with experimental data and with results of the modelling based on the common assumption of a constant temperature in the tube. The mathematical model developed here can be applied to designing thermal devices with low Mach number flows, where thermoacoustic issue is a concern.
