540:. With this model, the governing parameter is the ratio between a flow time-scale (or residence time in the reactor) and a chemical-time scale, and the key observable is the reactor's maximum temperature. The relationship between parameter and observable is given by the so-called S-shape curve (see figure). This curve results from the solution of the governing equations of the reactor model. It has three branches: an upper branch in which the flame is burning vigorously, i.e., it is "stable"; a middle branch in which the flame is "unstable" (the probability for solutions of the reactor-model equations to be in this unstable branch is small); and a lower branch in which there is no flame but a cold fuel-oxidizer mixture. The decrease of the fuel-oxidizer ratio or increase of oncoming velocity mentioned above correspond to a decrease of the ratio of the flow and chemical time scales. This in turn corresponds to a movement towards the left in the S-shape curve. In this way, a flame that is burning vigorously is represented by the upper branch, and its blow-off is the movement towards the left along this branch towards the quenching point Q. Once this point is passed, the flame enters the middle branch, becoming thus "unstable", or blows off. This is how this simple model captures qualitatively the more complex behavior explained in the above example of a swirl or bluff-body-stabilized flame.
487:
picture heat-release fluctuations due to mixture inhomogeneities, consider a pulsating stream of gaseous fuel upstream of a flame-holder. Such a pulsating stream may well be produced by acoustic oscillations in the combustion chamber that are coupled with the fuel-feed system. Many other causes are possible. The fuel mixes with the ambient air in a way that an inhomogeneous mixture reaches the flame, e.g., the blobs of fuel-and-air that reach the flame could alternate between rich and lean. As a result, heat-release fluctuations occur. Heat-release fluctuations produced by hydrodynamic instabilities happen, for example, in bluff-body-stabilized combustors when
236:
462:
losses. In other words, the above inequality is satisfied. Furthermore, note that in this region the response of the combustor to acoustic fluctuations peaks. Thus, the likelihood of a combustion instability in this region is high, making it a region to avoid in the operation of the combustor. This graphical representation of a hypothetical combustor allows to group three methods to prevent combustion instabilities: increase the losses; reduce the gains; or move the combustor's peak response away from the region where gains exceed losses.
27:
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521:) and the latter by the oncoming velocity. For a fixed oncoming velocity, decreasing the fuel-oxidizer ratio makes the flame change its shape, and by decreasing it further the flame oscillates or moves intermittently. In practice, these are undesirable conditions. Further decreasing the fuel-oxidizer ratio blows-off the flame. This is clearly an operational failure. For a fixed fuel-oxidizer ratio, increasing the oncoming velocity makes the flame behave in a similar way to the one just described.
500:
525:
57:(see figure). This process identifies a combustion-instability region and attempts to either eliminate this region or moved the operating region away from it. This is a very costly iterative process. For example, the numerous tests required to develop rocket engines are largely in part due to the need to eliminate or reduce the impact of thermoacoustic combustion instabilities.
209:. Such a pattern also forms in actual combustors, but takes a more complex form. The acoustic waves perturb the flame. In turn, the flame affects the acoustics. This feedback between the acoustic waves in the combustor and the heat-release fluctuations from the flame is a hallmark of thermoacoustic combustion instabilities. It is typically represented with a
474:
is achieved by releasing the heat via combustion at a higher pressure. Likewise, a stronger driving of a combustion instability happens when the heat is released at a higher pressure. But while high heat release and high pressure coincide (roughly) throughout the combustion chamber in an ICE, they
486:
The physical mechanisms producing the above heat-release fluctuations are numerous. Nonetheless, they can be roughly divided into three groups: heat-release fluctuations due to mixture inhomogeneities; those due to hydrodynamic instabilities; and, those due to static combustion instabilities. To
461:
Graphically, for a particular combustor, the extended
Rayleigh's criterion is represented in the figure on the right as a function of frequency. The left hand side of the above inequality is called gains, and the right hand side losses. Notice that there is a region where the gains exceeds the
239:
Thermoacoustic combustion instabilities happening in a bluff-body-flame-stabilized combustor. Dark regions indicated strong release of heat, and large deformations indicated high pressure. Notice that whenever and wherever large deformations happen, dark regions are seen. This is the hallmark
117:
In contrast with thermoacoustic combustion instabilities, where the role of acoustics is dominant, intrinsic flame instabilities refer to instabilities produced by differential and preferential diffusion, thermal expansion, buoyancy, and heat losses. Examples of these instabilities include the
508:
Static instability or flame blow-off refer to phenomena involving the interaction between the chemical composition of the fuel-oxidizer mixture and the flow environment of the flame. To explain these phenomena, consider a flame that is stabilized with swirl, as in a gas-turbine
395:
244:
Another necessary condition for the establishment of a combustion instability is that the driving of the instability from the above coupling must be larger than the sum of the acoustic losses. These losses happen through the tube's boundaries, or are due to viscous
456:
Graphical representation of the extended
Rayleigh's criterion for some combustor showing a region where gains exceeds losses and the combustor response is strong. This suggests a strong likelihood of having a combustion instability. This figure is adapted
448:
is a normal to the surface boundaries. The left hand side denotes the coupling between heat-release fluctuations and acoustic pressure fluctuations, and the right hand side represents the loss of acoustic energy at the tube boundaries.
503:
Flame from a swirl-stabilized, premixed, academic combustor undergoing blow-off. The flow is from right to left. The fuel-air ratio is decreased. This makes the flame to change its shape, then become unstable, and eventually
232:). In other words, instabilities will happen if heat-release fluctuations are coupled with acoustical pressure fluctuations in space-time (see figure). However, this condition is not sufficient for the instability to occur.
678:
Barrere, M., & Williams, F. A. (1969, January). Comparison of combustion instabilities found in various types of combustion chambers. In
Symposium (International) on Combustion (Vol. 12, No. 1, pp. 169-181).
465:
To clarify further the role of the coupling between heat-release fluctuations and pressure fluctuations in producing and driving an instability, it is useful to make a comparison with the operation of an
228:) criterion: Thermoacoustic combustion instabilities will occur if the volume integral of the correlation of pressure and heat-release fluctuations over the whole tube is larger than zero (see also
65:
In applications directed towards engines, combustion instability has been classified into three categories, not entirely distinct. This classification was first introduced by Marcel Barrère and
108:- instabilities arising due to the interaction between combustion processes in the chamber and anywhere else in the system (feed-system interactions, exhaust-system interactions, etc.,)
197:): Consider the flow through a horizontal tube open at both ends, in which a flat flame sits at a distance of one-quarter the tube length from the leftmost end. In a similar way to an
261:
424:
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coincide at a particular region or regions during a combustion instability. Furthermore, whereas in an ICE the high pressure is achieved through mechanical compression with a
517:. Moreover, say that the chemical composition and flow conditions are such that the flame is burning vigorously, and that the former is set by the fuel-oxidizer ratio (see
213:(see figure). Under some conditions, the perturbations will grow and then saturate, producing a particular noise. In fact, it is said that the flame of a Rijke tube sings.
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interact with the flame (see previous figure). Lastly, heat-release fluctuations due to static instabilities are related to the mechanisms explained in the next section.
903:
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536:, it is instructive to explain them with a simpler analysis. In this analysis, the interaction of the flame with the flow environment is modeled as a perfectly-mixed
169:). Furthermore, instabilities are known to destroy gas-turbine-engine components during testing. They represent a hazard to any type of combustion system.
34:
In many practical cases, the appearance of combustion instabilities is undesirable. For instance, thermoacoustic instabilities are a major hazard to
225:
23:) in which some perturbations, even very small ones, grow and then become large enough to alter the features of the flow in some particular way.
30:
Stability map of a hypothetical combustor. This combustor operates at conditions in which no dangerous combustion-instabilities will happen.
847:
Schadow, K. C. and
Gutmark, E. (1992). "Combustion instability related to vortex shedding in dump combustors and their passive control".
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119:
95:
91:
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86:- instabilities arising irrespective of whether combustion occurs inside a chamber or not (chemical-kinetic instabilities,
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the feedback between heat-release fluctuations (or flame fluctuations) with the combustor or combustion chamber acoustics
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with amplitudes high enough to pose a serious hazard to combustion systems. For example, in rocket engines, such as the
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144:
123:
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256:, leads to the extended Rayleigh's criterion. Mathematically, this criterion is given by the next inequality:
390:{\displaystyle \int _{0}^{T}\int _{V}p'q'dVdt>\int _{0}^{T}\int _{S}p'\mathbf {u'} \cdot \mathbf {n} dSdt.}
172:
Thermoacoustic combustion instabilities can be explained by distinguishing the following physical processes:
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program, instabilities can lead to massive damage of the combustion chamber and surrounding components (see
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216:
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The simplest example of a thermoacoustic combustion instability is perhaps that happening in a horizontal
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In this type of instabilities the perturbations that grow and alter the features of the flow are of an
801:"Thermoacoustic instabilities: Should the Rayleigh criterion be extended to include entropy changes?"
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483:, in a combustion instability high pressure regions form when a standing acoustic wave is formed.
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42:. Moreover, flame blowoff of an aero-gas-turbine engine in mid-flight is clearly dangerous (see
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S-shape curve resulting from the solution of an homogeneous reactor model representing a flame.
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Combining the above two conditions, and for simplicity assuming here small fluctuations and an
702:(1993). "Comprehensive review of liquid-propellant combustion instabilities in F-1 engines".
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Matalon, M. (2007). "Intrinsic flame instabilities in premixed and nonpremixed combustion".
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velocity fluctuations, T is a long enough time interval, V denotes volume, S surface, and
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coupling of pressure and heat-release seen in thermoacoustic combustion instabilities.
80:, shock instabilities, fluid-dynamic instabilities associated with the chamber, etc.,)
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Combustion instabilities represented with a block diagram as a feedback amplifier.
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76:- instabilities arising due to the occurrence of combustion inside a chamber (
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Even though the processes just described are studied with experiments or with
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The conditions under which perturbations will grow are given by
Rayleigh's (
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43:
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Here p' represents pressure fluctuations, q' heat release fluctuations,
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Pempie, P. and Vernin, H. "Liquid rocket engine test plan comparison".
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nature. Their associated pressure oscillations can have well defined
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the strength of this coupling in comparison with acoustic losses
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Unsteady
Motions in Combustion Chambers for Propulsion Systems
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travel up and down the tube producing a particular pattern of
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are physical phenomena occurring in a reacting flow (e.g., a
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the physical mechanisms behind the heat-release fluctuations
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Glassman, I. and Yetter, R. A. and Glumac, N. G. (2014).
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Williams, Forman A. Combustion theory. CRC Press, 2018.
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of engines involves the determination of a stability
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179:the coupling of these two processes in space-time
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849:Progress in Energy and Combustion Science
568:Culick, F. E. and Kuentzmann, P. (2006).
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755:Poinsot, T. and Veynante, D. (2005).
90:, hydrodynamic instabilities such as
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757:Theoretical and numerical combustion
495:Static instability or flame blow-off
799:Nicoud, F. and Poinsot, T. (2005).
820:10.1016/j.combustflame.2005.02.013
69:in 1969. The three categories are
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740:Lieuwen, T. C.; Yang, V. (2005).
617:Annual Review of Fluid Mechanics
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704:Journal of Propulsion and Power
88:diffusive-thermal instabilities
49:Because of these hazards, the
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921:. Cambridge University Press.
604:. Cambridge University Press.
419:{\displaystyle \mathbf {u'} }
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128:diffusive-thermal instability
113:Intrinsic flame instabilities
78:thermo-acoustic instabilities
861:10.1016/0360-1285(92)90020-2
786:The Theory of Sound Volume 2
534:Computational Fluid Dynamics
470:(ICE). In an ICE, a higher
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784:Rayleigh, J. W. S. (1896).
145:Thermo-acoustic instability
124:Rayleigh-Taylor instability
120:Darrieus–Landau instability
96:Rayleigh–Taylor instability
92:Darrieus–Landau instability
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602:Unsteady Combustor Physics
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51:engineering design process
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600:Lieuwen, T. C. (2012).
84:Intrinsic instabilities
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515:bluff body
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191:Rijke tube
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679:Elsevier.
578:cite book
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