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Combustion instabilities are physical phenomena occurring in a reacting flow (e.g., a flame) 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. These phenomena can be classified into the following three types: thermoacoustic combustion instabilities ; static instabilities or flame blowoff ; and, intrinsic flame instabilities. However, the term combustion instabilities usually refers to the thermoacoustic type.

In many practical cases, the appearance of combustion instabilities is undesirable. For instance, thermoacoustic instabilities are a major hazard to gas turbines and rocket engines. Moreover, flame blowoff of an aero-gas-turbine engine in mid-flight is clearly dangerous (see flameout).

Because of these hazards, the engineering design process of engines involves the determination of a stability map (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.



Thermoacoustic Combustion Instabilities
In this type of instabilities the perturbations that grow and alter the features of the flow are of an acoustics nature. Their associated pressure oscillations can have well defined frequencies with amplitudes as high as 180 dB, which is large enough to pose a serious hazard to combustion systems. For example, in rocket engines, such as the Rocketdyne F-1 rocket engine in the Saturn V program, instabilities can lead to massive damage of the combustion chamber and surrounding components. Furthermore, instabilities are known to destroy gas-turbine-engine components during testing.

Thermoacoustic combustion instabilities can be explained by distinguishing the following physical processes:

the feedback between heat-release fluctuations (or flame fluctuations) with the combustor or combustion chamber acoustics; the coupling of these two processes in space-time; the strength of this coupling in comparison with acoustic losses; and, the physical mechanisms behind the heat-release fluctuations.

The simplest example of a thermoacoustic combustion instability is perhaps that happening in a horizontal Rijke tube (see also thermoacoustics): 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 organ pipe, acoustic waves travel up and down the tube producing a particular pattern of standing waves. 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 block diagram (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.



The conditions under which perturbations will grow are given by Rayleigh's (John William Strutt, 3rd Baron Rayleigh) 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 thermoacoustics). 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.



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 dissipation.

Combining the above two conditions, and for simplicity assuming here small fluctuations and an inviscid flow, leads to the extended Rayleigh's criterion, which mathematically is: $$ \int_{0}^{T} \int_{V} p' q' dV dt > \int_{0}^{T} \int_{S} p' \mathbf{u'} \cdot \mathbf{n} dS dt. $$ Here p' represents pressure fluctuations, q' heat release fluctuations, $$ \mathbf{u'} $$ velocity fluctuations, T is a long enough time interval, V denotes volume, S surface, and $$ \mathbf{n} $$ 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 represent the loss of acoustic energy at the tube boundaries.

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 internal combustion engine (ICE). In a ICE, a higher thermal efficiency 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 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 piston or a compressor, in a combustion instability high pressure regions form when a standing acoustic wave is formed.

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 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 vortices interact with the flame (see previous figure).

Static Instability or Flame Blowoff
The combustion community also uses the term instability, more precisely the term static instability, to refer to the phenomena occurring when a flame that is burning vigorously (i.e., stably) is perturbed in such a way that it eventually blows-off.

Intrinsic Flame Instabilities
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 Darrieus–Landau instability, the Rayleigh-Taylor instability, and thermal-diffusive instabilities (see Double diffusive convection).