page_title: Combustion instability
section_title: Thermoacoustic combustion instabilities
hierarchical_section_title: Combustion instability / Thermoacoustic combustion instabilities
caption_attribution_description: English: Combustion instabilities represented with a block diagram as a feedback amplifier.
context_page_description: Combustion instabilities are physical phenomena occurring in a reacting flow 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.
  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.
  Because of these hazards, the engineering design process of engines involves the determination of a stability map. 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.
context_section_description: 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 high 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 (see rocket engines).  Furthermore, instabilities are known to destroy gas-turbine-engine components during testing.  They represent a hazard to any type of combustion system.
  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
  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.  Mathematically, this criterion is given by the next inequality:
   
  Here p' represents pressure fluctuations, q' heat release fluctuations,  velocity fluctuations, T is a long enough time interval, V denotes volume, S surface, and  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.
  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 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 r
caption: Combustion instabilities represented with a block diagram as a feedback amplifier.
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