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lecture_22 - 16.512, Rocket Propulsion Prof. Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 22: Liquid Motors: Combustion Instability (Low Frequency) Combustion Stability 1. General Discussion Elimination of instabilities has been historically one of the largest components of all new liquid rocket development programs. This is because there has been little reliable methodology to ensure stability through design, and also because of the potentially catastrophic consequences of instability. The situation has improved to some extent because of the vastly enlarged simulation capabilities existing now. As we will see, this area is intimately related to that of spray combustion, where a similar situation has prevailed. As in the combustion area, the advances in recent years are promising, but not yet sufficient to provide reliable tools for a priori design, at least against the high-frequency instability problem. In a system with the very large energy density of a rocket combustor, there are bound to be many mechanisms by which a small fraction of this energy can be channeled into undesirable oscillations. The resulting instabilities are usually categorized into “low frequency” and “high frequency” types. The former involve pressure oscillations which are slow enough compare to the acoustic passage time that the whole chamber participates in phase, while the latter exhibits acoustic behavior, with different parts of the combustor oscillating with different phase or amplitude. In either case, the instability arises when energy (or sometimes mass) can be added to the gas at, or near, peaks in its pressure oscillation (this is the classical Rayleigh criterion for instability, as explained) for example in Refs. (21) and (26)*. This implies a synchronization of two mechanisms, one which generates the energy or mass in some unsteady manner, and another one which allows the gas pressure and other thermodynamic quantities to oscillate. These two mechanisms must have comparable time constants for the mutual feedback to develop. The acoustic modes of typical rocket combustors have wavelengths which are some fraction of their linear size, and a wave speed (the speed of sound) of the order of 2000 m/sec. Thus their frequencies are in the KHz range, and hence the oscillation time constant is 10 -4 to 10 -3 sec, and potential couplings are to be sought to energy or mass release mechanisms with time constants of that order. To be more precise, it must be noted that a time lag in the release of combustion energy (such as, for example atomization, evaporation, mixing or reaction delays) will not per se provide coupling with the acoustic field. There must also be a sensitivity of the heat release rate, and hence of the time delay, to the pressure or other wave quantity.
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This note was uploaded on 11/07/2011 for the course AERO 16.512 taught by Professor Manuelmartinez-sanchez during the Fall '05 term at MIT.

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lecture_22 - 16.512, Rocket Propulsion Prof. Manuel...

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