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High Frequency Combustion Instability in Liquid Propellant Rocket with Concentrated Combustion and Distributed Time Lag


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The stability of high frequency small longitudinal disturbances superposed on a combustion system in a liquid propellant rocket operating at normal or steady state has been investigated on a linearized basis in references 1, 2, and 3. It is found that the configuration of the combustion system especially concerning the spacewise and the timewise distribution of combustion elements is of considerable importance in determining the stability of the small disturbances. It has been pointed out in reference 4 that under the assumption of instantaneouscombustion, the configuration of the combustion system can be schematically characterized by two distribution functions defining the "sensitive time lag" and the "total space lag" of propellant elements when the rocket is in steady state operation. The time lag is a scalar quantity while the space lag is a vector in general. In the simplified case of longitudinal oscillations, the space lag is also a scalar which is simply the distance from the injector end of the position where a propellant element is transformed into gaseous combustion products. Owing to the complexities of the mathematical formulation of the problem, previous treatments are only dealing with particular configurations. In references 1 and 2 all the propellant elements are assumed to have the same sensitive time lag and the same total space lag in steady state operation so that a concentrated or discontinuous combustion front is formed in the combustion chamber in both steady and unsteady state operation. In reference 3, the time lags of all the propellant elements are still assumed to be the same in steady state and the problem baa been formulated for arbitrary space lag distribution while solution of the problem has been obtained only for the simplest extreme case of uniformly distributed space lags.



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