Theory of Liquid PropelIant Rocket Combustion Instability and Its Experimental Verification

Abstract

A straightforward theoretical formulation of the longitudinal high frequency rocket stability criteria is presented. Based on Crocco's sensitive combustion time lag theory, the derivation ii considerably simpler, although somewhat less rigorous, than previously published detailed treatments. A series of rocket motor experiments is described, demonstrating that there exists ar upper limit to the chamber length at which each mode of longitudinal high frequency pressure oscillations will occur, and that this limit is accurately predicted by the theory over a wide rang* of mixture ratios on two different injectors. The method used to compare experimental result! with the theoretical stability limit predictions (including a simple experimental technique fo] determination of the sensitive time lag) is described. Phenomenon of Rocket Combustion InstabilityE XCEPT for starting and cutoff transients, rocket motors are designed for steady operation. Two kinds of unsteadiness have nevertheless been observed to be present. First, the combustion in a rocket is always more or less "rough"; that is, random pressure fluctuations of larger or smaller amplitude cannot be avoided. Second, under proper conditions organized pressure oscillations at well-defined frequencies and distributions may appear. The latter form of unsteady operation is given the general title of "combustion instability."There are three recognized types of combustion instability. The first, the "low frequency instability" (1-3,6,7) 5 is due to interaction between the processes taking place in the combustion chamber and the propellant feed system; it is now sufficiently understood and comparitively easy to avoid or cure.The second, the "intermediate frequency instability" (4,5), results from a so-called "entropy wave" produced C3^clically in the chamber and interacting with the exhaust nozzle. Of the three, it is the least frequent.The third, the "high frequency instability," consists of the excitation of acoustic vibrational modes of the combustion chamber. This is by far the most destructive kind of instability and the hardest to control. The present paper deals with certain theoretical and experimental results concerning this third type of instability.A possible cause for high frequency instability was first advanced in 1950 (6). It was speculated that if pressure waves are produced in the chamber, they must produce an effect on Presented at the rates of the various physico-chemical processes leading tc combustion. These modified rates, in turn, by causing periodic intensification or weakening of the local gas evolutior. or heat release, could sustain the pressure waves under the appropriate conditions. A somewhat oversimplified model introduced to express quantitatively the sensitivity of the combustion rates to the pressure oscillations, was able tc demonstrate that high frequency instability could indeed be produced (6). This simple model was refined over the years in order to treat the problem in a more realistic manner. The results of these theoretical t...

A review of calculations for unsteady burning of a solid propellant.

“…This has been a reasonably successful approach for liquid rockets (Ref. 25, for example,) principally, it seems, because the time lag is at most a very slow function of frequency; the dependence on combustion parameters (fuel/oxidizer ratio particularly) may be inferred from observation of the stability boundary. This happens to be a fortunate situation, since there exists no way of computing 'T for a liquid rocket.…”

“…Usually, an Arrhenius law has been assumed for the conversion of solid to gas, giving the total surface mass flux (25) In most cases, the dependence on pressure has been ignored (ns = 0). A general perturbed form of (25), to first order of small quantities, is (26) with E = Es/RoTs the dimensionless activation energy for the surface reaction.…”

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“…The third form of instability is the excitation of the acoustic vibrational modes of the combustion chamber (pressure mode). While these modes may act individually or in concert, both Markstein, 1964 andCrocco et al, 1960 noted that for flames enclosed in a duct, the pressure mode exhibits the dominant disturbance and can be the most destructive. Thus the pressure mode is the primary focus of this research study, however consideration is also given to the vorticity mode as a mechanism for variations in the heat release.…”

“…A considerable amount of research, both experimental and theoretical, has been performed in the area of combustion dynamics on these devices and from these studies, three general classifications of combustion instabilities have been identified (Crocco et al, 1960 andMarkstein, 1964). First, low-frequency oscillation due to the geometry of the combustion chamber and propellant feed system (shear mode).…”

Stability of High-Frequency Pressure Oscillations in Rocket Combustion Chambers

“…By neglecting the effects of the liquid phase in the momentum equation written for the gas phase (a similar simplification also has been used in more recent work by Crocc0 9 ) and by emphasizing the energy additions, one may deduce a single equation for pressure fluctuations. This differential equation then can be converted to an integral equation that may be solved approximately by a known perturbation-iteration technique.…”