Effect of temperature fluctuations on high frequency acoustic coupling

This article considers the influence of fluctuations in temperature on acoustic resonance characteristics of a combustion chamber. This analysis is concerned with acoustic coupling experienced in high frequency instabilities. Experiments carried out on a multiple injector combustor (MIC) operating with liquid oxygen and gaseous methane are used to simulate on a model scale the situation prevailing in a liquid rocket thrust chamber. External acoustic modulations are generated by periodically blocking an auxiliary nozzle with a rotating toothed wheel. By continuously changing the rotation velocity, it is possible to apply a linear frequency sweep and obtain the response of the system to an external excitation. It is found that the chamber quality factor under hot fire conditions is reduced with respect to the one measured under cold flow conditions. This is shown to be correlated with the level and spatial extension of temperature fluctuations inside the chamber. Temperature fluctuations induce variations in the speed of sound which in turn perturb the eigenfrequencies of the system and modify its response. This effect is modeled in a simplified way by considering a second order dynamical system featuring an eigenfrequency which fluctuates around its mean value. The dynamics is analyzed by making use of simulations and by the method of averaging. It is shown that when the eigenfrequency fluctuates, the system behaves as if it had an augmented level of dissipation and that this induces a reduction in the quality factor. It is concluded that this mechanism could have an important impact on the development of oscillations in liquid rocket engines.