Characterization and modeling of the flame response to high frequency propellant flow rates oscillations in the framework of thermo-acoustic instabilities in liquid rocket engines

Abstract

Pressure fluctuations induced by thermoacoustic self-sustained oscillations within the combustion chamber or the feeding domes (plenums) of a liquid rocket engine may induce temporal modulations of the injection velocities of the propellants. The dynamic response of a transcritical coaxial flame to such a modulation is investigated here as it is thought to be one of the mechanisms that can promote high frequency combustion instabilities in liquid rocket engines. This question is addressed through large eddy simulations of a single LOx/GCH${}_4$ coaxial flame, representative of next generation injection systems. Each of the propellant streams is successively acoustically modulated so that a harmonic flow rate oscillation is achieved. The unsteady heat release rate response of the flame is recorded and hydrodynamic features caused by the modulation are identified. It is first shown that both fuel and oxidizer flow rates, if unsteady, have the potential to trigger high amplitude heat release rate oscillations within frequency ranges that are typical of high frequency instabilities in liquid rocket engines. The fuel-modulated configuration is essentially linear even for high modulation amplitudes (at least up to 40%). On the contrary, the oxidizer-modulated case shows a strong dependence of the gain in terms of the modulation amplitude, while its phase remains virtually unaffected (at least up to 10% of the modulation amplitude in the present study). This study then reveals that both unsteady propellant injections can induce flame surface oscillations as well as variations of the rate of heat released by a unit flame surface element, explaining the unsteady heat release rate observed. The relative contributions of these two driving mechanisms are measured. They prove to be complex and strongly dependent on the modulation frequency. Reduced order models of the resulting flame response are finally proposed. The fuel-modulated case is modeled assuming a local increase of the turbulent mixing provoked by the annular velocity modulation. The oxidizer-modulated case is represented by an oscillation of flame length due to the inner stream modulation. Provided that a mean unmodulated and one modulated solutions are available, both models can give accurate predictions for a large range of frequencies, both in terms of gain and phase. In particular, the oxidizer model is natively non-linear and permits to retrieve the modulation amplitude dependence observed in the simulations.

Novelty and Significance Statement

The response of a cryogenic flame to the effect of the modulated injector flows is weakly documented in the literature, while being of high interest for the modeling and prediction of combustion instabilities in liquid rocket engine. Modulated flames are depicted in Nez et al. (2017) and Laurent et al. (2021), but only for a modulation of the annular stream. No models were provided. This work intends to complement these studies by investigating the dynamics of LOx/CH${}_4$ transcritical flames under both oxidizer and fuel mass flow-rate modulations. The dynamics are driven by flame surface oscillations as well as variations of the rate of heat released by a unit flame surface element. The response of the LOx-modulated case is strongly non-linear in terms of modulation amplitude, contrary to the fuel-modulated one. Semi-analytical models for the flame transfer functions are derived for both modulations.