Dynamical systems approach to study thermoacoustic transitions in a liquid rocket combustor

Abstract

Liquid rockets are prone to large amplitude oscillations, commonly referred to as thermoacoustic instability. This phenomenon causes unavoidable developmental setbacks and poses a stern challenge to accomplish the mission objectives. Thermoacoustic instability arises due to the nonlinear interaction between the acoustic and the reactive flow subsystems in the combustion chamber. In this paper, we adopt tools from dynamical systems and complex systems theory to understand the dynamical transitions from a state of stable operation to thermoacoustic instability in a self-excited model multielement liquid rocket combustor based on an oxidizer rich staged combustion cycle. We observe that this transition to thermoacoustic instability occurs through a sequence of bursts of large amplitude periodic oscillations. Furthermore, we show that the acoustic pressure oscillations in the combustor pertain to different dynamical states. In contrast to a simple limit cycle oscillation, we show that the system dynamics switches between period-3 and period-4 oscillations during the state of thermoacoustic instability. We show several measures based on recurrence quantification analysis and multifractal theory, which can diagnose the dynamical transitions occurring in the system. We find that these measures are more robust than the existing measures in distinguishing the dynamical state of a rocket engine. Furthermore, these measures can be used to validate models and computational fluid dynamics simulations, aiming to characterize the performance and stability of rockets.

Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

“…The different operating conditions of a thermoacoustic combustor have been extensively studied in the literature both in laboratory conditions and model system data [67]. Measures based both on RPs and recurrence networks have been successfully applied to detect dynamical transitions between different regimes [11,70].…”

“…Positive feedbacks between both may lead into a state called thermoacoustic instability, enhancing heat transfer to the walls of the combustion chamber and resulting in increased mechanical stress. This can cause severe damages to an aircraft's engine or shutdown in the case of a power plant [67]. The parameter which can drive the turbulent system into an unstable state is the fuel/air ratio.…”

Critical transitions and their early warning signals in thermoacoustic systems

“…Kasthuri et al [93] showed several measures based on multifractal theory and recurrence quantification analysis. They find that these are robust measures in distinguishing dynamical states occurring in a model rocket engine combustor.…”

Injector-coupled transverse instabilities in a multi-element premixed combustor

“…The design maintains similarities with several other rocket and gas turbine combustion experiments studied at Purdue University. 35,[37][38][39][40] VIPER-M was designed to promote self-excited, transverse instabilities while operating at a mean chamber pressure up to 825 kPa with an inlet air temperature up to 510 K. The multi-element configuration supports jet-stabilized combustion with flames anchored at the injector-exit plane (y ¼ 0), as labeled in Figure 1. This injector configuration is similar to the FLOX V R combustion experiments, which have been widely studied.…”