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We study the formation mechanism of high-frequency combustion oscillations in a model rocket combustor from the viewpoints of symbolic dynamics and complex networks. The flow velocity fluctuations in the fuel injector generated by the pressure fluctuations in the combustor give rise to the periodic ignition of the unburnt fuel/oxidizer mixture, resulting in a significant change in the heat release rate fluctuations in the combustor. The heat release rate fluctuations drive the pressure fluctuations in the combustor before a transition state, while the pressure fluctuations in the combustor gradually begin to significantly affect the heat release rate fluctuations during the transition to combustion oscillations. The directional feedback process during the transition and subsequent combustion oscillations is identified by the directionality index of the symbolic transfer entropy. The thermoacoustic power network enables us to understand the physical mechanism behind the transition and subsequent combustion oscillations.

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This study investigates the flow structures behind an atmospheric entry capsule at Mach number 0.4 through an improved detached eddy simulation and a modal analysis. The simulated flowfields reveal relatively low-frequency peaks of St ≈ 0.016 and St = 0.17–0.2 in the aerodynamic coefficient variation, where St is the nondimensional frequency. Then, the dominant fluid structures that cause the frequency peaks are identified through dynamic mode decomposition and the compressive-sensing-based mode selection method. Many of the dominant fluid phenomena have a frequency of St ≈ 0.2. In this frequency range, the fluid phenomena are mainly characterized with a large-scale vortex shedding separated from the capsule’s shoulder part and with a helical fluid structure in the wake. Moreover, the variation in the lift coefficient of the capsule is mainly attributed to the large-scale vortex shedding phenomenon. Furthermore, a fluid phenomenon at a frequency of St = O(0.01) is found, which describes the pulsation, or periodic growth or shrinkage, of the recirculation bubble, accompanied by pressure fluctuation behind the capsule that exerts a large drag fluctuation of the capsule. Additionally, this phenomenon seems related to the dynamic instability phenomena of the capsule, as indicated by its time scale, which is close to that of the capsule’s attitude motion.