Dynamic modeling and multi-mode characteristic analysis of buzz instability in ramjets

Ramjets exhibit multiple instability modes, including little buzz, mixed oscillatory patterns, and big buzz. However, there is currently a lack of mathematical models capable of accurately describing these modes, rendering real-time monitoring and control unfeasible. This study aims to develop a high-precision mathematical model to precisely characterize the multiple unstable oscillation modes of ramjets. First, unsteady simulation methods are employed to obtain the flow field and spillage characteristics under different instability modes, which are then incorporated into the modeling process. A ramjet instability model is constructed based on component-level modeling and inlet/engine flow matching principles. The model utilizes a dual calculation loop of backpressure and spillage to simulate oscillation characteristics. Modeling accuracy is improved by introducing a dynamic cavity mechanism, reducing the average frequency error by 18.86% and the average amplitude error by 21.28%. By fully simulating the start-unstart-restart process, the transition between little buzz and big buzz modes is captured. Additionally, hysteresis loops during the unstart and restart processes are identified, with the little buzz phase dominating the hysteresis time. Through oscillation loop analysis and statistical results, it is determined that under constant free-stream conditions, a spillage threshold exists that controls the switching between little buzz and big buzz. Finally, a statistical analysis is performed on the amplitude-frequency characteristics of the instability modes, revealing significant differences in amplitude-frequency characteristics among different ramjet instability modes. The mixed oscillatory pattern accounts for approximately 10% of all unstable operating conditions, which is much lower than the proportions of the big buzz and little buzz modes. The model constructed in this study enables the identification and monitoring of different instability modes, laying a foundation for the subsequent development of control strategies.