The coexistence of multiple stable states is indicative of self-organising processes occurring in the course of the combustor-inlet interactions in a ramjet engine and give rise to the appearance of various nonlinear phenomena. This paper provides a dynamic model that can describe the multiple stable states and the corresponding nonlinear effects to further investigate the dynamic interactions between combustor and inlet in a ramjet engine. Our study shows the whole engine can display distinct dynamic behaviours ranging from irreversibility to hysteresis and to various mode transitions, depending on different physical parameters. With the model, we also illustrate the role of the instability of the normal shock wave in impacting the whole engine’s nonlinear dynamics. Additionally, we extend the previous studies of the classification of combustor-inlet interactions from a static framework to a dynamic framework, which helps to clarify the transient processes of the nonlinear interactions. This work offers a quantitative illustration of the combustor-inlet interactions in a ramjet engine by revealing its nonlinear dynamics and associated characteristics, therefore advancing our understanding of the nonlinear phenomena that exhibit in ramjet engines.

中文翻译：

---

冲压发动机低阶动力学模型中的燃烧室-进气口相互作用

多个稳定状态的共存表明在冲压喷气发动机的燃烧室-进气口相互作用过程中发生了自组织​​过程，并导致各种非线性现象的出现。本文提供了一个动态模型，可以描述多个稳定状态和相应的非线性效应，以进一步研究冲压喷气发动机燃烧室和进气口之间的动态相互作用。我们的研究表明，根据不同的物理参数，整个发动机可以表现出不同的动态行为，从不可逆性到滞后以及各种模式转换。通过该模型，我们还说明了正常冲击波的不稳定性在影响整个发动机非线性动力学中的作用。此外，我们将先前对燃烧室-入口相互作用分类的研究从静态框架扩展到动态框架，这有助于阐明非线性相互作用的瞬态过程。这项工作通过揭示其非线性动力学和相关特性，为冲压喷气发动机中的燃烧室-进气口相互作用提供了定量说明，从而促进了我们对冲压喷气发动机中表现出的非线性现象的理解。