旋转爆轰波的数据驱动建模
Data-driven Modeling of Rotating Detonation Waves
摘要：
旋转爆震发动机（RDE）燃烧室的直接监测已经能够观察到的燃烧前动态组成的一些同向和/或反向旋转的相干行波的非线性锁模行为表现出分叉和不稳定性，这是没有很好地理解。计算流体动力学模拟在表征RDE的反应性、可压缩流的动力学方面是无处不在的。当考虑多种发动机几何形状、不同的操作条件和锁模相互作用的长时间动态时，这样的模拟是非常昂贵的。降阶模型（ROM）提供了一个关键的仿真框架，因为它们利用数据中的低秩结构来最大限度地减少计算成本，并允许快速参数化研究和长时间仿真。然而，ROM固有地受到RDE中存在的燃烧波所表现的平移不变性的限制。在这项工作中，我们利用机器学习算法来发现移动坐标系，数据被转移到其中，从而克服了RDE的基本平移不变性所带来的限制，并允许应用传统的降维技术。我们探索了一套不同的数据驱动的ROM策略，用于表征复杂的冲击波动力学和RDE中的相互作用。具体来说，我们采用动态模式分解和深度Koopman嵌入，以提供新的建模见解和理解燃烧波的相互作用RDES。
英文摘要：
The direct monitoring of a rotating detonation engine (RDE) combustion chamber has enabled the observation of combustion front dynamics that are composed of a number of co- and/or counter-rotating coherent traveling shock waves whose nonlinear mode-locking behavior exhibit bifurcations and instabilities which are not well understood. Computational fluid dynamics simulations are ubiquitous in characterizing the dynamics of RDE's reactive, compressible flow. Such simulations are prohibitively expensive when considering multiple engine geometries, different operating conditions, and the long-time dynamics of the mode-locking interactions. Reduced-order models (ROMs) provide a critically enabling simulation framework because they exploit low-rank structure in the data to minimize computational cost and allow for rapid parameterized studies and long-time simulations. However, ROMs are inherently limited by translational invariances manifest by the combustion waves present in RDEs. In this work, we leverage machine learning algorithms to discover moving coordinate frames into which the data is shifted, thus overcoming limitations imposed by the underlying translational invariance of the RDE and allowing for the application of traditional dimensionality reduction techniques. We explore a diverse suite of data-driven ROM strategies for characterizing the complex shock wave dynamics and interactions in the RDE. Specifically, we employ the dynamic mode decomposition and a deep Koopman embedding to give new modeling insights and understanding of combustion wave interactions in RDEs.
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