Koch James, Kurosaka Mitsuru, Knowlen Carl, Kutz J Nathan
William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195-2400, USA.
Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA.
Phys Rev E. 2021 Aug;104(2-1):024210. doi: 10.1103/PhysRevE.104.024210.
Proposed is a phenomenological modeling framework that is capable of reproducing the diverse experimental observations of the nonlinear, combustion wave propagation in a rotating detonation engine (RDE), specifically the nucleation and formation of combustion pulses, the soliton-like interactions between these combustion fronts, and the fundamental, underlying Hopf bifurcation to time-periodic modulation of the waves. In this framework, the mode-locked structures are classified as autosolitons or stably propagating nonlinear waves where the local physics of nonlinearity, gain, and dissipation exactly balance. We find that the global dominant balance physics in the RDE combustion chamber are dissipative and multiscale in nature: The fast combustion physics provide the energy input to form the fundamental mode-locked autosoliton state, while the slow physics of exhaust and propellant recovery shape the waveform and dictate the number of autosolitons. In this manner, the global multiscale balance physics give rise to the stable structures-not exclusively the frontal dynamics prescribed by classical detonation theory. Experimental observations and numerical models of the RDE combustion chamber are in strong qualitative agreement. Moreover, numerical continuation (computational bifurcation tracking) of the RDE analog system indicates that a Hopf bifurcation of the steadily propagating pulse train leads to the fundamental instability of the RDE, or time-periodic modulation of the waves. Along branches of Hopf orbits in parameter space exist a continuum of wave-pair interactions that exhibit solitonic interactions of varying strength.
提出了一种唯象建模框架，该框架能够再现旋转爆震发动机（RDE）中非线性燃烧波传播的各种实验观测结果，特别是燃烧脉冲的成核和形成、这些燃烧前沿之间类孤子相互作用以及波的时间周期调制的基本霍普夫分岔。在此框架中，锁模结构被分类为自孤子或稳定传播的非线性波，其中非线性、增益和耗散的局部物理特性精确平衡。我们发现，RDE燃烧室中的全局主导平衡物理特性本质上是耗散性和多尺度的：快速燃烧物理特性提供能量输入以形成基本锁模自孤子状态，而排气和推进剂回收的缓慢物理过程塑造波形并决定自孤子的数量。通过这种方式，全局多尺度平衡物理特性产生了稳定结构，而不仅仅是经典爆震理论规定的前沿动力学。RDE燃烧室的实验观测结果与数值模型在定性上高度一致。此外，RDE模拟系统的数值延拓（计算分岔跟踪）表明，稳定传播脉冲序列的霍普夫分岔导致RDE的基本不稳定性，即波的时间周期调制。在参数空间中霍普夫轨道分支上存在一系列波对相互作用，它们表现出不同强度的孤子相互作用。
