Proper orthogonal and dynamic mode decomposition analyses of nonlinear combustion instabilities in a solid-fuel ramjet combustor

In ramjet propulsion systems, syelf-excited combustion instability is highly undesirable. It may lead to violent structural vibration and even mission failure. For this, self-excited combustion instabilities in such SFRJ are investigated numerically by 2D unsteady Reynolds-Average Navier-Stokes (URANS) model and varying the inlet mass flow rate mair. When combustion instability occurs, large-amplitude temperature, velocity, and reacting species wavy motions are observed along the axial flow direction. To shed light on the flow features and the energy distribution among the unstable eigenmodes, proper orthogonal (POD) and dynamic mode decomposition (DMD) analyses of nonlinear combustion instabilities in a solid-fuel Ramjet (SFRJ) combustor are conducted. The POD studies reveal that the fluctuation energy of the first six modes contributes to 99% of the total fluctuation energy of all modes. It means that the main features of the SFRJ combustors could be captured by using the first six modes. Unlike POD studies, DMD analysis captures the frequency information and spatial structures in the entire flow field. Examining the DMD growth rate reveals that all dominant DMD eigenmodes are marginally stable (growth rate = 0) or unstable (positive growth rate). And the frequency of each dominant mode could be enhanced by 3-10 Hz as themair is increased by 0.2 kg/s. The mode energy decreases with the increase of the mode order, with the decrease up to around 90%. The DMD analysis on velocity field indicated that the flow separation could be observed near the backward facing step. And the DMD mode structure of the temperature field can significantly affect the mode structures of Mach number and YCO2 field. In general, the present work provides detailed analyses of the SFRJ flow field in the presence of self-excited combustion instability by using POD and DMD approaches.