Mode identification and decomposition analysis of self-excited thermodynamic oscillations in hypersonic inlet/isolator of a scramjet

The self-excited pressure and velocity oscillations caused by the downstream back pressure in a hypersonic inlet/ isolator directly affect the operational stability of a scramjet. In this work, we conduct the two-dimensional unsteady RANS (Reynolds averaged Navier-Stokes) simulation to predict the flow field in the Mach 7 inlet/ isolator with 147 times the freestream static pressure. With the model validated, the time evolution process of the instantaneous flow fields in the isolator is analyzed first. It is shown that the structure of the shock train exhibits an up-down asymmetry. The flow oscillations as observed near the upper wall are more complex than those near the lower wall. Furthermore, the dominant frequency of the wall pressure oscillations is approximately 520 Hz. However, the self-excited oscillations in the isolator flow are dominated with approximately 510 Hz mode but coupled with multiple harmonic higher frequencies. To identify and decompose the modes of these oscillations in the unsteady flow of the isolator, different mode decomposition technologies are applied to further examine the mechanism of such oscillations. By conducting Proper Orthogonal Decomposition (POD) analysis on the x-axis velocity and Mach number fields, it is shown that the first two modes consist of more than 77% of the total oscillations' kinetic energy. Additionally, the oscillations of the quadrilateral separation zone and low-speed zone near the upper wall largely determine the dominant frequency of the overall unsteady flow field. As Dynamic Mode Decomposition (DMD) investigation is conducted on the x-axis velocity and Mach number fields, it is found that the identified first mode is almost the same as that identified by using POD. It is also found that both DMD and POD can well predict the viscous flows such as the separation zone, shear layer, and low-speed zone. Finally, the dominant frequencies predicted by the POD and DMD are revealed to be very close to the dominant frequency of the wall static pressure oscillations. The movements of multiple shock waves near the upper wall are the major incentive for the complicated change in the entropy generation rate. In general, the self-excited thermodynamic oscillations phenomenon as observed in the hypersonic inlet/isolator in a scramjet could be well analyzed by decomposing and identifying the dominant modes, which contribute mostly to the total energy of such oscillations.