In this study, we propose a novel dynamic mode decomposition (DMD) energy sorting criterion that works in conjunction with the conventional DMD amplitude-frequency sorting criterion on the high-dimensional schlieren dataset of the unsteady flow of a spiked-blunt body at Ma = 2.2. The study commences by conducting a comparative analysis of the eigenvalues, temporal coefficients, and spatial structures derived from the three sorting criteria. Then, the proper orthogonal decomposition (POD) and dynamic pressure signals are utilised as supplementary resources to explore their effectiveness in capturing spectral characteristics and spatial structures. The study concludes by summarising the characteristics and potential applications of DMD associated with each sorting criterion, as well as revealing the predominant flow features of the unsteady flow field around the spiked-blunt body at supersonic speeds. Results indicate that DMD using the energy sorting criterion outperforms the amplitude and frequency sorting criteria in identifying the primary structures of unsteady pulsations in the flow field, which proves its superiority in handling an experimental dataset of unsteady flow fields. Moreover, the unsteady pulsations in the flow field around the spiked-blunt body under supersonic inflow conditions are observed to exhibit multi-frequency coupling, with the primary frequency of 3.3 kHz originating from the periodic motion of the aftershock.

The thermal turbulence phenomena were investigated by the direct numerical simulations (DNS) in a blade channel at a Reynolds number of 1.774 × 105, which included the laminar boundary layers, the natural transitions, the separation and reattachment, and the fully developed turbulence. The turbulence statistics and instantaneous vortex structures were analyzed through applying the spectral proper orthogonal decomposition (SPOD) to these high-fidelity DNS data, including the pressure, velocity, temperature, and vortex characteristics, represented by the state-of-the-art vortex identification quantity of Rortex. The frequency-domain reconstruction was adopted to reconstruct original physical quantities. The analyses suggest that the separation on the pressure side is relatively weak, while the separation on the suction side is strong and dominated by the inviscid Kelvin–Helmholtz (K–H) instabilities. The turbulence improves the heat transfer, which leads to large temperature gradients on blade surfaces. The modal analyses indicate that the SPOD method can effectively extract the primary field structures and characteristics. The modal information on the pressure surface exhibits a strong low-rank behavior due to the weak separation, whereas the SPOD modes on the suction surface are primarily associated with the frequency generated by the K–H rolls. The frequency-domain reconstruction found that fewer modes were required to reconstruct the pressure and velocity fields comparing to the temperature field. The current study provides an in-depth understandings and valuable insight for the thermal turbulence demanded in the aero-engine design of compressor cascade.