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.
Ma et al. (Mon,) studied this question.