The separation and turbulent transition of the flow in a compressor blade channel are investigated through direct numerical simulations (DNS) at a Reynolds number of 1.367 × 105. Based on the original DNS data, both time-averaged statistics and instantaneous vortex structures of the flow field are extensively analyzed. The vortices are visualized and studied by the Liutex method, and the streaming dynamic mode decomposition (SDMD), a low-storage variant of conventional DMD, is applied to the large datasets obtained on both pressure and suction sides. The physical quantity analyzed with SDMD is the Liutex magnitude R. The DNS results indicate that flow separation occurs on both sides of the blade. On the pressure surface, the separation is weak and the flow remains in a natural transition dominated by viscous Tollmien–Schlichting instabilities. In contrast, owing to the presence of a large laminar separation bubble, the flow experiences a separation transition governed by inviscid Kelvin–Helmholtz instabilities on the suction surface. The SDMD results suggest that a broad range of vortex frequencies exist in the transition flow, and the scale of the spatial structures is negatively correlated with the frequency of the mode. On the pressure surface, the extracted SDMD modes are primarily related to Kelvin–Helmholtz rolls, whereas on the suction side, influenced by the separated boundary layer, the modal structures exhibit greater diversity.

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.

This study employs Direct Numerical Simulation (DNS) to investigate the flow and heat transfer characteristics in a compressor blade passage at five Reynolds numbers ($Re=1.091\times {10}^5$, $1.229\times {10}^5$, $1.367\times {10}^5$, $1.506\times {10}^5$, and $1.645\times {10}^5$). A recent method based on local inviscid velocity reconstruction is applied to define and calculate boundary layer parameters, whereas the Rortex vortex identification method is used to analyze turbulent vortical structures. Results indicate that $Re$ significantly affects separation bubble size, transition location, and reattachment behavior, thereby altering wall heat transfer characteristics. On the pressure surface, separation and early transition are observed at higher $Re$, with the Nusselt number ($Nu$) remaining high after transition. On the suction surfaces, separation occurs such that large-scale separation at low $Re$ reduces $Nu$, while reattachment combined with turbulent mixing at high $Re$ significantly increases $Nu$. Turbulent vortical structures enhance near-wall fluid mixing through induced ejection and sweep events, thereby promoting momentum and heat transport. As $Re$ increases, the vortical structures become denser with reduced scales and the peaks in heat flux move closer to the wall, thus improving convective heat transfer efficiency.