Spectral proper orthogonal decomposition of turbine tip clearance flow under low-Reynolds number conditions

Spectral proper orthogonal decomposition, a data-based decomposition technique, was performed to extract key spatiotemporal coherent structures from large-eddy simulation data. Both velocity and vorticity were decomposed to identify the dominant unsteady features around the near-tip region. Four operating conditions for two different Reynolds numbers, with and without tip clearance were investigated, i.e., low_Re TC, low_Re, high_Re TC and high_Re. The energy spectra (eigenvalues) and their accumulation at each frequency exhibited the low-rank behavior, indicating the presence of a physically dominating mechanism. The velocity mode shapes (eigenvectors) revealed three typical coherent structures for the low_Re TC condition: vortex shedding from the blade wake and the tip leakage vortex, Kelvin-Helmholtz instability induced by the leakage jet, and complex interactions among the boundary layer separation, the tip leakage vortex and the horseshoe vortex. For the condition without tip clearance, the dominant structure was the vortex shedding from the wake only. The vorticity mode shapes indicated that high dissipation of the vorticity field occurred close to the suction side, where strong secondary vortices existed. The present research could develop a better understanding of turbine tip clearance flow and loss mechanisms at low Reynolds numbers.