Analysis of tip leakage flow unsteadiness in a transonic turbine cascade using data-driven modal decomposition methods

Abstract

This paper presents a novel characterization of the unsteady dynamics of turbine tip flow using two kinds of modal decomposition methods, which are applied to hybrid RANS (Reynolds Averaged Navier-Stokes)/LES (Large Eddy Simulation) simulation data at a transonic condition. The development of tip leakage flow and subsequent vortex breakdown are accompanied by intense unsteadiness. By combining these two methods, the most dominant flow structures, as well as associated frequencies, are well determined, and the differences between the obtained modes are also pronounced. Modal analysis from POD (Proper Orthogonal Decomposition) shows that the large-scale fluctuating structures are located near the suction-side trailing edge, which is mainly attributed to the shock-induced vortex instability. Using the quadruple POD method, the transient tip flow field is decomposed into a mean part, a coherent part, a transition part, and a small-scale part with different spatial scales. Three DMD (Dynamic Mode Decomposition) variants including the AP-DMD (Amplitude selecting) method, the DMDc (DMD with criterion) method, and the SP-DMD (Sparsity promoting) method are also compared in extracting dominant modes from the periodic tip flow, and the SP-DMD method which can distill modes of wide frequencies and low dissipation is proved to be more conducive to reconstructing the complex tip flow. Comparison between POD and DMD mode distributions manifests that the behavior of small-scale vortical interaction can be isolated with the Karman-type vortex layer shedding process via DMD, which also demonstrates that the DMD is more favorable to decomposing the complex tip flows into uncoupled single-frequency coherent structures.

Analysis of Tip Leakage Vortex Instability and Blade Force in a Low-Speed Compressor Cascade

“…Moreover, the LES turbulence model solves the flow far from the near-wall [31]. Some researchers have proved that DES has undeniable advantages in predicting tip leakage vortex characteristics in compressors [32] and turbines [33].…”