Hybrid RANS/LES study of tip leakage vortex instability and turbulence characteristics of a transonic turbine cascade

To conduct detailed investigations about vortex instability and turbulence characteristics near a transonic turbine tip region, a highly accuracy hybrid Reynolds averaged Navier Stokes (RANS) / large eddy simulation (LES) method, namely detached eddy simulation (DES)-type method, is adopted at the exit isentropic Mach number of 0.95. Validation results show that this hybrid method can provide an accurate prediction against experiments. In contrast with the RANS method, this method can exhibit superiority in capturing detailed small-scale flow structures and more realistic turbulence distribution. Based on various identification methods, two predominant instability patterns of tip leakage vortex (TLV), namely, vortex wandering and breakdown have been recognized successfully in its downstream progression. Due to the supplement of tip leakage flow (TLF), the TLV maintains a concentrated vortex morphology with a monotonically increasing transverse wandering magnitude inside the blade passage. Subsequently, the TLV breakdown phenomenon, which is mainly due to the high adverse pressure gradient aggravated by shock waves, can be observed downstream the trailing edge. Meanwhile, a “spiral-type” vortex breakdown is distinguished firstly in a transonic turbine environment, which cannot be found in the previous RANS literature. To investigate the nature of the vortex instability, we perform an analysis based on the vorticity transport equation, it's found that the convection term due to the velocity gradient dominated the leakage vorticity damping. Combined the triple decomposition with the proper orthogonal decomposition (POD) method, the mechanisms of vortex wandering have been further revealed, which exhibits non-zero perturbations in transverse modes and a helical mode in the streamwise direction. Furthermore, detailed analysis of the turbulence characteristics has been also conducted, which contains distributions of Reynolds stress terms and the turbulent kinetic energy (k) along the TLV core trajectory. It can be recognized that the high adverse pressure gradient by shock waves can result in a sharp increase of Reynolds normal stresses (τii), which can stretch the TLV in different directions and exerts detrimental effects on the vortex breakdown. As a complementary, the turbulent anisotropy is also evaluated by the Lumley triangle method, which exhibits a variation from the one-component anisotropy to a two-component morphology as the TLV migrating downstream, while a isotropic turbulence field may be formed downstream the trailing edge due to the intense mixing. Predicted turbulence characteristics, vortical instabilities, and their flow mechanism can provide guide towards lower loss design and flow control of the turbine blade.