Numerical investigation of the flow over a model transonic turbine blade tip

Direct numerical simulations (DNS) are used to investigate the unsteady flow over a model turbine blade tip at engine-scale Reynolds and Mach numbers. The DNS are performed with an in-house multiblock structured compressible Navier–Stokes solver. The particular case of a transonic tip flow is studied since previous work has suggested that compressibility has an important effect on the turbulent nature of the separation bubble at the inlet to the tip–casing gap and subsequent flow reattachment. The flow is simulated over an idealized tip geometry where the tip gap is represented by a constant-area channel with a sharp inlet corner to represent the pressure side edge of the turbine blade. The effects of free-stream disturbances, cross-flow and the pressure side boundary layer on the tip flow aerodynamics and heat transfer are studied. For ‘clean’ inflow cases we find that even at engine-scale Reynolds numbers the tip flow is intermittent in nature, i.e. neither laminar nor fully turbulent. The breakdown to turbulence occurs through the development of spanwise streaks with wavelengths of approximately 15 %–20 % of the gap height. Multidimensional linear stability analysis confirms the two-dimensional base state to be most unstable with respect to spanwise wavelengths of 25 % of the gap height. The linear stability analysis also shows that the addition of cross-flows with 25 % of the streamwise gap exit velocity increases the stability of the tip flow. This is confirmed by the DNS, which also show that the turbulence production is significantly reduced in the separation bubble. For the case when free-stream disturbances are added to the inlet flow, viscous dissipation and the rapid acceleration of the flow at the inlet to the tip–casing gap cause significant distortion of the vorticity field and reductions of turbulence intensity as the flow enters the tip gap. The DNS results also suggest that the assumption of the Reynolds analogy and a constant recovery factor are not accurate, in particular in regions where the skin friction approaches zero while significant temperature gradients remain, such as in the vicinity of flow reattachment.