Direct Numerical Simulations of a Transonic Tip Flow With Free-Stream Disturbances

In this paper we use direct numerical simulation to investigate the unsteady flow over a model turbine blade-tip at engine scale Reynolds and Mach numbers. The DNS is performed with a new in-house multi-block structured compressible Navier-Stokes solver purposely developed for exploiting high-performance computing systems. The particular case of a transonic tip flow is studied since previous work has suggested compressibility has an important influence on the turbulent nature of the separation bubble at the inlet to the gap and subsequent flow reattachment. The effects of free-stream turbulence, cross-flow and pressure-side boundary-layer on the tip flow aerodynamics and heat transfer are investigated. For ‘clean’ in-flow cases we find that even at engine scale Reynolds numbers the tip flow is intermittent in nature (neither laminar nor fully turbulent). The breakdown to turbulence occurs through the development of spanwise modes with wavelengths around 25% of the gap height. Cross-flows of 25% of the streamwise gap exit velocity are found to increase the stability of the tip flow, and to significantly reduce the turbulence production in the separation bubble. This is predicted through in-house linear stability analysis, and confirmed by the DNS. For the case when the inlet flow has free-stream turbulence, viscous dissipation and the rapid acceleration of the flow at the inlet to the tip-gap causes significant distortion of the vorticity field and reductions of turbulence intensity as the flow enters the tip gap. This means that only very high turbulence levels at the inlet to the computational domain significantly affect the tip heat transfer. The DNS results are compared with RANS predictions using the Spalart-Allmaras and k–ω SST turbulence models. The RANS and DNS predictions give similar qualitative features for the tip flow, but the size and shape of the inlet separation bubble and shock positions differ noticeably. The RANS predictions are particularly insensitive to free-stream turbulence.