The Influence of Streamwise Vorticity on Transition in the Presence of Sweep

Abstract

Experimental observations and theoretical predictions of streamwise vorticity on circular cylinders in crossflow and on turbine blades are considered. The observations on cylinders confirm earlier predictions and this forms a firm basis for referencing other measurements and predictions of vortical behavior. It also results directly in a correlation for predicting the spanwise wavelength of streamwise vortices on the convex surfaces of turbomachine blades. Highly resolved Large Eddy Simulation has shown that fine scale organized streamwise vorticity may exist on the convex surfaces of turbine and compressor blading and is predictable. For a turbine blade with a blunt leading edge the streamwise vorticity may persist on a time-average basis to influence the entire suction surface at suitably low Reynolds numbers typical of aircraft cruise conditions. The results emphasize the enormous computing resource required to resolve the flow on a routine basis for design purposes. It is demonstrated computationally that streamwise vorticity interacts with spanwise vorticity in leading edge bubbles to promote early transition and bubble closure. Time resolution is required to capture the flow complexity that is fundamental for an understanding of the physical behavior of the laminar boundary layer and its separation and transition. A narrow spanwise strip does not allow the streamwise vorticity to settle into the organized pattern. For streamwise vorticity to become organized, an adequate spanwise domain and run duration for time averaging are also essential. Any accurate treatment of laminar boundary layers at low Reynolds numbers needs to be performed three dimensionally and with a sufficiently fine spanwise spacing and duration of run to resolve streamwise vortical structures. Sweep of the body, wing or blade poses special problems. Not least is a serious lack of information on even the most basic cases. An attempt is made to relate the streamwise vorticity studied by Kestin and Wood to the more aggressive crossflow instability studied by Poll. More research is needed if designers are to be confident about the flow regimes they might expect to prevail for a given sweep angle. Nomenclature D Cylinder diameter n Amplification factor in inception prediction Re Reynolds number Tu Free-stream turbulence level u Velocity component in x direction x, y, z Coordinate directions    Angle between normal to the inflow and axis of the body    Spanwise spacing between vortex pairs  ___________________________________________________________________________________