Blasius Boundary Layer Perturbation for Optimal Wind Rotor

Abstract

Flow on the lee side of wind turbines has been assumed to be helical, with swirl constrained by a pressure increase with radius. This would imply secondary flow into the axis in the blade boundary layer with the heavy swirl optimal at low speed ratios. But in the DTU wind tunnel, tufts on the BEM optimal torque wind stator did not show secondary flow. In fact the straight smoke trails observed behind the stator imply uniform pressure. For BEM optimal and practicable rotors, the interference increases with local speed ratio so the pressure on the lee side actually decreases with radius. In the limit of high speed ratio the pressure gradient again vanishes and the difference between Coriolis and curvilinear secondary forcing terms is a simple function of the apparent wind. Using this function for all speed ratios avoids any pressure gradient and secondary flow towards the axis. The universal profile of such approximated secondary flow and its effect on the chordwise boundary layer are studied as perturbations of the Blasius flat plate layer for Glauert's BEM optimal rotor.