Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 61

In the limit of an infinite number of blades and ignoring expansion the tip vortices form a cylinder with surface vorticity that follows a helical path with a helix angle ϕ_t, which is the same as the flow angle at the outer edge of the disc. The strength of the vorticity is , where Δn is the distance along the tube surface in a direction normal to ΔΓ between two successive tip vortices. g has components g_θ in the azimuthal direction and g_x in the axial direction. Due to g_θ the axial (parallel to the axis of rotor rotation) induced velocity u_d at the rotor plane is uniform over the rotor disc and can be determined by means of the Biot–Savart law as

(3.27)

In the far wake the axial induced velocity u_w is also uniform within the cylindrical wake and is

(3.28)

The ratio of the two induced velocities corresponds to that of the simple momentum theory and justifies the assumption of a cylindrical vortex sheet.