On the motion of multiple helical vortices (Q2770204)

The determination of the velocity of a single, constant-diameter helical vortex in an inviscid fluid is extended to include the effects of equally spaced multiple vortices. The contributions of additional vortices are determined from straightforward application of Biot-Savart law that, apparently, cannot be evaluated in closed form. Based on Mellin-Barnes integral representation of the binormal velocity on one of the helices, the authors obtain asymptotic expansions for small and large pitch. It is demonstrated that the small-pitch limit is of practical significance for wind turbine and hovering rotor applications. It is also shown that the wake consisting only of helical tip vortices and hub vortices lying along the axis of rotation is consistent with one-dimensional wake analysis. The authors point out that the results can be used to assess the accuracy of various discretization schemes employed to study the model trailing helical vortices in free-wake computer simulations.