The velocity field, vector potential and velocity gradient of a vortex ring is derived in this chapter. The Biot-Savart law for the vector potential and velocity is expressed in a first section. Then, the flow is derived at specific locations: on the axis, near the axis and in the far field where the analogy to a doublet field is made. The following section derive the value of the vector potential and velocity field in the full domain. The expression for the velocity gradient is also provided since it may be relevant in a simulation with vortex particles and vortex rings. Most of this chapter is dedicated to vortex rings. Source rings are only briefly mentioned.
|Title of host publication||Wind Turbine Aerodynamics and Vorticity-Based Methods |
|Number of pages||10|
|Publication status||Published - 2017|
|Series||Research Topics in Wind Energy|