Axisymmetric Potential Flow Model of Single or Coaxial Actuator Disks

This paper presents a computationally efficient method for computing the axisymmetric three-dimensional flow field induced by the trailing vortex system of either a single actuator disk or a pair of closely spaced coaxial actuator disks. A rotor in axial flight or hover (or a pair of coaxial rotors) is modeled as an actuator disk (or disks); the associated wake is modeled using contracting cylindrical sheets of vorticity approximated by discrete vortex rings. The resulting system of vortex sheets is axisymmetric and aligned with flow streamlines. The location of the sheets of vorticity is found using Newton iteration. A singularity occurs where the outer vortex sheet vortex sheet terminates at the edge of the actuator disk. This singularity is resolved through the formation of a 45° logarithmic spiral in hover, which produces a non-uniform inflow at the face of the disk, particularly near the edge of the disk where the flow field is entirely reversed. Finally, the model is applied to coaxial actuator disks to quantify the mutual interference of coaxial rotors at various axial spacings, and when operating in either a torque-balanced or and equal circulation state.