Transient Lift on a Blade During Orthogonal Vortex Cutting

Vortex cutting imposes significant forces on blades in applications such as wind turbines operating in the wake of upstream turbines, helicopter rotor vortex impingement on the tail rotor, intake vortex interaction with a pump impellor, and streamwise vortex ingestion into a submarine propeller. The transient lift on a blade during orthogonal cutting of a vortex with non-zero axial flow was examined in the current paper using a combination of scaling theory, an analytical solution for instantaneous cutting and full Navier-Stokes simulations. The paper focuses on two distinct forces that occur during vortex cutting — the transient lift force that occurs during penetration of the blade leading edge into the vortex core and the steady-state lift force associated with the difference in vortex core radius over the blade surface. We show that the maximum value of the lift coefficient for the transient blade penetration force is proportional to the impact parameter and inversely proportional to the axial flow parameter. This observation is used to collapse predictions of the full Navier-Stokes simulations for lift coefficient over a wide range of values of the governing dimensionless parameters.