Wake Equilibrium Condition

The power absorbed by the rotor is also estimated by using the torque evaluation and the speed of rotation as

P = tQ (10.40)

The vortex sheets are considered in “equilibrium” when the power absorbed by the rotor matches the power deficit Ws in the far wake obtained from actuator disk theory, i. e. with the current notation

P = tQ = 2npU3 R2(1 + u)2 u (10.41)

This is a cubic equation for the average axial induced velocity u at the rotor

2 Ct

4(1 + u)2u = TSRCt = — = Cp (10.42)


The solution procedure consists in recalculating the solution with an updated vortex structure until it satisfies the equilibrium condition to acceptable accuracy (ACt/Ct | < 10-3).