The relationship between loads and power of a rotor and an actuator disc

Most state of the art rotor design methods are based on the actuator disc theory developed about one century ago. The actuator disc is an axisymmetric permeable surface carrying a load that represents the load on a real rotor with a finite number of blades N. However, the mathematics of the transition from a real rotor load to an axisymmetrically loaded disc is not yet presented in literature. By formulating an actuator disc equation of motion in which the Bernoulli constant H is expressed in kinematical terms, a comparison of the power conversion and load on the disc and rotor is possible. For both the converted power is expressed as a change of angular momentum times rotational speed. The limits for N → ∞ while the chord c → 0, the rotational speed Ω → ∞, the load F becoming uniform by ∂F/∂r → 0 and the thickness ε → 0 confirm that the classical disc represents the rotor with an infinite number of blades. Furthermore, the expressions for the blade load are compared to the expressions in current design and analysis tools. The latter do not include the load on chord-wise vorticity. Including this is expected to give a better modelling of the tip and root flow