Abstract
The article seeks to unify the treatment of conservative force interactions between axi-symmetric bodies and actuators in inviscid flow. Applications include the study of hub interference, diffuser augmented wind turbines and boundary layer ingestion propeller configurations. The conservation equations are integrated over infinitesimal streamtubes to obtain an exact momentum model contemplating the interaction between an actuator and a nearby body. No assumptions on the shape or topology of the body are made besides (axi)symmetry. Laws are derived for the thrust coefficient, power coefficient and propulsive efficiency. The proposed methodology is articulated with previous efforts and validated against the numerical predictions of a planar vorticity equation solver. Very good agreement is obtained between the analytical and numerical methods.
Highlights
Applications include the study of hub interference, diffuser augmented wind turbines and boundary layer ingestion propeller configurations
The conservation equations are integrated over infinitesimal streamtubes to obtain an exact momentum model contemplating the interaction between an actuator and a nearby body
Laws are derived for the thrust coefficient, power coefficient and propulsive efficiency
Summary
Questions on the performance of actuator disks with nearby bodies arose at the dawn of rotor aerodynamics. For constant loading symmetric actuator-body configurations, it can be shown that the vanishing of pressure perturbations at infinity implies that the terminal wake is aligned with the free-stream: xe ∈ ψe ⇒ U (xe) = Ueex ∧ Ue⊥xe. Conservation of momentum is entirely described by the streamwise component (ex) of the integrated equations, corresponding to the dot product of the free-stream unit vector ex with the system of n equations: Ue. The total force exerted on the flow by the actuator is related with the velocity field by integrating the momentum conservation statement accross the actuation surface: Fa = φadψa = ρ (Ue − Uo) U (xa) · nadψa +. The second parcel corresponds to the streamwise component of the resultant of pressure forces exerted on the flow crossing the actuator The present derivation is exact: by following a different path with fewer assumptions it reinforces and unifies these earlier works
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