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Blade element momentum theory is a theory that combines both blade element theory and momentum theory. It is used to calculate the local forces on a propeller or wind-turbine blade. Blade element theory is combined with momentum theory to alleviate some of the difficulties in calculating the induced velocities at the rotor.
This article emphasizes application of blade element theory to ground-based wind turbines, but the principles apply as well to propellers. Whereas the streamtube area is reduced by a propeller, it is expanded by a wind turbine. For either application, a highly simplified but useful approximation is the Rankine–Froude "momentum" or "actuator disk" model (1865,[1] 1889[2]). This article explains the application of the "Betz limit" to the efficiency of a ground-based wind turbine.
Froude's blade element theory (1878)[3] is a mathematical process to determine the behavior of propellers, later refined by Glauert (1926). Betz (1921) provided an approximate correction to momentum "Rankine–Froude actuator-disk" theory [4] to account for the sudden rotation imparted to the flow by the actuator disk (NACA TN 83, "The Theory of the Screw Propeller" and NACA TM 491, "Propeller Problems"). In blade element momentum theory, angular momentum is included in the model, meaning that the wake (the air after interaction with the rotor) has angular momentum. That is, the air begins to rotate about the z-axis immediately upon interaction with the rotor (see diagram below). Angular momentum must be taken into account since the rotor, which is the device that extracts the energy from the wind, is rotating as a result of the interaction with the wind.
^Rankine, William (6 April 1865). "On the Mechanical Principals of the Action of Propellors". Transactions of the Royal Institution of Naval Architects. 6: 13 – via Hathi Trust.
^Froude, Robert (12 April 1889). "On the Part Played in Propulsion by Differences in Fluid Pressure". Transactions of the Royal Institution of Naval Architects. 30: 390 – via Hathi Trust.
^Froude, William (11 April 1878). "The Elementary Relation between Pitch, Slip, and Propulsive Efficiency". Inst. Naval Architects. 19: 47 – via Hathi Trust.
^Wilson, Robert E.; Lissaman, Peter B.S. (1974). "Applied Aerodynamics of Wind Power Machines". NASA Sti/Recon Technical Report N. 75: 22669. Bibcode:1974STIN...7522669W.
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