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Keywords:

  • wind turbine;
  • general momentum theory;
  • wake rotation

Abstract

A general momentum theory for an energy-extracting actuator disc modelling a rotor with a multiplicity of blades having radially uniform circulation is presented that includes the effects of wake rotation and expansion. A parallel theory directed at the propeller has been published elsewhere, but not one intended for the wind turbine. The rotation of the wake is shown to be accompanied by a fall in static pressure that is additional to that which occurs across the actuator disc and accounts for the energy extraction from the wind. Energy extraction is recognized in the fully developed wake by the flow regaining the static pressure of the undisturbed wind at the expense of the kinetic energy in the wake. Because the wake is still rotating in the fully developed wake, the additional fall in static pressure appears there also and so does not augment the energy extraction. However, the additional fall in pressure would cause a discontinuity in pressure across the fully developed wake but is prevented by a further slowing down of the wake. The additional slowing down extracts a little more energy from the flow than that predicted by the simple momentum theory, which does not include wake rotation. The overall effect of wake rotation on energy extraction is very small for wind turbines operating at high tip speed ratios but can significantly increase the predicted power output for turbines operating at low tip speed ratios. Copyright © 2004 John Wiley & Sons, Ltd.