An impulse-based derivation of the Kutta–Joukowsky equation for wind turbine thrust

Abstract. Using the concept of impulse in control volume analysis, we derive general expressions for wind turbine thrust a constant, spatially uniform wind. The absence pressure equations allows their application near wake, where flow is assumed to be steady frame reference rotating with blades. assumption circumferential uniformity wake – as applies when number blades or tip speed ratio tends infinity needed reduce these Kutta–Joukowsky (KJ) equation blade-element thrust. present derivation improves upon classical based on Bernoulli by allowing rotational wake. also yields intermediate that are valid finite and trailing vortex sheets thickness. For circumferentially case, our analysis suggests magnitudes radial velocity axial induction factor must equal somewhere plane containing rotor, cite previous studies show this occur rotor across wide range coefficients. reveals one further complication; deriving KJ using annular volumes, existence vorticity lateral surfaces may cause local blade loading differ from equation, but magnitude deviations not explored. This complication visible due its neglect vorticity.