Rotor theories by Professor Joukowsky: Momentum theories

This paper is the first of two papers on the history of rotor aerodynamics with special emphasis on the role of Joukowsky. The present one focuses on the development of the momentum theory while the second one surveys the development of vortex theory for rotors. Joukowsky has played a major role in these developments. Although he cooperated with other famous aerodynamicists like Prandtl, his contribution is not well recognized as most of his publications are in Russian. The paper discusses the role of the English, Russian and German research schools in the beginning of the Twentieth Century, and the contributions by individual researchers like Lanchester, Prandtl, Betz and Joukowsky himself. After the one-dimensional momentum theory was well established, the introduction of torque and angular momentum was the next step. Joukowsky has led the basis for this step, but Glauert׳s Blade Element Momentum still is the basis of current rotor design codes. He applied some assumptions limiting the validity to moderate and high tip speed ratios. Sørensen and van Kuik published a solution for wind turbines with very low tip speed ratios, which is now expanded to propellers as well, with one remaining assumption of inviscid flow. For very low tip speed ratios the general momentum theory gives unphysical results which disappear after applying a perturbation parameter representing phenomena not captured by the Euler equations.