The rotor theories by Professor Joukowsky: Vortex theories

This is the second of two articles with the main, and largely self-explanatory, title “Rotor theories by Professor Joukowsky”. This article considers rotors with finite number of blades and is subtitled “Vortex theories”. The first article with subtitle “Momentum theories”, assessed the starring role of Joukowsky in aerodynamics in the historical context of rotor theory. The main focus in both articles is on wind turbine rotors, but much of the basic theory applies to propellers and helicopters as well. Thus this second article concentrates on the so-called blade element theory, the Kutta–Joukowsky theorem, and the development of the rotor vortex theory of Joukowsky. This article is to a large extent based on our own work, which constitutes the first successful completion and further development of Joukowsky׳s work by deriving the first analytical solution of his rotor. This rotor has a finite number of blades and will be compared with the rotor analysis of Betz and of others of the German school of aerodynamics.