Magnus effect and Rotor propulsion simulation

About this project

Rotating cylinder in a fluid creates lift, known as 'Magnus effect' which is proportional to stream speed and surface rotational speed of cylinder. I thought that it is a forgotten technology, remembering just experiments of Captain Cousteau with 'turbosail' in eighties. Then I discovered a modern ship construction with 'Sail-Rotors'. She is a German 'E-Ship 1' commercial cargo, equipped with four rotors of 4 meters of diameters. In 2013 Enercon company, the owner of the ship, published official document about performance of those rotating masts after navigating more than 150 000 miles. The capabilities of rotating cylinders to produce lift were studied first at Langley NACA Laboratory. Mr Raid found that in appropriate conditions rotor can develop very high values of lift to drag ratio. Such a simple form of propulsion system allows to test SimScale CFD tools quite easily and also to understand how lift / drag ratio relates to wind speed / rotation speed, as that relation is not linear. In my setup I created much smaller geometry: rotor diameter is 0.3 m and high 2.0 m. Sharp edges of cylinder were removed in order to avoid meshing overhead. Rotation is along Z axe, rotor position starts at Z equal 0 and extends to 2 m. Wind speed is setup to 10 m/s and rotor surface or peripheral speed to similar speed, about 50 rad/s. As rotating cylinder creates asymmetric air flow, walls instead of 'no-slip' were set to 'Custom' P and V to 'Zero gradient', k and omega to 'Fixed values' appropriate to air. Basically those walls are 'transparent' and will not impact on rotating body. I decided also to provide progressive rotation speed to rotor: on 120 seconds of simulation, rotor accelerates to final 50 rad/s for 50 seconds, using inversely parabolic slope. This allows to avoid a strong wake from body starting to rotate: That approach helps to maintain laminar flow and shorten the simulation time.