Quadrant analysis on vortex-induced autorotation of a rigid square cylinder

In some specific conditions, a solid body exposed to a fluid flow rotates continuously in spite of absence of external energy, which is known as autorotation. In explaining autorotation dynamics, vortex shedding and stagnation pressure have been mentioned as a cause for moments exerted on the body, but it is not comprehensible that how they generate moments on each corresponding side and how significantly they contribute to instantaneous net moments. To manifest these subjects for an autorotating square cylinder, the hybrid partition method, in which four sides of the cylinder are flagged respectively and then tracked in time only within a specific range of angle of rotation, is presented. Applying this method, we analyze the autorotation of a rigid square cylinder, studied by Ryu & Iaccarino (2017), to scrutinize quantitatively how the individual moments corresponding to each side contribute to the instantaneous net moments and to find a clue for the sustenance of autorotation. Our systematic study based on the hybrid partition reveals that the moments exerted on the windward side tend to act adversely to the instantaneous net moments, whereas those on the leeward side contribute favorably to the net moments. In addition, it is shown by comparing the two neighboring regimes of vortex-induced rotation, oscillatory rotation within +/- 180-degree and autorotation, that angular momentum should be large enough to maintain autorotation after the onset of an equilibrium state. Moreover, the synchronized self-control mechanism is claimed as a cause for the sustenance of autorotation.