Numerical simulation about the second instability in the two-dimensional laminar flow past a rotating circular cylinder

A numerical simulation method was taken to simulate the state that the flow was changing with Reynolds number and speed when a rotating circular cylinder was placed in a uniform stream. A comprehensive description was made to analyze the second instability state led by a rotating circular cylinder. The Reynolds numbers were set as Re=60, 80, 100, 130, 160, 240 with an increasing rotational speed until the flow was stable again. The different effect was analyzed and compared for the aerodynamic forces on the surface of cylinder, vorticity and the flow field around the cylinder in the first and second region of instability. The results show that when the flow is unstable with low rotational speeds, the critical rotational speeds are respectively α=1.40, 1.70, 1.80, 1.85, 1.90, 1.91 for the Reynolds numbers Re=60, 80, 100, 130, 160, 240. And in higher rotational speeds, the flow turns into unstable again and the related speed ranges are 5.1<α<5.6, 4.9<α<5.4, 4.6<α<5.2, 4.4<α<5.0, 4.3<α<4.9, 4.2<α<5.7 respectively.