Sub-harmonic Lock-in Of The Downstream Cylinder Wake With The Upstream One For Different Diameter Cylinders

Flow around circular cylinders is a classical problem in fluid dynamics, which has been studied for more than 100 years. It is widely applied in engineering field, for example, deep sea cables, piers of road bridge, remote transmission wires and the factory chimneys. As flow around a circular cylinder, the alternating vortex will shed from the cylinder which may cause the structure damage when the vertex shedding frequency equals to vibration frequency of the cylinder. Flow around two tandem circular cylinders is the fundamental type which is very different from the flow around an isolated single cylinder and has a significant value for the basic investigation and engineering applications.This dissertation mainly studies conditions for the occurrence of sub-harmonic lock-in and the corresponding flow characteristics around two tandem cylinders,including the significant parameters such as vortex shedding frequency(St), time-mean drag coefficient(CD), fluctuating drag coefficient(CD?), fluctuating lift coefficient(CL?)and flow structures. The diameter ratio d/D = 0.25 ~ 1.0 and the spacing ratio L/d = 5.5 ~ 20(L is the length from the center of upstream circular tube to downstream forward stagnation point, d is the diameter of the upstream cylinder, D is the diameter of downstream one), while Reynolds number Re = 0.8 × 104~ 2.42 × 104.With the varying L/d and Re, the phenomenon of sub-harmonic lock-in, when vortex shedding frequency of the downstream cylinder is half of the one of the upstream cylinder for d/D = 0.6 and d/D = 0.65, can be observed. The emergence of double relationship could not be observed constantly, as it is highly dependent on Re and L/d.For d/D = 1.0 and L/d = 5.5, two cylinders get the same vortex shedding frequency in the co-shedding regime, which means that lock-in exists for this case. For d/D = 0.25 and L/d = 5.5, vortex shedding frequency is also identical for both cylinders, as it is in the reattachment regime, which means that lock-in is not observed. In conclusion, theflow maps for sub-harmonic lock-in and lock-in at different Re are obtained, which can clearly summarize the occurrence conditions.