Dynamic evolution of Strouhal number in flexible pipes coupling rotation

The dynamic response evolution mechanism of the rotating and non-rotating pipe (RP-NRP) system remains inadequately explored, and there is a lack of a precise Strouhal-Reynolds (St -Re) model to effectively characterize the rotational and interference effects. To address this research gap, hydrodynamic experiments were conducted on flexible RP-NRP systems with varying spacing and angles. The spacing ratios ranged from 4-12 times the diameter, and the angle ranged from 0 degrees to 270 degrees. The experimental results reveal that St numbers in tandem systems are lower than those of the isolated pipe due to wake feedback inhibition and shadowing effect. Conversely, St numbers in side-by-side systems consistently exceed those of the isolated pipe due to the side-wall effect. Notably, the staggered systems exhibit fluctuations in St numbers, which are highly sensitive to the incident angle. A novel St -Re model accounting for rotation and interference effects was proposed based on the experimental data. The proposed model (Strms = 9.4 x 10-10 Re2-2.05 x 10-5 Re+0.26) demonstrates a "dumbbell-shaped" pattern, which can be categorized into regions of interference enhancement and attenuation based on the StRms curve. Furthermore, the critical Reynolds number of 6400 identifies the strong regions of interference enhancement and attenuation. Within these regions, 45.18 % of St numbers fell into the enhanced area of interference while 54.82 % in the weakened area. The St numbers of flexible pipes, accounting for rotation and interference effects, are lower than those of fixed cylinders and non-rotating vibrating flexible pipe systems. Additionally, the dominant frequencies are weakened in the 0 degrees, 180 degrees, and 135 - 180 degrees RP-NRP systems, these angles could guide the layout of the riserless drill string and drilling fluid recovery riser.