Study on the stability of multi-span U-shaped pipe conveying fluid with complex constraints

The vibration and instability of U-shaped pipe can be induced by the internal flow. This study examines the stability of multi-span U-shaped pipe conveying fluid with complex constraints. A two-dimensional straight pipecurve fluid theory is proposed, and the corresponding straight pipe-curve fluid element is constructed. Based on the proposed element and straight pipe-straight fluid element, the finite element model of in-plane vibration of multi-span U-shaped pipe conveying fluid is built, and the stability of system with complex constraints is showed. The results show that: (i) When U-shaped pipe is multi-span and flow velocity is large, a large bending deformation occurs, which could improve the stiffness of the system. Partial frequencies of the system increase with increasing the flow velocity under this condition, while the frequencies of the system decrease with the increase of flow velocity before the appearance of this phenomenon. (ii) In the considered velocity range, the system is stable when all constraints are valid. However, instability occurs when one end is free. When the length of the span with a free end is less than or equal to the maximum length of the spans with constrains at both ends, the system appears divergence or flutter depending on the location and the constraints of the maximum length span with constraints at both ends. When the length of the span with a free end is greater than that of other spans, the unstable pattern of the system is flutter.