Dynamic characteristics and stability of pipe-in-pipe system conveying two- phase flow in thermal environment

Pipe-in-pipe (PIP) systems are utilized widely in modern petroleum industry owing to their good insulation effect. In present work, a novel mathematical model for the free vibration of the fluid-conveying cantilevered PIP system considering thermal effect and two-phase flow is proposed. The insulation layer connecting two concentric pipes is simplified as the distributed springs and dampers here. The governing equation of the pipe system is then derived using Hamilton's principle based on Euler-Bernoulli beam theory. Then the Galerkin method is applied to the free vibration analysis. In the numerical section, parametric analysis is performed to elucidate the effects of different physical factors, such as environment temperature, equivalent stiffness and damper of the insulation layer, structural damping, two-phase flow, and axial load on the dynamic characteristic and stability of the PIP system through the forms of Argand diagram, stability map, and time history diagram. The results show that the PIP system has an advantage over a single fluid-conveying pipe in terms of stability considering thermal effect, axial load, and structural damping. Besides, different from single pipe, two different frequencies are found for each vibration mode, and two-pipe coupled flutter instability occurs to the PIP system as the fluid velocity exceeds the critical fluid velocity. The theoretical work is helpful to improve the analysis and design of the PIP system with consideration of internal two-phase flow and environmental temperature.