Dynamics and Stability of a Pipe Conveying Fluid Immersed in a Quiescent Viscous Fluid

This paper examines the dynamics and stability of a pipe conveying fluid, immersed in a quiescent viscous fluid. A linear theoretical model is developed by considering all the sources originating from the external fluid. The resulting partial differential equation is rendered dimensionless and then discretized using the Galerkin method. The first-order system of ordinary differential equations is then solved for the eigenvalues as the flow velocity is varied. The flutter speed and frequency are obtained for three different flexible pipes conveying water and immersed partially or fully in water. It is found that depending on the pipe parameters, the added mass or buoyancy due to the surrounding fluid can have the most significant effect on the flutter speed and frequency. On the other hand, the impact of the viscous drag appears to be marginal. Some numerical results are also obtained when the fluid surrounding the pipe is 100 times less/more viscous than water. It is shown that, depending on the system parameters, immersing the pipe partially or fully in a highly viscous fluid can make it dynamically more unstable.