An Analytical Study of the Dynamics of Pipes Conveying Fluid of Axially Varying Density

This paper investigates the dynamics of a slender, flexible pipe, conveying a fluid whose density varies axially along the length of the pipe. Specific applications for this system have appeared in the mining of submerged methane crystals [1], but a general interest also exists due to more common situations in which fluid density changes along the length of the pipe, such as when a gas is conveyed at high velocity. Therefore, following a brief review of related work and of the well-established theory concerning pipes conveying fluid of constant density, the current problem is approached from an analytical perspective. In particular, a linear model describing the system is derived using a Hamiltonian approach, for the cases of (i) a pipe clamped at both ends and (ii) a cantilevered pipe, and results obtained using a Galerkin approach. Ultimately, it is shown that, in both the cantilevered and clamped-clamped cases, the behaviour of the system is similar to that of a pipe conveying fluid of constant density — that is, loss of stability by flutter and buckling respectively — save for two crucial differences. The first and most important is that it is the density at the discharging end which has the most significant effect on the critical flow velocities, rather than any other. Second, in the case of a cantilevered pipe, the magnitude of the density change can strongly influence in which mode the system loses stability, thereby also impacting the critical flow velocities. The specifics of both these effects are addressed in the paper.