Dynamics of pipes conveying fluid of axially varying density

Abstract

The dynamics of a flexible slender pipe conveying fluid the density of which varies along the pipe-length is investigated in this paper analytically and numerically. Apart from its academic interest, this problem has application to the pipes used in mining methane crystals from the bottom of the ocean, and to more mundane situations involving piping conveying a gas at high speed or piping in a temperature environment varying along its length. Some CFD results are presented first, and then a linear analytical model is developed using a Hamiltonian approach. Pipes with clamped ends and cantilevered pipes are considered. The former lose stability by static divergence (buckling) and the latter by flutter, as for a constant-density fluid. The most important findings are two: (i) the density at the discharging end of the pipe influences stability most crucially; (ii) for cantilevered pipes, the magnitude of density variation strongly influences the mode and critical flow velocity of flutter.