A reduced-order model of a cantilevered extensible pipe conveying fluid: an investigation based on a consistent mass conservation approach via the extended Hamilton’s principle for nonmaterial volumes

Abstract

The oscillatory motion in flexible pipes due to internal flow constitutes one of the classical problems of fluid–structure interactions. Studies on the pipe dynamics must consider two features: (i) they are open systems, in which there is mass exchange through its boundaries, and (ii) the existence of dynamic instabilities, so there is a critical internal flow velocity above which the system becomes unstable. In this work, a nonlinear reduced-order model of a planar cantilevered pipe conveying fluid is derived via the extended Hamilton’s principle for nonmaterial volumes. The derivation considers the influence that the axial strain rate of the pipe must have in the internal plug flow velocity so that the proposed model becomes fully consistent in terms of conservation of mass. This condition makes the relative velocity of the flow explicitly dependent, not only on the instantaneous configuration of the pipe, but also on its rate of change, leading to the emergence of new terms in the equations of motion. Within the formalism of the extended Hamilton’s principle for nonmaterial volumes, some of these terms can be interpreted as being related to the “transport of kinetic energy”, which has not been discussed in previous studies. In order to assess the dynamic behavior of the proposed model, root loci graphs and parametric diagrams are obtained and comparisons are performed with selected models found in the literature. Also, the resulting nonlinear equations of motion are numerically integrated to show the dynamic behavior predicted by the linear analysis.