Nonlinear dynamics of an extensible flexible pipe conveying fluid and subjected to external axial flow

In this paper, the nonlinear equations representing the dynamics of a slender flexible pipe conveying fluid and subjected to external axial flow are formulated using the extended Hamilton's principle. The internal flow is assumed to be steady, fully developed turbulent and approximated by a plug flow, while the external flow is represented by the induced hydrodynamic forces associated with friction, hydrostatic and inviscid components. The pipe centerline is considered to be extensible, and hence two coupled nonlinear equations of motion associated with longitudinal and transverse displacements are derived to describe the dynamics of the system. The developed model takes into account the fluid pressurization force and the tension in the pipe, which may be externally applied or associated with the frictional forces. For verification purpose, comparisons were performed, wherein the developed formulation was reduced to some published linear models. Numerical solutions were obtained for a case study of a double-pipe heat exchanger, wherein the effects of internal flow, external flow, flowrate, and radial gap on the dynamic characteristics of the system were addressed.