Abstract
This paper studied the nonlinear vibrations of top-tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were derived based on Hamilton’s mechanics, with the centerline assumed to be extensible. Using the multiple-scale perturbation technique, natural frequencies, mode shapes, and first order approximate solutions of the steady-state response of the pipes were obtained. The multiple-scale assessment reveals that at some frequencies the system is uncoupled, while at some frequencies a 1:2 coupling exists between the axial and the transverse frequencies of the pipe. Nonlinear frequencies versus the amplitude displacement of the cantilever pipe, conveying two-phase flow at super-critical mixture velocity for the uncoupled scenario, exhibit a nonlinear hardening behavior; an increment in the void fractions of the two-phase flow results in a reduction in the pipe’s transverse vibration frequencies and the coupled amplitude of the system. However, increases in the temperature difference, pressure, and the presence of top tension were observed to increase the pipe’s transverse vibration frequencies without a significant change in the coupled amplitude of the system.
Highlights
Two-phase flow is a common flow phenomenon in various industrial pipes: in nuclear heat exchangers, pipes in process plants, thermal plants, subsea oil and gas explorations, and many more
In spite of the vast occurrences of two-phase flow in pipes, most of the existing publications on the flow-induced vibrations of pipes conveying fluids focus on the fluidelastic instability of pipes conveying single-phase flow
The pioneering work by Ghayesh et al [6] studied the nonlinear dynamics of a cantilevered extensible pipe conveying fluid, with equations of motion of the coupled transverse and longitudinal displacements derived using the Lagrange equations for a system containing non-material volumes, and highlighted that, to inextensible pipe, an extensible pipe elongates in the axial direction as the flow velocity increases
Summary
Two-phase flow is a common flow phenomenon in various industrial pipes: in nuclear heat exchangers, pipes in process plants, thermal plants, subsea oil and gas explorations, and many more. Some researchers working on the fluidelastic instability of pipes conveying fluids have adopted this technique to resolve the nonlinear dynamics of the pipes, including the works of Enz [19] on a simple supported straight pipe using perturbation analysis with a multiple time-scaled method and comparison with measurements made by Coriolis flowmeters; the study by Xiao-Dong et al [20] on the dynamic stability -supported viscoelastic pipe in transverse vibration for conveying pulsating fluid; the study on the transverse vibrations of tension pipes conveying fluid with time-dependent velocity using the multiple-scale perturbation technique by Oz and Pakdemirli [21]; and the study on the analysis of nonlinear vibrations of a pipe conveying an ideal fluid by Sinir and Demir [22] Most of these existing publications on the nonlinear dynamics of a cantilevered pipe conveying fluid were focused on single-phase flow, resolving the governing equations using various methods as highlighted in the review of literature. The governing equation of motion for the nonlinear coupled axial and transverse vibrations of a cantilever pipe conveying two-phase flow is derived and resolved by imposing the multiple-scale perturbation technique directly to the system equations (direct-perturbation method)
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