This two-part review article presents an overview of mechanics of pipes conveying fluid and related problems such as the fluid-elastic instability under conditions of turbulence in nuclear power plants. In the first part, different types of modeling, dynamic analysis, and stability regimes of pipes conveying fluid restrained by elastic or inelastic barriers are described. The dynamic and stability behaviors of pinned-pinned, clamped-clamped, and cantilevered pipes conveying fluid together with curved and articulated pipes will be discussed. Other problems such as pipes made of viscoelastic materials and active control of severe pipe vibrations are considered. This part will be closed by conclusions highlighting resolved and nonresolved controversies reported in literature. The second part will address the problem of fluid-elastic instability in single- and two-phase flows and fretting wear in process equipment such as heat exchangers and steam generators. Connors critical velocity will be discussed as a measure of initiating fluid-elastic instability. Vibro-impact of heat exchanger tubes and the random excitation by the cross-flow can produce a progressive damage at the supports through fretting wear or fatigue. Antivibration bar supports used to limit pipe vibrations are described. An assessment of analytical, numerical, and experimental techniques of fretting wear problem of pipes in heat exchangers will be given. Other topics related to this part include remote impact analysis and parameter identification, pipe damage-induced by pressure elastic waves, the dynamic response and stability of long pipes, marine risers together with pipes aspirating fluid, and carbon nanotubes conveying fluid.

Overview of Mechanics of Pipes Conveying Fluids—Part I: Fundamental Studies

https://www.repository.cam.ac.uk/bitstream/handle/1810/246007/Coriolis-draft-paper-V8.1-FMI-Larger-Fonts.pdf?sequence=1

Coriolis flowmeters: a review of developments over the past 20 years, and an assessment of the state of the art and likely future directions

A process parameter measurement device, and in particular a Coriolis mass flowmeter or vibrating tube densimeter, having a driver or drivers for inducing oscillation of at least one conduit. The drivers are attached at locations along the vibrating conduit selected to influence certain modes of interest. A driver is located near an area of maximum amplitude of a desired vibration mode and near an area of minimum amplitude of an undesired vibration mode. Various known experimental modal analysis or modeling techniques are used to determine the appropriate locations for one or more drivers. Multiple drivers located according to the present invention are used to influence, i.e. excite or suppress, multiple modes. In addition, multiple, separate drive circuits produce multiple, electronically isolated drive signals for delivering greater total power to the vibrating conduit.

Driver for oscillating a vibrating conduit

The simulation of coriolis meter response to pulsating flow using a general purpose f.e. code

An analytical study of the response of a simple Coriolis meter subjected to external mechanical vibrations and corresponding finite element studies of three commercially available meters are presented. These show that vibrations produce additional components in the meter sensor signals but that these components are only at the frequency of the vibrations. The results show that errors reported in vibration experiments, using any frequency except the meter drive frequency, are due to failure of the determination of the phase difference between the sensor signals. The results also show that external vibrations at the meter drive frequency produce a meter error regardless of the phase detection algorithm.

Effect of Mechanical Vibrations on Coriolis Mass Flow Meters

A finite element was developed for use in the vibration analysis of fluid-conveying pipes. The pipe was represented as a Timoshenko beam possessing stiffness and mass while the fluid was iciealized as incompressible and inviscid. With these simplifications the equations of motion were derived by the use of Hamilton's principle. Coriolis and centripetal terms in the equation of motion were the result of the fluid flowing in a moving frame of reference (Le. the vibrating pipe). Formulation of a two-node, Co continuous, fluid-conveying beam element followed from the weak form of the equation of motion. Inclusion of the Coriolis term is what made this element unique with respect to previous work. Verification of the element was accomplished by modeling Coriolis mass flowmeters and then predicting their frequency and relative phase delay for the mode of operation. Results compared favorably to experimental data for commercially available Coriolis mass flowmeters.

R. B. Garnett

Papers

A finite element for the vibration analysis of a fluid-conveying Timoshenko beam