Fluid-conveying Pipe Research Articles

Nonlinear Fractional-Order Dynamic Stability of Fluid-Conveying Pipes Constituted by the Viscoelastic Materials with Time-Dependent Velocity

Nonlinear Fractional-Order Dynamic Stability of Fluid-Conveying Pipes Constituted by the Viscoelastic Materials with Time-Dependent Velocity

Vibration of fluid-conveying pipe with nonlinear supports at both ends

Vibration of fluid-conveying pipe with nonlinear supports at both ends

On the impact process and stress field of functionally graded graphene reinforced composite pipes with a viscoelastic interlayer

In the paper, impact process of the fluid-conveying pipes composed of graphene-reinforced composite layers and a viscoelastic interlayer is studied. The bending stress field, midspan displacement and contact force are focused on. Based on the theory of high-order displacement field, the governing equations are derived through the Hamilton variational principle. To obtain the approximate solution for the impact dynamics of pipes, the Galerkin method is extended to expand the generalized displacements into the schemes of triangular series. Further, by utilizing the orthogonality of the trigonometric series, the differential equations of various orders for impact dynamics are established. The fourth-order Runge–Kutta method is introduced to the truncated solutions. Subsequently, the parameter sensitivity of the transient responses in the impact stage is emphatically discussed. It is revealed that the insensitive parameters to contact force and midspan displacement have a great influence on the stress field. Furthermore, the evolution characteristics of the bending normal stress field are highlighted. Numerical results illustrate that the attenuation characteristics of bending stress field are determined by the coupling effects of internal flow and structural features on structural stiffness and damping.

Vibration transmission characteristics analysis of the parallel fluid-conveying pipes system: Numerical and experimental studies

Complex parallel fluid-conveying pipes system may suffer from external excitation interference at local locations, and this interference signal will be transmitted to the target position along different paths, which involves the transmission of vibration. However, the vibration transmission characteristics analysis of the parallel pipes system has been rarely incorporated in the open research of the fluid-conveying pipe. Therefore, based on the improved transfer matrix method (ITMM) and power flow analysis, a vibration transmission model for the parallel fluid-conveying pipes system is developed for the first time. The developed model has natural advantages of simple operation and high computational efficiency in evaluating the vibration transmission characteristics of parallel fluid-conveying pipes since the power flow signals containing velocity and force information are well-matched with the state vector of the proposed model. Based on the proposed model, numerical and experimental methods are respectively utilized to investigate the vibration transmission characteristics from four different positions to the target position of the system, and the main transfer path is identified by collecting the power flow signal during the vibration transmission process. It is shown that the numerical results are basically consistent with the experimental results. Finally, the effects of clamp damping, fluid velocity, and pressure on vibration transmission characteristics of the parallel fluid-conveying pipes system are analyzed. The developed model can be more targeted to find the path that needs to reduce vibration in the parallel fluid-conveying pipes system, which provides a premise for the subsequent implementation of vibration reduction designs.

Natural Frequencies, Critical Velocity and Equilibriums of Fixed–Fixed Timoshenko Pipes Conveying Fluid

Natural Frequencies, Critical Velocity and Equilibriums of Fixed–Fixed Timoshenko Pipes Conveying Fluid

Critical velocity and supercritical natural frequencies of fluid-conveying pipes with retaining clips

Although retaining clips are widely used to constrain high-velocity fluid-conveying pipes, there are few studies on the influence of retaining clips on the supercritical vibration characteristics of the pipes. In this study, the vibration characteristics of the fluid-conveying pipe with retaining clip are firstly presented in the supercritical regime. According to the generalized Hamiltonian principle, the governing equation of the fluid-conveying pipe with the retaining clip is derived. When the flow velocity exceeds the critical velocity, the equilibrium configuration of the pipe becomes the non-trivial static equilibrium configuration. By coordinate transformation, the governing equation of the supercritical pipe around the non-trivial static equilibrium configuration is obtained. Emphasis is put on the effects of the clip stiffness and position on the critical flow velocity, equilibrium configuration and natural frequencies. It is found that variations in the retaining clip stiffness can cause different types of non-trivial equilibrium configurations. The natural frequencies will not be monotonic with the increasing clip stiffness in the supercritical flow. Furthermore, the two-span model of the pipe with the clip is obtained for verification. In conclusion, this work lays a foundation for the study of the dynamic response of the supercritical fluid-conveying pipe with retaining clip and can provide a reference for the analysis of the vibration characteristics of the clips and pipes system in engineering.

Vibration self-suppression of spinning fluid-conveying pipes composed of periodic composites

In this paper, a novel fluid-conveying phononic crystal (PC) pipe model is proposed. The pipe is composed of different materials arranged alternately, and an axially spinning motion is considered. The flexural wave motions along the orthogonally transverse directions trigger a two-dimensional (2D) PC structure. A planar spectral element (SE) model of the system is established, and the transverse free vibration and wave attenuation performance of such spinning periodic structure are explored thereby. The transfer matrix method is also utilized for validation. It is found that different pseudo Bragg band gaps (BGs) exist in the two transverse directions, while the effective BGs are actually located in their coupled regions, in which the vibration is truly self-suppressed. Such peculiar BG characteristic has not been theoretically revealed previously. Additionally, the spinning motion will reduce the effective BG regions of the periodic pipe. The impacts of the number of cells, flow velocity and component geometry on the natural frequencies and coupled BGs are also studied. The results obtained will provide theoretical basis and design reference for the potential applications of PC-type fluid-conveying devices.

Influence of Dry Friction on the Dynamics of Cantilevered Pipes Conveying Fluid

A cantilevered pipe conveying fluid can lose stability via flutter when the flow velocity becomes sufficiently high. In this paper, a dry friction restraint is introduced for the first time, to evaluate the possibility of improving the stability of cantilevered pipes conveying fluid. First, a dynamical model of the cantilevered pipe system with dry friction is established based on the generalized Hamilton’s principle. Then the Galerkin method is utilized to discretize the model of the pipe and to obtain the nonlinear dynamic responses of the pipe. Finally, by changing the values of the friction force and the installation position of the dry friction restraint, the effect of dry friction parameters on the flutter instability of the pipe is evaluated. The results show that the critical flow velocity of the pipe increases with the increment of the friction force. Installing a dry friction restraint near the middle of the pipe can significantly improve the stability of the pipe system. The vibration of the pipe can also be suppressed to some extent by setting reasonable dry friction parameters.

Nonlinear analysis of L-shaped pipe conveying fluid with the aid of absolute nodal coordinate formulation

By adopting the absolute nodal coordinate formulation, a novel and general nonlinear theoretical model, which can be applied to solve the dynamics of combined straight-curved fluid-conveying pipes with arbitrary initially configurations and any boundary conditions, is developed in the current study. Based on this established model, the nonlinear behaviors of a cantilevered L-shaped pipe conveying fluid with and without base excitations are systematically investigated. Before starting the research, the developed theoretical model is verified by performing three validation examples. Then, with the aid of this model, the static deformations, linear stability and nonlinear self-excited vibrations of the L-shaped pipe without the base excitation are determined. It is found that the cantilevered L-shaped pipe suffers from the static deformations when the flow velocity is subcritical, and will undergo the limit-cycle motions as the flow velocity exceeds the critical value. Subsequently, the nonlinear forced vibrations of the pipe with a base excitation are explored. It is indicated that period-n, quasi-periodic and chaotic responses can be detected for the L-shaped pipe, which has a strong relationship with the flow velocity, excitation amplitude and frequency.

Phononic Band Gap and Free Vibration Analysis of Fluid-Conveying Pipes with Periodically Varying Cross-Section

Phononic crystals (PCs) are a novel class of artificial periodic structure, and their band gap (BG) attributes provide a new technical approach for vibration reduction in piping systems. In this paper, the vibration suppression performance and natural properties of fluid-conveying pipes with periodically varying cross-section are investigated. The flexural wave equation of substructure pipes is established based on the classical beam model and traveling wave property. The spectral element method (SEM) is developed for semi-analytical solutions, the accuracy of which is confirmed by comparison with the available literature and the widely used transfer matrix method (TMM). The BG distribution and frequency response of the periodic pipe are attained, and the natural frequencies and mode shapes are also obtained. The effects of some critical parameters are discussed. It is revealed that the BG of the present pipe system is fundamentally induced by the geometrical difference of the substructure cross-section, and it is also related to the substructure length and fluid–structure interaction (FSI). The number of cells does not contribute to the BG region, while it has significant effects on the amplitude attenuation, higher order natural frequencies and mode shapes. The impact of FSI is more evident for the pipes with smaller numbers of cells. Moreover, compared with the conventional TMM, the present SEM is demonstrated more effective for comprehensive analysis of BG characteristics and free vibration of PC dynamical structures.

Wave Propagation for Axisymmetric Wave Motion in Buried Pipes Conveying Viscous Flowing Fluid

This work investigated the wave propagation characteristics of buried pipes conveying viscous flowing fluid under axisymmetric wave motion, where the coupling pipe–soil and pipe–fluid effects are both taken into account. The fluid was assumed to be viscous, isotropic, and irrotational. The coupled equations of wave motion were obtained based on Love’s thin shell theory. The analytical fluid-dominated (s=1) wave dispersion relations of buried fluid-conveying pipes are given. In addition, studies were carried out to scrutinize the effects of the soil, flow velocity, fluid viscosity, fluid mass density, and pipe geometry on wave propagation of buried fluid-conveying pipes. Results show that the higher fluid velocity can lead to larger phase velocity and smaller wave attenuation in buried pipes. In addition, viscous fluid leads to larger wave attenuation compared with ideal fluid.

Nonlinear vibration analysis of functionally graded material tubes with conveying fluid resting on elastic foundation by a new tubular beam model

In this paper, nonlinear free vibration analysis of shear deformable functionally graded material (FGM) tubes conveying fluid with immovable support conditions resting on a Pasternak-type foundation is presented. Based on Hamilton’s principle, the equations of motion and boundary conditions are obtained by using a new high-order shear deformation tubular beam model with von Kármán nonlinearity and the exact expression of curvature, in which contributions of fluid velocity to the kinetic energy and body forces are also considered. The differential quadrature method (DQM) is employed to determine the nonlinear frequencies and amplitude–frequency responses of fluid-conveying FGM tubes with different boundary conditions. A detailed parametric study is conducted to analyze the influences of different types of boundary conditions, geometric and physical properties. The numerical results reveal that the geometrical and physical properties, including elastic foundation, boundary conditions and flow velocity in the fluid-conveying pipes are crucial factors on their dynamical behavior.

Dynamics and enhanced stability properties of slender leaching tubings in salt cavern storage with a Y-type manifold fitted at free downstream end

Currently, the construction of salt cavern storages in China generally adopts solution mining technology with single-well convection and using a diesel cushion, however, leaching tubing is occasionally subjected to excessive bending and/or breaking during leaching process. Leaching tubing failure leads to the cavern shape being out of control or even scrapped. In this paper, regarding the leaching tubing as vertical hanging pipes conveying fluid, the dynamic equation of the leaching tubing with a Y-type manifold installed at the lower free end is established. The equation of motion is solved by means of Galerkin's truncation approximation method, and the dynamic response of the leaching tubing and the characteristics of the enhanced stability of the manifold are investigated. Since the downstream Y-type manifold has a select of the inclination angle, it is found through theoretical calculations that the flutter instability flow velocity of the fluid-conveying pipe can be conveniently controlled. The physical model experiment verifies that the Y-type manifold has a better enhancement effect on the stability of the leaching tubing. The proposed Y-type manifold may be helpful for the design and improvement of leaching tubing systems in the construction of salt cavern storage and salt mining.

Investigating impact-induced vibrations of fluid-conveying elastic pipes considering Hertz theory

This work tends to investigate the dynamic behavior of fluid-conveying pipes under the impact force caused by a ball collision. The contact force depends on parameters such as the ball and pipe mass, and the relative incidence velocity. In this paper, based on Hertz theory, the collision force is added to the fluid-conveying pipes governing equation of vibration. The impact force is assumed to be harmonic as a simplification, and the maximum impact force and frequency of its variations are obtained by considering two modes of pipe vibration and the steepest descent optimization method. Afterwards, several computer simulations are performed to investigate the effects of the fluid velocity in the pipe, relative impact velocity, the pipe material, and the ball radius on the maximum impact force. For validation, the accuracy of the results is verified through finite element analysis. Finally, the influences of the mentioned parameters on the amplitude and frequency of the pipe vibrations caused by collision of the ball is investigated. It was observed that the maximum impact force and the contact time did not change by the fluid velocity, while the pipe post-impact vibrations were largely affected by the fluid velocity.

Vibration and Snapthrough of Fluid-Conveying Graphene-Reinforced Composite Pipes Under Low-Velocity Impact

There exists complex fluid–structure coupling vibration in the fluid-conveying pipes under the combined actions of internal flow and external loads in the aircraft. The impact dynamic behaviors of the flow-inducing pre- and postbuckled pipes are studied with the surfaces made of functionally graded graphene-reinforced composites and an interlayer made of isotropic viscoelastic materials. It is assumed that the fluid is nonrotating, nonviscous, incompressible; and steady; and the pipe is simply supported at both ends. Under the framework of refined displacement fields, a reduced constitutive relation is developed. On this basis, the nonlinear governing equations are derived through the Hamilton variational principle. The two-step perturbation–Galerkin integral is extended to obtain the equilibrium paths as the initial configurations of the pipes for impact studies. The fourth-order Runge–Kutta method is employed to numerically obtain the contact force and the pipe vibration responses. The effects of flow velocity, impact velocity, structural material, and geometric factors on the dynamic responses are discussed. The numerical results reveal that even the parameters which have little influence on the contact force may have a great effect on the vibration response of the fluid-conveying pipe.

Prediction of Flow Velocity from the Flexural Vibration of a Fluid-Conveying Pipe Using the Transfer Function Method

This study presents a method to predict the flow velocity in a fluid-conveying pipe using vibration signals from the pipe surface. The flexural vibration of a fluid pipe is investigated through wave propagation. The wavenumbers and mode shapes of the pipe are determined based on its mechanical properties and flow velocities. The transient components of wavenumbers at low frequencies vary and converge on all values at higher frequencies as the flow velocity is increased. While the stationary fluid pipe exhibits symmetrical mode shapes, pipes with increasing flow velocities exhibit an asymmetric mode shape distribution skewed on one side of the axis. The resonant frequencies shift to the low frequency side as the flow velocity increases. The analytical results of the vibration analysis are used in the transfer function method to predict the flow velocities. To validate the accuracy of the prediction method, numerical vibration signals simulated by the finite element model are used. The actual input flow velocity is compared with the numerical results regarding the same to gauge the accuracy of the prediction method. This method can be used to monitor the flow rate without using flow meters, and thus protect pipelines from sudden malfunction.

Nonlinear vibration analysis of a supercritical fluid-conveying pipe made of functionally graded material with initial curvature

In the view of the dynamic behaviors of fluid-conveying pipes become more complex in the supercritical case that it is quite common in engineering, we concentrate on the supercritical fluid-conveying pipe composed of functionally graded material and study the nonlinear vibration for the first time to provide an insight reference for the possible applications of the practice pipe. Firstly, the nonlinear dynamic equations are deduced by Hamiltonian’s principle based on the Euler-Bernoulli and Timoshenko theories. Then the non-trivial equilibrium expressions and the critical fluid velocities are derived analytically for the straight pipe and pipe with initial curvature. For the straight FGM pipe, we conclude that the critical fluid velocity of the Euler-Bernoulli model is larger than that of the Timoshenko model. For the FGM pipe with initial curvature, it is shown that the equilibrium deformations of Euler–Bernoulli model are larger than those of Timoshenko model. For a larger initial curvature, the critical fluid velocity becomes smaller, and the bifurcation occurs earlier for both pipe models. Moreover, Galerkin method is used to analysis the frequencies of the supercritical fluid-conveying FGM Timoshenko pipes based on the buckling configuration. We obtain that the frequencies increase as the power-law exponent and initial tension increase.

Non-trivial equilibriums and natural frequencies of a slightly curved pipe conveying supercritical fluid

Despite extensive use of curved pipes conveying high-speed fluids in many engineering fields, few researches have been conducted on the supercritical dynamics of curved pipes to explore new dynamic behavior. For the first time, this paper investigates the vibration characteristics of a slightly curved pipe conveying fluids in a supercritical range. The generalized Hamilton's principle is adopted to derive the governing equation. The non-trivial equilibriums and the critical flow velocities are then analytically obtained. The analytical predictions agree well with the numerical results obtained using the finite difference method and the differential quadrature element method. By introducing the coordinate transformation, the governing equation of the curved pipe is established for the vibration about the non-trivial equilibrium position. The natural frequencies of the pipe are obtained by the Galerkin truncation method and verified with the discrete Fourier transform. It is found that the critical velocities and the natural frequencies are highly dependent on the initial curvature. The research results show an interesting phenomenon that the natural frequency of the curved pipe may increase as the pipe length increases, but may not in monotonous manner. The obtained results provide useful information for further studies of fluid-conveying pipes with geometric imperfection.

Vibration analysis of post-buckled fluid-conveying functionally graded pipe

The vibration of post-buckled fluid-conveying pipe made of functionally graded material is analyzed. The pipe material properties are assumed to be graded in the thickness direction according to power-law distribution. An exact solution is obtained for the post-buckling deformation of the fluid-conveying functionally graded pipe with various boundary conditions. The linear vibration problem is solved around the first buckled configuration and the natural frequencies of the three lowest vibration modes are obtained. The influences of power-law exponent, initial tension, fluid density and fluid velocity on the static deflection and free vibration frequencies are studied.

Measurement Method for Fluid Pressure Fluctuation in Fluid-Conveying Pipe Using PVDF Piezoelectric Film Sensor

As a representative fluid-transporting system, fluid-conveying pipes play an essential role in many fields. For a fluid-conveying pipe system in operation, fluid pulsation in pipes contains much information about fluid flow parameters (flow velocity, fluid pressure, etc.). Therefore, the measurement of fluid pulsation is important for understanding the internal fluid flow. To use polyvinylidene fluoride (PVDF) piezoelectric film sensors to indirectly measure the pressure fluctuation of the internal fluid, we simulated a fluid-conveying pipe with PVDF piezoelectric film sensors attached to the outer pipe wall. The simulation results showed that the variation of voltage signal of PVDF, circumferential stress and strain of the pipe wall, and the pressure fluctuation of internal fluid were highly positively correlated, which proved that the PVDF piezoelectric film sensor can be applied to indirectly measure the pressure fluctuation of internal fluid. We also studied the influences of flow velocity pulsation and mechanical vibration caused by the pipeline pump during operation. It is found that the flow velocity pulsation had little influence on the measurements of the variation of circumferential stress and strain of the pipe wall and the internal fluid pressure fluctuation. When both ends of the pipe were fixed by hoops, mechanical vibration had little influence on the measurement of the variation of circumferential stress and strain of the pipe wall as well as the fluid pressure fluctuation. Finally, simulation results were verified by experiments.