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.

Size-Dependent Stability of a Cantilevered Piezoelectrically Actuated Micropipe Conveying Fluid

Size-dependent effects of a cantilevered piezoelectrically actuated micropipe conveying fluid are investigated. Based on the modified strain gradient beam theory, the model of system is obtained using Hamilton's principle. The motion equation is discretized into ordinary differential equations by Generalized Differential Quadrature Method (GDQM). A stability analysis of the system is completed through eigenvalue analysis. Numerical results show the effect of geometrical shape size, and length scale parameters on critical flow velocity, and critical voltage. Results prove that the modified strain gradient theory (MSGT) has a higher critical flow velocity and critical voltage than predicted by modified couple stress theory (MCST) and classical theory (CT).

Stability and Modal Conversion Phenomenon of Pipe-in-Pipe Structures with Arbitrary Boundary Conditions by Means of Green’s Functions

In this paper, a closed-form frequency equation of the pipe-in-pipe (PIP) structure with arbitrary boundaries is obtained. The frequency equation is derived from Green’s function of the transverse forced vibration of the PIP structure and takes into account the effects of internal two-phase flow and axial pressure. The reliability of the method in this paper is proved by comparison with the published literature. In the numerical discussion part, the PIP structures with clamped-clamped, clamped-free, and elastic boundary conditions are used as examples to discuss. The effects of equivalent stiffness coefficient, internal flow velocity, and gas volume fraction on the stability of PIP structure are studied. The results show that the stability of the PIP structure is better than that of the single-pipe structure, and the greater the equivalent stiffness coefficient of the elastic layer, the higher the critical flow velocity of the structure. In addition, a modal conversion phenomenon existing in the PIP structure is discovered. There are different forms of modal conversion for different boundary conditions, and the modal conversion makes the order of instability of the PIP structure different from that of a single-pipe. The conclusion of this paper has positive significance for the dynamic research of PIP structure.

Particle removal by two-phase filtration flow from a porous medium under wave action

The paper discusses the influence of wave action on the process of detachment and removal of particles from a porous body by a two-phase filtration flow. When modeling this process, the problem of the influence of the wave field on the force under the action of which the particles are detached from the pore walls is solved. For the first time, a pore-size distribution function is used for its solution. An expression for the critical flow velocity under wave action has been obtained. Critical frequency value of wave action depends on the capillary radius and the smaller the capillary radius is, the higher frequency is needed to enhance the effect of the action. At higher frequency of oscillation the peak of maximum change in the thickness of the sedimentary layer is shifted towards the pores of small radius. To maintain the influence of the wave field on the filtration parameters of the porous medium, the wave action should be carried out at a dynamically changing frequency range to increase the coverage of the effect of as many pores as possible. It is shown that particle removal during wave action increases due to the action of inertial forces, which reduce the influence of forces holding the particles on the pore surface.

Numerical Study of Thermal Effect on the Stability of Carbon Nanotubes Resting on a Viscoelastic Foundation Subjected to Magnetic Field

Carbon nanotubes (CNTs) have emerged as efficient tools in drug delivery systems; therefore, it is essential to refer to the importance of the magnetic field, in addition to the fluid flow on the dynamic behavior of CNTs. Additionally, in such medical applications, the actual working environment of nanotube often contains temperature changes, and CNTs are surrounded by soft tissues with viscoelastic mechanical properties. In this study, the vibrational behavior of CNTs conveying magnetic-fluid flow and resting on a viscoelastic foundation is investigated under various temperature variations. To incorporate the influence of slip velocity at the nanoscale, a correction factor is employed on the basis of the Beskok–Karniadakis model. The nanotube is modeled by the Euler–Bernoulli beam theory, and governing equations of motion are derived by implementing Hamilton’s principle based on Eringen’s nonlocal elasticity theory. Results indicate that by applying a magnetic field with an intensity of 30[Formula: see text]T, the dimensionless critical flow velocity increases from 4.345 to 12.603. Also, the critical flow velocity shows an increase from 4.345 to 5.854 in the presence of a viscoelastic foundation. Furthermore, a temperature variation equal to 20[Formula: see text]K reduces the critical flow velocity dramatically from 4.345 to 1.802 at low temperatures, while an increase from 4.345 to 5.443 is observed at high temperatures. Consequently, while the magnetic field and the viscoelastic foundation affect the system stability, the temperature variation may improve or deteriorate the stability. Therefore, to plan for a medical application, the inclusion of temperature variation is required.

Stabilization of a cantilever pipe conveying fluid using electromagnetic actuators of the transformer type

The article presents an investigation of the stabilization of a cantilever pipe discharging fluid using electromagnetic actuators of the transformer type. With the flow velocity reaching a critical value, the straight equilibrium position of the pipe becomes unstable, and self-excited lateral vibrations arise. Supplying voltage to the actuators yields two opposite effects. First, each of the actuators attracts the pipe, thus introduces the effect of negative stiffness which destabilizes the middle equilibrium. Second, lateral vibrations change the gap in magnetic circuits of the actuators, which leads to oscillations of magnetic field in the cores and the electromagnetic phenomena of induction and hysteresis that impede the motion of the pipe. The combination of these two non-linear effects is ambiguous, so the problem is explored both theoretically and experimentally. First, a mathematical model of the system in form of a partial differential equation governing the dynamics of the pipe coupled with two ordinary differential equations of electro-magnetodynamics of the actuators is presented. Then, the equation of the pipe’s dynamics is discretized using the Galerkin procedure, and the resultant set of ordinary equations is solved numerically. It has been shown that the overall effect of actuators action is positive: the critical flow velocity has been increased and the amplitude of post-critical vibrations reduced. These results have been validated experimentally on a test stand.

Coupled Flow-Seepage–Elastoplastic Modeling for Competition Mechanism between Lateral Instability and Tunnel Erosion of a Submarine Pipeline

The instability of a partially embedded pipeline under ocean currents involves complex fluid–pipe–soil interactions, which may induce two typical instability modes; i.e., the lateral instability of the pipe and the tunnel erosion of the underlying soil. In previous studies, such two instability modes were widely investigated, but separately. To reveal the competition mechanism between the lateral instability and the tunnel erosion, a coupled flow-seepage–elastoplastic modeling approach was proposed that could realize the synchronous simulation of the pipe hydrodynamics, the seepage flow, and elastoplastic behavior of the seabed soil beneath the pipe. The coupling algorithm was provided for flow-seepage–elastoplastic simulations. The proposed model was verified through experimental and numerical results. Based on the instability criteria for the lateral instability and tunnel erosion, the two instability modes and their corresponding critical flow velocities could be determined. The instability envelope for the flow–pipe–soil interaction was established eventually, and could be described by three parameters; i.e., the critical flow velocity (Ucr), the embedment-to-diameter ratio (e/D), and the non-dimensional submerged weight of the pipe (G). There existed a transition line on the envelope when switching from one instability mode to the other. If the flow velocity of ocean currents gets beyond the instability envelope, either tunnel erosion or lateral instability could be triggered. With increasing e/D or concurrently decreasing G, the lateral instability was more prone to being triggered than the tunnel erosion. The present analyses may provide a physical insight into the dual-mode competition mechanism for the current-induced instability of submarine pipelines.

Hybrid Scour Depth Prediction Equations for Reliable Design of Bridge Piers

Numerous models have been proposed in the past to predict the maximum scour depth around bridge piers. These studies have all focused on the different parameters that could affect the maximum scour depth and the model accuracy. One of the main parameters individuated is the critical velocity of the approaching flow. The present study aimed at investigating the effect of different equations to determine the critical flow velocity on the accuracy of models for estimating the maximum scour depth around bridge piers. Here, 10 scour depth estimation equations, which include the critical flow velocity as one of the influencing parameters, and 8 critical velocity estimation equations were examined, for a total combination of 80 hybrid models. In addition, a sensitivity analysis of the selected scour depth equations to the critical velocity was investigated. The results of the selected models were compared with experimental data, and the best hybrid models were identified using statistical indicators. The accuracy of the best models, including YJAF-VRAD, YJAF-VARN, and YJAI-VRAD models, was also evaluated using field data available in the literature. Finally, correction factors were implied to the selected models to increase their accuracy in predicting the maximum scour depth.

Experimental Analysis of Incipient Motion for Uniform and Graded Sediments

So far, few studies have focused on the concept of critical flow velocity rather than bed shear stress for incipient sediment motion. Moreover, few studies have focused on sediment mixtures (graded sediment) and shape rather than uniform sediment for incipient motion condition. Different experiments were conducted at a hydraulic laboratory at the University of Guilan in 2015 to determine hydraulic parameters on the incipient motion condition. The aim of this study is to conduct a comparison between uniform and graded sediments, and a comparison between round and angular sediments. Experiments included rounded uniform bed sediments of 5.17, 10.35, 14 and 20.7 mm, angular uniform sediment of 10.35 mm, and graded sediment. Results demonstrated that angular sediment has a higher critical shear velocity than rounded sediment for incipient motion. Results also showed that for a given bed sediment, although critical shield stress and relative roughness increased with the bed slope, the particle Froude number (based on critical velocity) decreased. In terms of the sediment mixture, the critical shear stress (Vc*) was higher for the graded sediment than for the three finer uniform sediment sizes. The finer fractions of the mixture have a higher particle Froude number than their corresponding uniform sediment value, while the coarser fractions of the mixture showed a lower stability than their corresponding uniform sediment value. Results demonstrated that the reduction in the particle Froude number was more evident in lower relative roughness conditions. The current study provides a clearer insight into the interaction between initial sediment transport and flow characteristic, especially particle Froude number for incipient motion in natural rivers where stream beds have different gravel size distribution.