Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

In-plane forced vibration of curved pipe conveying fluid by Green function method

The Green function method （GFM） is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.

HOPF BIFURCATION OF A NONLINEAR RESTRAINED CURVED PIPE CONVEYING FLUID BY DIFFERENTIAL QUADRATURE METHOD

This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support.The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration.The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method.The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter, nonlinear spring stiffness.Based on this,the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness.The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.

Flow-Induced Vibration of A Nonlinearly Restrained Curved Pipe Conveying Fluid

Investigated in this study is the flow induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system under consideration. The spatial coordinate of the system is discretized by DQM (differential quadrature method). On the basis of the boundary conditions, the dynamic equation is solved by the Newton Raphson iteration method. The numerical solutions reveal several complex dynamic motions for the variation of the fluid velocity parameter, such as limit cycle motion, buckling and so on. The result obtained also shows that the sub parameter regions corresponding to the several motions may change with the variation of some parameters of the curved pipe. The present study supplies a new reference for investigating the nonlinear dynamic response of some other structures.

Force Analysis and Curve Design for Laying Pipe in Loop Laying Head of Wire Rod Mills

Laying head is a high-precision engineering device in hot-rolled high speed wire rod production line. Previously research works are focused on the laying pipe wear-resisting. Laying pipe curve design method based on wire rod kinematics and dynamics analyses are not reported before. In order to design and manufacture the laying pipe, the motion and force process of the wire rod in the laying pipe should be studied. In this paper, a novel approach is proposed to investigate the force modeling for hot-rolled wire rod in laying pipe. An idea of limited element method is used to analysis and calculates the forces between laying pipe inner surface and wire rod. The design requirements of laying pipe curve for manufacturing are discussed. The kinematics and dynamics modeling for numerical calculation are built. A laying pipe curve equation is proposed by discussing design boundary conditions. Numerical results with di erent laying pipe curves design parameters are plotted and compared. The proposed approach performs good result which can be applied for laying pipe curve design and analysis for engineering application.

FLOW AND HEAT TRANSFER OF OLDROYD-B FLUIDS IN A ROTATING CURVED PIPE

The flow and convected heat transfer of the Oldroyd-B fluids in a rotating curved pipe with circular cross-section were investigated by employing a perturbation method. A perturbation solution up to the second order was obtained for a small curvature ratio, κ. The variations of axial velocity distribution and secondary flow structure with F, Re and We were discussed in detail in order to investigate the combined effects of the three parameters on flow structure. The combined effects of the Coriolis force, inertia force and elastic force on the temperature distribution were also analyzed, which are greater than the adding independent effects of the three forces. The variations of the flow rate and Nusselt number with the rotation, inertia and elasticity were examined as well. The results show the characteristics of the heat and mass transfer of the Oldroyd-B fluids in a rotating curved pipe.

THE FLOW IN ROTATING CURVED CIRCULAR PIPE

The combined effects of the system rotation (Coriolis force) and curvature (centrifugal force) on the flow in rotating curved circular pipe with small curvature are examined by perturbation method. A second order perturbation solution is presented. The secondary flow structure and the primary axial velocity distributions are studied in detail. The loops of the secondary flow are more complex than those in a curved pipe without rotation or a rotating straight pipe. Its numbers depend on the body force ratio F which represents the ratio of the Coriolis to the centrifugal force. The maximum of the axial velocity is pushed to either outer bend or inner bend, which is also determined by F. The results are confirmed by the results of other authors who studied the same problem by different methods.

THE PERTURBATION SOLUTIONS OF THE FLOW IN A ROTATING CURVED ANNULAR PIPE

WT5”BZ]In this paper, the flow in a rotating curved annular pipe is examined by a perturbation method. A second order perturbation solution is presented. The characteristics of the secondary flow and the axial flow are studied in detail. The study indicates that the loops of the secondary flow are more complex than those in a curved annular pipe without rotation and its numbers depend on the ratio of the Coriolis force to centrifugal force F. As F≈-1, the secondary flow has eight loops and its intensity reaches the minimum value, and the distribution of the axial flow is like that of the Poiseuille flow. The position of the maximum axial velocity is pushed to either outer bend or inner bend, which is also determined by F. [WT5”HZ]

Nanoparticle distribution in a rotating curved pipe considering coagulation and dispersion

We study the evolution of the particle number concentration, mass concentration, particle polydispersity, particle diameter and geometric standard deviation considering particle coagulation and dispersion in a rotating curved pipe at different Reynolds number, Schmidt number and F number. It is found that, when the Coriolis force and the centrifugal force point to the same direction, particles concentrate near the outside edge of the pipe, which becomes more obvious as time goes by. The particle number and mass concentration increase faster at the early stage than that at the later stage, and approach a stable value finally. As the coagulation proceeds, the particle diameter, polydispersity and geometric standard deviation increase and have high values in the region close to the outside edge of the pipe. When the Coriolis force and the centrifugal force point to the oppo- site direction and the Coriolis force is more dominant than the centrifugal force, particles concentrate near the inside edge of the pipe. The particles in the region with a high number concentration have high mass concentration, large diameter and high polydispersity as well as large geometric standard deviation. The particle distribution is dependent on the balance of the pipe curvature and rotating speed. The Reynolds number and the Schmidt number have effects on the particle distribution when other parameters remain unchanged. An increase in the Reynolds number leads to an increase in particle number concentration and mass concentration, and a decrease in particle polydispersity, particle diameter and geometric standard deviation. With the increase of Schmidt number the particle number concentration and mass concentration increase, and the particle polydispersity, particle diameter and geometric standard deviation decrease.

LAMINAR DEVELOPING FLOW IN THE ENTRANCE REGION OF ROTATING CURVED PIPES

Three-dimensional laminar flow in the entrance region of rotating curved pipes was investigated. The governing equations were written in an orthogonal curvilinear coordinate system and solved with a fully three-dimensional numerical method. The development of secondary flow, axial velocity, local and average friction factors for different cases of rotation were given and discussed in detail. The results show that rotation influences the flow structure and friction factor greatly and that the secondary flow is sink-type in the early stage of development and then turns to vortex structure. The average friction factor and the intensity of secondary flow have drastic decrease near the entrance. At some proper rotation, the average friction factor can be noticeably reduced.

NUMERICAL ANALYSIS OF THE FLUID FLOW IN A ROTATING CURVED ELLIPTICAL PIPE

A numerical study was conducted for the fully developed laminar flow in rotating curved elliptical pipe. Due to the rotation, the Coriolis force can also contribute to the secondary flow. The interaction of rotation and curvature complicates the flow characteristics. The boundary-fitted coordinate was adopted to study the flow characteristic in the rotating systems. The effects of rotation on the flow transition were studied in detail. The generation and mergence of vortices in rotating curved elliptical pipes were also captured for the first time. The simulation results show that the flow for the case of large aspect ratio of the cross-section is more likely to be unstable than that for smaller one.

Feasibility evaluation for excavation of Naghshe Jahan Square subway station by underground methods

In recent years, in reaction to the increasing usage of urban areas, the excavation of underground spaces has been developed. One of the most challenging issues encountered by engineers is the construction of subway stations as large underground spaces at shallow depth with soft surrounding soils. In this paper, Naghshe Jahan Square subway station located in Isfahan, Iran, has been simulated by geomechanical fnite difference method(FDM). This station is located under important historical structures. Therefore, the ground displacement and surface settlement induced by the excavation of the subway station should be strictly controlled. Many of such problems are affected by selected excavation method. For these reasons, different underground excavation methods associated with construction have been studied. In this study, sequential excavation method and large-diameter curved pipe roofng method are used and the numerical results of the two methods are compared. The presence of groundwater table obliges us to choose special techniques for the stability of the ground around the subway station during construction; hence compressed air and ground freezing techniques are utilized in the simulations of the subway station. Finally, after choosing appropriate support systems, the large-diameter curved pipe roofng method with 1.5 m spacing between curved pipes is proposed.

NUMERICAL SIMULATION OF TURBULENT FLOW CHARACTERISTICS IN A CURVED PIPE WITH A BAFFLE

A numerical study on the characteristics of developing turbulent flow in a curved pipe with a baffle was carried out in body-fitted coordinates with the k-ε model turbulence. A curved duct of square cross-section was examined first, and the results agree very well with the experimental data. Then two kinds of pipes, a normal curved pipe and that with a baffle were studied. The computational results are presented and compared with each other to illustrate the changes of the flow after adding the baffle. The longitudinal velocity in the pipe with a baffle was characterized by outer velocity bigger than the inner one. The secondary flow was characterized by four-vortex structure with the intensity reduced, which results in the equability of the flow field of the cross-section compared with that without a baffle, and has much more significant meaning in engineering.

Numerical Investigation of Developing Turbulent Flow in a Helical Square Ductwith Large Curvature

A fully elliptic numerical study has been carried out to investigate the three-dimensional turbulent developing flow in a helical square duct with large curvature. A two-layer zonal model is proposed and used, in which the whole region is divided into a viscosity-affected near wall layer and a fully turbulent region. A DSM closure is applied in the former, and a one-equation model is solved in the latter. The results presented in this paper cover a Reynolds number range of (l- 10) x 104. The development of flow is found to be dominated by radial pressure gradient and Dean-type secondary motion. The distribution of Reynolds stresses in fully developed flow exhibit a complex pattern of turbulence anisotropy The development of peripherally averaged friction factor and the distribution of local friction factor in fully developed flow are given and discussed.