Elastic Pipe Research Articles

Nonlinear three-dimensional dynamics of flexible pipes conveying fluids

This paper presents a model which describes the non-planar vibrations of an elastic pipe induced by the pulsations of a flowing fluid. The motion of the pipe has been described by a set of four non-linear partial differential equations with periodically varying coefficients. The analysis has been conducted with the use of Galerkin method by applying functions describing the free vibrations of the beam as the shape functions. Floquet theory has been used to determine the unstable areas. The influence of the flow velocity and the pulsation frequency on the character and modes of vibrations and on the ranges of the increased vibration intensity has been examined. The possibility of the excitation of sub-harmonic and quasi-periodic vibrations in ranges of simple and combination parametric resonances has been proved. The results of experiments which confirm the occurrence of the parametric resonance phenomenon have also been presented.

The Accounting for Geometrical Nonlinearity for Thin-Walled Pressurized Elastic Pipe With Long Axial Surface Crack

Consideration of a geometrical nonlinearity is a common practice for thin-walled pressurized structures, especially when their cross section is not a perfectly circular one due to either initial imperfections or distortions caused by the nonsymmetrical loading. The application of inner pressure leads to so-called rerounding effect when decreasing of local flexibilities takes place. The crack can be also treated as the concentrated flexibility, so the goal of this work is the investigation of dependence of stress intensity factor (SIF) on applied pressure. Two cases of SIF calculation for 1D long axial surface crack in a pipe loaded by inner pressure are considered here: (a) cross section of pipe has an ideal circular form and (b) the form has a small distortion and crack is located at the place of maximal additional bending stresses. The theoretical analysis is based on: (a) well-known crack compliance method (CCM) (Cheng, W., and Finnie, I., 1986, “Measurement of Residual Hoop Stresses in Cylinders Using the Compliance Method,” ASME J. Eng. Mater. Technol., 108(2), pp. 87–92) and (b) analytically linearized solution for deformation of the curved beam in the case of action of uniform longitudinal stresses. It is shown that for moderately deep crack (crack depth to the wall thickness ratio of 0.5 and bigger) in thin-walled pipe (radius to thickness ratio of 25–40) and inner pressure which induce hoop stress up to 300 MPa, the effect investigated can be quite noticeable and can lead to 5–15% reduction of calculated SIF as compared with the linear case. The analytical results are supported by the geometrically nonlinear finite element method (FEM) calculations.

On the Dispersion and Attenuation of Guided Waves in Tubular Section with Multi-Layered Viscoelastic Coating — Part I: Axial Wave Propagation

Guided modes admissible in elastic hollow pipes are derived to establish their dispersion and attenuation characteristics in the presence of multi-layered viscoelastic coatings. Longitudinal waves propagating in the axial direction in response to displacement continuity boundary conditions signifying perfect interfacial bonds are evaluated against a baseline uncoated tubing. Viscoelastic bitumen and epoxy are coating materials applied to improve pipeline reliability. The impact of viscoelastic coating layers on wave dispersion and attenuation are investigated by incorporating complex material properties in the characteristic equation. The real and complex roots of the corresponding characteristic equation are determined, allowing the phase velocity and attenuation dispersion to be depicted as functions of the propagation frequency. The effects of varying attenuation parameter and coating thickness are also examined. Viscoelastic protective materials are found to have a substantial impact on the propagation and attenuation of longitudinal waveguide modes.

Nonlinear dynamics of a fluid-conveying pipe under the combined action of cross-flow and top-end excitations

We report a theoretical investigation of an elastic and slender fluid-conveying pipe with a top-end excitation subjected to uniform cross flows. Considering the mean drag force and the time varying vortex-induced lift force which is modeled using a nonlinear van der Pol oscillator, the nonlinear partial differential equations of the motion of coupled fluid-structure system are constructed and simplified to a reduced-order model through the Galerkin-type discretization. By virtue of quasi-static displacement conditions, the characteristics of vortex-induced vibration of the pipe are evaluated for the first two lock-in modes. The results show that the top-end excitation can increase the vibration amplitude of the pipe when the cross-flow speed is out of the lock-in regions. When the cross-flow speed is within the lock-in region, however, the top-end oscillation causes a transition between quasi-periodic and periodic in the responses of the pipe, significantly reducing or increasing the vibration amplitudes depending on the excitation acceleration and frequency. This finding has an important guidance in suppressing vortex-induced vibrations by balancing the internal fluid velocity and the top-end excitation.

Vibration analysis of conveying fluid pipe via He’s variational iteration method

In this paper, a recently new semi-analytical method, i.e., He’s variational iteration method is developed to apply to free vibration analysis of conveying fluid pipe. The critical flow velocity and frequency of pipe conveying fluid are obtained with considering the various boundary conditions. The results are compared with the ones of different transform method, and prove VIM that has the same precision and efficient with DTM. The mode shapes of cantilevered pipe and both ends with elastic support pipe are shown under different flow velocity.

Rancangan Irigasi Sprinkler Portable Tanaman Pakchoy

Salah satu teknologi yang dapat meningkatkan efisiensi dan efektivitas penggunaan air irigasi adalah irigasi sprinkler. Namun dalam penerapan sistem irigasi sprinkler di lapangan masih dijumpai banyak kendala, diantaranya adalah memerlukan biaya investasi awal dan operasional yang tinggi. Oleh karena itu, penelitian ini bertujuan untuk merancang irigasi sprinkler portable yang mudah dipindahkan (portable) dan penggunaannya pada budidaya tanaman pakchoy, khususnya pada luas lahan pertanian yang kecil dan terpisah-pisah (0,10 – 0,30 ha) dan terpisah-pisah tanpa adanya sarana irigasi. Metode yang digunakan dalam penelitian ini adalah penentuan panjang dan diameter pipa berdasarkan analisa hidrolika perpipaan, baik pipa lateral, manifold dan utama; perhitungan debit sprinkler menggunakan metode volumetrik; dan penentuan keseragaman irigasi menggunakan metode Christiansen. Sistem irigasi sprinkler portable yang telah dikembangkan memiliki spesifikasi: nozzle head sprinkler jenis Sprinkler Impact Plactic dengan ukuran nozzle 4 mm, tinggi total stick riser 1,3 meter dengan diameter ¾”, pipa lateral elastis dengan diameter 2” dan panjang 50 meter, pipa sub-main (manifold) dan pipa utama sebesar 2”. Adapun pompa yang digunakan memiliki total head 55 meter dengan tenaga penggerak 5,5 HP, serta selang hisap 2”. Sistem irigasi sprinkler ini dapat beroperasi pada tekanan operasi 1 sampai dengan 4 bar untuk spasi sprinkler dan lateral 10 m x 10 m. Debit sprinkler pada tekanan 1 bar adalah 0,12 l/s. Nilai keseragaman irigasi yang dihasilkan pada tekanan 1 bar sebesar 80%. Untuk memperoleh nilai keseragaman irigasi lebih dari 85%, maka disarankan penggunaan tekanan operasi minimal 2 bar.

Evaluation of Elastic Stiffness Parameters for Pipeline–Soil Interaction

This paper focuses on elastic stiffness parameters for axial, horizontal, and vertical motions of a pipeline relative to the seabed, with the aim of expressing these parameters in terms of fundamental elastic properties of the soil. Limited information exists in the literature on the axial elastic response of on-bottom pipelines, particularly for nonhomogeneous soil. Therefore, an approximate analytical approach was developed for axial stiffness, focusing on the case of shear modulus proportional to depth. The solution was then verified through numerical analysis. Further numerical analysis was carried out to obtain relationships for horizontal and vertical elastic stiffnesses of on-bottom pipelines. Finally, relationships among elastic stiffnesses were developed. Here recommendations are made for the selection of proper elastic stiffnesses in all three directions of motion. These recommendations allow consistent and rigorous modeling of elastic pipe–seabed interactions with application to the analysis of pipeline laying, buckling, walking, and on-bottom stability.

Experimental Evidence of Leaks in Elastic Pipes

Several studies have been carried out in recent decades to establish a relationship between total head and leaks. In literature, the leakage governing equations have been analysed in light of pipe materials, water head, leak dimension or shape. Most of these contributions questioned the classical Torricelli equation, demonstrating through experimental evidence that the classical orifice law can give unsatisfactory results. Nevertheless, starting from the Torricelli equation, other exponential or linear governing equations have been proposed as mathematical models able to reproduce the leakages in water distribution systems (WDSs). To investigate the validity of the proposed governing equations, an experimental campaign was carried out by means of a water distribution network composed of approximately 500 m of polyethylene pipes. The experiments were designed to investigate the effects of leak area and pipe rigidity on discharge. Furthermore, the effect of leak size enlargement with water head was analysed. Finally, the proposed research contributes to the population of a database for estimating the coefficients of head-discharge relationships.

Balancing of Forces in Segments of Axial Bearing by Dynamometers

The Francis turbine in water power plant station is positioned at top and bottom axial hanging bearings. During reparation work the turbine was disassembled and during assembling the adjusting segments in the hanging bearings were released. In the paper are described procedures that are necessary in order to provide correct distribution of axial forces in twelve segments of upper axial hanging bearing by strain-gages applied on elastic pipes positioned under individual bearing segments.

Elastic Pipe Control and Compensation for Managed Pressure Drilling Under Sea Wave Heave Conditions

Managed pressure drilling (MPD) was developed as a group of technologies to more precisely control the annular pressure profile for which accuracy of the estimation of the bottomhole pressure is important. Particularly, under severe wave heaves in deepwater environments, the estimation based on static state pipe movement models can result in underestimation/overestimation of bottomhole pressures. The purpose of this study is to investigate the dynamic axial response of the drillstring with friction to applied heaving velocity, with particular interest to the effect at the bottomhole pressure. The paper presents an efficient and accurate method for solving the dynamic axial drillstring with friction and it allows it to be applied to heave velocity at the surface. The model that couples the pipe motion solves the full balance of mass and balance of momentum for pipe and annulus flow, considering the compressibility of the fluids, the elasticity of the system, and the dynamic motions of pipes and fluids. Also considered are surge pressures related to fluid column length below the moving pipe, compressibility of the formation, and axial elasticity of the moving string. Fluid properties are adjusted to reflect the effects of pressure and temperature on the fluids. The modeling takes into account the pipe elasticity under different combinations of heave and pipe velocities. Furthermore, the real-time torque and drag models are calibrated to actual hole conditions in real-time using survey, temperature, pressure, and downhole tool data to calculate friction factors in a wellbore. It has been observed that different conditions exist, some resulting in velocity reversal; thus causing surge or swab pressures. It has also been observed that heave amplitude has significant influence on bottomhole pressure. The different conditions observed for periodic or time function of displacements include (1) surface pipe velocity attributed to wave heave is in phase with the bottom movement of the string; (2) surface velocity of the pipe is out of phase with the bottom velocity of the pipe; (3) wave velocity and surface pipe velocity can be out of sync, and the bottom pipe velocity can be in phase with the surface velocity; and (4) wave velocity and surface pipe velocity can be out of sync, and the bottom pipe velocity can be out of phase with the surface velocity. The results of these calculations can be coupled to a real-time hydraulics model to determine a setpoint pressure for the MPD choke system. (SPE 173|005)

THEORETICAL OF DYNAMIC LOADING AGAINST WATER-FILLED SIMPLY SUPPORTED PIPES

The primary aim of this study had been to investigate the effects of water-filled flow on the transient response of a simply supported pipe subjected to dynamically applied loading. The importance of this study is manifested in numerous applications, such as oil and gas transportations, where dynamic loading can be the result of an accident. The classical Bernoulli-Euler beam theory was adopted to describe the dynamic behavior of an elastic pipe and a new governing equation of a long pipe transporting gas or liquid was derived. This governing equation incorporated the effects of inertia, centrifugal, and Coriolis forces due to the flowing water. This equation can be normalized to demonstrate that only two non-dimensional parameters governed the static and the dynamic responses of the system incorporating a pipe and flowing water. The transient response of this system was investigated based on a standard perturbation approach. Moreover, it had been demonstrated that the previous dynamic models, which largely ignored the internal flow effects and interactions between the flow and the structure, normally produced a large error and are inapplicable to the analysis of many practical situations. One interesting effect identified was that at certain flow ratio, the system became dynamically unstable and any, even very small, external perturbation led to a growing unstable dynamic behavior. Such behavior, which is called pipe whip, is well-known to everyone who waters a garden using a flexible long hose.

On the Acoustic Radiation of Axisymmetric Fluid-Filled Pipes Using the Wave Finite Element (WFE) Method

This paper investigates the efficiency of the wave finite element (WFE) method to assess the vibroacoustic behavior of finite baffled axisymmetric elastic pipes interacting with internal and external acoustic fluids. The pipes, of either homogeneous or multi-layered cross-sections, are surrounded by an external fluid of infinite extent, which can be light or heavy. The Sommerfeld radiation condition is taken into account by considering a perfectly matched layer (PML) around the external fluid. The method involves the computation of waves traveling along an axisymmetric multi-physics waveguide that incorporates a pipe, internal and external fluids, as well as a PML. Numerical experiments are carried out which highlight the relevance of the WFE method in terms of accuracy and CPU time savings, in comparison with the conventional finite element analysis.

Deformations of an elastic pipe submitted to gravity and internal fluid flow

This paper describes the deformation of an elastic pipe submitted to gravity and to an internal fluid flow. The pipe is clamped horizontally at one end and free at the other end. As the fluid velocity increases, the shape changes from an elastic beam deflected by its own weight towards an horizontal position. The shape of the pipe is characterized experimentally and is compared with a theoretical model based on the Euler–Bernoulli approximation and the conservation of the fluid momentum. We study how the determination of the pipe deformation provides an estimation of the conveyed fluid flow. Finally, the vertical force produced by the conveyed fluid to lift off a mass is deduced.

Low Frequency Guided Wave Transmission in Water Pipe Systems

This paper addresses the multimodal acoustic wave propagation in elastic pipes which can carry multiphase fluids. The waveguide characteristics of circular fluid filled pipes and the influence of elasticity of the outer boundaries in relation to the compressibility of the filling liquid and the inner boundaries due to an additional fluid phase are discussed – in comparison to the assumption of rigid walls. As the main aspect for liquid monitoring systems the decrease of the sound velocity within the liquid below the bulk wave velocity is discussed in detail by numerical studies and empirical proofs. Further, it will be shown that an additional fluid phase causes a deterministic jumping of the wave modes and of the dispersion characteristics.

A polynomial expansion of axial velocity profiles to solve transient laminar flow in elastic pipe

A polynomial expansion of axial velocity profiles to solve transient laminar flow in elastic pipe

1P1-F10 湾曲鉗子のための回転運動伝達用二重管の曲げ剛性の最適化

In pharyngeal cancer surgery and single port surgery, arc-shaped forceps are used. Although some of them can rotate their tips in the axial direction, they have insufficient torsional rigidity because elastic inner pipes are used to transmit the torsional rotation. In this study, we propose a cracked metal pipe with ununiform intervals that can bend with a shape matching with an outer pipe still having sufficient torsional rigidity. We designed a cracked inner pipe by using computer simulation for a 5 mm diameter forceps. The contact force with an outer pipe is reduced, resulting in a small resistant torque caused by friction. We experimentally confirm that it can rotate with a torque of about 0.5 Nmm in the groove on an ABS plate.

Fluid‐structure interaction of an elastic pipe immersed in a coaxial rigid pipe: a model for the Tullio Phenomenon

AbstractAn axisymmetric, elastic pipe is filled with an incompressible fluid and is immersed in a second, coaxial rigid pipe which contains the same fluid. A pressure pulse in the outer fluid annulus deforms the elastic pipe which invokes a fluid motion in the fluid core. It is the aim of this study to investigate streaming phenomena in the core which may originate from such a fluid‐structure interaction. This work presents a numerical solver for such a configuration. It was developed in the OpenFOAM software environment and is based on the Arbitrary Lagrangian Eulerian (ALE) approach for moving meshes. The solver features a monolithic integration of the one‐dimensional, coupled system between the elastic structure and the outer fluid annulus into a dynamic boundary condition for the moving surface of the fluid core. Results indicate that our configuration may serve as a mechanical model of the Tullio Phenomenon (sound‐induced vertigo). (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling and Avoidance of Heave-Induced Resonances in Offshore Drilling

Summary The problem of heave-induced-pressure fluctuation during drilling is considered. The surge/swab pressures created by the vertical motion of the pipe can excite resonances that may amplify the magnitude of pressure oscillations by a factor of 10. The locations of the resonant frequencies depend on the topside-choke opening and can hence be avoided. By use of a model of the full coupled dynamics, it is shown that the elastic pipe and the mud-in-pipe can also exhibit resonant behavior significantly affecting the downhole pressure. Techniques to avoid resonances are discussed.

Elasticity of fractal materials using the continuum model with non-integer dimensional space

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

The boundary condition at the valve for numerical modelling of transient pipe flow with fluid structure interaction

Transient flows in pipes (water hammer = WH) do appear in various situations and the accompanying pressure waves may involve serious perturbations in system functioning. To model these effects properly in the case of elastic pipe the dynamic fluid-structure interaction (FSI) should be taken into account. Fluid-structure couplings appear in various manners and the junction coupling is considered to be the strongest. This effect can be especially significant if the pipe can move as a whole body, which is possible when all its supports are not rigid. In the current paper a similar effect is numerically modelled. The pipe is fixed rigidly, but the valve at the end has a spring-dashpot mounting system, thus its motion is possible when WH is excited by the valve closuring. The boundary condition at the moving valve is modelled as a differential equation of motion. The valve hydraulic characteristics during closuring period are assumed by a time dependence of its loss factor. Preliminary numerical tests of that algorithm were done with an own computer program and it was found that the proper valve fixing system may produce significant lowering of WH pressures.