Elastic Pipe Research Articles

Study of the influence of stochastic inhomogeneity of a pipe on stress-strain behavior

The paper is devoted to stress-strain behavior of an elastic heavy-wall pipe from incompressible material, which is under the influence of compression hydrostatic pressure. We have obtained the analyticity condition for the solution of the problem in small parameters close to zero. These parameters are independent random variables. They characterize the deviation of the cross-section outline from a circle, and the inhomogeneity of the pipe material. The solution has been found by perturbation method up to the second order of smallness. It has been concluded that in the case of experimental analysis of the pipe state under the load meeting the specified condition, the average values of stress and displacement will be close to the values obtained at axially symmetric state.

On the stress state of a pressurised pipe with an initial thickness variation, subjected to non-homogeneous internal corrosion

The paper concerns 2D problem of an elastic thick-walled pipe with an initial thickness variation, subjected to internal pressure and mechanochemical corrosion. The inner perimeter of the pipe cross-section is elliptical, while the outer is circular. The linear Dolinskii corrosion kinetics model is used. In the general case, structural instability of initial boundary value problems with unknown evolving boundaries can cause the divergence of numerical procedures when modelling the processes under study. It is observed that the attempts to circumvent the divergence of numerical procedure can suppress the manifestation of mechanochemical effect and yield inaccurate results. Thus, it is necessary to find a compromise between competing computational processes. Calculations revealed that the variation of the initial pipe wall thickness within the acceptable pipe wall tolerance can noticeably accelerate the growth of stresses and, consequently, reduce the durability of the pipe. The applicability of analytical solutions for a perfect circular pipe with a reduced thickness, equal to the minimum thickness of the imperfect pipe, to the case under study is also discussed.

Study on modes of wave properties based on the coupled wave theory of elastic pipes and fluids

Study on modes of wave properties based on the coupled wave theory of elastic pipes and fluids

Unsteady Pulsatile Hydromagnetic Counter-Current Flows of Cu–Water and CuO–Water Nanofluids Through Two Elastic Coaxial Pipes with Porous Blocks

In the present work, we study pulsatile magnetohydrodynamic mixed convection counter-current flows of Cu–Water and CuO–Water nanofluids through two elastic coaxial pipes with wall-mounted porous blocks. A two-phase model that takes the effects of Brownian motion and thermophoresis into consideration is used to describe the transfer of heat and the transport of nanoparticles within each nanofluid. The mixed finite element method with $$P_{2}-P_{1}$$ Taylor-Hood elements is employed in order to numerically solve the governing equations with the associated initial and boundary conditions. This numerical solution is used to investigate the effects of porous block thickness, Darcy number, ratio of the radii of the inner and outer channels, Hartmann number and Grashof number on heat transfer, fluid flow, nanoparticle concentration and pressure drop.

A one-dimensional beam-like model for double-layered pipes

A one-dimensional beam-like model is proposed to analyze the mechanical behavior of elastic double-layered pipes. Besides the classical kinematic descriptors of the Timoshenko beams, further terms are introduced to describe the local distortion of the cross-section, indeed able to warp, ovalize and perform longitudinal slipping of the two layers. A homogenization procedure is applied, making use of a corresponding three-dimensional model, in order to obtain the nonlinear, coupled, elastic response function of the beam-like model. Case studies for different load conditions are considered, and instability phenomena, which cause loss of the bearing capacity of the structure, are found by means of numerical integration of the relevant boundary value problems.

A smart pipe energy harvester excited by fluid flow and base excitation

This paper presents an electromechanical dynamic modelling of the partially smart pipe structure subject to the vibration responses from fluid flow and input base excitation for generating the electrical energy. We believe that this work shows the first attempt to formulate a unified analytical approach of flow-induced vibrational smart pipe energy harvester in application to the smart sensor-based structural health monitoring systems including those to detect flutter instability. The arbitrary topology of the thin electrode segments located at the surface of the circumference region of the smart pipe has been used so that the electric charge cancellation can be avoided. The analytical techniques of the smart pipe conveying fluid with discontinuous piezoelectric segments and proof mass offset, connected with the standard AC–DC circuit interface, have been developed using the extended charge-type Hamiltonian mechanics. The coupled field equations reduced from the Ritz method-based weak form analytical approach have been further developed to formulate the orthonormalised dynamic equations. The reduced equations show combinations of the mechanical system of the elastic pipe and fluid flow, electromechanical system of the piezoelectric component, and electrical system of the circuit interface. The electromechanical multi-mode frequency and time signal waveform response equations have also been formulated to demonstrate the power harvesting behaviours. Initially, the optimal power output due to optimal load resistance without the fluid effect is discussed to compare with previous studies. For potential application, further parametric analytical studies of varying partially piezoelectric pipe segments have been explored to analyse the dynamic stability/instability of the smart pipe energy harvester due to the effect of fluid and input base excitation. Further proof between case studies also includes the effect of variable flow velocity for optimal power output, 3-D frequency response, the dynamic evolution of the smart pipe system based on the absolute velocity-time waveform signals, and DC power output-time waveform signals.

3D numerical simulation of laminar water hammer considering pipe wall viscoelasticity and the arbitrary Lagrangian-Eulerian method

PurposeAnalysis of fast transient flow in water pipe systems is an important issue for the prevention of unfavorable pressure oscillations and severe damage to the pipelines. This paper aims to present the performance of three-dimensional (3D) simulation of laminar water hammer caused by fast closure of valve.Design/methodology/approachThe viscoelastic behavior of pipe wall is mathematically modeled by using the rheological model of Maxwell. The arbitrary Lagrangian–Eulerian (ALE) method is also used to simulate fluid–structure interaction. In this method, unlike the classical water hammer theory, the acoustic wave velocity is calculated during the numerical simulations and therefore it is not predetermined.FindingsInvestigating the velocity profiles and the shear stress diagrams for transient flow in elastic pipe showed that the strong effect of viscous forces on the near wall region in conjunction with the influence of inertial forces in the central region of the pipe leads to creation of reverse flow near the pipe wall. Comparing the numerical results obtained for elastic pipe with those of viscoelastic pipe revealed that during transient condition, the viscoelastic wall absorbs the energy of fluid and therefore pressure fluctuations of viscoelastic pipe are damped more quickly. Moreover, the 3D simulation of water hammer confirmed the plane wave hypothesis of water hammer.Originality/valueThe 3D Navier–Stokes equations are solved considering the viscoelasticity of the pipe and the ALE method using the software package of COMSOL Multiphysics.

Semi-implicit staggered discontinuous Galerkin schemes for axially symmetric viscous compressible flows in elastic tubes

We propose a novel family of staggered semi-implicit discontinuous Galerkin (DG) finite element schemes for the simulation of axially symmetric, weakly compressible and laminar viscous flows in elastic pipes. The equation of state (EOS) of the fluid is assumed to be barotropic and two different mathematical models derived from the compressible Navier-Stokes equations are considered in this paper.The first model describes cross-sectionally averaged 1D flows, including steady and frequency-dependent wall friction effects. The novelty of our numerical method compared to standard DG schemes consists in the use of a staggered mesh, where the pressure is defined over a primary grid and the velocity field is defined on edge-based staggered dual control volumes. This approach is well known from classical semi-implicit finite difference schemes for the incompressible Navier–Stokes equations, but it is still quite unusual for high order DG schemes. The continuity equation is integrated over the control volumes that belong to the main grid, while the momentum equation is integrated over the elements of the edge-based staggered dual grid. The nonlinear convective terms are discretized explicitly, while the pressure gradient and the mass flux are discretized implicitly. Up to second order of accuracy in time can be achieved with the so-called θ-method. Inserting the discrete momentum equation in the discrete mass conservation equation leads to a mildly nonlinear algebraic system for the degrees of freedom of the pressure. Such mildly nonlinear systems can be very efficiently solved using the Newton algorithm of Brugnano and Casulli. We observe that the linear part of the mildly nonlinear system is symmetric and positive definite.The second model is derived from the compressible Navier-Stokes equations in cylindrical coordinates. Assuming hydrostatic flow with constant pressure inside each cross section as well as axial symmetry, only the terms in the axial and the radial direction need to be considered. Therefore, we call the second model the 2Dxr model. Also in this case we use a staggered mesh for pressure and velocity and thus the same philosophy as for the 1D model can be applied to obtain the discrete pressure system. For the 2Dxr model a staggered DG scheme is also applied for the computation of the viscous stress tensor in the discrete momentum equation. However, in radial direction the resulting linear system for the friction terms is not symmetric and is thus solved using the Thomas algorithm for block three-diagonal systems.The use of a semi-implicit DG scheme leads to a very mild CFL condition based only on the fluid velocity and not on the sound speed, which makes the method very efficient, in particular in the limit cases when the speed of sound of the fluid tends to infinity (incompressible fluid) and in the rigid case where the wall strain of the pipe tends to zero. In addition, at every Newton step a symmetric positive definite and well conditioned block three-diagonal linear system is solved for the pressure, using a matrix-free conjugate gradient method. Moreover, when the polynomial degree of the basis and test functions is equal to zero the schemes reduce to classical semi-implicit finite volume methods.While in the 2Dxr model the viscous effects in radial direction are directly obtained from first principles via the Navier-Stokes equations, the 1D model requires an additional closure relation for the wall friction. For both models we perform several tests in order to validate the numerical methods for steady and unsteady flows of compressible and nearly incompressible fluids in elastic and rigid tubes. We also provide numerical convergence results in order to show that the developed schemes achieve high order of accuracy in space.

Detection of nonuniform residual strain in a pipe

On the basis of the general linearized statement of the problem on motion of prestressed elastic anisotropic body, we formulate the boundary value problem on steady-state radial vibration of elastic isotropic pipe. We present a comparative analysis of the influence of residual stress and strain levels on frequency response functions of the pipe. We formulate the inverse problem on identification of the inhomogeneous residual stress–strain state on the basis of the additional data on the displacement function at the external radius measured in some frequency range. To solve the inverse problem, we propose a special iterative approach based on the regularization technique. A representative series of computational experiments on a reconstruction of different residual strain functions is conducted.

Channel Characterization of Acoustic Waveguides Consisting of Straight Gas and Water Pipelines

Characterizing acoustic waveguide channels is becoming important for the development of communication and signal processing applications across diverse fields ranging from urban water supply systems to oil and gas distribution pipeline networks. These applications include sonar and transmission systems in support of leak detection, blockage location, sensing, monitoring, and signaling for example. In this paper, we provide experimental results and models for the wideband channel characterization of acoustic waveguides formed from gas and water pipelines over the 1–50 kHz frequency band. Experimental results are provided for two straight pipe systems comprising an acrylic pipe filled with air and a steel pipe filled with water. A mode-based analytical model for predicting acoustic wave propagation in rigid and elastic pipes is proposed with deterministic and stochastic characteristics both considered. Good matching is demonstrated between the model predictions and experimental results in terms of dispersion curves, channel spectrograms, and delay spread. A key finding is that acoustic waveguides filled with water should be treated as elastic pipes, and they have significantly different characteristics from those filled with gas, which can usually be treated as rigid pipes. Furthermore for the steel-water waveguide pipeline, link budget calculations and noise power spectral density measurements reveal that a communication range of more than 50 m can be obtained.

New Insight into Microvascular Perfusion by Analyzing Pipe Flow in a Cylindrical Elastic Shell

Background: Microvascular perfusion, a kind of regional perfusion, plays important roles in delivering oxygen and nutrients, and regulating blood pressure and responses to inflammation. Aim: The aim of this research is to analyze the characteristics of microvascular perfusion by conducting pipe flow in a circular elastic tube. Methods: A model was established with circular elastic tube to mimic microvascular perfusion. The velocity of pressure waves was calculated according to the time that the liquid took to spilt over. What’s more, the characteristics and significance of microvascular flow and arteriovenous anastomoses (AVAs) were analyzed. Results: It took the liquid about 0.1 second to spill over from the model, and the velocity of pressure waves is greater than 100 m/s in the elastic pipe. A mechanical switch structure and the corresponding mechanism were proposed for microvascular perfusion in AVAs. Conclusion: Microvascular perfusion maintains a considerable constancy of hemodynamics in different tissues, when ventricular contraction changes perfusion pressure to meet metabolic demands appropriately. This theory will help us to gain a new perspective in microvascular flow.

Численное исследование влияния дефектов поверхности на устойчивость цилиндрической трубы с жидкостью

Работа посвящена исследованию динамического поведения упругих цилиндрических труб, имеющих поверхностный дефект и взаимодействующих с внутренним потоком сжимаемой жидкости. Дефект в виде кольца прямоугольного сечения располагается на внутренней или внешней поверхности упругого тела и характеризуется собственным набором физико-механических параметров. Поведение идеальной сжимаемой жидкости описывается согласно потенциальной теории, а труба рассматривается в рамках линейной теории упругости. Для определения гидродинамического давления, действующего со стороны жидкости на внутреннюю поверхность трубы (дефекта), используется уравнение Бернулли. Математическая постановка задачи динамики упругого тела выполнена с помощью вариационного принципа возможных перемещений, а система уравнений для жидкой среды формируется с использованием метода Бубнова - Галeркина. Численная реализация алгоритма осуществляется на основе полуаналитического варианта метода конечных элементов. Оценка устойчивости базируется на вычислении и анализе комплексных собственных значений связанной системы уравнений. Верификация модели произведена для случая идеальной трубы путeм сопоставления результатов с известными экспериментальными и численными данными. Для цилиндрической трубы, жeстко защемлeнной с обоих краeв, изучено влияние геометрических и физико-механических параметров дефекта на критическую скорость потока жидкости, при которой система теряет устойчивость. Показано, что наличие дефекта снижает границу гидроупругой устойчивости. Установлено, что размещение дефекта на внешней поверхности трубы оказывает большее влияние, чем его расположение на смоченной поверхности.

Parameters affecting water hammer in metal pipelines

The water hammer related to rapid wave pressure changes in hydraulic systems have been subjected to intensive research for more than a hundred years. Nevertheless, a large number of new papers appear each year. Current literature indicates model differences resulting from the used material of the pipe. In the hydraulic machinery, elastic (metal) pipes are usually used, while water transport in water supply system is currently realized with pipes whose deformation of the walls is viscoelastic. In this paper, the individual and group impact of all parameters influencing the results of numerical modelling of the water hammer occurring in the pipes will be analysed. The method of characteristics will be used to solve partial differential equations describing the flow.

Hydraulic characteristic of selected installation valves installed on various pipes materials

Presented studies covered determination of minor pressure losses and values of minor loss coefficients for two selected installation valves: water control globe valve and angle valve, both DN 15. The tested valves were installed on three pipes, including PP 20x3.4 mm, PEX-Al-PEX 16x2.0 mm and Cu 15x1.0 mm. In order to reflect the real operating conditions of the angle valve, the elastic PVC pipe was used. Our researches were performed on the laboratory installation, for the variable flow rate. The obtained results of laboratory studies showed the clear dependence between minor pressure loss and minor loss coefficients of studied valves, and water flow rate (Reynolds number), degree of valves’ closure and, in some cases, manner of valves installation and material of pipes. The greatest values of minor pressure loss coefficients, of mean values relevantly statistically grater, were determined for the tested valves installed on the PEX-Al-PEX pipeline.

ВЗАИМОДЕЙСТВИЕ НЕУСТОЙЧИВОСТЕЙ ТРУБОПРОВОДА ПРИ СТАТИЧЕСКОМ НАГРУЖЕНИИ

Hydroelastic systems can be characterized by a simultaneous manifestation of elastic and hydrodynamic instabilities and their interaction. Mutual effects of pipe bending, internal and external pressures, the action of compression force and fluid with a set density flowing along the pipe are under consideration. A thin elastic pipe is fixed on clamped sliding supports. In this case the supports do not hinder the flow of fluid travelling inside the pipe along its axis. Outside the pipe there is the fluid at rest. At the supports, the pipe bending and rotation angle are equal to zero. Assumptions are made regarding the incompressibility of the pipe midline and also the ideality and incompressibility of the fluids. The pipe is subjected to longitudinal compression. The smallness of inertial forces is conditioned by a relatively slow change of disturbances under slowly changing external effects (compressive forces in the pipe, hydrostatic forces, velocity of fluid motion in the pipe). External effects can be both independent and interconnected with each other. Here, the static mutual influence between those instabilities is called the instability interaction in the pipeline. We have obtained the linearized equation of the pipe bend and the critical value of the force that squeezes the pipe, which represents a generalization of the classical critical value for the static longitudinal compressive force acting on the pipe in the Euler problem due to the action of pressures inside and outside the pipe and the fluid motion inside the pipe. The investigation is focused on static instability interactions depending on the compression force in the pipe, internal and external pressures and fluid velocity. Given the large number of input parameters, it is possible to identify a great number of particular cases being important in their own right. Some of them are considered here. The domains of change for these parameters are determined by the occurrence of stabilization and destabilization of the rectilinear shape. Bending rigidity, tensile forces and external hydrostatic pressure stabilize the pipe. By contrast, compressive forces, internal hydrostatic pressure and fluid movement inside the pipe at any velocity have a destabilizing effect.

The Brazier effect for elastic pipe beams with foam cores

Pipe beams are considered under the action of bending. In case of elastic material, an analytical model of a one-dimensional beam is introduced, where the internal constraint between ovalization and bending curvature is deduced from mechanical considerations. Then, the softening moment-curvature relationship, able to describe the Brazier effect, is evaluated applying equilibrium equations in the nonlinear field. The same model is extended to the case where a structural foam is present as core of the pipe. The contribution of the core is analyzed in terms of its action in preventing instability phenomena. Finally, a model of lumped ovalization is discussed.

Numerical investigation of pipe length determination in branched systems by transient tests

AbstractTransients are used as a diagnostic tool for pressurized pipes due to their capabilities to acquire and transmit information about system status. To interpret such information in complex systems, models obtained by the integration of the governing equations in the frequency domain are used, since they are computationally efficient and reliable. These models do not require a regular spatial grid for integration and introduce the pipe lengths as parameters. In this paper a calibration procedure based on this particular feature is introduced, to determine a basic item of information that can be lost about the water distribution system, that is the length of the pipes. The network admittance matrix method is implemented and its numerical efficiency allows the investigation of the calibration optimization function on a regular grid in the parameter space. The calibration is tested using in series a genetic and the Nelder–Mead algorithms, considering both elastic and viscoelastic material pipes. The results of the presented numerical investigation allow some insights into the existence of the solution and into the shape of the optimization function.

The research for partitioned algorithm of coupling of elastic pipe and cross-flow in a cylinder

In the marine flatbed, nuclear power stations and oil fields, the marine risers and heat exchangers are induced vibrations and collision, even caused failure with cross flow. This is a typical problem of bundles vibration in fluid-structure interaction. In this paper, the elastic pipe was separated into several beam elements. And the dynamical equation was adopted to describe the structure. The fluid domain of cylinder was separated into solid elements. And the computational fluid dynamics equation was adopted to describe the fluid. At the fluid-structure coupling interface, the formulas of displacement, velocity and load was derived and the corresponding convergence criterion was also derived. Thus, the partitioned coupling algorithm was established for the elastic pipe and the cross-flow in cylinder. The example showed that, comparing to the results of monolithic coupling algorithm, the error was small. Thus, it proved that the correctness of the partitioned coupling algorithm in this article. And it will provide an effective computational method for vibrations and collision of bundles in a more complex fluid domain.

Numerical study of pulsatile MHD counter-current nanofluid flows through two elastic coaxial pipes containing porous blocks

We investigate the MHD convective pulsatile flow through a counter-current two-nanofluid (Cu-water and CuO-water) system. This system consists of two elastic coaxial pipes, with porous blocks mounted on the walls of each channel. Hot CuO-water nanofluid flows upwards in the inner channel, while cold Cu-water nanofluid flows downwards in the outer channel. A two-phase model that considers the effects of thermophoresis and brownian motion on the concentration of nanoparticles within the fluid is used to describe heat and mass transfer within the system. The governing equations with the associated initial and boundary conditions are solved using the mixed finite element method with P2-P1 Taylor-Hood elements. The influence of time, pulsation frequencies and amplitudes of the inner and outer fluids, elastic modulus, Reynolds number, solid volume fractions of the inner and outer nanofluids, and the diameters of the Cu and CuO nanoparticles on fluid flow, heat transfer, nanoparticle concentration and pressure drop is studied. We found that heat transfer may be enhanced by increasing parameters such as the elastic modulus of the pipes, Reynolds number, solid volume fraction of nanoparticles in the inner fluid and nanoparticle size in the outer fluid. Similarly, heat transfer is enhanced by reducing the solid volume fraction of nanoparticles in the outer fluid and nanoparticle size in the inner fluid. In most cases, the heat transfer enhancement observed in the study is accompanied by increases in pressure drop.

A comparison of explicit and semi‐implicit finite volume schemes for viscous compressible flows in elastic pipes in fast transient regime

AbstractThis paper compares the accuracy and computational efficiency of fully explicit and semi‐implicit 1D and 2D finite volume schemes for the simulation of highly unsteady viscous compressible flows in laminar regime in axially symmetric compliant tubes. There are essentially two main classes of mathematical models that can be used to predict the pressure and velocity distribution along the tube: one class is based on the full compressible Navier‐Stokes equations in an axially symmetric geometry, leading to a two‐dimensional governing PDE system with moving boundaries, and the other class uses a simpler, cross‐sectionally averaged version of the Navier‐Stokes equations, which leads to a non‐conservative PDE system in only one space dimension along the axial direction of the tube. Within the first class of models, the influence of the wall friction on the flow field is directly obtained from first principles, without any further modelling assumptions and is thus valid even for highly unsteady flows. In the second case, only averaged flow quantities are available, and it is well known from previous studies published in the literature that the correct representation of the wall friction needs to be frequency dependent, since the use of a simple steady friction model, like the classical Darcy‐Weisbach law, is not sufficient to reproduce the wall friction effects in highly transient flows. For the cross‐sectionally averaged Navier‐Stokes equations, there are again two main classes of frequency‐dependent wall friction models: convolution integral (CI) models and instantaneous acceleration (IA) models.In this paper we provide a very thorough and critical comparison of all the above‐mentioned methods for the simulation of highly oscillatory flows in rigid and compliant tubes concerning accuracy and computational efficiency. From our numerical results we can conclude that the convolution integral models are significantly superior to instantaneous acceleration models concerning accuracy. Furthermore, the CI models require only a slight computational overhead if they are properly implemented by solving a set of additional ODEs for appropriate auxiliary variables, instead of directly computing the convolution integrals. We also find that semi‐implicit finite volume methods are clearly superior to conventional explicit finite volume schemes concerning computational efficiency, however, providing the same level of accuracy.