Elastic Pipe Research Articles

Numerical study on guided-wave reflection and transmission at water pipe joint using hybrid finite element method

AbstractThis study investigates guided-wave reflection and transmission at a water pipe joint. The system comprises a linearly elastic pipe filled with water with a joint that is modeled as a discontinuity of the solid region. Wave reflection and transmission are solved using the finite element method (FEM) with radiation conditions for reflected and transmitted guided waves into infinite waveguides. For the radiation conditions, the reflected and transmitted waves are expressed by modal expansion using the semi-analytical finite-element (SAFE) dispersion analysis method. This study extends the hybrid SAFE-FEM to the coupled fluid–solid axisymmetric problem. Numerical results demonstrate that the hybrid SAFE-FEM provides sufficiently accurate solutions. The propagation modes, similar to the modes in a solid pipe, are strongly or perfectly reflected by the joint. However, the modes are transmitted through the joint with little scattering after they converge to the modes in a water bar. The crossing of dispersion curves with those for modes in a solid pipe causes mode conversion and induces scattering attenuation.

The analysis of vertex feedback stabilisability of a star-shaped network of fluid-conveying pipes

It is an outstanding problem whether a pipe-flow system on a star-shaped network is stabilisable by a feedback control on the common vertex. In the present paper we deal with this problem. In particular, we study the equation governing the small vibrations of a stretched elastic pipe conveying fluid in a star-shaped network and examine the question of vertex feedback stabilisability of such a system via control moments. Finding an answer to the question is not straightforward, for the system operator associated with the corresponding closed-loop system is unbounded and nonselfadjoint. An approach to the study of the stabilisation problem for the closed-loop system is presented based on the spectral approach previously introduced by the authors for star graphs of stretched elastic beams. When the tension in the pipes is greater than the square of the fluid-flow velocity, we establish a positive result that in fact gives the strong property of uniform exponential stability of the closed-loop system.

Investigation on Gas-Liquid Two-Phase Flow-Induced Vibrations of a Horizontal Elastic Pipe

Abstract This paper is concerned with experimental analyses on the vibration behaviors of a horizontal pipe containing gas–liquid two-phase flow with different flow patterns. The effects of flow patterns and superficial velocities on pressure fluctuations and structural responses are evaluated in detail. Numerical simulations on the fluid–structure interactions within the pipe are carried out using the volume of fluid method and the finite element method. A strongly partitioned coupling method is adopted to ensure the compatibility and equilibrium interface conditions between the fluid and the elastic pipe. The accuracy of the numerical solutions is confirmed by comparing with experimental results. It is found that the fluctuation frequency of the pressure fluctuations of the two-phase flow ranges from 0 Hz to 5 Hz. The standard deviation (STD) value of the pressure fluctuation of the two-phase flow increases with an increase in the superficial liquid velocity, and the maximum magnitude appears in slug flows. The vibration responses of the pipe exhibit strong dependence on the momentum flux of the two-phase flow, which mainly excites the fundamental flexural vibration mode of the pipe. The magnitude of vertical vibration response of the pipe is equal to that of the lateral vibration response, and the vibration response measured at the middle of the pipe does not contain the second-order operating mode. Moreover, the STD value of the structural responses of the pipe increases proportionally with an increase in the gas flowrate, while the predominant vibration frequency of the pipe slightly increases.

ML-Based Approach to Predict Carotid Arterial Blood Flow Dynamics

In the current study, a numerical model has been developed to simulate the blood flow characteristics in the human carotid artery. The data thus generated is analyzed to understand the blood flow variations and predict the flow characteristics using Machine Learning techniques. In developing the numerical model, the key features of the system, namely, the blood, is modeled as an incompressible Newtonian fluid, and the artery is an elastic pipe. This model is simulated using COMSOL software by varying the material properties of the artery. Univariate analysis was performed to gain insight into the features' behaviour and target variables. Subsequently, machine-learning regression models were trained using the data generated from the idealized human carotid artery. Furthermore, the validity of the data was ensured by comparing it with flow division ratios available in the literature. The evaluation of these models was conducted by calculating the Mean Absolute Error values for the test dataset, resulting in the following values: polynomial regressor (0.0106), hyper-tuned support vector regressor (0.0487), decision tree regressor (0.000), random forest regressor (0.0156), Adaboost (0.0508), gradient-boosting (0.0044), and XGboost (0.0043). A quantile loss function was employed to assess the prediction uncertainty. According to the theory of loss function, models with low loss values are considered good predictors. The prediction uncertainty was measured by applying quantile loss function, and it identified that the random forest regressor as the best predictor model for the data, followed by the polynomial regression of degree 3. Prediction intervals for the target variable were computed by leveraging the random forest quantile regressor model. Moreover, the developed polynomial model was utilized to investigate the presence of stenosis in the artery.

Quantile Loss Function Empowered Machine Learning Models for Predicting Carotid Arterial Blood Flow Characteristics

This research presents a novel approach using machine learning models with the quantile loss function to predict blood flow characteristics, specifically the wall shear stress, in the common carotid artery and its bifurcated segments, the internal and external carotid arteries. The dataset for training these models was generated through a numerical model developed for the idealized artery. This model represented blood as an incompressible Newtonian fluid and the artery as an elastic pipe with varying material properties, simulating different flow conditions. The findings of this study revealed that the quantile linear regression model is the most reliable in predicting the target variable, i.e., wall shear stress in the common carotid artery. On the other hand, the quantile gradient boosting algorithm demonstrated exceptional performance in predicting wall shear stress in the bifurcated segments. Through this study, the blood velocity and the wall shear stress in the common carotid artery are identified as the most important features affecting the wall shear stress in the internal carotid artery, while the blood velocity and the blood pressure affected the same in the external carotid artery the most. Furthermore, for a given record of the feature dataset, the study revealed the efficacy of the quantile linear-regression model in capturing a possible prevalence of atherosclerotic conditions in the internal carotid artery. But then, it was not very successful in identifying the same in the external carotid artery. However, due to the use of idealized conditions in the study, these findings need comprehensive clinical verification.

Energy harvesting analysis of the magneto-electric and fluid-structure interaction parametric excited system

This research proposes an innovative design of a fluid-solid coupling vibration energy harvesting system (VEH system) that includes a downstream waterwheel driven by the flow field, which, in turn, drives gears and connecting rods to rotate a wheel equipped with magnets to generate electricity by changing the magnetic field. A piezoelectric patch (PZT) is installed upstream of the pipeline with a magnet attached to it. The repulsive force between the magnet on the wheel and the magnet on the PZT generates additional force while also creating vibration through fluid-solid coupling of the pipeline. The study derives a theoretical model of the nonlinear vibrating beam and couples it with the piezoelectric and magneto-electric equations to simulate the vibration of the fixed-fixed elastic pipe. The method of multiple scales (MOMS), fixed points plots, phase plots, and Poincaré maps are employed to verify the theoretically predicted parametric excitation properties of the system. The study uses the Biot-Savart Law to calculate the theoretical magnetic force and combines it with the fluid-conveying nonlinear beam and the PZT to create a magneto-electric coupling fluid pipeline vibration energy harvesting model. The study conducts a simple experiment to verify the feasibility of the theoretical model and demonstrates that the repulsive force of the magnet significantly enhances the electric generation benefit of the system. Regardless of whether the PZT is located in the curved or flat area (straight part) of the nonlinear beam, the addition of magnets to the system significantly increases voltage generation efficiency by more than 190 % when compared to systems without magnets.

Finite Volume Method for Transient Pipe Flow with an Air Cushion Surge Chamber Considering Unsteady Friction and Experimental Validation

In various water transmission systems such as long-distance water transfer projects and hydropower stations, accurate simulation of water hammer is extremely important for safe and stable operation and the realization of intelligent operations. Previous water hammer calculations usually consider only steady-state friction, underestimating the decay of transient pressure. A second-order Finite Volume Method (FVM) considering the effect of unsteady friction factor is developed to simulate the water hammer and the dynamic behavior of air cushion surge chamber in a water pipeline system, while an experimental pipe system is conducted to validate the proposed numerical model. Two unsteady friction models, Brunone and TVB models, were incorporated into the water hammer equations, which are solved by the MUSCL–Hancock method. One virtual boundary method was proposed to realize the FVM simulation of Air Cushion Surge Chamber. Comparisons with water hammer experimental results show that, while the steady friction model only accurately predicts the first pressure peak, it seriously underestimates pressure attenuation in later stages. Incorporating an unsteady friction factor can better predict the entire pressure attenuation process; in particular, the TVB unsteady friction model more accurately reproduces the pressure peaks and the whole pressure oscillation periods. For water pipeline systems with an air cushion surge chamber, energy attenuation of the elastic pipe water hammer is primarily due to pipe friction and the air cushion. The experimental results with the air cushion surge chamber demonstrate that the proposed FVM model with the TVB unsteady friction model and the air chamber polytropic exponent near 1.0 can well reproduce the experimental pressure oscillations.

Hemodynamic study of blood flow in the aorta during the interventional robot treatment using fluid–structure interaction

An interventional robot is a means for vascular diagnosis and treatment, and it can perform dredging, releasing drug and operating. Normal hemodynamic indicators are a prerequisite for the application of interventional robots. The current hemodynamic research is limited to the absence of interventional devices or interventional devices in fixed positions. Considering the coupling effect of blood, vessels and robots, based on the bi-directional fluid–structure interaction, using the computational fluid dynamics and particle image velocimetry methods, combined with the sliding and moving mesh technologies, we theoretically and experimentally study the hemodynamic indicators such as blood flow lines, blood pressure, equivalent stress, deformation and wall shear stress of blood vessels when the robot precesses, rotates or does not intervene in the pulsating blood flow. The results show that the intervention of the robot increase the blood flow rate, blood pressure, equivalent stress and deformation of the vessels by 76.4%, 55.4%, 76.5%, and 346%, respectively. The operating mode of the robot during low-speed operation has little impact on the hemodynamic indicators. Using the methyl silicone oil as the experimental fluid, the elastic silicone pipe as the experimental pipe, and the intervention robot having a bioplastic outer shell, the velocity of the fluid around the robot is measured on the developed experimental device for fluid flow field in a pulsating flow when the robot runs. The experimental results are similar to the numerical results. Our work provides an important reference for the hemodynamic study and optimization of the mobile interventional devices.

Lateral Buckling of an Elastic Pipe on a Frictional Seabed

Abstract Pipelines tend to buckle laterally under thermal expansion. In existing analytical solutions by Kerr and Hobbs, it is assumed that the seabed resistance q0 to lateral pipe movements is constant in magnitude and opposite in direction to the total displacement. Here, it is opposite to the velocity instead, i.e., the seabed is taken to be frictional rather than nonlinear elastic with a V-shaped potential function. A three-lobe (“mode 3f”) analytical solution is provided for the frictional case, using the same approximate end-of-buckle condition v = v′ = v″ = 0 used by Hobbs in his “mode 3” solution for the nonlinear elastic case. For both modes 3 and 3f solutions, the shape of the buckle does not change as it grows with increasing thermal expansion, though the scaling factors in the axial and lateral directions are different, i.e., the solutions are self-similar. A single finite element solution for the frictional case with an initial imperfection imposed by a bumper can be scaled to cover all such cases. It shows that the shape of the buckle depends on the amplitude of the initial triggering imperfection and is close to the mode 3f solution for very small initial imperfections. The difference between modes 3 and 3f is significant in regard to buckle shape and the relative size of the buckle lobes, but small in regard to the maximum bending moment for a given amount of thermal expansion accommodated by the buckle.

Investigation of hydraulic resistance of pulsating flows of viscous fluid in elastic pipe

In recent years, flexible pipes made of synthetic polymer materials are being rapidly introduced into practice. Pulsating currents are important in driving water and other liquids in main pipes. This paper examines the pulsating currents of a viscous incompressible fluid in an elastic pipe. The necessary hydrodynamic parameters will be determined by solving the problem, such as distributions of pressure, velocity, flow rate, propagation velocity of the pressure pulse wave, and their attenuation. For the first time in this article, the decrease in hydraulic resistance in a pulsating flow through pipes due to the elasticity of the wall will be determined. The dependence of the dimensionless value of the pressure pulse wave on the vibrational numberαis studied. The pulse wave speed is compared with the speed of Moens-Korteweg, c∞and significant differences between them are found. The dependence of the reciprocal value of attenuation, related to the wavelength, on the vibrational numberαis also studied; it is shown that the attenuation is free at lower values of the Womersley vibrational parameter, practically equals zero, and at large values of which it asymptotically approaches unity [1-9].

Application of finite difference method for solving problem of seismic resistance of underground pipelines

The paper analyzes the dynamic response of an underground main pipe under the action of a longitudinal wave propagating in soil along the pipe. The article assumes that the elastic pipe is of a finite length, and a linear viscoelastic model of the “pipe-soil” system interaction is considered. The problem is solved numerically using the explicit scheme of the finite difference method. A longitudinal wave in the soil is taken as a traveling sine wave. The article presents a comparative analysis of the results for certain values of elastic and viscous interaction coefficients, propagation velocity, and pulse duration. Under elastic interaction of the “pipe-soil” system, the reflection of the wave propagating in the underground pipeline at the boundaries of the pipeline coincides with the propagating wave in soil, leading to an increase in the maximum deformation of the underground pipeline, the value of which can double. The viscosity coefficient of interaction at the “pipe-soil” system contact leads to attenuation of the wavefront in the underground pipeline. For soils with values of viscous interaction coefficient of more than 100 kN·s/m2, this may lead to complete attenuation of the bursts at the wavefront in the pipeline. The choice of the step ratio in coordinate and time equal to the wave propagation velocity in the pipeline allows for obtaining results that coincide with the exact solution.

Post-extrapolation for specified time-step results without interpolation in MOC-based 1D hydraulic transients and gas release computations

The goal of the paper is to present a supplementary step called postextrapolation. When applied to the well-known method of characteristics (MOC), this assures the continuous use of the specified time steps or regular numerical grid without interpolations during computations of transients in 1D 2-phase flow in straight elastic pipes. The new method consists of two steps, the first being a typical MOC step, where the C− and C+ characteristics start from regular nodal points, allowing for the point of intersection to differ from a regular one. After defining the variables there the method transforms it corresponding to the near regular grid point, using the first derivatives contained in the original, nonlinear, governing equations, as evaluated numerically from the variables got earlier in the neighboring nodes. The procedure needs no interpolations; it deals with grid-point values only. Instead of the Courant-type stability conditions, shock-wave catching and smoothing techniques help to assure numerical stability between broad limits of parameters like the closing time of a valve and the initial gas content of the fluid. Comparison by runs with traditional codes under itemized boundary conditions and measurements on a simple TPV (tank-pipe-valve) setup show acceptable scatter.

Elastic orbital angular momentum transfer from an elastic pipe to a fluid

Research into the orbital angular momentum carried by helical wave-fronts has been dominated by the fields of electromagnetism and acoustics, owing to its practical utility in sensing, communication, and tweezing. Despite the huge research effort across the wave community, only recently has elastic orbital angular momentum been theoretically shown to exhibit similar properties. Here we experimentally observe the transfer of elastic orbital angular momentum from a hollow elastic pipe to a fluid in which the pipe is partially submerged, in an elastic analogue of Durnin’s slit-ring experiment for optical beams. This transfer is achieved by coupling the dilatational component of guided flexural waves in the pipe with the pressure field in the fluid; the circumferential distribution of the normal stress in the pipe acts as a continuous phased pressure source in the fluid resulting in the generation of Bessel-like acoustic beams. This demonstration has implications for future research into a new regime of orbital angular momentum for elastic waves, as well providing an alternative method to excite acoustic beams that carry orbital angular momentum that could create a paradigm shift for acoustic tweezing.

Fluid transients in viscoelastic pipes via an internal variable constitutive theory

This work presents a fluid transient model capable of handling the viscoelastic behavior of the pipe. A previously developed quasi-2D flow model is employed as a base, and the viscoelastic behavior of the pipe is incorporated by considering constitutive equations formulated in a thermodynamically consistent framework of an internal variable theory. Such an approach straightforwardly provides expressions for computing the rates of energy dissipation in the fluid and pipe accurately and separately. This novel feature discerns the local and overall impacts of the energy dissipation on the pressure oscillations caused by each medium. The governing equations of the model form a hyperbolic system of partial differential equations whose approximated solutions are obtained by the method of characteristics. Taking as reference pressure signals obtained by a classic reservoir-pipe-valve experiment found in the literature, it is shown that the model predictions are fully consistent. A comparison between the pressure responses of viscoelastic and elastic pipes reveals that in addition to delaying the pressure oscillations, the viscoelastic behavior causes a faster attenuation of them. The rates of energy dissipation in the viscoelastic pipe attain significant magnitudes during the first moments of the fluid transient and alters the hydrodynamical behavior of the flow. Such interference is exposed by comparing the responses of the same experimental setup when two different viscoelastic pipe materials are considered. It is also shown that the knowledge of the parcels of energy dissipated in the fluid and pipe individually can improve the comprehension of the phenomenon and be utilized for theoretical and applied research in the field.

A new model for fluid transients in piping systems taking into account the fluid–structure interaction

The present work extends a recently developed quasi-2D flow model for fluid transients in elastic pipes to accommodate fluid–structure interaction mechanisms. In this context, the primary goal of the proposed approach is to analyze energy transfer and dissipative effects in the fluid–pipe system. The fluid–structure interaction couples the flow dynamics with the axial movement of the tube, giving rise to friction, Poisson, and junction coupling mechanisms to take place. The mechanical model mathematical structure forms a quasi-linear hyperbolic system of partial differential equations for which approximated solutions are sought by employing the method of characteristics. The proposed model reproduces classical benchmark solutions and presents a good agreement with experimental data. In addition, the whole thermomechanical consistent framework in which the model is established allows an accurate description of the flow’s internal structure. This feature allows a better comprehension of the phenomenon when compared to the classic frictionless and quasi-steady-friction-based four-equation models. The present approach allows a better description of the friction coupling mechanism and unveils uneven shear stress distributions in the unsteady flow. As a result, the energy dissipation in the fluid is captured with accuracy. Due to the absence or limited ability to describe these dispersive and dissipative effects, the traditional approaches are proved to lose their accuracy as the fluid transient goes. The coupled and uncoupled models are also analyzed and are proven to respond differently due to localized pipe–fluid interface effects in addition to the bulk mechanisms of transfer of energy that occur differently in both approaches.

Numerical Modelling of Cavitation in an Elastic Pipe

This study is devoted to a theoretical and numerical modeling of transient vaporous cavitation in a horizontal pipeline. The model approach is, essentially, based on that of the column separation model (CSM). The basic system of partial differential equations to solve is a hyperbolic type and adapts perfectly to the method of characteristics. This code, allows us, taking into account the unsteady part of the friction term, to determine at any point of the pipe, and at each instant, the average piezometric head, the average discharge and the change in volume of the vapor cavity. This study illustrates the coupled effect of the presence of air pockets resulting in cavitation and the unsteady term of friction, on the amplitude of the pressure wave. The calculation results are in good agreement with those reported in the literature.

Numerical Analysis of a Laminar Transient Flow of a Pseudo-Plastic Fluid

This study is devoted to a numerical modeling of a transient pseudo plastic fluid flow in an elastic pipe. The set partial equations for both the fluid are derived from the law conservations of mass, momentum and energy for the fluid and Hooke’s law for the wall pipe. The system governing this problem is presented and then solved numerically. The non-Newtonian character behavior of the fluid s modeled by the power law. The coupled method of characteristics, finite differences and Runge Kutta are used for spatial and temporal discretization respec-tively. Some results obtained are in good agreement with those found in the literature.

Instantaneous acceleration-based modeling of pumping systems response under transient events

Water hammer can cause pipeline eruptions after uncontrolled pump trip. In order to protect the pipeline from water hammer effects and monitor the transient flow, it is imperative to accurately predict pressure oscillation and surge energy dissipation for longer simulation periods. This study investigates the effectiveness of the water hammer control strategy by adjusting the rotational inertia of a pumping system alongside valve closing operations. In addition, it also explores the complex nature of the transient energy dissipation by using the one-dimensional instantaneous acceleration-based (IAB) unsteady friction models. To this end, the IAB unsteady friction (UF) models were improved to calculate the water hammer pressure by investigating the elastic pipe's response under transient events that are caused by pump trip and valve closure. Various boundary equations were derived and combined with water hammer governing equations to form the final system of equations to predict the transient pressure variation with time. After that, the numerical results of two IAB friction models (i.e., one and two-decay coefficient models, respectively) were compared with previous experimental data to verify the proposed transient solver. This solver was based on Method of Characteristics (MOC) and UF models. The results indicate that one-coefficient and two-coefficients UF models yield almost similar results that match with the experimental outcomes; however, the latter model is comparatively more complex in terms of formulation. Furthermore, a parametric study shows that increasing the moment of inertia of the pump and integrating it with the optimal operation of the valve helps in significantly controlling the transient pressure. This helps in reducing the check-valve slam and controls the water hammer with no need for additional protection devices. Results of the integral energy equation describe that the role of UF on the total dissipation of transient energy diminishes with an increase in the valve's closing time and inertia of the pumping system. Finally, the IAB-UF model acts as a valuable numerical tool that provides comprehensive information about the physical parameters required to protect high-head water supply systems from transient incidents.

Comparison of meshfree displacement and stress error recovery of finite element solutions using moving least squares interpolation

The moving least square (MLS) interpolation based the recovery procedures have been successfully applied to recover the finite element solution errors in the analysis of elastic plates and pipes problems and can be advantageously applied for large deformation and fracture problems. The study presents the displacement and stress error recovery characteristics in the error estimation analysis employing Moving Least Squares interpolation approach. The study considers quartic spline, cubic spline, and exponential weight function with three different order of basis function in Moving Least Squares interpolation based error recovery analysis. The displacement/stress errors in finite element solution are quantified in energy norm. The cylinder and plate benchmark examples using triangular and quadrilateral elements are analyzed to compare the convergence, effectivity and adaptively improved meshes obtained using the various displacement/stress recovery procedures. The study shows that cubic spline weight function and quadratic basis function found to perform better in MLS based meshfree recovery technique for stress as well as displacement errors recovery of finite element solution. It is observed from the study that increasing the order of basis function will enhance the error estimation quality that is, rate of convergence become faster with improved effectivity of the results. The increase in convergence rate with the increase of the order of basis function is more in displacement recovery technique as compared to stress recovery technique. It is observed in the analysis of benchmark example with linear triangular meshing that the error reduction using meshfree MLS interpolation based displacement and stress recovery is about 10% and 150% respectively for the displacement and stress recovery over the mesh dependent least square based displacement and stress recovery. The study concludes that the effectiveness and efficiency of meshfree displacement/stress error recovery technique strongly depends on the weight and basis functions of MLS method to recover the errors.

Vertical frequency‐domain compliance of an elastic pipe pile embedded in a liquid‐filled and porous‐viscoelastic soil

AbstractThe analytical dynamic compliance of an elastic pipe pile fully buried in a fluid‐filled and porous‐viscoelastic soil stratum resting on rigid bedrock and subjected to a vertical time‐harmonic load is proposed. In this study, the Hamilton's principle of dynamics is employed to establish the governing equations for the pipe pile, which is treated as a two‐dimensional (2D) hollow bar structure. The outer and inner soil media surrounding the pipe pile are considered as three‐dimensional (3D), homogenous, and liquid‐saturated porous continuum, besides they are described by the porous‐elastic media model proposed by de Boer. The governing equations for the pipe pile and the soils are solved with the aid of the separation technique of variables, and also utilizing the boundary and contact conditions of the pipe pile and the soils. Then, the analytical solution for the vertical dynamic compliance of the pipe pile is derived. By comparing with the existing solutions and finite element model (FEM), the results from the newly proposed method confirm its validation. Comparative analyses of numerical examples are finally conducted to reveal the variations and response principle of the dynamic compliance of the pipe pile under different material/geometry parameters.