Viscoelastic Pipe Research Articles

Interaction of a bush with a complex internal profile and a coated viscoelastic pipe worn on a rigid cylinder

Abstract The present study is devoted to obtaining an analytical solution to the contact problem for a rigid bush and a viscoelastic aging cylindrical coated tube mounted on a rigid shaft or cylinder. A feature of the formulation is the fact that the inner profile of the bush is described by a complex function, which introduces certain difficulties in numerical calculations. The article demonstrates how it is possible to simultaneously take into account both the rheological properties of the layers and the geometric features of the contacting bodies, so that the obtained analytical solution turns out to be effective in real numerical calculations. In the resulting analytical solution, the function describing the inner profile of the bush is included in a separate term. This makes it possible to use a small number of terms of an infinite functional series and at the same time obtain results with high accuracy.

Sensitivity of creep parameters to pressure fluctuation of transient flow in viscoelastic pipes

ABSTRACT A stepwise method is one of the efficient approaches in the calibration of transient flow in viscoelastic pipes. However, there is the lack of comprehensive research on the calibration method for retarded time and creep compliance. Therefore, the sensitivity of the order of magnitude of the creep parameters in the presence of interactions to transient flow pressure damping and phase in the case of the two-element Kelvin–Voigt model is investigated. Also, the calibration methods of retarded time and creep compliance in the stepwise method of transient flow parameter calibration for viscoelastic pipes are proposed. The results indicate that the creep compliances do not affect the phase of the pressure fluctuations when the selected retarded times are greater than the order of magnitude 10−1. For the first Kelvin–Voigt element, when the order of magnitude of the retarded time exceeds 10−2, an increase in creep compliance results in an increase in the degree of damping of pressure fluctuations. When the order of magnitude of the retarded time is less than 10−2, the rule is reversed. For the second Kelvin–Voigt element, an increase in creep compliance results in an increase in the degree of damping of transient flow pressure fluctuations independent of the retarded time.

MOC-Z Model of Transient Cavitating Flow in Viscoelastic Pipe

In this paper, a unitary method for the solution of transient cavitating flow in viscoelastic pipes is proposed in the framework of the method of characteristics (MOC) and a Z-mirror numerical scheme (MOC-Z model). Assuming a standard form of the continuity equation allows the unified treatment of both viscoelasticity and cavitation. An extension of the MOC-Z is used for Courant numbers less than 1 to overcome a few cases with numerical instabilities. Four viscoelastic models were considered: a Kelvin–Voigt (KV) model without the instantaneous strain, and three generalised Kelvin–Voigt models with one, two, and three KV elements (GKV1, GKV2, and GKV3, respectively). The use of viscoelastic parameters of KV and GKV models calibrated for transient flow tests without cavitation allows good comparisons between experimental and numerical pressure versus time for transient tests with cavitation. Whereas for tests without cavitation, the mean absolute error (MAE) always decreases when the complexity of the model increases (from KV to GKV1, GKV2, and GKV3) for all the considered tests, this does not happen for tests with cavitation, probably because the decreasing capacity of parameter generalization for the increasing complexity of the model. In particular, in the examined cases, the KV model performs better than the GKV1 and the GKV3 models in three cases out of five, and the GKV2 model performs better than the GKV3 model in three cases out of five. Furthermore, the GKV2 model performs better than the KV model only in three cases out of five.

Improving the prediction of turbulent kinetic energy for drag reduction in turbulent viscoelastic pipe flow

Reducing turbulence in pipe flows using polymer additives is crucial for industrial applications like crude oil, water, and sewage transportation. While previous research has accurately predicted friction factor and velocity profiles, none has fully understood turbulent kinetic energy (TKE) behavior in such fluids. Authors are now focusing on exploring turbulence models to better understand the TKE behavior. In this research, we have introduced a model to improve the behavior of TKE in a modified generalized Newtonian fluid (GNF). The developed model aims to simulate the viscoelastic effects of fluids that result in drag reduction in turbulent pipe flow. The work is noteworthy as it integrates turbulence and viscoelastic components, offering a comprehensive understanding of the phenomenon. By incorporating the rheological properties of viscoelastic fluids and replacing the damping function with a non-Newtonian alternative proposed by Cruz and Pinho, the Launder–Sharma k–ε turbulence model is now suitable for simulating dilute non-Newtonian viscoelastic fluids. The viscoelastic aspect of the model employs the modified GNF model. The developed model has been subjected to simulations using the computational fluid dynamics software. The results obtained for fluid TKE demonstrate a significant improvement in comparison to our previous research and the findings of other researchers. Furthermore, the model's prediction for the Darcy friction factor has been enhanced, resulting in an average error of only 3.71% in this section. It is noteworthy that the model consistently maintains a high level of accuracy in predicting other essential flow parameters such as mean axial velocity and Reynolds stresses. The provided model advances our understanding of viscoelastic fluid behavior in turbulent pipe flow by applying the modified GNF model.

Dynamic Behavior and Mechanism of Transient Fluid–Structure Interaction in Viscoelastic Pipes Based on Energy Analysis

The term “viscoelastic pipe” refers to high polymer pipes that exhibit both elastic and viscoelastic properties. Owing to their widespread use in water transport systems, it is important to understand the transient flow characteristics of these materials for pipeline safety. Despite extensive research, these characteristics have not been sufficiently explored. This study evaluates the impact of friction models on the transient flow of viscoelastic pipes across various Reynolds numbers by employing an energy analysis approach. Given the complexity and computational demands of two-dimensional models, this paper compares the accuracy of one-dimensional and quasi-two-dimensional models. Notably, the superiority of the quasi-two-dimensional model in simulating viscoelastic pipelines is demonstrated. Owing to the interaction between pressure waves and fluid within viscoelastic pipes, fluid–structure coupling significantly attenuates pressure waves during transmission. These findings shed light on the constitutive properties of viscoelastic pipes and the influence of pipe wall friction models on transient hydraulic characteristics, building upon prior studies focused on elastic pipes. Nevertheless, numerous factors affecting transient flow in viscoelastic pipes remain unexplored. This paper suggests further analysis of strain effects, starting with temperature and pipe dynamics, to enhance the understanding of the coupling laws and flow mechanisms in viscoelastic pipelines.

Non-smooth dynamics of impacting viscoelastic pipes conveying pulsatile fluid

This paper aims to investigate the stability and nonlinear dynamics of an initially curved viscoelastic clamped–clamped pipe conveying pulsatile fluid, with special attention to the non-smooth dynamics of this gyroscopic system under the influence of initial curvature and gravity. In this study, the impacting contact is modeled as a trilinear repulsive force. Based on the Euler–Bernoulli beam theory, the nonlinear governing equations, which take into account geometric, curvature, and damping nonlinearities, are developed using Hamilton’s principle. The continuous model is discretized using the Galerkin method and then solved using the arc-length technique and a time integration method. A linear analysis of the natural frequency and complex mode shape shows the unexpected frequency intersection and modal asymmetry. The qualitative changes in the nonlinear dynamics of the impacting pipe in both sub- and super-critical regions are examined and presented in the form of bifurcation diagrams, frequency–amplitude curves, force–amplitude curves, time histories, and phase portraits. Numerical results show that some complex dynamical behaviors can occur in different impact constraint cases, including a grazing bifurcation, sticking, period doubling, and chaos at the impact location, may occur. The initial curvature and gravity result in different behaviors, such as the asymmetry change of the equilibrium configuration and the occurrence of the flutter instability. The current analysis is significant to understand the non-smooth dynamic mechanisms and also provide design and technology guidance for the pipe system with motion-limiting constraints.

Nonlinear vibrations of a slightly curved Maxwell viscoelastic pipe conveying two phase flow under various boundary conditions

Two phase flows are common in pipeline engineering, and most times, the assumption of single phase flow is usually assumed. In this paper, the dynamics of a slightly curved Maxwell viscoelastic pipe conveying two phase flow under four boundary conditions; cantilever, simple supported, clamped simply supported and clamped clamped supported is investigated. Eigenfunction expansion was used to discretize the PDE into four modes. The linear analysis results show that the Maxwell viscoelastic parameter has no significant effect on the first and the second modes of the vibration, but on the third and fourth modes for the three boundaries conditions considered. The void fraction has effects on the frequency and critical velocity only if the densities of the components of the two phase fluid are significantly large. The nonlinear dynamics shows that Maxwell viscoelastic parameter reduces the bifurcation position and changes the bifurcation point from being sharp to a gentle curve at the bifurcation point. Further results were presented for the Maxwell parameter and velocity of fluid and temperature loading on the pipe, which are very important to understanding the behavior of Maxwell viscoelastic pipe conveying two phase flow.

Tackling of hydraulic cavitation in pressurized pipe flow using high- or low-density polyethylene penstock and short-section

Abstract Recent studies have proved that the utilization of polyethylene (PE) short-section or penstock is a promising water hammer control tool. However, the interplay between the magnitude attenuation and the phase offset of pressure-wave oscillations remains challenging. This study aimed at inspecting the capacity of a dual PE penstock/short-section-based control technique, with regard to the aforementioned interplay. In this technique, a PE penstock was lumped to the transient initiating zone of the main pipe and a short-section of the counter extremity of the pipe was replaced with PE. The transient pressure-wave behavior in a gravitational viscoelastic pipe involving cavitation was described by the extended 1D water hammer equations embedding the Vitkovsky and Kelvin–Voigt add-ons. The numerical solution was performed by the fixed grid method of characteristics. The high- (HDPE) and low-density (LDPE) were demonstrated in this study. Analysis revealed that upgrading techniques based on LDPE enabled a desirable tradeoff between the magnitude attenuation and the phase offset of pressure-wave oscillations. Particularly, the dual penstock/short-section specific upgrading technique allowed a more important attenuation magnitude of pressure peak (or crest), and led to a similar expansion of the wave oscillation period. Furthermore, results evidenced that the proposed technique outperformed the renewal of the original piping system.

Nonlinear Dynamics of Viscoelastic Pipe Conveying Pulsating Fluid Subjected to Base Excitation

Nonlinear Dynamics of Viscoelastic Pipe Conveying Pulsating Fluid Subjected to Base Excitation

Time-reversal technique for pipeline defect detection.

In this paper, time-reversal (TR) technique is proposed for the detection of discrete defects (e.g., leaks and blockages) in pressurized fluid-filled pipelines using active transient waves. The proposed technique is based on the one-dimensional wave equation and decouples the search for the location from that of the size of the defect. Another key feature of this method is that the measured pressure head signal can be truncated so as to eliminate undesirable reflections from unknown or uncertain parts of the pipe system so as not to compromise the accuracy and robustness of the detection. The proposed method is tested through numerical simulations for a single leak, multiple leaks, and multiple mixed-type of defects (i.e., leaks and blockages) in elastic as well as visco-elastic pipe systems. The proposed method is also validated through laboratory experiments wherein leaks and blockages of various sizes are considered. The sensitivity analysis of the method with respect to wave speed and signal-to-noise ratio (SNR) is also performed. In all cases, the method has shown accurate results in terms of localization, classification, and size estimation of the defects even for SNR as low as 0 dB.

Energy analysis of transient flow with cavitation by considering the effect of water temperature in viscoelastic pipes

Abstract Numerous studies on the pressure fluctuations and cavity volume variations of a transient cavitation flow in viscoelastic pipes are available in the literature. However, the effect of water temperature on the cavity volume and energy conversion has been studied less often. This paper employs the discrete vapor cavity model using quasi-steady friction and quasi-two-dimensional friction models to calculate the cavity volume for different water temperatures and investigates the effects of water temperature on the appearance of the first cavitation at the downstream valve, and on the pressure damping in a tank-piping-valve system using an integrated energy analysis approach. The results show that the differences between the pressure and energy variations of the transient cavitation flow simulated using different models were minimal under different water temperature conditions. Moreover, as the water temperature increased, the appearance time of the cavity is postponed, and the volume of the cavity decreases. The energy dissipation increases continuously with an increase in the volume of the cavitation and water temperature in viscoelastic pipes. This study provides valuable insights into the variation pattern of the cavity and the effect of vapor cavities on the rise and decay of the pipeline pressure in different situations.

Transient flow modeling in viscoelastic pipes: A comprehensive review of literature and analysis

Water hammer or flow transients occur due to a sudden variation (over time) in flow properties that can lead to pipe system failure or damage. In addition, research on wave propagation and signal processing theories has developed different ways to detect anomalies in pipe systems. The two developments concerning pipe system safety and damage localization are of essential need in viscoelastic (VE) pipes, as their application in various industries is growing, given their favorable mechanical properties. With no literature review focusing on the topic, this paper aims to fill the current literary gap on transient waves in VE pipes. It highlights developments in the research field and elaborates on relevant water hammer concepts in VE pipes, including mathematical modeling, experimental setups, numerical solutions, parameter calibration, defect detection, and surge control. The comprehensive review concludes that a reliable transient wave model in viscoelastic pipes is yet to be fully confirmed despite the significant progress in the recent two decades.

An analysis of fluid–structure interaction coupling mechanisms in liquid-filled viscoelastic pipes subject to fast transients

An extension of a recently developed quasi-2D flow model for fluid transients in viscoelastic pipes to handle fluid–structure interaction mechanisms is presented. In a context in which the fluid flow is devised as a structured pseudo-mixture and the pipe’s viscoelasticity is rooted in an internal variable theory, the axial movement of the pipe wall is allowed to occur, giving rise to friction, Poisson, and junction coupling mechanisms. The resulting governing equations of the model form a quasi-linear hyperbolic system of partial differential equations, which approximated solution is achieved by means of the method of characteristics. The proposed approach is validated against pressure traces acquired from a reservoir–pipe–valve experimental setup found in the literature. In the course of the validating process, different pipe anchoring conditions are employed to study the system responses. Focus is given to pipe–fluid interface interactions, energy dissipation, and transfer of energy between both media.

Frequency varying rheology-based fluid–structure-interactions waves in liquid-filled visco-elastic pipes

This contribution proposes a new rheology-based model for water-hammer wave propagation in visco-elastic pipes. Using a long wavelength analysis and a generalized frequency-dependent Hooke-law for the stress/strain relation, the pressure/longitudinal stress coupled wave system is derived. In this general framework, a visco-elastic Fluid–Structure Interaction (FSI) four equations model is derived by having four visco-elastic kernels associated with the non-local time response of the visco-elastic solid. The explicit dependence of these kernels with the material creep function and the pipe dimension is found. Considering a general linear visco-elastic rheology, the four visco-elastic kernels, and the corresponding creep function are explicitly derived in frequency and time-domain versus four visco-elastic parameters. For a given set of boundary conditions, a general analytical solution for the pressure/stress water hammer wave is obtained in frequency domain. The model’s predictions are successfully compared with experimental measurements as well as with other models adjusted to the same experimental data set by calibrating the model’s parameter. The proposed model can be used in many other contexts with the specific ability to distinguish the intrinsic visco-elastic rheology from the considered pipe geometry and boundary conditions.

Nonlinear dynamics of inclined viscoelastic pipes subjected to pulsatile flow and multi-harmonic excitations

Nonlinear dynamics of inclined viscoelastic pipes subjected to pulsatile flow and multi-harmonic excitations

Reynolds-Averaged Simulation of Drag Reduction in Viscoelastic Pipe Flow with a Fixed Mass Flow Rate

A high molecular polymer solution with viscoelasticity has the effect of reducing frictional drag, which is quite practical for energy saving. Effective simulations of viscoelastic flows in a pipeline with a high Reynolds number is realized by incorporating the constitutive equation of viscoelasticity into the k−ε−v′2¯−f turbulence model. The Finitely Extensive Nonlinear Elastic Peterlin (FENE-P) model is employed for characterizing the viscoelasticity. The drag reduction of fully developed viscoelastic pipe flow with a fixed mass flow rate is studied. Different from increasing the center velocity and without changing the velocity near the wall at a fixed pressure drop rate, the addition of a polymer reduces the velocity near the wall and increases the velocity at the center of the pipe and makes the flow tend to be a laminar flow. Decreasing the solvent viscosity ratio or increasing the maximum extensibility or the Weissenberg number can effectively reduce the turbulence intensity and the wall friction. Under the premise of ensuring calculation accuracy, this Reynolds-averaged simulation method for viscoelastic flow has significant advantages in both computational cost and accuracy, which is promising for drag reduction simulation and practical engineering applications.

Transient wave-leak interaction analysis for improved leak detection in viscoelastic pipelines

Transient wave reflection methods (TWRMs) have exhibited favorable capability in leak detection for elastic pipelines, but applications have demonstrated their relatively low accuracy for viscoelastic pipelines. This paper investigates the transient wave behaviour, the principal tenet for leak detection by TWRMs, in a leaky viscoelastic pipeline to understand the mechanism of wave modification by leaks and viscoelasticity. Based on the correspondence principle, this research derives analytical formulations of the leak-induced wave reflection and phase difference at any measurement point in a viscoelastic pipe. According to the measured reflection coefficient, an optimization algorithm is further developed to detect the leak. The methodologies are then assessed and discussed through sinusoidal and sigmoid perturbations in numerical and laboratory tests. The extensive analyses indicate that measurement distance and leak ratio affect the magnitude of the reflected wave, yet, the wave phase shift is relatively independent of the leak ratio for practical applications.

Simulation of oscillations of composite pipelines conveying pulsating fluid

The article considers the problem of vibrations of straight sections of the pipeline based on the theory of beams. A mathematical model of the dynamics of a straight viscoelastic pipe with a pulsating fluid is developed. The speed of a pulsating fluid is assumed to be harmonically fluctuating and has the following form: V(t) = υ0 (1 + μ1cosϖt). The mathematical model of the problem is simplified using the Bubnov-Galerkin approach to the solution of a set of common integro-differential equations with time as an independent variable. A numerical approach based on the removal of the singularity in the relaxation kernel of the integral operator is used to solve integro-differential equations. A numerical approach for the unknowns was used to get the system of algebraic equations. The Gauss technique is used to resolve a set of algebraic equations. The dynamics of fluid-transporting viscoelastic pipes have difficulties that can be solved computationally.

Viscoelastic Solutions and Investigation for Creep Behavior of Composite Pipes under Sustained Compression

Composite pipes, which are widely used for transporting fluids, have a high strength, good impermeability and strong resistance to external pressure. Because the pipe bears a sustained load, and its constituent materials usually possess time-dependent properties, the creep phenomenon unavoidably occurs in the composite pipes in the long run. The aim of this study is to propose analytical viscoelastic solutions, which are then applied to a composite pipe structure to explore the creep behavior of composite pipes under sustained compression. The pipe layers and the bonding interlayer both exhibit viscoelastic properties, which are the novelty of this study. The governing equations for the viscoelastic composite pipe are built on the basis of exact elasticity theory combined with the viscoelastic theory. General solutions are derived by means of a Fourier series expansion in which the coefficients are further determined by a Laplace transform. The research results indicate that the present solution has a higher computational efficiency than the finite element solution, because of the latter involving the time discretization method. In addition, for the viscoelastic pipe, if the modulus degradation of the neighboring laminar layers is proportional, the stresses can keep constant with time, as in a purely elastic material.

Modified Factorized Transient Wave Model in Tree Pipe Networks for Leak Localization With Less Boundary Measurements

AbstractPressure measurement within each boundary pipe of a tree network has been the prerequisite to the formulation of its factorized transient wave propagation model, which is essential for developing a robust and efficient leak localization algorithm. However, the accessibility of all boundary pipes cannot be always guaranteed in underground pipe networks. The inaccessibility of any one boundary pipe for pressure sensor placement would result in the complete invalidity of this elegant algorithm. To address this problem, this paper reformulates and modifies the factorized wave propagation model, which allows the leak localization algorithm to be implemented without the strict accessibility requirement of all boundary pipes. This is realized by linearizing and factorizing the point transfer matrices of boundary pipes based on the small leak approximation. Numerical experiments demonstrate that the modified algorithm can accurately localize a single leak and give a good estimation of multiple co‐existing leaks in a tree network. Moreover, the modified algorithm is verified by recent laboratory experiments conducted in a tree network of viscoelastic pipes, where a leak is successfully localized.