Poisson Coupling Research Articles

Dynamic Analysis of Submarine-Buried Pipelines Considering Fluid–Structure Interaction

Buried pipes are widely used for submarine water transportation, but the complex operating conditions in the seabed pose challenges for the modeling of buried pipes. In order to more accurately capture the dynamic behavior of the buried pipes in the seabed, in this study, considering the pipeline and soil as a systematic structure is proposed, improving the fluid–structure interaction four-equation model to make it applicable for the calculation of buried pipe system modes. After verifying the practicality of the model, considering the external seawater as uniform pressure, the coupling at the joints, and the Poisson coupling of submarine pipelines during transient processes are discussed, revealing that structural vibrations under both forms of coupling will cause greater hydraulic oscillations. The impact of soil elastic modulus on the system’s response is further discussed, revealing that increasing the modulus from 0 to 1015 Pa raises the wave speed from 498 m/s to 1483 m/s, causing a 40% increase in the amplitude of pressure oscillations. Finally, the vibration modes of the combined structure of pipe wall and soil are discussed, revealing that the vibration modes are mainly dominated by water hammer pressure, with the superposition of pipeline stress waves and soil stress waves. In this study, the dynamic behavior of submarine pipelines is elucidated, providing a robust foundation for regulating and mitigating fatigue failures in such systems.

Research on digital vibration model of typical components in pipe system

The spatial distribution of pipe system is complex, long span and multi-point elastic support, so vibration analysis of pipe system is required in the pipeline design. This paper takes the pipe system as a typical component, based on the Timoshenko beam model, establishes a dynamic procedure for straight pipe elements that considers the axial flow rate of fluid, the pressure on the pipe wall, the Poisson coupling effect of fluid and pipeline structure, and the axial, transverse and torsional vibration. Through Laplace transform, the frequency simplified dynamic model is established. And the frequency transfer matrix model of straight pipe elements and the boundary constraint matrix of common boundary (such as fixed support) is established. Finally, the frequency domain transfer matrix model of different pipeline elements are set to the overall transfer matrix of the flow pipe system, providing a convenient means for rapid optimization of pipe system vibration.

Dynamic Responses in a Pipe Surrounded by Compacted Soil Suffering from Water Hammer with Fluid–Structure–Soil Interactions

The current literature analyzing the dynamic response of coupled pipelines neglects the crucial interplay between the pipelines themselves and these constraints. This overlooked interaction has substantial influence on the fluid–structure coupling response, particularly in scenarios involving continuous constraints. We focus on a piping system surrounded by compacted soil, which is regarded as unbounded homogeneous elastic soil that suffers from water hammer. This study established a one-dimensional model for water pipe-embedded compacted soil with fluid–structure–soil interaction. Taking fluid–structure–soil interaction into account, fluid–structure interactions (FSIs) include Poisson coupling, junction coupling emerging at the fluid–structure interface, and pipe–soil coupling (PSC) emerging at the pipe–soil interface. In this study, as soil is assumed to be a homogeneous, isotropic elastic material, the coupling responses are more complex than those of an exposed pipe, and the relevant mechanisms justify further exploration to obtain well-predicted results. To mathematically describe this system considering fluid–structure–soil interaction, the four-equation FSI model was modified to accommodate the piping system surrounded by unbounded homogeneous elastic soil, employing the finite volume method (FVM) as a means to tackle and solve the dynamic problems with FSI and PSC, which partitions the computational domain into a finite number of control volumes and discretizes governing equations within each volume. The results were validated by the experimental and numerical results. Then, dynamic FSI responses to water hammer were studied in a reservoir–pipe–reservoir physical system. The hydraulic pressure, pipe wall stress, and axial motion were discussed with respect to different parameters. With the PSC and FSI taken into account, fluid, soil, and pipe signals were obviously observed. The results revealed the structural and fluid modes. Dynamic responses have been proven to be difficult to understand and predict. Despite this, this study provides a tractable method to capture more accurate systematic characteristics of a water pipe embedded in soil.

Fluid-structure interaction characteristics between natural gas fluid and tubing string in high-pressure high-temperature high-production gas wells

The transient internal flow in high-pressure high-temperature high-production (three-high) gas wells may bring about serious fluid-structure interaction (FSI) between natural gas fluid and tubing string. Then, fatigue failure, wear and leakage of tubing string can easily be caused to threaten the wellbore safety and integrity. However, it is difficult to directly adopt the existing FSI model owing to particularity environment of the three-high gas wells. Based on water hammer, FSI and Timoshenko beam theory, a mathematical model expounding FSI phenomenon of the three-high gas wells is established by Poisson, friction and junction coupling, which considers unsteady friction effect, centrifugal and Coriolis force to make FSI characteristics more consistent with the engineering practice. Then, the improved method of characteristics (MOC) is applied into combination solution of the model. Later, the model and solution method is verified by comparing the results with different reference's ones respectively. On this basis, the effects of shut-in time, well depth position, unsteady friction on FSI characteristics are analyzed and discussed systematically. The calculation results are shown that shut-in time and well depth position have a more significant influence on FSI characteristics in three-high gas wells. In addition, FSI characteristics under action of unsteady friction decay faster, the time of the peak value also is delayed accordingly, and cumulative attenuation and cumulative delayed time of FSI characteristics increases with decrease of shut-in time. The FSI model, solution method proposed in this paper and results can provide theoretical basis and reference for the research on FSI and the formulation of shut-in operation for three-high gas wells, and even for highly deviated or horizontal gas wells.

Adaptive symplectic model order reduction of parametric particle-based Vlasov–Poisson equation

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of parameters. In this work, we derive reduced order models for the semi-discrete Hamiltonian system resulting from a geometric particle-in-cell approximation of the parametric Vlasov–Poisson equations. Since the problem’s nondissipative and highly nonlinear nature makes it reducible only locally in time, we adopt a nonlinear reduced basis approach where the reduced phase space evolves in time. This strategy allows a significant reduction in the number of simulated particles, but the evaluation of the nonlinear operators associated with the Vlasov–Poisson coupling remains computationally expensive. We propose a novel reduction of the nonlinear terms that combines adaptive parameter sampling and hyper-reduction techniques to address this. The proposed approach allows decoupling the operations having a cost dependent on the number of particles from those that depend on the instances of the required parameters. In particular, in each time step, the electric potential is approximated via dynamic mode decomposition (DMD) and the particle-to-grid map via a discrete empirical interpolation method (DEIM). These approximations are constructed from data obtained from a past temporal window at a few selected values of the parameters to guarantee a computationally efficient adaptation. The resulting DMD-DEIM reduced dynamical system retains the Hamiltonian structure of the full model, provides good approximations of the solution, and can be solved at a reduced computational cost.

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.

Transient longitudinal waves on impact excited viscoelastic rods with lateral inertia.

An analytical and numerical Fourier transform based approach is presented to investigate the space-time dependence for the longitudinal velocity resulting from the longitudinal impact force excitation of viscoelastic rods with lateral inertia. A one-dimensional dissipative Rayleigh-Love wave equation including material memory, dissipation, and/or transverse effects due to Poisson coupling is developed from a generic model of the time dependent stress strain relationship for the rod material. A Gaussian signal with a suitable time scale is used to represent the hammer impact forces. Fourier transform, standing wave, and modal methods are utilized to develop analytical solutions for the longitudinal velocity resulting from the impact excitation of semi-infinite and finite length free-free elastic rods with no transverse effects to provide a baseline and segue to analogous results for viscoelastic rods with transverse effects. Numerical results from an FFT approach are presented to illustrate the effects of material losses and transverse effects on attenuation and dispersion in viscoelastic rods using the Kelvin-Voigt model for the constitutive equation of the rods.

Response analysis and safety control of tubing vibration in HPHT and ultra-deep gas wells

Under the condition of high pressure, high temperature(HPHT) and high yield in ultra-deep wells, the buckling deformed tubing will produce violent vibration when opening and closing the well or production fluctuation, which will make the tubing bear large periodic fluctuating load, cause the failure of tubing thread seal, form fluid leakage channel, and induce the problem of sustained casing pressure(SCP). Serious annulus pressure will lead to increased tubing leakage, casing failure or more serious consequences. In order to explore the failure process of well barrier caused by tubing vibration in HPHT and ultra-deep wells, a fluid solid coupling vibration model of tubing is established, and the coupling vibration equation is numerically solved by the characteristic line method. Finally, an example of a gas well in the west is analyzed. The calculation results show that there is an obvious Poisson coupling effect between the tubing and the gas in the pipe in well X. The axial stress of the tubing is always in an unstable pulsating alternating stress state, reciprocating vibration along the axis and gradually attenuated to stability; the closer to the wellhead, the more violent the gas fluctuation in the pipe, and the greater the axial vibration amplitude of the upper part of the tubing away from the wellhead; large vibration of tubing may induce seal failure, resulting in oil jacket connection and pressure on a annulus; finally, the allowable annulus pressure of the example well is calculated, and the annulus pressure control measures are put forward. The research results have good guiding significance for well barrier failure analysis and annulus pressure control caused by tubing vibration in HPHT ultra-deep wells.

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.

Macroscopic approximation of a Fermi-Dirac statistics: Unbounded velocity space setting

An approximation by diffusion of a nonlinear Boltzmann equation modeling a Fermi-Dirac statistics is analyzed for an unbounded velocity space and Poisson coupling. A careful analysis of the entropy and entropy-dissipation allows to control the distribution function and to pass to the limit using duality method.

Vibration transmission characteristics of complex lubricating oil pipeline system

Considering the axial, lateral and torsional vibrations and considering the effect of Poisson coupling in the axial vibration, ignoring the effect of friction, based on the Timoshenko beam model, a dynamic model of the lubricating oil pipeline system with force and speed as variables is established. Using lubricating oil pumps and valves as vibration sources, the vibration characteristics of multi-branch lubricating oil pipeline systems including elbows are studied. The results show that due to the coupling of lubricating oil and pipeline structure, the vibration peak and peak frequency of pipeline system are significantly reduced, but the frequency lateral vibration response amplitude increases significantly at some characteristic frequency; when the pipeline support stiffness increases, the natural frequency of the pipeline increases, causing the peak frequency of pipeline vibration to shift to high frequency, and the peak frequency resolution increases.

$$\text {L}^2$$-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov–Poisson–Fokker–Planck System

This paper is devoted to the linearized Vlasov–Poisson–Fokker–Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar product adapted to the presence of a Poisson coupling. Our framework provides estimates which are uniform in the diffusion limit. As an application in a simple case, we study the one-dimensional case and prove the exponential convergence of the nonlinear Vlasov–Poisson–Fokker–Planck system without any small mass assumption.

Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus

The Vlasov-Poisson system with massless electrons (VPME) is widely used in plasma physics to model the evolution of ions in a plasma. It differs from the Vlasov-Poisson system (VP) for electrons in that the Poisson coupling has an exponential nonlinearity that creates several mathematical difficulties. In particular, while global well-posedness in 3 D is well understood in the electron case, this problem remained completely open for the ion model with massless electrons. The aim of this paper is to fill this gap by proving uniqueness for VPME in the class of solutions with bounded density, and global existence of solutions with bounded density for a general class of initial data, generalising all the previous results known for VP.

Micropolar homogenization of wavy tetra-chiral and tetra-achiral lattices to identify axial–shear coupling and directional negative Poisson's ratio

Chiral lattices are generally considered to possess auxetic properties with negative Poisson's ratios and high compressibility. However, the effects of anisotropy and handedness (chirality) on their mechanical properties, such as directional moduli, Poisson's ratio, and other coupling effects, are not clearly understood due to the lack of analytical methods to handle both anisotropy and chirality. Herein, we construct a generalized micropolar homogenization method to characterize the elastic constants of tetra-chiral and tetra-achiral lattices having different joint types. The developed method can identify the directional moduli and Poisson's ratio and coupling effects in the anisotropic wavy lattices. The generalized micropolar homogenization of the wavy square lattices reveals i) the axial–shear coupling effect of tetra-chiral structures, ii) the weak correlation of the chirality of tetra-chiral lattices to auxeticity, and iii) the directional positive and negative Poisson's ratio of tetra-achiral lattices. This work offers a powerful platform for metamaterials' design via geometric reconfiguration of lattice structures to adjust both anisotropy and chirality.

Transient-based leak detection in the frequency domain considering fluid–structure interaction and viscoelasticity

Waterhammer induced fluid–structure interaction (FSI) of a leaky viscoelastic (VE) pipe is simulated in the frequency-domain. The developed model is then applied to assess the accuracy of leak detection when both FSI and VE phenomena are represented. FSI arises due to the coupling of wall stress and pressure waves, which can significantly distort the response spectra. The frequency response of the transient waves is derived using the transfer matrix method, which is then exploited for localization using a maximum likelihood estimate. Several numerical cases including one or two leaks are studied while Poisson and junction coupling both with and without VE wall behaviour. The results demonstrate that including FSI effects can allow leaks to be more accurately located. Not surprisingly, the importance of FSI mechanisms in leak detection is shown to be more crucial in VE pipes than in elastic pipes because of their larger Poisson effects.

On the global existence for the compressible Euler–Poisson system, and the instability of static solutions

We consider the Cauchy problem for the barotropic Euler system coupled to Poisson equation, in the whole space. Our main aim is to exhibit a simple functional framework that allows to handle solutions with density going to zero at infinity, but that need not be compactly supported. We have in mind in particular the 3D static solution, when the polytropic index $$\gamma $$ of the gas is equal to 6/5. Our first result is the local existence of classical solutions in a simple functional framework that does not require the velocity to tend to 0 at infinity and the density to be compactly supported. Next, following the work by Grassin and Serre dedicated to the compressible Euler system Grassin and Serre (C R Acad Sci Paris Ser I 325:721–726, 1997, Grassin (Indiana Univ Math J, 47:1397–1432, 1998), we show that if the initial density is small enough, and the initial velocity is close to some reference vector field $$u_0$$ such that the spectrum of $$Du_0$$ is positive and bounded away from zero, then the corresponding classical solution is global, and satisfies algebraic time decay estimates. Compared to our recent paper (Blanc et al. in The global existence issue for the compressible Euler system with Poisson or Helmholtz coupling), we are able to handle the 3D static solution that was mentioned above, and to show its instability, within our functional framework.

Fluid-structure interaction during water hammer in a pipeline with different performance mechanisms of viscoelastic supports

The aim of this research is to model various types of viscoelastic supports and to investigate their effects on the fluid-structure interaction (FSI) during the water hammer in straight pipeline systems. Three performance mechanisms of viscoelastic supports are considered. The first is the viscoelastic supports with axial deformation, the second is viscoelastic supports with shear deformation and the third is the viscoelastic supports with both sliding and shear deformation mechanisms. The Poisson and junction coupling were taken into account as the main interacting mechanisms. The viscoelastic behavior of the pipe-wall and the supports was described by the generalized Kelvin-Voigt mechanical model. By providing boundary conditions for the different types of viscoelastic supports modeling at the valve location and along the pipe, the governing equations were solved using the full MOC method in the time domain. The results demonstrated that the use of viscoelastic supports with axial and shear deformation mechanisms are effective in the damping of the pressure head vibrations and reducing the displacement of the pipe-wall caused by FSI. The viscoelastic supports with the shear deformation mechanism exhibited better performance compared to those with the axial deformation mechanism. The results also showed that the behavior of viscoelastic supports with both sliding and shear mechanisms depended on the amount of frictional force in the supports. Using plates with an appropriate friction coefficient for the sliding viscoelastic supports caused a significant reduction in the amount of pressure head and displacement of the pipe-wall as well as considerable pressure head fluctuations damping compared to the performance of two other mechanisms of viscoelastic supports in a similar situation, especially in the elastic pipe.

Frequency response of water hammer with fluid-structure interaction in a viscoelastic pipe

Fluid-structure interaction (FSI) during water hammer in a viscoelastic (VE) pipe is studied in the frequency domain. The main aim is to investigate pressure and stress waves using Transfer Matrix Method (TMM) in a typical reservoir-VE pipe-valve (RPV) system. Both major coupling mechanisms namely Poisson and junction are taken into account. The generalized Kelvin-Voigt model simulates VE behavior during water hammer, which is generated by a quick closing/opening of downstream valve. The effect of viscoelasticity is modeled by Volterra integrals (in time) which are written as the products of transforms of the creep function and pressure (or stress) in the Laplace domain. The developed formulation is adopted to solve two well-known FSI problems from literature, and both demonstrate favorable agreement with available analytical and experimental data. To investigate the sole/simultaneous effect of Poisson and/or junction coupling and viscoelasticity, a hypothetical case study is considered and the corresponding results are closely investigated. The robust performance of the Transfer Matrix Method (TMM) allows for deducing the drop of pressure amplitudes due to viscoelasticity, frequency shift of Poisson coupling, and remarkable discrepancy of odd frequencies (relative to classical model) induced by junction coupling. This research is of crucial importance when frequency-response-based methods are utilized for defect detection of unrestrained pipes.

Fluid-Structure Interaction Response of a Water Conveyance System with a Surge Chamber during Water Hammer

Fluid–structure interaction (FSI) is a frequent and unstable inherent phenomenon in water conveyance systems. Especially in a system with a surge chamber, valve closing and the subsequent water level oscillation in the surge chamber are the excitation source of the hydraulic transient process. Water-hammer-induced FSI has not been considered in preceding research, and the results without FSI justify further investigations. In this study, an FSI eight-equation model is presented to capture its influence. Both the elbow pipe and surge chamber are treated as boundary conditions, and solved using the finite volume method (FVM). After verifying the feasibility of using FVM to solve FSI, friction, Poisson, and junction couplings are discussed in detail to separately reveal the influence of a surge chamber, tow elbows, and a valve on FSI. Results indicated that the major mechanisms of coupling are junction coupling and Poisson coupling. The former occurs in the surge chamber and elbows. Meanwhile, a stronger pressure pulsation is produced at the valve, resulting in a more complex FSI response in the water conveyance system. Poisson coupling and junction coupling are the main factors contributing to a large amount of local transilience emerging on the dynamic pressure curves. Moreover, frictional coupling leads to the lower amplitudes of transilience. These results indicate that the transilience is induced by the water hammer–structure interaction and plays important roles in the orifice optimization in the surge chamber.

Experimental investigation of transients-induced fluid–structure interaction in a pipeline with multiple-axial supports

Fluid–Structure Interaction (FSI) in pipes can significantly affect pressure fluctuations during water hammer event. In transmission pipelines, anchors with axial stops have an important role in the waterhammer-induced FSI as they can suppress or allow the propagation of additional stress waves in the pipe wall. More specifically, a reduction in the number of axial stops and/or their stiffness causes significant oscillations in the observed pressure signal due to the enhancement of Poisson’s coupling. To confirm these physical arguments, this research conducts experimental investigations and then processes the collected pressure signals. The laboratory tests were run on an anchored pipeline with multiple axial supports which some of them removed at some sections to emerge Poisson’s coupling. The collected pressure signals are analyzed in the time and frequency domain in order to decipher fluctuations that stem from Poisson coupling and other anchors effects. The analysis of the laboratory data reveals that the pattern of the time signals of pressure is primarily affected by the stiffness and location of the supports. Likewise, the properties of structural boundaries characterize the frequency spectrum of the transient pressures, which is manifested by altering the amplitudes corresponding to dominant frequencies of the system. The study is of particular importance in practice of transient based defect detections and pipe system design.