Un nouveau modele mathematique a ete developpe pour calculer les regimes transitoires hydrauliques des systemes de conduites pressurisees en polyethylene (PE). Ce modele hydraulique (nomme HTS) integre des termes additionnels pour simuler la friction pendant le regime transitoire et l'effet de la viscoelasticite de la conduite. Les resultats numeriques obtenus ont ete compares avec la solution classique du coup de belier et avec les resultats experimentaux collectes a partir d'un systeme de conduites simples en PE construit au Imperial College (Londres, Royaume Unit). Contrairement au modele classique, le modele HTS est capable de predire rigoureusement les fluctuations transitoires de pression dans la conduite de PE ainsi que l'extension de la circonference des parois de la conduite. Le grand challenge de ce travaille est la distinction entre l'effet dynamique de la friction transitoire et l'effet mecanique de la deformation retardee de la conduite. Dans un premier temps, le modele HTS a ete calibre et teste en considerant les deux effets separement. Lorsque la friction en regime transitoire est consideree seule, de grandes differences entre les resultats experimentaux et numeriques sont observees. Si l'effet viscoelastique de la conduite est considere seul, meme avec une bonne correlation entre les resultats experimentaux et numeriques, les fonctions des fluage calibrees varient avec le flux initial. Dans un deuxieme temps, la combinaison de ces deux effets a ete analysee et une bonne correspondance entre les resultats experimentaux et numeriques a ete observee. Enfin, le modele HTS a ete verifie avec succes en utilisant la fonction de fluage mesuree lors d'un test mecanique negligeant la friction en regime transitoire.

The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II—model development, calibration and verification

The mechanical behaviour of the pipe material determines the pressure response of a fluid system during the occurrence of transient events. in viscoelastic pipes, typically made of polyethylene (pe), maximum or minimum transient pressures are rapidly attenuated and the overall pressure wave is delayed in time. this is a result of the retarded deformation of the pipe-wall. this effect has been observed in transient data collected in a high-density pe pipe-rig, at imperial college (london, uk). several transient tests were carried out to collect pressure and circumferential strain data. the pipe material presented a typical viscoelastic mechanical behaviour with a sudden pressure drop immediately after the fast valve closure, a major dissipation and dispersion of the pressure wave, and transient mechanical hysteresis. the creep-function of the pipe material was experimentally determined by creep tests, and, its order-of-magnitude was estimated based on pressure-strain data collected from the pipe-rig. a goo...

The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part I—experimental analysis and creep characterization

A state-of-the-art mathematical model has been developed to calculate hydraulic transients in pressurized polyethylene (PE) pipe systems. This hydraulic transient solver (HTS) incorporates additional terms to take into account unsteady friction and pipe-wall viscoelasticity. Numerical results obtained were compared with the classic waterhammer solution and with experimental data collected from a PE pipe-rig at Imperial College (London, UK). Unlike the classical model, the developed HTS is capable of accurately predicting transient pressure fluctuations in PE pipes, as well as circumferential strains in the pipe-wall. The major challenge was the distinction between frictional and mechanical dynamic effects. First, the HTS was calibrated and tested considering these two effects separately: if only unsteady friction was considered, a major disagreement between collected data and numerical results was observed; when only the viscoelastic effect was considered, despite the good agreement between data and numerical results, the calibrated creep function depended on the initial flow rate. In a second stage, the combination of these dynamic effects was analysed: creep was calibrated for laminar flow and used to test the solver for turbulent conditions, and a good agreement was observed. Finally, the HTS was tested using creep measured in a mechanical test, neglecting unsteady friction, and a good agreement was obtained.

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The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II— model development, calibration and verification L'effet dynamique de la viscoélasticité de la conduite en régimes transitoires hydrauliques. Partie II—développement, calibrage and vérification du modèle mathématique

This two-part review article presents an overview of mechanics of pipes conveying fluid and related problems such as the fluid-elastic instability under conditions of turbulence in nuclear power plants. In the first part, different types of modeling, dynamic analysis, and stability regimes of pipes conveying fluid restrained by elastic or inelastic barriers are described. The dynamic and stability behaviors of pinned-pinned, clamped-clamped, and cantilevered pipes conveying fluid together with curved and articulated pipes will be discussed. Other problems such as pipes made of viscoelastic materials and active control of severe pipe vibrations are considered. This part will be closed by conclusions highlighting resolved and nonresolved controversies reported in literature. The second part will address the problem of fluid-elastic instability in single- and two-phase flows and fretting wear in process equipment such as heat exchangers and steam generators. Connors critical velocity will be discussed as a measure of initiating fluid-elastic instability. Vibro-impact of heat exchanger tubes and the random excitation by the cross-flow can produce a progressive damage at the supports through fretting wear or fatigue. Antivibration bar supports used to limit pipe vibrations are described. An assessment of analytical, numerical, and experimental techniques of fretting wear problem of pipes in heat exchangers will be given. Other topics related to this part include remote impact analysis and parameter identification, pipe damage-induced by pressure elastic waves, the dynamic response and stability of long pipes, marine risers together with pipes aspirating fluid, and carbon nanotubes conveying fluid.

Overview of Mechanics of Pipes Conveying Fluids—Part I: Fundamental Studies

This two-part paper investigates key parameters that may affect the pressure waveform predicted by the classical theory of water-hammer. Shortcomings in the prediction of pressure wave attenuation, shape and timing originate from violation of assumptions made in the derivation of the classical waterhammer equations. Possible mechanisms that may significantly affect pressure waveforms include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction (FSI) effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Engineers should be able to identify and evaluate the influence of these mechanisms, because first these are usually not included in standard water-hammer software packages and second these are often “hidden” in practical systems. Part 1 of the two-part paper describes mathematical tools for modelling the aforementioned mechanisms. The method of characteristics transformation of the classical water-hammer equations is used herein as the basic solution tool. In separate additions: a convolution-based unsteady friction model is explicitly incorporated; discrete vapour and gas cavity models allow cavities to form at computational sections; coupled extended water-hammer and steel-hammer equations describe FSI; viscoelastic behaviour of the pipe-wall material is governed by a generalised Kelvin–Voigt model; and blockages and leakages are modelled as end or internal boundary conditions.

http://www.civil.ist.utl.pt/~didia/Publications/RI_11%20(2008)%20Bergant%20et%20al_Part%20I%20(JHR).pdf

Parameters affecting water-hammer wave attenuation, shape and timing—Part 1: Mathematical tools Paramètres affectant l'atténuation, la forme et le retard du coup de bélier—Partie 1: Modèles mathématiques

This theoretical study of the effect of viscoelastic material properties of a pipe conveying one-dimensional, non-stationary flow shows that, in addition to exponential attenuation of wave fronts, the disturbance is transformed into a diffusion front whose thickness increases as √t, and which propagates at a velocity corresponding to the retarded elasticity of the pipe material [E(∞)] The behaviour of pressure disturbances in the special case of water-hammer resulting from sudden closure of a valve is illustrated by a numerical application based on the characteristics method For a pipe of finite length L fed from a constant-level tank, a damped oscillation of period 2L/ā is observed, corresponding to a pseudo-velocity of propagation ā which is calculated on the assumption that deformations associated with relaxation times smaller than 2L/a 0 are instantaneous, where a 0is the true elastic wave celerity (a 0>ā)

A. Blanchard

Papers

Pulsating Viscoelastic Pipe Flow - Water-Hammer