No abstract

This paper reviews a number of unsteady friction models for transient pipe flow. Two distinct unsteady friction models, the Zielke and the Brunone models, are investigated in detail. The Zielke model, originally developed for transient laminar flow, has been selected to verify its effectiveness for "low Reynolds number" transient turbulent flow. The Brunone model combines local inertia and wall friction unsteadiness. This model is verified using the Vardy's analytically deduced shear decay coefficient C* to predict the Brunone's friction coefficient k rather than use the traditional trial and error method for estimating k. The two unsteady friction models have been incorporated into the method of characteristics water hammer algorithm. Numerical results from the quasi-steady friction model and the Zielke and the Brunone unsteady friction models are compared with results of laboratory measurements for water hammer cases with laminar and low Reynolds number turbulent flows. Conclusions about the range of validity for the three friction models are drawn. In addition, the convergence and stability of these models are addressed. RESUMELe papier passe en revue un certain nombre de modeles de friction non permanente en ecoulement transitoire en conduite. Deux modeles de friction non permanente, celui de Zielke et celui de Brunone sont investigues en details. Le modele de Zielke, developpe a l'origine pour les ecoulements transitoires laminaires, a ete selectionne pour tester l'efficacite du modele pour les ecoulements transitoires turbulents a faible nombre de Reynolds. Le modele de Brunone combine la variation de l'inertie locale et de la friction de paroL Ce modele est verifie en utilisant Ie coefficient C* d'amortissement du cisaillement de Vardy dCduit analytiquement pour predire Ie coefficient de friction k de Brunone, plutot que la method traditionnelle par essais et erreurs pour estimer k. Les deux modeles de friction non permanente ont ete incorpores dans un algorithme de calcul du coup de belier par la methode des caracteristiques. Les resultats numeriques obtenus a partir d'un modele de friction quasi permanente et a partir des modeles non permanents de Zielke et de Brunone sont compares avec des resultats de mesures en laboratoire pour des ecoulements laminaires ou turbulents a faible nombre de Reynolds. Des conclusions sont tirees sur les domaines de validite des trois modeles de friction. En complement, la convergence et la stabilite des modeles sont abordees. IntroductionTraditionally the steady or quasi-steady friction terms are incorporated into the standard water hammer algorithms. This assumption is satisfactory for slow transients where the wall shear stress has a quasi-steady behaviour. Experimental validation of steady friction models for rapid transients [1,2,3,4,5] previously has shown significant discrepancies in attenuation and phase shift of pressure traces when the computational results are compared to the results of measurements. The discrepancies are introduced by a difference in ve...

Emptying of an initially water-filled horizontal PVC pipeline driven by different upstream compressed air pressures and with different outflow restriction conditions, with motion of an air-water front through the pressurized pipeline, is investigated experimentally. Simple numerical modeling is used to interpret the results, especially the observed additional shortening of the moving full water column due to formation of a stratified water-air "tail." Measured discharges, water-level changes, and pressure variations along the pipeline during emptying are compared using control volume (CV) model results. The CV model solutions for a nonstratified case are shown to be delayed as compared with the actual measured changes of flow rate, pressure, and water level. But by considering water-column mass loss due to the water-air tail and residual motion, the calibrated CV model yields solutions that are qualitatively in good agreement with the experimental results. A key interpretation is that the long air-cavity celerity is close to its critical value at the instant of minimum flow acceleration. The influences of driving pressure, inertia, and friction predominate, with the observed water hammer caused by the initiating downstream valve opening insignificantly influencing the water-air front propagation.

A generalized set of pipeline column separation equations is presented describing all conventional types of low-pressure regions. These include water hammer zones, distributed vaporous cavitation, vapor cavities, and shocks (that eliminate distributed vaporous cavitation zones). Numerical methods for solving these equations are then considered, leading to a review of three numerical models of column separation. These include the discrete vapor cavity model, the discrete gas cavity model, and the generalized interface vaporous cavitation model. The generalized interface vaporous cavitation model enables direct tracking of actual column separation phenomena (e.g., discrete cavities, vaporous cavitation zones), and consequently, better insight into the transient event.Numerical results from the three column separation models are compared with results of measurements for a number of flow regimes initiated by a rapid closure of a downstream valve in a sloping pipeline laboratory apparatus. Finally, conclusions are drawn about the accuracy of the modeling approaches. A new classification of column separation (active or passive) is proposed based on whether the maximum pressure in a pipeline following column separation results in a shortduration pressure pulse that exceeds the magnitude of the Joukowsky pressure rise for rapid valve closure. INTRODUCTIONWater hammer in a pipeline results in column separation when the pressure drops to the vapor pressure of the liquid. A negligible amount of free and released gas in the liquid is assumed during column separation in most industrial systems (Hansson et al. 1982;Wylie 1984). Two distinct types of column separation may occur. The first type is a localized vapour cavity with a large void fraction. A localized (discrete) vapour cavity may form at a boundary (e.g., closed valve or dead end) or at a high point along the pipeline. In addition, an intermediate cavity may form as a result of the interaction of two low-pressure waves along the pipe. The second type of column separation is distributed vaporous cavitation that may extend over long sections of the pipe. The void fraction for the mixture of the liquid and liquid-vapor bubbles in distributed vaporous cavitation is small (close to zero). This type of cavitation occurs when a rarefaction wave progressively drops the pressure in an extended region of the pipe to the liquid vapour pressure. Both the collapse of a discrete vapor cavity and the movement of the shock wave front into a distributed vaporous cavitation region condenses the vapor phase back to the liquid phase. Piping systems may therefore experience combined water hammer and column separation effects during transient events (Streeter 1983;Bergant and Simpson 1992;Wylie and Streeter 1993).

This twin 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 water-hammer 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 pipewall 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 waterhammer software packages and second these are often "hidden" in practical systems.This Part 1 of the twin paper describes mathematical tools for modelling the aforementioned mechanisms. The method of characteristics (MOC) 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

Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. ABSTRACTThis study presents results from detailed experiments of the two-phase pressurized flow behavior during the rapid filling of a large-scale pipeline. The physical scale of this experiment is close to the practical situation in many industrial plants. Pressure transducers, water level meters, thermometers, void fraction meters and flow meters were used to measure the two-phase unsteady flow dynamics. The main focus is on the water-air interface evolution during filling and the overall behavior of the lengthening water column. It is observed that the leading liquid front does not entirely fill the pipe cross section; flow stratification and mixing occurs. Although flow regime transition is a rather complex phenomenon, certain features of the observed transition pattern are explained qualitatively and quantitatively. The water flow during the entire filling behaves as a rigid column as the open empty pipe in front of the water column provides sufficient room for the water column to occupy without invoking air compressibility effects. As a preliminary evaluation of how these large-scale experiments can feed into improving mathematical modeling of rapid pipe filling, a comparison with a typical one-dimensional rigid-column model is made.

This twin paper investigates parameters that may significantly affect water-hammer wave attenuation, shape and timing. Possible sources that may affect the waveform predicted by classical water hammer-theory 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. Part 1 of the twin paper presents the mathematical tools needed to model these sources. Part 2 of the paper presents a number of case studies showing how these modelled sources affect pressure traces in a simple reservoir-pipelinevalve system. Each case study compares the obtained results with the standard (classical) waterhammer model, from which conclusions are drawn concerning the transient behaviour of real systems. RÉSUMÉCet article, publié en deux parties, étudie les paramètres qui peuvent avoir un effet significatif sur l'atténuation, la forme et le retard de la variation de pression pendant un coup de bélier. Les phénomènes non considérés par la théorie classique du coup de bélier qui peuvent modifier la forme d'onde sont notamment la friction transitoire, la cavitation (y compris la séparation de la 2 colonne et les poches d'air), l'interaction entre le fluide et la structure (FSI), le comportement viscoélastique du matériel de la conduite, les fuites et les blocages. La première partie de cet article présente les modèles mathématiques de calcul des effets de ces phénomènes. La deuxième partie présente une étude de cas qui illustre l'effet de ces phénomènes sur la variation de pression dans un système simple, composé d'un réservoir, d'une conduite et d'une valve. Dans l'étude de cas, les résultats obtenus sont comparés avec ceux du modèle classique du coup de bélier. Les conclusions sur le comportement réel des systèmes de conduites pendant le régime transitoire du coup de bélier sont tirées à partir de ces résultats.

In this paper, basic unsteady flow types and transient event types are categorised, and then Additionally, numerical errors arising from the approximate implementation of the instantaneous acceleration-based model are determined, suggesting some previous good fits with experimental data are due to numerical error rather than the unsteady friction model.The convolution-based model is successful for all transient event types. Both approaches are tested against experimental data from a laboratory pipeline.