Effects of Two-Dimensionality on Pipe Transients Modeling

Brunone, Bruno; Golia, Umberto M.; Greco, Massimo

doi:10.1061/(asce)0733-9429(1995)121:12(906)

Cited by 163 publications

(63 citation statements)

References 10 publications

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“…7 fails to predict the correct sign in case of closure of the upstream end valve in a simple pipeline system with initial flow is in positive x direction. The original Brunone formulation performs correctly in case of closure of the downstream end valve [5], [8].…”

Section: The Original Brunone Model and The Vftkovsky Formulation Of mentioning

confidence: 99%

“…The magnitude of the discrepancies is governed by flow conditions (fast or slow transients, laminar or turbulent flow) and liquid properties (viscosity). The inaccuracies in numerical model results may lead to erroneous prediction of column separation and vaporous cavitation events [5,6,7,8]. Real time monitoring and control of piping systems requires accurate prediction of the pressure time history [9].…”

Section: Introductionmentioning

confidence: 99%

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Developments in unsteady pipe flow friction modelling

Bergant

Simpson

Vìtkovsk

2001

Journal of Hydraulic Research

278

121

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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...

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Section: The Original Brunone Model and The Vftkovsky Formulation Of mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Developments in unsteady pipe flow friction modelling

Bergant

Simpson

Vìtkovsk

2001

Journal of Hydraulic Research

278

121

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“…To include the effect of unsteady behavior of wall shear stress, the Brunone friction model is used [5]. In this case the friction head loss J u is dependent on instantaneous mean flow velocity and instantaneous flow acceleration (temporal acceleration).…”

Section: Unsteady Friction Modelmentioning

confidence: 99%

“…The main reason of these disagreements was the inappropriate definition of the fiction factor that in such rapid events should account for unsteady behavior of wall shear stress. To include such effects, several constitutive models were suggested for quantifying the contribution of frictional forces [5,6,7]. The implementation of such constitutive models in a onedimensional flow model was explored for different numerical methods such as: finite difference method (FDM), finite volume method, finite element method, wave plan method and method of characteristics (MOC).…”

Section: Introductionmentioning

confidence: 99%

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A mixed MOC/FDM numerical formulation for hydraulic transients

Travaš

Basara

2015

Teh. vjesn.

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Original scientific paper A mixed numerical formulation, based on the method of characteristics (MOC) and finite difference method (FDM), is proposed for the computational simulations of hydraulic transients. To include the effects of unsteady friction, i.e. the contribution of unsteady behavior of wall shear stress, the numerical algorithm includes the Brunone friction model. The governing water hammer equations are discretized by MOC and the discretization of the local and convective acceleration term in the unsteady friction model is conducted by FDM. The procedure results in an explicit-implicit time marching scheme used for predicting the unknown values of piezometric head and discharge from the known initial conditions. The resulting system of equations is resolved in an iterative fashion. Due to its relatively low complexity, the obtained numerical algorithm is attractive for computational implementation. At the end of the paper a few illustrative numerical examples are presented, compared with available experimental data, and discussed. Keywords: Brunone friction model; fluid transients in pipes; method of characteristics; unsteady friction; water hammer Miješana numerička formulacija za hidrauličke tranzijente (MK/MKR)Izvorni znanstveni članak U radu je predložena miješana numerička formulacija, bazirana na metodi karakteristika (MK) i metodi konačnih razlika (MKR) te je namijenjena za provedbu računalnih simulacija hidrauličkih tranzijenata. U svrhu uključivanja utjecaja nestacionarnog trenja tj. doprinosa posmičnih naprezanja na stijenkama cijevi karakterističnih za nestacionarni tok, prikazan numerički algoritam uključuje Brunoneov modela trenja. Osnovne diferencijalne jednadžbe hidrauličkog udara su diskretizirane MK te je lokalna i konvektivna akceleracija u nestacionarnom modelu trenja diskretizirana MKR. Navedeno dovodi do eksplicitno-implicitne numeričke sheme za predikciju nepoznatih veličina piezometarskog potencijala i protoka iz poznatih početnih uvjeta. Dobiveni sustav jednadžbi je riješen iterativnim postupkom. Obzirom na relativno malu kompleksnost, numerički algoritam je atraktivan za računalnu implementaciju. Na kraju rada su prikazani ilustrativni numerički primjeri koji su uspoređeni sa eksperimentalno dobivenim podacima te je priložena diskusija.Ključne riječi: Brunoneov model trenja; hidraulički tranzijenti u cijevima; hidraulički udar; metoda karakteristika; nestacionarno trenje

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Runge–Kutta time‐stepping schemes with TVD central differencing for the water hammer equations

Wahba

2006

Numerical Methods in Fluids

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SUMMARYIn the present study, Runge-Kutta schemes are used to simulate unsteady ow in elastic pipes due to sudden valve closure. The spatial derivatives are discretized using a central di erence scheme. Secondorder dissipative terms are added in regions of high gradients while they are switched o in smooth ow regions using a total variation diminishing (TVD) switch. The method is applied to both oneand two-dimensional water hammer formulations. Both laminar and turbulent ow cases are simulated.Di erent turbulence models are tested including the Baldwin-Lomax and Cebeci-Smith models. The results of the present method are in good agreement with analytical results and with experimental data available in the literature. The two-dimensional model is shown to predict more accurately the frictional damping of the pressure transient. Moreover, through order of magnitude and dimensional analysis, a non-dimensional parameter is identiÿed that controls the damping of pressure transients in elastic pipes.

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Effects of Two-Dimensionality on Pipe Transients Modeling

Cited by 163 publications

References 10 publications

Developments in unsteady pipe flow friction modelling

Developments in unsteady pipe flow friction modelling

A mixed MOC/FDM numerical formulation for hydraulic transients

Runge–Kutta time‐stepping schemes with TVD central differencing for the water hammer equations

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