Numerical Comparison of Pipe‐Column‐Separation Models

Simpson, Angus R.; Bergant, Anton

doi:10.1061/(asce)0733-9429(1994)120:3(361)

Cited by 55 publications

(39 citation statements)

References 16 publications

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“…A simple form of the method of characteristics water hammer compatibility equations C1 and C2 is used in most column separation models (Wylie and Streeter 1993;Simpson and Bergant 1994)…”

Section: Analytical and Numerical Toolsmentioning

confidence: 99%

“…Incorporating discrete vapor cavities into the water hammer solution methods leads to the DVCM (Streeter 1969;Wylie and Streeter 1993;Simpson and Bergant 1994). Coupling the complete set of column separation methods gives the interface vaporous cavitation (consolidation) model-GIVCM (Streeter 1983;Bergant and Simpson 1992).…”

Section: Analytical and Numerical Toolsmentioning

confidence: 99%

“…The volume of a discrete cavity given by (7) is solved by numerical integration using a weighting factor c in the time direction within the staggered grid of the method of characteristics (Wylie 1984;Simpson and Bergant 1994)…”

Section: Numerical Integration Of Discrete Vapor Cavity Continuity Eqmentioning

confidence: 99%

“…The DGCM developed by Provoost and Wylie (1981) performs consistently over a broad range of parameters when a small gas void fraction at the computational section (α g ≤ 10 -7 ) is selected (Barbero and Ciaponi 1992;Bergant 1992;Simpson and Bergant 1994). The growth and collapse of the gas cavity is calculated from (8), (9), and (18) and the ideal gas equation (Wylie and Streeter 1993).…”

Section: Dvcmmentioning

confidence: 99%

“…The standard DVCM algorithm allows cavities to form at computational sections in the staggered grid of the method of characteristics (Wylie and Streeter 1993;Simpson and Bergant 1994) and has been used as a basis for the development of the GIVCM. The incorporation of the distributed vaporous cavitation zones, shock waves, and various types of discrete cavities are important features in modifying the standard DVCM.…”

Section: Givcmmentioning

confidence: 99%

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Pipeline Column Separation Flow Regimes

1999

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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).

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“…A simple form of the method of characteristics water hammer compatibility equations C1 and C2 is used in most column separation models (Wylie and Streeter 1993;Simpson and Bergant 1994)…”

Section: Analytical and Numerical Toolsmentioning

confidence: 99%

Section: Analytical and Numerical Toolsmentioning

confidence: 99%

Section: Numerical Integration Of Discrete Vapor Cavity Continuity Eqmentioning

confidence: 99%

Section: Dvcmmentioning

confidence: 99%

Section: Givcmmentioning

confidence: 99%

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Pipeline Column Separation Flow Regimes

1999

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Distortions From a Simplified Approach to Fatigue Analysis in PVC Pipes

Malekpour¹,

Karney

McPherson³

2018

Journal AWWA

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This work examines the extent to which simplifications suggested for fatigue analysis of polyvinyl chloride (PVC) pipes can cause distortion in system evaluation. To this end, fatigue analysis is performed on a hypothetical pipe system using two independent approaches: first, using a recommended method that calculates the fatigue parameters through thorough transient modeling and, second, through a highly simplified but widely used approach arising from direct application of the Joukowsky equation (through Plastics Pipe Institute's program Pipeline Analysis & Calculation Environment).The results show that the simplified approach significantly overestimates the transient loading and tends to devalue the expected fatigue resistance of PVC pipe. This devaluation arises from the fact that the Joukowsky approach, along with several other assumptions, is too conservative and simplified for fatigue analysis. This study concludes that for the PVC pipe systems exposed to significant pressure cycles, fatigue analysis is a required design check, but only a thorough and thoughtful consideration of transient loading can provide accurate and meaningful results.

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Fast and accurate modelling of frictional transient pipe flow

Urbanowicz

2018

Z Angew Math Mech

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This paper is devoted to the one‐dimensional (1D) modelling of hydraulic losses during transient flow of liquids in pressure lines. Unsteady pipe wall shear stress is present in the form of a convolution of liquid acceleration with a weighting function. The weighting function depends on the dimensionless time and the Reynolds number. In the original model of Zielke (1968), computation of the convolution integral had a complex and inefficient mathematical structure (featured power growth of computational time). Therefore, further work aimed at developing efficient models for estimation of unsteady hydraulic resistance (with nearly linear growth of computational time). In the present paper, a correction to the erratic recursive formula by Schohl (1993), being used to calculate the unsteady wall shear stresses during transient flow, is presented. The simulation results obtained with the corrected Schohl's recursive formula are consistent with the classic but computationally inefficient formula proposed recently by Vardy and Brown (2010). The accuracy of the efficient weighting function obtained in wall shear stress models is verified. The results of pressure pulsation obtained when taking into account cavitating flow, or not, are surprising in the sense that the weighting function does not need to be built by a lengthy sum of exponential terms to accurately simulate the transient event.

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Numerical Comparison of Pipe‐Column‐Separation Models

Cited by 55 publications

References 16 publications

Pipeline Column Separation Flow Regimes

Pipeline Column Separation Flow Regimes

Distortions From a Simplified Approach to Fatigue Analysis in PVC Pipes

Fast and accurate modelling of frictional transient pipe flow

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