Time-Line Interpolation Errors in Pipe Networks

Shimada, Masashi; Brown, Jim; Leslie, Della; Vardy, Alan

doi:doi:10.1061/(ASCE)0733-9429(2006)132:3(294)

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Time-Line Interpolation Errors in Pipe Networks

J. Hydraul. Eng. 132, 294 (2006); http://dx.doi.org/10.1061/(ASCE)0733-9429(2006)132:3(294) (13 pages)

Masashi Shimada¹, Jim Brown², Della Leslie³, and Alan Vardy, F.ASCE⁴

¹Professor, Dept. of Biological and Environmental Engineering, Univ. of Tokyo, Tokyo, Japan.
²Research Fellow, Civil Engineering Division, Univ. of Dundee, Dundee, Scotland DD1 4HN.
³Formerly, Civil Engineering Division, Univ. of Dundee, Dundee, Scotland DD1 4HN.
⁴Research Professor, Civil Engineering Division, Univ. of Dundee, Dundee, Scotland DD1 4HN.

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(Submitted 30 December 2003; accepted 19 May 2005)

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Abstract

References (23)

Citing Articles (3)

Article Objects (9)

An exact method of assessing numerical errors in analyses of unsteady flows in pipe networks is introduced. The assessment is valid for fixed-grid method of characteristics analyses using time-line interpolations. A pipe polynomial transfer matrix is developed and is analogous to transfer function matrices used in free oscillation theory. The influence of reachback is assessed by comparing exact numerical predictions using a polynomial transfer matrix with exact analytical predictions obtained using free oscillation theory. The investigation is part of a long-term project aimed at automating the selection of numerical grid sizes in unsteady flow analyses. The eventual goal is to enable users of unsteady flow software to prescribe required degrees of accuracy instead of specifying the numerical grid itself. This paper is only a first step toward the long-term aim, but it is a big step toward an intermediate objective of providing exact benchmarking data for the assessment of approximate methods of automatic grid selection.

Article Outline

Introduction
1. Numerical Responses in Transient Flows
2. Outline of Paper
MOC with Time-Line Interpolation
1. Reachback and Interpolation Parameters ( m and ξ )
2. MOC Equations
3. Standing Waves
4. Properties of the MOC Response
5. Polynomial Transfer Matrix
Application to Single Pipes
1. Grid Size Dependence
2. Influence of the Reachback Factor, m
3. Influence of the Interpolation Factor, ξ
Application to Networks
1. Pipe End Conditions
2. Polynomial Transfer Matrix—Pipes in Series
3. Polynomial Transfer Matrix—Branches
Free-Oscillation Theory
Three-Pipe Branch
Four-Pipe Loop
Multibranch Network
High versus Low Frequencies
Future Use of the Polynomial Transfer Method
Conclusions

KEYWORDS

ASCE SUBJECT HEADINGS

Water hammers, Pipe networks, Errors, Resonance, Unsteady flow, Pipe flow

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ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1061/(ASCE)0733-9429(2006)132:3(294)

PUBLICATION DATA

ISSN

0733-9429 (print)

1943-7900 (online)

Publisher

ASCE

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