Efficient Second-Order Accurate Shock-Capturing Scheme for Modeling One- and Two-Phase Water Hammer Flows
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 7
Abstract
This paper focuses on the formulation and assessment of a second-order accurate finite volume (FV) shock-capturing scheme for simulating one- and two-phase water hammer flows. The two-phase flow model is based on the single-equivalent fluid concept. The proposed scheme for one- and two-phase flows is the same, except for the Riemann solvers used to evaluate fluxes between computational cells. For one-phase flows, the accuracy and numerical efficiency of the proposed scheme is contrasted against the fixed-grid method of characteristics (MOC) and a recently proposed FV scheme. For two-phase flows, the accuracy and numerical efficiency of the proposed scheme are compared to the fixed-grid MOC scheme. The results for one-phase flows show that, when a Courant number (Cr) very close to 1.0 (around 0.99 or higher) is used, the MOC scheme is more efficient than the proposed scheme and the other FV scheme. In this case, the latter two schemes have similar numerical efficiency. When Cr drops below about 0.95, the proposed scheme is more efficient than the MOC scheme and the other FV scheme, especially for smooth transient flows (no discontinuities). For two-phase water hammer flows, all the simulations were carried out using a maximum Courant number of 0.95 to avoid numerical instability problems. The results for two-phase flows show that the proposed scheme is much more efficient than the fixed-grid MOC scheme. The fixed-grid MOC and the proposed scheme are also used to reproduce a set of two-phase flow experiments reported in the literature. Good agreement between simulated and experimental data is found.
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Acknowledgments
The writers gratefully acknowledge Dr. C. Samuel Martin for providing us his two-phase flow experimental data and Dr. Ming Zhao for providing us his one-phase FV and MOC codes. The first, third, and fourth writers are grateful for the financial support of the Metropolitan Water Reclamation District of Greater Chicago (Research Project Specification No. UNSPECIFIEDRPS-03). The second writer wishes to thank the Research Grant Council of Hong Kong Grant No. UNSPECIFIEDHKUST6113/03E.
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Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 7 • July 2008
Pages: 970 - 983
Copyright
© 2008 ASCE.
History
Received: Mar 3, 2006
Accepted: Oct 24, 2007
Published online: Jul 1, 2008
Published in print: Jul 2008
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