Abstract
An approach combining the Brunone unsteady friction model and first- and second-order Godunov-type scheme (GTS) is developed to simulate transient pipe flow. The exact solution to the Riemann problem calculates the mass and momentum fluxes while implicitly considering the Brunone unsteady friction factor. The boundary cells can either be computed by applying the Rankine–Hugoniot condition or through virtual boundary cells adapted to achieve a uniform solution for both interior and boundary cells. Predictions of the proposed model are compared both with experimental data and with method of characteristics (MOC) predictions. Results show the first-order GTS and MOC scheme have identical accuracy, but both approaches sometimes produce severe attenuation when used with small Courant numbers. The presented second-order GTS numerical model is more accurate, stable, and efficient, even for Courant numbers less than one, a particularly important attribute for unsteady-friction simulations, which inevitably create numerical dissipation in both the MOC and proposed first-order Godunov-type schemes. In fact, even with a coarse discretization, the new second-order GTS Brunone model accurately reproduces the entire experimental pressure oscillations including their physical damping in all transient flows considered here.
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Data Availability Statement
All of the data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The writers gratefully acknowledge the financial support for this research from the National Natural Science Foundation of China (Grant Nos. 51679066 and 51839008), the Fundamental Research Funds for the Central Universities (Grant No. 2018B43114), Fok Ying Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 161068), and Open Research Fund Program of State Key Laboratory of Water Resources and Hydropower Engineering Science (Wuhan University) (Grant No. 2016SDG01).
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© 2021 American Society of Civil Engineers.
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Received: Jun 16, 2020
Accepted: Feb 18, 2021
Published online: Apr 30, 2021
Published in print: Jul 1, 2021
Discussion open until: Sep 30, 2021
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