Rational Approximation of Unsteady Friction Weighting Functions in the Laplace Domain
Publication: Journal of Hydraulic Engineering
Volume 147, Issue 9
Abstract
This paper aims at improving the weighting function based-method (WFB) for modeling the transient behavior of a laminar flow in cylindrical pipes in a one-dimensional approach. Two improvements for the numerical computation of the unsteady friction term are presented. First, a rational approximation of the weighting function in the Laplace domain is preferred instead of an exponential series fit in the time domain. It allows the WFB method to be improved in terms of validity for small time steps, accuracy, and computational efficiency. Second, the use of auxiliary differential equations to compute convolution makes the high order time-integration of the frequency-dependent friction term straightforward, without the assumption of a constant acceleration during the time step. The simulation results for a well-known experimental test case show a good agreement of the derived methods with the experiment. Finally, the time stability of the discretized problem is fully analyzed, and a stability condition for the WFB method is brought out.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the LabEx Centre Lyonnais d’Acoustique of Université de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ANR-11-IDEX-0007). This work is part of the project ESSENCYELE (moteur ESSENCe injection directe hYbride Electrique abordabLE), financed by the French Agency for Environment and Energy Management (ADEME).
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Published In
Journal of Hydraulic Engineering
Volume 147 • Issue 9 • September 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jul 21, 2020
Accepted: Mar 18, 2021
Published online: Jul 6, 2021
Published in print: Sep 1, 2021
Discussion open until: Dec 6, 2021
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