Laplace-Domain Fluid–Structure Interaction Solutions for Water Hammer Waves in a Pipe
Publication: Journal of Hydraulic Engineering
Volume 150, Issue 2
Abstract
Numerical methods generally need analytical solutions as test cases and validations in simplified problems. This work provides Laplace-domain explicit analytic solutions for fluid–structure interaction (FSI) water hammer waves within a pipe. Rather than applying the transfer matrix method (TMM) to the FSI four equations, it is transposed to the equivalent two-wave propagating problem considered instead. Using the classical wave matrix diagonalization approach permits decoupling the waves’ propagation while at the same time coupling boundary conditions in the diagonal base. This approach permits the transfer matrix for coupled waves boundary conditions to be provided so as to obtain a Laplace-domain solution for the pressure/stress vector solution. This solution is written in a general framework that can be adapted for general applied boundary conditions for a single pipe. Three sets of boundary conditions are considered as examples and illustrations from solving the inverse Laplace transform of the considered explicit solutions. Consistent results with recently proposed time-domain solutions are found, and a one-to-one mapping between Laplace-domain and time-domain approaches is also established. This permits finding the discrete spectrum of FSI water hammer wave mode decomposition from TMM solutions.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This work was supported by the collaborative ANRT Grant CIFRE 2019/1453 cofunded by SETOM, dedicated society of Veolia for the public drinking water service of Toulouse Métropole operating under the brand Eau de Toulouse Métropole. We thank the referees and the editor for their handling of the editorial process.
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© 2023 American Society of Civil Engineers.
History
Received: May 10, 2023
Accepted: Sep 5, 2023
Published online: Nov 21, 2023
Published in print: Mar 1, 2024
Discussion open until: Apr 21, 2024
ASCE Technical Topics:
- Boundary conditions
- Boundary value problem
- Business management
- Coupling
- Differential equations
- Engineering fundamentals
- Equations (by type)
- Fluid mechanics
- Hydrologic engineering
- Infrastructure
- Laplace transform
- Legal affairs
- Mathematical functions
- Mathematics
- Matrix (mathematics)
- Permits
- Pipeline hydraulics
- Pipeline management
- Pipeline systems
- Pipes
- Practice and Profession
- Structural engineering
- Structural members
- Structural systems
- Water and water resources
- Water hammer
- Water waves
- Waves (fluid mechanics)
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