Abstract
This paper presents a theoretical and numerical analysis of the length required for roll waves to become stationary in a free-surface laminar flow of a Newtonian fluid. Two types of stability analysis are brought to verify flow stability and obtain parameters for wave growth rate in a Saint-Venant like system. Then, numerical simulations are performed of the free-surface laminar transient flow of glycerin. The Navier-Stokes equations were solved using the finite volumes method, Euler schemes and PIMPLE, and the VoF technique to solve the interface. Boundary conditions were specified to obtain a steady and uniform regime given a Froude number. Then, a sinusoidal perturbation with controllable properties was applied to the inlet velocity. From the numerical results, the spatial development of the roll waves was evaluated, focusing on the establishment length as a function of the Froude number and the perturbation amplitude. The analyses performed allowed the verification of the influence of flow hydraulic regime over the establishment length, and it was possible to obtain a new equation as a function of the perturbation amplitude.
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Data Availability Statement
All data, models, and codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The author of this paper thanks the Sombrio Advanced Campus of the Catarinense Federal Institute for granting a full time leave for doctoral studies, through notice No. 21/2019. In particular, the author thanks the IFC Dean’s Office, which made possible to use a computer lab with the OpenFOAM software installed. This resource was of paramount importance for carrying out the numerical simulations that resulted in this study.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 148 • Issue 10 • October 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Nov 23, 2021
Accepted: May 17, 2022
Published online: Jul 27, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 27, 2022
ASCE Technical Topics:
- Engineering fundamentals
- Equations (by type)
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid flow
- Fluid mechanics
- Free surfaces
- Froude number
- Hydrologic engineering
- Laminar flow
- Mathematics
- Methodology (by type)
- Models (by type)
- Navier-Stokes equations
- Numerical models
- Research methods (by type)
- Transient flow
- Verification
- Water and water resources
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