Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T17:58:48.543Z Has data issue: false hasContentIssue false
  • English
  • Français

Immersed body motion: near-bottom added mass effects

Published online by Cambridge University Press:  30 March 2022

Shayan Maleki Open the ORCID record for Shayan Maleki [Opens in a new window]  and
Virgilio Fiorotto Open the ORCID record for Virgilio Fiorotto [Opens in a new window]
Shayan Maleki*
Affiliation:
Dams and Hydropower, Stantec, Brisbane, Australia
Virgilio Fiorotto
Affiliation:
Formerly Department of Engineering and Architecture, University of Trieste, Piazzale Europa, 1, 34100Trieste, Italy
*
† Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The presence of a solid boundary can cause a substantial increase in added mass due to a solid body movement in the fluid. If the body is very close to the boundary, the added mass increases at an even greater rate. The added mass can be of considerable importance in many dams and hydropower, water/ocean, civil and mechanical engineering problems; furthermore, it has an important effect on the dynamics of the vibrating body in the fluid. The principal aim of this paper is to define a novel model to properly evaluate the near-bottom effects of the added mass and to investigate the instantaneous pressure field due to a body movement that changes the thickness of a compressible thin fluid film close to a solid boundary. The body movement can be due to the application of an external force according to Newton's law. This phenomenon is studied theoretically in this paper, and a hydrodynamic model able to compute the instantaneous pressure field in the thin fluid film is drawn out. The fluid film thickness variation, producing compression and decompression waves, tends to reduce the mean body displacement due to external forces, but it generates both high-frequency fluctuations in body force and in body displacements. For the first time, this novel study provides the near-bottom added mass and justifies the strong body accelerations measured in the laboratory experiments that have not been evidenced in the theoretical studies in the known literature.

JFM classification

Turbulent Flows: Turbulent boundary layers Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 939 , 25 May 2022 , A18
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Asadollahi, P., Tonon, F., Federspiel, M. & Schleiss, A. 2011 Prediction of rock block stability and scour depth in plunge pools. J. Hydraul. Res. 49 (6), 750–756.CrossRefGoogle Scholar
Barjastehmaleki, S., Fiorotto, V. & Caroni, E. 2016 a Spillway stilling basins lining design via Taylor hypothesis. J. Hydraul. Engng 142 (6), 04016010.CrossRefGoogle Scholar
Barjastehmaleki, S., Fiorotto, V. & Caroni, E. 2016 b Design of stilling basin linings with sealed and unsealed joints. J. Hydraul. Engng 142 (12), 04016064.CrossRefGoogle Scholar
Bollaert, E. 2002 Transient water pressures in joints and formation of rock scour due to high—velocity jet impact. In Communication No. 13 of the Laboratory of Hydraulic Construction (ed. A. Schleiss). École polytechnique fédérale de Lausanne.Google Scholar
Bollaert, E. & Schleiss, A. 2005 Physically-based model for evaluation of rock scour due to high velocity jet impact. J. Hydraul. Engng 131 (3), 153–165.CrossRefGoogle Scholar
Brennen, C.B. 1982 A review of added mass and fluid inertial forces. Naval Civil Engineering Laboratory, Port Hueneme, California (USA), Grant number N62583-81-MR-554.Google Scholar
Brennen, C.E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.Google Scholar
Brennen, C.B. 2006 An internet book on fluid dynamic – additional effects on the added mass. California Institute of Technology, Pasadena, CA, USA.Google Scholar
Castillo, L.G., Carrillo, J.M. & Blazquez, A. 2015 Plunge pool dynamic pressures: a temporal analysis in the nappe flow case. J. Hydraul. Res. 53 (1), 101–118.CrossRefGoogle Scholar
Chung, H. & Chen, S.S. 1984 Hydrodynamic mass. Technology Division Argonne National Laboratory, CONF-840647—9, DE84 009184, Argonne, IL, USA.Google Scholar
Duarte, R., Pinheiro, A. & Schleiss, A. 2016 Dynamic response of an embedded block impacted by aerated high-velocity jets. J. Hydraul. Res. 54 (4), 399–409.CrossRefGoogle Scholar
Ervine, D.A. & Falvey, H.T. 1987 Behaviour of turbulent water jets in the atmosphere and in plunge pools. Proc. Inst. Civil Engrs, Part 2 83, 295–314.Google Scholar
Ervine, D.A., Falvey, H.T. & Withers, W. 1997 Pressure fluctuations on plunge pool floors. J. Hydraul. Res. 35 (2), 257–279.CrossRefGoogle Scholar
Federspiel, M. 2011 Response of an embedded block impacted by high-velocity jets. Doctoral thesis No. 5160, Laboratory of Hydraulic Construction, EPFL.Google Scholar
Fiorotto, V., Barjastehmaleki, S. & Caroni, E. 2016 Stability analysis of plunge pool linings. J. Hydraul. Engng 142 (11), 04016044.CrossRefGoogle Scholar
Fiorotto, V. & Rinaldo, A. 1989 Sul dimensionamento delle protezioni di fondo in bacini di dissipazione: nuovi risultati teorici e sperimentali. Giornale del Genio Civile 179–201 (in Italian).Google Scholar
Fritz, J. 1982 Partial Differential Equations, 4th edn. Springer-Verlag.Google Scholar
Ghidaoui, M.S., Zhao, M., McInnis, D.A. & Axworthy, D.H. 2005 A review of water hammer theory and practice. Appl. Mech. Rev. 58, 49–76.CrossRefGoogle Scholar
Henry, W. 1803 Experiments on the quantity of gases absorbed by water, at different temperatures, and under different pressures. Phil. Trans. R. Soc. Lond. 93, 29–43.Google Scholar
Maleki, S. & Fiorotto, V. 2021 Hydraulic brittle fracture in a rock mass. Rock Mech. Rock Engng 54, 5041–5056.CrossRefGoogle Scholar
Maleki, S. & Fiorotto, V. 2019 a Scour due a falling jet: a comprehensive approach. J. Hydraul. Engng 145 (4), 04019008.CrossRefGoogle Scholar
Maleki, S. & Fiorotto, V. 2019 b Blocks stability in plunge pools under turbulent rectangular jets. J. Hydraul. Engng 145 (4), 04019007.CrossRefGoogle Scholar
Strauss, W.A. 1992 Partial Differential Equations: An Introduction. Wiley.Google Scholar
Streeter, V.L. & Wyle, E.B. 1967 Hydraulic Transient. McGraw-Hill Book Company.Google Scholar
Tufillaro, N.B. 1989 Nonlinear and chaotic string vibrations. Am. J. Phys. 57 (5), 408.CrossRefGoogle Scholar
Ugural, A.C. & Fenster, S.K. 2003 Advanced Strength and Applied Elasticity, 4th edn. Prentice-Hall.Google Scholar