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Resonance wave pumping with surface waves

Published online by Cambridge University Press:  06 December 2016

Remi A. Carmigniani ,
Michel Benoit ,
Damien Violeau  and
Morteza Gharib
Remi A. Carmigniani*
Affiliation:
Saint-Venant Hydraulics Laboratory, Joint Research Unit EDF – Cerema – Ecole des Ponts, 78401 Chatou, France
Michel Benoit
Affiliation:
Institut de Recherche sur les Phénomènes Hors-Equilibre (IRPHE, UMR 7342), Aix-Marseille Université, CNRS, Centrale Marseille, 13013 Marseille, France
Damien Violeau
Affiliation:
EDF and Saint-Venant Hydraulics Laboratory, Joint Research Unit EDF – Cerema – Ecole des Ponts, 78401 Chatou, France
Morteza Gharib
Affiliation:
Aeronautics and Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we present a novel extension of impedance (Liebau) wave pumping to a free-surface condition where resonance pumping could be used for hydraulic energy harvesting. Similar pumping behaviours are reported. Surface envelopes of the free surface are shown and outline two different dynamics: U-tube oscillator and wave/resonance pumping. The latter is particularly interesting, since, from an oscillatory motion, a unidirectional flow with small to moderate oscillations is generated. A linear theory is developed to evaluate pseudo-analytically the resonance frequencies of the pump using eigenfunction expansions, and a simplified model is proposed to understand the main pumping mechanism in this type of pump. It is found that the Stokes mass transport is driving the pump. The conversion of energy from paddle oscillation to mean flow is evaluated. Efficiency up to 22 % is reported.

JFM classification

Waves/Free-surface Flows: Wave breaking Waves/Free-surface Flows: Waves/Free-surface Flows Waves/Free-surface Flows: Wave-structure interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 811 , 25 January 2017 , pp. 1 - 36
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Copyright
© 2016 Cambridge University Press 

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References

Avrahami, I. & Gharib, M. 2008 Computational studies of resonance wave pumping in compliant tubes. J. Fluid Mech. 608, 139–160.CrossRefGoogle Scholar
Bringley, T., Childress, S., Vandenberghe, N. & Zhang, J. 2008 An experimental investigation and a simple model of valveless pump. Phys. Fluids 20 (3), 033602.Google Scholar
Chamberlain, P. G. & Porter, D. 1999 On the solution of the dispersion relation for water waves. Appl. Ocean Res. 21 (4), 161–166.CrossRefGoogle Scholar
Dias, F., Dyachenko, A. I. & Zakharov, V. E. 2008 Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions. Phys. Lett. A 372 (8), 1297–1302.CrossRefGoogle Scholar
Dutykh, D. & Dias, F. 2007 Viscous potential free-surface flows in a fluid layer of finite depth. C. R. Math. 345 (2), 113–118.CrossRefGoogle Scholar
Graw, K.-U. 1992 The submerged plate as a wave filter: the stability of the pulsating flow phenomenon. In Proc. 23rd Conf. Coastal Engng. Venice, Italy, vol. 4, pp. 1153–1160.Google Scholar
Graw, K.-U. 1993 Shore protection and electricity by submerged plate wave energy converter. In Proc. European Wave Energy Symposium, Edinburgh, Scotland, pp. 379–384.Google Scholar
Hasselmann, K. 1971 On the mass and momentum transfer between short gravity waves and larger-scale motions. J. Fluid Mech. 50, 189–205.Google Scholar
Hickerson, A. I. & Gharib, M. 2006 On the resonance of a pliant tube as a mechanism for valveless pumping. J. Fluid Mech. 555, 141–148.Google Scholar
Jung, E. 2007 A mathematical model of valveless pumping: a lumped model with time-dependent compliance, resistance, and inertia. Bull. Math. Biol. 69 (7), 2181–2198.Google Scholar
Jung, E., Lim, S., Lee, W. & Lee, S. 2008 Computational models of valveless pumping using the immersed boundary method. Comput. Meth. Appl. Engng 197 (25–28), 2329–2339.CrossRefGoogle Scholar
Kozlovsky, P., Rosenfeld, M., Jaffa, A. J. & Elad, D. 2015 Dimensionless analysis of valveless pumping in a thick-wall elastic tube: application to the tubular embryonic heart. J. Biomech. 48 (9), 1652–1661.Google Scholar
Lee, J.-F. 1995 On the heave radiation of a rectangular structure. Ocean Engng 22 (1), 19–34.CrossRefGoogle Scholar
Liebau, G. 1954 Über ein ventilloses pumpprinzip. Naturwissenschaften 41, 327–327.CrossRefGoogle Scholar
Liebau, G. 1955 Prinzipien kombinierter ventilloser Pumpen, abgeleitet vom menschlichen Blutkreislauf. Naturwissenschaften 42, 339–339.CrossRefGoogle Scholar
Linton, C. & McIver, P. 2001 Handbook of Mathematical Techniques for Wave/Structure Interactions. Chapman & Hall/CRC Press.Google Scholar
Martin, P. A. 1995 Asymptotic approximations for functions defined by series, with some applications to the theory of guided waves. IMA J. Appl. Maths 54 (2), 139–157.Google Scholar
Mei, C. C. & Black, J. L. 1969 Scattering of surface waves by rectangular obstacles in waters of finite depth. J. Fluid Mech. 38, 499–511.Google Scholar
Meier, J.2011 A novel experimental study of a valveless impedance pump for applications at lab-on-chip, microfluidic and biomedical device size scales. PhD thesis, California Institute of Technology.Google Scholar
Miche, A. 1944 Mouvements ondulatoires de la mer en profondeur croissante ou décroissante. Première partie. Mouvements ondulatoires périodiques et cylindriques en profondeur constante. Annal. des Ponts et Chaussées 114, 42–78.Google Scholar
Ottesen, J. T. 2003 Valveless pumping in a fluid-filled closed elastic tube-system: one-dimensional theory with experimental validation. J. Math. Biol. 46 (4), 309–332.Google Scholar
Rinderknecht, D., Hickerson, A. I. & Gharib, M. 2005 A valveless micro impedance pump driven by electromagnetic actuation. J. Micromech. Microengng 15 (4), 861–866.Google Scholar
Takano, K. 1960 Effets d’un obstacle parallélépipédique sur la propagation de la houle. La Houille Blanche 15, 247–267.Google Scholar
Thielicke, W. & Stamhuis, E. J. 2014a PIVlab – time-resolved digital particle image velocimetry tool for MATLAB. Figshare. doi:10.6084/m9.figshare.1092508.v6.Google Scholar
Thielicke, W. & Stamhuis, E. J. 2014b PIVlab – towards user-friendly, affordable and accurate digital particle velocimetry in MATLAB. J. Open Res. Soft. 2 (1), e30.Google Scholar
Thomann, H. 1978 A simple pumping mechanism in a valveless tube. Z. Angew. Math. Phys. 29 (2), 169–177.CrossRefGoogle Scholar
Timmermann, S. & Ottesen, J. T. 2009 Novel characteristics of valveless pumping. Phys. Fluids 21 (5), 053601.CrossRefGoogle Scholar
Touboul, J. & Rey, V. 2012 Bottom pressure distribution due to wave scattering near a submerged obstacle. J. Fluid Mech. 702, 444–459.Google Scholar
Zheng, Y. H., You, Y. G. & Shen, Y. M. 2004 On the radiation and diffraction of water waves by a rectangular buoy. Ocean Engng 31 (8–9), 1063–1082.Google Scholar