zbMATH — the first resource for mathematics

Resonance wave pumping with surface waves. (English) Zbl 1383.76045
Summary: 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.
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76R10 Free convection
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Full Text: DOI
[1] Avrahami, I.; Gharib, M., Computational studies of resonance wave pumping in compliant tubes, J. Fluid Mech., 608, 139-160, (2008) · Zbl 1145.76355
[2] Bringley, T.; Childress, S.; Vandenberghe, N.; Zhang, J., An experimental investigation and a simple model of valveless pump, Phys. Fluids, 20, 3, (2008) · Zbl 1182.76087
[3] Chamberlain, P. G.; Porter, D., On the solution of the dispersion relation for water waves, Appl. Ocean Res., 21, 4, 161-166, (1999)
[4] Dias, F.; Dyachenko, A. I.; Zakharov, V. E., Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions, Phys. Lett. A, 372, 8, 1297-1302, (2008) · Zbl 1217.76018
[5] Dutykh, D.; Dias, F., Viscous potential free-surface flows in a fluid layer of finite depth, C. R. Math., 345, 2, 113-118, (2007) · Zbl 1117.76023
[6] Graw, K.-U.1992The 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.
[7] Graw, K.-U.1993Shore protection and electricity by submerged plate wave energy converter. In Proc. European Wave Energy Symposium, Edinburgh, Scotland, pp. 379-384.
[8] Hasselmann, K., On the mass and momentum transfer between short gravity waves and larger-scale motions, J. Fluid Mech., 50, 189-205, (1971) · Zbl 0229.76010
[9] Hickerson, A. I.; Gharib, M., On the resonance of a pliant tube as a mechanism for valveless pumping, J. Fluid Mech., 555, 141-148, (2006) · Zbl 1156.76320
[10] Jung, E., A mathematical model of valveless pumping: a lumped model with time-dependent compliance, resistance, and inertia, Bull. Math. Biol., 69, 7, 2181-2198, (2007) · Zbl 1296.92099
[11] Jung, E.; Lim, S.; Lee, W.; Lee, S., Computational models of valveless pumping using the immersed boundary method, Comput. Meth. Appl. Engng, 197, 25-28, 2329-2339, (2008) · Zbl 1158.76454
[12] Kozlovsky, P.; Rosenfeld, M.; Jaffa, A. J.; Elad, D., Dimensionless analysis of valveless pumping in a thick-wall elastic tube: application to the tubular embryonic heart, J. Biomech., 48, 9, 1652-1661, (2015)
[13] Lee, J.-F., On the heave radiation of a rectangular structure, Ocean Engng, 22, 1, 19-34, (1995)
[14] Liebau, G., Über ein ventilloses pumpprinzip, Naturwissenschaften, 41, 327-327, (1954)
[15] Liebau, G., Prinzipien kombinierter ventilloser Pumpen, abgeleitet vom menschlichen Blutkreislauf, Naturwissenschaften, 42, 339-339, (1955)
[16] Linton, C.; Mciver, P., Handbook of Mathematical Techniques for Wave/Structure Interactions, (2001), Chapman & Hall/CRC Press · Zbl 0989.76001
[17] Martin, P. A., Asymptotic approximations for functions defined by series, with some applications to the theory of guided waves, IMA J. Appl. Maths, 54, 2, 139-157, (1995) · Zbl 0832.41020
[18] Mei, C. C.; Black, J. L., Scattering of surface waves by rectangular obstacles in waters of finite depth, J. Fluid Mech., 38, 499-511, (1969) · Zbl 0187.25502
[19] 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.
[20] Miche, A., 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, (1944)
[21] Ottesen, J. T., Valveless pumping in a fluid-filled closed elastic tube-system: one-dimensional theory with experimental validation, J. Math. Biol., 46, 4, 309-332, (2003) · Zbl 1039.92015
[22] Rinderknecht, D.; Hickerson, A. I.; Gharib, M., A valveless micro impedance pump driven by electromagnetic actuation, J. Micromech. Microengng, 15, 4, 861-866, (2005)
[23] Takano, K., Effets d’un obstacle parallélépipédique sur la propagation de la houle, La Houille Blanche, 15, 247-267, (1960)
[24] Thielicke, W. & Stamhuis, E. J.2014aPIVlab – time-resolved digital particle image velocimetry tool for MATLAB. Figshare. doi:10.6084/m9.figshare.1092508.v6.
[25] Thielicke, W.; Stamhuis, E. J., PIVlab – towards user-friendly, affordable and accurate digital particle velocimetry in MATLAB, J. Open Res. Soft., 2, 1, e30, (2014)
[26] Thomann, H., A simple pumping mechanism in a valveless tube, Z. Angew. Math. Phys., 29, 2, 169-177, (1978) · Zbl 0393.76074
[27] Timmermann, S.; Ottesen, J. T., Novel characteristics of valveless pumping, Phys. Fluids, 21, 5, (2009) · Zbl 1183.76520
[28] Touboul, J.; Rey, V., Bottom pressure distribution due to wave scattering near a submerged obstacle, J. Fluid Mech., 702, 444-459, (2012) · Zbl 1248.76022
[29] Zheng, Y. H.; You, Y. G.; Shen, Y. M., On the radiation and diffraction of water waves by a rectangular buoy, Ocean Engng, 31, 8-9, 1063-1082, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.