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Reduction of pressure losses and increase of mixing in laminar flows through channels with long-wavelength vibrations

Published online by Cambridge University Press:  11 February 2019

J. M. Floryan Open the ORCID record for J. M. Floryan [Opens in a new window]  and
Sahab Zandi
J. M. Floryan*
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada, N6A 5B9
Sahab Zandi
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada, N6A 5B9
*
†Email address for correspondence: floryan@uwo.ca
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Abstract

Pressure losses and mixing in vibrating channels were analysed. The vibrations in the form of long-wavelength travelling waves were considered. Significant reduction of pressure losses can be achieved using sufficiently fast waves propagating downstream, while significant increase of such losses is generated by waves propagating upstream. The mechanisms responsible for pressure losses were identified and discussed. The interaction of the pressure field with the waves can create a force which assists the fluid movement. A similar force can be created by friction, but only under conditions leading to flow separation. An analysis of particle trajectories was carried out to determine the effect of vibrations on mixing. A significant transverse particle movement takes place, including particle trajectories with back loops. The downstream-propagating out-of-the phase waves provide a large reduction of pressure gradient and significant potential for mixing intensification. Analysis of energy requirements demonstrates that it is possible to identify waves which reduce power requirements, i.e. the cost of actuation is smaller than the energy savings associated with the reduction of pressure gradient. The fast forward moving waves provide an opportunity for the development of alternative propulsion methods which can be more efficient than methods based on the pressure difference.

JFM classification

Flow Control: Drag reduction
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 670 - 707
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Copyright
© 2019 Cambridge University Press 

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References

Aboelkassem, Y. & Staples, A. E. 2012 Flow transport in a microchannel induced by moving wall contractions: a novel micro-pumping mechanism. Acta Mech. 223, 463–480.10.1007/s00707-011-0574-zGoogle Scholar
Agostini, L., Touber, E. & Leschziner, M. A. 2014 Spanwise oscillatory wall motion in channel flow: drag-reduction mechanisms inferred from DNS-predicted phase-wise property variations at Re 𝜏 = 1000. J. Fluid Mech. 743, 606–635.Google Scholar
Ali, N., Sajid, M., Abbas, Z. & Javed, T. 2010 Non-Newtonian fluid flow induced by peristaltic waves in a curved channel. Eur. J. Mech. (B/Fluids) 29, 387–394.10.1016/j.euromechflu.2010.04.002Google Scholar
Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1–21.10.1017/S0022112084001233Google Scholar
Bergles, A. E. & Webb, R. L. 1983 Performance Evaluation Criteria for Selection of Heat Transfer Surface Geometries Used in Low Reynolds Number Heat Exchangers. pp. 735–752. Hemisphere.Google Scholar
Bewley, T. R. 2009 A fundamental limit on the balance of power in a transpiration-controlled channel flow. J. Fluid Mech. 632, 443–446.10.1017/S0022112008004886Google Scholar
Carlsson, F., Sen, M. & Löfdahl, L. 2005 Fluid mixing induced by vibrating walls. Eur. J. Mech. (B/Fluids) 24, 366–378.Google Scholar
El-Shehawy, E. F., El-Dabe, N. T. & I.M, El-Desoky 2006 Slip effects on the peristaltic flow of a non-Newtonian Maxwellian fluid. Acta Mech. 186, 141–159.10.1007/s00707-006-0343-6Google Scholar
Espin, L. & Papageorgiou, D. T. 2012 Viscous pressure-driven flows and their stability in channels with vertically oscillating walls. Phys. Fluids 24, 023604.Google Scholar
Fiebig, M. 1995a Embedded vortices in internal flow: heat transfer and pressure loss enhancement. Intl J. Heat Fluid Flow 1 (6), 376–388.Google Scholar
Fiebig, M. 1995b Vortex generators for compact heat exchangers. J. Enhanced Heat Transfer 2, 43–61.Google Scholar
Fiebig, M. 1998 Vortices, generators and heat transfer. Chem. Engng Res. Des. 76, 108–123; 5th UK National Heat Transfer Conference.Google Scholar
Fiebig, M. & Chen, Y. 1999 Heat transfer enhancement by wing-type longitudinal vortex generators and their application to finned oval tube heat exchanger elements. In Heat Transfer Enhancement of Heat Exchangers (ed. Kaka, S., Bergles, A. E., Mayinger, F. & Ync, H.), Nato ASI Series, vol. 355, pp. 79–105. Springer.10.1007/978-94-015-9159-1_6Google Scholar
Floryan, J. M. 2003 Vortex instability in a diverging–converging channel. J. Fluid Mech. 482, 17–50.10.1017/S0022112003003987Google Scholar
Floryan, J. M. 2015 Flow in a meandering channel. J. Fluid Mech. 770, 52–84.Google Scholar
Floryan, J. M. & Floryan, C. 2009 Traveling wave instability in a diverging–converging channel. Fluid Dyn. Res. 42, 025509.Google Scholar
Floryan, J. M., Szumbarski, J. & Wu, X. 2002 Stability of flow in a channel with vibrating walls. Phys. Fluids 14, 3927–3936.10.1063/1.1511545Google Scholar
Fukagata, K., Sugiyama, K. & Kasagi, N. 2009 On the lower bound of net driving power in controlled duct flows. Physica D 238, 1082–1086.Google Scholar
Gepner, S. W. & Floryan, J. M. 2016 Flow dynamics and enhanced mixing in a converging-diverging channel. J. Fluid Mech. 807, 167–204.Google Scholar
Hall, P. & Papageorgiou, D. T. 1999 The onset of chaos in a class of Navier–Stokes solutions. J. Fluid Mech. 393, 59–87.10.1017/S0022112099005364Google Scholar
Hayat, T., Ali, N. & Asghar, S. 2007 An analysis of peristaltic transport for flow of a Jeffrey fluid. Acta Mech. 193, 101–112.Google Scholar
Hœpffner, J. & Fukagata, K. 2009 Pumping or drag reduction? J. Fluid Mech. 635, 171–187.10.1017/S0022112009007629Google Scholar
Jacobi, A. M. & Shah, R. K. 1995 Heat transfer surface enhancement through the use of longitudinal vortices: a review of recent progress. Exp. Therm. Fluid Sci. 11, 295–309.10.1016/0894-1777(95)00066-UGoogle Scholar
Jaffrin, M. Y. & Shapiro, A. H. 1971 Peristaltic pumping. Annu. Rev. Fluid Mech. 3, 13–37.Google Scholar
Jeffrey, D. J. & Rich, A. D. 1994 The evaluation of trigonometric integrals avoiding spurious discontinuities. ACM Trans. Math. Softw. 20, 124–135.Google Scholar
Jiménez-Lozano, J., Sen, M. & Dunn, P. F. 2009 Particle motion in unsteady two-dimensional peristaltic flow with application to the ureter. Phys. Rev. E 79, 041901.Google Scholar
Mamori, H., Iwamoto, K. & Marata, A. 2014 Effect of the parameters of travelling waves created by blowing and suction on the relaminarization phenomena in fully developed turbulent channel flow. Phys. Fluids 26, 015101.Google Scholar
Marusic, I., Joseph, D. D. & Nahesh, K. 2007 Laminar and turbulent comparisons for channel flow and flow control. J. Fluid Mech. 570, 467–477.10.1017/S0022112006003247Google Scholar
Meijing, L. & Brasseur, J. G. 1993 Non-steady peristaltic transport in finite-length tubes. J. Fluid Mech. 248, 129–151.Google Scholar
Min, T., Kang, S. M., Speyer, J. L. & Kim, J. 2006 Sustained sub-laminar drag in a fully developed channel flow. J. Fluid Mech. 558, 309–318.Google Scholar
Mingalev, S. V., Lyubimova, T. P. & Filippov, L. O. 2015 Flow rate in a channel with small-amplitude pulsating walls. Eur. J. Mech. (B/Fluids) 51, 1–7.Google Scholar
Mohammadi, A. & Floryan, J. M. 2012 Mechanism of drag generation by surface corrugation. Phys. Fluids 24, 013602.Google Scholar
Mohammadi, A. & Floryan, J. M. 2013a Pressure losses in grooved channels. J. Fluid Mech. 725, 23–54.Google Scholar
Mohammadi, A. & Floryan, J. M. 2013b Groove optimization for drag reduction. Phys. Fluids 25, 113601.Google Scholar
Mohammadi, A., Moradi, H. V. & Floryan, J. M. 2015 New instability mode in a grooved channel. J. Fluid Mech. 778, 691–720.10.1017/jfm.2015.399Google Scholar
Moradi, H. V., Budiman, A. C. & Floryan, J. M. 2017 Use of natural instabilities for generation of streamwise vortices in a channel. Theor. Comput. Fluid Dyn. 31, 233–250.Google Scholar
Moradi, H. V. & Floryan, J. M. 2014 Stability of flow in a channel with longitudinal grooves. J. Fluid Mech. 757, 613–648.Google Scholar
Nakanishi, R., Mamori, H. & Fukagata, K. 2012 Relaminarization of turbulent channel flow using travelling wave-like wall deformation. Intl J. Heat Fluid Flow 35, 152–159.Google Scholar
Quadrio, M. 2011 Drag reduction in turbulent boundary layers by in-plane wall motion. Phil. Trans. R. Soc. Lond. A 369, 1428–1442.Google Scholar
Ramachandra Rao, A. & Mishra, M. 2004 Nonlinear and curvature effects on peristaltic flow of a viscous fluid in an asymmetric channel. Acta Mech. 168, 35–39.Google Scholar
Secomb, T. W. 1978 Flow in a channel with pulsating walls. J. Fluid Mech. 88, 273–288.Google Scholar
Selverov, K. P. & Stone, H. A. 2001 Peristaltically driven channel flow with applications toward micromixing. Phys. Fluids 13, 1837–1859.Google Scholar
Stroock, A. D., Dertinger, S. K. W., Ajdari, A., Mezič, I., Stone, H. A. & Whitesides, G. M. 2002 Chaotic mixer for microchannels. Science 295, 647–651.10.1126/science.1066238Google Scholar
Sturman, S., Ottino, J. M. & Wiggins, S. 2006 The Mathematical Foundations of Mixing, Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press.10.1017/CBO9780511618116Google Scholar
Takagi, D. & Balmforth, N. J. 2011a Peristaltic pumping of viscous fluid in an elastic tube. J. Fluid Mech. 672, 196–218.Google Scholar
Takagi, D. & Balmforth, N. J. 2011b Peristaltic pumping of rigid objects in an elastic tube. J. Fluid Mech. 672, 219–244.10.1017/S0022112010005926Google Scholar
Yadav, N., Gepner, S. W. & Szumbarski, J. 2017 Instability in a channel with grooves parallel to the flow. Phys. Fluids 29, 084104.Google Scholar