Hostname: page-component-7bb8b95d7b-dvmhs Total loading time: 0 Render date: 2024-09-25T01:25:56.691Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow in a meandering channel

Published online by Cambridge University Press:  30 March 2015

J. M. Floryan
J. M. Floryan*
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada
*
†Email address for correspondence: mfloryan@eng.uwo.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

A comprehensive analysis of the pressure-gradient driven flow in a meandering channel has been presented. This geometry is of interest as it can be used for the creation of streamwise vortices which magnify the transverse transport of scalar quantities, e.g. heat transfer. The linear stability theory has been used to determine the meandering wavelengths required for the vortex formation. It has been demonstrated that reduction of the wavelength results in the onset of flow separation which, when combined with the wall geometry, results in an effective channel narrowing: the stream ‘lifts up’ above the wall and becomes nearly rectilinear, thus eliminating vortex-generating centrifugal forces. Increase of the wavelength also leads to a nearly rectilinear stream, as the slope of the wall modulations becomes negligible. As shear-driven instability may interfere with the formation of vortices, the conditions leading to the onset of such instability have also been investigated. The attributes of the geometry which lead to the most effective vortex generation without any interference from the shear instabilities and with the smallest drag penalty have been identified.

JFM classification

Flow Control: Flow Control Flow Control: Mixing enhancement Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 770 , 10 May 2015 , pp. 52 - 84
Check for updates
Copyright
© 2015 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

Bai, Y. C. & Yang, Y. H. 2011 The dynamic stability of the flow in a meander channel. Sci. China, Technol. Sci. 54, 931–940.Google Scholar
Bergles, A. E., Jensen, M. K. & Shome, B. 1996 The literature on enhancement of convective heat and mass transfer. J. Enhanced Heat Transfer 4, 1–6.Google Scholar
Bergles, A. E. & Webb, R. L. 1985 A guide to the literature on convective heat transfer augmentation. In Advances in Heat Transfer 1985 (ed. Shenkman, S. M., O’Brien, J. E., Habib, I. S. & Kohler, J. A.), ASME Symposium, HTD, vol. 43, pp. 81–90.Google Scholar
Bloch, F. 1928 Über die Quantenmechanik der Elektronen in Kristallgittern. Z. Phys. 52, 555–600.Google Scholar
Castelain, C., Mokrani, A., Legentilhomme, P. & Peerhossaini, H. 1997 Residence time distribution in twisted pipe flows: helically coiled system and chaotic system. Exp. Fluids 22, 359–368.Google Scholar
Castelain, C., Mokrani, A., Le Guer, Y. & Peerhossaini, H. 2001 Experimental study of chaotic advection regime in a twisted duct flow. Eur. J. Mech. B 20, 205–232.Google Scholar
Coddington, E. A. & Levinson, N. 1965 Theory of Ordinary Differential Equations. McGraw-Hill.Google Scholar
Colombini, M. & Parker, G. 1995 Longitudinal streaks. J. Fluid Mech. 304, 161–183.Google Scholar
Dean, W. 1928 Fluid motion in a curved channel. Proc. R. Soc. Lond. A 121, 402–412.Google Scholar
Fiebeg, M. 1995a Vortex generators for compact heat exchangers. J. Enhanced Heat Transfer 2, 43–61.Google Scholar
Fiebeg, M. 1995b Embedded vortices in internal flow: heat transfer and pressure loss enhancement. Intl J. Heat Fluid Flow 16, 376–388.CrossRefGoogle Scholar
Fiebeg, M. 1998 Vortices, generators and heat transfer. Chem. Engng Res. Des. 76, 108–123.Google Scholar
Fiebeg, 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. Kakaç, S., Bergles, A. E, Mayinger, F. & Yüncü, H.), pp. 79–105. Kluwer.CrossRefGoogle Scholar
Floryan, J. M. 1986 Görtler instability of boundary layers over concave and convex walls. Phys. Fluids 29, 2380–2387.Google Scholar
Floryan, J. M. 1991 On the Görtler instability of boundary layers. Prog. Aeronaut. Sci. 28, 235–271.Google Scholar
Floryan, J. M. 1997 Stability of wall-bounded shear layers in the presence of simulated distributed surface roughness. J. Fluid Mech. 335, 29–55.CrossRefGoogle Scholar
Floryan, J. M. 2002 Centrifugal instability of Couette flow over a wavy wall. Phys. Fluids 14, 312–322.Google Scholar
Floryan, J. M. 2003 Vortex instability in a converging–diverging channel. J. Fluid Mech. 482, 17–50.Google Scholar
Floryan, J. M. 2007 Three-dimensional instabilities of laminar flow in a rough channel and the concept of hydraulically smooth wall. Eur. J. Mech. B 26, 305–329.CrossRefGoogle Scholar
Floryan, J. M. & Asai, M. 2011 On the transition between distributed and isolated surface roughness and its effect on the stability of channel flow. Phys. Fluids 23, 104101.Google Scholar
Gong, L., Kota, K., Tao, W. & Joshi, Y. 2011 Parametric numerical study of flow and heat transfer in microchannels with wavy walls. Trans. ASME J. Heat Transfer 133, 051702.Google Scholar
Görtler, H. 1941 Instabilität laminarer Grenzschichten an konkaven Wänden gegenüber gewissen dreidimensionalen Störungen. Z. Angew. Math. Mech. 21, 250–252.CrossRefGoogle Scholar
Gschwind, P., Regele, A. & Kottke, V. 1995 Sinusoidal wavy channels with Taylor–Görtler vortices. Exp. Therm. Sci. 11, 270–275.Google Scholar
Guzmán, A. M., Cárdenas, M. J., Urzúa, F. A. & Araya, P. E. 2009 Heat transfer enhancement by flow bifurcation in asymmetric wavy wall channels. Intl J. Heat Mass Transfer 52, 3778–3789.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.Google Scholar
Hossain, M. Z., Floryan, D. & Floryan, J. M. 2012 Drag reduction due to spatial thermal modulations. J. Fluid Mech. 713, 398–419.CrossRefGoogle Scholar
Husain, S. Z. & Floryan, J. M. 2010 Spectrally-accurate algorithm for moving boundary problems for the Navier–Stokes equations. J. Comput. Phys. 229, 2287–2313.Google Scholar
Husain, S. Z. & Floryan, J. M. 2013 Effective solvers for the immersed boundaries method. Comput. Fluids 84, 127–140.Google Scholar
Husain, S. Z., Floryan, J. M. & Szumbarski, J. 2009 Over-determined formulation of the immersed boundary conditions method. J. Comput. Meth. Appl. Mech. Engng 199, 94–112.Google Scholar
Ikeda, S., Parker, G. & Sawai, K. 1981 Bend theory of river meanders. Part 1. Linear development. J. Fluid Mech. 112, 363–377.Google 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.CrossRefGoogle Scholar
Ligrani, P. M., Oliveira, M. M. & Blaskovitch, T. 2003 Comparison of heat transfer augmentation techniques. AIAA J. 41, 337–362.Google Scholar
Loh, S. A. & Blackburn, H. M. 2011 Stability of steady flow through an axially corrugated pipe. Phys. Fluids 23, 111703.CrossRefGoogle Scholar
Mack, L. M. 1976 A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer. J. Fluid Mech. 73, 497–520.Google Scholar
Metwally, H. M. & Manglik, R. M. 2004 Enhanced heat transfer due to curvature-induced lateral vortices in laminar flows in sinusoidal corrugated-plate channels. Intl J. Heat Mass Transfer 47, 2283–2292.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
Moradi, H. & Floryan, J. M. 2013a Flows in annuli with longitudinal grooves. J. Fluid Mech. 716, 280–315.Google Scholar
Moradi, H. & Floryan, J. M. 2013b Maximization of heat transfer across micro-channels. Intl J. Heat Mass Transfer 66, 517–530.Google Scholar
Nishimura, T., Murakami, S., Arakawa, S. & Kawamura, Y. 1990a Flow observations and mass transfer characteristics in symmetrically wavy-walled channels at moderate Reynolds numbers for steady flow. Intl J. Heat Mass Transfer 33, 835–845.Google Scholar
Nishimura, T., Yano, K., Yoshino, T. & Kawamura, Y. 1990b Occurrence and structure of Taylor–Görtler vortices induced in two-dimensional wavy channels for steady flow. J. Chem. Engng Japan 23, 697–703.Google Scholar
Oviedo-Tolentino, F., Romero-Méndez, R., Hernández-Guerrero, A. & Girón-Palomares, B. 2008 Experimental study of fluid flow in the entrance of a sinusoidal channel. Intl J. Heat Fluid Flow 29, 1233–1239.CrossRefGoogle Scholar
Parker, G. 1976 On the cause and characteristic scales of meandering and braiding in rivers. J. Fluid Mech. 76, 457–480.Google Scholar
Parker, G. & Andrews, E. D. 1986 On the time development of meander bends. J. Fluid Mech. 162, 139–156.Google Scholar
Parker, G., Sawai, K. & Ikeda, S. 1982 Bend theory of river meanders. Part 2. Nonlinear deformation of finite-amplitude bends. J. Fluid Mech. 115, 303–314.CrossRefGoogle Scholar
Patera, A. T. & Mikic, B. B. 1986 Exploiting hydrodynamic instabilities: Resonant heat transfer enhancement. Intl J. Heat Mass Transfer 29, 1127–1138.Google Scholar
Pham, M. V., Plourde, F. & Doan, S. K. 2008 Turbulent heat and mass transfer in sinusoidal wavy channels. Intl J. Heat Fluid Flow 29, 1240–1257.Google Scholar
Rayleigh, L. 1920 On the dynamics of revolving fluids. Sci. Pap. 6, 447–453.Google Scholar
Rosaguti, N. R., Fletcher, D. F. & Haynes, B. S. 2007 Low-Reynolds number heat transfer enhancement in sinusoidal channels. Chem. Engng Sci. 62, 694–702.Google Scholar
Rush, T. A., Newell, T. A. & Jacobi, A. M. 1999 An experimental study of flow and heat transfer in sinusoidal wavy passages. Intl J. Heat Mass Transfer 42, 1541–1553.CrossRefGoogle Scholar
Saad, Y. 2003 Iterative Methods for Sparse Linear Systems. SIAM.CrossRefGoogle Scholar
Saric, W. S. & Benmalik, A. 1991 Görtler vortices with periodic curvature. In FED, vol. 114, Boundary Layer and Transition to Turbulence, pp. 37–45. ASME.Google Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129–162.Google Scholar
Sui, Y., Teo, C. J. & Lee, P. S. 2012 Direct numerical simulation of fluid flow and heat transfer in periodic wavy channels with rectangular cross-sections. Intl J. Heat Mass Transfer 55, 73–88.Google Scholar
Szumbarski, J. & Floryan, J. M. 1999 A direct spectral method for determination of flows over corrugated boundaries. J. Comput. Phys. 153, 378–402.Google Scholar
Szumbarski, J. & Floryan, J. M. 2006 Transient disturbance growth in a corrugated channel. J. Fluid Mech. 568, 243–272.Google Scholar
Taylor, G. 1923 Stability of viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. A 223, 289–293.Google Scholar
Webb, R. L. & Bergles, A. E. 1983 Performance evaluation criteria for selection of heat transfer surface geometries used in low Reynolds number heat exchangers. In Low Reynolds Number Flow Heat Exchangers, Advanced Study Institute Book (ed. Kakaç, S., Shah, R. K. & Bergles, A. E.). Hemisphere.Google Scholar
Zhang, J., Kundu, J. & Manglik, R. M. 2004 Effects of fin waviness and spacing on the lateral vortex structure and laminar heat transfer in wavy-plate-fin core. Intl J. Heat Mass Transfer 47, 1719–1730.Google Scholar