Technical Papers
Oct 11, 2013

Transient Mass Transport within Stokes Eddies Induced in a Junction of Orthogonal Flow Branches

Publication: Journal of Hydraulic Engineering
Volume 140, Issue 5

Abstract

The model of junction of four orthogonal channels is used to investigate mass transport within viscous eddies developing through channel networks. These viscous eddies may develop in low flow rate branches of channel networks and may control solute transport. Thus, to contribute to the knowledge of the influence of viscous eddies on solute transport in channel networks, the analysis of the streamline patterns is conducted for various flow rates and the threshold of the flow rate for the appearance of eddies is determined. Following this, the calculation of the mass transport is carried out in function of time when a permanent source of solute is applied at the inlet of the system. This calculation is carried out for different values of the Péclet number in order to highlight diffusive and convective transport mechanisms. The results show that the effect of eddies for transporting the solute may be significant.

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References

Adler, P. M., and Thovert, J. F. (1999). Fractures and fracture networks, Kluwer Academic, The Netherlands.
Arega, F., and Sanders, B. F. (2004). “Dispersion model for tidal wetlands.” J. Hydraul. Eng., 739–754.
Austin, R., Waanders, B., McKenna, S., and Choi, C. (2008). “Mixing at cross junctions in water distribution systems. II: Experimental study.” J. Water Resour. Plann. Manage., 295–302.
Batchelor, G. K. (1967). An introduction to fluid dynamics, Cambridge University Press, Cambridge, U.K.
Berkowitz, B., Naumann, C., and Smith, L. (1994). “Mass transfer at fracture intersections: An evaluation of mixing models.” Water Resour. Res., 30(6), 1765–1773.
Bouquain, J., Méheust, Y., Bolster, D., and Davy, P. (2012). “The impact of inertial effects on solute dispersion in a channel with periodically varying aperture.” Phys. Fluids, 24(8), 083602.
Bourot, J. M. (1984). “Sur la structure cellulaire des écoulements plans de Stokes, à débit moyen nul, en canal indéfini à parois parallèles.” C. R. Acad. Sci. II, 298(2), 161–164.
Brody, J. P., Yager, P., Goldstein, R. E., and Austin, R. H. (1996). “Biotechnology at low Reynolds numbers.” Biophys. J., 71(6), 3430–3441.
Bruderer, C., and Bernabé, Y. (2001). “Network modeling of dispersion: Transition from Taylor dispersion in homogeneous networks to mechanical dispersion in very heterogeneous ones.” Water Resour. Res., 37(4), 897–908.
Bryden, M. D., and Brenner, H. (1996). “Multiple-timescale analysis of Taylor dispersion in converging and diverging flows.” J. Fluid Mech., 311, 343–359.
Cachile, M., Talon, L., Gomba, J. M., Hulin, J. P., and Auradou, H. (2012). “Stokes flow paths separation and recirculation cells in X-junctions of varying angle.” Phys. Fluids, 24(2), 021704.
COMSOL Multiphysics 4.2 [Computer software], Sweden, Comsol.
Csanady, G. T. (1973). Turbulent diffusion in the environment, Reidel Publications, Dordrecht, Netherlands.
Dentz, M., and Berkowitz, B. (2003). “Transport behavior of a passive solute in continuous time random walks and multirate mass transfer.” Water Resour. Res., 39(5), WR001163.
Driesen, C. H., Kuerten, J. G. M., and Kuiken, H. K. (2000). “Mass transport in a partially covered fluid-filled cavity.” Int. J. Heat Mass Transfer, 43(10), 1823–1834.
Endo, H. K., and Long, J. C. S. (1984). “A model for investigating mechanical transport in fracture networks.” Water Resour. Res., 20(10), 1390–1400.
EPANET 2 [Computer software], Washington, U.S. Environmental Protection Agency.
Fagherazzi, S., and Sun, T. (2004). “A stochastic model for the formation of channel networks in tidal marshes.” Geophys. Res. Letters, 31(21), L21503-1–L21503-4.
Fang, L. C., Nicolaou, D., and Cleaver, J. W. (1999). “Transient removal of a contaminated fluid from a cavity.” Int. J. Heat Fluid Flow, 20(6), 605–613.
Faure, T. M., Adrianos, P., Lusseyran, F., and Pastur, L. (2007). “Visualizations of the flow inside an open cavity at medium range Reynolds numbers.” Exp. Fluids, 42(2), 169–184.
Floryan, J. M., and Czechowski, L. (1995). “On the numerical treatment of corner singularity in the vorticity field.” J. Comp. Physiol., 118(2), 222–228.
Georgiadou, M., Mohr, R., and Alkire, R. C. (2000). “Local mass transport in two-dimensional cavities in laminar shear flow.” J. Electrochem. Soc., 147(8), 3021–3028.
Gylling, B., Moreno, L., and Neretnieks, I. (1999). “The channel network model—A tool for transport simulations in fractured media.” Ground Water, 37(3), 367–375.
Hajjam, M. (1996). Contribution à l’étude de différents types d’écoulements en régime de Stokes, Thèse de Doctorat ès Sciences Physiques, Poitiers, France (in French).
Happel, J., and Brenner, H. (1973). Low Reynolds number hydrodynamics. Mechanics of fluids and transport processes, Noordhoff International Publishing, The Netherlands.
Hasimoto, H., and Sano, O. (1980). “Stokeslests and eddies in creeping flow.” Annu. Rev. Fluid Mech., 12, 335–363.
Hellou, M. (2004). “ Inversion transformation of Stokes flows bounded by parallel planes.” Z. Angew. Math. Phys., 55(4), 642–657.
Hellou, M., and Bach, T. D. P. (2011). “Stokes flow in a junction of two-dimensional orthogonal channels.” Z. Angew. Math. Phys., 62(1), 135–147.
Hellou, M., and Coutanceau, M. (1992). “Cellular Stokes flow induced by rotation of a cylinder in a closed channel.” J. Fluid Mech., 236, 557–577.
Hellou, M., Martinez, J., and El Yazidi, M. (2004). “Stokes flow through microstructural model of fibrous media.” Mech. Res. Comm., 31(1), 97–104.
Ho, C. K. (2008). “Solute mixing models for water distribution pipe networks.” J. Hydraul. Eng., 1236–1244.
Ho, C. K., and O’Rear, J. R. L. (2009). “Evaluation of solute mixing in water distribution pipe junctions.” J. Am. Water Works Assoc., 101(9), 116–127.
Hull, L. C., and Koslow, K. N. (1986). “Streamline routing through fracture junctions.” Water Resour. Res., 22(12), 1731–1734.
Jeong, J. T. (2001). “Slow viscous flow in a partitioned channel.” Phys. Fluids, 13(6), 1577–1582.
Kondo, K., and Fukui, K. (1998). “Shape evolution of electrodeposited bumps with deep cavities.” J. Electrochem. Soc., 145(9), 3007–3010.
Kosakowski, G., and Berkowitz, B. (1999). “Flow pattern variability in natural fracture intersections.” Geophys. Res. Letters, 26(12), 1765–1768.
Lee, J., and Koplik, J. (2001). “Network model for deep bed filtration.” Phys. Fluids, 13(5), 1076–1086.
Li, G. (2002). “Tracer mixing at fracture intersections.” Environ. Geol., 42(2–3), 137–144.
Lightbody, A. F., Nepf, H. M., and Bays, J. S. (2007). “Mixing in deep zones within constructed treatment wetlands.” Ecol. Eng., 29(2), 209–220.
Mignot, E., Rivière, N., Paquier, A., and Perkins, R. J. (2011). “Hydraulic models of the flow distribution in a four branch open channel junction with supercritical flow.” J. Hydraul. Eng., 289–299.
Moffatt, H. K. (1964). “Viscous and resistive eddies near a sharp corner.” J. Fluid Mech., 18(1), 1–18.
Moreau, F., and Bourot, J. M. (1993). “Ecoulements cellulaires de Stokes produits en canal plan illimité par la rotation de deux cylindres.” Z. Angew. Math. Phys., 44(5), 777–798.
Moreau, F., Hellou, M., and El Yazidi, M. (1998). “Ecoulements cellulaires de Stokes dans un canal plan obstrué par une file de cylindres.” Z. Angew. Math. Phys., 49(1), 31–45.
Mourzenko, V. V., Yousefian, F., Kolbah, B., Thovert, J. F., and Adler, P. M. (2002). “Solute transport at fracture intersections.” Water Resour. Res., 38(1), 1–14.
Nicklow, J. W., and Mays, L. W. (2000). “Optimization of multiple reservoir networks for sedimentation control.” J. Hydraul. Eng., 232–242.
Occhialini, J. M., and Higdon, J. J. L. (1992). “Convective mass transport from rectangular cavities in viscous flow.” J. Electrochem. Soc., 139(10), 2845–2855.
O’Neill, M. E. (1983). “On angles of separation in Stokes flow.” J. Fluid Mech., 133, 427–442.
Park, Y. J., and Lee, K. K. (1999). “Analytical solutions for solute transfer characteristics at continuous fracture junctions.” Water Resour. Res., 35(5), 1531–1537.
Park, Y. J., Lee, K. K., and Berkowitz, B. (2001). “Effects of junction transfer characteristics on transport in fracture networks.” Water Resour. Res., 37(4), 909–923.
Patil, D. V., Lakshmisha, K. N., and Rogg, B. (2006). “Lattice Boltzmann simulation of lid-driven flow in deep cavities.” Comput. Fluids, 35(10), 1116–1125.
Pozrikidis, C. (1992). Boundary integral and singularity methods for linearized viscous flow, Cambridge University Press, Cambridge, U.K.
Pozrikidis, C. (2000). Little book of streamlines, Academic Press, San Diego.
Romero-Gomez, P., Ho, C. K., and Choi, C. Y. (2008). “Mixing at cross junctions in water distribution systems. I: Numerical study.” J. Water Resour. Plann. Manage., 285–294.
Sahimi, M. (1995). Flow and transport in porous media and fractured rock, Wiley-VCH, Weinheim, Germany.
Sangani, A. S., and Acrivos, A. (1982). “Slow flow past periodic arrays of cylinders with application to heat transfer.” Int. J. Multiphase Flow, 8(3), 193–206.
Schakelford, C. D. (1991). “Laboratory diffusion testing for waste disposal—A review.” J. Contam. Hydrol., 7(3), 177–217.
Shankar, P. N. (2005). “Moffatt eddies in the cone.” J. Fluid Mech., 539, 113–135.
Shankar, P. N. (2007). Slow viscous flows, Imperial College Press, London, U.K.
Shankar, P. N., and Deshpande, M. D. (2000). “Fluid mechanics in the driven cavity.” Annu. Rev. Fluid Mech., 32, 93–136.
Stockman, H. W., Johnson, J., and Brown, S. R. (2001). “Mixing at fracture intersections: Influence of channel geometry and the Reynolds and Peclet numbers.” Geophys. Res. Lett., 28(22), 4299–4302.
Stone, H. A., Stroock, A. D., and Ajdari, A. (2004). “Engineering flows in small devices: Microfluidics toward a lab-on-a-chip.” Annu. Rev. Fluid Mech., 36, 381–411.
Taneda, S. (1979). “Visualization of separating Stokes flow.” J. Phys. Soc. Jpn., 46(6), 1935–1942.
van Bloemen Waanders, B. G., Hammond, G., Shadid, J., Collis, S., and Murray, R. (2005). “A comparison of Navier Stokes and network model to predict chemical transport in municipal water distribution systems.” Proc., 2005 Wold Water and Environmental Ressources Congress, ASCE, Reston, VA.
Wang, C. Y. (2002). “Slow viscous flow between hexagonal cylinders.” Transp. Porous Media, 47(1), 67–80.
Wang, C. Y. (2010). “Flow through a finned channel filled with a porous medium.” Chem. Eng. Sci., 65(5), 1826–1831.
Wang, J. T., Han, J. J., and Yu, D. M. (2012). “Numerical studies of geometry effects of a two-dimensional microfluidic four-roll mill on droplet elongation and rotation.” Eng. Anal. Bound. Elem., 36(10), 1453–1464.

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Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 140Issue 5May 2014

History

Received: Aug 21, 2012
Accepted: Oct 9, 2013
Published online: Oct 11, 2013
Published in print: May 1, 2014
Discussion open until: Jul 14, 2014

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Mustapha Hellou [email protected]
Professor, Université Européenne de Bretagne, Institut National des Sciences Appliquées, Laboratoire de Génie Civil et Génie Mécanique, EA3913, 35708 Rennes, France (corresponding author). E-mail: [email protected]
Olivier Bour
Professor, Université Européenne de Bretagne, Université de Rennes1, Géosciences, Unité Mixte de Recherche 6118, 35042 Rennes, France.

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