TECHNICAL PAPERS
Apr 15, 2002

Numerical Modeling of Helical Static Mixers for Water Treatment

Publication: Journal of Environmental Engineering
Volume 128, Issue 5

Abstract

To improve the understanding of how static mixers work and how to better utilize them in environmental engineering (or, specifically, drinking water treatment), a numerical model for simulating turbulent flows in helical static mixers is developed. The model solves the three-dimensional, Reynolds-averaged Navier-Stokes equations, closed with the k-ω turbulence model, using a second-order-accurate finite-volume numerical method. Numerical simulations are carried out for a two-element helical static mixer, and the computed results are analyzed to elucidate the complex, three-dimensional features of the flow. The results show that the flow field within the mixer is characterized by the presence of pockets of reversed flow and the growth and interaction of strong longitudinal vortices. As an example of the kind of practical insights that can be gained from such detailed three-dimensional computations, the simulated flow field is used to investigate two quantities that are often used to characterize mixing within a static mixer and to discuss the merits of these quantities for coagulant mixing in drinking water treatment.

Get full access to this article

View all available purchase options and get full access to this article.

References

Amirtharajah, A. (1978). “Design of rapid mix units.” Water treatment plant design, R. L. Sanks, ed., Butterworth-Heinemann, Boston, 131–147.
Amirtharajah, A., and Jones, S. C. (1996). “Mixing for coagulation: Organic polymers, static mixers and modeling.” Chemical water and wastewater treatment IV, H. H. Hahn et al., eds., Springer-Verlag, Berlin, 3–15.
Amirtharajah, A., Jones, S. C., Skeens, B. M., Heindel, H. L., Latimer, R. J., Hardy, S. A., and Li, W. (2001). Static mixers for coagulation and disinfection, American Water Works Association (AWWA) Research Foundation, Denver.
Amirtharajah, A., and Mills, K. M.(1982). “Rapid-mix design for mechanisms of alum coagulation.” J. Am. Water Works Assoc., 74(4), 210–216.
Amirtharajah, A., and Trusler, S. L.(1986). “Destabilization of particles by turbulent rapid mixing.” J. Environ. Eng., 112(6), 1085–1108.
Bałdyga, J., and Bourne, J. R.(1984). “A fluid mechanical approach to turbulent mixing and chemical reaction. Part II. Micromixing in the light of turbulence theory.” Chem. Eng. Commun., 28, 243–258.
Bałdyga, J., and Bourne, J. R. (1999). Turbulent mixing and chemical reactions. Wiley, New York.
Bałdyga, J., Bourne, J. R., and Hearn, S. J.(1997). “Interaction between chemical reactions and mixing on various scales.” Chem. Eng. Sci., 52(4), 457–466.
Bourne, J. R., Lenzner, J., and Petrozzi, S.(1992). “Micromixing in static mixers: An experimental study.” Ind. Eng. Chem. Res., 31(4), 1216–1222.
Bourne, J. R., and Maire, H.(1990). “Micromixing and fast chemical reactions in static mixers.” Chem. Eng. Process., 30(1), 23–30.
Burke, J. C. (1996). “Effectiveness of static mixers for enhanced coagulation.” MS thesis, Georgia Institute of Technology, Atlanta.
Byrde, O. (1997). “Massively parallel flow computation with application to fluid mixing.” PhD thesis No. 1736, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
Byrde, O., and Sawley, M. L.(1999). “Optimization of a Kencis static mixer for non-creeping flow conditions.” Chem. Eng. J., 72(2), 163–169.
Camp, T. R., and Stein, P. C.(1943). “Velocity gradients and internal work in fluid friction.” J. Boston Soc. Civ. Eng., 30(4), 219–237.
Chorin, A. J.(1967). “A numerical method for solving incompressible viscous flow problems.” J. Comput. Phys., 2(1), 12–26.
Clark, M. M.(1985). “Critique of Camp and Stein’s RMS velocity gradient.” J. Environ. Eng., 111(6), 741–754.
Clark, M. M. (1987). “Effect of micromixing on product selectivity.” Proc., AWWA Annual Conf., Denver, 1957–1975.
Clark, M. M., Srivastava, R. M., and David, R.(1993). “Mixing and aluminum precipitation.” Environ. Sci. Technol., 27(10), 2181–2189.
Clark, M. M., Srivastava, R. M., Lang, J. S., Trussell, R. R., McCollum, L. J., Bailey, D., Christie, J. D., and Stolarik, G. (1994). Selection and design of mixing processes for coagulation, AWWA Research Foundation, Denver.
Delichatsios, M. A., and Probstein, R. F.(1975). “Coagulation in turbulent flow: Theory and experiment.” J. Colloid Interface Sci., 51(6), 394–405.
Ducoste, J. J., and Clark, M. M.(1998a). “The influence of tank size and impeller geometry on turbulent flocculation: I. Experimental.” Environ. Eng. Sci., 15(3), 215–224.
Ducoste, J. J., and Clark, M. M.(1998b). “The influence of tank size and impeller geometry on turbulent flocculation: II. Model.” Environ. Eng. Sci., 15(3), 225–235.
Graber, S. D.(1994). “A critical review of the use of the G-value (RMS velocity gradient) in environmental engineering.” Dev. Theor. Appl. Mech., 17, 533–556.
Heindel, H. L., Hardy, S. A., Amirtharajah, A., and Arrowood, M. J. (1999). “Disinfection of cryptosporidium parvum with static mixers.” Proc., AWWA Water Quality Technology Conf., Denver.
Hobbs, D. M. (1998). “Characterization of a Kenics static mixer under laminar flow conditions,” PhD thesis, Rutgers, State Univ. of New Jersey, New Brunswick, N.J.
Hobbs, D. M., and Muzzio, F. J.(1998). “Reynolds number effects on laminar mixing in the kenics static mixer.” Chem. Eng. J., 70(2), 93–104.
Hobbs, D. M., Swanson, P. D., and Muzzio, F. J.(1998). “Numerical characterization of low Reynolds number flow in the kenics static mixer.” Chem. Eng. Sci., 53(8), 1565–1584.
Jones, S. C. (1999). “Static mixers for water treatment: A computational fluid dynamics model,” PhD thesis, Georgia Institute of Technology, Atlanta.
Kawamura, S. (1991). Integrated design of water treatment facilities, Wiley, New York.
Lang, E., Drtina, P., Streiff, F., and Fleischli, M.(1995). “Numerical simulation of the fluid flow and the mixing process in a static mixer.” Int. J. Heat Mass Transf., 38(12), 2239–2250.
Latimer, R. J., and Amirtharajah, A. (1998). “Pilot scale comparison of static mixers and backmix reactors for water treatment.” Proc., AWWA Annual Conf., Denver, 705–740.
Lin, F.-B., and Sotiropoulos, F.(1997a). “Assessment of artificial dissipation models for three-dimensional incompressible flow solutions.” J. Fluids Eng., 119(2), 331–340.
Lin, F.-B., and Sotiropoulos, F.(1997b). “Strongly-coupled multigrid method for 3-D incompressible flows using near-wall turbulence closures.” J. Fluids Eng., 119(2), 314–324.
Martin, N., and Galey, C.(1994). “Use of static mixer for oxidation and disinfection by ozone.” Ozone. Sci. Eng., 16, 455–473.
McKenna, C. J., Humble, D. E., and Hobson, K. L. (1986). “Static mixer performance for chlorine mixing.” Proc., Water Pollution Control Federation Annual Conf., Washington, D.C.
Menter, F. R.(1994). “Two-equation eddy-viscosity turbulence model for engineering applications.” AIAA J., 32(8), 887–914.
Rauline, D., Tanguy, P. A., Blévec, J.-M. L., and Bousquet, J.(1998). “Numerical investigation of the performance of several static mixers.” Can. J. Chem. Eng., 76(3), 527–535.
Saffman, P. G., and Turner, J. S.(1956). “On the collision of drops in turbulent clouds.” J. Fluid Mech., 1(16), 16–30.
Schulgen, B. F., Amirtharajah, A., and Jones, S. C. (1996). “Effectiveness of static mixers for coagulation in water treatment.” Proc., AWWA Annual Conf., Denver, 121–147.
Sotiropoulos, F., and Patel, V. C.(1995). “On the role of turbulence anisotropy and near-wall modeling in predicting three-dimensional shear-flows.” AIAA J., 33(3), 504–514.
Sotiropoulos, F., and Ventikos, Y.(1998). “Flow through a curved duct using nonlinear two-equation turbulence models.” AIAA J., 36(7), 1256–1262.
Sudo, K., Sumida, M., and Hibara, H.(1998). “Experimental investigation on turbulent flow in a circular-sectioned 90-degree bend.” Exp. Fluids, 25(1), 42–49.
Wilcox, D. C. (1994). Turbulence modeling for CFD, DCW Industries, La Cañada, Calif.

Information & Authors

Information

Published In

Go to Journal of Environmental Engineering
Journal of Environmental Engineering
Volume 128Issue 5May 2002
Pages: 431 - 440

History

Received: Jan 26, 2001
Accepted: Aug 8, 2001
Published online: Apr 15, 2002
Published in print: May 2002

Permissions

Request permissions for this article.

Authors

Affiliations

S. Casey Jones, A.M.ASCE
Postdoctoral Fellow, School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0355.
Fotis Sotiropoulos, M.ASCE
Associate Professor, School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0355.
Appiah Amirtharajah, F.ASCE
Professor, School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0512.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share