Articles | Volume 14, issue 1
https://doi.org/10.5194/dwes-14-53-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/dwes-14-53-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
09 Feb 2021
Research article |
| 09 Feb 2021
| 09 Feb 2021
Can terminal settling velocity and drag of natural particles in water ever be predicted accurately?
Onno J. I. Kramer
CORRESPONDING AUTHOR
Department of Water Management, Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA, Delft, the Netherlands
Department of Process and Energy, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628 CB, Delft, the Netherlands
Waternet, P.O. Box 94370, 1090 GJ, Amsterdam, the Netherlands
Institute for Life Science and Chemistry, HU University of Applied Sciences Utrecht, P.O. Box 12011, 3501 AA, Utrecht, the Netherlands
Peter J. Moel
Omnisys VOF, Eiberlaan 23, 3871 TG, Hoevelaken, the Netherlands
Shravan K. R. Raaghav
Department of Process and Energy, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628 CB, Delft, the Netherlands
Eric T. Baars
Waternet, P.O. Box 94370, 1090 GJ, Amsterdam, the Netherlands
Wim H. Vugt
Institute for Life Science and Chemistry, HU University of Applied Sciences Utrecht, P.O. Box 12011, 3501 AA, Utrecht, the Netherlands
Wim-Paul Breugem
Department of Process and Energy, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628 CB, Delft, the Netherlands
Johan T. Padding
Department of Process and Energy, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 39, 2628 CB, Delft, the Netherlands
Jan Peter Hoek
Department of Water Management, Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA, Delft, the Netherlands
Waternet, P.O. Box 94370, 1090 GJ, Amsterdam, the Netherlands
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Modeling particle transport and discoloration risk in drinking water distribution networks
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Cited articles
Abraham, F. F.: Functional dependence of drag coefficient of a sphere on
Reynolds number, Phys. Fluids, 13, 2194–2195,
https://doi.org/10.1063/1.1693218, 1970.
Albright, J.: Albright's chemical engineering handbook, CRC Press, New York, USA, 2009.
Almedeij, J.: Drag coefficient of flow around a sphere: Matching
asymptotically the wide trend, Powder Technol., 186, 218–223,
https://doi.org/10.1016/j.powtec.2007.12.006, 2008.
Amburgey, J. E.: Optimization of the extended terminal subfluidization wash
(ETSW) filter backwashing procedure, Water Res., 39, 314–330,
https://doi.org/10.1016/j.watres.2004.09.020, 2005.
Arsenijević, Z. L., Grbavčić, Ž. B., Garić-Grulović,
R. V., and Bošković-Vragolović, N. M.: Wall effects on the
velocities of a single sphere settling in a stagnant and counter-current
fluid and rising in a co-current fluid, Powder Technol., 203, 237–242,
https://doi.org/10.1016/j.powtec.2010.05.013, 2010.
Auguste, F. and Magnaudet, J.: Path oscillations and enhanced drag of light
rising spheres, J. Fluid Mech., 841, 228–266,
https://doi.org/10.1017/jfm.2018.100, 2018.
Bagheri, G. and Bonadonna, C.: On the drag of freely falling non-spherical
particles, Powder Technol., 301, 526–544,
https://doi.org/10.1016/j.powtec.2016.06.015, 2016.
Baldock, T. E., Tomkins, M. R., Nielsen, P., and Hughes, M. G.: Settling
velocity of sediments at high concentrations, Coast. Eng., 51,
91–100, https://doi.org/10.1016/j.coastaleng.2003.12.004, 2004.
Barati, R. and Neyshabouri, S. A. A. S.: Comment on “Summary of frictional
drag coefficient relationships for spheres: Evolving solution strategies
applied to an old problem”, Chem. Eng. Sci., 168, 339–343, https://doi.org/10.1016/j.ces.2017.04.037, 2018.
Barati, R., Neyshabouri, S. A. A. S., and Ahmadi, G.: Development of
empirical models with high accuracy for estimation of drag coefficient of
flow around a smooth sphere: an evolutionary approach, Powder Technol.,
257, 11–19, https://doi.org/10.1016/j.powtec.2014.02.045, 2014.
Beeftink, M., Hofs, B., Kramer, O. J. I., Odegard, I., and van der Wal, A.:
Carbon footprint of drinking water softening as determined by life cycle
assessment, J. Clean. Prod., 278, 123925,
https://doi.org/10.1016/j.jclepro.2020.123925, 2021.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N.: Transport phenomena,
Wiley, New York, USA, 2007.
Breakey, D. E. S., Vaezi, G. F., Masliyah, J. H., and Sanders, R. S.:
Side-view-only determination of drag coefficient and settling velocity for
non-spherical particles, Powder Technol., 339, 182–191,
https://doi.org/10.1016/j.powtec.2018.07.056, 2018.
Brown, P. P. and Lawler, D. F.: Sphere drag and settling velocity revisited,
J. Environmen. Eng., 129, 222–231,
https://doi.org/10.1061/(ASCE)0733-9372(2003)129:3(222), 2003.
Camp, T. R.: Sedimentation and the design of settling tanks, T.
Am. Soc. Civ. Eng., 111, 895–936, 1946.
Cheng, N. S.: Comparison of formulas for drag coefficient and settling
velocity of spherical particles, Powder Technol., 189, 395–398,
https://doi.org/10.1016/j.powtec.2008.07.006, 2009.
Cheng, N.-S.: Simplified settling velocity formula for sediment particle,
J. Hydraul. Eng., 123, 149–152,
https://doi.org/10.1061/(ASCE)0733-9429(1997)123:2(149), 1997.
Cheremisinoff, N. P.: Handbook of water and wastewater treatment
technologies, Butterworth-Heinemann, Boston, USA, 2002.
Chhabra, R. P., Agarwal, S., and Chaudhary, K.: A note on wall effect on the
terminal falling velocity of a sphere in quiescent Newtonian media in
cylindrical tubes, Powder Technol., 129, 53–58,
https://doi.org/10.1016/S0032-5910(02)00164-X, 2003.
Chien, S. F.: Settling velocity of irregularly shaped particles, SPE Drill. Completion, 9, 281–289, https://doi.org/10.1016/0148-9062(95)92494-3, 1994.
Cleasby, J. L., Arboleda, J., Burns, D. E., Prendiville, P. W., and Savage,
E. S.: Backwashing of granular filters, J. Am. Water Works
Ass., 69, 115–126, 1977.
Clift, R. and Gauvin, W. H.: Motion of entrained particles in gas streams, Can. J. Chem. Eng., 49, 439–448, https://doi.org/10.1002/cjce.5450490403, 1971.
Clift, R., Grace, J. R., and Weber, M. E.: Bubbles, drops, and particles,
Academic Press, San Diego, CA, USA, 1978.
Concha, F. and Almendra, E. R.: Settling velocities of particulate systems,
1. settling velocities of individual spherical particles, Int.
J. Miner. Process., 5, 349–367,
https://doi.org/10.1016/0301-7516(79)90044-9, 1979.
Crittenden, J. C., Trussell, R. R., Hand, D. W., Howe, K. J., and
Tchobanoglous, G.: MWH's water treatment: principles and design,
Wiley, New York, USA, 2012.
Dabrowski, W., Spaczyńska, M., and Mackie, R. I.: A model to predict
granular activated carbon backwash curves, Clean-Soil Air Water, 36,
103–110, https://doi.org/10.1002/clen.200600033, 2008.
Dallavalle, J. M.: Micromeritics – the technology of fine particles, 2nd ed., Pitman Publishing Ltd, London, UK, 1948.
Dharmarajah, A. H.: Effect of particle shape on prediction of
velocity-voidage relationship in fluidized solid-liquid systems, Retrospective Theses and Dissertations, Iowa State University, Ames, USA, 7535, 1982.
Di Felice, R. and Gibilaro, L. G.: Wall effects for the pressure drop in
fixed beds, Chem. Eng. Sci., 59, 3037–3040,
https://doi.org/10.1016/j.ces.2004.03.030, 2004.
Dioguardi, F. and Mele, D.: A new shape dependent drag correlation formula
for non-spherical rough particles. Experiments and results, Powder
Technol., 277, 222–230, https://doi.org/10.1016/j.powtec.2015.02.062, 2015.
Dioguardi, F., Mele, D., and Dellino, P.: A new one-equation model of fluid
drag for irregularly shaped particles valid over a wide range of Reynolds
number, J. Geophys. Res.-Sol. Ea., 123, 144–156,
https://doi.org/10.1002/2017JB014926, 2018.
Đuriš, M., Garić-Grulović, R., Arsenijević, Z.,
Jaćimovski, D., and Grbavčić, Ž.: Segregation in water
fluidized beds of sand particles, Powder Technol., 235, 173–179,
https://doi.org/10.1016/j.powtec.2012.10.004, 2013.
Edzwald, J. K.: Water quality and treatment: a handbook on drinking water,
American Water Works Association and American
Society of Civil Engineers, McGraw-Hill, NY, USA, 2011.
Fair, G. M., Geyer, J. C., and Okun, D. A.: Elements of water supply and waste water disposal, 1st edn., John Wiley & Sons, New York, USA, 1954.
Filho, W. L. and Sümer, V.: Sustainable water use and management
examples of new approaches and perspectives, Springer, Cham, Switzerland, 2015.
Flemmer, R. L. C. and Banks, C. L.: On the drag coefficient of a sphere, Powder Technol., 48, 217–221, https://doi.org/10.1016/0032-5910(86)80044-4, 1986.
Ganser, G. H.: A rational approach to drag prediction of spherical and
nonspherical particles, Powder Technol., 77, 143–152,
https://doi.org/10.1016/0032-5910(93)80051-B, 1993.
Geldart, D.: Estimation of basic particle properties for use in
fluid-particle process calculations, Powder Technol., 60, 1–13,
https://doi.org/10.1016/0032-5910(90)80099-K, 1990.
Gibilaro, L. G., Di Felice, R., Waldram, S. P., and Foscolo, P. U.:
Generalized friction factor and drag coefficient correlations for fluid
particle interactions, Chem. Eng. Sci., 40, 1817–1823,
1985.
Goossens, W. R. A.: Review of the empirical correlations for the drag
coefficient of rigid spheres, Powder Technol., 352, 350–359,
https://doi.org/10.1016/j.powtec.2019.04.075, 2019.
Graveland, A., van Dijk, J. C., de Moel, P. J., and Oomen, J. H. C. M.:
Developments in water softening by means of pellet reactors, J.
Am. Water Works Ass., 75, 619–625, 1983.
Haider, A. and Levenspiel, O.: Drag coefficients and terminal velocity of
spherical and nonspherical particles, Powder Technol., 58, 63–70,
1989.
Hölzer, A. and Sommerfeld, M.: New simple correlation formula for the
drag coefficient of non-spherical particles, Powder Technol., 184,
361–365, https://doi.org/10.1016/j.powtec.2007.08.021, 2008.
Horowitz, M. and Williamson, C. H. K.: The effect of Reynolds number on the
dynamics and wakes of freely rising and falling spheres, J. Fluid Mech., 651, 251–294, https://doi.org/10.1017/S0022112009993934, 2010.
Howe, K. J., Hand, D. W., Crittenden, J. C., Rhodes Trussell, R., and
Tchobanoglous, G.: Principles of water treatment, Wiley, New Jersey, USA, 2012.
Hunce, S. Y., Soyer, E., and Akgiray, Ö.: On the backwash expansion of
graded filter media, Powder Technol., 333, 262–268,
https://doi.org/10.1016/j.powtec.2018.04.032, 2018.
Jenny, M., Dušek, J., and Bouchet, G.: Instabilities and transition of a
sphere falling or ascending freely in a Newtonian fluid, J. Fluid
Mech., 508, 201–239, https://doi.org/10.1017/S0022112004009164, 2004.
Karamanev, D. G.: Equations for calculation of the terminal velocity and
drag coefficient of solid spheres and gas bubbles, Chem. Eng.
Commun., 147, 75–84, https://doi.org/10.1080/00986449608936496, 1996.
Khan, A. R. and Richardson, J. F.: The resistance to motion of a solid
sphere in a fluid, Chem. Eng. Commun., 62, 135–150,
https://doi.org/10.1080/00986448708912056, 1987.
Kramer, O. J. I., de Moel, P. J., Baars, E. T., van Vugt, W. H., Padding, J.
T., and van der Hoek, J. P.: Improvement of the Richardson-Zaki liquid-solid
fluidisation model on the basis of hydraulics, Powder Technol., 343,
465–478, https://doi.org/10.1016/j.powtec.2018.11.018, 2019.
Kramer, O. J. I., de Moel, P. J., Padding, J. T., Baars, E. T., el Hasadi,
Y. M. F., Boek, E. S., and van der Hoek, J. P.: Accurate voidage prediction
in fluidisation systems for full-scale drinking water pellet softening
reactors using data driven models, J. Water Process Eng.,
37, 101481, https://doi.org/10.1016/j.jwpe.2020.101481, 2020a.
Kramer, O. J. I., Padding, J. T., van Vugt, W. H., de Moel, P. J., Baars, E.
T., Boek, E. S., and van der Hoek, J. P.: Improvement of voidage prediction
in liquid-solid fluidized beds by inclusion of the Froude number in
effective drag relations, Int. J. Multiphas. Flow,
127, 101481, https://doi.org/10.1016/j.ijmultiphaseflow.2020.103261, 2020b.
Kramer, O. J. I., Raaghav, S. K. R., and Breugem, W. P.: Videos of terminal
settling experiments in water: path instabilities, 4TU.Centre for
Research Data, https://doi.org/10.4121/uuid:3ffdfa51-38f0-4188-aec5-8cd8fc8f1941, 2020c.
Ku, H. H.: Notes on the use of propagation of error formulas, J.
Res. Nat. Bur. Stand., 70, 263, https://doi.org/10.6028/jres.070C.025, 1966.
Lapple, C. E. and Shepherd, C. B.: Calculation of particle trajectories,
Ind. Eng. Chem., 32, 605–617,
https://doi.org/10.1021/ie50365a007, 1940.
Loeffler, A. L.: Mechanism of hindered settling and fluidization, Retrospective Theses and Dissertations, Iowa State University, Ames, USA, 13317, 1953.
Loth, E.: Drag of non-spherical solid particles of regular and irregular
shape, Powder Technol., 182, 342–353,
https://doi.org/10.1016/j.powtec.2007.06.001, 2008.
Marques, R. C., da Cruz, N. F., and Pires, J.: Measuring the sustainability
of urban water services, Environ. Sci. Policy, 54, 142–151,
https://doi.org/10.1016/j.envsci.2015.07.003, 2015.
Morrison, F. A.: An introduction to fluid mechanics, Cambridge University Press, New York, USA, 2013.
Munson, B. R., Rothmayer, A. P., Okiishi, T. H., and Huebsch, W. W.:
Fundamentals of fluid mechanics, Wiley, New York, USA,
2020.
Ouchene, R., Khalij, M., Arcen, B., and Tanière, A.: A new set of
correlations of drag, lift and torque coefficients for non-spherical
particles and large Reynolds numbers, Powder Technol., 303, 33–43,
https://doi.org/10.1016/j.powtec.2016.07.067, 2016.
Raaghav, S. K. R.: Path instabilities of a rising or falling sphere in a
fluid at rest – an experimental study, Delft, available at:
http://resolver.tudelft.nl/uuid:cbaf6de1-dcf9-41ab-a5bc-3a4d364bfd45 (last access: 1 February 2021), 2019.
Ray, C. and Jain, R.: Drinking water treatment focusing on appropriate
technology and sustainability introduction, Springer, Dordrecht, the Netherlands, 2011.
Riazi, A. and Türker, U.: The drag coefficient and settling velocity of
natural sediment particles, Computational Particle Mechanics, 6,
427–437, https://doi.org/10.1007/s40571-019-00223-6, 2019.
Richardson, J. F. and Zaki, W. N.: Sedimentation and fluidisation: part I,
T. I. Chem. Eng.-Lond., 32, 35–53,
https://doi.org/10.1016/S0263-8762(97)80006-8, 1954.
Rietveld, L. C.: Improving operation of drinking water treatment through
modelling, available at:
http://resolver.tudelft.nl/uuid:4f4e110a-a1ea-4d51-b645-3c9c58c67c92 (last access: 1 February 2021), 2005.
Schetters, M. J. A., van der Hoek, J. P., Kramer, O. J. I., Kors, L. J.,
Palmen, L. J., Hofs, B., and Koppers, H.: Circular economy in drinking water
treatment: re-use of ground pellets as seeding material in the pellet
softening process, Water Sci. Technol., 71, 479–486,
https://doi.org/10.2166/wst.2014.494, 2015.
Schiller, L. and Naumann, A.: Über die grundlegenden berechnungen bei
der schwerkraftaufbereitung, Z. Ver. Dtsch. Ing.,
29, 318–320, 1933.
Song, X., Xu, Z., Li, G., Pang, Z., and Zhu, Z.: A new model for predicting
drag coefficient and settling velocity of spherical and non-spherical
particle in Newtonian fluid, Powder Technol., 321, 242–250,
https://doi.org/10.1016/j.powtec.2017.08.017, 2017.
Soyer, E. and Akgiray, O.: A new simple equation for the prediction of
filter expansion during backwashing, J. Water Supply Res. T., 58, 336–345, https://doi.org/10.2166/aqua.2009.090, 2009.
Terfous, A., Hazzab, A., and Ghenaim, A.: Predicting the drag coefficient and
settling velocity of spherical particles, Powder Technol., 239, 12–20,
https://doi.org/10.1016/j.powtec.2013.01.052, 2013.
Tomkins, M. R., Baldock, T. E., and Nielsen, P.: Hindered settling of sand
grains, Sedimentology, 52, 1425–1432,
https://doi.org/10.1111/j.1365-3091.2005.00750.x, 2005.
Turton, R. and Levenspiel, O.: A short note on the drag correlation for spheres, Powder Technol., 47, 83–86, https://doi.org/10.1016/0032-5910(86)80012-2, 1986.
US-IACWR: A study of methods used in measurement and analysis of sediment
loads in streams. Some fundamentals of particle size analysis, Report no. 12, United States Inter-Agency Committee on Water Resources, Prepared for Publication by Project Offices of Cooperating Agencies at St. Anthony Falls Hydraulic Laboratory, Minneapolis, Minnesota, USA, 1957.
van Schagen, K. M.: Model-based control of drinking-water treatment plants,
Delft, available at:
http://repository.tudelft.nl/view/ir/uuid:fc4d865d-1ed7-409e-83ba-6270dacdec67/ (last access: 29 January 2021),
2009.
van Schagen, K. M., Rietveld, L. C., Babuška, R., and Kramer, O. J. I.: Model-based operational constraints for fluidised bed crystallisation, Water Res., 42, 327–337, https://doi.org/10.1016/j.watres.2007.07.019, 2008.
Veldhuis, C. H. J. and Biesheuvel, A.: An experimental study of the regimes
of motion of spheres falling or ascending freely in a Newtonian fluid,
Int. J. Multiphas. Flow, 33, 1074–1087,
https://doi.org/10.1016/j.ijmultiphaseflow.2007.05.002, 2007.
Veldhuis, C. H. J., Biesheuvel, A., and Lohse, D.: Freely rising light solid
spheres, Int. J. Multiphas. Flow, 35, 312–322,
https://doi.org/10.1016/j.ijmultiphaseflow.2009.01.005, 2009.
Whiten, W. J. and Özer, C. E.: New relation for the computation of
settling velocities and diameters of spheres, Min. Proc.
Ext. Met. Rev., 36, 92–102,
https://doi.org/10.1080/08827508.2014.885904, 2015.
Wu, W., Asce, M., Wang, S. S. Y., and Asce, F.: Formulas for sediment
porosity and settling velocity, J. Hydraul. Eng., 132, 858–862, https://doi.org/10.1061/(ASCE)0733-9429(2006)132:8(858), 2006.
Yang, H., Fan, M., Liu, A., and Dong, L.: General formulas for drag
coefficient and settling velocity of sphere based on theoretical law,
International Journal of Mining Science and Technology, 25, 219–223,
https://doi.org/10.1016/j.ijmst.2015.02.009, 2015.
Yang, W. C.: Handbook of fluidization and fluid-particle systems,
CRC Press, New York, USA, 2003.
Zhiyao, S., Tingting, W., Fumin, X., and Ruijie, L.: A simple formula for
predicting settling velocity of sediment particles, Water Sci.
Engi., 1, 37–43, https://doi.org/10.1016/s1674-2370(15)30017-x, 2008.
Zhou, W. and Dušek, J.: Chaotic states and order in the chaos of the
paths of freely falling and ascending spheres, Int. J.
Multiphas. Flow, 75, 205–223, https://doi.org/10.1016/j.ijmultiphaseflow.2015.05.010,
2015.
Short summary
Our work investigates the settling behaviour of natural granules applied in drinking water treatment plants. We show that these natural granules have a tendency to show a considerably large deviation in terms of their settling velocity; this is contrary to what many velocity prediction models assume. In the current work, we present and discuss the factors which contribute to the observed deviation in drag and settling velocity. It connects full-scale operations and research.
Our work investigates the settling behaviour of natural granules applied in drinking water...
