Abstract
The formation of irregularly shaped particle agglomerates is a recurring phenomenon observed in equipment with particle-laden flows, which directly interferes in the flow profile, due to drag effects. To observe the capability of computational fluid dynamics to predict the drag coefficient in particle agglomerates, laboratory experiments were performed, aiming the validation of simulations. Experimental assays were performed to obtain both the fluids’ properties and the terminal velocities of the particle agglomerates. To evaluate the drag coefficient, simulations were carried out at steady state for the experimental conditions and the results were compared. Simulations presented good agreement with the experimental assays, with most of deviations lower than ±10%. Simulations of the agglomerates of four and five particles falling in water presented higher deviations, \(-\)12.73% and \(-\)19.92%, respectively. Higher deviations are expected in these agglomerates due to the difficulties to represent the wake region in the rear of the agglomerates, observed in flows with Reynolds number greater than 1000.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40430-023-04366-9/MediaObjects/40430_2023_4366_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40430-023-04366-9/MediaObjects/40430_2023_4366_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40430-023-04366-9/MediaObjects/40430_2023_4366_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40430-023-04366-9/MediaObjects/40430_2023_4366_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40430-023-04366-9/MediaObjects/40430_2023_4366_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40430-023-04366-9/MediaObjects/40430_2023_4366_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40430-023-04366-9/MediaObjects/40430_2023_4366_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40430-023-04366-9/MediaObjects/40430_2023_4366_Fig8_HTML.png)
Similar content being viewed by others
References
Deglon D, Meyer C (2006) CFD modelling of stirred tanks: numerical considerations. Miner Eng 19:1059–1068
Lane GL (2017) Improving the accuracy of CFD predictions of turbulence in tank stirred by a hydrofoil impeller. Chem Eng Sci 169:188–211
Senior RC, Brereton C (1992) Modelling of circulating fluidized-bed solids flow and distribution. Chem Eng Sci 47:281–296
Kuwagi K, Takano K, Horio M (2000) The effect of tangential lubrication by bridge liquid on the behavior of agglomerating fluidized beds. Powder Technol 133:287–298
Beetstra R, van der Hoef M, Kuipers J (2006) A lattice-Boltzmann simulation study of the drag coefficient of clusters of spheres. Comput Fluids 35:966–970
Deen NG, Kriebitzsch SHL, van der Hoef MA, Kuipers JAM (2012) Direct numerical simulation of flow and heat transfer in dense fluid-particle systems. Chem Eng Sci 81:329–344
Goossens WRA (2019) Review of the empirical correlations for the drag coefficient of rigid spheres. Powder Technol 352:350–359
Wang K, Ge W, Li J (2008) Eulerian simulation of heterogeneous gas-solid flows in CFB risers: EMMS-based sub-grid scale model with a revised cluster description. Chem Eng Sci 63:1553–1571
Nikolopoulos A, Papafotiou D, Nikolopoulos N, Grammelis P, Kakaras E (2010) An advanced EMMS scheme for the prediction of drag coefficient under a 1.2 MWth CFBC isothermal flow - part I: Numerical formulation. Chem Eng Sci 65:4080–4088
Wang L, Wu C, Ge W (2017) Effect of particle clusters on mass transfer between gas and particles in gas-solid flows. Powder Technol 319:221–227
Tran-Cong S, Gay M, Michaelides EE (2004) Drag coefficients of irregularly shaped particles. Powder Technol 139:21–32
Haider A, Levenspiel O (1989) Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol 58:63–70
Ganser GH (1993) A rational approach to drag prediction of spherical and nonspherical particles. Powder Technol 77:143–153
Hölzer A, Sommerfeld M (2008) New simple correlation formula for the drag coefficient of non-spherical particles. Powder Technol 184:361–365
Bagheri G, Bonadonna C (2016) On the drag of freely falling non-spherical particles. Powder Technol 301:526–544
Marchildon EK, Clamen A, Gauvin WH (1964) Drag and oscillatory motion of freely falling cylindrical particles. Can J Chem Eng 42:178–182
Jayaweera KOLF, Mason BJ (1965) The behavior of freely falling cylinders and cones in viscous fluids. J Fluid Mech 22:709–720
Lasso IA, Weidman PD (1986) Stokes drag on hollow cylinders and conglomerates. Phys Fluids 29:3921–3934
McKay G, Murphy WR, Hillis M (1988) Settling characteristics of discs and cylinders. Chem Eng Res Des 66:107–112
Willmarth WW, Hawks NE, Harvey RL (1964) Steady and unsteady motions and wakes of freely disks. Phys Fluids 7:197–208
Pettyjohn ES, Christiansen ER (1948) Effect of particle shape on free-settling rates of isometric particles. Chem Eng Prog 44:157–172
Heiss JF, Coull J (1952) The effect of orientation and shape on the settling velocity of non-isometric particles in a viscous medium. Chem Eng Prog 48:133–140
Fan M, Su D, Yang L (2022) Development of a benchmark for drag correlations of nonspherical particles based on settling experiments of super-ellipsoidal particles. Powder Technol 409:117811
Roostaee A, Vaezi M (2022) Develo** a standard platform to predict the drag coefficient of irregular shape particles. Powder Technol 395:314–337
Loth E (2008) Drag of non-spherical solid particles of regular and irregular shape. Powder Technol 182:342–353
Çengel YA, Cimbala JM (2000) Fluid mechanics: fundamentals and applications. McGraw-Hill Education, New York
Van Doormal JP, Raithby GD (1983) Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numer Heat Transf 7:147–163
Oliveira RAF, Zanata JH, Lopes GC (2023) Numerical study of turbulence on drag coefficient determination for particle agglomerates. Chem Ind Chem Eng Q. https://doi.org/10.2298/CICEQ221206021O
Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge
Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32:1598–1605
Wilcox DC (2004) Turbulence modeling for CFD. DCW Industries, New York
Ferziger JH, Perić M (2002) Computational methods for fluid dynamics. Springer, New York
Graf WH (1971) Hydraulics of sediment transport. McGraw-Hill, New York
Choi H, Moin P (2012) Grid-point requirements for large eddy simulation: Chapman’s estimates revisited. Phys Fluids 24:011702
Goossens D (1987) A drag coefficient equation for natural, irregularly shaped particles. CATENA 14:73–99
Lapple CE, Shepherd CB (1940) Calculation of particle trajectories. Ind Eng Chem 32:605–617
Acknowledgements
The authors would like to thank also the National Council for Scientific and Technological Development (CNPq) and the Coordination for the Improvement of Higher Education Personnel (CAPES) for the financial support of this work.
Funding
This study was financed in part by the Coordination for the Improvement of Higher Education Personnel (CAPES)—Finance Code 001. The authors would like to thank also the National Council for Scientific and Technological Development (CNPq, grant number 140412/2020-4) for the financial support of this work
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors would like to declare that there are no potential conflicts of interest with respect to the authorship, research, and publication of this article.
Additional information
Technical Editor: Dirceu Noriler.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
de Oliveira, R.A.F., Lopes, G.C. Drag coefficient on particle agglomerates: a CFD study with experimental validation. J Braz. Soc. Mech. Sci. Eng. 45, 473 (2023). https://doi.org/10.1007/s40430-023-04366-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-023-04366-9