Abstract
This work evaluated the accuracy of viscosity regularization models employed by different computational fluid dynamics (CFD) codes in the modeling of viscoplastic flows. Extensive numerical simulations of viscoplastic Hagen–Poiseuille pipe flows were carried out in ANSYS Fluent 20.0, employing both the Herschel–Bulkley–Papanastasiou model and the bi-viscosity model. Three slightly different implementations of the bi-viscosity model were taken into account in the analyses. The numerical results were then compared to the analytical solution of the velocity profile regarding the studied case. While the Herschel–Bulkley–Papanastasiou and the bi-viscosity regularizations employed by OpenFOAM (Tanner and O’Donovan model) and ANSYS Fluent (releases 19.2 onwards) provide satisfactory results, it was observed that the bi-viscosity model employed by previous ANSYS Fluent releases (12.0–19.2) was not adequate to simulate viscoplastic Hagen–Poiseuille flows, indicating that solving more complex flows using such model could yield incorrect results. Although the viscosity regularization model employed by ANSYS Fluent on releases 19.2 onwards has been already corrected, this work recommends CFD users and researchers to be cautious while using outdated releases of the software and consulting scientific works that employed these releases.
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References
Coussot P (2014) Yield stress fluid flows: a review of experimental data. J Non-Newton Fluid 211:31–49. https://doi.org/10.1016/j.jnnfm.2014.05.006
Balmforth NJ, Frigaard IA, Ovarlez G (2014) Yielding to stress: recent developments in viscoplastic fluid mechanics. Annu Rev Fluid Mech 46:121–146. https://doi.org/10.1146/annurev-fluid-010313-141424
Barnes HA, Walters K (1985) The yield stress myth? Rheol acta 24(4):323–326. https://doi.org/10.1007/BF01333960
Astarita G (1990) Letter to the Editor: the engineering reality of the yield stress. J Rheol 34(2):275–277. https://doi.org/10.1122/1.550142
Sun A, Gunasekaran S (2009) Yield stress in foods: measurements and applications. Int J Food Prop 12(1):70–101. https://doi.org/10.1080/10942910802308502
De Larrard F, Ferraris CF, Sedran T (1998) Fresh concrete: a Herschel–Bulkley material. Mater Struct 31(7):494–498. https://doi.org/10.1007/BF02480474
Frigaard IA, Nouar C (2005) On the usage of viscosity regularization methods for visco-plastic fluid flow computation. J Non-Newton Fluid 127:1–26. https://doi.org/10.1016/j.jnnfm.2005.01.003
Papanastasiou TC (1987) Flows of materials with yield. J Rheol 31(5):385–404. https://doi.org/10.1122/1.549926
O’Donovan EJ, Tanner RI (1984) Numerical study of the Bingham squeeze film problem. J Non-Newton Fluid 15(1):75–83. https://doi.org/10.1016/0377-0257(84)80029-4
Bercovier M, Engelman M (1980) A finite-element method for incompressible non-Newtonian flows. J Comput Phys 36(3):313–326. https://doi.org/10.1016/0021-9991(80)90163-1
Pereira JB, Sáo YT, Maciel GF (2022) Numerical and experimental application of the automated slump test for yield stress evaluation of mineralogical and polymeric materials. Rheol Acta 61(2):163–182. https://doi.org/10.1007/s00397-021-01321-0
Han Z, Su B, Li Y, Wang W, Wang W, Huang J, Chen G (2019) Numerical simulation of debris-flow behavior based on the SPH method incorporating the Herschel–Bulkley–Papanastasiou rheology model. Eng Geol 255:26–36. https://doi.org/10.1016/j.enggeo.2019.04.013
De Schryver R, El Cheikh K, Lesage K, Yardimci MY, De Schutter G (2021) Numerical reliability study based on rheological input for Bingham paste pum** using a finite volume approach in OpenFOAM. Materials 14(17):5011. https://doi.org/10.3390/ma14175011
Franci A, Zhang X (2018) 3D numerical simulation of free-surface Bingham fluids interacting with structures using the PFEM. J Non-Newton Fluid 259:1–15. https://doi.org/10.1016/j.jnnfm.2018.05.001
ANSYS Inc. (2012) ANSYS FLUENT 14.5 user’s guide. ANSYS Inc., Canonsburg
The OpenFOAM Foundation (2021) OpenFOAM, user’s guide version 9.0. The OpenFOAM Foundation, London
Ansys Fluent v.12.0 theory guide, Fluent Inc. (2009), 816 p
ANSYS Inc. (2018) ANSYS FLUENT 19.2 user’s guide. ANSYS Inc., Canonsburg
ANSYS Inc. (2020) ANSYS FLUENT 20.1 user’s guide. ANSYS Inc., Canonsburg
Güzel B, Burghelea T, Frigaard IA, Martinez DM (2009) Observation of laminar–turbulent transition of a yield stress fluid in Hagen–Poiseuille flow. J Fluid Mech 627:97–128. https://doi.org/10.1017/S0022112009005813
Bentrad H, Esmael A, Nouar C, Lefevre A, Ait-Messaoudene N (2017) Energy growth in Hagen–Poiseuille flow of Herschel–Bulkley fluid. J Non-Newton Fluid 241:43–59. https://doi.org/10.1016/j.jnnfm.2017.01.007
Liu R, Ding Z, Hu KX (2018) Stabilities in plane Poiseuille flow of Herschel–Bulkley fluid. J Non-Newton Fluid 251:132–144. https://doi.org/10.1016/j.jnnfm.2017.11.007
Usha R, Sahu KC (2019) Interfacial instability in pressure-driven core-annular pipe flow of a Newtonian and a Herschel-Bulkley fluid. J Non-Newton Fluid 271:104144. https://doi.org/10.1016/j.jnnfm.2019.104144
Bicalho IC, Dos Santos DBL, Ataíde CH, Duarte CR (2016) Fluid-dynamic behavior of flow in partially obstructed concentric and eccentric annuli with orbital motion. J Petrol Sci Eng 137:202–213. https://doi.org/10.1016/j.petrol.2015.11.029
Gharib N, Bharathan B, Amiri L, McGuinness M, Hassani FP, Sasmito AP (2017) Flow characteristics and wear prediction of Herschel–Bulkley non-Newtonian paste backfill in pipe elbows. Can J Chem Eng 95(6):1181–1191. https://doi.org/10.1002/cjce.22749
Kazemzadeh A, Ein-Mozaffari F, Lohi A, Pakzad L (2016) Effect of the rheological properties on the mixing of Herschel–Bulkley fluids with coaxial mixers: applications of tomography, CFD, and response surface methodology. Can J Chem Eng 94(12):2394–2406. https://doi.org/10.1002/cjce.22601
Manjeet K, Sujatha C (2019) Magnetorheological valves based on Herschel–Bulkley fluid model: modelling, magnetostatic analysis and geometric optimization. Smart Mater Struct 28(11):115008. https://doi.org/10.1088/1361-665X/ab421a
Pang B, Wang S, Liu G, Jiang X, Lu H, Li Z (2018) Numerical prediction of flow behavior of cuttings carried by Herschel–Bulkley fluids in horizontal well using kinetic theory of granular flow. Powder Technol 329:386–398. https://doi.org/10.1016/j.powtec.2018.01.065
Mehta D, Thota Radhakrishnan AK, Van Lier J, Clemens F (2018) Sensitivity analysis of a wall boundary condition for the turbulent pipe flow of Herschel–Bulkley fluids. Water 11(1):19. https://doi.org/10.3390/w11010019
Coussot P (1994) Steady, laminar, flow of concentrated mud suspensions in open channel. J Hydraul Res 32(4):535–559. https://doi.org/10.1080/00221686.1994.9728354
Peixinho J, Desaubry C, Lebouche M (2008) Heat transfer of a non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow. Int J Heat Mass Transf 51:198–209. https://doi.org/10.1016/j.ijheatmasstransfer.2007.04.012
Bird RB, Dai GC, Yarusso BJ (1983) The rheology and flow of viscoplastic materials. Rev Chem Eng 1(1):1–70. https://doi.org/10.1515/revce-1983-0102
Burger J, Haldenwang R, Alderman N (2010) Friction factor-Reynolds number relationship for laminar flow of non-Newtonian fluids in open channels of different cross-sectional shapes. Chem Eng Sci 65(11):3549–3556. https://doi.org/10.1016/j.ces.2010.02.040
Celik IB, Ghia U, Roache PJ, Freitas CJ (2008) Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J Fluid Eng Trans ASME 130(7):8001
Gao J, Fourie A (2015) Spread is better: an investigation of the mini-slump test. Miner Eng 71:120–132
Acknowledgements
The authors would like to thank the two anonymous reviewers for their careful reading of the manuscript and their suggestions. The authors would also like to thank FAPESP – Fundação de Amparo à Pesquisa do Estado de São Paulo (2020/07822-0 and 2022/05184-1) and CAPES – Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (88882.433524/2019-01 and 88887.640433/2021-00) for providing the financial support for this research and scholarship for the first author.
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Taglieri Sáo, Y., de Freitas Maciel, G. Accuracy of viscosity regularization models employed by computational fluid dynamics codes. J Braz. Soc. Mech. Sci. Eng. 45, 527 (2023). https://doi.org/10.1007/s40430-023-04431-3
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DOI: https://doi.org/10.1007/s40430-023-04431-3