A numerical study of the flow of Bingham-like fluids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics (SPH) based method. (English) Zbl 1274.76237

Summary: In this paper, a Lagrangian formulation of the Navier-Stokes equations, based on the smoothed particle hydrodynamics (SPH) approach, was applied to determine how well rheological parameters such as plastic viscosity can be determined from vane rheometer measurements. First, to validate this approach, a Bingham/Papanastasiou constitutive model was implemented into the SPH model and tests comparing simulation results to well established theoretical predictions were conducted. Numerical simulations for the flow of fluids in vane and coaxial cylinder rheometers were then performed. A comparison to experimental data was also made to verify the application of the SPH method in realistic flow geometries. Finally, results are presented from a parametric study of the flow of Bingham fluids with different yield stresses under various applied angular velocities of the outer cylindrical wall in the vane and coaxial cylinder rheometers. The stress, strain rate and velocity profiles, especially in the vicinity of the vane blades, were computed. By comparing the calculated stress and flow fields between the two rheometers, the validity of the assumption that the vane could be approximated as a cylinder for measuring the rheological properties of Bingham fluids at different shear rates was tested.


76H05 Transonic flows
76M28 Particle methods and lattice-gas methods
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[1] Nguyen, Q. D.; Boger, D. V.: Yield stress measurement for concentrated suspensions, J. rheol. 27, 321-349 (1983)
[2] Barnes, H. A.; Nguyen, Q. D.: Rotating vane rheometry — a review, J. non-newt. Fluid mech. 98, 1-14 (2001) · Zbl 0963.76520
[3] Barnes, H. A.; Carnali, J. O.: The vane-in-cup as a novel rheometer geometry for shear thinning and thixotropic materials, J. rheol. 34, 841-866 (1990)
[4] Yan, J.; James, A. E.: The yield surface of viscoelastic and plastic fluids in a vane viscometer, J. non-newt. Fluid mech. 70, 237-253 (1997)
[5] Keentok, J. F.; Milthorpe, M. J. F.; O’donovan, E.: On the shearing zone around rotating vanes in plastic liquids: theory and experiment, J. non-newt. Fluid mech. 17, 23-35 (1985)
[6] Griffiths, D. V.; Lane, P. A.: Finite element analysis of the shear vane test, Comput. struct. 37, 1105-1116 (1990)
[7] Lucy, L. B.: A numerical approach to the testing of the fission hypothesis, Astron. J. 83, 1013-1024 (1977)
[8] Gingold, R. A.; Monaghan, J. J.: Smoothed particle hydrodynamics theory and application to non-spherical stars, Mon. not. R. astron. Soc. 181, 375-389 (1977) · Zbl 0421.76032
[9] Cologrossi, A.; Landrini, M.: Numerical simulation of interfacial flows by smoothed particle hydrodynamics, J. comput. Phys. 191, 448-475 (2003) · Zbl 1028.76039
[10] Hu, X. Y.; Adams, N. A.: A multi-phase SPH method for macroscopic and mesoscopic flows, J. comput. Phys. 213, 844-861 (2006) · Zbl 1136.76419
[11] Monaghan, J. J.; Kocharyan, A.: SPH simulation of multi-phase flow, Comput. phys. Commun. 87, 225-235 (1995) · Zbl 0923.76195
[12] Morris, J. P.: Simulating surface tension with smoothed particle hydrodynamics, Int. J. Numer. methods fluids 33, 333-353 (2000) · Zbl 0985.76072
[13] Oger, L.; Savage, S. B.: Smoothed particle hydrodynamics for cohesive grains, Comput. methods appl. Mech. eng. 180, 169-183 (1999) · Zbl 0963.74078
[14] Cleary, P. W.; Prakash, M.: Discrete-element modelling and smoothed particle hydrodynamics: potential in the environmental sciences, Philos. trans. R. soc. Lond. A 362, 2003-2030 (2004) · Zbl 1205.76213
[15] Antoci, C.; Gallati, M.; Sibilla, S.: Numerical simulation of fluid – structure interaction by SPH, Comput. struct. 85, 879-890 (2007)
[16] Ellero, M.; Kroger, M.; Hess, S.: Viscoelastic flows studied by smoothed particle dynamics, J. non-newt. Fluid mech. 105, 35-51 (2002) · Zbl 1021.76043
[17] Ellero, M.; Tanner, R. I.: SPH simulation of transient viscoelastic flows at low Reynolds number, J. non-newt. Fluid mech. 132, 61-72 (2005) · Zbl 1195.76088
[18] Fang, J.; Owens, R. G.; Tacher, L.; Parriaux, A.: A numerical study of the SPH method for simulating transient viscoelastic free surface flows, J. non-newt. Fluid mech. 139, 68-84 (2006) · Zbl 1195.76091
[19] Papanastasiou, T. C.: Flows of materials with yield, J. rheol. 31, 385-404 (1987) · Zbl 0666.76022
[20] Alexandrou, A. N.; Le Menn, P.; Georgiou, G.; Entov, V.: Flow instabilities of Herschel – Bulkley fluids, J. non-newt. Fluid mech. 116, 19-32 (2003) · Zbl 1088.76532
[21] Burgos, G. R.; Alexandrou, A. N.; Entov, V.: On the determination of yield surfaces in Herschel – Bulkley fluids, J. rheol. 43, 463-483 (1999)
[22] Zhu, H.; De Kee, D.: A numeric study for the cessation of Couette flow of non-Newtonian fluids with a yield stress, J. non-newt. Fluid mech. 143, 64-70 (2005) · Zbl 1195.76077
[23] Gray, J. P.; Monaghan, J. J.; Swift, R. P.: SPH elastic dynamics, Comput. mech. Appl. mech. Eng. 190, 6641-6662 (2001) · Zbl 1021.74050
[24] Monaghan, J. J.: SPH without a tensile instability, J. comput. Phys. 159, 290-311 (2000) · Zbl 0980.76065
[25] Press, W. H.; Teukolsky, S. A.; Flannery, B. P.: Numerical recipe in C: The art of scientific computing, (1992) · Zbl 0778.65002
[26] Monaghan, J. J.: Smoothed particle hydrodynamics, Annu. rev. Astron. astrophys. 30, 543-574 (1992)
[27] Morris, J. P.; Fox, P. J.; Zhu, Y.: Modeling low Reynolds number incompressible flows using SPH, J. comput. Phys. 136, 214-226 (1997) · Zbl 0889.76066
[28] Monaghan, J. J.: Simulating free surface flows with SPH, J. comput. Phys. 110, 399-406 (1994) · Zbl 0794.76073
[29] Cummins, S. J.; Rudman, M.: An SPH projection method, J. comput. Phys. 152, 584-607 (1999) · Zbl 0954.76074
[30] Colin, F.; Egli, R.; Lin, F. Y.: Computing a null divergence velocity field using smoothed particle hydrodynamics, J. comput. Phys. 217, 680-692 (2006) · Zbl 1099.76052
[31] Ellero, M.; Serrano, M.; Español, P.: Incompressible smoothed particle hydrodynamics, J. comput. Phys. 226, 1731-1752 (2007) · Zbl 1121.76050
[32] Chatzimina, M.; Georgiou, G. C.; Argyropaidas, I.; Mitsoulis, E.; Huilgol, R. R.: Cessation of Couette and Poiseuille flows of a Bingham plastic and finite stopping times, J. non-Newton fluid mech. 129, 117-127 (2005) · Zbl 1195.76012
[33] Bird, R. B.; Stewart, W. E.; Lightfoot, E. N.: Transport phenomena, (1960)
[34] Chatzimina, M.; Georgiou, G.; Alexandrou, A.: Wall shear rates in circular Couette flow of a Herschel – Bulkley fluid, Appl. rheol. 19, No. 3, 34288 (2009)
[35] Atkinson, C.; Sherwood, J. D.: The torque on a rotating n-bladed vane in a Newtonian fluid or linear elastic, Proc. math. Phys. sci. 438, 183-196 (1992) · Zbl 0759.76007
[36] Savamand, S.; Heniche, M.; Bechard, V.; Bertand, F.; Carreau, P. J.: Analysis of the vane rheometer using 3-D finite element simulation, J. rheol. 51, 161-177 (2007)
[37] C.F. Ferraris, L.E. Brower, Comparison of concrete rheometers: international tests at MB (Cleveland, OH, USA) in May, 2003, NISTIR 7154.
[38] Landry, M. P.; Frigaard, I. A.; Martinez, D. M.: Stability and instability of Taylor – Couette flows of a Bingham fluid, J. fluid mech. 560, 321-353 (2006) · Zbl 1161.76473
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