Finite Element Modeling of Rotating Mixing of Toothpaste
The objective of this research is to examine the shear thinning behaviour of mixing flow of non-Newtonian fluid like toothpaste in the dissolution container with rotating stirrer. The problem under investigation is related to the chemical industry. Mixing of fluid is performed in a cylindrical container with rotating stirrer, where stirrer is eccentrically placed on the lid of the container. For the simulation purpose the associated motion of the fluid is considered as revolving of the container, with stick stirrer. For numerical prediction, a time-stepping finite element algorithm in a cylindrical polar coordinate system is adopted based on semi-implicit Taylor-Galerkin/pressure-correction scheme. Numerical solutions are obtained for non-Newtonian fluids employing power law model. Variations with power law index have been analysed, with respect to the flow structure and pressure drop.
[1] Portillo, P. M., Muzzio, F. J. and Ierapetritou, M. G., ÔÇÿHybrid DEMCompartment
Modelling Approach for Granular Mixing-, AIChE
Journal, 53(1), 119-128, 2007.
[2] Zlokarnik, M., "Stirring: Theory and Practice", Wiley-VCH, Weinheim,
2001.
[3] Wichterle, K. and Wein, O., "Threshold of mixing of non-Newtonian
liquids", Int. Chem. Eng. V. 21, pp. 116-121, 1981.
[4] Luo, J. Y., Gosman, A. D., and Issa, R. I., "Prediction of impeller
induced flows in mixing containers using multiple frames of reference",
Inst. Chem. Eng. Symp. Ser., V. 136, pp. 549-556, 1994.
[5] Deen, N. G., Solberg, T., and Hjertager, B. H., "Flow generated by an
aerated Rushton impeller: two-phase PIV experiments and numerical
simulations", Can. J. Chem. Eng. V. 80, pp. 1-15, 2002.
[6] Tabor, G., Gosman, A. D., and Issa, R., "Numerical simulation of the
flow in a mixing container stirred by a Rushton turbine", Inst. Chem.
Eng. Symp. Ser. V. 140, pp. 25-34, 1996.
[7] Jaworski, Z. and Nienow, A. W., "LDA measurements of flow fields
with Hydrofoil impellers in fluids with different rheological properties",
Proceedings of 8th European Conference on Mixing, Cambridge, UK,
pp. 105-112, 1993.
[8] Lane, G. and Koh, P. T. L., "CFD simulation of a Rushton turbine in a
baffled tank", Proceedings of International Conference on
Computational Fluid Dynamics in Mineral and Metal Processing and
Power Generation, CSIRO, Melbourne, pp. 377-385, 1997.
[9] Buwa, V., Dewan, A., Nasser, A. F. and Durst, F., "Fluid dynamics and
mixing of single-phase flow in a stirred container with a grid disc
impeller: experimental and numerical investigations", Chem. Eng. Sci.
V. 61, pp. 2815-2822, 2006.
[10] Saeed, S., Ein-Mozaffari, F. and Upreti, S. R., "Using computational
fluid dynamics modelling and ultrasonic Doppler velocimetry to study
pulp suspension mixing", Ind. Eng. Chem. Res. V. 46, pp. 2172-2179,
2007.
[11] Murthy, S. S. and Jayanti, S., "Mixing of power-law fluids using
anchors: Metzner-Otto concept revisited", AIChE J. V.49, pp. 30-40,
2003.
[12] Kelly, W. and Gigas, B., "Using CFD to predict the behaviour of power
law fluids near axial-flow impellers operating in the transitional flow
regime", Chem. Eng. Sci. V. 58, pp. 2141-2152, 2003.
[13] Moore, I. P. T., Cossor, G. and Baker, M. R., "Velocity distributions in a
stirred tank containing a yield stress fluid", Chem. Eng. Sci., V. 50, pp.
2467-2481, 1995.
[14] Townsend, P. and Webster, M. F., ÔÇÿAn algorithm for the threedimensional
transient simulation of non-Newtonian fluid flows-, in: G.
Pande, J. Middleton (Eds.), Proc. Int. Conf. Num. Meth. Eng.: Theory
and Applications, NUMETA, Nijhoff, Dordrecht, pp. T12/1-11, 1987.
[15] Hawken, D. M., Tamaddon-Jahromi, H. R., Townsend, P., Webster, M.
F., ÔÇÿA Taylor-Galerkin-based algorithm for viscous incompressible flow-,
Int. J. Num. Meth. Fluids, 10, 327-351, 1990.
[16] Baloch, A., Grant, P. W. and Webster, M. F., "Parallel computation of
two dimensional rotational flows of viscoelastic fluids in cylindrical
container", Int. Journal for computer-Aided Engineering and Software,
V. 19, No. 7, pp. 820-853, 2002.
[17] Baloch, A., Solangi, M. A. and Memon, G. Q., ÔÇÿSimulation of
Rotational Flows in Cylindrical Container with Rotating Single Stirrer-,
Punjab University Journal of Mathematics, 2008.
[18] Baloch, A., and Webster, M. F., ÔÇÿDistributed Parallel Computation for
Complex Rotating Flows of Non-Newtonian Fluids-, Int. J. Numer.
Meth. Fluids, 43, 1301-1328, 2003.
[1] Portillo, P. M., Muzzio, F. J. and Ierapetritou, M. G., ÔÇÿHybrid DEMCompartment
Modelling Approach for Granular Mixing-, AIChE
Journal, 53(1), 119-128, 2007.
[2] Zlokarnik, M., "Stirring: Theory and Practice", Wiley-VCH, Weinheim,
2001.
[3] Wichterle, K. and Wein, O., "Threshold of mixing of non-Newtonian
liquids", Int. Chem. Eng. V. 21, pp. 116-121, 1981.
[4] Luo, J. Y., Gosman, A. D., and Issa, R. I., "Prediction of impeller
induced flows in mixing containers using multiple frames of reference",
Inst. Chem. Eng. Symp. Ser., V. 136, pp. 549-556, 1994.
[5] Deen, N. G., Solberg, T., and Hjertager, B. H., "Flow generated by an
aerated Rushton impeller: two-phase PIV experiments and numerical
simulations", Can. J. Chem. Eng. V. 80, pp. 1-15, 2002.
[6] Tabor, G., Gosman, A. D., and Issa, R., "Numerical simulation of the
flow in a mixing container stirred by a Rushton turbine", Inst. Chem.
Eng. Symp. Ser. V. 140, pp. 25-34, 1996.
[7] Jaworski, Z. and Nienow, A. W., "LDA measurements of flow fields
with Hydrofoil impellers in fluids with different rheological properties",
Proceedings of 8th European Conference on Mixing, Cambridge, UK,
pp. 105-112, 1993.
[8] Lane, G. and Koh, P. T. L., "CFD simulation of a Rushton turbine in a
baffled tank", Proceedings of International Conference on
Computational Fluid Dynamics in Mineral and Metal Processing and
Power Generation, CSIRO, Melbourne, pp. 377-385, 1997.
[9] Buwa, V., Dewan, A., Nasser, A. F. and Durst, F., "Fluid dynamics and
mixing of single-phase flow in a stirred container with a grid disc
impeller: experimental and numerical investigations", Chem. Eng. Sci.
V. 61, pp. 2815-2822, 2006.
[10] Saeed, S., Ein-Mozaffari, F. and Upreti, S. R., "Using computational
fluid dynamics modelling and ultrasonic Doppler velocimetry to study
pulp suspension mixing", Ind. Eng. Chem. Res. V. 46, pp. 2172-2179,
2007.
[11] Murthy, S. S. and Jayanti, S., "Mixing of power-law fluids using
anchors: Metzner-Otto concept revisited", AIChE J. V.49, pp. 30-40,
2003.
[12] Kelly, W. and Gigas, B., "Using CFD to predict the behaviour of power
law fluids near axial-flow impellers operating in the transitional flow
regime", Chem. Eng. Sci. V. 58, pp. 2141-2152, 2003.
[13] Moore, I. P. T., Cossor, G. and Baker, M. R., "Velocity distributions in a
stirred tank containing a yield stress fluid", Chem. Eng. Sci., V. 50, pp.
2467-2481, 1995.
[14] Townsend, P. and Webster, M. F., ÔÇÿAn algorithm for the threedimensional
transient simulation of non-Newtonian fluid flows-, in: G.
Pande, J. Middleton (Eds.), Proc. Int. Conf. Num. Meth. Eng.: Theory
and Applications, NUMETA, Nijhoff, Dordrecht, pp. T12/1-11, 1987.
[15] Hawken, D. M., Tamaddon-Jahromi, H. R., Townsend, P., Webster, M.
F., ÔÇÿA Taylor-Galerkin-based algorithm for viscous incompressible flow-,
Int. J. Num. Meth. Fluids, 10, 327-351, 1990.
[16] Baloch, A., Grant, P. W. and Webster, M. F., "Parallel computation of
two dimensional rotational flows of viscoelastic fluids in cylindrical
container", Int. Journal for computer-Aided Engineering and Software,
V. 19, No. 7, pp. 820-853, 2002.
[17] Baloch, A., Solangi, M. A. and Memon, G. Q., ÔÇÿSimulation of
Rotational Flows in Cylindrical Container with Rotating Single Stirrer-,
Punjab University Journal of Mathematics, 2008.
[18] Baloch, A., and Webster, M. F., ÔÇÿDistributed Parallel Computation for
Complex Rotating Flows of Non-Newtonian Fluids-, Int. J. Numer.
Meth. Fluids, 43, 1301-1328, 2003.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:57491", author = "Inamullah Bhatti and Ahsanullah Baloch and Khadija Qureshi", title = "Finite Element Modeling of Rotating Mixing of Toothpaste", abstract = "The objective of this research is to examine the shear thinning behaviour of mixing flow of non-Newtonian fluid like toothpaste in the dissolution container with rotating stirrer. The problem under investigation is related to the chemical industry. Mixing of fluid is performed in a cylindrical container with rotating stirrer, where stirrer is eccentrically placed on the lid of the container. For the simulation purpose the associated motion of the fluid is considered as revolving of the container, with stick stirrer. For numerical prediction, a time-stepping finite element algorithm in a cylindrical polar coordinate system is adopted based on semi-implicit Taylor-Galerkin/pressure-correction scheme. Numerical solutions are obtained for non-Newtonian fluids employing power law model. Variations with power law index have been analysed, with respect to the flow structure and pressure drop.
", keywords = "finite element simulation, mixing fluid, rheology, rotating flow, toothpaste", volume = "4", number = "1", pages = "69-6", }
