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MODELLING OF GENERALIZED NEWTONIAN LID-DRIVEN CAVITY FLOW USING AN SPH METHOD

Part of: Basic methods in fluid mechanics

Published online by Cambridge University Press:  01 January 2008

ASHKAN RAFIEE
ASHKAN RAFIEE*
Affiliation:
Center of Excellence in Energy Conversion, School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran (email: [email protected])
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Abstract

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In this paper a smoothed particle hydrodynamics (SPH) method is introduced for simulating two-dimensional incompressible non-Newtonian fluid flows, and the non-Newtonian effects in the flow of a fluid which can be modelled by generalized Newtonian constitutive equations are investigated. Two viscoplastic models including Bingham-plastic and power-law models are considered along with the Newtonian model. The governing equations include the conservation of mass and momentum equations in a pseudo-compressible form. The spatial discretization of these equations is achieved by using the SPH method. The temporal discretization algorithm is a fully explicit two-step predictor–corrector scheme. In the prediction step, an intermediate velocity field is obtained using a forward scheme in time without enforcing incompressibility. The correction step consists of solving a pressure Poisson equation to satisfy incompressibility by providing a trade-off between the pressure and density variables. The performance of the proposed scheme is evaluated by studying a benchmark problem including flow of viscoplastic fluids in a lid-driven cavity. Both Newtonian and non-Newtonian cases are investigated and the results are compared with available numerical data. It was shown that in all cases the method is stable and the results are in very good agreement with available data.

Keywords

smoothed particle methodincompressible non-Newtonian flowsgeneralized Newtonian constitutive equations

MSC classification

Secondary: 76M28: Particle methods and lattice-gas methods
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 3 , January 2008 , pp. 411 - 422
Copyright
Copyright © Australian Mathematical Society 2008

References

[1]Bell, B. C. and Surana, K. S., “p-version least squares finite element formulation for two-dimensional, incompressible, non-Newtonian, isothermal and non-isothermal flow”, Internat. J. Numer. Methods Fluids 18 (1994) 127–162.CrossRefGoogle Scholar
[2]Bird, R. B., Armstrong, R. C. and Hassager, O., Dynamics of polymeric liquids–fluid mechanics, 2nd edn (Wiley-Interscience, New York, 1987).Google Scholar
[3]Bose, A. and Carrey, G. F., “Least-square p-r finite element methods for incompressible non-Newtonian flows”, J. Comput. Methods Appl. Engrg. 180 (1999) 431–458.CrossRefGoogle Scholar
[4]Colagrossi, A. and Landrini, M., “Numerical simulation of interfacial flows using smoothed particle hydrodynamics”, J. Comput. Phys. 191 (2003) 448–475.CrossRefGoogle Scholar
[5]Cummins, S. J. and Rudman, M., “An SPH projection method”, J. Comput. Phys. 152 (1999) 584–607.Google Scholar
[6]Ellero, M., Kroger, M. and Hess, S., “Viscoelastic flows studied by smoothed particle hydrodynamics”, J. Non-Newtonian Fluid Mech. 105 (2002) 35–51.CrossRefGoogle Scholar
[7]Ellero, M. and Tanner, R. I., “SPH simulation of transient viscoelastic flows at low Reynolds number”, J. Non-Newtonian Fluid Mech. 132 (2005) 61–72.CrossRefGoogle Scholar
[8]Gartling, D. K., “Finite element methods of non-Newtonian flows”, Sandia Report SAND 92-0886, UC-705, 1992.Google Scholar
[9]Ghia, U., Ghia, K. N. and Shin, C. T., “High-resolution for incompressible flow using Navier–Stokes equations and a multigrid method”, J. Comput. Phys. 481 (1982) 387–411.CrossRefGoogle Scholar
[10]Gingold, R. A. and Monaghan, J. J., “Smoothed particle hydrodynamics: theory and application to nonspherical stars”, Mon. Not. Roy. Astr. Soc. 181 (1977) 275–389.Google Scholar
[11]Hosseini, S. M., Manzari, M. T. and Hannani, S. K., “A fully explicit three-step SPH algorithm for simulation of non-Newtonian fluid flow”, Internat. J. Numer. Methods Heat Fluid Flow 17 (2007) 715–735.Google Scholar
[12]Lucy, L. B., “A numerical approach to the testing of fission hypothesis”, Astron. J. 82 (1977) 1013–1020.CrossRefGoogle Scholar
[13]Matallah, H., Townsend, P. and Webster, M. F., “Viscoelastic computations of polymeric wire-coating flows”, Internat. J. Numer. Methods. Heat Fluid Flow 12 (2002) 404–433.CrossRefGoogle Scholar
[14]Monaghan, J. J., “Smoothed particle hydrodynamics”, Annu. Rev. Astron. Astrophys. 30 (1992) 543–574.Google Scholar
[15]Monaghan, J. J., “Simulating free surface flows with SPH”, J. Comput. Phys. 110 (1994) 399–406.CrossRefGoogle Scholar
[16]Morris, J. P., Fox, P. J. and Zhu, Y., “Modelling low Reynolds number incompressible flows using SPH”, J. Comput. Phys. 136 (1997) 214–226.CrossRefGoogle Scholar
[17]Neofytou, P., “A 3rd order upwind finite volume method for generalized Newtonian fluid flows”, Adv. Engrg. Software 36 (2005) 664–680.CrossRefGoogle Scholar
[18]Shao, S. and Lo, E. Y. M., “Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface”, Adv. Water Resources 26 (2003) 787–800.Google Scholar
[19]Takeda, H., Miyama, S. M. and Sekiya, M., “Numerical simulation of viscous flow by smoothed particle hydrodynamics”, Prog. Theor. Phys. 92 (1994) 939–960.CrossRefGoogle Scholar
[20]Vola, D., Babik, F. and Latche, J. C., “On a numerical strategy to compute gravity currents of non-Newtonian fluids”, J. Comput. Phys. 201 (2004) 397–420.Google Scholar
[21]Webster, M. F., Tamaddon-Jahromi, H. R. and Aboubacar, M., “Transient viscoelastic flow in planar contractions”, J. Non-Newtonian Fluid Mech. 118 (2004) 83–101.CrossRefGoogle Scholar