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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

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