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Numerical simulations of non-stationary flows of non-Newtonian fluids between concentric and eccentric cylinders by stream-tube method and domain decomposition

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Abstract

This study involves a theoretical formulation of the stream-tube method in non-stationary flows. Initially, this approach allowed flow computations by determining an unknown transformation between the physical domain and a mapped domain where the streamlines are rectilinear and parallel. To take into account vortex zones, we define local transformations of subregions of the physical domain that are mapped into rectangular domains where the transformed streamlines are still parallel and straight. The local functions must be determined numerically from the governing equations and boundary conditions put together with compatibility equations. The method enables to compute streamlines and flow data at every time, using distinguishing properties, as verification of mass conservation and definition of rectangular meshes allowing to adopt finite-difference schemes. The numerical simulations concern different non-Newtonian fluids under various geometrical and kinematic specifications related to flows between concentric and eccentric cylinders, leading to comparisons with literature data. The results also highlight the influence of the rheological properties on the flow characteristics in unsteady conditions.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of British Columbia, 2054-6250, Applied Science Lane, Vancouver, BC, Canada, V6T 1Z4

    Dana Grecov

  2. Laboratoire de Rhéologie, UMR 5520 CNRS – Université Joseph-Fourier-Institut National Polytechnique de Grenoble, Domaine Universitaire, B.P. No 53, 38041, Grenoble Cedex 9, France

    Jean-Robert Clermont

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  1. Dana Grecov
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  2. Jean-Robert Clermont
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Correspondence to Jean-Robert Clermont.

Additional information

Paper presented at the 4th Annual European Rheology Conference (AERC), April 12–14, 2007, Naples, Italy.

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Grecov, D., Clermont, JR. Numerical simulations of non-stationary flows of non-Newtonian fluids between concentric and eccentric cylinders by stream-tube method and domain decomposition. Rheol Acta 47, 609–620 (2008). https://doi.org/10.1007/s00397-007-0252-1

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  • DOI: https://doi.org/10.1007/s00397-007-0252-1

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