Korea-Australia Rheology Journal

The Korean Society of Rheology (한국유변학회)
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Finite element analysis of viscoelastic flows in a domain with geometric singularities

  • Yoon, Sung-Ho (School of Applied Chemistry and Chemical Engineering, Sungkyunkwan University) ;
  • Kwon, Young-Don (School of Applied Chemistry and Chemical Engineering, Sungkyunkwan University)
  • Published : 2005.09.01
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Abstract

This work presents results of finite element analysis of isothermal incompressible creeping viscoelastic flows with the tensor-logarithmic formulation of the Leonov model especially for the planar geometry with singular comers in the domain. In the case of 4:1 contraction flow, for all 5 meshes we have obtained solutions over the Deborah number of 100, even though there exists slight decrease of convergence limit as the mesh becomes finer. From this analysis, singular behavior of the comer vortex has been clearly seen and proper interpolation of variables in terms of the logarithmic transformation is demonstrated. Solutions of 4:1:4 contraction/expansion flow are also presented, where there exists 2 singular comers. 5 different types spatial resolutions are also employed, in which convergent solutions are obtained over the Deborah number of 10. Although the convergence limit is rather low in comparison with the result of the contraction flow, the results presented herein seem to be the only numerical outcome available for this flow type. As the flow rate increases, the upstream vortex increases, but the downstream vortex decreases in their size. In addition, peculiar deflection of the streamlines near the exit comer has been found. When the spatial resolution is fine enough and the Deborah number is high, small lip vortex just before the exit comer has been observed. It seems to occur due to abrupt expansion of the elastic liquid through the constriction exit that accompanies sudden relaxation of elastic deformation.

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References

  1. Fan, Y., R. I. Tanner and N. Phan-Thien, 1999, Galerkin/leastsquare finite-element methods for steady viscoelastic flows, J. Non-Newtonian Fluid Mech. 84, 233-256 https://doi.org/10.1016/S0377-0257(98)00154-2
  2. Fattal, R. and R. Kupferman, 2004, Constitutive laws of the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123, 281-285 https://doi.org/10.1016/j.jnnfm.2004.08.008
  3. Guenette, R. and M. Fortin, 1995, A new mixed finite element method for computing viscoelastic flows, J. Non-Newtonian Fluid Mech. 60, 27-52 https://doi.org/10.1016/0377-0257(95)01372-3
  4. Gupta, M., 1997, Viscoelastic modeling of entrance flow using multimode Leonov model, Int. J. Numer. Meth. Fluids 24, 493-517 https://doi.org/10.1002/(SICI)1097-0363(19970315)24:5<493::AID-FLD502>3.0.CO;2-W
  5. Hulsen, M. A., 2004, Keynote presentation in Internatioan Congress on Rheology 2004, Seoul, Koreaa
  6. Hulsen, M. A., R. Fattal and R. Kupferman, 2005, Flow of viscoelastic fluids past a cylinder at high Weissenberg number: Stabilized simulations using matrix logarithms, J. Non-Newtonian Fluid Mech. 127, 27-39 https://doi.org/10.1016/j.jnnfm.2005.01.002
  7. Kwon, Y., 2004, Finite element analysis of planar 4:1 contraction flow with the tensor-logarithmic formulation of differential constitutive equations, Korea-Australia Rheology J. 16, 183-191
  8. Kwon, Y. and A. I. Leonov, 1995, Stability constraints in the formulation of viscoelastic constitutive equations, J. Non-Newtonian Fluid Mech. 58, 25-46 https://doi.org/10.1016/0377-0257(94)01341-E
  9. Leonov, A. I., 1976, Nonequilibrium thermodynamics and rheology of viscoelastic polymer media, Rheol. Acta 15, 85-98 https://doi.org/10.1007/BF01517499
  10. Szabo, P., J. M. Rallison and E. J. Hinch, 1997, Start-up of flow of a FENE-fluid through a 4:1:4 constriction in a tube, J. Non-Newtonian Fluid Mech. 72, 73-86 https://doi.org/10.1016/S0377-0257(97)00023-2