DIRECT NUMERICAL SIMULATION OF PARTICLE SUSPENSIONS IN A POLYMERIC LIQUID

미세입자분산 고분자 현탁액의 3차원 직접수치해석

  • 황욱렬 (경상대학교 기계항공공학부, 항공기부품기술연구소) ;
  • ;
  • Published : 2009.12.31

Abstract

We present a new finite-element scheme for direct numerical simulation of particle suspensions in simple shear flow of a viscoelastic fluid in 3D. The sliding tri-periodic representative cell concept has been combined with DEVSS/DG finite element scheme by introducing constraint equations along the domain boundary. Rigid body motion of the freely suspended particle is described by the rigid-shell description and implemented by Lagrangian multipliers on particle boundaries. We present the bulk rheology of suspensions through the numerical examples of single-, two- and many-particle problems, which represent a large number of such systems in simple shear flow. We report the steady bulk viscosity and the first normal stress coefficient, which show shear-thickening behavior for both properties.

Keywords

References

  1. 2006, Hwang, W.R., Peters, G.W.M., Hulsen, M.A. and Meijer, H.E.H., "Modeling of flow-induced crystallization of particle-filled polymer," Macromolecules, Vol.39, pp.8389-8398 https://doi.org/10.1021/ma061205g
  2. 2002, Schrauwen, B.A.G., Govaert, L.E., Peters, G.W.M. and Meijer, H.E.H., "The influence of flow-induced crystallization on the impact toughness of high-density polyethylene," Macromolecular Symposium, Vol.185, pp.89-102 https://doi.org/10.1002/1521-3900(200208)185:1<89::AID-MASY89>3.0.CO;2-I
  3. 2004, Hwang, W.R., Hulsen, M.A. and Meijer, H.E.H., "Direct simulations of particle suspensions in sliding bi-periodic frames," J. Comput. Phys., Vol. 194, pp.742-772 https://doi.org/10.1016/j.jcp.2003.09.023
  4. 2004, Hwang, W.R., Hulsen, M.A. and Meijer, H.E.H., "Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames," J. Non-Newtonian Fluid Mech., Vol.121, pp.15-33 https://doi.org/10.1016/j.jnnfm.2004.03.008
  5. 1988, Larson, R.G., Constitutive equations for polymeric melts and solutions, Butterworths
  6. 1996, Hu, H.H., "Direct simulation of flows of solid-liquid mixtures," Int. J. Multiphase Flow, Vol.22, pp.335-352. https://doi.org/10.1016/0301-9322(95)00068-2
  7. 1999, Glowinski, R., Pan, T.W., Hesla, T.I. and Joseph, D.D., "A distributed Lagrangian multipliers/fictitious domain method for particulate flows," Int. J. Multiphase Flow, Vol.25, pp.755-794 https://doi.org/10.1016/S0301-9322(98)00048-2
  8. 2002, Lauren, T.A., Computational contact and impact mechanics, Springer-Verlag, Heidelberg
  9. 2001, Baaijens, F.P.T., "A fictitious domain/mortar element method for fluid.structure interaction," Int. J. Numer. Meth. Fluids, Vol.35, p.743 https://doi.org/10.1002/1097-0363(20010415)35:7<743::AID-FLD109>3.0.CO;2-A
  10. 1995, Guenette, R. and Fortin, M., "A new mixed finite element method for computing viscoelastic flows," J. Non-Newtonian Fluid Mech., Vol.60, pp.27-52 https://doi.org/10.1016/0377-0257(95)01372-3
  11. 1998, Baaijens, F.P.T., "Mixed finite element methods for viscoelastic flow analysis: a review," J. Non-Newtonian Fluid Mech., Vol.79, pp.361-385 https://doi.org/10.1016/S0377-0257(98)00122-0
  12. 1989, Fortin, M. and Fortin, A., "A new approach for the FEM simulation of viscoelastic flows," J. Non-Newtonian Fluid Mech., Vol.32, pp.295-310 https://doi.org/10.1016/0377-0257(89)85012-8
  13. 1970, Batchelor, G.K., "The stress system in a suspension of force-free particles," J. Fluid Mech., Vol.41, p.545 https://doi.org/10.1017/S0022112070000745
  14. 2002, N, P-T., .Understanding Viscoelasticity, Springer, Berlin
  15. 1997, Kuijlaars, S., The Mathematical Intelligence, Vol.19, pp.5-11
  16. 1984, Brady, J.F., "The Einstein viscosity correction in n dimensions," Int. J. Multiphase Flow, Vol.10, pp.113-114 https://doi.org/10.1016/0301-9322(83)90064-2
  17. 2002, Sierou, A. and Brady, J.F., "Rheology and microstructure in concentrated non-colloidal suspensions," J. Rheology, Vol.46, pp.1031-1056 https://doi.org/10.1122/1.1501925
  18. 2005, Hwang, W.R., Anderson, P.D. and Hulsen, M.A., "Chaotic advection in a cavity flow with rigid particles," Phys. Fluids, Vol.17, 043602 https://doi.org/10.1063/1.1884465
  19. 2001, Patankar, N.A. and Hu, H.H., "Rheology of a suspension of particles in viscoelastic fluids," J. Non-Newtonian Fluid Mech. Vol.96, pp.423-443 https://doi.org/10.1016/S0377-0257(00)00154-3
  20. MUMPS: Multifrontal Massively Parallel Sparse Direct Solver, http://mumps.enseeiht.fr/
  21. 2005, Elman, H.C., Silvester, D.J. and Wathen, A.J., Finite Elements and Fast Iterative Solvers, Oxford
  22. 2009, Hwang, W.R., Walkley, M.A. and Harlen, O.G., "An O(N) iterative solver for viscoelastic flow simulations with DEVSS," IMA Workshop on Flowing Complex Fluids, Oct. 12-16, Minneapolis, USA