화학공학소재연구정보센터
홈 로그인 로그아웃 연락처 사이트맵
Korea-Australia Rheology Journal, Vol.22, No.4, 237-245, December, 2010
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Convergence limit in numerical modeling of steady contraction viscoelastic flow and time-dependent behavior near the limit
Youngdon Kwon†, and JungHyun Han1
  • School of Chemical Engineering, Sungkyunkwan University, 300 Cheoncheon-dong,Jangan-gu, Suwon, Gyeonggi-do 440-746, Korea
  • 1College of Information and Communication, Korea University, 1-5 Anam-Dong, Sungbuk-Gu, Seoul, 136-701, Korea
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In the framework of finite element analysis we numerically analyze both the steady and transient 4:1 contraction creeping viscoelastic flow. In the analysis of steady solutions, there exists upper limit of available numerical solutions in contraction flow of the Leonov fluid, and it is free from the frustrating mesh dependence when we incorporate the tensor-logarithmic formulation (Fattal and Kupferman, 2004). With the time dependent flow modeling with pressure difference imposed slightly below the steady limit, the 1st and 2nd order conventional approximation schemes have demonstrated fluctuating solution without approaching the steady state. From the result, we conclude that the existence of upper limit for convergent steady solution may imply flow transition to highly elastic time-fluctuating field without steady asymptotic. However definite conclusion certainly requires further investigation and devising some methodology for its proof.
Keywords:viscoelastic flow;finite element;Leonov model;contraction flow;Deborah number;elastic instability
  1. Arratia PE, Thomas CC, Diorio J, Collub JP, Phys. Rev. Lett., Elastic instabilities of polymer solutions in cross-channel flow, 96, 144502 (2006)
  2. Baaijens FPT, J. Non-Newtonian Fluid Mech., Mixed finite element methods for viscoelastic flow analysis: a review, 79, 361 (1998)
  3. Bird RB, Curtiss CF, Armstrong RC, Hassager O, Dynamics of Polymeric Liquids, Wiley, New York. (1987)
  4. Bogaerds ACB, Hulsen MA, Peters GWM, Baaijens FPT, J. Rheol., 48(4), 765 (2004)
  5. Boger DV, Walters K, Rheological Phenomena in Focus, Elsevier, Amsterdam. (1993)
  6. Coronado OM, Arora D, Behr M, Pasquali M, J. Non-Newton. Fluid Mech., 147(3), 189 (2007)
  7. Fattal R, Kupferman R, J. Non-Newtonian Fluid Mech., Constitutive laws for the matrix-logarithm of the conformation tensor., 123, 287 (2004)
  8. Grillet AM, Bogaerds ACB, Peters GWM, Baaijens FPT, J. Rheol., 46(3), 651 (2002)
  9. Hulsen MA, J. Non-Newtonian Fluids Mech., A sufficient condition for a positive definite configuration tensor in differential models., 38, 93 (1990)
  10. Hulsen MA, Fattal R, Kupferman R, J. Non-Newton. Fluid Mech., 127(1), 27 (2005)
  11. Joseph DD, Fluid dynamics of viscoelastic liquids, Springer-Verlag, New York. (1990)
  12. Keshtibana IJ, Puangkird B, Tamaddon-Jahromi H, Webster MF, J. Non-Newton. Fluid Mech., 151(1-3), 2 (2008)
  13. Keunings R, J. Non-Newtonian Fluid Mech., On the high weissenberg number problem, 20, 209 (1986)
  14. Kwon Y, Korea-Aust. Rheol. J., 16(4), 183 (2004)
  15. KWON Y, LEONOV AV, J. Non-Newton. Fluid Mech., 58(1), 25 (1995)
  16. Lee J, Yoon S, Kwon Y, Kim S, Rheol. Acta, 44(2), 188 (2004)
  17. Leonov AI, Rheol. Acta., Nonequilibrium thermodynamics and rheology of viscoelastic polymer media, 15, 85 (1976)
  18. McKinley BH, Byars JA, Brown RA, Armstrong RC, J.Non-Newtonian Fluid Mech., Observations on the elastic instability in cone-and-plate and parallel-plate flows of a polyisobutylene Boger fluid, 40, 201 (1991)
  19. Owens RG, Phillips TN, Computational Rheology, Imperial College Press, London. (2002)
  20. Poole RJ, Alves MA, Oliveira PJ, Phys. Rev. Lett., 99, 164503 (2007)
  21. Shaqfeh ESG, Ann. Rev. Fluid Mech., Purely elastic instabilities in viscometric flows, 28, 129185 (1996)
  22. Soulages J, Oliveira MSN, Sousa PC, Alves MA, McKinley GH, J. Non-Newton. Fluid Mech., 163(1-3), 9 (2009)
  23. Tanner RI, Engineering Rheology, Oxford, New York. (2000)
  24. Xue SC, Tanner RI, Phan-Thien N, J. Non-Newton. Fluid Mech., 123(1), 33 (2004)