CMNE/CILAMCE 2007 Porto, 13 a 15 de Junho, 2007 © APMTAC, Portugal 2007 APPLICATION OF THE LOG-CONFORMATION TENSOR APPROACH TO THREE DIMENSIONAL VISCOELASTIC FLOWS Alexandre M. Afonso 1,* , Manuel A. Alves 1 , Fernando T. Pinho 2,3 and Paulo J. Oliveira 4 1: Departamento de Engenharia Química CEFT - Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia da Universidade do Porto Rua Dr. Roberto Frias, 4200-465 Porto, Portugal e-mail: {aafonso,mmalves}@fe.up.pt, web: http://www.fe.up.pt 2: Universidade do Minho, Largo do Paço, 4704-553 Braga, e-mail: fpinho@dem.uminho.pt, web: http://www.uminho.pt 3: CEFT - Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia da Universidade do Porto Rua Dr. Roberto Frias, 4200-465 Porto, Portugal e-mail: fpinho@fe.up.pt, web: http://www.fe.up.pt 4: Departamento de Engenharia Electromecânica MTP – Unidade Materiais Têxteis e Papeleiros Universidade da Beira Interior 6201-001 Covilhã, Portugal e-mail: pjpo@ubi.pt, web: http://www.ubi.pt Key words: Square/Square contraction; Viscoelastic flows; Log-conformation tensor; Finite- volume method. Summary. A finite-volume method is applied to the numerical simulation of creeping flows of viscoelastic fluids through a 4:1 square-square three dimensional abrupt contraction. The calculation of the polymer stress contribution is carried out with the log-conformation methodology [1]. The log-conformation scheme allowed converged solutions at higher Deborah numbers for the Oldroyd-B fluid than the standard method when imposing steady flow conditions, but not for the UCM model. This does not mean that the log-conformation technique is less effective for the UCM fluid, but suggests that this flow is most probably time-dependent above a critical Deborah number. In any case, this work confirms the advantages of the log-conformation approach vis-a-vis the standard procedure.