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.