Pressure losses in the laminar flow of shear-thinning power-law fluids across a sudden axisymmetric expansion F.T. Pinho a, * , P.J. Oliveira b , J.P. Miranda c a Centro de Estudos de Fen omenos de Transporte, DEMEGI, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal b Departamento de Eng. Electromec^ anica, Universidade da Beira Interior, Rua Marqu^ esDÕ  Avila e Bolama, 6201-001 Covilh~ a, Portugal c Instituto Polit ecnico de Braganc ßa, Escola Superior de Tecnologia e Gest ~ ao, Campus de Santa Apol onia, 5301-857 Braganc ßa, Portugal Received 29 July 2002; accepted 8 May 2003 Abstract A numerical investigation was carried out to study the laminar non-Newtonian flow through an axisymmetric sudden expansion having a diameter ratio of 1 to 2.6. The fluids were inelastic and shear thinning with a viscosity obeying the power law model. The recirculation length and strength and, most importantly, the local loss coefficient C I were quantified as a function of the inlet pipe Reynolds number and shear-thinning intensity. When using the generalised Reynolds number introduced by Metzner and Reed [AIChEJ 1 (1955) 434] (Re gen ), at low Reynolds numbers C I increased by more than 100% when n varied from 1.0 to 0.2, whereas C I decreased by more than 50% at high Reynolds numbers. However, this feature was shown to be related to the definition of the Reynolds number. A correlation between C I , Re gen and n is presented at the end. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Sudden expansion; Pressure loss; Shear thinning; Recirculation length 1.Introduction Sudden expansion flows occur frequently in many industrial applications and bring together geometric simplicity with a not so simple flow behaviour. They have been extensively investigated in the past for New- tonian fluids both numerically (Habib and Whitelaw, 1982; Macagno and Hung, 1967; Oliveira and Pinho, 1997) and experimentally (Stieglmeier et al., 1989; Khezzar et al., 1985; Back and Roschke, 1972) amongst others, in the laminar and mainly in the turbulent flow regimes. When the fluids exhibit non-Newtonian characteris- tics the literature is scarcer. Halmos and Boger (1975) investigated experimentally some mean flow character- istics in a 1:2 sudden expansion in laminar flow and their measurements showed that the length of the recircula- tion bubble was increased by the shear-thinning inten- sity. The numerical works of Halmos et al. (1975) and Perera and Walters (1977) reached similar conclusions as far as the role of shear-thinning and elasticity are concerned, although the flow conditions were not the same. Halmos et al. (1975) considered fully developed flow at the inlet of the expansion and their numerical results showed a systematic over-prediction of the re- circulation length by 7% relative to the measurements of Halmos and Boger (1975). Perera and Walters (1977) studied the hydrodynamics of an expansion/contraction/ expansion duct and their concern was the investigation of elastic effects. They concluded that there were no significant changes of hydrodynamic behaviour between shear-thinning fluids and equivalent Newtonian liquids due to pure viscous effects. The definition of an equiv- alent Newtonian fluid embedding some of the differences between non-Newtonian and Newtonian fluids, helped to reach this conclusion. On the effect of elasticity, however, Halmos and Boger (1976) observed a reduc- tion in recirculation length when the stress ratio ex- ceeded a critical value and found it to be proportional to the Weissenberg number of the flow. This was attributed to a die swelling type of effect. * Corresponding author. Tel.: +351-225-081-762; fax: +351-225-081- 763. E-mail addresses: fpinho@fe.up.pt (F.T. Pinho), pjpo@ubi.pt (P.J. Oliveira), jmiranda@ipb.pt (J.P. Miranda). 0142-727X/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0142-727X(03)00083-3 International Journal of Heat and Fluid Flow 24 (2003) 747–761 www.elsevier.com/locate/ijhff