The effect of expansion ratio for creeping expansion flows of UCM fluids

A systematic numerical investigation on creeping flows in planar sudden expansions of viscoelastic fluids obeying the upper-convected Maxwell model is carried out to assess the combined effects of viscoelasticity, through the Deborah number, and expansion ratio (ER), which was varied between 1.25 and 32. At large expansion ratios (ER ≥ 4) the flow becomes dominated by the downstream duct size and appropriately normalized quantities tend to be independent of ER. The recirculation size and strength become decreasing functions of De, whereas the Couette correction (the normalized entry pressure drop due to the presence of the expansion) increases. At small ER (ER ≤ 3), however, no simple scaling laws are found and there is a complex interaction between De and ER leading to non-monotonic variations, with an initial decrease in the recirculation length at low Deborah numbers, followed by an enhancement as De increases.

[1]  Christopher C. Pain,et al.  Creeping Flow Through an Axisymmetric Sudden Contraction or Expansion , 2002 .

[2]  F. Durst,et al.  Asymmetric flows and instabilities in symmetric ducts with sudden expansions , 1978, Journal of Fluid Mechanics.

[3]  D. Drikakis.  Bifurcation phenomena in incompressible sudden expansion flows , 1997 .

[4]  M. Schäfer,et al.  Numerical study of bifurcation in three-dimensional sudden channel expansions , 2000 .

[5]  J. Whitelaw,et al.  Turbulence Characteristics of the Flow Downstream of a Symmetric, Plane Sudden Expansion , 1978 .

[6]  Robert J. Poole,et al.  Turbulent flow of viscoelastic liquids through an axisymmetric sudden expansion , 2004 .

[7]  W. Devenport,et al.  An experimental study of two flows through an axisymmetric sudden expansion , 1993 .

[8]  John R. Whiteman,et al.  Numerical modelling of viscoelastic liquids using a finite-volume method , 1992 .

[9]  M. Escudier,et al.  Laminar flow of a viscoelastic shear-thinning liquid through a plane sudden expansion preceded by a gradual contraction , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[10]  Robert J. Poole,et al.  Plane sudden expansion flows of viscoelastic liquids , 2007 .

[11]  F. Pinho,et al.  Effect of contraction ratio upon viscoelastic flow in contractions: The axisymmetric case , 2007 .

[12]  Robert J. Poole,et al.  Bifurcation phenomena in viscoelastic flows through a symmetric 1:4 expansion , 2007 .

[13]  F. Pinho,et al.  Turbulent expansion flow of low molecular weight shear-thinning solutions , 1995 .

[14]  Paulo J. Oliveira,et al.  Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries , 2003 .

[15]  G. McKinley,et al.  Stability of planar stagnation flow of a highly viscoelastic fluid , 1997 .

[16]  F. Pinho,et al.  A convergent and universally bounded interpolation scheme for the treatment of advection , 2003 .

[17]  G. McKinley,et al.  Rheological and geometric scaling of purely elastic flow instabilities , 1996 .

[18]  M. Escudier,et al.  Turbulent flow of a viscoelastic shear-thinning liquid through a plane sudden expansion of modest aspect ratio , 2003 .

[19]  F. Pinho,et al.  Turbulent characteristics of shear-thinning fluids in recirculating flows , 2000 .

[20]  Fernando T. Pinho,et al.  Pressure losses in the laminar flow of shear-thinning power-law fluids across a sudden axisymmetric expansion , 2003 .

[21]  Enzo O. Macagno,et al.  Laminar eddies in a two-dimensional conduit expansion , 1966 .

[22]  Pakdel,et al.  Elastic Instability and Curved Streamlines. , 1996, Physical review letters.

[23]  Enzo O. Macagno,et al.  Computational and experimental study of a captive annular eddy , 1967, Journal of Fluid Mechanics.

[24]  Dionysis Assimacopoulos,et al.  A finite volume approach in the simulation of viscoelastic expansion flows , 1998 .

[25]  F. Pinho,et al.  Numerical simulation of non-linear elastic flows with a general collocated finite-volume method , 1998 .

[26]  F. Pinho,et al.  Numerical investigation of the velocity overshoots in the flow of viscoelastic fluids inside a smooth contraction , 2006 .

[27]  R. Thompson,et al.  A general transformation procedure for differential viscoelastic models , 2003 .

[28]  H. Thompson,et al.  Laser Velocimeter Measurements in Highly Turbulent Recirculating Flows , 1984 .

[29]  F. Pinho,et al.  On the effect of contraction ratio in viscoelastic flow through abrupt contractions , 2004 .

[30]  Gianni Astarita,et al.  Objective and generally applicable criteria for flow classification , 1979 .

[31]  J. Oldroyd.  On the formulation of rheological equations of state , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[32]  Panagiotis Neofytou,et al.  Non-Newtonian flow instability in a channel with a sudden expansion , 2003 .