Viscoelastic secondary flows in serpentine channels

Journal of Non-Newtonian Fluid Mechanics

Volumn 201, Issue , 2013, Pages 10-16

  Poole, R J ^a   Lindner, A ^b   Alves, M A ^c  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

^b ESPCI   (France)

^c UNIVERSITY OF PORTO   (Portugal)

Author keywords

Finite volume method; Oldroyd B model; Secondary flow; Serpentine channel; UCM model

Indexed keywords

NEWTONIAN FLUID FLOW; NUMERICAL INVESTIGATIONS; OLDROYD-B MODELS; RADIUS OF CURVATURE; SERPENTINE CHANNEL; UCM MODEL; VISCOELASTIC FLUID FLOWS; VISCOSITY RATIOS;

ASPECT RATIO; FIBROUS MEMBRANES; FINITE VOLUME METHOD; NEWTONIAN LIQUIDS; SERPENTINE; VISCOELASTICITY;

SECONDARY FLOW;

EID: 84881243878     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2013.07.001     Document Type: Article

References (31)

1. Dean W.R. Note on the motion of fluid in a curved pipe. Philos. Magn. 1927, 20:208-223.
2. Dean W.R. The streamline motion of fluid in a curved pipe. Philos. Magn. 1928, 5(7):673-695.
3. Malheiro J.M., Oliveira P.J., Pinho F.T. Parametric study on the three-dimensional distribution of velocity of a FENE-CR fluid flow through a curved channel. J. Non-Newt. Fluid Mech. 2013, In press.
4. Lauga E., Stroock A.D., Stone H.A. Three-dimensional flows in slowly varying planar geometries. Phys. Fluids 2004, 16:3051-3062.
5. Melling A., Whitelaw J.H. Turbulent flow in a rectangular duct. J. Fluid Mech. 1976, 78:289-315.
6. Escudier M.P., Smith S. Fully developed turbulent flow of non-Newtonian liquids through a square duct. Proc. Roy. Soc. London A 2001, 457:911-936.
7. Green A.E., Rivlin R.S. Steady flow of non-Newtonian fluids through tubes. Q. Appl. Math. 1956, 14:299-308.
8. Townsend P., Walters K., Waterhouse W.M. Secondary flows in pipes of square cross-section and measurements of the second normal stress difference. J. Non-Newt. Fluid Mech. 1976, 1:107-123.
9. Gervang B., Larsen P.S. Secondary flows in straight ducts of rectangular cross section. J. Non-Newt. Fluid Mech. 1991, 39:217-237.
10. Debbaut B., Avalosse T., Dooley J., Hughes K. On the development of secondary motions in straight channels induced by the second normal stress difference: experiments and simulations. J. Non-Newt. Fluid Mech. 1997, 69:255-271.
11. Xue S.C., Phan-Thien N., Tanner R.I. Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method. J. Non-Newt. Fluid Mech. 1995, 59:191-213.
12. Yue P., Dooley J., Feng J.F. A general criterion for viscoelastic secondary flow in pipes of noncircular cross section. J. Rheol. 2008, 52:315-332.
13. Speziale C.G. On nonlinear K-l and K-ε models of turbulence. J. Fluid Mech. 1987, 178:459-475.
14. Barnes H.A., Hutton J.F., Walters K. An Introduction to Rheology 1989, Elsevier.
15. Oldroyd J.G. On the formulation of rheological equations of state. Proc. Roy. Soc. London A 1950, 200:523-541.
16. Phan-Thien N., Tanner R.I. A new constitutive equation derived from network theory. J. Non-Newt. Fluid Mech. 1977, 2:353-365.
17. Bird R.B., Dotson P.J., Johnson N.L. Polymer solution rheology based on a finitely extensible bead-spring chain model. J. Non-Newt. Fluid Mech. 1980, 7:213-235.
18. Chilcott M.D., Rallison J.M. Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newt. Fluid Mech. 1988, 29:381-432.
19. Joo Y.L., Shaqfeh E.S.G. Viscoelastic poiseuille flow through a curved channel - a new elastic instability. Phys. Fluids A 1991, 3:1691-1694.
20. Fan Y., Tanner R.I., Phan-Thien N. Fully developed viscous and viscoelastic flows in curved pipes. J. Fluid Mech. 2001, 440:327-357.
21. Norouzi M., Kayhani M.H., Shu C., Nobari M.R.H. Flow of second-order fluid in a curved duct with square cross-section. J. Non-Newt. Fluid Mech. 2010, 165:323-339.
22. R.B. Bird, R.C. Armstrong, O. Hassager. Dynamics of Polymeric Liquids. Vol. 1: Fluid Mechanics, Wiley, New York, 1987.
23. Groisman A., Steinberg V. Efficient mixing at low reynolds numbers using polymer additives. Nature 2001, 410:905-908.
24. Zilz J., Poole R.J., Alves M.A., Bartolo D., Levache B., Lindner A. Geometric scaling of a purely elastic flow instability in serpentine channels. J. Fluid Mech. 2012, 72:203-218.
25. Poole R.J., Alves M.A., Oliveira P.J. Purely elastic flow asymmetries. Phys. Rev. Lett. 2007, 99. 164503.
26. Alves M.A., Poole R.J. Divergent flow in contractions. J. Non-Newt. Fluid Mech. 2007, 144:140-148.
27. Fattal R., Kupferman R. Constitutive laws of the matrix-logarithm of the conformation tensor. J. Non-Newt. Fluid Mech. 2004, 123:281-285.
28. Afonso A., Oliveira P.J., Pinho F.T., Alves M.A. The log-conformation tensor approach in the finite-volume method framework. J. Non-Newt. Fluid Mech. 2009, 157(1-2):55-65.
29. Afonso A., Oliveira P.J., Pinho F.T., Alves M.A. Dynamics of high-Deborah number entry flows: a numerical study. J. Fluid Mech. 2011, 677:272-304.
30. Alves M.A., Oliveira P.J., Pinho F.T. Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions. J. Non-Newt. Fluid Mech. 2003, 110:45-75.
31. Oliveira P.J., Pinho F.T., Pinto G.A. Numerical simulation of non-linear elastic flows with a general collocated finite-volume method. J. Non-Newt. Fluid Mech. 1998, 79:1-43.