Linear stability analysis of flow of an Oldroyd-B fluid through a linear array of cylinders

Journal of Non-Newtonian Fluid Mechanics

Volumn 109, Issue 1, 2003, Pages 13-50

  Smith, M D ^a   Joo, Y L ^a   Armstrong, R C ^a   Brown, R A ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Cylinder; Protean coordinates; Stability; Three dimensional perturbation

Indexed keywords

CYLINDERS (SHAPES); EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; PERTURBATION TECHNIQUES; POLYMERS; STRESSES; VISCOELASTICITY;

LINEAR STABILITY;

STEADY FLOW;

CYLINDER; FLOW ANALYSIS; FLOW AROUND OBJECT; FLOW STABILITY; OLDROYD-B FLUID;

EID: 0037138222     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0257(02)00162-3     Document Type: Article

References (27)

1. A.W. Liu, Viscoelastic Flow of Polymer Solutions around Arrays of Cylinders: Comparison of Experiment and Theory, Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA, 1997.
2. Y.L. Joo E.S.G. Shaqfeh Observations of purely elastic instabilities in the Taylor–Dean flow of a Boger fluid J. Fluid Mech. 262 1994 27 73
3. Y.L. Joo E.S.G. Shaqfeh A purely elastic instability in Dean and Taylor–Dean flow Phys. Fluids 4 1992 524 543
4. R.G. Larson E.S.G. Shaqfeh S.J. Muller A purely elastic instability in Taylor–Couette flow J. Fluid Mech. 218 1990 573 600
5. M. Avgousti A.N. Beris Non-axisymmetric modes in viscoelastic Taylor–Couette flow J. Non-Newtonian Fluid Mech. 50 1993 225 251
6. P. Pakdel G.H. McKinley Elastic instability and curved streamlines Phys. Rev. Lett. 77 1996 2459 2462
7. G.H. McKinley R.C. Armstrong R.A. Brown The wake instability in viscoelastic flow past confined circular cylinders Phil. Trans. R. Soc. Lond. A 344 1993 265 304
8. R. Sureshkumar M.D. Smith R.C. Armstrong R.A. Brown Linear stability and dynamics of viscoelastic flows using time-dependent simulations J. Non-Newtonian Fluid Mech. 82 1999 57 104
9. M.D. Smith R.C. Armstrong R.A. Brown R. Sureshkumar Finite element analysis of two-dimensional viscoelastic flows to three-dimensional perturbations J. Non-Newtonian Fluid Mech. 93 2000 203 244
10. R. Glowinski O. Pironneau Finite element methods for Navier–Stokes equations Ann. Rev. Fluid Mech. 24 1989 167 204
11. P. Saramito A new ϑ -scheme algorithm and incompressible FEM for viscoelastic fluid flows Math. Model. Numer. Anal. 28 1994 1 35
12. Harwell Subroutine Library Release 11, available from AEA Technology, Building 424.4, Harwell, Oxfordshire OX11 0RA, UK.
13. A.E. Caola Y.L. Joo R.C. Armstrong R.A. Brown Highly parallel time integration of viscoelastic flows J. Non-Newtonian Fluid Mech. 100 2001 191 216
14. B. Hendrickson, R. Leland, The CHACO User’s Guide Version 2.0, 1995
15. Y. Saad, Numerical Methods for Large Eigenvalue Problems, Manchester University Press, Manchester, UK, 1992.
16. L.N. Trefethen, D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997.
17. R.B. Lehoucq, D.C. Sorensen, C. Yang, ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods, ftp://ftp.caam.rice.edu/pub/software/ARPACK .
18. V.V. Ramanan K.A. Kumar M.D. Graham Stability of viscoelastic shear flows subjected to steady or oscillatory transverse flow J. Fluid Mech. 379 1999 255 277
19. R. Sureshkumar A.N. Beris M. Avgousti Non-axisymmetric subcritical bifurcations in viscoelastic Taylor–Couette flow Proc. R. Soc. Lond. A 447 1994 135 153
20. K. Adachi Calculation of strain histories in Protean coordinate systems Rheol. Acta 22 1983 326 335
21. H.J. Wilson M. Renardy Y. Renardy Structure of the spectrum in zero Reynolds shear flow of the UCM and Oldroyd-B liquids J. Non-Newtonian Fluid Mech. 80 1999 251 268
22. M.D. Graham Effect of axial flow on viscoelastic Taylor–Couette instability J. Fluid Mech. 360 1998 341 374
23. R.A. Brown M.J. Szady P.J. Northey R.C. Armstrong On the numerical stability of mixed finite-element methods for viscoelastic flows governed by differential constitutive equations Theor. Comput. Fluid Dyn. 5 1993 77 106
24. P.G. Drazin, W.H. Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge, UK, 1981.
25. J.A. Byars, Experimental Characterization of Viscoelastic Flow Instabilities, Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA, 1996.
26. Y.L. Joo, I. Ghosh, R.C. Armstrong, R.A. Brown, Use of a New Adaptive Length Scale Model in the Simulation of Flow of a Viscoelastic Fluid around a Linear Array of Cylinders in a Channel, in preparation.
27. I. Ghosh Y.L. Joo G.H. McKinley R.A. Brown R.C. Armstrong A new model for dilute polymer solutions in flows with strong extensional components J. Rheol. 46 2002 1057 1090