Delaying transition to turbulence in channel flow: Revisiting the stability of shear-thinning fluids

Journal of Fluid Mechanics

Volumn 592, Issue , 2007, Pages 177-194

  Nouar, C ^a   Bottaro, A ^b   Brancher, J P ^a  

^a NANCY UNIVERSITÉ   (France)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; REYNOLDS NUMBER; RHEOLOGY; TURBULENCE; VISCOSITY;

CARREAU RHEOLOGICAL LAW; PERTURBATION EQUATIONS; SHEAR-THINNING FLUIDS; VISCOUS STRATIFICATION;

CHANNEL FLOW;

CHANNEL FLOW; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; REYNOLDS NUMBER; RHEOLOGY; TURBULENCE; VISCOSITY;

CHANNEL FLOW; LAMINAR-TURBULENT TRANSITION; MODELING; REYNOLDS NUMBER; VISCOSITY;

EID: 36348932065     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007008439     Document Type: Article

References (39)

1. BIAU, D. & BOTTARO, A. 2004 Optimal perturbations and minimal defects: Initial paths of transition to turbulence in plane shear flows. Phys. Fluids 16, 3515.
2. BIRD, R. B., ARMSTRONG, R. & HASSAGER, O. 1987 Dynamics of polymeric liquids. Wiley-Interscience.
3. CARREAU, P. J. 1972 Rheological equations from molecular network theories. Trans. Soc. Rheolo. 16, 1, 99.
4. CHARRU, F. & HINCH, E. J. 2000 "Phase diagram" of interfacial instabilities in a two-layer Couette flow and mechanism of the long-wave instability. J. Fluid Mech. 414, 195.
5. CHIKKADI, V., SAMEEN, A. & GOVINDARAJAN, R. 2005 Preventing transition to turbulence: A viscosity stratification does not always help. Phys. Rev. Lett. 95, 264504.
6. CORBETT, P. & BOTTARO, A. 2000 Optimal perturbations for boundary layers subject to stream-wise pressure gradient. Phys. Fluids 12, 120.
7. CRAIK, A. D. D. 1969 The stability of plane Couette flow with viscosity stratification. J. Fluid Mech. 36, 685.
8. DE ANGELIS, E., CASCIOLA, C. M. & PIVA, R. 2002 DNS of wall turbulence: Dilute polymers and self-sustaining mechanisms. Comput. Fluids 31, 495.
9. DRAZlN, P. G. & REID, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
10. ERN, P., CHARRU, F. & LUCHINI, P. 2003 Stability analysis of a shear flow with strongly stratified viscosity. J. Fluid Mech. 496, 295.
11. FARRELL, B. F. & IOANNOU, P. J. 1998 Perturbation structure and spectra in turbulent channel flow. Theor. Comput. Fluid Dyn. 11 237.
12. FRANSSON, J. H. M. & CORBETT, P. 2003 Optimal linear growth in the asymptotic suction boundary layer. Eur. J. Mech. B Fluids 22, 259.
13. GAD-EL-HAK, M. 2000 Flow Control: Passive, Active, and Reactive Flow Management. Cambridge University Press.
14. GOVINDARAJAN, R. 2002 Surprising effects of minor viscosity gradients. J. Indian Inst. Sci. 82, 121.
15. GOVINDARAJAN, R., L'VOV, V. S. & PROCACCIA, I. 2001 Retardation of the onset of turbulence by minor viscosity contrasts. Phys. Rev. Lett. 87, 174501.
16. GOVINDARAJAN, R., L'vov, V. S., PROCACCIA, I. & SAMEEN, A. 2003 Stabilization of hydrodynamic flows by small viscosity variations. Phys. Rev. E 67, 026310.
17. GUPTA, G. K. 1999 Hydrodynamic stability of the plane Poiseuille flow of an electro-rheological fluid. Intl J. Non Linear Mech. 34, 589.
18. HINCH, E. J. 1984 A note on the mechanism of the instability at the interface between two viscous fluids. J. Fluid Mech. 144 463.
19. HOOPER, A. & BOYD, W. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507.
20. LI, W., XI, L. & GRAHAM, M., D. 2006 Nonlinear travelling waves as a framework for understanding turbulent drag reduction. J. Fluid Mech. 565, 353.
21. LUMLEY, J. L. 1969 Drag reduction by additives. Annu. Rev. Fluid Mech. 1, 367.
22. MALIK, S. V. & HOOPER, A. P. 2005 Linear stability and energy growth of viscosity stratified flows. Phys. Fluids 17, 024101.
23. METZNER, A. B. 1977 Polymer solution and fiber suspension rheology and their relationship to turbulent drag reduction. Phys. Fluids 20, S145.
24. NOUAR, C., KABOUYA, N., DUSEK, K. & MAMOU, M. 2007 Modal and non-modal linear stability of the plane-Bingham-Poiseuille flow. J. Fluid Mech. 577, 211.
25. ORLANDI, P. 1997 A tentative approach to the direct simulation of drag reduction by polymers. J. Non-Newtonian Fluid Mech. 60, 277.
26. PEIXINHO, J., NOUAR, C., DESAUBRY, C. & THÉRON, B. 2005 Laminar transitional and turbulent flow of yield stress fluid in a pipe. J. Non-Newtonian Fluid Mech. 128, 175.
27. PINARBASI, A. & LIAKOPOULOS, A. 1995 The role of variable viscosity in the stability of channel flow. Intl Commun. Heat Mass Transfer 22, 837.
28. PINARBASI, A. & OZALP, C. 2001 Effect of viscosity models on the stability of a Non-Newtonian fluid in a channel with heat transfer. Intl Commun. Heat Mass Transfer 28, 369.
29. RANGANATHAN, B. T. & GOVINDARAJAN, R. 2001 Stabilization and destabilization of channel flow by location of viscosity-stratified fluid layer. Phys. Fluids 13, 1.
30. SAMEEN, A. & GOVINDARAJAN, R. 2007 The effect of wall heating on instability of channel flow. J. Fluid Mech. 577, 417.
31. SCHMID, P. J. & HENNINOSON, D. S. 1994 Optimal energy density growth in Hagen-Poiseuille flow. J. Fluid Mech. 277, 197.
32. SCHMID, P. J. & HENNINGSON, D. S. 2001 Stability and Transition in Shear Flows. Springer.
33. STONE, P. A., ROY, A., LARSON, R., WALEFFE, F. & GRAHAM, M. D. 2004 Polymer drag reduction in exact coherent structures of plane shear flow. Phys. Fluids. 16, 3470.
34. SURESHKUMAR, R., BERIS, A. N. & HANDLER, R. A. 1997 Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9, 743.
35. TANNER, R. 2000 Engineering Rheology. Oxford University Press.
36. TREFETHEN, L. N., TREFETHEN, A. E., REDDY, S. C. & DRISCOLL, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261 578.
37. WALL, D. P. & WILSON, S. K. 1996 The linear stability of channel flow of fluid with temperature-dependent viscosity. J. Fluid Mech. 323, 107.
38. YIH, C.-S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337.
39. ZHANG, K., ACRIVOS, A. & SCHAFLINGER, U. 1992 Stability in a two-dimensional Hagen-Poiseuille resuspension flow. Intl J. Multiphase Flow 18, 51.