The effects of drag reducing polymers on flow stability : Insights from the Taylor-Couette problem

Cari S. Dutcher; Susan J. Muller

Korea-Australia Rheology Journal, Vol.21, No.4, 213-233, December, 2009

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The effects of drag reducing polymers on flow stability : Insights from the Taylor-Couette problem

Cari S. Dutcher, and Susan J. Muller^†

Department of Chemical Engineering, University of California, Berkeley, Berkeley, CA 94720-1462, U.S.A., USA

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Taylor-Couette flow (i.e., flow between concentric, rotating cylinders) has long served as a paradigm for studies of hydrodynamic stability. For Newtonian fluids, the rich cascade of transitions from laminar, Couette flow to turbulent flow occurs through a set of well-characterized flow states (Taylor Vortex Flow, wavy Taylor vortices, modulated wavy vortices, etc.) that depend on the Reynolds numbers of both the inner and outer cylinders (Re(i) and Re(o)). While extensive work has been done on (a) the effects of weak viscoelasticity on the first few transitions for Re(o)=0 and (b) the effects of strong viscoelasticity in the limit of vanishing inertia (Re(i) and Re(o) both vanishing), the viscoelastic Taylor-Couette problem presents an enormous parameter space, much of which remains completely unexplored. Here we describe our recent experimental efforts to examine the effects of drag reducing polymers on the complete range of flow states observed in the Taylor-Couette problem. Of particular importance in the present work is 1) the rheological characterization of the test solutions via both shear and extensional (CaBER) rheometry, 2) the wide range of parameters examined, including Re(i), Re(o), and Elasticity number El, and 3) the use of a consistent, conservative protocol for accessing flow states. We hope that by examining the stability changes for each flow state, we may gain insights into the importance of particular coherent structures in drag reduction, identify simple ways of screening new drag reducing additives, and improve our understanding of the mechanism of drag reduction.

Keywords:instabilities;Taylor-Couette;drag reduction;elastic turbulence

[References]

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Baumert BM, Muller SJ, Phys. Fluids, 9, 566 (1997)
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Cole JA, J. Fluid Mech., 75, 1 (1976)
Coles D, J. Fluid Mech., 21, 385 (1965)
Coles D, J. Appl. Mech., 34, 529 (1967)
Crumeyrolle O, Mutabazi I, Grisel M, Phys. Fluids, 14, 1681 (2002)
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Di Prima RC, Swinney HL, Instabilities and transition in flow between concentric rotating cylinders, in Hydrodynamic Instabilities and the Transition to Turbulence, 2nd ed., Swinney HL, Gollub JP, editors, Springer-Verlag, Berlin. (1985)
Dutcher CS, Experimental investigations into the transitions to turbulence in newtonian and drag-reducing polymeric taylor-couette flows, Ph.D. Dissertation, University of California, Berkeley. (2009)
Dutcher CS, Muller SJ, Phys. Rev. E, 755, 047301 (2007)
Dutcher CS, Muller SJ, J. Fluid Mech., 641, 85 (2009)
Dutcher CS, Muller SJ, Effects of low elasticity on the stability of high Reynolds number co- and counter-rotating Taylor-Couette flows, in preparation. (2009)
Esser A, Grossmann S, Phys. Fluids., 8, 1814 (1996)
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Walden RW, Donnelly RJ, Phys. Rev. Lett., 42, 301 (1979)
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[1] Andereck CD, Liu SS, Swinney HL, J. Fluid Mech., 164, 155 (1986)

[2] BAUMERT BM, MULLER SJ, Rheol. Acta, 34(2), 147 (1995)

[3] Baumert BM, Liepmann D, Muller SJ, J. Non-Newton. Fluid Mech., 69(2-3), 221 (1997)

[4] Baumert BM, Muller SJ, Phys. Fluids, 9, 566 (1997)

[5] Baumert BM, Muller SJ, J. Non-Newton. Fluid Mech., 83(1-2), 33 (1999)

[6] Cole JA, J. Fluid Mech., 75, 1 (1976)

[7] Coles D, J. Fluid Mech., 21, 385 (1965)

[8] Coles D, J. Appl. Mech., 34, 529 (1967)

[9] Crumeyrolle O, Mutabazi I, Grisel M, Phys. Fluids, 14, 1681 (2002)

[10] Denn MM, Roisman JJ, AIChE J., 15, 454 (1969)

[11] Di Prima RC, Swinney HL, Instabilities and transition in flow between concentric rotating cylinders, in Hydrodynamic Instabilities and the Transition to Turbulence, 2nd ed., Swinney HL, Gollub JP, editors, Springer-Verlag, Berlin. (1985)

[12] Dutcher CS, Experimental investigations into the transitions to turbulence in newtonian and drag-reducing polymeric taylor-couette flows, Ph.D. Dissertation, University of California, Berkeley. (2009)

[13] Dutcher CS, Muller SJ, Phys. Rev. E, 755, 047301 (2007)

[14] Dutcher CS, Muller SJ, J. Fluid Mech., 641, 85 (2009)

[15] Dutcher CS, Muller SJ, Effects of low elasticity on the stability of high Reynolds number co- and counter-rotating Taylor-Couette flows, in preparation. (2009)

[16] Esser A, Grossmann S, Phys. Fluids., 8, 1814 (1996)

[17] Giesekus H, Rheol. Acta, 5, 239 (1966)

[18] Giesekus H, On instabilities in poiseuille and couette flows of viscoelastic fluids, in Progress in Heat and Mass Transfer, 5, ed. Schowalter WR, Luikov AV, Minkowycz WJ, Afgan NH, Permagon, NY, pp. 187-193. (1972)

[19] Ginn RF, Denn MM, AIChE Journal, 15, 450 (1969)

[20] Groisman A, Steinberg V, Phys. Rev. Lett., 77, 1480 (1996)

[21] Groisman A, Steinberg V, Phys. Rev. Lett, 78, 1460 (1997)

[22] Groisman A, Steinberg V, Phys Fluids, 10, 2451 (1998)

[23] Haas R, Buhler K, Rheol Acta, 28, 402 (1989)

[24] Koschmieder EL, Benard cells and Taylor vortices, Cambridge University Press, Cambridge. (1993)

[25] Larson RG, Rheologica Acta, 31, 213 (1992)

[26] Muller SJ, Korea-Aust. Rheol. J., 20(3), 117 (2008)

[27] Petrie CJS, Denn MM, AIChE J., 22, 209 (1976)

[28] Rubin H, Elata C, Phys. Fluids, 9, 1929 (1966)

[29] Shaqfeh ESG, Annual Rev. Fluid Mech., 28, 129 (1996)

[30] Tagg R, Nonlinear Sci. Today, 4, 2 (1994)

[31] Thomas DG, Khomami B, Sureshkumar R, J. Fluid Mech., 620, 353 (2009)

[32] Thomas DG, Sureshkumar R, Khomami B, Phys. Rev. Lett., 97, 054501 (2006)

[33] Thomas DG, Al-Mubaiyedh UA, Sureshkumar R, Khomami B, J. Non-Newton. Fluid Mech., 138(2-3), 111 (2006)

[34] Walden RW, Donnelly RJ, Phys. Rev. Lett., 42, 301 (1979)

[35] White JM, Experimental Investigation of Instabilities in Newtonian and Viscoelastic Taylor-Couette Flows, Ph.D. Dissertation, Flows, Ph.D. Dissertation,

[36] White JM, Muller SJ, J. Fluid Mech., 462, 133 (2002)

[37] White JM, Muller SJ, Phys. Fluids, 14, 3880 (2002)

[38] White JM, Muller SJ, J. Rheol., 47(6), 1467 (2003)

[39] Yi MK, Kim C, J. Non-Newton. Fluid Mech., 72(2-3), 113 (1997)