Start-up times in viscoelastic channel and pipe flows

A.I.P. Miranda; P.J. Oliveira

Korea-Australia Rheology Journal, Vol.22, No.1, 65-73, March, 2010

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Start-up times in viscoelastic channel and pipe flows

A.I.P. Miranda, and P.J. Oliveira^{1, †}

Departamento de Matem´atica, Universidade da Beira Interior, 6200-001 Covilh~a, Portugal
¹Departamento de Engenharia Electromec^anica, Unidade de Materiais T^exteis e Papeleiros, Universidade da Beira Interior, 6200-001 Covilh~a, Portugal

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Start-up times in viscoelastic channel and pipe flows generated by the sudden imposition of a pressure gradient are here determined by a mixed analytical/numerical procedure. The rheological models considered are the upper convected Maxwell and the Oldroyd-B equations. With these models the flow evolves asymptotically to the steady state solution after a transient regime presenting strong oscillations of the velocity fields, hence implying a special procedure for the calculation of the start-up time. This time interval required for establishment of steady flow tends to increase significantly with elasticity, at a constant rate of increase for the UCM model, but the increase becoming less than linear for the Oldroyd-B model. No wiggles or artificial oscillations were observed for the variation of the start-up times with the elasticity number.

Keywords:start-up flow;channel or pipe flow;transient viscoelastic flow;Oldroyd-B;UCM

[References]

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[1] Akyildiz FT, Jones RS, Rheologica Acta, 32, 499 (1993)

[2] Bird RB, Armstrong RC, Hassager O, Dynamics of Polymeric Liquids, Vol. 1: Fluid Mechanics, 2nd ed., John Wiley, New York. (1987)

[3] Balmer RT, Fiorina MA, J. Non-Newtonian Fluid Mech., 7, 189 (1980)

[4] Bromwich TJ, J. London Math. Soc., 5, 10 (1930)

[5] Duarte ASR, Miranda AIP, Oliveira PJ, J. Non-Newton. Fluid Mech., 154(2-3), 153 (2008)

[6] Letelier MF, Cespedes JF, Laminar Unsteady Flow of Elementary Non-Newtonian Fluids in Long Pipes, Chapter 3 in Encyclopedia of Fluid Mechanics, Vol. 7, Rheology and Non-Newtonian Flows, Ed. N.P. Cheremisinoff, Golf Publishing Company, Houston, 55-87. (1988)

[7] Oldroyd JG, Proc R. Soc. A, 200, 523 (1950)

[8] Park KS, Kwon YD, Korea-Aust. Rheol. J., 21(1), 47 (2009)

[9] RAHAMAN KD, RAMKISSOON H, J. Non-Newton. Fluid Mech., 57(1), 27 (1995)

[10] Ren L, Zhu KQ, Chin. Phy. Let., 21, 114 (2004)

[11] Sestak J, Charles ME, Chem. Eng. Sci., 23, 1127 (1968)

[12] Szymanski P, J. Math. Pures Appl. (Series 9), 11, 67 (1932)

[13] Waters ND, King MJ, Rheologica Acta, 9, 345 (1970)

[14] Waters ND, King MJ, J. Phys.D: Appl. Phys., 4, 204 (1971)

[15] Wood WP, J. Non-Newton. Fluid Mech., 100(1-3), 115 (2001)

[16] Zhen L, Zhu KQ, Acta Mech. Sin., (in press), 26 (2010)