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TECHNICAL PAPERS

On the Nearly Viscometric Torsional Motion of Viscoelastic Liquids Between Shrouded Rotating Disks

[+] Author and Article Information
Dennis A. Siginer

Department of Mechanical Engineering, College of Engineering, Wichita State University, Wichita, KS 67260-0133e-mail: dennis.siginer@wichita.edu

J. Appl. Mech 71(3), 305-313 (Jun 22, 2004) (9 pages) doi:10.1115/1.1651538 History: Received January 02, 2001; Revised September 19, 2003; Online June 22, 2004
Copyright © 2004 by ASME
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References

Dorfman,  L. A., and Romanenko,  Yu. B., 1966, “Flow of a Viscous Fluid in a Cylindrical Vessel With a Rotating Cover,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1, pp. 63–69.
Pao,  H., 1970, “A Numerical Computation of the Confined Rotating Flow,” ASME J. Appl. Mech., 37, pp. 480–487.
Pao,  H., 1972, “Numerical Solution of the Navier-Stokes Equations for Flows in the Disk-Cylinder System,” Phys. Fluids, 15, pp. 4–11.
Dijkstra,  D., and Van Heijst,  G. J. F., 1983, “The Flow Between Finite Rotating Disks Enclosed by a Cylinder,” J. Fluid Mech., 128, pp. 123–154.
Duck,  P. W., 1986, “On the Flow Between Two Rotating Shrouded Disks,” Comput. Fluids, 14, pp. 183–196.
Kramer,  J. M., and Johnson,  M. W., 1972, “Nearly Viscometric Flow in the Disk and Cylinder System. I: Theoretical,” Trans. Soc. Rheol., 16, pp. 197–212.
Hill,  C. T., 1972, “Nearly Viscometric Flow of Viscoelastic Fluids in the Disk and Cylinder System II: Experimental,” Trans. Soc. Rheol., 16, pp. 213–245.
Escudier,  M. P., and Cullen,  L. M., 1996, “Flow of a Shear-Thinning Liquid in a Container With a Rotating End Well,” Exp. Therm. Fluid Sci., 12, pp. 381–387.
Itoh,  M., Moroi,  T., and Toda,  H., 1998, “Viscoelastic Flow due to a Rotating Disc Enclosed in a Cylindrical Casing,” Trans. Jpn. Soc. Mech. Eng.,64, (621), pp. 1351–1358.
Itoh, M., Suzuki, M., and Moroi, T., 2003, “Swirling Flow of Viscoelastic Fluids in a Cylindrical Casing,” Proceedings of the 4th ASME-JSME Joint Fluids Engineering Conference, Honolulu, HI, July 6–10, ASME, New York.
Moroi,  T., Itoh,  M., and Fujita,  K., 1999, “Viscoelastic Flow due to a Rotating Disc in a Cylindrical Casing (Numerical Simulation and Experiment),” Trans. Jpn. Soc. Mech. Eng., 65 (639), pp. 3361–3568 (in Japanese).
Moroi,  T., Itoh,  M., Fujita,  K., and Hamasaki,  H., 2001, “Viscoelastic Flow due to Rotating Disc Enclosed in a Cylindrical Casing (Influence of Aspect Ratio),” JSME Int. J. Ser. B: Fluids Therm. Eng., 44 (3), pp. 465–475.
Stokes,  J. R., Graham,  L. J. W., Lawson,  N. J., and Boger,  D. V., 2001, “Swirling Flow of Viscoelastic Fluids, Part I: Interaction Between Inertia and Elasticity,” J. of Fluid Mech., 429, pp. 67–115.
Stokes,  J. R., Graham,  L. J. W. Lawson,  N. J., and Boger,  D. V., 2001, “Swirling Flow of Viscoelastic Fluids, Part II: Elastic Effects,” J. Fluid Mech.,429, pp. 117–153.
Hort,  W., 1920, “Die Geschwindigkeitsverteilung im Inneren rotierender zäher Flüssigkeiten,” Z. Tech. Phys. (Leipzig), 1, pp. 213–221.
Siginer,  D. A., and Knight,  R., 1993, “Swirling Free Surface Flow in Cylindrical Containers,” J. Eng. Math., 27, pp. 245–264.
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Figures

Grahic Jump Location
Level lines of azimuthal velocity: δ=0.5; caps counterrotating with the top cap twice as fast as the bottom, λ=−2
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Level lines of azimuthal velocity: δ=0.5; same sense rotation with the top cap rotating twice as fast as the bottom, λ=2
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Contour lines of the dimensionless Newtonian second-order stream function δ=2, λ=−2
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Meridional flow configurations in a tall cylinder, δ=2, at fixed cap rotation ratio |λ|=2, with varying dimensionless elasticity parameter β. (a) β<0.01; (b) β<βcr; (c) β=βcr+ε; (d) β=βcr−ε; (e) β=β⁁cr+ε; (f) β>β⁁cr; (g) β≫β⁁cr; (h) β=0.1.
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Meridional flow configurations in a tall cylinder, δ=2, at a fixed value of the elasticity parameter β such that β<β⁁cr, with varying cap ratio λ. (a) −2<λ<−1; λ→−1; (b) λ=±1; (c) −1<λ<0; λ→0; (d) λ=0 (e) 0<λ<1; λ→1; (f) 1<λ<2; λ→2; (g) λ=λcr+ε (h) λ>λcr (i) λ≫λcr.
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Same as Fig. 6 except for β>β⁁cr. (a) λ=±1; (b) −1<λ<0; λ→0; (c) λ=0; (d) λ=λcr+ε (e) λ>λcr; (f) λ≫λcr.
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Bifurcated flow field configuration in the meridional plane. β is slightly larger than βcr. β=0.03, δ=2, λ=−2.
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Bifurcated flow field configuration in the meridional plane. β is slightly larger than β⁁cr. β=0.0375, δ=2, λ=−2.
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Dimensionless meridional stream function contours. β=0.1, δ=2, λ=−2.
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Dimensionless meridional stream function contours. β=0.03, δ=2, λ=−1.
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Same as Fig. 11 except for β=0.0375
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Same as Fig. 11 except for λ=0
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Same as Fig. 13 except for β=0.0375
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Bifurcated meridional flow field configuration. β is slightly larger than βcr; β=0.03, δ=1, λ=−2.
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Bifurcated meridional flow field configuration. β is slightly larger than β⁁cr; β=0.0375, δ=1, λ=−2.
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Dimensionless meridional stream function contours. β=0.1, δ=1, λ=−2.
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Dimensionless meridional stream function contours. β=0.0375, δ=1, λ=0.
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Contour lines of the dimensionless Newtonian second-order stream function; δ=0.5, λ=2. If λ=−2, the field is qualitatively the same with a stronger and weaker corner and central eddy, respectively.
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Bifurcated meridional flow field configuration. β is slightly larger than βcr. β=0.02, δ=0.5, λ=−2.
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Bifurcated meridional flow field configuration. β is somewhat larger than βcr. β=0.0375, δ=0.5, λ=−2.
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Dimensionless meridional stream function contours. β=0.1, δ=0.5, λ=−2.

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