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Research Papers: Fundamental Issues and Canonical Flows

Numerical Investigation of the Three-Dimensional Pressure Distribution in Taylor Couette Flow

[+] Author and Article Information
David Shina Adebayo

Department of Engineering,
University of Leicester,
University Road,
Leicester LE1 7RH, UK
e-mail: dsa5@le.ac.uk

Aldo Rona

Department of Engineering,
University of Leicester,
University Road,
Leicester LE1 7RH, UK
e-mail: ar45@le.ac.uk

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 31, 2016; final manuscript received May 10, 2017; published online August 8, 2017. Assoc. Editor: Daniel Livescu.

J. Fluids Eng 139(11), 111201 (Aug 08, 2017) (10 pages) Paper No: FE-16-1714; doi: 10.1115/1.4037083 History: Received October 31, 2016; Revised May 10, 2017

An investigation is conducted on the flow in a moderately wide gap between an inner rotating shaft and an outer coaxial fixed tube, with stationary end-walls, by three-dimensional Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD), using the realizable kε  model. This approach provides three-dimensional spatial distributions of static and dynamic pressures that are not directly measurable in experiment by conventional nonintrusive optics-based techniques. The nonuniform pressure main features on the axial and meridional planes appear to be driven by the radial momentum equilibrium of the flow, which is characterized by axisymmetric Taylor vortices over the Taylor number range 2.35×106Ta6.47×106. Regularly spaced static and dynamic pressure maxima on the stationary cylinder wall follow the axial stacking of the Taylor vortices and line up with the vortex-induced radial outflow documented in previous work. This new detailed understanding has potential for application to the design of a vertical turbine pump head. Aligning the location where the gauge static pressure (GSP) maximum occurs with the central axis of the delivery pipe could improve the head delivery, the pump mechanical efficiency, the system operation, and control costs.

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References

Mallock, A. , 1888, “ Determination of the Viscosity of Water,” Proc. R. Soc. London, 45(273–279), pp. 126–132. [CrossRef]
Mallock, A. , 1896, “ Experiments on Fluid Viscosity,” Philos. Trans. R. Soc. London Ser. A, 187, pp. 41–56. [CrossRef]
Taylor, G. I. , 1923, “ Stability of a Viscous Liquid Contained Between Two Rotating Cylinders,” Philos. Trans. R. Soc. London Ser. A, 223(605–615), pp. 289–343. [CrossRef]
Chandrasekhar, S. , 1958, “ The Stability of Viscous Flow Between Rotating Cylinders,” Proc. R. Soc. London Ser. A, 246(1246), pp. 301–311. [CrossRef]
Davis, M. W. , and Weber, E. J. , 1960, “ Liquid-Liquid Extraction Between Rotating Concentric Cylinders,” Ind. Eng. Chem. Res., 52(11), pp. 929–934. [CrossRef]
Bernstein, G. J. , Grodsvenor, D. E. , Lenc, J. F. , and Levitz, N. M. , 1973, “ Development and Performance of a High-Speed Annular Centrifugal Contactor,” Argonne National Laboratory, Lemont, IL, Report No. ANL-7968.
Ogihara, T. , Matsuda, G. , Yanagawa, T. , Ogata, N. , and Fujita, N. M. , 1995, “ Continuous Synthesis of Monodispersed Silica Particles Using Couette-Taylor Vortex Flow,” J. Ceram. Soc. Jpn., 103(1194), pp. 151–154. [CrossRef]
Imamura, T. , Saito, K. , Ishikura, S. , and Nomura, M. , 1993, “ A New Approach to Continuous Emulsion Polymerization,” Polym. Int., 30(2), pp. 203–206. [CrossRef]
Tsao, Y. M. D. , Boyd, E. , and Spaulding, G. , 1994, “ Fluid Dynamics Within a Rotating Bioreactor in Space and Earth Environments,” J. Spacecr. Rockets, 31(6), pp. 937–943. [CrossRef]
Sczechowski, J. G. , Koval, C. A. , and Noble, R. D. , 1995, “ A Taylor Vortex Reactor for Heterogeneous Photocatalysis,” Chem. Eng. Sci., 50(20), pp. 3163–3173. [CrossRef]
Nicholas, A. , 2009, “ Reducing Electrical Energy Consumption by Five Percent,” Grundfos Holding A/S, Bjerringbro, Denmark.
International Energy Agency, 2015, Key World Energy Statistics, Chirat Press, Paris, France.
Couette, M. , 1890, “ Études sur le frottement des liquids,” Ann. Chim. Phys., 6, pp. 433–510.
Jeffreys, H. , 1928, “ Some Cases of Instability in Fluid Motion,” Proc. R. Soc. London Ser. A, 118(779), pp. 195–208. [CrossRef]
Chandrasekhar, S. , 1961, Hydrodynamic and Hydromagnetic Stability, 1st ed., Oxford University Press, Oxford, UK.
Di Prima, R. C. , 1961, “ Stability of Non-Rotationally Symmetric Disturbances for Viscous Flow Between Rotating Cylinders,” Phys. Fluids, 4(6), pp. 751–755. [CrossRef]
Andereck, C. D. , Liu, S. S. , and Swinney, H. L. , 1986, “ Flow Regimes in a Circular Couette System With Independently Rotating Cylinders,” J. Fluid Mech., 164, pp. 155–183. [CrossRef]
Coles, D. , 1965, “ Transition in Circular Couette Flow,” J. Fluid Mech., 21(03), pp. 385–425. [CrossRef]
Koschmieder, E. L. , 1979, “ Turbulent Taylor Vortex Flow,” J. Fluid Mech., 93(03), pp. 515–527. [CrossRef]
Liao, C. B. , Jane, S. J. , and Young, D. L. , 1999, “ Numerical Simulation of Three-Dimensional Couette-Taylor Flows,” Int. J. Numer. Methods Fluids, 29(7), pp. 827–847. [CrossRef]
Czarny, O. , Serre, E. , Bontoux, P. , and Lueptow, R. M. , 2002, “ Spiral and Wavy Vortex Flows in Short Counter-Rotating Taylor-Couette Cells,” Theor. Comput. Fluid Dyn., 16(1), pp. 5–15. [CrossRef]
Serre, E. , Crespo del Arco, E. , and Bontoux, P. , 2001, “ Annular and Spiral Patterns in Flows Between Rotating and Stationary Discs,” J. Fluid Mech., 434, pp. 65–100. [CrossRef]
Adebayo, D. , and Rona, A. , 2015, “ The Persistence of Vortex Structures Between Rotating Cylinders in the 106 Taylor Number Range,” Int. Rev. Aerosp. Eng., 8(1), pp. 16–25.
Adebayo, D. , and Rona, A. , 2015, “ PIV Study of the Flow Across the Meridional Plane of Rotating Cylinders With Wide Gap,” Int. Rev. Aerosp. Eng., 8(1), pp. 26–34.
Wereley, S. T. , and Lueptow, R. M. , 1994, “ Azimuthal Velocity in Supercritical Circular Couette Flow,” Exp. Fluids, 18(1), pp. 1–9. [CrossRef]
Wereley, S. T. , and Lueptow, R. M. , 1998, “ Spatio-Temporal Character of Non-Wavy and Wavy Taylor-Couette Flow,” J. Fluid Mech., 364, pp. 59–80. [CrossRef]
Baier, G. , 1999, “ Liquid-Liquid Extraction Based on a New Flow Pattern: Two-Fluid Taylor-Couette Flow,” Ph.D. thesis, University of Wisconsin, Madison, WI. https://pdfs.semanticscholar.org/d2f0/9b03aeccdf70050b2749bf4050941857a480.pdf
Haut, B. , Amor, H. B. , Coulon, L. , Jacquet, A. , and Halloin, V. , 2003, “ Hydrodynamics and Mass Transfer in a Couette-Taylor Bioreactor for the Culture of Animal Cells,” Chem. Eng. Sci., 58(3–6), pp. 777–784. [CrossRef]
Parker, J. , and Merati, P. , 1996, “ An Investigation of Turbulent Taylor-Couette Flow Using Laser Doppler Velocimetry in a Refractive Index Matched Facility,” ASME J. Fluids Eng., 118(4), pp. 810–818. [CrossRef]
Deng, R. , Arifin, D. Y. , Mak, Y. C. , and Wang, C. , 2009, “ Characterisation of Taylor Vortex Flow in a Short Liquid Column,” J. Am. Inst. Chem. Eng., 55(12), pp. 3056–3065. [CrossRef]
Deng, D. , 2007, “ A Numerical and Experimental Investigation of Taylor Flow Instabilities in Narrow Gaps and Their Relationship to Turbulent Flow in Bearings,” Ph.D. thesis, The University of Akron, Akron, OH. https://etd.ohiolink.edu/rws_etd/document/get/akron1185559974/inline
Deshmukh, S. S. , Vedantam, S. , Joshi, J. B. , and Koganti, S. B. , 2007, “ Computational Flow Modeling and Visualization in the Annular Region of Annular Centrifugal Extractor,” Ind. Eng. Chem. Res., 46(25), pp. 8343–8354. [CrossRef]
Adebayo, D. , and Rona, A. , 2016, “ The Three-Dimensional Velocity Distribution of Wide Gap Taylor-Couette Flow Modelled by CFD,” Int. J. Rotating Mach., 2016, p. 8584067. [CrossRef]
FLUENT, 2009, “FLUENT 12.0 User's Manual Guide,” Fluent, Inc., Lebanon, NH. http://users.ugent.be/~mvbelleg/flug-12-0.pdf
Versteeg, H. K. , and Malalasekera, W. , 1995, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Prentice Hall, Essex, UK.
Anderson, J. D. , 1995, Computational Fluid Dynamics: The Basics With Applications, McGraw-Hill, New York.
Chorin, A. J. , 1968, “ Numerical Solution of the Navier–Stokes Equations,” Math. Comput., 22(104), pp. 745–762. [CrossRef]
Shih, T.-H. , Liou, W. W. , Shabbir, A. , Yang, Z. , and Zhu, J. , 1995, “ A New k-Epsilon Eddy-Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation,” Comput. Fluids, 24(3), pp. 227–238. [CrossRef]
Launder, B. E. , Reece, G. J. , and Rodi, W. , 1975, “ Progress in the Development of a Reynolds-Stress Turbulence Closure,” J. Fluid Mech., 68(3), pp. 537–566. [CrossRef]
Donnelly, R. J. , and Schwarz, K. W. , 1965, “ Experiments on the Stability of Viscous Flow Between Rotating Cylinders. VI. Finite-Amplitude Experiments,” Proc. R. Soc. London Ser. A, 283(1395), pp. 531–556. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) Hexahedral computational mesh structure and (b) computational mesh detail at the end-wall. One mesh point every two in X, r, and θ has been plotted for clarity.

Grahic Jump Location
Fig. 2

Radial velocity profiles at r=Ri+0.500d for three different levels of computational mesh refinement for test cases: (a) Γ = 7.81 and (b) Γ = 11.36. (⋄) Mesh type 1, (◻) mesh type 2, and (⊹) mesh type 3.

Grahic Jump Location
Fig. 3

Normalized (a) axial and (b) radial velocity profiles from PIV and CFD at the constant radial positions r=Ri+0.125d and r=Ri+0.500d on the meridional plane at θ=−0.5π, with the PIV error band. Γ = 7.81.

Grahic Jump Location
Fig. 4

Normalized velocity vectors in the meridional plane of the annulus for test cases: (a) Γ= 7.81 and (b) Γ = 11.36. The reference velocity vector is 0.5 ΩRi.

Grahic Jump Location
Fig. 5

Velocity vectors on different axial planes normalized byΩRi: (a) X/Ri = 0.05, Γ = 7.81, (b) X/Ri = 0.92, Γ = 7.81, (c) X/Ri = 1.47, Γ = 7.81, (d) X/Ri = 1.41, Γ = 11.36, (e) X/Ri = 1.84, Γ = 11.36, and (f) X/Ri = 9.95, Γ = 11.36

Grahic Jump Location
Fig. 6

Normalized gauge static pressure profiles in the meridional plane at constant radial positions: (⊹) r=Ri+0.045d, (⋄) r=Ri+0.500d, and (◻) r=Ri+0.955d for the test cases (a) Γ = 7.81 and (b) Γ = 11.36. (−)  θ=0.5π and (- -) θ=−0.5π.

Grahic Jump Location
Fig. 7

Normalized dynamic pressure profiles in the meridional plane at constant radial positions: (⊹) r=Ri+0.045d, (⋄) r=Ri+0.500d, and (◻) r=Ri+0.955d for the test cases (a) Γ = 7.81 and (b) Γ  = 11.36. (−) θ=0.5π and (- -) θ=−0.5π.

Grahic Jump Location
Fig. 8

Azimuthal profiles of normalized dynamic pressure atdifferent radii on selected axial planes for the test cases:(a)Γ = 7.81 and (b) Γ = 11.36. (⊹) r=Ri+0.045d, (⋄) r=Ri+0.500d, and (◻) r=Ri+0.955d.

Grahic Jump Location
Fig. 9

Normalized gauge static pressure profiles on different axial planes at θ=−0.5π: (a) Γ = 7.81 and (b) Γ = 11.36

Grahic Jump Location
Fig. 10

Normalized dynamic pressure profiles on different axial planes at θ=−0.5π: (a) Γ = 7.81 and (b) Γ = 11.36

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