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Research Papers: Fundamental Issues and Canonical Flows

Measurement of Fluid Flow Thickness Within a Rotating Cone

[+] Author and Article Information
Digby D. Symons

Cambridge University Engineering Department,
Trumpington Street,
Cambridge CB2 1PZ, UK
e-mail: digby.symons@eng.cam.ac.uk

Arnaud F. M. Bizard

Cambridge University Engineering Department,
Trumpington Street,
Cambridge CB2 1PZ, UK
e-mail: abizard@gmail.com

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 12, 2014; final manuscript received January 12, 2015; published online March 11, 2015. Assoc. Editor: Riccardo Mereu.

J. Fluids Eng 137(6), 061206 (Jun 01, 2015) (7 pages) Paper No: FE-14-1507; doi: 10.1115/1.4029728 History: Received September 12, 2014; Revised January 12, 2015; Online March 11, 2015

This paper reports experimental measurements of film thickness for continuous fluid flow on the internal surface of a cone rotating about a vertical axis. Measurements were obtained via an optical method based on photographing the displacement of a grid projected onto the surface of the flow within the cone. Results are compared to analytical theory for axisymmetric, steady state, free-surface laminar flow of a Newtonian fluid in a spinning cone. The theory assumes that the flow is thin but takes account of gravity. The theoretical model is found to be in good agreement with the experimental results.

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References

Bruin, S., 1969, “Velocity Distributions in a Liquid Film Flowing Over a Rotating Conical Surface,” Chem. Eng. Sci., 24(11), pp. 1647–1654. [CrossRef]
Makarytchev, S. V., Xue, E., Langrish, T. A. G., and Prince, R. G. H., 1997, “On Modeling Fluid Flow Over a Rotating Conical Surface,” Chem. Eng. Sci., 52(6), pp. 1055–1057. [CrossRef]
Makarytchev, S. V., Langrish, T. A. G., and Prince, R. G. H., 1998, “Structure and Regimes of Liquid Film Flow in Spinning Cone Columns,” Chem. Eng. Sci., 53(8), pp. 1541–1550. [CrossRef]
Symons, D. D., 2011, “Integral Methods for Flow in a Conical Centrifuge,” Chem. Eng. Sci., 66(13), pp. 3020–3029. [CrossRef]
Ruschak, K. J., and Weinstein, S. J., 2003, “Laminar, Gravitationally Driven Flow of a Thin Film on a Curved Wall,” ASME J. Fluids Eng., 125(1), pp. 10–17. [CrossRef]
Miyasaka, Y., 1974, “On the Flow of a Viscous Free Boundary Jet on a Rotating Disk (2nd Report Comparison of Experimental Results With Calculated Values by Means of Film Thickness),” Bull. JSME, 17(113), pp. 1469–1475. [CrossRef]
Thomas, S., Faghri, A., and Hankey, W., 1991, “Experimental Analysis and Flow Visualization of a Thin Liquid Film on a Stationary and Rotating Disk,” ASME J. Fluids Eng., 113(1), pp. 73–80. [CrossRef]
Makarytchev, S. V., Langrish, T. A. G., and Prince, R. G. H., 2001, “Thickness and Velocity of Wavy Liquid Films on Rotating Surfaces,” Chem. Eng. Sci., 56(1), pp. 77–87. [CrossRef]
Lan, H., Wegener, J. L., Armaly, B. F., and Drallmeier, J. A., 2010, “Developing Laminar Gravity-Driven Thin Liquid Film Flow Down an Inclined Plane,” ASME J. Fluids Eng., 132(8), p. 081301. [CrossRef]
Symons, D. D., and Bizard, A. F. M., 2014, “Measurement of Film Thickness for Continuous Fluid Flow Within a Spinning Cone,” 12th Biennial Conference on Engineering Systems Design and Analysis, Volume 2: Dynamics, Vibration and Control; Energy; Fluids Engineering; Micro and Nano Manufacturing, July 25, Paper No. ESDA2014-20129.
Bizard, A. F. M., 2011, “Design of Conical Centrifugal Filters—An Analytical Approach,” Ph.D. thesis, Cambridge University Engineering Department, Cambridge, UK.

Figures

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Fig. 2

Experimental setup

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Fig. 4

Thickness measurement setup: (a) general principle and (b) grid displacement with calibration gauge

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Fig. 5

Typical grid picture. The coordinates of the 1st, ith, and nth grid points are indicated.

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Fig. 6

Thickness t versus grid displacement for the calibration gauges at midpoint (i ≈ n/2) for α = 30 deg

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Fig. 7

Black treacle viscosity versus temperature: data and second-order hyperbolic interpolation

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Fig. 8

Experimental profiles compared to theory for α = 30 deg and m·≈1.2 kg/min

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Fig. 9

Nondimensional thickness profile compared to the theoretical model for α = 30 deg, G = 2.29, and H∧ = 0.11

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Fig. 10

Error against slenderness ratio H∧ for the set of experiments described in Table 3

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Fig. 11

Error against relative centripetal acceleration G for the set of experiments described in Table 3

Tables

Errata

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