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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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. 2

Experimental setup

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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

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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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