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Research Papers: Fundamental Issues and Canonical Flows

Laminar, Radial Flow of Two Immiscible Fluids in Slender Wedge-Shaped Passages

[+] Author and Article Information
H. M. Soliman

Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB R3T 5V6, Canada
e-mail: hassan.soliman@umanitoba.ca

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 17, 2016; final manuscript received March 1, 2017; published online May 17, 2017. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 139(8), 081201 (May 17, 2017) (8 pages) Paper No: FE-16-1375; doi: 10.1115/1.4036266 History: Received June 17, 2016; Revised March 01, 2017

The Jeffery–Hamel problem for laminar, radial flow between two nonparallel plates has been extended to the case of two immiscible fluids in slender channels. The governing continuity and momentum equations were solved numerically using the fourth-order Runge–Kutta method. Solutions were obtained for air–water at standard conditions over the void-fraction range of 0.4–0.8 (due to its practical significance) and the computations were limited to conditions where unique solutions were found to exist. The void fraction, pressure gradient, wall friction coefficient, and interfacial friction coefficient are dependent on the Reynolds numbers of both fluids and the complex nature of this dependence is presented and discussed. An attempt to use a one-dimensional two-fluid model with simplified assumptions succeeded in producing a qualitatively similar form of the void-fraction dependence on the two Reynolds numbers; however, quantitatively there are significant deviations between these results and those of the complete model.

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Copyright © 2017 by ASME
Topics: Fluids , Radial flow
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Figures

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Fig. 1

Geometry and coordinate system for the single-fluid problem

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Fig. 2

Comparison between the full model and the slender model

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Fig. 3

Geometry and coordinate system for the two-fluid problem

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Fig. 4

Rea versus Reb at high α

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Fig. 5

(a) Shape of velocity profile at point 1 at high α, (b) shape of velocity profile at point 2, and (c) shape of velocity profile at point 3

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Fig. 6

Rea versus Reb at low α

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Fig. 7

Shape of velocity profile at point 1 at low α

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Fig. 8

Rea versus Reb for 0.4≤α≤0.8

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Fig. 10

Contours of Cf,w*

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Fig. 11

Contours of Cf,i*

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Fig. 12

Rea versus Reb at various α from the simplified one-dimensional model

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