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Research Papers: Fundamental Issues and Canonical Flows

A Numerical Investigation of Developing Flow in Concentric and Eccentric Curved Square Annuli

[+] Author and Article Information
M. R. H. Nobari

Professor
e-mail: mrnobari@aut.ac.ir

D. Rajaei

Department of Mechanical Engineering,
Amirkabir University of Technology,
424 Hafez Avenue,
P. O. Box 15875-4413,
Tehran, Iran

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 19, 2011; final manuscript received February 24, 2013; published online June 3, 2013. Editor: Malcolm J. Andrews.

J. Fluids Eng 135(8), 081201 (Jun 03, 2013) (12 pages) Paper No: FE-11-1451; doi: 10.1115/1.4024182 History: Received November 19, 2011; Revised February 24, 2013

In this article developing incompressible viscous fluid flow in concentric and eccentric curved square annuli are numerically studied. A second order finite difference method based on the projection algorithm is implemented to solve the governing equations, including the full Navier–Stokes and continuity equations in a cylindrical coordinate system. To discretize the governing equations in the square annulus, a uniform staggered grid is used to enforce an exact second order numerical scheme. The effects of the governing nondimensional parameters involving the aspect ratio, curvature, Reynolds number, Dean number, and eccentricity on the flow field, both in developing and fully developed regions of the curved annular square duct, are studied in detail. The numerical results obtained indicate that the friction factor in the eccentric curved square annulus increases with the square root of the Dean number (κ1/2) and the aspect ratio and decreases with the eccentricity. Furthermore, when the square root of the Dean number becomes larger than about 17.3, the friction factor increases linearly with the square root of the Dean number in the range of the current study.

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Figures

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Fig. 1

Cylindrical coordinates and geometry of the curved annular duct

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Fig. 9

Secondary flow streamlines in the developing region for δr = 0.3 and δc = 1/15: (a) ε = 0.2, κ = 51.64 (Re = 100), (b) ε = 0.4, κ = 103.28 (Re = 200), and (c) ε = 0.6, κ = 206.56 (Re = 400)

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Fig. 10

Axial velocity contour lines and the secondary flow field at six different eccentricities of the eccentric curved annulus for κ = 226.78 (Re = 300) and δc = 1/7

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Fig. 11

Development history of the axial velocity on the plane of symmetry and on the midplane between the symmetry plane and the top plane of the inner duct for four different eccentricities, δc = 1/7, and δr = 0.3

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Fig. 12

Friction factor versus the square root of the Dean number for different eccentricities at δc = 1/15

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Fig. 13

Friction factor versus the square root of the Dean number for different eccentricities at δc = 1/7

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Fig. 8

Contours of the axial velocity in the developing region for δr = 0.3 and δc = 1/15: (a) ε = 0.2, κ = 51.64 (Re = 100), (b) ε = 0.4, κ = 103.28 (Re = 200), and (c) ε = 0.6, κ = 206.56 (Re = 400)

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Fig. 7

Friction factor versus the square root of the Dean number

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Fig. 6

Development history of the axial velocity on the symmetry plane and on the midplane between the symmetry plane and the top plane of the inner duct for δc = 1/7 at δr = 0.3

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Fig. 5

Axial velocity contour (lines) in the fully developed region at three different aspect ratios and two curvatures for Re 200 (a) δc = 1/7, κ = 151.18, and (b) δc = 1/15, κ = 103.28

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Fig. 4

Secondary flow streamlines for κ = 453.6 and δc = 1/7

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Fig. 3

Contours of the axial velocity in the developing region for κ = 453.6 and δc = 1/7

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Fig. 2

Friction factor ratio versus the axial direction of the eccentric curved square annulus at κ = 189, δc = 1/7, and δr = 0.5 for four different eccentricities

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