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Research Papers: Flows in Complex Systems

Flow Characteristics in a Curved Rectangular Channel With Variable Cross-Sectional Area

[+] Author and Article Information
Avijit Bhunia

 Teledyne Scientific Company, 1049 Camino Dos Rios, MC A10, Thousand Oaks, CA 91360abhunia@teledyne.com

C. L. Chen

 Teledyne Scientific Company, 1049 Camino Dos Rios, MC A10, Thousand Oaks, CA 91360

J. Fluids Eng 131(9), 091102 (Aug 13, 2009) (16 pages) doi:10.1115/1.3176970 History: Received September 10, 2008; Revised May 29, 2009; Published August 13, 2009

Laminar air flow through a curved rectangular channel with a variable cross-sectional (c/s) area (diverging-converging channel) is computationally investigated. Such a flow passage is formed between the two fin walls of a 90 deg bend curved fin heat sink, used in avionics cooling. Simulations are carried out for two different configurations: (a) a curved channel with long, straight, constant c/s area inlet and outlet sections (entry and exit lengths); and (b) a short, curved channel with no entry and exit lengths. Formation of a complex 3D flow pattern and its evolution in space is studied through numerical flow visualization. Results show that a secondary motion sets in the radial direction of the curved section, which in combination with the axial (bulk) flow leads to the formation of a base vortex. In addition, under certain circumstances the axial and secondary flow separate from multiple locations on the channel walls, creating Dean vortices and separation bubbles. Velocity above which the Dean vortices appear is cast in dimensionless form as the critical Dean number, which is calculated to be 129. Investigation of the friction factor reveals that pressure drop in the channel is governed by both the curvature effect as well as the area expansion effect. For a short curved channel where area expansion effect dominates, pressure drop for developing flow can be even less than that of a straight channel. A comparison with the flow in a constant c/s area, curved channel shows that the variable c/s area channel geometry leads to a lower critical Dean number and friction factor.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A schematic of curved fin heat sink. Representative air flow paths between two sets of fins are shown by red arrows.

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Figure 2

Schematics of secondary flow structures in a curved channel. (a) Secondary flow conformal to all the walls occurs at low axial flow velocity (Vi), (b) secondary flow separation from multiple walls at higher Vi, and (c) main/base secondary flow and additional recirculation cells due to secondary flow separation.

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Figure 3

Schematic of an individual flow passage between two fins, a long channel, and the numerical simulation domain

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Figure 8

Formation of secondary flow at various angular positions along a 90 deg bend of a long (diverging-converging) VACC. Re=2017 and De=1008 based on uniform flow velocity (Vi) and hydraulic diameter (Dh) at channel inlet, and properties at average temperature [Tav=(Ti+Tw)/2]. Lav/Dh=39.1, Lentry/Dh=16.1, and Lexit/Dh=16.1. AR=2.3, CR=5.6. Views: (a) angular position 11 deg, (b) 22.5 deg, (c) 56 deg, (d) 67.5 deg, and (e) 90 deg outlet from the curved portion of the channel or beginning of the straight constant c/s area exit channel.

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Figure 9

Oil flow lines on the curved section (90 deg bend) of a long VACC. Re=2017 and De=1008, Lav/Dh=39.1, Lentry/Dh=16.1, Lexit/Dh=16.1. AR=2.3, and CR=5.6. (a) ICW or concave wall, (b) OCW or convex wall, and (c) TW. All views are looking into the wall from front.

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Figure 10

Schematics of various 3D flow patterns in the curved section (90 deg bend) of a long VACC. Re=2017 and De=1008, Lav/Dh=39.1, Lentry/Dh=16.1, Lexit/Dh=16.1. AR=2.3, and CR=5.6. (a) Axial flow separation near OCW and the resulting base vortex structure at the early part of the curved channel, (b) axial and secondary flow separation from ICW, and formation of closed separation bubble, and (c) base vortex, split base vortex, and multiple Dean vortices at the converging section of the channel.

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Figure 12

Formation of secondary flow at various angular positions along a 90 deg bend of a short VACC. Re=2017, and De=1008, Lav/Dh=6.8, Lentry/Dh=Lexit/Dh=0, AR=2.3, and CR=5.6. View (a) angular position 11 deg, (b) 37 deg, (c) 45 deg, (d) 67.5 deg, and (e) 89 deg, just prior to the channel and curvature outlet.

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Figure 13

The effects of flow velocity and channel geometry on the pressure drop (ΔP) between the channel inlet and outlet. Pressure drop expressed in dimensionless form as product of friction factor and Reynolds number (f Re), and velocity as L+. (a) Long channel and (b) short channel.

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Figure 4

Validation of the numerical model against the experimental data of Sugiyama (6). (a) Schematic of the experimental channel geometry—constant cross-sectional area curved channel with a 180 deg bend. Lentry=1000 mm, b=20 mm, CR=R/b=5, and H and AR(=H/b) variable; (b) comparison of numerical prediction of the critical Dean number (Decrit) with the experimental data (6).

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Figure 5

Formation of secondary flow at various angular positions along a 90 deg bend of a long CACC. Re=2017 and De=1008 based on uniform flow velocity (Vi) and hydraulic diameter (Dh) at channel inlet, and properties at average temperature [Tav=(Ti+Tw)/2]. Lav/Dh=39.1, Lentry/Dh=16.1, Lexit/Dh=16.1, AR=2.3, and CR=5.6. Views: (a) angular position 11 deg, (b) 22.5 deg, (c) 37 deg, (d) 56 deg, and (e) 90 deg (outlet from the curved portion of the channel or beginning of the straight constant c/s area exit channel).

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Figure 6

Oil flow lines on the walls of the curved section (90 deg bend) of a long CACC. Re=2017 and De=1008, Lav/Dh=39.1, Lentry/Dh=16.1, Lexit/Dh=16.1, AR=2.3, and CR=5.6. (a) ICW or concave wall, (b) OCW or convex wall, and (c) TW. All views are looking into the wall from front.

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Figure 7

Schematics of various 3D flow patterns in the curved section (90 deg bend) of a long CACC. Re=2017 and De=1008, Lav/Dh=39.1, Lentry/Dh=16.1, Lexit/Dh=16.1, AR=2.3, and CR=5.6. (a) Axial flow separation from ICW near the corner region and formation of a separation bubble, and (b) base vortex and other Dean vortices, such as corner region Dean vortex, ICW Dean vortex, and OCW Dean vortex.

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Figure 11

Effect of axial flow velocity (Re and De) on the growth of secondary flow at the curvature outlet (at the 90 deg bend) of a long VACC. Lav/Dh=39.1, Lentry/Dh=16.1, Lexit/Dh=16.1. AR=2.3, and CR=5.6. (a) Re=183, De=92; (b) Re=366, De=183; and (c) Re=732, De=366. Re and De are based on uniform inlet flow velocity (Vi), hydraulic diameter (Dh) at channel inlet, and properties at average temperature [Tav=(Ti+Tw)/2].

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