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Research Papers: Fundamental Issues and Canonical Flows

Effect of Cross Aspect Ratio on Flow in Diverging and Converging Microchannels

[+] Author and Article Information
V. S. Duryodhan

Mechanical Engineering Department,
Indian Institute of Technology Bombay,
Powai, Mumbai 400076, India
e-mail: vijud25@gmail.com

Shiv Govind Singh

Electrical Engineering Department,
Indian Institute of Technology Hyderabad,
Hyderabad 502205, India
e-mail: sgsingh@iith.ac.in

Amit Agrawal

Mechanical Engineering Department,
Indian Institute of Technology Bombay,
Powai, Mumbai 400076, India
e-mail: aagrawal.iitb@gmail.com

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 15, 2016; final manuscript received January 17, 2017; published online April 20, 2017. Assoc. Editor: Moran Wang.

J. Fluids Eng 139(6), 061203 (Apr 20, 2017) (9 pages) Paper No: FE-16-1610; doi: 10.1115/1.4035945 History: Received September 15, 2016; Revised January 17, 2017

Aspect ratio is an important parameter in the study of flow through noncircular microchannel. In this work, three-dimensional numerical study is carried out to understand the effect of cross aspect ratio (height to width) on flow in diverging and converging microchannels. Three-dimensional models of the diverging and converging microchannels with angle: 2–14 deg, aspect ratio: 0.05–0.58, and Reynolds number: 130–280 are employed in the simulations with water as the working fluid. The effects of aspect ratio on pressure drop in equivalent diverging and converging microchannels are studied in detail and correlated to the underlying flow regime. It is observed that for a given Reynolds number and angle, the pressure drop decreases asymptotically with aspect ratio for both the diverging and converging microchannels. At small aspect ratio and small Reynolds number, the pressure drop remains invariant of angle in both the diverging and converging microchannels; the concept of equivalent hydraulic diameter can be applied to these situations. Onset of flow separation in diverging passage and flow acceleration in converging passage is found to be a strong function of aspect ratio, which has not been shown earlier. The existence of a critical angle with relevance to the concept of equivalent hydraulic diameter is identified and its variation with Reynolds number is discussed. Finally, the effect of aspect ratio on fluidic diodicity is discussed which will be helpful in the design of valveless micropump. These results help in extending the conventional formulae made for uniform cross-sectional channel to that for the diverging and converging microchannels.

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Figures

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Fig. 1

Schematic representation of the location of the equivalent hydraulic diameter for (a) diverging microchannel and (b) converging microchannel. (Note: the rectangle drawn using full line indicates the equivalent straight uniform cross-sectional microchannel of diverging and converging microchannels with widths equal to the width at their corresponding characteristic locations.)

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Fig. 2

Schematic of diverging and uniform cross-sectional microchannels with constant equivalent hydraulic diameter at L/3

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Fig. 3

(a) Pressure drop versus divergence angle and (b) variation of f · Re with divergence angle at different aspect ratios

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Fig. 4

(a) Pressure drop versus convergence angle and (b) variation of f · Re with convergence angle at different aspect ratios

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Fig. 5

Velocity vector along flow direction in 8 deg ((a)–(c)) and 12 deg ((d)–(f)) diverging microchannels with varying aspect ratios. (f) The formation of secondary flow in 12 deg diverging microchannel at aspect ratio of 0.5. (A) Diverging (θ = 8 deg)—(a) θ = 8 deg, α = 0.05, (b) θ = 8 deg, α = 0.27, and (c) θ = 8 deg, α = 0.50 and (B) diverging (θ = 12 deg)—(d) θ = 12 deg, α = 0.05, (e) θ = 12 deg, α = 0.27, and (f) θ = 12 deg, α = 0.50.

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Fig. 6

Variation in ratio of inertial to viscous force with aspect ratio for three converging microchannels

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Fig. 7

Critical angle in (a) diverging and (b) converging microchannels (curves shown in both the plots demarcate the boundaries of different flow regimes in diverging and converging microchannels)

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Fig. 8

Fluidic diodicity versus angle of divergence at different aspect ratios, for (a) Re = 130, (b) Re = 180, and (c) Re = 230

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