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TECHNICAL PAPERS: Forced Convection

Turbulent Plane Couette Flow and Scalar Transport at Low Reynolds Number

[+] Author and Article Information
Chun-Ho Liu

Department of Mechanical Engineering, The University of Hong Kong, Hong Kong

J. Heat Transfer 125(6), 988-998 (Nov 19, 2003) (11 pages) doi:10.1115/1.1571084 History: Received May 02, 2002; Revised February 05, 2003; Online November 19, 2003
Copyright © 2003 by ASME
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Figures

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Vertical profiles of mean vertical turbulent heat flux 〈Tw〉 (–), mean vertical viscous heat flux −1/(Re Pr) ∂〈T〉/∂z ([[dashed_line]] [[dashed_line]]), and their sum (⋯⋯) normalized by Tτuτ for turbulent Couette flow at Re=3000
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Vertical profiles of mean streamwise turbulent heat flux 〈Tu〉 normalized by Tτuτ for turbulent plane Couette flow at Re=3000
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Vertical profiles of dimensionless mean streamwise velocity 〈u〉 for turbulent Couette flow at Re=3000: (a) dimensionless global coordinates; and (b) wall coordinates. ○: present calculation, ⋯⋯: u+=z+, —⋅ —⋅ —⋅: u+=4.7 ln z+−2.56, –⋅⋅–⋅⋅–⋅⋅: u+=2.33 ln z++4.96, ⋄: DNS from Kim et al. 4, and □: measurements from Žukauskas and Šlančiauskas 28.
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Vertical profiles of mean vertical turbulent flux 〈uw〉 (–), mean viscous flux −1/Re ∂〈u〉/∂z ([[dashed_line]][[dashed_line]]), and their sum (⋯⋯), normalized by uτ2 for turbulent Couette flow at Re=3000.
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Vertical profiles of root-mean-square velocity fluctuation normalized by wall friction velocity for turbulent Couette flow at Re=3000: (a) dimensionless global coordinates; and (b) wall coordinates. –: 〈uu1/2/uτ, [[dashed_line]] [[dashed_line]]: 〈vv1/2/uτ and ⋯⋯: 〈ww1/2/uτ. ⋄: measurement from Aydin and Leutheusser 30, □: measurement from Bech et al. 11, ▵: DNS from Lee and Kim 10, and ○: DNS from Papavassiliou and Hanratty 13.
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Vertical profiles of dimensionless mean temperature 〈T〉 for turbulent Couette flow at Re=3000: (a) dimensionless global coordinates; and (b) wall coordinates. ○: present calculation, ⋯⋯: T+=Prz+, — ⋅ —⋅—⋅: T+=2.63 ln z++1.2, □: measurement from Žukauskas and Šlančiauskas 28, ▵: DNS from Kim and Moin 17, and ⋄: LES from Cabot and Moin 34.
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Vertical profiles of correlation coefficients between streamwise u and vertical w velocities (–), temperature T and streamwise velocity u ([[dashed_line]] [[dashed_line]]), and temperature T and vertical velocity w (⋯⋯)
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Vertical profile of root-mean-square temperature fluctuation 〈TT1/2 normalized by friction temperature Tτ for turbulent Couette flow at Re=3000: (a) dimensionless global coordinates; and (b) wall coordinates.
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Vertical profiles of the terms in turbulent kinetic energy 〈uiui/2〉 budget Eq. (7) for turbulent Couette flow at Re=3000. – production, ⋯⋯ dissipation, ⋄ viscous diffusion, × velocity-pressure gradient correlation, ▿ turbulent diffusion and [[dashed_line]] [[dashed_line]] total diffusion
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Vertical profiles of the terms in Reynolds stress 〈uw〉 budget Eq. (8) for turbulent Couette flow at Re=3000. –turbulent production, ⋯⋯ dissipation,⋄ viscous diffusion, ▿ turbulent diffusion, [[dashed_line]] [[dashed_line]] total diffusion, □ velocity-pressure gradient correlation −〈u∂p/∂z〉, ▵ velocity-pressure gradient correlation −〈w∂p/∂x〉 and — ⋅ — ⋅ — ⋅ total velocity-pressure gradient correlation
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Vertical profiles of the terms in temperature variance 〈TT〉 budget Eq. (9) for turbulent Couette flow at Re=3000. –turbulent production, ⋯⋯ dissipation, ⋄ viscous diffusion, ▿ turbulent diffusion and [[dashed_line]] [[dashed_line]]total diffusion.
Grahic Jump Location
Vertical profiles of the terms in streamwise turbulent heat flux 〈Tu〉 budget Eq. (10) for turbulent Couette flow at Re=3000. □ turbulent production −〈uw〉∂〈T〉/∂z, ▵ turbulent production −〈Tw〉∂〈u〉/∂z, – total turbulent production, ⋯⋯ dissipation, ⋄ viscous diffusion 1/Re ∂/∂z〈u∂T/∂z〉, ○ conductive diffusion 1/(Re Pr)∂/∂z〈T∂u/∂z〉, ▿ turbulent diffusion, [[dashed_line]] [[dashed_line]] total diffusion, and — ⋅ — ⋅ —⋅ temperature-pressure gradient correlation.
Grahic Jump Location
Vertical profiles of the term in vertical turbulent heat flux 〈Tw〉 budget Eq. (11) for turbulent Couette flow at Re=3000. –total turbulent production, ⋯⋯ dissipation, ⋄ viscous diffusion 1/Re ∂/∂z〈w∂T/∂z〉, ○ conductive diffusion 1/(Re Pr)∂/∂z〈T∂w/∂z〉, ▿ turbulent diffusion, [[dashed_line]]total diffusion, and —⋅—⋅—⋅ temperature-pressure gradient correlation.
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Contours of fluctuating variables on the x-z plane in the middle of the y domain: (a) u contours; (b) w contours; and (c) T contours.
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Contours of streamwise velocity fluctuation u on the x-y plane at: (a) z+=5 and (b) z=0.5.
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Contours of temperature fluctuation T on the x-y plane at: (a) z+=5 and (b) z=0.5.
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Contours of fluctuating variables on the y-z plane in the middle of the x domain: (a) v contours, (b) w contours, and (c) T contours.

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