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Technical Brief

Eddy Viscosity and Reynolds Stress Models of Entropy Generation in Turbulent Channel Flows

[+] Author and Article Information
J. Sun

Department of Mechanical
and Manufacturing Engineering,
University of Manitoba,
15 Gillson Street,
Winnipeg, MB R3T 2N2, Canada

D. Kuhn

Professor
Head of Department of Mechanical
and Manufacturing Engineering,
University of Manitoba,
15 Gillson Street,
Winnipeg, MB R3T 2N2, Canada

G. Naterer

Professor
Department of Mechanical Engineering,
Memorial University,
St. John's, NF A1B 3X5, Canada

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 29, 2015; final manuscript received October 21, 2016; published online January 20, 2017. Assoc. Editor: Elias Balaras.

J. Fluids Eng 139(3), 034501 (Jan 20, 2017) (6 pages) Paper No: FE-15-1217; doi: 10.1115/1.4035138 History: Received March 29, 2015; Revised October 21, 2016

This paper presents new models of entropy production for incompressible turbulent channel flows. A turbulence model is formulated and analyzed with direct numerical simulation (DNS) data. A Reynolds-averaged Navier–Stokes (RANS) approach is used and applied to the turbulence closure of mean and fluctuating variables and entropy production. The expression of the mean entropy production in terms of other mean flow quantities is developed. This paper presents new models of entropy production by incorporating the eddy viscosity into the total shear stress. Also, the Reynolds shear stress is used as an alternative formulation. Solutions of the entropy transport equations are presented and discussed for both laminar and turbulent channel flows.

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References

Adeyinka, O. B. , and Naterer, G. F. , 2004, “ Modeling of Entropy Production in Turbulent Flows,” ASME J. Fluids Eng., 126(6), pp. 893–899. [CrossRef]
Kock, F. , and Herwig, H. , 2004, “ Local Entropy Production in Turbulent Shear Flows: A High-Reynolds Number Model With Wall Functions,” Int. J. Heat Mass Transfer, 47(10), pp. 2205–2215. [CrossRef]
Moore, J. , and Moore, J. G. , “ Entropy Production Rates from Viscous Flow Calculations, Part I. A Turbulent Boundary Layer Flow,” ASME Paper No. 83-GT-70.
Cervantes, J. , and Solorio, F. , 2002, “ Entropy Generation in a Plane Turbulent Oscillating Jet,” Int. J. Heat Mass Transfer, 45(15), pp. 3125–3129. [CrossRef]
Naterer, G. F. , and Camberos, J. A. , 2003, “ Entropy and the Second Law in Fluid Flow and Heat Transfer Simulation,” AIAA J., 17(3), pp. 360–371.
Bejan, A. , 1995, Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time, CRC Press, Boca Raton, FL.
Munson, B. R. , Young, D. F. , Okiishi, T. H. , and Huebsch, W. W. , 2008, Fundamentals of Fluid Mechanics, Wiley, New York.
Iwamoto, K. , 2002, “ Database of Fully Developed Channel Flow,” Department of Mechanical Engineering, University of Tokyo, Tokyo, Japan.

Figures

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Fig. 1

Schematic of laminar flow between fixed parallel plates

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Fig. 2

Schematic of entropy production rate of laminar flow between fixed parallel plates

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Fig. 3

Entropy distribution

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Fig. 4

Mean velocities across the half channel height

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Fig. 5

Reynolds shear stresses across the half channel height

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Fig. 6

Kinetic energy production across the half channel height

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Fig. 7

Kinetic energy dissipation across the half channel height

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Fig. 8

Irreversibility due to mean viscous stress across the half channel height

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Fig. 9

Irreversibility due to turbulent viscous stresses across the half channel height

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Fig. 10

Irreversibility due to Reynolds shear stresses across the half channel height

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Fig. 11

Entropy production rate across the half channel height (TVD, turbulent viscosity/dissipation model and RSS, Reynolds shear stress model)

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