Near-wall turbulence models for the velocity and temperature fields based on the transport equations for the Reynolds stresses, the dissipation rate of turbulent kinetic energy, and the temperature variance and its dissipation rate are formulated for flows with widely different Prandtl numbers. Conventional high-Reynolds-number models are used to close these equations and modifications are proposed to render them asymptotically correct near a wall compared to the behavior of the corresponding exact equations. Thus formulated, two additional constants are introduced into the definition of the eddy conductivity. These constants are found to be parametric in the Prandtl number. The near-wall models are used to calculate flows with different wall thermal boundary conditions covering a wide range of Reynolds numbers and Prandtl numbers. The calculated Nusselt number variations with Prandtl number are in good agreement with established formulae at two different Reynolds numbers. Furthermore, the mean profiles, turbulence statistics, heat flux, temperature variance, and the dissipation rates of turbulent kinetic energy and temperature variance are compared with measurements and direct numerical simulation data. These comparisons show that correct near-wall asymptotic behavior is recovered for the calculated turbulence statistics and the calculations are in good agreement with measurements over the range of Prandtl numbers investigated.
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A Near-Wall Eddy Conductivity Model for Fluids With Different Prandtl Numbers
R. M. C. So,
R. M. C. So
Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106
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T. P. Sommer
T. P. Sommer
Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106
Search for other works by this author on:
R. M. C. So
Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106
T. P. Sommer
Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106
J. Heat Transfer. Nov 1994, 116(4): 844-854 (11 pages)
Published Online: November 1, 1994
Article history
Received:
November 1, 1992
Revised:
November 1, 1993
Online:
May 23, 2008
Citation
So, R. M. C., and Sommer, T. P. (November 1, 1994). "A Near-Wall Eddy Conductivity Model for Fluids With Different Prandtl Numbers." ASME. J. Heat Transfer. November 1994; 116(4): 844–854. https://doi.org/10.1115/1.2911457
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