A rule of minimal energy dissipation in modeling of channel flow turbulence

References

• I. V. Lebed, On the Inapplicability of Navier–Stokes Equations to Interpreting the Turbulence, Physica A, vol. 315, pp. 228–235, 2002.
   Web of Science ®Google Scholar
• I. V. Lebed, Multimoment Hydrodynamics in Problem on Flow around a Sphere: Entropy Interpretation of the Appearance and Development of Instability, Open J. Fluid Dynam., vol. 4, pp. 163–206, 2014.
   Google Scholar
• L. Prandtl, Ueber die ausgebildete Turbulenz, Zeitungen, Z. angew. Math. Mech., vol. 5, pp. 136–139, 1925.
   Google Scholar
• W. P. Jones and B. E. Launder, The Prediction of Laminarization with a 2-Equation Model of Turbulence, Int. J. Heat Mass Transfer, vol. 15, p. 301, 1972.
   Web of Science ®Google Scholar
• B. E. Launder and D. B. Spalding, Lectures in Mathematical Models of Turbulence, Academic Press, London, 1972.
   Google Scholar
• B. E. Launder and D. B. Spalding, The Numerical Computation of Turbulent Flows, Comput. Meth. Appl. Mech. Eng., vol. 3, no. 2, pp. 269–289, 1974.
   Google Scholar
• B. E. Launder, and B. I. Sharma, Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow near a Spinning Disc, Lett. Heat Mass Transfer, vol. 1, pp. 131– 138, 1974.
   Google Scholar
• Y. Nagano and M. Tagawa, An Improved k–ε Model for Boundary Layer Flows, J. Fluids Eng., vol. 112, pp. 33–39, 1990.
   Web of Science ®Google Scholar
• T. H. Shih, J. Zhu, and J. L. Lumley, NASA Tech. Rep. TM-16721, 1994.
   Google Scholar
• T. H. Shih, W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu, New k–ε Eddy Viscosity for High Reynolds Number Turbulent Flows, Comput. Fluids, vol. 24, pp. 227–238, 1995.
   Web of Science ®Google Scholar
• B. E. Launder, Second-Moment Closure: Present…and Future?, Int. J. Heat Fluid Flow, vol. 10, pp. 282–300, 1989.
   Web of Science ®Google Scholar
• B. E. Launder and N. Shima, Second-Moment Closure for the Near-Wall Sublayer: Development and Application, AIAA J., vol. 27, pp. 1319–1325, 1989.
   Google Scholar
• D. C. Wilcox, Re-assessment of the Scale-Determining Equation for Advanced Turbulence Models, AIAA J., vol. 26, pp. 1299–1310, 1988.
   Google Scholar
• F. R Menter, Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA J., vol. 32, pp. 1598–1605, 1994.
   Google Scholar
• H. M. Hofmann, R. Kaiser, M. Kind, and H. Martin, Calculating of Steady and Pulsating Impinging Jets—An Assessment of 13 Widely Used Turbulence Models, Numer. Heat Transfer B, vol. 51, pp. 565–583, 2007.
   Web of Science ®Google Scholar
• E. Pulat, M. K. Isman, A. B. Etemoglu, and M. Can, Effect of Turbulence Models and Near-Wall Modeling Approaches on Numerical Results in Impingement Heat Transfer, Numer. Heat Transfer B, vol. 60, pp. 486–519, 2011.
   Web of Science ®Google Scholar
• Y. Chen, F. Arbeiter, and G. Schlindwein, A Comparative Study of Turbulence Models for Conjugate Heat Transfer to Gas Flow in a Heated Mini-Channel, Numer. Heat Transfer A, vol. 61, pp. 38–60, 2012.
   Web of Science ®Google Scholar
• J. Bredberg, On the Wall Boundary Condition for Turbulence Models, Internal Report 00/4, Department of Thermo and Fluid Dynamics, Chalmes University. of Technology, Göteborg, Sweden, 2000.
   Google Scholar
• N. I. Buleev, Theoretical Model of Turbulent Exchange in Fluid Flow and Heat-Transfer Problems, in Heat-Transfer, USSR Academy of Sciences, pp. 64–98, 1962.
   Google Scholar
• W. Pfeninger, Transition Experiments in the Inlet Length of Tubes at High Reynolds Numbers, in G.V. Lachman (ed.), Boundary Layer and Flow Control, Pergamon Press, pp. 970–980, 1961.
   Google Scholar
• D. G. Christopherson and D. Dowson, An Example of Minimum Energy Dissipation in Viscous Flow, Proc. Roy. Soc. Lond. Ser. A, Math. Phys. Sci., vol. 251, no. 1267, pp. 550–564, 1959.
   Web of Science ®Google Scholar
• H. Reichardt, Vollstandige Darstellung der turbulenten beschwindigkeitsverteilung in glatten, Zeitungen, Z. angew. Math. Mech., vol. 31, no. 7, pp. 208–219, 1951.
   Google Scholar
• M. V. Zagarola and A. Smits, Mean-Flow Scaling of Turbulent Pipe Flow, J. Fluid Mech., vol. 373, pp. 33–79, 1998.
   Web of Science ®Google Scholar
• R. D. Moser, J. Kim, and N. N. Mansour, DNS of Turbulent Channel Flow up to Re_tau = 590, Phys. Fluids, vol. 11, pp. 943–945, 1998.
   Web of Science ®Google Scholar