0
Technical Briefs

Analytical Solutions for the Modeled k Equation

[+] Author and Article Information
Rafik Absi

 EBI, 32 Boulevard du Port, 95094 Cergy-Pontoise Cedex, Francer.absi@ebi-edu.com

J. Appl. Mech 75(4), 044501 (May 13, 2008) (4 pages) doi:10.1115/1.2912722 History: Received February 20, 2006; Revised March 27, 2007; Published May 13, 2008

The semitheoretical function of Nezu and Nakagawa (1993, Turbulence in Open-Channel Flows, A. A. Balkema, ed., Rotterdam, The Netherlands) for the turbulent kinetic energy k is valid only where local equilibrium is a good approximation. From an estimation of the difference between the energy production and its dissipation Gϵ, we present in this study an analytical solution for the modeled k equation. Comparisons with direct numerical simulation data of turbulent channel flows show good agreement. A universal function for k+ is deducted for y+<20.

FIGURES IN THIS ARTICLE
<>
Copyright © 2008 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Turbulent kinetic energy. ○, DNS data (4) for Reτ=642; curve, Eq. 17 with A1+=360 and D1=4.2.

Grahic Jump Location
Figure 2

Dimensionless turbulence generation and dissipation rate versus dimensionless distance. (a) Turbulence generation. ○, measurements (5) (Profile 3). Curves, approximation 18; dashed line, with CG=1; solid line, with CG=0.6. (b) Turbulence dissipation rate. ×, measurements (5) (Profile 3). Curves, approximation 19; dashed line, with Cϵ=1; solid line, with Cϵ=0.5.

Grahic Jump Location
Figure 3

Turbulent kinetic energy. ○, DNS data (4) for Reτ=642; curves, proposed analytical solution 26 with C=1, A+=8 and B=0.14 for y+⩽20.

Grahic Jump Location
Figure 4

Turbulent kinetic energy for y+⩽20. ○, DNS data of Iwamoto (4); ×, DNS data of Kim (7); curves, proposed analytical solution 27. (a) Reτ=642; curve, A+=8 and B=0.14; (b) Reτ=395; curve, A+=8 and B=0.132; (c) Reτ=298; curve, A+=8 and B=0.127; (d) Reτ=150; A+=8 and B=0.116; (e) Reτ=109; A+=8 and B=0.11.

Grahic Jump Location
Figure 5

Dependency of the coefficient B on the Reynolds number Reτ. ○, values obtained from DNS data (4); curve, proposed function 28.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In