Turbulent Kinetic Energy

Turbulence Kinetic Energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. It is a concept used to assess what contribution to buoyancy is brought by turbulence.

The production of TKE equals the sum of mechanical/shear/frictional turbulence plus the buoyancy, and must match with the heat dissipated. Balancing the two, we get an equation and thus can make a budget about the TKE. [Baldocchi, D. (2005), " [http://nature.berkeley.edu/biometlab/espm129/pdf/Lecture%2018%20espm%20129.pdf Lecture 18, Wind and Turbulence, Part 1, Surface Boundary Layer: Theory and Principles ] ", Ecosystem Science Division, Department of Environmental Science, Policy and Management, University of California, Berkeley, CA: USA.]

In Computational Fluid Dynamics (CFD) it is common to hear of the k-epsilon (k-ε) model for turbulence. What is useful for users of CFD is a method by which to calculate reasonable values of turbulence kinetic energy, k and the turbulence dissipation rate, ε. [Fluent 6.2 User's Guide, " [http://www.engres.odu.edu/Applications/fluent6.2/help/html/ug/node180.htm] "]

: $k\; =\; 1.5\; (UI)^2$

Where $I$ is the initial turbulence intensity [%] given below, and $U$ is the initial velocity magnitude

: $epsilon\; =\; \{c\_mu\}^\{3/4\}\; k^\{3/2\}\; l^\{-1\}$

Where $l$ is the turbulence or eddy length scale give below, and $\{c\_mu\}$ is a k-ε model parameter whose value is typically given as 0.09.

: $I\; =\; 0.16Re^\{-1/8\}$

Where $Re$ is the Reynolds number

: $l\; =\; 0.07L$

Where $L$ is the characteristic length. For internal flows this may take the value of the inlet duct (or pipe) width (or diameter) or the hydraulic diameter.

References