Turbulent Kinetic Energy

Turbulent 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.

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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. ^[1]

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.

k = 1.5U²I²

Where I is the initial turbulence intensity [%] U is the initial velocity magnitude

ε = k^{3 / 2} / l

Where l is the turbulence or eddy length scale. This represents the largest eddies in the flow.

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

1. ^ Baldocchi, D. (2005), 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.