Physical base of turbulent length scale
Hi, I am using Airpak of Fluent Inc. In the mannual, I found that the turbulence length scale in fully-developed turbulent pipe flow is about 7% of the hydraulic diameter. [Charpter 6, pp.6-25]
Could anyone tell me that where I can find the exact source of this expression, in which book, and which pages?
Thanks very much.
Re: Physical base of turbulent length scale
In the Fluent Manual Chapter 6.2.2 the relation: l = 0.07*D, where D = pipe diameter, is based on the maximum value of the mixing length in a fully-developed turbulent pipe flow, according to Nikuradses formula: l/R=0.14 -0.08*(1-y/R)^2-0.06*(1-y/R)^4, where R = pipe radius, thus MAX(l/D) = 0.07. The relation is given in Schlichting (79) "Boundary-layer Theory", and Rodi(1980) "Turbulence models and their application in Hydraulics". An interesting discussion about boundary conditions is found in Merci et. al "Determination of epsilon at inlet boundaries", Int. J. of Numerical Methods for Heat & Fluid Flow, Vol 12, No 1, 2002, pp.65-80.
Thanks very, very much
Thanks you very much for your kindly help. I am deeply appreciated for your knowledge. Thanks again for what you have done.
Waseda University, Japan
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