About the physics of turbulence...

gRomK13 · July 10, 2009, 03:33

I still would like to have some further explanations about the formula $I=0.16 \cdot Re^{-1/8}$ (turbulence intensity in a fully developped pipe flow) which I quoted in my previous post.

- How comes the turbulence intensity decreases when mean velocity gets bigger? Would it be that fluctuations are smoothed when a flow becomes faster?

- What range of Re this expression if valid for? I cannot believe turbulence intensity exceeds 6% for laminar flows....!

Thank you in advance

gRomK13 · July 10, 2009, 05:28

I guess I won't be more successful than this poster whose question was asked more than a year ago.......

http://www.cfd-online.com/Forums/flu...intensity.html

Please, make an effort, I cannot believe that nobody here is able to answer that simple question

f-w · July 10, 2009, 16:55

The formula is an approximation of turbulent intensity from pipe flow empirical correlations, and is valid only for developed turbulent flow. The Re is actually Re_Dh:
http://www.cfd-online.com/Wiki/Hydraulic_diameter

The actual definition of turbulent intensity is velocity fluctuation divided by the mean flow velocity. So, to answer your first question, the empirical correlations tell us that velocity fluctuation growth is small compared to the increase in mean flow velocity.

henrik · July 11, 2009, 05:15

in other words:

$I=\frac{u'}{u} = 0.16\left(\frac{uD_h}{\nu}\right)^{-1/8}$

$u' = 0.16 \left(\frac{D_h}{\nu}\right)^{-1/8} u^{7/8}$

Henrik

gRomK13 · July 11, 2009, 05:18

Hello f-w

I'm okay with this correlation valid for fully developped turbulent flows only, I just wondered how low could the Reynolds actually get. The transition is known to occur between 2000 and 3000, so I guess I can still use the formula for $Re_ {D_{h}}=7000$ ? Anyway, my simulation is rather not sensitive to turbulent boundary conditions, so I may use the formula without commiting too much error. I was just surprised such a low Re could yield to 5% turbulence intensity...

You're right, that is just the competition between <u'²> and U0 turning in favor of U0 when Re grows. My question was kind of metaphysical: why?

Thank you for your precisions!

gRomK13 · July 11, 2009, 05:26

Thank you henrik

Actually f-w had made me realized my dumb mistake in confusing <u'²> and I..... Your formula clearly shows <u'²> grows with u (thus Re), which seems logical. But after all, this still does not answer what is the physical reason for I decreasing with u... Are the fluctuations "smoothed" when flow goes faster, as I said in my first post?

f-w · July 11, 2009, 18:33

As long as your Re_Dh is two times the expected transitional value (~2300 for pipes), you're fine. Otherwise, some additional considerations must be taken for an accurate analysis, where transition might be delayed.

Turbulent intensity is undefined for laminar flows, so careful how you use it. It does grow with decreasing Re, and can get pretty large with complex geometries where you can have large fluctuations with low mean velocities (like in forest flows).

As henrik pointed out, fluctuations can be rewritten (with the help of a correlation) as a function of mean velocity. At higher mean velocities, you can imagine having more powerful eddies, which in turn mix all the gradients (velocity, pressure, temperature, ...) to a greater degree.

July 10, 2009, 03:33	About the physics of turbulence...	#1
gRomK13 New Member Join Date: Jul 2009 Location: near Marseille, France Posts: 7 Rep Power: 16	I still would like to have some further explanations about the formula $I=0.16 \cdot Re^{-1/8}$ (turbulence intensity in a fully developped pipe flow) which I quoted in my previous post. - How comes the turbulence intensity decreases when mean velocity gets bigger? Would it be that fluctuations are smoothed when a flow becomes faster? - What range of Re this expression if valid for? I cannot believe turbulence intensity exceeds 6% for laminar flows....! Thank you in advance

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Question on Turbulence Intensity	Eric	FLUENT	1	March 7, 2012 04:30
Discussion: Reason of Turbulence!!	Wen Long	Main CFD Forum	3	May 15, 2009 09:52
Code release: Flow Transition and Turbulence	Chaoqun Liu	Main CFD Forum	0	September 26, 2008 17:15
Natural convection - Inlet boundary condition	max91	CFX	1	July 29, 2008 20:28

July 10, 2009, 05:28		#2
gRomK13 New Member Join Date: Jul 2009 Location: near Marseille, France Posts: 7 Rep Power: 16	I guess I won't be more successful than this poster whose question was asked more than a year ago....... http://www.cfd-online.com/Forums/flu...intensity.html Please, make an effort, I cannot believe that nobody here is able to answer that simple question

July 10, 2009, 16:55		#3
f-w Senior Member Join Date: Apr 2009 Posts: 154 Rep Power: 17	The formula is an approximation of turbulent intensity from pipe flow empirical correlations, and is valid only for developed turbulent flow. The Re is actually Re_Dh: http://www.cfd-online.com/Wiki/Hydraulic_diameter The actual definition of turbulent intensity is velocity fluctuation divided by the mean flow velocity. So, to answer your first question, the empirical correlations tell us that velocity fluctuation growth is small compared to the increase in mean flow velocity.

July 11, 2009, 05:15		#4
henrik Senior Member Henrik Rusche Join Date: Mar 2009 Location: Wernigerode, Sachsen-Anhalt, Germany Posts: 281 Rep Power: 18	in other words: $I=\frac{u'}{u} = 0.16\left(\frac{uD_h}{\nu}\right)^{-1/8}$ $u' = 0.16 \left(\frac{D_h}{\nu}\right)^{-1/8} u^{7/8}$ Henrik

July 11, 2009, 05:18		#5
gRomK13 New Member Join Date: Jul 2009 Location: near Marseille, France Posts: 7 Rep Power: 16	Hello f-w I'm okay with this correlation valid for fully developped turbulent flows only, I just wondered how low could the Reynolds actually get. The transition is known to occur between 2000 and 3000, so I guess I can still use the formula for $Re_ {D_{h}}=7000$ ? Anyway, my simulation is rather not sensitive to turbulent boundary conditions, so I may use the formula without commiting too much error. I was just surprised such a low Re could yield to 5% turbulence intensity... You're right, that is just the competition between <u'²> and U0 turning in favor of U0 when Re grows. My question was kind of metaphysical: why? Thank you for your precisions!

July 11, 2009, 05:26		#6
gRomK13 New Member Join Date: Jul 2009 Location: near Marseille, France Posts: 7 Rep Power: 16	Thank you henrik Actually f-w had made me realized my dumb mistake in confusing <u'²> and I..... Your formula clearly shows <u'²> grows with u (thus Re), which seems logical. But after all, this still does not answer what is the physical reason for I decreasing with u... Are the fluctuations "smoothed" when flow goes faster, as I said in my first post?

July 11, 2009, 18:33		#7
f-w Senior Member Join Date: Apr 2009 Posts: 154 Rep Power: 17	As long as your Re_Dh is two times the expected transitional value (~2300 for pipes), you're fine. Otherwise, some additional considerations must be taken for an accurate analysis, where transition might be delayed. Turbulent intensity is undefined for laminar flows, so careful how you use it. It does grow with decreasing Re, and can get pretty large with complex geometries where you can have large fluctuations with low mean velocities (like in forest flows). As henrik pointed out, fluctuations can be rewritten (with the help of a correlation) as a function of mean velocity. At higher mean velocities, you can imagine having more powerful eddies, which in turn mix all the gradients (velocity, pressure, temperature, ...) to a greater degree.