Relation between integral time and integral length scale

kepler123 · January 24, 2019, 12:04

Hi everyone, I was wondering if any of you could help me figure this out. I basically need a relation between the integral length scale and the integral time scale, so that knowing one of them I would be able to calculate the other.

This is what I have:

Measurement of velocity at just one point, i.e.: A Time series measurement of inflow velocity on a wind turbine blade. Using this I can calculate the integral time scale using a simple two-point (in time) correlation.

Since I know the velocity through this point in time, I could calculate the mean and fluctuating velocity components.

What I need:

The integral length scale.

So, is it possible for me to use a simple relation of length = velocity*time such that I have:

Integral_length_scale = velocity*integral_time_scale

If this does work, what would I have to use as the velocity? Would I have to use the mean inflow velocity, the RMS or something else?

P.S: I do remember seeing a relation somewhere a few months ago when I first got into turbulence, etc. It does make sense that the relation also has something to do with the Reynolds number. I know for certain it's no direct relation as it's a flow based phenomena and some parameter such as the Reynolds number plays a role in relating the two.

LuckyTran · January 24, 2019, 14:09

This paper comes to mind: On the Calculation of Length Scales for Turbulent Heat Transfer Correlation
There are several methods for estimating the length scale from single point data.

kepler123 · January 24, 2019, 14:56

Thanks for the recommendation. It's behind a paywall and I can't even read the abstract

LuckyTran · January 25, 2019, 00:41

You can always email the author and ask them how to do it. Emails are free.

You can calculate the power spectrum and extrapolate it to the zero frequency (example here in this NASA-TM). There are many ways you can find if you google turbulence length scale from hot wire.

kepler123 · January 25, 2019, 05:54

Awesome. Thanks a lot for your help, the power spectrum way seems to be something I can work with.

DJF · January 25, 2019, 10:14

Assuming Taylor's hypothesis of "frozen turbulence", the length scale in streamwise direction (Lx) can be estimated from the mean velocity (U) and time scale (Tx) by following relationship:

Lx = U*Tx

kepler123 · January 25, 2019, 18:01

Awesome, thanks!

January 24, 2019, 12:04	Relation between integral time and integral length scale	#1
kepler123 Member Brandon Join Date: Jun 2018 Location: Germany Posts: 46 Rep Power: 8	Hi everyone, I was wondering if any of you could help me figure this out. I basically need a relation between the integral length scale and the integral time scale, so that knowing one of them I would be able to calculate the other. This is what I have: Measurement of velocity at just one point, i.e.: A Time series measurement of inflow velocity on a wind turbine blade. Using this I can calculate the integral time scale using a simple two-point (in time) correlation. Since I know the velocity through this point in time, I could calculate the mean and fluctuating velocity components. What I need: The integral length scale. So, is it possible for me to use a simple relation of length = velocitytime such that I have: Integral_length_scale = velocityintegral_time_scale If this does work, what would I have to use as the velocity? Would I have to use the mean inflow velocity, the RMS or something else? P.S: I do remember seeing a relation somewhere a few months ago when I first got into turbulence, etc. It does make sense that the relation also has something to do with the Reynolds number. I know for certain it's no direct relation as it's a flow based phenomena and some parameter such as the Reynolds number plays a role in relating the two.

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January 24, 2019, 14:09		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,761 Rep Power: 66	This paper comes to mind: On the Calculation of Length Scales for Turbulent Heat Transfer Correlation There are several methods for estimating the length scale from single point data.

January 24, 2019, 14:56		#3
kepler123 Member Brandon Join Date: Jun 2018 Location: Germany Posts: 46 Rep Power: 8	Thanks for the recommendation. It's behind a paywall and I can't even read the abstract

January 25, 2019, 00:41		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,761 Rep Power: 66	You can always email the author and ask them how to do it. Emails are free. You can calculate the power spectrum and extrapolate it to the zero frequency (example here in this NASA-TM). There are many ways you can find if you google turbulence length scale from hot wire.

January 25, 2019, 05:54		#5
kepler123 Member Brandon Join Date: Jun 2018 Location: Germany Posts: 46 Rep Power: 8	Awesome. Thanks a lot for your help, the power spectrum way seems to be something I can work with.

January 25, 2019, 10:14		#6
DJF New Member Join Date: Jan 2019 Posts: 12 Rep Power: 7	Assuming Taylor's hypothesis of "frozen turbulence", the length scale in streamwise direction (Lx) can be estimated from the mean velocity (U) and time scale (Tx) by following relationship: Lx = U*Tx

January 25, 2019, 18:01		#7
kepler123 Member Brandon Join Date: Jun 2018 Location: Germany Posts: 46 Rep Power: 8	Awesome, thanks!