Turbulent kinetic Energy

Cfd00d · December 4, 2013, 20:32

Hello,

I have a 3x3x3 mesh grid (chosen for simplicity) that I am using to analyze turbulent velocities. The turbulence is isotropic.

I have u-velocity measurements (fluctuations) made on the grid that were taken at some time, t. I also have v and w velocities that are the same size.

I would like to find the turbulent kinetic energy by using the equation $\frac{1}{2}$ (u $^{2}_{ii}$ )

What I am stuck on is understanding how to apply this equation to my data.

In example, if I wanted to plot TKE vs. t, I should only get a single point, right?

How do I boil down this data to get the single point?

Any help is appreciated.

pbachant · December 5, 2013, 11:45

You could pick a point and look at the turbulence kinetic energy over time. You could also average over the volume.

If your data is a sequence of 3D velocity fluctuation arrays, you can create a new k array by
$\frac{1}{2}\left( u'^2 + v'^2 + w'^2 \right),$
or squaring each element of the velocity fluctuation arrays and adding the arrays for each component to each other. If you have arrays of the total velocity, you will need to compute the time average for each point and subtract.

Cfd00d · December 5, 2013, 16:30

Thank you for your reply pbachant

December 4, 2013, 20:32	Turbulent kinetic Energy	#1
Cfd00d New Member El Join Date: Dec 2013 Posts: 2 Rep Power: 0	Hello, I have a 3x3x3 mesh grid (chosen for simplicity) that I am using to analyze turbulent velocities. The turbulence is isotropic. I have u-velocity measurements (fluctuations) made on the grid that were taken at some time, t. I also have v and w velocities that are the same size. I would like to find the turbulent kinetic energy by using the equation $\frac{1}{2}$ (u $^{2}_{ii}$ ) What I am stuck on is understanding how to apply this equation to my data. In example, if I wanted to plot TKE vs. t, I should only get a single point, right? How do I boil down this data to get the single point? Any help is appreciated.

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December 5, 2013, 11:45		#2
pbachant Senior Member Pete Bachant Join Date: Jun 2012 Location: Boston, MA Posts: 173 Rep Power: 14	You could pick a point and look at the turbulence kinetic energy over time. You could also average over the volume. If your data is a sequence of 3D velocity fluctuation arrays, you can create a new k array by $\frac{1}{2}\left( u'^2 + v'^2 + w'^2 \right),$ or squaring each element of the velocity fluctuation arrays and adding the arrays for each component to each other. If you have arrays of the total velocity, you will need to compute the time average for each point and subtract.

December 5, 2013, 16:30		#3
Cfd00d New Member El Join Date: Dec 2013 Posts: 2 Rep Power: 0	Thank you for your reply pbachant