Calculating resolved turbulent kinetic energy for nonstationary flow

Jasper Z · April 8, 2021, 15:21

Dear Foamers,

I am struggling with the method of calculating resolved turbulent kinetic energy in LES. I have read a lot of threads and see that we can calculate TKE by: 0.5*(Uprime2Mean_XX+Uprime2Mean_YY+Uprime2Mean_ZZ) . But Uprime2Mean is calculated from: u-UMean, where UMean is time-averaged velocity. I know this should work with the statistically stationary flow. However, what if we have a nonstationary flow, like the figure below?

Shouldn't we get the Uprime2Mean by subtracting ensemble-averaged velocity from the instantaneous velocity? If we use UMean, the results will be totally different. Any ideas?

Kind Regards,
Jasper

KTG · April 9, 2021, 21:22

I think in that function object the UMean and will be over whatever window you specify - its not automatically going to use the full time period.

Tobermory · April 10, 2021, 05:33

Jasper - yes, you are right, that is the correct definition in a non-stationary flow (that is - Uprime2Mean needs to be calculated from u - Umean, but Umean must be the ensemble mean in this case).

To do the ensemble average you have to either run the simulation many many times (unlikely!) or find a homogeneous direction (eg. spanwise in a channel flow, as well as top half & bottom half) and average over that direction. To get a (statistically) good ensemble average, you need to ensure that you have a large enough homogenous direction.

You can dig up the old postChannel utility, and modify/use that, to do the spatial averaging. Good luck!

Jasper Z · April 10, 2021, 14:25

Quote:

Originally Posted by Tobermory

Jasper - yes, you are right, that is the correct definition in a non-stationary flow (that is - Uprime2Mean needs to be calculated from u - Umean, but Umean must be the ensemble mean in this case).

To do the ensemble average you have to either run the simulation many many times (unlikely!) or find a homogeneous direction (eg. spanwise in a channel flow, as well as top half & bottom half) and average over that direction. To get a (statistically) good ensemble average, you need to ensure that you have a large enough homogenous direction.

You can dig up the old postChannel utility, and modify/use that, to do the spatial averaging. Good luck!

Thank you very much Tobermory. I will take a look at the postChannel utility!

Best Regards,

Jasper

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April 9, 2021, 21:22		#2
KTG Senior Member Abe Join Date: May 2016 Posts: 119 Rep Power: 10	I think in that function object the UMean and will be over whatever window you specify - its not automatically going to use the full time period.

April 10, 2021, 05:33		#3
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 670 Rep Power: 14	Jasper - yes, you are right, that is the correct definition in a non-stationary flow (that is - Uprime2Mean needs to be calculated from u - Umean, but Umean must be the ensemble mean in this case). To do the ensemble average you have to either run the simulation many many times (unlikely!) or find a homogeneous direction (eg. spanwise in a channel flow, as well as top half & bottom half) and average over that direction. To get a (statistically) good ensemble average, you need to ensure that you have a large enough homogenous direction. You can dig up the old postChannel utility, and modify/use that, to do the spatial averaging. Good luck!