[Falu]

Hey CFD Community,

I want to track the TKE in a free jet pulsating simulationen. I formulated the needed variables and simulated my model. In the post processing i realized a mistake i made. My jet puls every 0.1s for 0.1s, with a velocity of 5m/s. But in my TKE calculation Im using the averaged velocity to calculate the fluctuating component. In this case, my average velocity is ~2.5m/s, because half of the time my jet does have a velocity of 0. I could formulate my average, so that its ~5 m/s, but then its calculating a 5m/s fluctuation for the timesteps where the puls is equal to zero.

Does someone know a way to fox this issue? For a moment i thought i could do a for condition, which is either 5 or 0 and use this as my average. But I think this is very unscientific and would be too much of a simplification.

Thanks in advance for the Help

[ghorrocks]

The definition of the turbulent component and the fluctuating component is not clear in periodic flows, or transient flows in general for that matter.

Three main ways of doing it are:
* Transient averaging - define a time scale which is large compared to the turbulent fluctuations and small compared to the bulk flow fluctuations. Then use a transient average with this time scale as your bulk flow, and any deviation from it as your fluctuating component. The big problem here is that for many flows you cannot easily separate the time scales.
* Spatial averaging - At any instant in time, do a spatial filtering of the flow. Make the length scale of the spatial filtering big compared to the turbulent eddies but small compared to the bulk flow. Then the filtered result is your bulk flow component and the deviation from it is your fluctuating component. This approach suffers from the same issues as the transient average in that it is often difficult to define a clear separation in the length scales.
* Ensemble averaging - For periodic flows (like yours appears to be) you can average the flow across multiple cycles. If you run the simulation for a number of cycles, then work out the average flow field at each time step in the cycle you can define this as the bulk flow, and any deviation from it as the fluctuating component. This approach works very well and avoids the time/length scale issues in the previous two approaches, but only works for periodic flows.

I talk a bit about these approaches in my PhD thesis from years ago: http://hdl.handle.net/10453/20133 (see the chapter on the square cylinder engine model).

Also a very useful thing to do is to draw a turbulence spectrum. Map the turbulence energy versus frequency. This will help identify if you have a clear distinction between turbulent and bulk flow time scales, and also help you estimate the accuracy of your simulation (as most flows will end up with a -1/7 gradient - deviation from that indicates excessive dissipation).

[ghorrocks]

The definition of the turbulent component and the fluctuating component is not clear in periodic flows, or transient flows in general for that matter.

Three main ways of doing it are:
* Transient averaging - define a time scale which is large compared to the turbulent fluctuations and small compared to the bulk flow fluctuations. Then use a transient average with this time scale as your bulk flow, and any deviation from it as your fluctuating component. The big problem here is that for many flows you cannot easily separate the time scales.
* Spatial averaging - At any instant in time, do a spatial filtering of the flow. Make the length scale of the spatial filtering big compared to the turbulent eddies but small compared to the bulk flow. Then the filtered result is your bulk flow component and the deviation from it is your fluctuating component. This approach suffers from the same issues as the transient average in that it is often difficult to define a clear separation in the length scales.
* Ensemble averaging - For periodic flows (like yours appears to be) you can average the flow across multiple cycles. If you run the simulation for a number of cycles, then work out the average flow field at each time step in the cycle you can define this as the bulk flow, and any deviation from it as the fluctuating component. This approach works very well and avoids the time/length scale issues in the previous two approaches, but only works for periodic flows.

I talk a bit about these approaches in my PhD thesis from years ago: http://hdl.handle.net/10453/20133 (see the chapter on the square cylinder engine model).

Also a very useful thing to do is to draw a turbulence spectrum. Map the turbulence energy versus frequency. This will help identify if you have a clear distinction between turbulent and bulk flow time scales, and also help you estimate the accuracy of your simulation (as most flows will end up with a -1/7 gradient - deviation from that indicates excessive dissipation).