[Captain Convergence]

Hi all!

I am simulating the flow over a delta wing at high angles of attack using DDES with the k-omega SST as URANS model close to the wall. I managed to put a rake with points very close to the vortex core in order to study the turbulence in detail on its core (see the attached image "Vortex_rake" to check which points I am studying). I performed a power spectrum density study and I plot the results for the same points in my 3 cases. According to the theory, a well-resolved turbulence spectrum should follow the slopes -5/3 and -7 corresponding to the Inertial Sub-Range (Resolved Spectrum) and the Viscous Dissipation (Modelled Spectrum) respectively. However my results do not follow that trend, which leads me to 2 options:

1) The DDES model has a strong influence of the URANS model due to the fact that the models switching function creates a "grey" region where both models (URANS and LES) are being used simultaneously and this would explain why the aforementioned trends are wrong (not a pure LES simulation).

2) My analysis is wrong.

I would love to hear some comments about this. Thank you in advance!

[FMDenaro]

Originally Posted by Captain Convergence

Hi all!

I am simulating the flow over a delta wing at high angles of attack using DDES with the k-omega SST as URANS model close to the wall. I managed to put a rake with points very close to the vortex core in order to study the turbulence in detail on its core (see the attached image "Vortex_rake" to check which points I am studying). I performed a power spectrum density study and I plot the results for the same points in my 3 cases. According to the theory, a well-resolved turbulence spectrum should follow the slopes -5/3 and -7 corresponding to the Inertial Sub-Range (Resolved Spectrum) and the Viscous Dissipation (Modelled Spectrum) respectively. However my results do not follow that trend, which leads me to 2 options:

1) The DDES model has a strong influence of the URANS model due to the fact that the models switching function creates a "grey" region where both models (URANS and LES) are being used simultaneously and this would explain why the aforementioned trends are wrong (not a pure LES simulation).

2) My analysis is wrong.

I would love to hear some comments about this. Thank you in advance!

I am not sure about what you are doing. My question:
1) Is the geometry only a half of the delta wing and symmetric conditions are used? That has influence on the flow structures.
2) Are you sampling in time at these stations? The spectra are computed on the whole set of data or you performed a mean over several time-windows?
3) The general -5/3 law is valid for homogeneous isotropic turbulence, that means you can hope to see such scaling only far from the wing. I would suggest to fix one station and doing the spectral analysis at increasing y+ positions. Then try to do the analysis in the shear. Of course, the effect of the RANS formulation has a strong impact close to the wing.

[Captain Convergence]

1) I am simulating a delta wing at high angles of attack. I haven't used symmetry because at such angles the interactions between the vortices is quite significant. I am using pressure far-field as boundary condition. I have attached 2 more images with the instantaneous Q-crit isosurfaces and the averaged static Cp so you can have a better picture of my simulation.

2) Yes, every iteration I am exporting the velocities in every point. So knowing the instantaneous velocity magnitude, the sampling period, the length of the signal and the sampling frequency I can calculate the power spectrum density of a certain point.

3) I see... I wasn't aware of that fact, I have a significant lack of experience with these simulations and probably the vortex spectrum density is not the same as a wall bounded flow or any other type of flow.

Thanks for your answer FMDenaro!

[FMDenaro]

I suggest to check first the spectra for a position far from the trailing edge. You should improve the statistics by doing a proper ensemble averaging. You should be able to describe the inertial cascade, be aware that in LES the dissipation range should not appear.

[Captain Convergence]

Unfortunately I don't have statistical data far from the trailing edge, I have only monitored the velocities in points equally distributed in 8 rakes over the wing (see the attached figure to check their position).

And why is the ensemble averaging technique useful in this case? I haven't heard of it.

[FMDenaro]

Originally Posted by Captain Convergence

Unfortunately I don't have statistical data far from the trailing edge, I have only monitored the velocities in points equally distributed in 8 rakes over the wing (see the attached figure to check their position).

And why is the ensemble averaging technique useful in this case? I haven't heard of it.

You are assuming the signal is periodic in time over a certain characteristic window. The spectra should be done in each window and then an ensemble averaging should be performed.