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Old   February 1, 2002, 16:27
Default Convection velocity of Coherent structures
Jongdae Kim
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From the numerical simulation of wake region of bluff body, I got phase averaged flow fields. Coherent eddies from phase averaging - let's say these as coherent structures - is moving along streamwise direction with some convective velocity.

When I substracted 86% of free stream velocity from the phase averaged flow field, the streamlines of coherent structures look reasonable.

Now, I'd like to calculate more accurate convective velocity explicitly. Because the convecitve velocity of coherent structure is not constant not only along the lateral (or across wind) direction but also steamwise direction.

Please let me know how to calculate it,

At every mointoring points, the convective velocities are calculated based on the correlations between the point and other points. Considering the slope of the line connecting max. correlation points as convective velocity,the convective velocities are more than 90 % of the free stream velocity.

There are two possibilities :

First,the max. position of the correlation of the velocity between two points can not explain the coherent structures from phase averaging.

Second, the data size is not enough to calculate correlation. The velocity data is about one-second long in time. The shedding freq. of the vertical (or across wind direction) is about 48 Hz.
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Old   February 4, 2002, 11:54
Default Re: Convection velocity of Coherent structures
Lionel Larcheveque
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I had a quite similar problem. I used two points-two times correlations and phase averaged velocity field (2D because I have an homogeneous direction that I use to increase the number of samples of my statistics data) to compute the velocity of coherent structures in a shear layer above a cavity.

1 : classical way : two points-two times velocity correlations and then I look at the time evolution of the correlation peak when distance increase.

2 : I educe my structure using Weiss criterion W (similar to Q or lamda_2 criterion for 2D flows) for each phase (i.e I use phase averaged velocity field as an instantaneous velocity field). I define a region (elliptic area in my problem) surrounding each of the structures at each phase. Then I compute the centroid of Weiss criterion for phase phi and each structure n on the area Omega_(phi,n):

<x_i>_(phi,n)=int_OMEGA_(phi,n)[x_i*W.dOMEGA] / int_OMEGA_(phi,n)[W.dOMEGA]

with W=-.5[ (du/dx)^2 + (dv/dy)^2 + 2*(du/dy)*(dv/dx)]

Instead of using Weiss criterion, it is possible to use rot magnitude with quite correct results.

Hope this helps

Best regards
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Old   February 4, 2002, 12:54
Default Re: Convection velocity of Coherent structures
Jongdae Kim
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Thank you Lionel. I'll try the method you recommended.

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Old   February 5, 2002, 05:04
Default Re: Convection velocity of Coherent structures
Lionel Larcheveque
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Just one more remark:

If you use Weiss criterion to compute centroids, you have to use a cutoff as negative value of Weiss criterion means shear and not rotation (as for Q criterion, vortical regions are educed by W > 0). Personally, I set the cut-off to 0.5 (U_inf/L)^2.

For the vorticity version, you can have a look at: Lyn et al., 1995 : A laser-doppler velocimetry study of ensemble-averaged characteristics of a turbulent wake of a square cylinder JFM 304, pp. 285-319

Best regards
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