[zhangxc0223]

Hi, all. I am pretty new for this, so sorry for this stupid simple question.

Now I would like to plot the Reynolds stress (u'v’) for my jet flow on a certain cross section. I have totally 36000 groups of data that sampled from the cross section based on 100 time steps multiplied 360 radial lines, each group have the u, v, w velocity of 200 points on the radial line, i.e. totally I have a 200×36000 mat in MATLAB.

So my question is that how can I get the figure of Reynolds stress versus radial locations (u'v' versus r/D), as well as the turbulence intensity (u'u', v'v', w'w' versus r/D).

Really thanks for any suggestion.

[FMDenaro]

Originally Posted by zhangxc0223

Hi, all. I am pretty new for this, so sorry for this stupid simple question.

Now I would like to plot the Reynolds stress (u'v’) for my jet flow on a certain cross section. I have totally 36000 groups of data that sampled from the cross section based on 100 time steps multiplied 360 radial lines, each group have the u, v, w velocity of 200 points on the radial line, i.e. totally I have a 200×36000 mat in MATLAB.

So my question is that how can I get the figure of Reynolds stress versus radial locations (u'v' versus r/D), as well as the turbulence intensity (u'u', v'v', w'w' versus r/D).

Really thanks for any suggestion.

First, you should compute the fluctuations. If you have data sampled along a sufficient time interval, you can first compute the time-averaged fields. Then use this field to compute the fluctuations at each time you have the sample. This way, you get the vector field v'(x,t) and then you can compute the Reynolds tensor. Usually, supplementary spatial averaging are used (for example in azimuthal direction) along with the time averaging.

[LuckyTran]

You have u(x,y,z,t) v(x,y,z,t) and w(x,y,z,t) where (x,y,z) are coordinates or u(x,t), v(x,t), w(x,t) if you consider x the position vector.

Ok so for every x,y,z / x you average in time to get the mean velocities at each location. So you should have 360*200x3 average velocities. Since you have a 200x3600 matrix in matlab, you can probably accomplish this using

uMean = mean(u,1)

Now you need to get the u',v',w'. So at each of the (360*200) locations, you take u'(x,t)=u(x,t) - uMean(x). Of course in matlab the dimension of uMean is 1 less than u so it will throw a bug. You can fix it easily by say

uPrime = u - uMean(ones(200,1),:);

Then multiply the components and average in time to get the Reynolds sterss, which can be done in one line like so:

uu = mean(uPrime.*uPrime,1);
uv = mean(uPrime.*vPrime,1);

Note in matlab you need to give the . for element by element operations, otherwise it does the full matrix multiplication.

It really is as simple as these few lines of code. And then happy plotting.

[zhangxc0223]

Originally Posted by FMDenaro

First, you should compute the fluctuations. If you have data sampled along a sufficient time interval, you can first compute the time-averaged fields. Then use this field to compute the fluctuations at each time you have the sample. This way, you get the vector field v'(x,t) and then you can compute the Reynolds tensor. Usually, supplementary spatial averaging are used (for example in azimuthal direction) along with the time averaging.

Originally Posted by LuckyTran

You have u(x,y,z,t) v(x,y,z,t) and w(x,y,z,t) where (x,y,z) are coordinates or u(x,t), v(x,t), w(x,t) if you consider x the position vector.
...
It really is as simple as these few lines of code. And then happy plotting.

Really thank you for your responses. but I am still struggling for plotting it. some more simple questions please.

1. The correct plots of u'u'_vs_x/D and u'v'_vs_x/D, and my plot are attached. It seems that my results are far away from the correct one. First issue is the y axis value, my value is normalized by Uc, the centre line axial velocity of the cross section of the jet. Is that correct?

2. For the plot of u'v'_vs_x/D, is the u'v' come from simply uPrime multiplying by vPrime? If so, how can the y axis value u'v'=0 at x=0, because both my uPrime and vPrime at x=0 are not 0.

Thanks again for your patient reply.

[LuckyTran]

2. You still have to take the average in time.

[zhangxc0223]

Originally Posted by LuckyTran

2. You still have to take the average in time.

Actually I have average the data both on time (100 timesteps) and space (360 radial lines). So is that means the time is not long enough for the data? Now the 100 time steps are extracted from 0.5 second for the flowing.

Cheers.

[FMDenaro]

Originally Posted by zhangxc0223

Actually I have average the data both on time (100 timesteps) and space (360 radial lines). So is that means the time is not long enough for the data? Now the 100 time steps are extracted from 0.5 second for the flowing.

Cheers.

The time-averaging must be performed over a large interval. Considering the non-dimensional time unit using a characteristic integral time scale. you need to average over 20-30 time units.
I suggest to plot the time averaged velocity profiles

[khattak]

Hello, I am realitively new to matlab and couldnt figure out a script for my Reynolds Normal stresses. Can you please help me write the whole script.

[khattak]

We are only given velocities in the x and y direction.

[LuckyTran]

Originally Posted by khattak

Hello, I am realitively new to matlab and couldnt figure out a script for my Reynolds Normal stresses. Can you please help me write the whole script.

Did you check out post #3? You only need to add two lines, one for vMean and vPrime and maybe change the 1 to either a 2 (or 3) depending on what format your data actually is in.