how to azimuthally average a N*N data ?

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AMIT 2024-8-11

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https://ww2.mathworks.cn/matlabcentral/answers/2144464-how-to-azimuthally-average-a-n-n-data

回答： Star Strider 2024-8-11

I have a 291*291 velocity data from LES . I want to azimuthally average the data so that for any angle from the origin at a particular radial distance i get the same value of velocity.

please suggest the way to do it.

Following figure shows the pictorial reperesentation of velocity data in yz plane

here is the attached file for the data

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Answer 1

Star Strider 2024-8-11

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I seriously doubt that what you want to do is possible, simply because your data do not work that way,

Likely the best you can do is to use the scatteredInterpolant function to interpolate one value as a function of the other two.

That would go something like this —

files = dir('*.txt');

for k = 1:numel(files)

filename = files(k).name

A{k} = readmatrix(filename);

end

filename = 'u11.txt'

filename = 'y1.txt'

filename = 'z1.txt'

V = A{1};

X = A{2};

Y = A{3};

[Vmin,Vmax] = bounds(V,'all')

Vmin = -0.0094

Vmax = 0.3075

[Xmin,Xmax] = bounds(X,'all')

Xmin = -6.4631

Xmax = 5.5760

[Ymin,Ymax] = bounds(Y,'all')

Ymin = -6.4583

Ymax = 5.5812

[A,R,Z] = cart2pol(X, Y, V);

[Amin,Amax] = bounds(A,'all')

Amin = -3.1389

Amax = 3.1411

[Rmin,Rmax] = bounds(R,'all')

Rmin = 0.0056

Rmax = 9.1315

[Vmin,Vmax] = bounds(Z,'all')

Vmin = -0.0094

Vmax = 0.3075

Farv = scatteredInterpolant(A(:),R(:),Z(:)); % Velocity As A Function Of Angle & Radius

Favr = scatteredInterpolant(A(:),Z(:),R(:)); % Radius As A Function Of Angle & Velocuty

Frva = scatteredInterpolant(R(:),Z(:),A(:)); % Angle As A Function Of Radius & Velocity

N = 10;

Aq = linspace(Amin, Amax, N).';

Rq = linspace(Rmin, Rmax, N).';

Vi = Farv(Aq, Rq);

ARV_Interpolations = table(Aq, Rq, Vi, 'VariableNames',{'Angle (radians)','Radius','Velocity'})

ARV_Interpolations = 10x3 table

Angle (radians) Radius Velocity _______________ _________ __________ -3.1389 0.0056004 0.30167 -2.4411 1.0196 0.23859 -1.7433 2.0336 0.12867 -1.0456 3.0476 0.072741 -0.34777 4.0616 0.024575 0.35 5.0755 -0.0064853 1.0478 6.0895 -0.0058249 1.7456 7.1035 -0.0059815 2.4433 8.1175 -0.0057644 3.1411 9.1315 -0.0058383

N = 10;

Aq = linspace(Amin, Amax, N).';

Vq = linspace(Vmin, Vmax, N).';

Ri = Favr(Aq, Vq);

AVR_Interpolations = table(Aq, Vq, Ri, 'VariableNames',{'Angle (radians)','Velocity','Radius'})

AVR_Interpolations = 10x3 table

Angle (radians) Velocity Radius _______________ __________ _______ -3.1389 -0.0093831 9.4498 -2.4411 0.025822 3.8114 -1.7433 0.061027 2.6731 -1.0456 0.096232 2.5875 -0.34777 0.13144 2.5345 0.35 0.16664 1.6565 1.0478 0.20185 1.0082 1.7456 0.23705 0.77004 2.4433 0.27226 0.52475 3.1411 0.30746 0.43572

N = 10;

Rq = linspace(Rmin, Rmax, N).';

Vq = linspace(Vmin, Vmax, N).';

Ai = Frva(Rq, Vq);

RVA_Interpolations = table(Rq, Vq, Ai, 'VariableNames',{'Radius','Velocity','Angle (radians)'})

RVA_Interpolations = 10x3 table

Radius Velocity Angle (radians) _________ __________ _______________ 0.0056004 -0.0093831 -873.3 1.0196 0.025822 -176.62 2.0336 0.061027 0.53339 3.0476 0.096232 0.73956 4.0616 0.13144 2.5574 5.0755 0.16664 -0.52377 6.0895 0.20185 0.68435 7.1035 0.23705 0.83499 8.1175 0.27226 -0.071844 9.1315 0.30746 -2.0362

figure

hs = surfc(X, Y, V, 'EdgeColor','interp');

colormap(turbo)

xlabel('X')

ylabel('Y')

zlabel('Velocity')

daspect([1 1 0.05])

figure

[c,hc] = contour(X, Y, V, 'ShowText',1);

colormap(turbo)

axis('equal')

This gives an example of thte interpolation approach. The various funcitons created by scatteredInterpolant will return appropriate values for any of the first two arguments that are within their limits, as calculated using the bounds calls.

.