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I am currently trying to calculate the velocity distribution over an airfoil for a problem at work and am stuck on how to properly type this into Matlab. I know that x′ is a dummy chordwise coordinate I should use in the integral to distinguish it from x, but am confused how to relay that to Matlab. How do I distinguish x' from x and then sum up all those values to get the full velocity distribution over the chord in Matlab?

My coworker recommends using traps, but I am unsure how to work with x'. T

Vt = zeros(length(XC), 1); % XC corresponds to the x value used to calculate dT/dxfor i = 1:length(XC)        
Prime = XC(i);      % x'
    dT = dT(i);   % dT/dx'
    X = XC;         
    X(X==XPrime) = 0; % remove the x = x' singularity to allow proper integration
    int_expression = (1/2*pi)*dT*(X-XPrime);
Vt(i) =-trapz(X, int_expression); 
end

The integral is in the link and simple, with dT/dx posted as a photo as well. dT/dx that plugs into the equation that is being integrated

The equation that needs to be integrated

dT/dx that plugs into the equation that is being integrated

SecretAgentMan
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  • Is dT/dx a function of x or x'? – David Jan 22 '20 at 22:21
  • This looks like an integral equation where the outcome is tangential velocity as a function of x. You're integrating w.r.t. x' here. Since dT/dx is a sum of five different terms, I'd recommend that you treat each one individually. That last one is special. You'll have a singularity at x = 0. What do you plan to do about that? What is its physical significance? – duffymo Jan 23 '20 at 18:18
  • I'm guessing that x = 0 is the leading edge of your airfoil. The flow splits at that point into the upper and lower contour. That would be the source of your singularity, true? – duffymo Jan 23 '20 at 19:35

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