How to iterate with fsolve to find Mach number

Asked by Hailey on 10 Sep 2019

Latest activity Edited by Torsten on 10 Sep 2019

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I'm trying to interate static pressure ratio to find Mach number using fsolve, but I can't get the syntax correct. The Mathworks explaination didn't really help me. Could anyone out there help?

I have a set range for the pressure ratio, but the Mach number is unknown. Here is the equation:

This is what I have so far for the code:

pt2pinf = [1.9, 2.7, 3.5, 4.3, 5.1, 5.9, 6.7, 7.5, 27.5, 47.5, 67.5 ,87.5 ,107.5,127.5, 147.5, 200, 252.5, 305, 357.5, 410, 462.5 ,515 ,567.5, 620, 672.5, 725, 777.5, 830 ,882.5, 935, 987.5, 1000];
Me0=ones(1,32);
g=1.2;
pt2pinf_test = fsolve(@(Me)(((1+((g-1)/2)*Me.^2)^(g/(g-1)))/((((2*g)/(g+1))*Me.^2)-((g-1)/(g+1)))),Me0);

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Hailey on 10 Sep 2019

But I need to have the Mach number values. I need an array of Mach numbers that match up with it's respective pressure ratio value. This did not do that.

Torsten on 10 Sep 2019

They are stored in the fsolve return parameter (pt2pinf_test in your case).

Hailey on 10 Sep 2019

The values are too small to be a Mach number after a shock wave.

Not sure what I did wrong.

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Answer by Torsten on 10 Sep 2019

Edited by Torsten on 10 Sep 2019

Accepted Answer

function main
  pt2pinf = [1.9, 2.7, 3.5, 4.3, 5.1, 5.9, 6.7, 7.5, 27.5, 47.5, 67.5 ,87.5 ,107.5,127.5, 147.5, 200, 252.5, 305, 357.5, 410, 462.5 ,515 ,567.5, 620, 672.5, 725, 777.5, 830 ,882.5, 935, 987.5, 1000];
  Me0 = 5.0;
  g = 1.2;
  fun = @(Me,pquot)((((1+((g-1)/2)*Me.^2).^(g/(g-1)))./((((2*g)/(g+1))*Me.^2)-((g-1)/(g+1))))-pquot).^2
  for i = 1:numel(pt2pinf)
    pquot = pt2pinf(i);
    machnumber(i) = fminsearch(@(Me)fun(Me,pquot),Me0,optimset('TolFun',1e-10));
  end
  machnumber
  fun(machnumber,pt2pinf)
end

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