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I'm doing a project of Off-Shore Wind Energy where I am designing a turbine. This includes to define some of the features of the turbine.

I need to solve a system of 3 non linear equations with 3 variables.

3 equations to solve

3 equations to solve

The 3 variables (unknowns) are:

  • a
  • ai
  • Bi

The other values are given.

Attempts to solve

I already tried using fsolve, sym.nonlinsolve, and a couple more and I can't figure it out.

On my last attempt I substituted Bi from the first 2 equations with the 3rd equation. I add my minimal reproducible example by substituting the values I already know with the actual numbers:

def prueba(q):
    x = q[0]
    y = q[1]
    

    f1 = ((2.118182068620592)*(math.degrees(math.cos(math.degrees(math.atan((1-x)/((10.0)*(1+y)))))))*((1)+((0.016313)*(math.degrees(math.tan(math.degrees(math.atan((1-x)/((10.0)*(1+y)))))))))-((x)/(1-x))
    f2 = ((2.118182068620592)/((8)*(math.pi)*(16.609991369048576)*(math.degrees(math.cos(math.degrees(math.atan((1-x)/((10.0)*(1+y))))))))*((1)-((0.016313)*(math.degrees(mpmath.cot(math.degrees(math.atan((1-x)/((10.0)*(1+y)))))))))-((y)/(1+y))
    
    
    return np.array([f1,f2])

guessArray = [0.3329,0.00373] 

answer = fsolve(prueba,guessArray)
x = answer[0]
y = answer[1]
print(x,y)

If someone knows how to solve this I would really appreciate it.

Oscar Larrabure
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    Please format your code appropriately so it can be more easily read. https://stackoverflow.com/help/formatting explains how quite nicely. – thornejosh Mar 26 '21 at 19:22
  • Oscar, have a look at the __formatting and markdown__ of your question. I edited to give you an example (learning purpose) and to attract answers ️ – hc_dev Mar 26 '21 at 19:41
  • Can you **explain the equations**, their purpose (which turbine features) and mathematical terms (like `Zc Cl` or `8 pi kr`) !? – in human language Although you claim attempts using `fsolve` etc. I miss them in your [example] Please add to your question! – hc_dev Mar 27 '21 at 09:42
  • sure, I'm new to the plattform so sorry for any format mistakes: - The first equation of the image is for the axial induction factor (how much the wind speed (in axial direction) decreases because of the presence of the turbine). In this equation "a" represents the axial induction factor. - The second equation is the rotational induction factor (same thing but for the rotational speed). "a1" represents rotational induction factor. The other terms are values that I already calculated: Z: number of blades c: chord of the airfoil (length of the profile of the blade) CONTINUE NEXT COMM – Oscar Larrabure Mar 27 '21 at 13:07
  • Cl: lift coefficient (how much lift force the turbine has according to it's geometry) k: Prandtl factor f: load funtion And the 3rd equation Betai is the angle between rotational speed and relative speed (combination of axial wind speed, rotational speed and the induction factors)....and Betai relates both induction factors so it should help us to solve the equation – Oscar Larrabure Mar 27 '21 at 13:13
  • I updated the code with the minimal reproducible example (attempt)... Thank you!!! :) – Oscar Larrabure Mar 27 '21 at 13:41

0 Answers0