How to Calculate Drag Values Using Matlab and Blade Element Theory?

[Thusithatck]

I am trying to estimate the Thrust and Torque generated by a propeller blade by utilising the Blade Element Theory. I was able to get Lift but not Drag. Below is the code generated by Matlab.

The calculation procedure is,

T1 = twist pitch ratio
RTheta = root pitch angle
Phi = atan(V/(Omega*r))
ro = 1.225 (density)
C = 0.15 m
Cdo = 0.008 (zero lift drag)

Alpha = RTheta + T1*r - Phi

Here the twist is negative which makes the tip to have a small pitch angle.


for i = 1:3:132 % Forward Speed of the A/C
for j = 1:3:39 % rps (rpm/60)

syms r

omega(j) = 2*pi*j;
W2(i,j) = i^2 + (omega(j)*r)^2;
Alpha(i,j) = deg2rad(RTheta) + deg2rad(T1)*r - atan(i/(omega(j)*r));
CD(i,j) = Cdo + K*(a*Alpha(i,j))^2;

W2CD(i,j) = expand (W2(i,j)*CD(i,j));

Drag(i,j) = double(0.5*ro*Cr*int(W2CD(i,j),r,Hr,D/2));
end
end

As the calculation is run, I always gets a message saying below details,

? Error using ==> sym.maple at 87
Error, (in IntegrationTools:-Utils:-Simplify) too many levels of recursion

Error in ==> sym.int at 51
r = reshape(maple('map','int',f(:),[x.s '=(' a.s ')..(' b.s ')']),size(f));

Error in ==> New at 74
Drag(i,j) = double(0.5*ro*Cr*int(W2CD(i,j),r,Hr,D/2));

I would like to know how to get the drag values. I have tried every possible method, but I still get this message.

Furthermore, independent to the above question, is it OK to get the real part of a complex number to calculations?

Say if,

R = 2*D

where,
D = 0.45 + 09i

and if you take only the real number then,

R = 0.90

Is it correct? or possible? if so or not, is there is an exception where you can take R=0.90?
Advice me on both questions please. Thank you in advanced

 

[mmwave]

.

I understand that you are having trouble calculating the drag values for your propeller blade using the Blade Element Theory. I will try my best to provide some advice and insights on your questions.

Firstly, in order to accurately calculate the drag using the Blade Element Theory, it is important to have a good understanding of the theory and its assumptions. One of the main assumptions of this theory is that the lift and drag coefficients are only a function of the local angle of attack, and not the local airspeed. This means that the lift and drag coefficients should remain constant along the span of the blade. However, in your code, you have used a variable Alpha which is dependent on the local airspeed. This could be causing the error message you are receiving. I suggest double-checking your equations and making sure they align with the assumptions of the Blade Element Theory.

Additionally, it is important to note that the Blade Element Theory is a simplified model and may not accurately capture all the complexities of propeller blade performance. Therefore, it is always a good idea to validate your results with experimental data or other more advanced methods.

Regarding your second question about taking the real part of a complex number, it is possible to do so, but it is important to understand the implications of doing this. In your example, if you take the real part of the complex number D, you will lose the information about the imaginary part which represents the complex geometry of the propeller blade. This could affect the accuracy of your calculations. Therefore, it is important to carefully consider whether taking the real part is appropriate for your specific case.

I hope this helps and good luck with your calculations!A scientist