How to Calculate Drag from Matlab Code Using 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 Aircraft
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]

.

Thank you for your question. I understand that you are trying to estimate the Thrust and Torque generated by a propeller blade using the Blade Element Theory, and you have been able to calculate the lift but not the drag. I have reviewed your code and have some suggestions to help you get the drag values and also some general advice for your calculations.

Firstly, for calculating the drag using Blade Element Theory, it is important to consider the induced drag and profile drag separately. The induced drag is caused by the lift generated by the blade and is dependent on the angle of attack. The profile drag is caused by the friction of the air against the blade surface and is dependent on the airfoil shape and the airspeed. Therefore, your code should include separate calculations for both types of drag.

To calculate the induced drag, you can use the formula D = L^2/(pi*AR*e), where D is the induced drag, L is the lift, AR is the aspect ratio of the blade, and e is the Oswald efficiency factor. This formula can be implemented in your code by using the lift values that you have already calculated and the aspect ratio of the blade can be determined based on the blade geometry.

For the profile drag, you can use the formula D = 0.5*rho*Cd*A*V^2, where D is the profile drag, rho is the air density, Cd is the drag coefficient, A is the reference area of the blade, and V is the airspeed. The drag coefficient can be determined based on the airfoil shape and can be found in literature or by conducting wind tunnel experiments. The reference area of the blade can be calculated based on the blade geometry.

Additionally, I noticed that you are using the variable "Cr" in your code, but it is not defined anywhere. I assume it is the chord length of the blade, which is also needed for calculating the drag.

Regarding your second question, it is possible to take the real part of a complex number in calculations, but it is important to consider if it is appropriate for the specific situation. In the case of your example, if the imaginary part represents a physical quantity, then it would not be correct to only consider the real part. It would be best to consult with a mathematician or a colleague familiar with the specific problem to determine the appropriate approach.

I hope this helps you in your calculations. If you have any further questions, please do