Use result of the for ith iteration of the for loop to compute the i+1 iteration

Hi all,

I am using relatively complex equations in order to derive the values of the variables: a and a_prime. These variables are derived following an iterative approach, starting with a = a_prime = 0 , and going through the for loop to obtain better values.

I am having however difficulty with using the final result of the a and a_prime as derived at the end of each for loop, in order to re-run the for loop with that value. Below is the code:

 % Input Data

    R = 5 ; % m
    V = 10 ; % m/s
    B = 3 ; % blades
    lambda = 6 ; % tip speed ratio

    % Input Matrix
    %     r(m)  g(deg)  c(m)  
    M = [ 0.20  53.0    0.65 ; ...
          0.15  74.3    0.76 ; ...
          2.50  84.9    0.44 ; ...
          3.75  89.1    0.30 ; ...
          5.00  92.6    0.19 ] ; 

    % Variables
    r = M(:,1) ; 
    gamma = M(:,2) ; 
    c = M(:,3) ;

 % Calculations

    Omega = lambda * V / R ; % rad/s

    % First guesses
    a = 0 ; 
    a_prime = 0 ; 

    % Iterations
    for k = 1:2 %length(M)

        % Local factors
        sigma = B * c(k) / (2 * pi * r(k)) ; % Local solidity 
        lambda_r = Omega * r(k) / V ; % Local tip speed

        beta = atan(lambda_r * (1 + a_prime) / (1 - a) ) ; %relative flow anlge onto the blades
        i = gamma(k) - beta * 180/pi ; % angle of incidence
        C_L = 0.327 + 0.1059 * i - 0.0013 * i^2 ; % lift coefficient

        % New a and a'
        a = 1 / (1 + (4 * cos(beta)^2 ) / (sigma * C_L * sin(beta) )) ;
        a_prime = (sigma * C_L / 4 / lambda_r / cos(beta) ) * (1 - a) ;

    end

Any help would be appreciated.

Kind Regards,

KMT.

Answer 1

[Ameer Hamza]

Instead of overwriting the variables, create an array. In the end, it will also help you to look at values of a and a_prime during each iteration.

a = zeros(1, length(M)+1) ;
a_prime = zeros(1, length(M)+1) ;
% Iterations
for k = 1:2 %length(M)
  % Local factors
  sigma = B * c(k) / (2 * pi * r(k)) ; % Local solidity
  lambda_r = Omega * r(k) / V ; % Local tip speed
  beta = atan(lambda_r * (1 + a_prime(k)) / (1 - a(k)) ) ; %relative flow anlge onto the blades
  i = gamma(k) - beta * 180/pi ; % angle of incidence
  C_L = 0.327 + 0.1059 * i - 0.0013 * i^2 ; % lift coefficient
  % New a and a'
  a(k+1) = 1 / (1 + (4 * cos(beta)^2 ) / (sigma * C_L * sin(beta) )) ;
  a_prime(k+1) = (sigma * C_L / 4 / lambda_r / cos(beta) ) * (1 - a(k)) ;
end