My integral results are not correct.
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I'm writing a code for the propeller design, but the integral values and results are not coming out as I want. I use this publicition. https://doi.org/10.2514/3.23779.
newzeta_ps needs to be equal to zeta. Also, Tc should be 0.0498.
There are 4 derivative equations in the code.
I looked many times but couldn't solve the problem.
clear
clc
V = 49.1744; % [m/s]
epsilon = 0.016789342857143;
zeta = 0.214700101676;
B = 2;
alpha = deg2rad(3.5007);
Cl = 0.7;
rho = 1.225;
D = 1.7526; % [m]
hub = 0.1524; % [m]
R = D/2; % [m]
r = linspace(hub, R, 7);
PropRPM = 2400;
i = 1;
PropRPS = PropRPM/60; %[dev/s]
omega = 2*pi*PropRPS;
x = omega/V*r(i);
xi = r(i)/R;
lambda = V/(omega*R);
J = V/(PropRPS*D);
phi_t = lambda*(1+(zeta/2)); rad2deg(phi_t);
phi = atan((tan(phi_t))/xi); rad2deg(phi);
f = (B/2)*(1-xi)/(sin(phi_t));
F = (2/pi)*acos(exp(-f));
a = (zeta/2)*((cos(phi))^2)*(1-(epsilon*tan(phi)));
aprime = (zeta/(2*x))*((cos(phi))*(sin(phi)))*(1+(epsilon/tan(phi)));
W = (V*(1+a))/sin(phi);
Mach = W/343;
G = F*x*cos(phi)*sin(phi);%dogru
gamma = (2*pi*(V^2)*zeta*G)/(B*omega);
c = (gamma*2)/(W*Cl);
c_ft = c/0.3048;
sigma = (B*c)/(2*pi*r(i));
xint = xi;
I1 = integral(@(xint) 4*xint*G*(1-(epsilon*tan(phi))),xint,1);
I2 = integral(@(xint) lambda*(4*xint*G*(1-epsilon*tan(phi)))/2.*xint*(1+epsilon/tan(phi))*sin(phi)*cos(phi),xint,1);
J1 = integral(@(xint) 4*xint*G*(1+epsilon/tan(phi)),xint,1);
J2 = integral(@(xint) ((4*xint*G*(1+epsilon/tan(phi)))/2)*(1-epsilon*tan(phi))*((cos(phi))^2),xint,1);
% Pc = (SHP/(2*rho*(PropRPS^3)*(D^5)))
Pc = 0.0402;
ccc = J1/2*J2;
newzeta_ps = (-1*(ccc))+sqrt((ccc^2)+Pc/J2);
Tc = (I1*zeta)-(I2*(zeta^2));
eta = (Tc/Pc)*J;
formatSpec = '%9.2f %9.3f %9.3f %9.4f %9.2f %9.4f %9.4f \n';
disp(' phi zeta newzeta Tc eta a aprime')
disp(' ______ ______ ______ ______ ______ ______ ______')
fprintf(formatSpec,rad2deg(phi),zeta, newzeta_ps, Tc, eta, a, aprime);
2 Comments
Torsten
on 3 Apr 2022
xint as lower bound of integration for your integrals is wrong.
It mustn't be zeta, but zeta0 which is a fixed value.
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