Simple For cycle (a small problem with the indexes)

I have a small problem with the last loop in the code:

clear
clc
close all

load matlab_10.mat
init= 24500;

%% Gas properties
k = 1.4;          %Gas constant ratio, cp/cv()
R = 287.05;       %Ideal gas constant [J/Kg*K]
p01 = 1e5;        %Compressor inlet pressure(Pa)
T01 = 303.35;     %Compressor inlet temperature(K)
cp = 1005;        %Specific heat capacity for constant pressure, property of gas(J/(kg*K))
ro1 = 1.15;       %Gas density(kg/m^3)
AFR = 14.71;      %Air Fuel Ratio

%% Turbine's parameters
A_eff = .03;       %[m^2]
A_0 = A_eff/.6;
E_R = [1:0.001:4]; %Expansion ratio
T_3 = 1173.15;     %Discharge temperature [K]
eta_t = 0.6;

%% Compressor's parameters
eta_c = 0.95;
I = 0.001;                                  %Moment of inertia for the compressor spool(kg*m^2)
mass_flow_compressor = 0.273675009794891;   %adimensional mass flow from Greitzer steady-state [kg/s]
% m_c = mass_flow_compressor*(ro1*Ac*U);    %actual compressor's mass flow [kg/s]  
mass_flow_compressor_corrected = (mass_flow_compressor*(T01^0.5))./p01; %[m*s*(k)^0.5]
P_R = 2.591609007038750; %pressure ratio from Greeitzer
p2 = P_R*p01;  %[Pa] 

%% 
mass_flow_compressor_corrected = (mass_flow_compressor_corrected*ones(1,length(E_R))).*(1+(1./AFR));
mass_flow_turbine_corrected = A_eff.*((k./R).^0.5).*((1./E_R).^(1/k)).*(((2./k-1).*(1-(1./E_R).^((k-1)./k))).*0.5);
% mass_flow_corrected = (mass_flow).*p01;

x_ER = interp1(mass_flow_turbine_corrected - mass_flow_compressor_corrected, E_R, 0);
y_ER = A_eff.*((k./R).^0.5).*((1./x_ER).^(1/k)).*(((2./k-1).*(1-(1./x_ER).^((k-1)./k))).*0.5);

figure()
plot(E_R,mass_flow_turbine_corrected,...
    E_R,mass_flow_compressor_corrected,'linewidth',3)
grid on
grid minor
xlabel('ER')
legend('turbine','compressor')
ylabel('m*s*K^{0.5}')
title('ER vs mass flow')
hold on
plot(x_ER, y_ER, 'pg','linewidth',3)
hold off
text(x_ER, y_ER, sprintf('\\uparrow\nIntersection:\nx\\_ER = %.3f\ny\\_ER = %.3f', x_ER, y_ER),...
    'HorizontalAlignment','left', 'VerticalAlignment','top')

%% Power Steady Case

Pt = ((y_ER.*p01)./(T01^0.5)).*eta_t.*(k./(k-1)).*R.*T_3.*(1-(1./(x_ER.^((k-1)./k))));
Pc = ((y_ER.*p01)./(T01^0.5)).*(1./eta_c).*(k./(k-1)).*R.*T01.*((p2./p01).^((k-1)./k)-1);

%% Pulsating

mass_flow_compressor_vet = phi_10(init:end);
mass_flow_compressor_vet_corrected = (mass_flow_compressor_vet*(T01^0.5))./p01; %[m*s*(k)^0.5]
mass_flow_compressor_vet_corrected = mass_flow_compressor_vet_corrected*ones(1,length(E_R)).*(1+(1./AFR));

for i=1:length(phi_10(init:end))
%        
   x_ER_vet(i,:) = interp1(mass_flow_turbine_corrected - mass_flow_compressor_vet_corrected(i,:), E_R, 0);
   y_ER_vet(i,:) = A_eff.*((k./R).^0.5).*((1./x_ER_vet(i,:)).^(1/k)).*(((2./k-1).*(1-(1./x_ER_vet(i,:)).^((k-1)./k))).*0.5);
% 
%    Pt_vet = ((y_ER_vet.*p01)./(T01^0.5)).*eta_t.*(k./(k-1)).*R.*T_3.*(1-(1./(x_ER_vet.^((k-1)./k))));
%    Pc_vet = ((y_ER_vet.*p01)./(T01^0.5)).*(1./eta_c).*(k./(k-1)).*R.*T01.*((p2./p01).^((k-1)./k)-1);
%    omega_vet = (2.*((Pt_vet-Pc_vet)./(I))+55000.^2).^0.5;

end

figure()
plot(t_10(init:end),omega_vet,'linewidth',3)
grid on
grid minor
xlabel('t [s]')
legend('\omega')
ylabel('rpm')
hold on
title('\omega')

my problem is I have the first omega, let's call it omega(1), and by that iteration I need to find the others.

The algorithm I wrote on paper foor the first two steps is in the following figure: (anyway I've already written the code in the comment inside the for-loop, i just miss the indexes)

Answer 1

[Mischa Kim]

There you go:

omega_vet(1) = 55000;
for i=1:length(phi_10(init:end))
       
   x_ER_vet(i) = interp1(mass_flow_turbine_corrected - mass_flow_compressor_vet_corrected(i), E_R, 0);
   y_ER_vet(i) = A_eff.*((k./R).^0.5).*((1./x_ER_vet(i)).^(1/k)).*(((2./k-1).*(1-(1./x_ER_vet(i)).^((k-1)./k))).*0.5);
   Pt_vet(i)   = ((y_ER_vet(i).*p01)./(T01^0.5)).*eta_t.*(k./(k-1)).*R.*T_3.*(1-(1./(x_ER_vet(i).^((k-1)./k))));
   Pc_vet(i)   = ((y_ER_vet(i).*p01)./(T01^0.5)).*(1./eta_c).*(k./(k-1)).*R.*T01.*((p2./p01).^((k-1)./k)-1);
   
   omega_vet(i+1) = (2.*((Pt_vet(i)-Pc_vet(i))./(I)) + omega_vet(i).^2).^0.5;

end
figure()
plot(t_10(init:end),omega_vet(1:end-1),'linewidth',3)

[Paul Rogers]

thanks a lot, but nope, since the first value of the omega_vet is 55000.

[Mischa Kim]

Right you are. For some reason I missed the info on your paper. See the updated code above. Note that in the final plot command you need to account for the fact that omega is always one index ahead. So you need to adjust the length of the time or the omega vector.