# Simple For cycle (a small problem with the indexes)

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Paul Rogers on 5 Jan 2021
Commented: Mischa Kim on 5 Jan 2021
I have a small problem with the last loop in the code:
clear
clc
close all
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)
% 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')
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)

Mischa Kim on 5 Jan 2021
Edited: Mischa Kim on 5 Jan 2021
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)
##### 2 CommentsShowHide 1 older comment
Mischa Kim on 5 Jan 2021
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.

R2014b

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