Project 2 - Rankine cycle Simulator
Rankine Cycle Simulator
Aim
Creation of Rankine cycle simulator from given input and reading the data from standard thermodynamic library of steam table.
Code Explanation.
- The creation of Rankine cycle simulator starts with some input value which are required to calculate the other state point in cycle eventually.
- The Rankine cycle process is displayed in the command window and then inputs are entered which are inlet pressure for turbine, temperature at turbine inlet and pressure at condenser.
- Then we are using XSteam function file for reading state point. First, we get the value of enthalpy and entropy at state point 1 from the XSteam function file.
- As process from 1-2 is isentropic compression the entropy at point 1 is equal to point 2. The term ‘(s_pT, p1, T1)’ refers to entropy at pressure and temperature point 1.
- The term ‘sg’ and ‘sf’ are referred to saturated liquid and saturated vapor entropy respectively. This value is used to calculate other function according to mathematical relations.
- Similarly, other points are taken from XSteam function file which are necessary to calculate other parameters. After that work done in turbine and pump are calculated for further getting the net work done Rankine cycle.
- After calculating the net work done the efficiency of the Rankine cycle is calculated along with specific steam consumption which is steam consumed by a locomotive cylinders per unit of output of work done.
- Then temperature at each point of cycle is calculated using input taken from start of the program and data taken from XSteam file. For given temperature range from lower to higher entropy points are calculated to create the T-S plot. Similarly, another for loop is used to create the saturation curve in each plot.
- Then plotting is done respectively for T-s and H-s graph in Rankine cycle and each state point value has been put in command window.
- Processes and Working
- Process 1-2 : Isentropic Expansion in the turbine .
- Process 2-3 : Constant pressure Heat rejection in condenser
- Process 3-4 : Isentropic compression in the pump
- Process 4-1 : Constant pressure heat addition in the boiler
- Given Inputs:
- Turbine Inlet temperature (T1)= 400° C
- Turbine Inlet Pressure (p1) = 30 bars
- Turbine Outlet Pressure(p2) = 0.05 bars = Condenser Inlet Pressure
- Rankine Cycle Simulator Coding.
% Rankine Cycle Simulator
clear all
close all
clc
fprintf(' Rankine Cycle\n ')
fprintf('1-2 is Isentropic Expansion in Turbine\n')
fprintf(' 2-3 is constant pressure heat removal\n')
fprintf(' 3-4 is Isentropic Compression in Pump \n')
fprintf(' 4-1 Constant pressure Heat addition in Boiler\n')
% Entering the input data for calculation of state points
p1 = 30; %Pressure at Turbine Inlet
T1 = 400; %Temperature at Turbine Inlet
p2 = 0.05; %Pressure at Condenser
% Taking data from Xsteam file for State point 1
h1 = XSteam('h_pT', p1, T1); % Enthaply at pressure and Temp 1
s1 = XSteam('s_pT', p1, T1); % Entropy at pressure and Temp 1
% Taking data from Xsteam file for State point 2
s2 = s1; % Because of Isentropic Expansion
sf2 = XSteam('sL_p', p2); % Saturated liquid entropy at pressure 2
sg2 = XSteam('sV_p', p2); % Saturated vapour entropy at pressure 2
x2 = (s2-sf2)/(sg2-sf2); % Vapour Fraction at state point 2
hf2 = XSteam('hL_p', p2); % Saturated liquid Enthalpy at pressure 2
hg2 = XSteam('hV_p', p2); % Saturated vapour Enthalpy at pressure 2
h2 = hf2 + (x2*(hg2-hf2)); % Enthalpy at state point 2
% Taking data from Xsteam file for state point 3
p3 = p2; % Constant Pressure heat removal process
s3 = XSteam('sL_p', p3); % Saturated liquid entropy at Pressure 3
h3 = XSteam('hL_p', p3); % Saturated liquid Enthalpy at Pressure 3
% Taking data from Xsteam file for State point 4
s4 = s3; % Isentropic Compression process
p4 = p1; % Constant Pressure heat rejection
% Work done in Turbine for the rankine cycle
W_T = h1-h2;
% Work done required for pump
v3 = XSteam('vL_p',p3); % Saturated Liquid Vapour at pressure 3
W_P = v3*(p4-p3)*100; % Work done for pump
h4 = h3 - W_P; % Enthalpy at State point 4
% Net work done for Rankine Cycle
W_net = W_T - W_P;
% Heat Addition to System
Q_in = h1-h4;
% Heat Rejection from System
Q_out = h2-h3;
% Thermal Efficiency of Rankine Cycle
T_eff = (W_net/Q_in)*100;
%specific steam consumption = (Mass flow rate / Net work done)
Sp_S = (3600/W_net);
% Calculation of Temperature at All state Point 2, 3 and 4
T3 = XSteam('Tsat_p',p3); % Saturation Temperature at Pressure 3
T2 = T3; % Becuase of Constant Pressure Heat addition
Cp4 = XSteam('Cp_ps',p4,s4); % Specific isobaric heat capacity
Cv4 = XSteam('Cv_ps',p4,s4); % Specific isochoric heat capacity
k = Cp4/Cv4;
T4 = T3/((p3/p4)^((k-1)/k)); % Temperature at State point 4
% Calculation of Other constant for saturated liquid and Vapour
T6 = XSteam('Tsat_p', p1); % Saturated Temperature at Pressure 1
s5 = XSteam('sL_p', p1); % Saturated Liquid entropy at pressure 1
s6 = XSteam('sV_p', p1); % Saturated Vapour entropy at Pressure 1
h5 = XSteam('hL_p', p1); % Saturated Liquid Enthalpy at Pressure 1
h6 = XSteam('hV_p', p1); % Saturated Vapour Enthalpy at pressure 1
T5 = T6;
%Plotting for Saturation Line
T = linspace(1,560,1000);
for i = 1:length(T)
sf(i) = XSteam('sL_T' ,T(i)); % Saturated Liquid Entropy
sg(i) = XSteam('sV_T' ,T(i)); % Saturated Vapour Entropy
hf(i) = XSteam('hL_T' ,T(i)); % Saturated Liquid Enthalpy
hg(i) = XSteam('hV_T' ,T(i)); % Saturated Vapour Enthalpy
end
% Plotting T-S Diagram for Rankine Cycle
figure(1)
hold on
plot(sf,T,'color','b','linewidth',2)
plot(sg,T,'color','b','linewidth',2)
plot([s1 s2],[T1 T2], 'color', 'r', 'linewidth',3)
plot([s2 s3],[T2 T3], 'color', 'r', 'linewidth',3)
plot([s3 s4],[T3 T4], 'color', 'r', 'linewidth',3)
plot([s4 s5],[T4 T5], 'color', 'r', 'linewidth',3)
plot([s5 s6],[T5 T6], 'color', 'r', 'linewidth',3)
s_1 = linspace(s6,s1,1000);
for j = 1:length(s_1)
Tc(j) = XSteam('T_ps',p1,s_1(j));
end
plot(s_1,Tc,'color','r','linewidth',3)
text(s1+0.1, T1, '1')
text(s2+0.1, T2, '2')
text(s3, T3-20, '3')
text(s4, T4+20, '4')
title('Temperature Vs Entropy')
xlabel('Entropy (Kj/kg-k)')
ylabel('Temeperature (Deg. Celcius)')
legend('Saturation Curve')
% Plotting H-S Diagram for Rankine Cycle
figure(2)
hold on
plot(sf,hf,'color','b','linewidth',2)
plot(sg,hg,'color','b','linewidth',2)
plot([s1 s2],[h1 h2],'color','r','linewidth',3)
plot([s2 s3],[h2 h3],'color','r','linewidth',3)
plot([s3 s4],[h3 h4],'color','r','linewidth',3)
hc = linspace(h4,h5,100);
for k = 1:length(hc)
s_c(k) = XSteam('s_ph',p1,hc(k));
end
plot(s_c,hc,'color','r','linewidth',3)
plot([s5 s6],[h5 h6],'color','r','linewidth',3)
for l = 1:length(s_1)
h_c(l) = XSteam('h_ps',p1,s_1(l));
end
plot(s_1,h_c,'color','r','linewidth',3)
text(s1+0.1,h1,'1')
text(s2+0.1,h2,'2')
text(s3,h3-100,'3')
text(s4,h4+200,'4')
title('Enthalpy Vs Entropy')
xlabel('Entropy (Kj/kg-k)')
ylabel('Enthalpy (KJ/Kg)')
legend('Saturation Curve')
% Displaying Results in Command window
disp('Results of Rankine Cycle')
fprintf('At state point 1\t\t\t\t\t')
fprintf('At state Point 2\n')
fprintf('P1 = %10f in Bar\t\t\t\t',p1);
fprintf('P2 = %10f in Bar\n',p2);
fprintf('T1 = %11f in Deg.Celcius\t\t',T1);
fprintf('T2 = %11f in Deg.Celcius\n',T2);
fprintf('H1 = %12f in KJ/Kg\t\t\t',h1);
fprintf('H2 = %12f in KJ/Kg\n',h2);
fprintf('S1 = %9f in KJ/Kg-k\t\t\t',s1);
fprintf('S2 = %9f in KJ/Kg-k\n',s2);
fprintf('\n')
fprintf('At state point 3\t\t\t\t\t')
fprintf('At state Point 4\n')
fprintf('P3 = %10f in Bar\t\t\t\t',p3);
fprintf('P4 = %10f in Bar\n',p4);
fprintf('T3 = %11f in Deg.Celcius\t\t',T3);
fprintf('T4 = %11f in Deg.Celcius\n',T4);
fprintf('H3 = %12f in KJ/Kg\t\t\t',h3);
fprintf('H4 = %12f in KJ/Kg\n',h4);
fprintf('S3 = %9f in KJ/Kg-k\t\t\t',s3);
fprintf('S4 = %9f in KJ/Kg-k\n',s4);
fprintf('\n')
fprintf('Turbine Work Done = %14f in KJ/Kg\n',W_T)
fprintf('Pump Work Done = %15f in KJ/Kg\n',W_P)
fprintf('Net Work Done = %17f in KJ/Kg\n',W_net)
fprintf('Thermal Efficiency = %13f in percent\n',T_eff)
fprintf('Sp. Steam Consumption = %f in KJ/Kw\n',Sp_S)
- Coding
% Rankine Cycle Simulator
clear all
close all
clc
fprintf(' Rankine Cycle\n ')
fprintf('1-2 is Isentropic Expansion in Turbine\n')
fprintf(' 2-3 is constant pressure heat removal\n')
fprintf(' 3-4 is Isentropic Compression in Pump \n')
fprintf(' 4-1 Constant pressure Heat addition in Boiler\n')
% Entering the input data for calculation of state points
p1 = 30; %Pressure at Turbine Inlet
T1 = 400; %Temperature at Turbine Inlet
p2 = 0.05; %Pressure at Condenser
% Taking data from Xsteam file for State point 1
h1 = XSteam('h_pT', p1, T1); % Enthaply at pressure and Temp 1
s1 = XSteam('s_pT', p1, T1); % Entropy at pressure and Temp 1
% Taking data from Xsteam file for State point 2
s2 = s1; % Because of Isentropic Expansion
sf2 = XSteam('sL_p', p2); % Saturated liquid entropy at pressure 2
sg2 = XSteam('sV_p', p2); % Saturated vapour entropy at pressure 2
x2 = (s2-sf2)/(sg2-sf2); % Vapour Fraction at state point 2
hf2 = XSteam('hL_p', p2); % Saturated liquid Enthalpy at pressure 2
hg2 = XSteam('hV_p', p2); % Saturated vapour Enthalpy at pressure 2
h2 = hf2 + (x2*(hg2-hf2)); % Enthalpy at state point 2
% Taking data from Xsteam file for state point 3
p3 = p2; % Constant Pressure heat removal process
s3 = XSteam('sL_p', p3); % Saturated liquid entropy at Pressure 3
h3 = XSteam('hL_p', p3); % Saturated liquid Enthalpy at Pressure 3
% Taking data from Xsteam file for State point 4
s4 = s3; % Isentropic Compression process
p4 = p1; % Constant Pressure heat rejection
% Work done in Turbine for the rankine cycle
W_T = h1-h2;
% Work done required for pump
v3 = XSteam('vL_p',p3); % Saturated Liquid Vapour at pressure 3
W_P = v3*(p4-p3)*100; % Work done for pump
h4 = h3 - W_P; % Enthalpy at State point 4
% Net work done for Rankine Cycle
W_net = W_T - W_P;
% Heat Addition to System
Q_in = h1-h4;
% Heat Rejection from System
Q_out = h2-h3;
% Thermal Efficiency of Rankine Cycle
T_eff = (W_net/Q_in)*100;
%specific steam consumption = (Mass flow rate / Net work done)
Sp_S = (3600/W_net);
% Calculation of Temperature at All state Point 2, 3 and 4
T3 = XSteam('Tsat_p',p3); % Saturation Temperature at Pressure 3
T2 = T3; % Becuase of Constant Pressure Heat addition
Cp4 = XSteam('Cp_ps',p4,s4); % Specific isobaric heat capacity
Cv4 = XSteam('Cv_ps',p4,s4); % Specific isochoric heat capacity
k = Cp4/Cv4;
T4 = T3/((p3/p4)^((k-1)/k)); % Temperature at State point 4
% Calculation of Other constant for saturated liquid and Vapour
T6 = XSteam('Tsat_p', p1); % Saturated Temperature at Pressure 1
s5 = XSteam('sL_p', p1); % Saturated Liquid entropy at pressure 1
s6 = XSteam('sV_p', p1); % Saturated Vapour entropy at Pressure 1
h5 = XSteam('hL_p', p1); % Saturated Liquid Enthalpy at Pressure 1
h6 = XSteam('hV_p', p1); % Saturated Vapour Enthalpy at pressure 1
T5 = T6;
%Plotting for Saturation Line
T = linspace(1,560,1000);
for i = 1:length(T)
sf(i) = XSteam('sL_T' ,T(i)); % Saturated Liquid Entropy
sg(i) = XSteam('sV_T' ,T(i)); % Saturated Vapour Entropy
hf(i) = XSteam('hL_T' ,T(i)); % Saturated Liquid Enthalpy
hg(i) = XSteam('hV_T' ,T(i)); % Saturated Vapour Enthalpy
end
% Plotting T-S Diagram for Rankine Cycle
figure(1)
hold on
plot(sf,T,'color','b','linewidth',2)
plot(sg,T,'color','b','linewidth',2)
plot([s1 s2],[T1 T2], 'color', 'r', 'linewidth',3)
plot([s2 s3],[T2 T3], 'color', 'r', 'linewidth',3)
plot([s3 s4],[T3 T4], 'color', 'r', 'linewidth',3)
plot([s4 s5],[T4 T5], 'color', 'r', 'linewidth',3)
plot([s5 s6],[T5 T6], 'color', 'r', 'linewidth',3)
s_1 = linspace(s6,s1,1000);
for j = 1:length(s_1)
Tc(j) = XSteam('T_ps',p1,s_1(j));
end
plot(s_1,Tc,'color','r','linewidth',3)
text(s1+0.1, T1, '1')
text(s2+0.1, T2, '2')
text(s3, T3-20, '3')
text(s4, T4+20, '4')
title('Temperature Vs Entropy')
xlabel('Entropy (Kj/kg-k)')
ylabel('Temeperature (Deg. Celcius)')
legend('Saturation Curve')
% Plotting H-S Diagram for Rankine Cycle
figure(2)
hold on
plot(sf,hf,'color','b','linewidth',2)
plot(sg,hg,'color','b','linewidth',2)
plot([s1 s2],[h1 h2],'color','r','linewidth',3)
plot([s2 s3],[h2 h3],'color','r','linewidth',3)
plot([s3 s4],[h3 h4],'color','r','linewidth',3)
hc = linspace(h4,h5,100);
for k = 1:length(hc)
s_c(k) = XSteam('s_ph',p1,hc(k));
end
plot(s_c,hc,'color','r','linewidth',3)
plot([s5 s6],[h5 h6],'color','r','linewidth',3)
for l = 1:length(s_1)
h_c(l) = XSteam('h_ps',p1,s_1(l));
end
plot(s_1,h_c,'color','r','linewidth',3)
text(s1+0.1,h1,'1')
text(s2+0.1,h2,'2')
text(s3,h3-100,'3')
text(s4,h4+200,'4')
title('Enthalpy Vs Entropy')
xlabel('Entropy (Kj/kg-k)')
ylabel('Enthalpy (KJ/Kg)')
legend('Saturation Curve')
% Displaying Results in Command window
disp('Results of Rankine Cycle')
fprintf('At state point 1\t\t\t\t\t')
fprintf('At state Point 2\n')
fprintf('P1 = %10f in Bar\t\t\t\t',p1);
fprintf('P2 = %10f in Bar\n',p2);
fprintf('T1 = %11f in Deg.Celcius\t\t',T1);
fprintf('T2 = %11f in Deg.Celcius\n',T2);
fprintf('H1 = %12f in KJ/Kg\t\t\t',h1);
fprintf('H2 = %12f in KJ/Kg\n',h2);
fprintf('S1 = %9f in KJ/Kg-k\t\t\t',s1);
fprintf('S2 = %9f in KJ/Kg-k\n',s2);
fprintf('\n')
fprintf('At state point 3\t\t\t\t\t')
fprintf('At state Point 4\n')
fprintf('P3 = %10f in Bar\t\t\t\t',p3);
fprintf('P4 = %10f in Bar\n',p4);
fprintf('T3 = %11f in Deg.Celcius\t\t',T3);
fprintf('T4 = %11f in Deg.Celcius\n',T4);
fprintf('H3 = %12f in KJ/Kg\t\t\t',h3);
fprintf('H4 = %12f in KJ/Kg\n',h4);
fprintf('S3 = %9f in KJ/Kg-k\t\t\t',s3);
fprintf('S4 = %9f in KJ/Kg-k\n',s4);
fprintf('\n')
fprintf('Turbine Work Done = %14f in KJ/Kg\n',W_T)
fprintf('Pump Work Done = %15f in KJ/Kg\n',W_P)
fprintf('Net Work Done = %17f in KJ/Kg\n',W_net)
fprintf('Thermal Efficiency = %13f in percent\n',T_eff)
fprintf('Sp. Steam Consumption = %f in KJ/Kw\n',Sp_S)- Output of the code.
Rankine Cycle
1-2 is Isentropic Expansion in Turbine
2-3 is constant pressure heat removal
3-4 is Isentropic Compression in Pump
4-1 Constant pressure Heat addition in Boiler
Results of Rankine Cycle
At state point 1 At state Point 2
P1 = 30.000000 in Bar P2 = 0.050000 in Bar
T1 = 400.000000 in Deg.Celcius T2 = 32.875490 in Deg.Celcius
H1 = 3231.571027 in KJ/Kg H2 = 2110.708212 in KJ/Kg
S1 = 6.923259 in KJ/Kg-k S2 = 6.923259 in KJ/Kg-k
At state point 3 At state Point 4
P3 = 0.050000 in Bar P4 = 30.000000 in Bar
T3 = 32.875490 in Deg.Celcius T4 = 36.935287 in Deg.Celcius
H3 = 137.765119 in KJ/Kg H4 = 134.754182 in KJ/Kg
S3 = 0.476254 in KJ/Kg-k S4 = 0.476254 in KJ/Kg-k
Turbine Work Done = 1120.862815 in KJ/Kg
Pump Work Done = 3.010937 in KJ/Kg
Net Work Done = 1117.851878 in KJ/Kg
Thermal Efficiency = 36.096803 in percent
Sp. Steam Consumption = 3.220462 in KJ/Kw
>> - ScreenShot of the output with plots
- Commoand Window With Plots
- Plor for Enthalpy Vs Entropy
- Plot for Temperature Vs Entropy
- Workspace Screen Shot.
- Link
https://drive.google.com/drive/folders/1kui2lUBAaneafd2qQKw7AcwxZ-qQ4eMF?usp=sharing
- References