Rankine cycle Simulator

AIM:

To create a basic 'RANKINE CYCLE SIMULATOR'.

THEORY:

The Rankine cycle is the fundamental operating cycle of all power plants where an operating fluid is continuously evaporated and condensed. The selection of operating fluid depends mainly on the available temperature range.

The above figure shows us the basic rankine cycle.

Here:

PROCESS 1-2: iSENTROPIC EXPANSION IN TURBINE.

PROCESS 2-3: ISOBARIC HEAT REJECTION BY THE CONDENSOR.

PROCESS 3-4: iSENTROPIC COMPRESSION IN PUMP.

PROCESS 4-1: ISOBARIC HEAT ADDITION BY THE BOILER.

GOVERNING EQUATION:

1)Turbine Work(W_T):

W_T = H₁ - H₂

2)Pump Work(W_P):

W_P = H₄ - H₃

3)Net Work(W_NET):

W_NET = W_T - W_P

4)Thermal Efficiency(`η`):

`eta` = W_NET/(H₁ - H₄)

5)Back Work Ratio(BWR):

BWR = W_P /W_T

6)Specific Steam Conductivity(S.S.C):

S.S.C = 3600/W_T

Where,

H₁,H₂,H₃,H₄ are the enthalpy at the respective state points.

OBJECTIVE:

The main objective of the program is to obtain all the values of the state point and plot the T-S and H-S curve for the Rankine Cycle.

WORKFLOW OF THE PROJECT:

1. Initially we assign the values to the inputs P!,T1 and P2 which are given in the problem.
2. After that we find the unknown values of P,T,H and S at all the state ponits from the XSteam library.
3. Then we find the values of Turbine work ,Pump work,Net work ,Thermal Efficiency,Back Work Ratio and Specific Steam Conductivity.
4. Then we display the values of all the things that we have found out earlier.
5. At last, we plot the curve for T-S and H-S graph of the Rankine Cycle.

The link for the standard Xsteam library to get the steam table data for water is given below:

https://drive.google.com/file/d/1RK_fvrOj38CIaQvmLT1S3daqHnxKCGU-/view

PROGRAMMING LANGUAGE USED: MATLAB

MATLAB CODE:

%PROGRAM FOR RANKINE CYCLE SIMULATOR
clear all
close all
clc

disp('         RANKINE CYCLE SIMULATOR          ');
disp('1-2 is Isentropic Expansion in the Turbine');
disp('2-3 is Constant Pressure Heat Rejection by the Condenser');
disp('3-4 is Isentropic Compression in the Pump');
disp('4-1 is Constant Pressure Heat Addition by the Boiler');
fprintf('\n');

%inputs to be specified
P1 = input('Enter the Pressure at the Turbine Inlet(in bar): ');
T1 = input('Enter the Temperature at the Turbine Inlet(in Degree Celcius): ');
P2 = input('Enter the Pressure at the Condenser (in bar): ');

%calculating the value of P,T,H,S at each state points
%At state point 1
H1 = XSteam('h_pT',P1,T1);
S1 = XSteam('s_pT',P1,T1);
H_L1 = XSteam('hL_p',P1);
H_G1 = XSteam('hV_p',P1);
S_L1 = XSteam('sL_p',P1);
S_G1 = XSteam('sV_p',P1);
T_sat1 = XSteam('Tsat_p',P1);

%At state point 2
S2 = S1;
S_L2 = XSteam('sL_p',P2);
S_G2 = XSteam('sV_p',P2);
D = (S2-S_L2)/(S_G2-S_L2); %Calculating the dryness fraction
H_L2 = XSteam('hL_p',P2);
H_G2 = XSteam('hV_p',P2);
H2 = H_L2 + D*(H_G2 - H_L2);  %Calculating the enthalpy at point 2
T2 = XSteam('T_ph',P2,H2);
T_sat2 = XSteam('Tsat_p',P2);

%At state point 3
P3 = P2;
T3 = T2;
H3 = H_L2;
S3 = S_L2;

%At state point 4
P4 = P1;
S4 = S3;
T4 = XSteam('T_ps',P4,S4);
H4 = XSteam('H_ps',P4,S4);

%Calculating Work and Efficiency of the Rankine Cycle
%Turbine Work
W_T = H1 - H2;

%Pump Work
W_P = H4 - H3;

%Net Work
W_NET = W_T - W_P;

%Thermal Efficiency of the Rankine Cycle
EFF = (W_NET/(H1 - H4))*100 ;

%Back Work Ratio
BWR = W_P/W_T;

%Specific Steam Conductivity
SSC = 3600/W_T;

%Displaying the results
%Values of state point 1
disp('                    RESULTS                ');
disp('At State point 1');
fprintf('P1 is : %.2f Bar \n',P1);
fprintf('T1 is : %.2f Deg Celcius \n',T1);
fprintf('H1 is : %.2f KJ/kg \n',H1);
fprintf('S1 is : %.2f KJ/kgK \n',S1);
fprintf('\n');

%Values of state point 2
disp('At State point 2');
fprintf('P2 is : %.2f Bar \n',P2);
fprintf('T2 is : %.2f Deg Celcius \n',T2);
fprintf('H2 is : %.2f KJ/kg \n',H2);
fprintf('S2 is : %.2f KJ/kgK \n',S2);
fprintf('\n');

%Values of state point 3
disp('At State point 3');
fprintf('P3 is : %.2f Bar \n',P3);
fprintf('T3 is : %.2f Deg Celcius \n',T3);
fprintf('H3 is : %.2f KJ/kg \n',H3);
fprintf('S3 is : %.2f KJ/kgK \n',S3);
fprintf('\n');

%Values of state point 4
disp('At State point 4');
fprintf('P4 is : %.2f Bar \n',P4);
fprintf('T4 is : %.2f Deg Celcius \n',T4);
fprintf('H4 is : %.2f KJ/kg \n',H4);
fprintf('S4 is : %.2f KJ/kgK \n',S4);
fprintf('\n');

%Turbine Work
fprintf('Wt is : %.2f KJ/kg \n',W_T);

%Pump Work
fprintf('Wp is : %.2f KJ/kg \n',W_P);

%Net Work
fprintf('Wnet is : %.2f KJ/kg \n',W_NET);

%Thermal Efficiency
fprintf('Ntherm is : %.2f Percent \n',EFF);

%Specific Steam Conductivity
fprintf('S.S.C is : %.2f kg/KWh \n',SSC);

%Back Work ratio
fprintf('Back Work Ratio is : %f \n',BWR);

%plotting of T-S curve
t = linspace(0,373.5,200);
figure(1)
hold on

for i = 1:length(t)
plot(XSteam('sL_T',t(i)),t(i),'r.')
plot(XSteam('sV_T',t(i)),t(i),'r.')
end

plot([S1 S2],[T1 T2],'linewidth',2,'color','black')
text(S1,T1,'1','FontSize',10)
if D>1
T3 = T_sat2;
plot([S2 S_G2 S3 S4],[T2 T_sat2 T3 T4],'linewidth',2,'color','black')
T2 = T_sat2;
text(S2,T2,'2','FontSize',10)
text(S3,T3,'3','FontSize',10)
else
plot([S2 S3 S4],[T2 T3 T4],'linewidth',2,'color','black')
text(S2,T2,'2','FontSize',10)
text(S3,T3,'3','FontSize',10)
end

n = linspace(T1,T2,500);
for i = 1:length(n)
plot(XSteam('s_pT',P1,n(i)),n(i),'.','linewidth',2,'color','black')
end

plot([S_L1 S_G1],[T_sat1 T_sat1],'linewidth',2,'color','black')
text(S_L1,T_sat1,'4','FontSize',10)
xlabel('Entropy(kJ/kg-K)')
ylabel('Temperature(k)')
title('T-S Graph')


%Plotting of H-S Curve
figure(2) 
hold on
for i = 1:length(t)
 plot(XSteam('sL_T',t(i)),XSteam('hL_T',t(i)),'r.')
 plot(XSteam('sV_T',t(i)),XSteam('hV_T',t(i)),'r.')
end
plot([S1 S2 S3 S4 S1],[H1 H2 H3 H4 H1],'linewidth',2,'color','black')
text(S1,H1,'1','FontSize',10)
text(S2,H2,'2','FontSize',10)
text(S3,H3,'3','FontSize',10)
text(S4,H4,'4','FontSize',10)
xlabel('Entropy(kJ/kg-K)')
ylabel('Enthalpy(kJ/kg)')
title('H-S Graph')

CODE EXPLAINATION:

1. Initially we display the the different process from 1-4 by using the disp command.
2. After that we assign the values to input parameters like P1,T1 and P2.
3. Then we calculate the value of pressure,ṭemperature,enthalpy and entropy at different state points by using the XSteam library.
4. Then we find the values of Turbine work ,Pump work,Net work ,Thermal Efficiency,Back Work Ratio and Specific Steam Conductivity by using their suitable formulas.
5. The we print the values of all the quantities that we have found in the earlier stepsby using the fprintf command.
6. At last we plot the curve of T-S and H-S for Rankine Cycle.

OUTPUT:

The above figure shows the output in the command window.

The above curve shows the T-S Graph of the Rankine Cycle.

The above curve shows the H-S Graph of the Rankine Cycle.

CONCLUSION:

Thus we have obtained the values of P,T,H and S for different state points and also the work,Efficiency,Back work ratio and Specific steam conductivity was calculated.Also the plot of T-S and H-S of Rankine Cycle was drawn.

ERRORS OBTAINED AND IT'S SOLUTION:

Initially the desired plot for T-S curve was not obtained ,there was some values printed in the plot beyond state point 2 as shown in the figure below by the green circular mark:

To overcome this error i used if else condition in the program for dryness fraction (D) as shown below:

Also a large number of typing errors were obtained that were corrected after observation.

REFERENCES:

https://en.wikipedia.org/wiki/Rankine_cycle

http://www.thermopedia.com/content/1072/

https://youtu.be/SQjbu7Yhkmc