RANKINE CYCLE SIMULATOR

1.AIM :

WRITE A MATLAB PROGRAM TO CREATE A BASIC RANKINE CYCLE SIMULATOR

2.OBJECTIVES :

1. To calculate the state points of the cycle.
2. To plot the T-S and H-S curve for the rankine cycle.

3.THEORY AND GOVERNING EQUATIONS :

Rankine cycle is a power producing cycle which is widely used in steam based power plants. The Rankine cycle produces high pressure and temperature steam which strikes the blade of the turbine and ultimately turbine rotates with high speed,further this turbine is coupled with a generator which converts the mechanical energy to electrical energy.

The figure below shows a basic rankine cycle

The 4 processes invloved in working of a rankine cycle are:-

1) Isentropic Expansion (1-2)

The saturated steam is expanded in the turbine and the rotation of turbine thus producing work which may be converted to electricity using a generator.

2) Isobaric Heat Rejection (2-3)

The vapor-liquid mixture leaving the turbine is condensed at constant low pressure.

3) Isentropic Compression (3-4)

The pressure of the working fluid which is in liquid form at this stage is raised in the pump. The pump requires very less work input.

4) Isobaric Heat Addition (4-1)

High pressure liquid enters the boiler where addition of energy at constrant pressure causes evaporation of the liquid until it is fully converted to saturated steam.

The equations used are

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`):

`η` = 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 state points 1,2,3,and 4 respectively.

The link for the standard Xsteam library which provides the steam table data for water is given below:

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

4.MATLAB PROGRAM :

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');


%Taking inputs from user
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 state values 

%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, Back Work Ratio, Specific Steam Conductivity and Efficiency

%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 results
%state point 1
disp('                    RESULTS                ');
disp('At State point 1');
fprintf('\nP1 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\n',S1);

%Values of state point 2
disp('At State point 2');
fprintf('\nP2 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\n',S2);

%Values of state point 3
disp('At State point 3');
fprintf('\nP3 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\n',S3);

%Values of state point 4
disp('At State point 4');
fprintf('\nP4 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);

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

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

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

%Thermal Efficiency
fprintf('thermal efficiency : %.2f %',EFF);

%Specific Steam Conductivity
fprintf('\nSpecific Steam Conductivity : %.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),'g.')
plot(XSteam('sV_T',t(i)),t(i),'g.')
end

plot([S1 S2],[T1 T2],'linewidth',2,'color','k')
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','k')
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','k')
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','k')
end

plot([S_L1 S_G1],[T_sat1 T_sat1],'linewidth',2,'color','k')
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)),'b.')
 plot(XSteam('sV_T',t(i)),XSteam('hV_T',t(i)),'b.')
end
plot([S1 S2 S3 S4 S1],[H1 H2 H3 H4 H1],'linewidth',2,'color','k')
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')

Explanation:-

1. Program initally displays the processes invlolved in rankine cycle.
2. State 1 & 2 pressure and state 1 temperature are taken as inout from user.
3. The values from the Xsteam library are extracted and the state values such as pressure, temperature, enthalphy and entropy are calculated.
4. Further the values of Turbine work ,Pump work,Net work ,Thermal Efficiency,Back Work Ratio and Specific Steam Conductivity are calculated.
5. All the calculated values are displayed in the command window.
6. Finally the T-S and H-S graph of the Rankine Cycle is plotted.

5.RESULTS :

Output in command window

T-S Graph of the Rankine Cycle:-

H-S Graph of the Rankine Cycle:-

Errors faced:-

1)At first there was difficulty to understand the Xsteam library but the videos by skill-lync helped.

2)There was an spelling mistake in writing 'Xsteam', instead 'Xstream' was written

6.CONCLUSION :

1. The values of Pressure,Temperature,Enthalphy and Entropy for different state points and also the Work, Efficiency, Back work ratio and Specific steam conductivity was calculated.
2. Also the graph of T-S and H-S for Rankine Cycle was plotted.

7.REFERENCES :

https://www.sciencedirect.com/topics/engineering/specific-steam-consumption

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