Project 2 - Rankine cycle Simulator

Aim-

1. To Simulate a Rankine cycle using matlab.
2. Extracting Steam and water properties from Xstram file.
3. Calculating all the state points of the cycle based on User inputs.
4. Plotting the T vs S and H vs S plot for the given input.

Theory- A rankine cycle is an idealised Thermodynamic cycle which governs the working of a Heat Engine. In Rankine cycle,the friction losses of a heat engine are neglected. It is a cycle which converts heat into mechanical energy which usually is converted into electrical energy . There are four components in this cycle which work on four different processes.The four components are turbine,Condensor,Pump and Boiler. Rankine cycle is nothing but a modification of Carnot cycle. Ideal Rankine cycle is very useful in steam power plants and gas power plants. To improve the efficiency of Rankine cycle in the steam power plant, there are some changes in Rankine cycle which differs from the Carnot cycle. Firstly, a pump is used in place of condenser to handle only liquid, not a mixture of liquid and vapour.Secondly, exhaust steam from the turbine is completely condensed in the condenser, see in the following diagram:

Processes and Working :

There are four processes in the rankine cycle :

1. Process 1-2 : Isentropic Expansion in the turbine
2. Process 2-3 : Constant pressure Heat rejection in condenser
3. Process 3-4 : Isentropic compression in the pump
4. Process 4-1 : Constant pressure heat addition in the boiler

Rankine cycle efficiency ηR is -

Back Work Ratio:

The fraction of the work produced by the turbine that is consumed by the compressor.

BW ratio=Wp/Wt

MATLAB PROGRAM FOR RANKINE CYCLE SIMULATOR

clear all
close all
clc

disp(' RANKINE CYCLE ');
disp('1-2 is Constant pressure heat addition in the boiler');
disp('2-3 is Isentropic Expansion in the Turbine');
disp('3-4 is Constant pressure heat removal in the Condenser');
disp('4-1 is Isentropic compression in the pump');

p1 = input('nValue of pressure at turbine inlet, p1(in bar) = ');
T1 = input('nValue of temperature at turbine inlet, T1(in degree.C) = ');
p2 = input('nValue of pressure at condenser inlet, p2(in bar) = ');

% At State 1
h1 = XSteam('h_pT', p1, T1); % Extracting Enthalpy at state pt 1
s1 = XSteam('s_pT', p1, T1); % Similarly

% At State 2
s2 = s1; % Isentropic Expansion
sf2= XSteam('sL_p', p2); % Saturated Liquid Entropy
sg2 = XSteam('sV_p', p2); % Saturated Vapour Entropy
x2 = (s2-sf2)/(sg2-sf2);
hf2 = XSteam('hL_p', p2);
hg2 = XSteam('hV_p', p2);
h2 = hf2 + (x2*(hg2-hf2));

% At State 3
p3 = p2; % Constant pressure Heat rejection in Condenser
s3= XSteam('sL_p', p3);
h3 = XSteam('hL_p', p3);

% At State 4
s4 = s3;
p4 = p1;

% Work done by turbine
Wt = h1 - h2;

% Work done to run pump
v3 = XSteam('vL_p', p3);
Wp = v3*(p4 - p3)*100;
h4 = h3 + Wp;

%Net work
Wnet = Wt - Wp;

%Heat into the system
Qin = h1 - h4;

%Heat out of the system
Qout = h2 - h3;

%Thermal efficiency
thermal_eff = (Wnet/Qin)*100;

%Specific Steam Consumption
%SSC = mass flow rate/power
SSC = (3600/Wnet);

% Back Work ratio
BW = (Wp/Wt)

% Calculation of Temperatures at the state points
T3 = XSteam('Tsat_p', p3);
T2 = T3;
Cp4 = XSteam('Cp_ps', p4, s4);
Cv4 = XSteam('Cv_ps', p4, s4);
k = Cp4/Cv4;
T4 = T3/((p3/p4)^((k-1)/k));

%Calculating Temperature, Entropy and Enthalpy at the vapour and liquid line for plotting
T6 = XSteam('Tsat_p', p1);
s5 = XSteam('sL_p', p1);
s6 = XSteam('sV_p', p1);
h5 = XSteam('hL_p', p1);
h6 = XSteam('hV_p', p1);
T5 = T6;

%Plotting the saturation curve
T = linspace(1,375,1000);
for i = 1:length(T)

sf(i) = XSteam('sL_T', T(i));
sg(i) = XSteam('sV_T', T(i));
hf(i) = XSteam('hL_T', T(i));
hg(i) = XSteam('hV_T', T(i));
end

%Plotting T-s diagram
figure(1)
hold on
plot(sf, T, 'r','linewidth',1)
plot(sg, T, 'r','linewidth',1)
plot([s1 s2], [T1 T2], 'b', 'linewidth', 2)
plot([s2 s3], [T2 T3] ,'b', 'linewidth', 2)
plot([s3 s4], [T3 T4], 'b', 'linewidth', 2)
plot([s4 s5], [T4 T5], 'b', 'linewidth', 2)
plot([s5 s6], [T5 T6], 'b', 'linewidth', 2)
sc1 = linspace(s6, s1, 1000);
for l = 1:length(sc1)
Tc1(l) = XSteam('T_ps', p1, sc1(l));
end
plot(sc1, Tc1, 'b', 'linewidth', 2)
text(s1+0.1, T1, '1')
text(s2+0.1, T2, '2')
text(s3, T3-20, '3')
text(s4, T4+20, '4')
title('Temp vs Entropy plot')
xlabel('Entropy ,S (Kj/kgk')
ylabel('Temperature (degree C) ')
legend('Saturation curve')

%Plotting h-s diagram
figure(2)
hold on
plot(sf, hf, 'k', 'linewidth', 1)
plot(sg, hg, 'k', 'linewidth', 1)
plot([s1 s2], [h1 h2], 'r', 'linewidth', 2)
plot([s2 s3], [h2 h3], 'r', 'linewidth', 2)
plot([s3 s4], [h3 h4], 'r', 'linewidth', 2)
hc = linspace(h4, h5, 100);
for r = 1:length(hc)
sch(r) = XSteam('s_ph', p1, hc(r));
end
plot(sch,hc, 'r', 'linewidth', 2)
plot([s5 s6], [h5 h6], 'r', 'linewidth', 2)
for m = 1:length(sc1)
hc1(m) = XSteam('h_ps', p1, sc1(m));
end
plot(sc1, hc1, 'r', 'linewidth', 2)
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 plot')
xlabel('Entropy , S (KJ/kgk) ')
ylabel('Enthalpy , H (KJ/kg)')
legend('Saturation curve','location','northwest')

% Displaying the Results in the Command Window:
disp('Results');
p1 = p1;
T1 = T1;
p2 = p2;
disp('At stage point 1');
n1 = sprintf('P1 is %.3f bar',p1);
disp(n1);
n2 = sprintf('T1 is %.3f C',T1);
disp(n2);
n3 = sprintf('h1 is %.3f kJ/kg',h1);
disp(n3);
n4 = sprintf('s1 is %.3f kJ/kgK',s1);
disp(n4);
disp('At stage point 2');
n11 = sprintf('P2 is %.3f bar',p2);
disp(n11);
n21 = sprintf('T2 is %.3f C',T2);
disp(n21);
n31 = sprintf('h2 is %.3f kJ/kg',h2);
disp(n31);
n41 = sprintf('s2 is %.3f kJ/kgK',s2);
disp(n41);
disp('At stage point 3');
n12 = sprintf('P3 is %.3f bar',p3);
disp(n12);
n22 = sprintf('T3 is %.3f C',T3);
disp(n22);
n32 = sprintf('h3 is %.3f kJ/kg',h3);
disp(n32);
n42 = sprintf('s3 is %.3f kJ/kgK',s3);
disp(n42);
disp('At stage point 4');
n13 = sprintf('P4 is %.3f bar',p4);
disp(n13);
n23 = sprintf('T4 is %.3f C',T4);
disp(n23);
n33 = sprintf('h4 is %.3f kJ/kg',h4);
disp(n33);
n43 = sprintf('s4 is %.3f kJ/kgK',s4);
disp(n43);
n14 = sprintf('Wt is %.3f kJ/kg',Wt);
disp(n14);
n15 = sprintf('Wp is %.3f kJ/kg',Wp);
disp(n15);
n16 = sprintf('Wnet is %.3f kJ/kg',Wnet);
disp(n16);
n17 = sprintf('Thermal_efficiency is %.2f Percent',thermal_eff);
disp(n17);
n18 = sprintf('SSC is %.2f kg/kWh',SSC);
disp(n18);
n19 = sprintf('Back work ratio is %.3f ',BW);
disp(n19);

Explanation of Program

1. Xsteam data is used to extract steam and water properties of enthaly , entropy at specific pressure and temperatures for sat liquid, sat vapour conditions etc .
2. The program requires the input of Pressure ( in bar) at state point 1 ( turbine inlet) , Temperature at same point (degree celcius) and pressure at condenser inlet (point 2).
3. With the help of these inlets & from Xsteam data, the program calculates all the state points of the Rankine cycle .
4. The Xsteam data works as , h1 = XSteam('h_pT' , p1 , T1) it returns the enthalpy of water at given pressure and temperature in bar and degC respectively.
5. As we extract the data , we use thermodynamic relation to further find state points and extract their data from XSteam which are mentioned after studying the Rankine cycle.
6. Sf and sg , hf and hg , where f and g stands for saturated liquid and saturated vapour respectively are calculayed after studying the plots of Rankine cycles and extracting data from Xsteam file.
7. The net work , work done by turbine , work done to run the pump , Heat in and heat out are calculated using standard thermodynamic relation
8. Efficiency and Specific steam consumption (s.s.c) of the Rankine cycle is calculated from thermodynamic relations and mentioning them in program using relations.
9. T , s and h are extracted at vapour and liquid line for plotting purpose , after 4th point for the variation you observe in the plot .
10. Saturation curve is plotted in red for saturated liquid and saturated gas in T-S and in H-S it is black .
11. Plot of T vs s and h vs s is created from all the points obtained from the program using the plot command and mentioning all the lables, linewidth, color and title.
12. The plot changes as the user input changes for the above mentioned inputs .
13. Results are displayed in the command window by using sprint command .

Result - The input, ouput screen and the various state points with various parameters generated in the command window are shown below

RESULTS and PLOTS

The performance of the Heat Engine was calculated and the following Observations were made:

1. Net Work = 1120.863kJ/kg
2. Thermal Efficiency = 36.17%
3. Back Work Ratio = 0.003
   The T-S and H-S performance curves of the Rankine Cycle were plotted.