Simulation of Rankine Cycle using MATLAB

Aim-Understand the concept of Rankine cycle and simulate using matlab.

Theory-

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:

Diagram-

Efficiency of rankin cycle-

Program-

disp(' RANKINE CYCLE ');                                   
disp('1-2 is Constant pressure heat addition in boiler');
disp('2-3 is Isentropic Expansion in Turbine');
disp('3-4 is Constant pressure heat removal Condenser');
disp('4-1 is Isentropic compression in 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 1
h1 = XSteam('h_pT', p1, T1);        
s1 = XSteam('s_pT', p1, T1);        

%at 2
s2 = s1;                                            
sf2= XSteam('sL_p', p2);            
sg2 = XSteam('sV_p', p2);           
x2 = (s2-sf2)/(sg2-sf2);
hf2 = XSteam('hL_p', p2);           
hg2 = XSteam('hV_p', p2);
h2 = hf2 + (x2*(hg2-hf2));

%at 3
p3 = p2;                            
s3= XSteam('sL_p', p3);
h3 = XSteam('hL_p', p3);

%at 4
s4 = s3;
p4 = p1;

Wt = h1 - h2;

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;

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

% Work ratio
BW = (Wp/Wt)


% Calculation of Temperatures 
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;


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 plot
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')


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')



%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);


 

Code explanation-

• 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).
• With the help of these inlets & from Xsteam data, the program calculates all the state points of the Rankine cycle .
• 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.
• 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.
• 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.
• The net work , work done by turbine , work done to run the pump , Heat in and heat out are calculated using standard thermodynamic relation
• Efficiency and Specific steam consumption (s.s.c) of the Rankine cycle is calculated from thermodynamic relations and mentioning them in program using relations.
• 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 .
• Saturation curve is plotted in red for saturated liquid and saturated gas in T-S and in H-S it is black .
• 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.
• The plot changes as the user input changes for the above mentioned inputs .

Results-