Rankine Cycle

INTRODUCTION

A simple steam plant working on a Rankine Cycle consists of a boiler, turbine, condenser and a feed pump. For any process in the vapour cycle, it is possible to assume a ideal process when performs the basic intended operation and involves no extraneous effects. For steam boiler, this ideal process would be a reversible constant pressure heating process of water to form steam, for turbine it would be a reversible adiabatic expansion of steam, for the condenser it would be reversible constant pressure heat rejection as the steam condenses till it becomes saturated liquid and for the pump the ideal process would be the reversible adiabatic compression of this liquid ending at the initial pressure. When all these processes are ideal, the cycle is called Rankine Cycle.

There are four processes in a typical Rankine cycle.

• Process 1–2(Reversible adiabatic compression): The working fluid is pumped from low to high pressure. As the fluid is a liquid at this stage, the pump requires little input energy.
• Process 2–3(Reversible constant volume heat addition): The high-pressure liquid enters a boiler, where it is heated at constant pressure by an external heat source to become a dry saturated vapour. The input energy required can be easily calculated graphically, using an enthalpy–entropy chart (h–s chart, or Mollier diagram), or numerically, using steam tables.
• Process 3–4(Reversible adiabatic expansion): The dry saturated vapour expands through a turbine, generating power. This decreases the temperature and pressure of the vapour, and some condensation may occur. The output in this process can be easily calculated using the chart or tables noted above.
• Process 4–1(Reversible constant volume heat rejection): The wet vapour then enters a condenser, where it is condensed at a constant pressure to become a saturated liquid.

Objective:

• To calculate the state points of the Rankine Cycle based on the given inputs.

• To plot the corresponding T-s and h-s plots for the given set of inputs.

clear all 
close all
clc

disp(\'Rankine Cycle\')
disp(\'Process 1-2 Isentropic Compression in the pump\')
disp(\'Process 2-3 Constant Pressure Heat addition by Boiler\')
disp(\'Process 3-4 Isentropic Expansion in the Turbine\')
disp(\'Process 4-1 Constant Pressure Heat Rejection by Condensor\')

p3= input( \'Enter the pressure at the entry of the Turbine in Bar \\n\');
T3= input( \'Enter the temperature at the entry of the Turbine in degree celcius \\n\');
p4= input( \'Enter the pressure at the exit of the Turbine in Bar \\n\');

p1=p4;
p2=p3;

% state point 1

h1=XSteam(\'hL_p\',p1);
v1=XSteam(\'vL_p\',p1);
T1=XSteam(\'T_ph\',p1,h1);
s1=XSteam(\'sL_T\',T1);

% state piont 2

wp= v1*(p2-p1)*100; % work done by the pump
h2= h1 +wp;
s2=s1;
% To find T2
cp2=XSteam(\'CpL_p\',p1); 
cv2=XSteam(\'CvL_p\',p1);
gamma=cp2/cv2;
powterm= (gamma-1)/gamma;
prratio= p2/p1;
T2= T1*(prratio)^powterm;

% state point 3

h3= XSteam(\'h_pT\',p3,T3);
s3= XSteam(\'s_pT\',p3,T3);
v3=XSteam(\'v_pT\',p3,T3);
wt=v3*(p3-p4);  % work done by turbine

% state point 4

sf4= XSteam(\'sL_p\',p4);
sg4= XSteam(\'sV_p\',p4);
hf4= XSteam(\'hL_p\',p4);
hg4= XSteam(\'hV_p\',p4);
s4=s3;
T4=T1;
x4= (s4-sf4)/(sg4-sf4);
h4= hf4 + x4*(hg4-hf4);

Qin= h3-h2; % heat input to the system
Qout= h4-h1; % heat Output by the system
wnet= Qin+wp;
N_thermaal=(1-(Qout/wnet))*100;


%Plot of T-S diagram

Tsat=linspace(0,374,500);

for i=1:length(Tsat)
    
    sll(i)=XSteam(\'sL_T\', Tsat(i));
    svl(i)=XSteam(\'sV_T\', Tsat(i));
    hll(i)=XSteam(\'hL_T\', Tsat(i));
    hvl(i)=XSteam(\'hV_T\', Tsat(i));
end


figure(1)
title(\'T-S Diagram\')
xlabel(\'Entropy in kJ/kg\')
ylabel(\'Temperature in deg celcius\')

hold on


plot(sll,Tsat)
plot(svl,Tsat)
plot(s1,T1,\'*\',\'color\',\'r\')
text(s1,T1,\' 1\')
plot(s2,T2,\'*\',\'color\',\'g\')
text(s2,T2,\' 2\')
plot(s3,T3,\'*\',\'color\',\'b\')
text(s3,T3,\' 3\')
plot(s4,T4,\'*\',\'color\',\'y\')
text(s4,T4,\' 4\')
plot([s1 s2],[T1 T2],\'linewidth\', 1,\'color\',\'r\')
Tsatb=XSteam(\'Tsat_p\',p2);
ssatbb= XSteam(\'sL_T\',Tsatb);
plot([s2 ssatbb], [T2 Tsatb],\'linewidth\', 1,\'color\',\'g\')
sstab=XSteam(\'sL_p\',p2);
ssatb2=XSteam(\'sV_p\',p2);
plot([sstab ssatb2 ],[Tsatb Tsatb ],\'linewidth\', 1, \'color\',\'g\')
plot([ssatb2 s3], [Tsatb T3],\'linewidth\', 1,\'color\',\'g\')
plot([s3 s4], [T3 T4],\'linewidth\', 1,\'color\',\'b\')
plot([s4 s1],[T1 T4],\'linewidth\', 1,\'color\',\'y\')
legend(\'saturated liq line\', \'saturated vap line\',\'state piont 1\',\'state piont 2\',\'state piont 3\',\'state piont 4\', \'isentropic compression\', \'const pr heat addtn\',\'\',\'\',\'isentropic heat rej\', \'const pr heat rem\',\'location\',\'northwest\')

% plot of H-S diagram

figure(2)

hold on

plot(sll,hll)
plot(svl,hvl)
plot(s1,h1,\'*\',\'color\',\'r\')
text(s1,h1,\' 1\')
plot(s2,h2,\'*\',\'color\',\'g\')
text(s2,h2,\' 2\')
plot(s3,h3,\'*\',\'color\',\'b\')
text(s3,h3,\' 3\')
plot(s4,h4,\'*\',\'color\',\'y\')
text(s4,h4,\' 4\')

plot([s1 s2], [h1 h2])
plot([s2 s3], [h2 h3])
plot([s3 s4], [h3 h4])
plot([s4 s1], [h4 h1])

title(\'H-S Diagram\')
xlabel(\'Entropy\')
ylabel(\'Enthalpy\')
legend(\'saturated liq line\', \'saturated vap line\',\'state piont 1\',\'state piont 2\',\'state piont 3\',\'state piont 4\', \'isentropic compression\', \'const pr heat addtn\',\'isentropic heat rej\', \'const pr heat rem\',\'location\',\'northwest\')


% Output Screen to show the values at various state points

fprintf(\'\\n\')
fprintf(\'Pressure,Enthalpy, Entropy and Temperature values at state points\')
fprintf(\'\\n\')
fprintf(\'At State Point 1:\\r\\n\')
fprintf(\'P1 is : %f Bar\\r\\n\',p1)
fprintf(\'T1 is : %f Deg Celcius\\r\\n\',T1)
fprintf(\'H1 is : %f KJ/Kg\\r\\n\',h1)
fprintf(\'S1 is : %f KJ/KgK\\r\\n\',s1)
fprintf(\'\\n\')

fprintf(\'At State Point 2:\\r\\n\')
fprintf(\'P2 is : %f Bar\\r\\n\',p2)
fprintf(\'T2 is : %f Deg Celcius\\r\\n\',T2)
fprintf(\'H2 is : %f KJ/Kg\\r\\n\',h2)
fprintf(\'S2 is : %f KJ/KgK\\r\\n\',s2)
fprintf(\'\\n\')

fprintf(\'At State Point 3:\\r\\n\')
fprintf(\'P3 is : %f Bar\\r\\n\',p3)
fprintf(\'T3 is : %f Deg Celcius\\r\\n\',T3)
fprintf(\'H3 is : %f KJ/Kg\\r\\n\',h3)
fprintf(\'S3 is : %f KJ/KgK\\r\\n\',s3)
fprintf(\'\\n\')

fprintf(\'At State Point 4:\\r\\n\')
fprintf(\'P4 is : %f Bar\\r\\n\',p4)
fprintf(\'T4 is : %f Deg Celcius\\r\\n\',T4)
fprintf(\'H4 is : %f KJ/Kg\\r\\n\',h4)
fprintf(\'S4 is : %f KJ/KgK\\r\\n\',s4)

% Output of the thermal efficiency
fprintf(\'\\r\\n\')
fprintf(\'Heat Input to the system : %f \\r\\n\',Qin)
fprintf(\'Heat Output of the system : %f \\r\\n\',Qout)
fprintf(\'Thermal Efficiency of the Rankine cycle is : %.3f  percent \\r\\n\',N_thermaal)

Plots:

T-s Diagram:

h-s diagram:

Outputs: