Rankine Cycle

RANKINE CYCLE SIMULATOR:

The Rankine cycle or Rankine Vapor Cycle is the process widely used by power plants such as coal-fired power plants or nuclear reactors. In this mechanism, a fuel is used to produce heat within a boiler, converting water into steam which then expands through a turbine producing useful work. This process was developed in 1859 by Scottish engineer William J.M. Rankine. This is a thermodynamic cycle which converts heat into mechanical energy—which usually gets transformed into electricity by electrical generation

COMPONENTS OF RANKINE CYCLE:

The four basic components of Rankine cycle are shown in figure 1 each component in the cycle is regarded as control volume, operating at steady state.

Pump: The liquid condensate leaving the condenser at the state 1 is pumped to the operating pressure of the boiler. The pump operation is considered isentropic.

Boiler: The heat is supplied in the working fluid (feed water) in the boiler and thus vapor is generated. The vapor leaving the boiler is either at saturated at the state 3 or superheated at the state 3, depending upon the amount of heat supplied by the boiler.

Turbine: The vapor leaving the boiler enters the turbine, where it expands isentropically to the condenser pressure at the state 4. The work produced by the turbine is rotary (shaft) work and is used to drive an electric generator or machine.

Condenser: The condenser is attached at the exit of the turbine. The vapor leaving the turbine is wet vapor and it is condensed completely in the condenser to the state 1, by giving its latest heat to some other cooling fluid like water.

The efficiency of the Rankine cycle is limited by the high heat of vaporization by the fluid. The fluid must be cycled through and reused constantly, therefore, water is the most practical fluid for this cycle. This is not why many power plants are located near a body of water—that\'s for the waste heat.

MATLAB CODE:

clear all
close all
clc

% User Inputs for the Rankine Cycle

disp(\'    RANKINE CYCLE SIMULATOR\');
disp(\'1-2 is Isentropic Expansion in the turbine\');
disp(\'2-3 is const Pressure heat Rejection by the Condenser\');
disp(\'3-4 is Isentropic Compression in the pump\');
disp(\'4-1 is const Pressure heat Addition by the Boiler\');

p1=input(\'nEnter 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):\');

%inlet of the Turbine
tsat=XSteam(\'Tsat_p\',p1);
sf1=XSteam(\'sL_p\',p1);
sg1=XSteam(\'sV_p\',p1);
if t1>tsat
    tsup=t1;
    h1=XSteam(\'h_pT\',p1,tsup);
    s1=XSteam(\'s_pT\',p1,tsup);
elseif t1==tsat
    h1=XSteam(\'hL_p\',p1);
    s1=XSteam(\'sL_p\',p1);
else
    disp(\'Temperature entered must be greater than or equal to saturation temperature\')
end

%condenser inlet 
t2=XSteam(\'Tsat_p\',p2);
hf2=XSteam(\'hL_p\',p2);
hg2=XSteam(\'hV_p\',p2);
s2=s1;
sg2=XSteam(\'sV_p\',p2);
sf2=XSteam(\'sL_p\',p2);
x2=(s2-sf2)/(sg2-sf2);
h2=hf2+(x2*(hg2-hf2));

%condenser exit
p3=p2;
t3=t2;
h3=hf2;
s3=sf2;

%boiler inlet
p4=p1;
s4=s3;
cp4=XSteam(\'Cp_ps\',p4,s4);
cv4=XSteam(\'Cv_ps\',p4,s4);
gamma=cp4/cv4;
t4=t3*(p4/p3)^((gamma-1)/gamma);
vf=XSteam(\'vL_p\',p3);
wp=vf*(p1-p2)*100;
h4=wp+h3;

% work output from turbine
wt=h1-h2;

%heat input
Qin=h1-h4;

%heat output
Qout=h2-h3;

%net work
wnet=wt-wp; 

% thermalefficiency
therm_efficiency=(wnet/Qin)*100;

% heat added in the boiler
q_in=h1-h4;

% heat rejected in the condensor
q_out=h2-h3;

%specific fuel consumption
sfc=3600/wnet;

%plotting of T-S and H-S diagram
%T-S diagram

figure(1)
hold on
%plotting saturation lines
temp = linspace(1, 373, 500);

hl=zeros(1,100);
hv=zeros(1,100);
sl=zeros(1,100);
sv=zeros(1,100);

for i = 1 : length(temp)
     hl(i) = XSteam(\'hL_T\', temp(i));
     hv(i) = XSteam(\'hV_T\', temp(i));
     sl(i) = XSteam(\'sL_T\', temp(i));
     sv(i) = XSteam(\'sV_T\', temp(i));
end
plot(sl, temp, \'k\', \'linestyle\',\'-\',\'linewidth\', 1.5)
plot(sv, temp, \'k\', \'linestyle\',\'-\',\'linewidth\', 1.5)
xlabel(\'Specific Entropy (kJ/kgK)\')
ylabel(\'Temprature (degC)\')

title(\'T-S diagram\');
plot([s1 s2 s3 s4 sf1 sg1],[t1 t2 t3 t4 tsat tsat],\'color\',\'g\',\'linewidth\', 1.5)
text(s1,t1,\'1\')
text(s2,t2,\'2\')
text(s3,t3-10,\'3\')
text(s4,t4+10,\'4\')

t=linspace(tsat,tsup,1000); 
    for j =1:length(t)
        sp(j) = XSteam(\'s_pT\',p1,t(j));
    end
 plot(sp,t,\'color\',\'g\',\'linewidth\', 1.5);

%H-S diagram
figure(2)
hold on

title(\'H-S diagram\');
plot(sl, hl, \'r\',\'linestyle\',\'-\', \'linewidth\', 1.5)
plot(sv, hv, \'r\',\'linestyle\',\'-\', \'linewidth\', 1.5)      
plot([s1 s2 s3 s4 s1], [h1 h2 h3 h4 h1], \'color\', \'black\',\'linewidth\', 1.5);
text(s1,h1,\'1\')
text(s2,h2,\'2\')
text(s3,h3-100,\'3\')
text(s4,h4+100,\'4\')
ylabel(\'Specific Enthalpy (kJ/kg)\')
xlabel(\'Specific Entropy (kJ/kgK)\')

%output
%at state 1
disp(\'RESULTS\');
disp(\'At State point 1:\');
fprintf(\'P1 is : %.2f Bar\',p1);
fprintf(\'\\n T1 is : %.2f Deg Celcius\',t1);
fprintf(\'\\n H1 is : %.2f kJ/kg\',h1);
fprintf(\'\\n S1 is : %.2f kJ/kgK\\r\\n\',s1);

%at state 2
disp(\' At State point 2:\');
fprintf(\'P2 is : %.2f Bar\',p2);
fprintf(\'\\n T2 is : %.2f Deg Celcius\',t2);
fprintf(\'\\n H2 is : %.2f kJ/kg\',h2);
fprintf(\'\\n S2 is : %.2f kJ/kgK\\r\\n\',s2);

%at state 3
disp(\' At State point 3:\');
fprintf(\'P3 is : %.2f Bar\',p3);
fprintf(\'\\n T3 is : %.2f Deg Celcius\',t3);
fprintf(\'\\n H3 is : %.2f kJ/kg\',h3);
fprintf(\'\\n S3 is : %.2f kJ/kgK\\r\\n\',s3);

%at state 4
disp(\'At State point 4:\');
fprintf(\'P4 is : %.2f Bar\',p4);
fprintf(\'\\n T4 is : %.2f Deg Celcius\',t4);
fprintf(\'\\n H4 is : %.2f kJ/kg\',h4);
fprintf(\'\\n S4 is : %.2f kJ/kgK\\r\\n\',s4);

fprintf(\'Work output by the Turbine (Wt) is : %.2f kJ/kg\',wt);
fprintf(\'\\n Work input by the pump (Wp) is : %.2f kJ/kg\',wp);
fprintf(\'\\n Net Work is : %.2f kJ/kg\',wnet);
fprintf(\'\\n Thermodynamic efficiency is : %.2f Percent\',therm_efficiency);
fprintf(\'\\n  %s  Heat input in Boiler:%.2f \',q_in,\' KJ/kg\');
fprintf(\'\\n  %s  Heat rejected in condenser:%.2f \',q_out,\' KJ/kg\');
fprintf(\'\\n Specific Fuel Consumption is : %.2f kg/kWh\',sfc);

OUTPUT:

T vs S plot:

H vs S plot: