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Project 2 - Rankine cycle Simulator

AAswin Os20 May 2022

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Rankine Stimulator

Rankine cycle consist of four processes as follows.

Process 1-2: Reversible adiabatic expansion in the turbine (or steam engine).

Process 2-3: Constant-pressure transfer of heat in the condenser.

Process 3-4: Reversible adiabatic pumping in the feed pump.

Process 4-1: Constant-pressure transfer of heat in boiler.

Applying steady flow energy equation (S.F.E.E) to boiler ,turbine , condenser and pump:

  • For Boiler as the control volume, we get

                              hf4 +Q4=h1

                               Q1=h1-hf4

  • For turbine as the control volume, we get

                               h1=wt+h2 , where wt= turbine work

                                wt=h1-h2                 

  • For condenser, we get

                          h2=Q2+hf3

                                Q2=h2-hf3

  • For the feed pump, we get

                                  hf3+wp=hf4

                                  wp=hf4-hf3

       Efficiency of the Rankine cycle is given by,

                                   Effi.mu=w/Qnet1=wp/Q1

Main code explanation

Before we writing this program ,we are using XSteam.m which is basically a steam table

close all

clear all

clc

 

  • Clearing workspace, command window ad close all plots.

 

 

 

 

%Print process Desscription

fprintf('1-2 Isobaric heat Transfer\n')

fprintf('2-3 Isentropic Expansion\n')

fprintf('3-4 Isobaric heat Rejection\n')

fprintf('4-1 Isentropoic compression \n')

  • Print description of all process in the command window.

%step-1:Enter Input

p1=input('Enter the preassure at the turbine inlet(in bar): ');

T1=input('Enter the Trmperature at the turbine inlet (in degree Celcius): ');

p2=input('Enter the pressure at the condenser(in bar): ');

  • Taking all input argument.

%step-2 calculate each state point values.

% State Points -1

h1=XSteam('h_pt',p1,T1);

s1=XSteam('s_pt',p1,T1);

 

%Step-3: state point 2

s2=s1;

sf2=XSteam('sL_p',p2);

sg2=XSteam('sV_p',p2);

hf2=XSteam('hL_p',p2);

hg2=XSteam('hV_p',p2);

                

T2=XSteam('Tsat_p',p2);

x2=(s2-sf2)/(sg2-sf2);

h2=hf2+(x2*(hg2-hf2));

%step 4:state point 3

p3=p2;

T3=XSteam('Tsat_p',p3);

s3=XSteam('sL_p',p3);

h3=XSteam('hL_p',p3);

 

 

%step-5 : state point 4

p4=p1;

s4=s3;

Cp4=XSteam('Cp_ps',p4,s4);

Cv4=XSteam('Cv_ps',p4,s4);

%calculating gamma

gamma=Cp4/Cv4;

r=(gamma-1)/gamma;

T4=T3*(p4/p3).^r;

h4=XSteam('h_ps',p4,s4);

%step 6 Calculate other output values

%turbine work

wt=h1-h2;

%pump work

wp=h4-h3;

 

w_net=wt-wp;  %network unit in kg/kg

Qi=h1-h4; %heat supplied

Qo=h2-h3; %heat rejected

 

N_per=(w_net/Qi).*100; %efficiency

SSC= 3600/(wt-wp) ; %steam rate per second

Bwr=Qi/Qo;

  • Calculation of cp values at p1 &p2 for saturated liquid and vapour.
  • Calculation of saturation temperature at p1 and p2.
  • Calculation of saturation property, process property of different stages.
  • Calculation of work done, heat, SC and efficiency.

%step 7: statepoint 5 and 6 which help in plotting

T5=XSteam('Tsat_p',p1);

T6=T5;

s5=XSteam('sL_p',p1);

s6=XSteam('sV_p',p1);

h5=XSteam('hL_p',p1);

h6=XSteam('hV_p',p1);

%plotting the required graph

 

%T-S graph

figure(1)

T_r1=linspace(T5,T1,500);

for i=1:length(T_r1)

    s(i)=XSteam('s_pt',p1,T_r1(i));

end

hold on

plot([s1 s2 s3 s4 s5 s6 s],[T1 T2 T3 T4 T5 T6 T_r1],'LineWidth',3,'Color','k')

axis([0 10 0 430])

text(s1,T1,'1','FontSize',15)

text(s2,T2,'2','FontSize',15)

text(s3,T3,'3','FontSize',15,'VerticalAlignment','top')

text(s4,T4,'4','FontSize',15,'VerticalAlignment','bottom','HorizontalAlignment','right')

text(s5,T5,'5','FontSize',15,'VerticalAlignment','top')

text(s6,T6,'6','FontSize',15,'VerticalAlignment','top','HorizontalAlignment','right')

 

T_r2=linspace(0,T1,500);

for j = 1: length(T_r2)

    sl(j)=XSteam('sL_T',T_r2(j));

    sv(j)=XSteam('sv_T',T_r2(j));

    hl(j)=XSteam('hL_T',T_r2(j));

    hv(j)=XSteam('hv_T',T_r2(j));

end

plot(sl,T_r2,'LineWidth',1.5,'Color','r')

plot(sv,T_r2,'LineWidth',1.5,'Color','r')

xlabel('Entropy')

ylabel('Temperature')

title('entropy vs Temperature')

 

%H-S Graph

figure(2)

hold on

plot([s1 s2 s3 s4 s1],[h1 h2 h3 h4 h1],'LineWidth',3,'Color','k')

axis([0 10 -100 1000])

text(s1,h1,'1','FontSize',15)

text(s2,h2,'2','FontSize',15)

text(s3,h3,'3','FontSize',15,'VerticalAlignment','top','HorizontalAlignment','right')

text(s4,h4,'4','FontSize',15,'VerticalAlignment','bottom','HorizontalAlignment','right')

 

 

plot(sv,hv,'LineWidth',1.5,'Color','r')

plot(sl,hl,'LineWidth',1.5,'Color','r')

xlabel('Entropy')

ylabel('enthalpy')

title('entropy vs Temperature')

  • Calculation and plotting of saturation liquid and vapour lines.
  • Plotting T-s plot
  • Plotting h-s plot

 

%Displaying the results

fprintf('\n______RESULTS_______\n')

fprintf('\n At State Point 1 : \n')

fprintf('P1 is : %f Bar \n',p1)

fprintf('T1 is : %f Deg Celcius \n',T1)

fprintf('H1 is : %f kJ/kg \n',h1)

fprintf('S1 is : %f kJ/kgK\n',s1)

 

fprintf('\n At State Point 2 : \n')

fprintf('P2 is : %f Bar \n',p1)

fprintf('T2 is : %f Deg Celcius \n',T2)

fprintf('H2 is : %f kJ/kg \n',h2)

fprintf('S2 is : %f kJ/kgK\n',s2)

fprintf('X2 is : %f \n',x2)

 

fprintf('\n At State Point 3 : \n')

fprintf('P3 is : %f Bar \n',p3)

fprintf('T3 is : %f Deg Celcius \n',T3)

fprintf('H3 is : %f kJ/kg \n',h3)

fprintf('S3 is : %f kJ/kgK\n',s3)

 

fprintf('\n At State Point 4 : \n')

fprintf('P4 is : %f Bar \n',p4)

fprintf('T4 is : %f Deg Celcius \n',T4)

fprintf('H4 is : %f kJ/kg \n',h4)

fprintf('S4 is : %f kJ/kgK\n',s4)

 

 

fprintf('wt : %f kJ/kg\n',wt)

fprintf('wp : %f  kJ/kg\n',wp)

fprintf('wnet : %f kJ/kg \n',w_net)

fprintf('Ntherm : %f percent\n',N_per)

fprintf('SSC is : %f kg/kwh\n',SSC)

fprintf('BWR is : %f \n',Bwr)

  • Displaying all output

MAIN CODE

close all
clear all
clc

%Print process Desscription
fprintf('1-2 Isobaric heat Transfer\n')
fprintf('2-3 Isentropic Expansion\n')
fprintf('3-4 Isobaric heat Rejection\n')
fprintf('4-1 Isentropoic compression \n')

%step-1:Enter Input
p1=input('Enter the preassure at the turbine inlet(in bar): ');
T1=input('Enter the Trmperature at the turbine inlet (in degree Celcius): ');
p2=input('Enter the pressure at the condenser(in bar): ');

%step-2 calculate each state point values.
% State Points -1 
h1=XSteam('h_pt',p1,T1);
s1=XSteam('s_pt',p1,T1);

%Step-3: state point 2
s2=s1;
sf2=XSteam('sL_p',p2);
sg2=XSteam('sV_p',p2);
hf2=XSteam('hL_p',p2);
hg2=XSteam('hV_p',p2); 
                
T2=XSteam('Tsat_p',p2);
x2=(s2-sf2)/(sg2-sf2);
h2=hf2+(x2*(hg2-hf2));
%step 4:state point 3
p3=p2;
T3=XSteam('Tsat_p',p3);
s3=XSteam('sL_p',p3);
h3=XSteam('hL_p',p3);


%step-5 : state point 4
p4=p1;
s4=s3;
Cp4=XSteam('Cp_ps',p4,s4);
Cv4=XSteam('Cv_ps',p4,s4);
%calculating gamma
gamma=Cp4/Cv4;
r=(gamma-1)/gamma;
T4=T3*(p4/p3).^r;
h4=XSteam('h_ps',p4,s4);
%step 6 Calculate other output values
%turbine work
wt=h1-h2;
%pump work
wp=h4-h3;

w_net=wt-wp;  %network unit in kg/kg
Qi=h1-h4; %heat supplied
Qo=h2-h3; %heat rejected

N_per=(w_net/Qi).*100; %efficiency
SSC= 3600/(wt-wp) ; %steam rate per second
Bwr=Qi/Qo;

%step 7: statepoint 5 and 6 which help in plotting
T5=XSteam('Tsat_p',p1);
T6=T5;
s5=XSteam('sL_p',p1);
s6=XSteam('sV_p',p1);
h5=XSteam('hL_p',p1);
h6=XSteam('hV_p',p1);

%plotting the required graph

%T-S graph
figure(1)
T_r1=linspace(T5,T1,500);
for i=1:length(T_r1)
    s(i)=XSteam('s_pt',p1,T_r1(i));
end
hold on
plot([s1 s2 s3 s4 s5 s6 s],[T1 T2 T3 T4 T5 T6 T_r1],'LineWidth',3,'Color','k')
axis([0 10 0 430])
text(s1,T1,'1','FontSize',15)
text(s2,T2,'2','FontSize',15)
text(s3,T3,'3','FontSize',15,'VerticalAlignment','top')
text(s4,T4,'4','FontSize',15,'VerticalAlignment','bottom','HorizontalAlignment','right')
text(s5,T5,'5','FontSize',15,'VerticalAlignment','top')
text(s6,T6,'6','FontSize',15,'VerticalAlignment','top','HorizontalAlignment','right')

T_r2=linspace(0,T1,500);
for j = 1: length(T_r2)
    sl(j)=XSteam('sL_T',T_r2(j));
    sv(j)=XSteam('sv_T',T_r2(j));
    hl(j)=XSteam('hL_T',T_r2(j));
    hv(j)=XSteam('hv_T',T_r2(j));
end
plot(sl,T_r2,'LineWidth',1.5,'Color','r')
plot(sv,T_r2,'LineWidth',1.5,'Color','r')
xlabel('Entropy')
ylabel('Temperature')
title('entropy vs Temperature')

%H-S Graph
figure(2)
hold on 
plot([s1 s2 s3 s4 s1],[h1 h2 h3 h4 h1],'LineWidth',3,'Color','k')
axis([0 10 -100 1000])
text(s1,h1,'1','FontSize',15)
text(s2,h2,'2','FontSize',15)
text(s3,h3,'3','FontSize',15,'VerticalAlignment','top','HorizontalAlignment','right')
text(s4,h4,'4','FontSize',15,'VerticalAlignment','bottom','HorizontalAlignment','right')


plot(sv,hv,'LineWidth',1.5,'Color','r')
plot(sl,hl,'LineWidth',1.5,'Color','r')
xlabel('Entropy')
ylabel('enthalpy')
title('enthalpy vs Temperature')

%Displaying the results
fprintf('\n______RESULTS_______\n')
fprintf('\n At State Point 1 : \n')
fprintf('P1 is : %f Bar \n',p1)
fprintf('T1 is : %f Deg Celcius \n',T1)
fprintf('H1 is : %f kJ/kg \n',h1)
fprintf('S1 is : %f kJ/kgK\n',s1)

fprintf('\n At State Point 2 : \n')
fprintf('P2 is : %f Bar \n',p1)
fprintf('T2 is : %f Deg Celcius \n',T2)
fprintf('H2 is : %f kJ/kg \n',h2)
fprintf('S2 is : %f kJ/kgK\n',s2)
fprintf('X2 is : %f \n',x2)

fprintf('\n At State Point 3 : \n')
fprintf('P3 is : %f Bar \n',p3)
fprintf('T3 is : %f Deg Celcius \n',T3)
fprintf('H3 is : %f kJ/kg \n',h3)
fprintf('S3 is : %f kJ/kgK\n',s3)

fprintf('\n At State Point 4 : \n')
fprintf('P4 is : %f Bar \n',p4)
fprintf('T4 is : %f Deg Celcius \n',T4)
fprintf('H4 is : %f kJ/kg \n',h4)
fprintf('S4 is : %f kJ/kgK\n',s4)


fprintf('wt : %f kJ/kg\n',wt)
fprintf('wp : %f  kJ/kg\n',wp)
fprintf('wnet : %f kJ/kg \n',w_net)
fprintf('Ntherm : %f percent\n',N_per)
fprintf('SSC is : %f kg/kwh\n',SSC)
fprintf('BWR is : %f \n',Bwr)

RESULT

input inlet tuerbine temperature of 400degree celcius

inlet pressure of turbine of 30bar

presure at condenser is 0.05bar

Graph of Entropy vs Temperature

Graph of Enthalpy vs Temperature

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