Project 2 - Rankine cycle Simulator
AIM:
To create a rankine cycle simulator using matlab and plot the T-S and H-S diagram and calculating the state points.
SOLUTION:
RANKINE CYCLE:
Rankine Cycle: Rankine cycle is the fundamental operating cycle of all the power plants where a working fluid is water. Rankine cycle is nothing but a advance version of Carnot cycle. In Rankine cycle, there are four components. Turbine, Condenser, Pump, Boiler. Turbine is the core equipment, which convert the heat energy by burning fossil fuel in to a use full work at shaft end. (Generally Electricity Generation). There are four thermodynamics processes, in the four different equipment. In Rankine cycle, heat added and rejection being held while pressure is constant. (Isobaric Heat Addition or Rejection). And Isentropic expansion and Isentropic compression.
Isobaric Heat Transfer : High pressure liquid enters the boiler from the feed pump and is heated to the saturation temperature . Further addition of energy causes evaporation of the liquid until it is fully converted to saturated steam. (4-1)
Isentropic Expansion: The vapor is expanded in the turbine, thus producing work which may be converted to electricity. In practice, the expansion is limited by the temperature of the cooling medium and by the erosion of the turbine blades by liquid entrainment in the vapor stream as the process moves further into the two-phase region. Exit vapor qualities should be greater than 90%. (1-2)
Isobaric Heat Rejection: The vapor-liquid mixture leaving the turbine (4) is condensed at low pressure, usually in a surface condenser using cooling water. In well designed and maintained condensers, the pressure of the vapor is well below atmospheric pressure, approaching the saturation pressure of the operating fluid at the cooling water temperature. (2-3)
Isentropic Compression: The pressure of the condensate is raised in the feed pump. Because of the low specific volume of liquids, the pump work is relatively small and often neglected in thermodynamic calculations. (3-4)
Back Work Ratio - The back work indicates the amount of work required to run the compressor. It has the negative value because compressor runs at the expanse of work. And not producing any work.
Back work ratio or BWR= Work done by compressor/ Work done by turbine
MAIN CODE
%Rankine cycle simulation
clear all
close all
clc
fprintf('\n RANKINE CYCLE SIMULATOR\n')
fprintf('\n process 1-2 isentropic expansion in turbine/n')
fprintf('\n process 2-3 constant pressure heat rejection in condenser')
fprintf('\n process 3-4 Isentropic compression in pump')
fprintf('\n process 4-1 constant pressure heat addition by the boiler\n')
%process 1-2 isentropic expansion in turbine
%process 2-3 constant pressure heat rejection in condenser
%process 3-4 Isentropic compression in pump
%process 4-1 constant pressure heat addition by the boiler
%required inputs
%Turbine Inlet temperature = 400° C
t1 = 400;
%Turbine Inlet Pressure = 44 bars
p1 = 30;
%Turbine Outlet Pressure = 0.05 bars = Condenser Inlet Pressure
p2= 0.05;
p3=p2;
p4=p1;
fprintf('\n Enter the pressure at the turbine inlet(in bar): %f',p1)
fprintf('\n Enter the temperature at the turbine inlet(in degree celcius): %f',t1)
fprintf('\n Enter the pressure at the condenser inlet (in bar): %f',p2)
%state 1 variables
h1 = XSteam('h_pT',p1,t1);
s1 = XSteam('s_pT',p1,t1);
%state 2 variables
%t2 = t3
%p2
t2 = XSteam('Tsat_p',p2);
t3 = t2;
%h2 = hf2+x2*hfg2
s2 = s1;
%s2 = sf2+x2*sfg2
sf2 = XSteam('sL_p',p2);
sg2 = XSteam('sV_p',p2);
hf2 = XSteam('hL_p',p2);
hg2 = XSteam('hV_p',p2);
x2 = ((s2 - sf2) /(sg2-sf2));
h2 = hf2 + (x2*(hg2-hf2));
%state 3 variables
%p3,t3 known
h3 = XSteam('hL_p',p3);
s3 = XSteam('SL_p',p3);
v3 = XSteam('vL_p',p3);
%state 4 variables
%p4 known
s4 =s3;
%gaama = cp4/cv4
%cp4-cv4 =R
cp4 = XSteam('Cp_ps',p4,s4);
cv4 = XSteam('Cv_ps',p4,s4);
gaama4 = cp4/cv4;
r = (gaama4-1)/gaama4;
t4 = t3*((p4/p3)^r);
%state 5 and 6 variables
t5 = XSteam('Tsat_p',p1);
t6=t5;
hL5 = XSteam('hL_p',p1);
sL5 = XSteam('sL_p',p1);
hV6 = XSteam('hV_p',p1);
sV6 = XSteam('sV_p',p1);
%workdone by pump
%wp = hf4-hf3
%hf4-hf3 = v3(p1-p2)*10^5 J/kg;
wp = v3*(p4-p3)*100;
h4 = h3+wp;
%workdone by turbine
%wt = h1 - h2
wt = h1-h2;
%net work done
wnet = wt-wp;
%heat transfer in boiler
Qin = h1-h4;
%heat transfer in condenser
Qout = h2-h3;
%Thermal efficiency of rankine cycle
Ntherm = ((wnet/Qin)*100);
%specific steam consumption
ssc = 3600/wnet;
�ck work ratio
%bwr = wp/wt
bwr = wp/wt;
%T-S Diagram
figure(1)
hold on
Temp = linspace(10,550,500);
for i = 1:length(Temp);
s_l(i) = XSteam('sL_T',Temp(i));
s_v(i) = XSteam('sV_T',Temp(i));
h_l(i) = XSteam('hL_T',Temp(i));
h_v(i) = XSteam('hV_T',Temp(i));
end
plot(s_l,Temp,'LineWidth',1,'Color','b');
plot(s_v,Temp,'LineWidth',1,'Color','b');
%getting the saturation curve wrt to pressure and temp from state 5 to state 1
TS = linspace(t5,t1,400);
for j =1:length(TS)
swrtpt(j) = (XSteam('s_pT',p1,TS(j)));%swrtpt=s with respect to pressure and temperature
end
plot(s1,t1,'Color','g','Marker','*')
text(s1,t1,'1');
plot(s2,t2,'Color','g','Marker','*')
text(s2,t2,'2');
plot(s3,t3,'Color','g','Marker','*')
text(s3,t3,'3','HorizontalAlignment','center','VerticalAlignment','top');
plot(s4,t4,'Color','g','Marker','*')
text(s4,t4,'4','HorizontalAlignment','center','VerticalAlignment','bottom');
plot(sL5,t5,'Color','g','Marker','*')
text(sL5,t5,'5','HorizontalAlignment','right','VerticalAlignment','bottom');
plot(sV6,t6,'Color','g','Marker','*')
text(sV6,t5,'6','HorizontalAlignment','center','VerticalAlignment','top');
plot([s1 s2 s3 s4 sL5 sV6 ],[t1 t2 t3 t4 t5 t6 ],'LineWidth',1,'Color','r')
plot(swrtpt,TS,'Color','r','LineWidth',1);
title('T-S DIAGRAM');
xlabel('Entropy-S');
ylabel('Temperature-T');
legend('sat-curve','Location','northwest');
%H-S Diagram
figure(2)
hold on
plot(s_l,h_l,'LineWidth',2,'Color','b');
plot(s_v,h_v,'LineWidth',2,'Color','b');
plot(s1,h1,'Color','g','Marker','*')
text(s1,h1,'1');
plot(s2,h2,'Color','g','Marker','*')
text(s2,h2,'2');
plot(s3,h3,'Color','g','Marker','*')
text(s3,h3,'3','HorizontalAlignment','center','VerticalAlignment','top');
plot(s4,h4,'Color','g','Marker','*')
text(s4,h4,'4','HorizontalAlignment','center','VerticalAlignment','bottom');
plot([s1 s2 s3 s4 s1],[h1 h2 h3 h4 h1],'LineWidth',1,'Color','r');
title('H-S DIAGRAM');
xlabel('Entropy-S');
ylabel('Enthalpy-H');
legend('sat-curve','Location','northwest');
%printing the result
fprintf('\n ____________RESULTS______________')
fprintf('\n At state point 1:')
fprintf('\n P1 is: �ar',p1)
fprintf('\n T1 is: �egree celsius',t1)
fprintf('\n H1 is: %f KJ/kg',h1)
fprintf('\n S1 is: %f KJ/kgk',s1)
fprintf('\n')
fprintf('\n At state point 2:')
fprintf('\n P2 is: �ar',p2)
fprintf('\n T2 is: �egree celsius',t2)
fprintf('\n H2 is: %f KJ/kg',h2)
fprintf('\n S2 is: %f KJ/kgk',s2)
fprintf('\n')
fprintf('\n At state point 3:')
fprintf('\n P3 is: �ar',p3)
fprintf('\n T3 is: �egree celsius',t3)
fprintf('\n H3 is: %f KJ/kg',h3)
fprintf('\n S3 is: %f KJ/kgk',s3)
fprintf('\n')
fprintf('\n At state point 4:')
fprintf('\n P4 is: �ar',p4)
fprintf('\n T4 is: �egree celsius',t4)
fprintf('\n H4 is: %f KJ/kg',h4)
fprintf('\n S4 is: %f KJ/kgk',s4)
fprintf('\n')
fprintf('\n Workdone by turbine Wt is : %f KJ/kg',wt)
fprintf('\n Workdone by Pump Wp is : %f KJ/kg',wp)
fprintf('\n Net Workdone Wnet is : %f KJ/kg',wnet)
fprintf('\n Thermal efficiency Ntherm is : %f percent',Ntherm)
fprintf('\n Specific steam consumpton SSC is : %f KJ/kwh',ssc)
%ENDEXPLANATION OF PROGRAM OF CALCULATING STATE POINTS:
- Initially print the process 1-2,2-3,3-4 and 4-1 using fprintf command.
- %process 1-2 isentropic expansion in turbine
%process 2-3 constant pressure heat rejection in condenser
%process 3-4 Isentropic compression in pump
%process 4-1 constant pressure heat addition by the boiler - Define the given input values
- %required inputs
%Turbine Inlet temperature = 400° C
t1 = 400;
%Turbine Inlet Pressure = 44 bars
p1 = 30;
%Turbine Outlet Pressure = 0.05 bars = Condenser Inlet Pressure
p2= 0.05; - process 2-3 and 4-1 is constant pressure process so p3=p2 and p4=p1.
- Xsteam function is like the steam table using the XSteam function command we get the values of entropy,enthalpy,temperature,pressure for the state points we need.
- calculate the enthalpy,entropy,temp for all the state points using the formula and XSteam function.
- calculate the work done by pump,work done by turbine,net work done, heat transfer in boiler,heat transfer in condenser,thermal efficiency and specific steam consumption ,back work ratio using the formulas of rankine cycle referred from text book.
- Plotting of T-S diagram
- To get the saturation curve for the liquid and vapour separately using the linspace command and for loop calculate the entropy and enthalpy for the given temperature range.
- To get and plot the exact curve from the state points 5 to 1 using linspace and for loop calculate the entropy for the respective pressure and temperature.
- plot the state points and saturation dome curve using the plot commands and display the state points using the text command.
- Similarly plot the H-S diagram using the plot and text commands.
- x labels,y labels,title and legend commands are used to plot both the T-s and H-s diagram.
- Results are print in the command window using fprintf command for each state points.
COMMAND WINDOW OUTPUT:
T-S DIAGRAM PLOT:
H-S DIAGRAM:
CONCLUSION:
Rankine cycle simulator is created by matlab program,all the state points are calculated and T-s and H-s diagram plots are plotted using matlab program and results are shown in command window.