Project 2 - Rankine cycle Simulator

AIM:-

1. To simulate a Rankine cycle using MATLAB.
2. Extracting Steam and water properties from XSteam data(IAPWS-97 standard)
3. Calculate all the state points of the cycle based on user inputs.
4. Plotting the T vs s and H vs s plot for the given input.

Rankine Cycle:

• Rankine cycle is an idealized thermodynamic cycle or heat engine in which 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. It is a cycle which converts heat into mechanical energy which usually is converted into electrical energy.
• In this project an idealized cycle is simulated. Hence neglecting losses.
• 
• Rankine cycle is derived out of carnot cycle. Its power depends on the temperature difference between the heat source and a cold source. The more the difference the more mechanical power can be efficiently extracted out of heat energy.
• Since ideal cycles are only in theory , efficiency of rankine cycle is limited by high heat vaporization of the working fluid , friction losses etc,
• Water is usually the fluid of choice due to its favorable properties, such as its non-toxic and unreactive chemistry, abundance, and low cost, as well as its thermodynamic properties. By condensing the working steam vapour to liquid the pressure at the turbine outlet is lowered and the energy required by the feed pump consumes only 1% to 3% of the turbine output power and these factors contribute to a higher efficiency for the cycle. The benifit of this is offset by the low temperatures of steam admitted to the turbine.

Process and Working:

There are four processes in the rankine cycle (order may be varied):

1. Process 1-2:Isentropic Expansion in the turbine.
2. Process 2-3:Constant pressure Heat rejection in condenser
3. Process 3-4:Isentropic compression in the pump
4. Process 4-1:Constant pressure heat addition in the boiler

• Working of the rankine cycle simulator

1. In Process 1-2 , the dry saturated vapour expands through a turbine , generating power. This decreases the temperature and pressure of the vapour , and some condensation may occur. Wt = m(h1-h2).
2. Process2-3, The vapour-liquid mixture leaving the turbine(2) is condensed at low pressure , usually in a surface condenser using cooling water. In well designed and maintained condensers, the pressure of the vapour is well below atmospheric pressure , approaching the saturation pressure of the operating fluid at the cooling water temperature. Qadd = m(h2-h3).
3. Process 3-4, 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. Wp = m(h3-h4).
4. Process 4-1 , high pressure liquid enters the boiler from the feed pump(4) and is heated to the saturation temperature (on the saturation curve). Further addition of energy causes evaporation of thr liquid until it is fully converted to saturated steam(1) or superheated(1). Qrej=m(h1-h4).

Thermal efficiency of Rankine cycle is given by

Back Work Ratio

Elaborating(Rankine cycle paragraph point v):As the water condenses in the condenser , waste heat is given off in the form of water vapour which can be seen billowing from a plant's cooling towers. This waste heat is necessary in any thermodynamic cycle. Due to this condensation step , the pressure at the turbine outlet is lowered. This means the pump requires less work to compress the water-resting in higher overall efficiencies.

here input parameter from user are

pressure at Turbine inlet(p1)=30 bar,

Temperature at aaaaaturbine inlet(T1)=400 deg C.

Pressure at Condenser inlet(p2)=0.05 bar.

%Rankine Cycle Simulator`

% Objective of this program is to simulate the rankine cycle
% Plotting t-s and h-s diagram using data from XSteam data
% Water and steam properties according to IAPWS IF-97
clear all
close all
clc
 
disp(' RANKINE CYCLE ');    % Displaying
disp('l-2 is Isentropic Expansion in the turbine');
disp('2-3 is constant pressure heat removal in the condenser');
disp('3-4 is Isentropic compression in the pump');
disp('4-l is Constant pressure heat addition in the boiler');
 

%Obtaining the input data
p1 = input('Value of pressure at turbine inlet, p1(in bar) = ');
T1 = input('Value of temperature at turbine inlet, T1(in degree.C)= ');
p2 = input('Value of temperature at condenser inlet, p2(in bar)= ');

 
% Extracting data_defining variales
% State 1
 
h1= XSteam('h_pT',p1,T1);   % extracting enthalpy at state pt 1
s1 = XSteam('s_pT',p1,T1);   % similarly

% State 2
s2 = s1;  % Isentropic expansion
sf2= XSteam('sL_p',p2); % Saturated liquid Entropy
sg2 = XSteam('sV_p',p2); % Saturated Vapour Entropy
x2 = (s2-sf2)/(sg2-sf2);
hf2 = XSteam('hL_p',p2);
hg2 = XSteam('hV_p',p2);
h2 = hf2+(x2*(hg2-hf2)); 
% State 3
p3 = p2; % Constant pressure Heat rejection in condenser
s3 = XSteam('sL_p',p3);
h3 = XSteam('hL_p',p3);

% State 4
s4 = s3;
p4 = p1;

% Work done by turbine
Wt = h1-h2;
 
% Work done to run pump
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 
Ntherm = (Wnet/Qin)*100;
 
%Specific Steam Consumption
%SSC = mass flow rate/power 
SSC = (3600/Wnet);

%Back work ratio in Rankine cycle
back_work_ratio = Wp/Wt;
 

%Calculating temperatures at the state points 
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;
 
%Plotting the saturation curve
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 diagram
figure(1)
hold on
plot(sf,T,'r','linewidth',1)
plot(sg,T,'r','linewidth',1)
plot([s1 s2],[T1 T2],'k','linewidth',2)
plot([s2 s3],[T2 T3],'k','linewidth',2)
plot([s3 s4],[T3 T4],'k','linewidth',2)
plot([s4 s5],[T4 T5],'k','linewidth',2)
plot([s5 s6],[T5 T6],'k','linewidth',2)
sc1 = linspace(s6,s1,1000);
for  i = 1:length( sc1)
Tc1(1) = XSteam('T_ps',p1,sc1(1));
end
plot(sc1, Tc1,'k','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')
 
%Plotting h -s diagram
figure(2)
hold on
plot(sf,hf,'r','linewidth',1)
plot(sg,hg,'r','linewidth',1)
plot([s1 s2],[h1 h2],'k','linewidth',2)
plot([s2 s3],[h2 h3],'k','linewidth',2)
plot([s3 s4],[h3 h4],'k','linewidth',2)
hc = linspace(h4,h5,100);
for k=1:length(hc)
sch(k)= XSteam('s_ph',p1,hc(k));
end
plot(sch,hc,'k','linewidth',2)
plot([s5 s6],[h5 h6],'k','linewidth',2)
for m=1:length(sc1)
hc1(m)= XSteam('h_ps',p1,sc1(m));
end
plot(sc1,hc1,'k','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')

% Displaying Results
disp('RESULTS');
fprintf('At State Point 1\n');
fprintf('p1: %8.3f bar\n',p1); 
fprintf('T1: %8.3f C\n',T1);   
fprintf('h1: %8.3f KJ/kg\n',h1);
fprintf('s1: %8.3f KJ/kgK\n',s1); 
fprintf('At State Point 2:\n');  
fprintf('p2: %8.3f bar\n',p2);        
fprintf('T2: %8.3f C\n', T2);
fprintf('h2: %8.3f kJ/kg\n',h2);
fprintf('s2: %8.3f kJ/kgK\n',s2);
fprintf('x2: %8.3f\n',x2);
fprintf('At State Point 3:\n');
fprintf('p3: %8.3f bar\n',p3);
fprintf('T3: %8.3f K\n',T3);
fprintf('h3: %8.3f kJ/kg\n',h3);
fprintf('s3: %8.3f kJ/kgK\n',s3);
fprintf('At State Point 4:\n');
fprintf('p4: %8.3f bar\n',p4);
fprintf('T4: %8.3f K\n',T4);
fprintf('h4: %8.3f KJ/kg\n',h4);
fprintf('s4: %8.3f kJ/kgK\n',s4);
fprintf('Turbine Work: %8.3f kJ/kg\n',Wt);
fprintf('pump Work: %8.3f KJ/Kg\n',Wp);
fprintf('Wnet:%8.3f KJ/kg\n',Wnet);
fprintf('back work ratio:%8.3f\n',back_work_ratio);
fprintf('Efficiency:%8.3f percent\n ',Ntherm);
fprintf('S.S.C:%8.3f KJ/Kwh',SSC);

1. Xsteam data is used to extract steam and water properties of enthalpy , entropy at specific pressure and temperatures for sat liquid , sat vapour conditions etc.
2. The program requires the input of pressure (in bar) at state point 1 (turbine inlet) , Temperature at same point(deg celcius) and Temp at condenser inlet(point2).
3. With the help of these inlets & from XSteam data, the program calculates alll the state points of the rankine cycle.
4. The XSteam data works as, h1=XSteam('h_pT',p1,T1); (Returns the enthalpy of water at given pressure at temperature in bar and deg c respectively)
5. As we extract the data, we use thermodynamic relation to further find state points and extract their data from XSteam.
6. Sf and sg ,hf and hg , where f and g stand for saturated liquid and saturated vapour respectively.
7. The net work , work done by turbine , work done to run the pump , Heat in and heat out are calculated using standard thermodynamic relation
8. Efficiency and Specific steam consuption(s.s.c) of the Rankine cycle is calculated.
9. 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.
10. Saturation curve is plotted in red for saturated liquid and saturated gas.
11. Plot of T vs s and h vs s is created from all the points obtained from the program.
12. The plot changes as the user input changes for the above mentioned inputs.
13. Results are displayed in the command window.

Results in the command window for entire Calculation:

References:

1. https://en.wikipedia.org/wiki/Rankine_cycle
2. https://energyeducation.ca/encyclopedia/Rankine_cycle
3. https://in.mathworks.com/matlabcentral/fileexchange/9817-x-steam-thermodynamic-properties-of-water-and-steam
4. https://www.sciencedirect.com/topics/earth-and-planetary-sciences/rankine-cycle