Project 2 - Rankine cycle Simulator

AIM: Create a Rankine Cycle Simulator using MATLAB.

OBJECTIVE:

• Calculate each state points of the Rankine Cycle (any type of your choice) based on user inputs.
• Plot the corresponding T-s and h-s plots for the given set of inputs.
• Calculate Efficiency.

THEORY:

The Rankine cycle is the fundamental operating cycle of all power plants where an operating fluid is continuously evaporated and condensed. The selection of operating fluid depends mainly on the available temperature range. Figure 1 shows the idealized Rankine cycle. The Rankine cycle operates in the following steps:

1-2 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% to increase the life of turbine blade.

2-3 Isobaric Heat Rejection. The vapor-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 vapor is well below atmospheric pressure, approaching the saturation pressure of the operating fluid at the cooling water temperature.

3-4 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.

4-1 Isobaric Heat Transfer. High pressure liquid enters the boiler from the feed pump (4) and is heated to the saturation temperature . Further addition of energy causes evaporation of the liquid until it is fully converted to saturated steam (1).

1-2: Isentropic Expansion

Turbine (1-2): Superheated steam enters into the Turbine and expands isentropically resulting in the production of work. The shaft of the turbine is connected to the generator. This results in the production of electricity i.e Mechanical energy gets converted into electric energy. Work produced by the turbine,

WT=m(h1−h2)KWT=m(h1-h2)K

2-3: Constant Pressure Heat Rejection

Condenser (2-3): The expanded vapour is then passed through a condenser, where it gets condensed and converts into liquid again. This liquid is again pumped to the boiler.

Qr=m(h2−h3)KQr=m(h2-h3)K

3-4: Isentropic Compression by the Pump

Pump (3-4): The water enters into the pump in a saturated state. Then the liquid is compressed isentropically until it meets the boiler pressure. Work done by the pump is,

WP=m(h3−h4)KWP=m(h3-h4)K

4-1: Constant Pressure Heat Addition

Boiler (4-1): The water enters into the boiler as compressed and leaves as superheated from the boiler. Thus the phase changes from liquid to vapour. The heat supplied by the boiler is

Qb=m(h1−h4)KQb=m(h1-h4)K

Here we take mass flow rate m = 1 for this code.

• The efficiency of the Steam Cycle is given by

η=WnQ1=WT−WPQ1η=WnQ1=WT-WPQ1

• Applying the Steady Flow Energy Equation (SFEE) to all the process, neglecting the Friction losses and changs in Kinetic & Potential Energy,

  • Q1=h1-h4 @Boiler
  • Wt=h1-h2 @Turbine
  • Q2=h2-h3 @Condenser
  • Wp=h4-h3 @Pump
• The Capacity of the Steam Plant is often expressed interms of Steam Rate (SR) or Specific Steam Consumption (SSC) S.S.C.=3600WnkgkWh

Required Inputs:

Turbine Inlet temperature = 400° C

Turbine Inlet Pressure = 30 bars

Turbine Outlet Pressure = 0.05 bars = Condenser Inlet Pressure

MATLAB CODE:

close all
clear all
clc

% Print Process Description
fprintf('1-2 Isobaric heat Transfer\n')
fprintf('2-3 Isentropic Expansion\n')
fprintf('3-4 Isobaric heat Rejection\n')
fprintf('4-1 Isentropic Compression\n')

%step 1:Enter Inputs
p1 = input('Enter the Pressure at the Turbine Inlet (in bar):');
T1 = input('Enter the Temperature at the Turbineinlet (in Degree Celcius):');
p2 = input('Enter the Pressure at the Condensor (in bar):');

%step 2: Calculate each state point values.
% state point 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);   %x2 = (s2-sf2)/(sg2-sf2);
s2 = sg2;
h2 = hg2;                  %hf2 +(x2*(hg2-hf2));
T2=XSteam('T_hs',h2,s2);

%step 4: state point 3
T3=T2;
p3= p2;
s3=XSteam('sL_T',T3);
h3=XSteam('hL_T',T3);
v3 = XSteam('vL_p',p2);

%step 5: state point 4
p4 =p1;
s4= s3;
Cp4 = XSteam('Cp_ps',p4,s4);
Cv4 = XSteam('Cv_ps',p4,s4);
gamma = Cp4/Cv4;
r = (gamma - 1)/gamma;
T4 = T3 *(p4/p3)^r; 

%step 6: Calculate other output values.
Wt = h1-h2;      % Turbine Work      
Wp = v3*(p1-p2)*100;   % Pump Work
h4 = Wp + h3;
W_net = Wt-Wp;     % Net Work unit in kj/kg
Qs = h1 - h4;%heat suppied
N_per = (W_net/Qs)*100;%Efficiency
steam_rate = 3600/(Wt - Wp);%Steam rate per second
BWR=(h1-h4)/(h2-h3);

%step 7: state point 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);

%step 8: print all state poont values to show.
fprintf('\n------------------RESULT------------------\n')
fprintf('At State point 1:\nP1 is : %4.2f Bar\nT1 is : %4.2f Degree Celcius\nH1 is : %4.2f kJ/kg\nS1 is : %4.2f kJ/kgk\n\n',p1,T1,h1,s1)
fprintf('At State point 2:\nP2 is : %4.2f Bar\nT2 is : %4.2f Degree Celcius\nH2 is : %4.2f kJ/kg\nS2 is : %4.2f kJ/kgk\n\n',p2,T2,h2,s2)
fprintf('At State point 3:\nP3 is : %4.2f Bar\nT3 is : %4.2f Degree Celcius\nH3 is : %4.2f kJ/kg\nS3 is : %4.2f kJ/kgk\n\n',p3,T3,h3,s3)
fprintf('At State point 4:\nP4 is : %4.2f Bar\nT4 is : %4.2f Degree Celcius\nH4 is : %4.2f kJ/kg\nS4 is : %4.2f kJ/kgk\n\n',p4,T4,h4,s4)
fprintf('Wt is :%4.2f kJ/kg\nWp is : %4.2f kJ/kg\nWnet is : %4.2f kJ/kg\nNtherm is : %4.2f percent\nS.S.C is : %4.2f kg/kWh\nBWR is : %4.2f',Wt,Wp,W_net,N_per,steam_rate,BWR)

%step 9:plot T-S Diagram
subplot(1,2,1)
T_rankine = linspace(T5,T1,5000);
for i = 1:length(T_rankine)
       s_rankine(i) = XSteam('s_pT',p1,T_rankine(i));
end
plot([s1 s2 s3 s4 s5 s6 s_rankine],[T1 T2 T3 T4 T5 T6 T_rankine],'linewidth',1.5);
hold on
T_curve = linspace(1,400,500);
for i=1:length(T_curve)
    s_l(i) = XSteam('sL_T',T_curve(i));
    s_v(i) = XSteam('sV_T',T_curve(i));
    h_l(i) = XSteam('hL_T',T_curve(i));
    h_v(i) = XSteam('hV_T',T_curve(i));
end
plot(s_l,T_curve);
plot(s_v,T_curve);
text(s1,T1,'1','FontSize',15)
text(s2,T2,'2','FontSize',15)
text(s3,T3,'3','FontSize',15,'HorizontalAlignment','right','VerticalAlignment','top')
text(s4,T4,'4','FontSize',15,'HorizontalAlignment','right','VerticalAlignment','bottom')
text(s5,T5,'5','FontSize',15)
text(s6,T6,'6','FontSize',15)
xlabel('Entropy in kJ/KgK');
ylabel('Temperature in Degree Celcius');

%step 10:plot H-S diagram
subplot(1,2,2)
plot([s1 s2 s3 s4 s1],[h1 h2 h3 h4 h1],'linewidth',2)
hold on
plot(s_v,h_v,'color','r')
plot(s_l,h_l,'color','r')
text(s1,h1,'1','FontSize',15)
text(s2,h2,'2','FontSize',15)
text(s3,h3,'3','FontSize',15,'HorizontalAlignment','right','VerticalAlignment','top')
text(s4,h4,'4','FontSize',15,'HorizontalAlignment','right','VerticalAlignment','bottom')
xlabel('Entropy in kJ/KgK')
ylabel('Enthalpy in kJ/kg')

EXPLANATION

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

ERRORS

wrong spelling of function- rectified by changing it to the correct one

OUTPUTS

1. GRAPHS

2. COMMAND WINDOW SCREENSHOTS

NET WORK OUTPUT AND BACKWORK RATIO

Conclusion

1)Rankine cycle is a power generating cycle.

2)Superheating increase the thermal efficiency of cycle.

3)It is the most practical cycle.