Project 2 - Rankine cycle Simulator

Aim:

1) To Develop a basic program that calculates the state points

2) To add the thermodynamic relation to get the points inbetween the state variables.

3) To plot rankine cycle on T-s and H-s curve.

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).

Figure1 Idealized Rankine cycle

The efficiency of power cycles is defined as

Rankine cycle consists of 4 stages:

Process 1-2: Isentropic compression in pump

Process 2-3: Constant pressure Heat addition in Boiler

Process 3-4: Isentropic expansion in Turbine

Process 4-1: Constant pressure Heat rejection in Condenser

Code:

Xsteam is function to get steam data

Main 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

%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',Wt,Wp,W_net,N_per,steam_rate)

%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:

• The Program begins with clear all, close all, clc to erase the workspace and plots..
• Input variables p1,T1,p2 are given by input command whose values are entered in command window while executing the Program.
• @State-1, Values for Enthalpy & Entropy are extracted as a function of Pressure & Temperature.
• h_pT, s_pT, hL_p, sV_p etc.... are the default variables whose value is stored in XSteam file.
• Similarly, all the variables for all states are extracted using a suitable format.[**The Formulae for the State Variables and other depending factors are referred from Power Plant Reference Books.]
• Pressure, Temperature, Enthalpy, Entropy for all the State Variables are Extracted as a function of the dependent variable from the XSteam File.
• @State 2 is a Condenser inlet where the High-Pressure Steam is converted into Low-Pressure Water and hence Dryness Fraction, Enthalpy & Entropy for Saturated Vapour & Saturated Water are considered to Calculate the Specific Enthalpy.
• @State-3 The water is condensed back to its Saturation Temperature and fed to the Pump, This temperature of water at the exit of the Condenser and entry of Pump is the same.
• @State-4 This is Constant Pressure Heat addition, hence pressure is equal to p1, but the temperature increases on heating at Constant Pressure & Constant Volume as our Entropy remains same and hence Cp/Cv=gamma is considered to find temperature T4.
• define two more points 5 and 6 to plot cycle in detail.
• Finally Work done and Heat Evolved & SSC are calculated by basic formulae.
• To plot the Saturation Curve, a Temperature range is defined using linspace command and for the overall length of this Temperature values of Enthalpy and Entropy are calculated at every temperature point. The Break in the Saturation Curve separates the Liquid Phase & Vapour Phase.
• Now all the necessary data is found out, Plotting is done for both T-S & H-S curves using the plot commands. Annotations are assigned using text command.
• Results of the Cycle Simulation is displayed over Comand window using fprintf command.

Result:

The Rankine cycle plots have generated by calculating the state points, efficiency and the output is printed in the command window.

Output:

ERROR:

• The error occurs while calling data from Xsteam library. Solve by adding proper syntex.

Conclusion:

1)Rankine cycle is a power generating cycle.

2)Superheating increase the thermal efficiency of cycle.

3)It is the most practical cycle.