Project 2 - Rankine cycle Simulator

RANKINE CYCLE USING MATLAB CODING

To be performed

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

2) To add the thermodynamic relation to get the points in between 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

Code:-

Xsteam is function to get steam data

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')

Results

1-2 Isobaric heat Transfer

2-3 Isentropic Expansion

3-4 Isobaric heat Rejection

4-1 Isentropic Compression

Enter the Pressure at the Turbine Inlet (in bar):30

Enter the Temperature at the Turbineinlet (in Degree Celcius):400

Enter the Pressure at the Condensor (in bar):.05

------------------RESULT------------------

At State point 1:

P1 is : 30.00 Bar

T1 is : 400.00 Degree Celcius

H1 is : 3231.57 kJ/kg

S1 is : 6.92 kJ/kgk

At State point 2:

P2 is : 0.05 Bar

T2 is : 32.87 Degree Celcius

H2 is : 2560.77 kJ/kg

S2 is : 8.39 kJ/kgk

At State point 3:

P3 is : 0.05 Bar

T3 is : 32.87 Degree Celcius

H3 is : 137.73 kJ/kg

S3 is : 0.48 kJ/kgk

At State point 4:

P4 is : 30.00 Bar

T4 is : 36.92 Degree Celcius

H4 is : 140.74 kJ/kg

S4 is : 0.48 kJ/kgk

Wt is :670.81 kJ/kg

Wp is : 3.01 kJ/kg

Wnet is : 667.79 kJ/kg

Ntherm is : 21.61 percent

S.S.C is : 5.39 kg/kWh>>

Plots

Conclusion

1)Rankine cycle is a power generating cycle.

2)Superheating increase the thermal efficiency of cycle.

3)It is the most practical cycle.

Errors :

• I had faced several errors like syntax error in code but at last I rectified it by my own.