Project 2 - Rankine cycle Simulator

Rankine Cycle Simulator

Aim:

Creation of Rankine cycle simulator from given input and reading the data from standard thermodynamic library of steam table.

Objective:

1. To create a Rankine Cycle simulator in MATLAB.
2. To calculate the state point using function XSteam.
3. To plot the T-S and H-S curve for given input in Rankine Cycle.
4. To get output in the command window for each state point in cycle.

Description:

The Rankine cycle is one of the vapor powered cycle. This cycle is somewhat different than gas powered cycle in which working fluid remained gas throughout the entire cycle. In vapor powered cycle the working fluid is steam because of its many desirable characteristics such as low cost of production, availability and high enthalpy of vaporization. There are many impracticalities associated with Carnot cycle which can be eliminated by superheating the steam and condense in condenser which makes it best for nuclear power plants and other steam related power generation sources.

The process in Rankine cycle are given as:

1. Isentropic Compression in Pump.
2. Constant pressure heat addition in boiler.
3. Isentropic expansion in a turbine.
4. Constant pressure heat rejection in condenser.

Code Explanation:

1. The creation of Rankine cycle simulator starts with some input value which are required to calculate the other state point in cycle eventually.
2. The Rankine cycle process is displayed in the command window and then inputs are entered which are inlet pressure for turbine, temperature at turbine inlet and pressure at condenser.
3. Then we are using XSteam function file for reading state point. First, we get the value of enthalpy and entropy at state point 1 from the XSteam function file.
4. As process from 1-2 is isentropic compression the entropy at point 1 is equal to point 2. The term ‘(s_pT, p1, T1)’ refers to entropy at pressure and temperature point 1.
5. The term ‘sg’ and ‘sf’ are referred to saturated liquid and saturated vapor entropy respectively. This value is used to calculate other function according to mathematical relations.
6. Similarly, other points are taken from XSteam function file which are necessary to calculate other parameters. After that work done in turbine and pump are calculated for further getting the net work done Rankine cycle.
7. After calculating the net work done the efficiency of the Rankine cycle is calculated along with specific steam consumption which is steam consumed by a locomotive cylinders per unit of output of work done.
8. Then temperature at each point of cycle is calculated using input taken from start of the program and data taken from XSteam file. For given temperature range from lower to higher entropy points are calculated to create the T-S plot. Similarly, another for loop is used to create the saturation curve in each plot.
9. Then plotting is done respectively for T-s and H-s graph in Rankine cycle and each state point value has been put in command window.

The code for Rankine Cycle Simulator is given as:

clear all
close all
clc

disp(' RANKINE CYCLE ');                                   
disp('1-2 is Constant pressure heat addition in the boiler');
disp('2-3 is Isentropic Expansion in the Turbine');
disp('3-4 is Constant pressure heat removal in the Condenser');
disp('4-1 is Isentropic compression in the pump');

p1 = input('nValue of pressure at turbine inlet, p1(in bar) = ');
T1 = input('nValue of temperature at turbine inlet, T1(in degree.C) = ');
p2 = input('nValue of pressure at condenser inlet, p2(in bar) = ');
 

% At State 1
h1 = XSteam('h_pT', p1, T1);        % Extracting Enthalpy at state pt 1
s1 = XSteam('s_pT', p1, T1);        % Similarly

% At 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));

% At State 3
p3 = p2;                            % Constant pressure Heat rejection in Condenser
s3= XSteam('sL_p', p3);
h3 = XSteam('hL_p', p3);

% At 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
thermal_eff = (Wnet/Qin)*100;

%Specific Steam Consumption
%SSC = mass flow rate/power
SSC = (3600/Wnet);

% Back Work ratio
BW = (Wp/Wt)


% Calculation of 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], 'b', 'linewidth', 2)
plot([s2 s3], [T2 T3] ,'b', 'linewidth', 2)
plot([s3 s4], [T3 T4], 'b', 'linewidth', 2)
plot([s4 s5], [T4 T5], 'b', 'linewidth', 2)
plot([s5 s6], [T5 T6], 'b', 'linewidth', 2)
sc1 = linspace(s6, s1, 1000);
for l = 1:length(sc1)
 Tc1(l) = XSteam('T_ps', p1, sc1(l));
end
plot(sc1, Tc1, 'b', '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, 'k', 'linewidth', 1)
plot(sg, hg, 'k',  'linewidth', 1)
plot([s1 s2], [h1 h2], 'r', 'linewidth', 2)
plot([s2 s3], [h2 h3], 'r', 'linewidth', 2)
plot([s3 s4], [h3 h4], 'r', 'linewidth', 2)
hc = linspace(h4, h5, 100);
for r = 1:length(hc)
sch(r) = XSteam('s_ph', p1, hc(r));
end
plot(sch,hc, 'r', 'linewidth', 2)
plot([s5 s6], [h5 h6], 'r', 'linewidth', 2)
for m = 1:length(sc1)
hc1(m) = XSteam('h_ps', p1, sc1(m));
end
plot(sc1, hc1, 'r', '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 the Results in the Command Window:
disp('Results');
p1 = p1;
T1 = T1;
p2 = p2;
disp('At stage point 1');
n1 = sprintf('P1 is %.3f bar',p1);
disp(n1);
n2 = sprintf('T1 is %.3f C',T1);
disp(n2);
n3 = sprintf('h1 is %.3f kJ/kg',h1);
disp(n3);
n4 = sprintf('s1 is %.3f kJ/kgK',s1);
disp(n4);
disp('At stage point 2');
n11 = sprintf('P2 is %.3f bar',p2);
disp(n11);
n21 = sprintf('T2 is %.3f C',T2);
disp(n21);
n31 = sprintf('h2 is %.3f kJ/kg',h2);
disp(n31);
n41 = sprintf('s2 is %.3f kJ/kgK',s2);
disp(n41);
disp('At stage point 3');
n12 = sprintf('P3 is %.3f bar',p3);
disp(n12);
n22 = sprintf('T3 is %.3f C',T3);
disp(n22);
n32 = sprintf('h3 is %.3f kJ/kg',h3);
disp(n32);
n42 = sprintf('s3 is %.3f kJ/kgK',s3);
disp(n42);
disp('At stage point 4');
n13 = sprintf('P4 is %.3f bar',p4);
disp(n13);
n23 = sprintf('T4 is %.3f C',T4);
disp(n23);
n33 = sprintf('h4 is %.3f kJ/kg',h4);
disp(n33);
n43 = sprintf('s4 is %.3f kJ/kgK',s4);
disp(n43);
n14 = sprintf('Wt is %.3f kJ/kg',Wt);
disp(n14);
n15 = sprintf('Wp is %.3f kJ/kg',Wp);
disp(n15);
n16 = sprintf('Wnet is %.3f kJ/kg',Wnet);
disp(n16);
n17 = sprintf('Thermal_efficiency is %.2f Percent',thermal_eff);
disp(n17);
n18 = sprintf('SSC is %.2f kg/kWh',SSC);
disp(n18);
n19 = sprintf('Back work ratio is %.3f ',BW);
disp(n19);

Inference of Plot:

To make the graph more deliberate we are changing some value in the inputs by increasing the inlet pressure and temperature along with condenser pressure also which results in following graphs.

From the above diagram as we can see along the saturation curve point 1 start with turbine from which heat rejection is started which is again isentropic process. The steam is get cooled in condenser and in form of saturated liquid as it is under the curve. Then it was pumped to enter in boiler where its temperature is increased to change it from saturated liquid to saturated vapor form.

As we can see from above plot the steam entropy changes during the process with respect to enthalpy. As the heat added in the system the entropy has been increased and similarly as the heat removed from the system the entropy drops with similar rates.

For the parameters given in the challenge the graph will look like this:

The values for the state point in command windows are given as:

For Inlet pressure in Turbine as = 50 bar

Inlet temperature in Turbine = 500 deg.cel

Pressure in condenser = 5 bar