Project 2 - Rankine cycle Simulator

Aim:

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

Objective:

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

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 wok . 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 of 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 vapor to a 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 benefit of this is offset by the low temperatures of steam admitted to the turbine

Processes and Working :

There are four processes in the rankine cycle (order maybe 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.
2. Process 2-3 , 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. 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.
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 the liquid until it is fully converted to saturated steam (1) or superheated (1).

clear all
close all
clc


disp(' RANKINE CYCLE ');                                    % Displaying
disp('1-2 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('4-1 is Constant pressure heat addition in the boiler');


%Obtaining the input data
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 temperature at condenser inlet, p2(in bar) = ');

% Extracting data _ defining variables
% 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
eff = (Wnet/Qin)*100;

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

%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 l = 1:length(sc1)
 Tc1(l) = XSteam('T_ps', p1, sc1(l));
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\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\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\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\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('Efficiency: %8.3f Percent \n ', eff);
fprintf('S.S.C: %8.3f kJ/kWh', SSC);

Code explanation:

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 .

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).

With the help of these inlets & from Xsteam data, the program calculates all the state points of the Rankine cycle .

The xsteam data works as ,

h1 = XSteam('h_pT' , p1 , T1) ; ( Returns the enthalpy of water at given pressure and temperature in bar and degC resp .)

As we extract the data , we use thermodynamic relation to further find state points and extract their data from XSteam .

Sf and sg , hf and hg , where f and g stands for saturated liquid and saturated vapour respectively.

The net work , work done by turbine , work done to run the pump , Heat in and heat out are calculated using standard thermodynamic relation

Efficiency and Specific steam consumption (s.s.c) of the Rankine cycle is calculated .

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 .

Saturation curve is plotted in red for saturated liquid and saturated gas .

Plot of T vs s and h vs s is created from all the points obtained from the program .

The plot changes as the user input changes for the above mentioned inputs .

Results are displayed in the command window .

Output:

T-S and H-S diagrams:

Errors:

Some typing errors occured.

Conclusion:

So, we have created the Rankine cycle simulator for the given input, in which we have taken the data from XSteam function file.