Project 2 - Rankine cycle Simulator

AIM:- Create a rankine cycle simulator and plot T-s and h-s diagram.

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 pressure-enthalpy (p-h) and temperature-entropy (T-s) diagrams of this cycle are given in Figure 2. The Rankine cycle operates in the following steps:

1-2-3 Isobaric Heat Transfer. High pressure liquid enters the boiler from the feed pump (1) and is heated to the saturation temperature (2). Further addition of energy causes evaporation of the liquid until it is fully converted to saturated steam (3).

3-4 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%.

4-5 Isobaric Heat Rejection. The vapor-liquid mixture leaving the turbine (4) 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.

5-1 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.

OCTAVE CODE:-

close all
clear all
clc
% displaying rankine cycle simulator and its processess
disp(" Rankine cycle simulator")
fprintf('\n 1-2 is the isentropic expansion process')
fprintf('\n 2-3 is the constant pressure heat rejection process')
fprintf('\n 3-4 is the isentropic compression process')
fprintf('\n 4-1 is the constant pressure heat addition process')
% variables for stage1
p1 = 30;
t1 = 400;
h1 = XSteam('h_pT',30,400);
s1 = XSteam('s_ph',30,h1);
fprintf('\n\n Results')
fprintf('\n\n At state point 1')
fprintf('\n P1 is:%f bar',p1)
fprintf('\n T1 is:%f deg celcius',t1)
fprintf('\n H1 is:%f KJ/Kg',h1)
fprintf('\n S1 is:%f KJ/KgK',s1)

% variables for stage2
p2 = 0.05;
s2 = s1;
t2 = XSteam('T_ps',0.05,6.1858);
sf2 = XSteam('sL_p',p2);
sg2 = XSteam('sV_p',p2);
hf2 = XSteam('hL_p',p2);
hg2 = XSteam('hV_p',p2);
x = ((s2 - sf2)/(sg2 - sf2));
h2 = hf2 + (x*(hg2 - hf2));
v2 = XSteam('v_ph',p2,h2);
fprintf('\n\n At state point 2')
fprintf('\n P2 is:%f bar',p2)
fprintf('\n T2 is:%f deg celcius',t2)
fprintf('\n H2 is:%f KJ/Kg',h2)
fprintf('\n S2 is:%f KJ/KgK',s2)

% variables for stage3
t3 = t2;
p3 = p2;
s3 = XSteam('sL_p',p3);
h3 = XSteam('hL_T',32.875);
v3 = XSteam('v_ph',p3,h3);
fprintf('\n\n At state point 3')
fprintf('\n P3 is:%f bar',p3)
fprintf('\n T3 is:%f deg celcius',t3)
fprintf('\n H3 is:%f KJ/Kg',h3)
fprintf('\n S3 is:%f KJ/KgK',s3)

% variables for stage4
s4 = s3;
v4 = v3;
p4 = p1;
h4 = XSteam('h_ps',p4,s4);
t4 = XSteam('T_hs',h4,s4);
fprintf('\n\n At state point 4')
fprintf('\n P4 is:%f bar',p4)
fprintf('\n T4 is:%f deg celcius',t4)
fprintf('\n H4 is:%f KJ/Kg',h4)
fprintf('\n S4 is:%f KJ/KgK',s4)

% variables for stage6
p5 = p4;
t5 = XSteam('Tsat_p',p5);
h5 = XSteam('hL_T',t5);
s5 = XSteam('sL_p',p5);
fprintf('\n\n At state point 5')
fprintf('\n P5 is:%f bar',p5)
fprintf('\n T5 is:%f deg celcius',t5)
fprintf('\n H5 is:%f KJ/Kg',h5)
fprintf('\n S5 is:%f KJ/KgK',s5)

% variables for stage6
t6 = t5;
p6 = XSteam('psat_T',t5);
s6 = XSteam('sV_T',t6);
h6 = XSteam('hV_T',t6);
fprintf('\n\n At state point 6')
fprintf('\n P6 is:%f bar',p6)
fprintf('\n T6 is:%f deg celcius',t6)
fprintf('\n H6 is:%f KJ/Kg',h6)
fprintf('\n S6 is:%f KJ/KgK',s6)

% loop to find variables on saturation lines
t = linspace(0,400,1000);
for i=1:length(t)
s_line1(i)=XSteam('sL_T',t(i));
end

for j=1:length(t)
s_line2(j)=XSteam('sV_T',t(j));
end
for i=1:length(t)
h_line1(i)=XSteam('hL_T',t(i));
end

for j=1:length(t)
h_line2(j)=XSteam('hV_T',t(j));
end

% net work output calculation
w_turbine = h1 - h2; % work done by turbine
w_pump = h4 - h3; % work taken by pump
work = w_turbine - w_pump; % net work output
q_in = h1 - h4; % heat addition
q_out = h2 -h3; % heat rejection

% thermal efficiency
n = work/q_in;

%Back work ratio
BWR = w_pump/w_turbine;

% Specific steam consumption
ssc = 3600/work;

%plotting T-s graph
figure(1)
hold on
plot([s_line1 s_line2],[t t])
plot([s1 s2 s3 s4 s5 s6 s1],[t1 t2 t3 t4 t5 t6 t1])
text(s1,t1,'1')
text(s2,t2,'2')
text(s3,t3,'3')
text(s4,t4,'4')
text(s5,t5,'5')
text(s6,t6,'6')
title("Rankine cycle T-S Diagram")
xlabel('Entropy(KJ/KgK)')
ylabel('Temperature(K)')
axis([0,8,0,450])
%plotting h-s graph
figure(2)
hold on
plot([s_line1 s_line2],[h_line1 h_line2])
plot([s1 s2 s3 s4 s5 s6 s1],[h1 h2 h3 h4 h5 h6 h1])
text(s1,h1,'1')
text(s2,h2,'2')
text(s3,h3,'3')
text(s4,h4,'4')
text(s5,h5,'5')
text(s6,h6,'6')
title("Rankine cycle H-S Diagram")
xlabel('Entropy(KJ/KgK)')
ylabel('Enthalpy(KJ/Kg)')
axis([0,8,0,3500])

OCTAVE CODE SCREEN SHOTS:-

OUT-PUT RESULTS:-

CODE EXPLANATION:-

1. first of all display – Rankine cycle simulator, using disp command.
2. Now write rankine cycle’s all process using fprintf command.
3. Assign the values of given parameters ,Turbine inlet pressure(p_1) = 30 bar, Turbine inlet temperature(t_1) = 400 deg celsius ,Turbine outlet pressure(p_2) = 0.05 bar.
4. Put XSteam. m file in same directory and call the XSteam function with suitable arguments to find the values of enthalpy, entropy for state 1.
5. Use fprintf command to print values of variables we found. Repeat the procedure for all other states to find unknows.
6. Now apply a for loop to find values of enthalpy and entropy at saturated temperature and store them into variables.
7. Find net work output and back work ratio with suitable formulas.
8. Plot the T-s and h-s diagram using all the value we have found in different states and give proper x and y label and add state number by text command.
9. Plot saturation line using the values we have found by for loop.