RANKINE CYCLE SIMULATOR
AIM: TO CREATE A RANKINE CYCLE SIMULATOR USING OCTAVE/MATLAB
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.
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%.
· ‘2-3’ Isobaric Heat Rejection. The vapor-liquid mixture leaving the turbine 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 and is heated to the saturation temperature. Further addition of energy causes evaporation of the liquid until it is fully converted to saturated steam.
The link for the standard XSteam library to get the steam table data for water, is given below. It must be used to calculate the points in between the state variables.
“https://drive.google.com/file/d/1RK_fvrOj38CIaQvmLT1S3daqHnxKCGU-/view”
OBJECTIVE:
1. Calculating the state points of the Rankine Cycle.
2. Plotting T-s and h-s Diagrams for given set of inputs.
PROGRAM:
clear all
close all
clc
% Creating Rankine Cycle Simulator
disp('RANKINE CYCLE SIMULATOR')
disp('1-2 : Isentropic Expansion in the Turbine')
disp('2-3 : Isobaric Heat Rejection by the Condenser')
disp('3-4 : Isentropic Compression in the Pump')
disp('4-1 : Isobaric Heat Addition by the Boiler')
disp(' ')
t = linspace(0,373.15,300);
% Inputs to be specified
P1 = input('Enter the Pressure at the Turbine Inlet (in bar): ');
T1 = input('Enter the Temperature at the Turbine Inlet (in Degree Celsius): ');
P2 = input('Enter the Pressure at the Condenser (in bar): ');
disp(' ')
% State Point 1
h1 = XSteam('h_pT',P1,T1);
s1 = XSteam('s_pT',P1,T1);
h_l1 = XSteam('hL_p',P1);
h_g1 = XSteam('hV_p',P1);
s_l1 = XSteam('sL_p',P1);
s_g1 = XSteam('sV_p',P1);
T_sat1 = XSteam('Tsat_p',P1);
% State Point 2
s2 = s1;
s_l2 = XSteam('sL_p',P2);
s_g2 = XSteam('sV_p',P2);
% Dryness Fraction
x = (s2 - s_l2)/(s_g2 - s_l2);
h_l2 = XSteam('hL_p',P2);
h_g2 = XSteam('hV_p',P2);
h2 = h_l2 + x*(h_g2 - h_l2);
T2 = XSteam('T_ph',P2,h2);
T_sat2 = XSteam('Tsat_p',P2);
% State Point 3
h3 = h_l2;
s3 = s_l2;
P3 = P2;
T3 = T2;
% State Point 4
s4 = s3;
P4 = P1;
h4 = XSteam('h_ps',P4,s4);
T4 = XSteam('T_ps',P4,s4);
% Plotting
% T-s Diagram
figure(1), clf
hold on
% Saturation curve
for i = 1:length(t)
plot(XSteam('sL_T',t(i)),t(i),'r.')
plot(XSteam('sV_T',t(i)),t(i),'r.')
end
% Rankine Cycle
plot([s1 s2],[T1 T2],'linewidth',2,'color','g')
text(s1,T1,'1','FontSize',15)
% Beyond saturation curve
if x > 1
T3 = T_sat2;
plot([s2 s_g2 s3 s4],[T2 T_sat2 T3 T4],'linewidth',2,'color','g')
text(s1,T2,'2','FontSize',15)
text(s3,T3,'3','FontSize',15,'HorizontalAlignment','left','VerticalAlignment','top')
% Beneath saturation curve
else
plot([s2 s3 s4],[T2 T3 T4],'linewidth',2,'color','g')
text(s1,T2,'2','FontSize',15)
text(s3,T3,'3','FontSize',15,'HorizontalAlignment','left','VerticalAlignment','top')
end
n = linspace(T1,T2,500);
for i = 1:length(n)
plot(XSteam('s_pT',P1,n(i)),n(i),'.','linewidth',2,'color','g')
end
plot([s_l1 s_g1],[T_sat1 T_sat1],'linewidth',2,'color','g')
text(s_l1,T_sat1,'4','FontSize',15,'VerticalAlignment','bottom')
xlabel('Entropy(kJ/kg-K)')
ylabel('Temperature(k)')
title('T-s Diagram')
% h-s Diagram
figure(2), clf
hold on
% Saturation curve
for i = 1:length(t)
plot(XSteam('sL_T',t(i)),XSteam('hL_T',t(i)),'r.')
plot(XSteam('sV_T',t(i)),XSteam('hV_T',t(i)),'r.')
end
% Rankine Cycle
plot([s1 s2 s3 s4 s1],[h1 h2 h3 h4 h1],'linewidth',2,'color','g')
text(s1,h1,'1','FontSize',15)
text(s2,h2,'2','FontSize',15)
text(s3,h3,'3','FontSize',15)
text(s4,h4+90,'4','FontSize',15)
xlabel('Entropy(kJ/kg-K)')
ylabel('Enthalpy(kJ/kg)')
title('h-s Diagram')
% Calculation of desired quantities
% Work done by turbine
W_t = h1 - h2;
% Work done by pump
W_p = h4 - h3;
% Net work done
W_net = W_t - W_p;
% Thermal efficiency
n_thermal = (1 - ((h2 - h3)/(h1 - h4)))*100;
% Back work ratio
BWR = W_p/W_t;
% Specific Steam Conductivity
SSC = 3600/W_t;
% Displaying results in command window
disp('RESULTS:')
disp('At state point 1: ')
fprintf('P1 = %.2f bar\n',P1)
fprintf(['T1 = %.2f' char(176) 'C\n'],T1)
fprintf('h1 = %.2f kJ/kg\n',h1)
fprintf('s1 = %.2f kJ/kgK\n',s1)
disp(' ')
disp('At state point 2: ')
fprintf('P2 = %.2f bar\n',P2)
fprintf(['T2 = %.2f' char(176) 'C\n'],T2)
fprintf('h2 = %.2f kJ/kg\n',h2)
fprintf('s2 = %.2f kJ/kgK\n',s2)
disp(' ')
disp('At state point 3: ')
fprintf('P3 = %.2f bar\n',P3)
fprintf(['T3 = %.2f' char(176) 'C\n'],T3)
fprintf('h3 = %.2f kJ/kg\n',h3)
fprintf('s3 = %.2f kJ/kgK\n',s3)
disp(' ')
disp('At state point 4: ')
fprintf('P4 = %.2f bar\n',P4)
fprintf(['T4 = %.2f' char(176) 'C\n'],T4)
fprintf('h4 = %.2f kJ/kg\n',h4)
fprintf('s4 = %.2f kJ/kgK\n',s4)
disp(' ')
fprintf('Work done by turbine = %.2f kJ/kg\n', W_t)
fprintf('Work done by pump = %.2f kJ/kg\n', W_p)
fprintf('Net work done = %.2f kJ/kg\n', W_net)
fprintf('Thermal efficiency = %.2f %%\n', n_thermal)
fprintf('Back-work ratio = %f\n', BWR)
fprintf('Specific Steam Conductivity = %.2f kg/kWh\n', SSC)EXPLANATION OF PROGRAM:
· Initially, a platform for filling required inputs is established.
· It is followed by specifying all state point variables from the XSteam library.
· The T-s and h-s Diagrams are plotted containing the Rankine Cycle and the Saturation Curve.
· Now, the work done by individual equipments and the net work done is calculated.
· Adding to the other desired variables, back work ratio is calculated.
· The values of state point variables is printed on the command window with the work output values.
OUTPUT: (Command Window)
RESULTS:
1. Net Work Output = 603.81 kJ/kg
2. Back Work Ratio = 0.006911
PLOTS:
· T-S DIAGRAM:
· H-S DIAGRAM:
CONCLUSION: The Rankine Cycle Simulator has been established with required inputs fed. The required variables have been calculated and respective plots have been set up. It is possible to modify the Rankine Cycle by adding desired equipment based on our preference of functionality.
REFERENCES:
https://en.wikipedia.org/wiki/Rankine_cycle
http://www.thermopedia.com/content/1072/