Project 2 - Rankine cycle Simulator
REPORT:
Aim: To Create a Rankine Cycle Simulator using MATLAB.
Objective:
- Calculate the state points of the Rankine Cycle based on user inputs.
- Plot the corresponding T-s and h-s plots for the given set of inputs.
-
Calculate the followings
- Net work output
- Back work ratio
Description:
The Rankine cycle is one of the vapor powered cycle. It consists of 4 processes.
The processes in Rankine cycle are given as:
- 1 - 2 Isentropic Compression in pump.
- 2 - 3 Constant pressure heat addition in boiler.
- 3 - 4 Isentropic expansion in a turbine.
- 4 - 1 Constant pressure heat rejection in condenser.
Process 1–2: The working fluid is pumped from low to high pressure. As the fluid is a liquid at this stage, the pump requires little input energy.
Process 2–3: The high-pressure liquid enters a boiler, where it is heated at constant pressure by an external heat source to become a dry saturated vapour.
Process 3–4: The dry saturated vapour expands through a turbine, generating power. This decreases the temperature and pressure of the vapour, and some condensation may occur.
Process 4–1: The wet vapour then enters a condenser, where it is condensed at a constant pressure to become a saturated liquid.
All the four components of Rankine cycle are steady flow devices hence the process regarding this device can be evaluated as steady state process. The steady state flow energy equation per unit mass of steam reduces to:
(qIn-qout)+(WIn-Wout)=he-hi">(qIn−qout)+(WIn−Wout) = he − hi
The boiler and condenser are not involved in any mechanical work whereas pump and turbine are assumed to isentropic in nature while working throughout the cycle, then conservation of energy relation for each device can be expressed as:
Wpump=h2-h1">Wpump = h2 − h1
Where,
h1=hfatP1andv1=vfatP1">h1 = hf and v1 = vf (at P1)
The heat added in boiler can be given as:
qIn=h3-h2">qIn = h3 − h2
The work which can be taken out of cycle from turbine is given as:
Wout=h3-h4">Wout = h3 − h4
The heat removed from the condenser is given as:
qout=h4-h1">qout = h4 − h1
The thermal efficiency of Rankine cycle is given as:
ηth=WNetqIn=1-qoutqIn">ηth = WNet/qIn = 1−(qout/qIn)
Where,
WNet=qIn-qout=Wturb-Wpump">WNet = qIn − qout = Wturb − Wpump
Program:
clear all
close all
clc
% Rankine Cycle Simulator
fprintf(' Rankine Cycle\n ')
fprintf('1-2 is Isentropic Expansion in Turbine\n')
fprintf(' 2-3 is constant pressure heat removal\n')
fprintf(' 3-4 is Isentropic Compression in Pump \n')
fprintf(' 4-1 Constant pressure Heat addition in Boiler\n')
% Entering the input data for calculation of state points
p1 = 30; %Pressure at Turbine Inlet
T1 = 400; %Temperature at Turbine Inlet
p2 = 0.05; %Pressure at Condenser
% Taking data from Xsteam file for State point 1
h1 = XSteam('h_pT', p1, T1); % Enthaply at pressure and Temp 1
s1 = XSteam('s_pT', p1, T1); % Entropy at pressure and Temp 1
% Taking data from Xsteam file for State point 2
s2 = s1; % Because of Isentropic Expansion
sf2 = XSteam('sL_p', p2); % Saturated liquid entropy at pressure 2
sg2 = XSteam('sV_p', p2); % Saturated vapour entropy at pressure 2
x2 = (s2-sf2)/(sg2-sf2); % Vapour Fraction at state point 2
hf2 = XSteam('hL_p', p2); % Saturated liquid Enthalpy at pressure 2
hg2 = XSteam('hV_p', p2); % Saturated vapour Enthalpy at pressure 2
h2 = hf2 + (x2*(hg2-hf2)); % Enthalpy at state point 2
% Taking data from Xsteam file for state point 3
p3 = p2; % Constant Pressure heat removal process
s3 = XSteam('sL_p', p3); % Saturated liquid entropy at Pressure 3
h3 = XSteam('hL_p', p3); % Saturated liquid Enthalpy at Pressure 3
% Taking data from Xsteam file for State point 4
s4 = s3; % Isentropic Compression process
p4 = p1; % Constant Pressure heat rejection
% Work done in Turbine for the rankine cycle
W_T = h1-h2;
% Work done required for pump
v3 = XSteam('vL_p',p3); % Saturated Liquid Vapour at pressure 3
W_P = v3*(p4-p3)*100; % Work done for pump
h4 = h3 - W_P; % Enthalpy at State point 4
% Net work done for Rankine Cycle
W_net = W_T - W_P;
% Heat Addition to System
Q_in = h1-h4;
% Heat Rejection from System
Q_out = h2-h3;
% Thermal Efficiency of Rankine Cycle
T_eff = (W_net/Q_in)*100;
%specific steam consumption = (Mass flow rate / Net work done)
Sp_S = (3600/W_net);
% Calculation of Temperature at All state Point 2, 3 and 4
T3 = XSteam('Tsat_p',p3); % Saturation Temperature at Pressure 3
T2 = T3; % Becuase of Constant Pressure Heat addition
Cp4 = XSteam('Cp_ps',p4,s4); % Specific isobaric heat capacity
Cv4 = XSteam('Cv_ps',p4,s4); % Specific isochoric heat capacity
k = Cp4/Cv4;
T4 = T3/((p3/p4)^((k-1)/k)); % Temperature at State point 4
% Calculation of Other constant for saturated liquid and Vapour
T6 = XSteam('Tsat_p', p1); % Saturated Temperature at Pressure 1
s5 = XSteam('sL_p', p1); % Saturated Liquid entropy at pressure 1
s6 = XSteam('sV_p', p1); % Saturated Vapour entropy at Pressure 1
h5 = XSteam('hL_p', p1); % Saturated Liquid Enthalpy at Pressure 1
h6 = XSteam('hV_p', p1); % Saturated Vapour Enthalpy at pressure 1
T5 = T6;
%Plotting for Saturation Line
T = linspace(1,560,1000);
for i = 1:length(T)
sf(i) = XSteam('sL_T' ,T(i)); % Saturated Liquid Entropy
sg(i) = XSteam('sV_T' ,T(i)); % Saturated Vapour Entropy
hf(i) = XSteam('hL_T' ,T(i)); % Saturated Liquid Enthalpy
hg(i) = XSteam('hV_T' ,T(i)); % Saturated Vapour Enthalpy
end
% Plotting T-S Diagram for Rankine Cycle
figure(1)
hold on
plot(sf,T,'color','b','linewidth',2)
plot(sg,T,'color','b','linewidth',2)
plot([s1 s2],[T1 T2], 'color', 'r', 'linewidth',3)
plot([s2 s3],[T2 T3], 'color', 'r', 'linewidth',3)
plot([s3 s4],[T3 T4], 'color', 'r', 'linewidth',3)
plot([s4 s5],[T4 T5], 'color', 'r', 'linewidth',3)
plot([s5 s6],[T5 T6], 'color', 'r', 'linewidth',3)
s_1 = linspace(s6,s1,1000);
for j = 1:length(s_1)
Tc(j) = XSteam('T_ps',p1,s_1(j));
end
plot(s_1,Tc,'color','r','linewidth',3)
text(s1+0.1, T1, '1')
text(s2+0.1, T2, '2')
text(s3, T3-20, '3')
text(s4, T4+20, '4')
title('Temperature Vs Entropy')
xlabel('Entropy (Kj/kg-k)')
ylabel('Temeperature (Deg. Celcius)')
legend('Saturation Curve')
% Plotting H-S Diagram for Rankine Cycle
figure(2)
hold on
plot(sf,hf,'color','b','linewidth',2)
plot(sg,hg,'color','b','linewidth',2)
plot([s1 s2],[h1 h2],'color','r','linewidth',3)
plot([s2 s3],[h2 h3],'color','r','linewidth',3)
plot([s3 s4],[h3 h4],'color','r','linewidth',3)
hc = linspace(h4,h5,100);
for k = 1:length(hc)
s_c(k) = XSteam('s_ph',p1,hc(k));
end
plot(s_c,hc,'color','r','linewidth',3)
plot([s5 s6],[h5 h6],'color','r','linewidth',3)
for l = 1:length(s_1)
h_c(l) = XSteam('h_ps',p1,s_1(l));
end
plot(s_1,h_c,'color','r','linewidth',3)
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')
xlabel('Entropy (Kj/kg-k)')
ylabel('Enthalpy (KJ/Kg)')
legend('Saturation Curve')
% Displaying Results in Command window
disp('Results of Rankine Cycle')
fprintf('At state point 1\t\t\t\t\t')
fprintf('At state Point 2\n')
fprintf('P1 = %10f Bar\t\t\t\t',p1);
fprintf('P2 = %10f Bar\n',p2);
fprintf('T1 = %11f Deg.Celcius\t\t',T1);
fprintf('T2 = %11f Deg.Celcius\n',T2);
fprintf('H1 = %12f KJ/Kg\t\t\t',h1);
fprintf('H2 = %12f KJ/Kg\n',h2);
fprintf('S1 = %9f KJ/Kg-k\t\t\t',s1);
fprintf('S2 = %9f KJ/Kg-k\n',s2);
fprintf('\n')
fprintf('At state point 3\t\t\t\t\t')
fprintf('At state Point 4\n')
fprintf('P3 = %10f Bar\t\t\t\t',p3);
fprintf('P4 = %10f Bar\n',p4);
fprintf('T3 = %11f Deg.Celcius\t\t',T3);
fprintf('T4 = %11f Deg.Celcius\n',T4);
fprintf('H3 = %12f KJ/Kg\t\t\t',h3);
fprintf('H4 = %12f KJ/Kg\n',h4);
fprintf('S3 = %9f KJ/Kg-k\t\t\t',s3);
fprintf('S4 = %9f KJ/Kg-k\n',s4);
fprintf('\n')
fprintf('Turbine Work Done = %14f KJ/Kg\n',W_T)
fprintf('Pump Work Done = %15f KJ/Kg\n',W_P)
fprintf('Net Work Done = %17f KJ/Kg\n',W_net)
fprintf('Thermal Efficiency = %13f percent\n',T_eff)
fprintf('Sp. Steam Consumption = %f KJ/Kw\n',Sp_S)Step-wise Explanation:
- Started with clear all, close all, and clc for clear all the previous values in workspace, to close all the previous graphs and clear command window.
- Rankine cycle simulator starts with some input value which are required to calculate the other state point in cycle eventually.
- 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.
- 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.
- 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.
- 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.
- 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 by Rankine cycle.
- 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 work done.
- 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.
- Then plotting is done respectively for T-s and H-s graph in Rankine cycle. Labels, titles , and legends are added for each graph.
- Each state point value has been put in command window.
Command window:
Graphs:
fig 1 Temperature vs Entropy graph:
fig 2 Enthalpy vs Entropy graph:
Conclusion:
Thus, the rankine cycle simulator is created for given input and xsteam function file is refer for more required data. The obtained output is shown in command window.
References: