Rankine cycle Simulator

AIM: Create a Rankine Cycle Simulator using MATLAB.

OBJECTIVE:

• Calculate each state points of the Rankine Cycle (any type of your choice) based on user inputs.
• Plot the corresponding T-s and h-s plots for the given set of inputs.
• Calculate Efficiency.

THEORY:

The Rankine cycle is an idealized thermodynamic cycle of a heat engine that converts heat into mechanical work while undergoing a phase change. It is an idealized cycle in which friction losses in each of the four components are neglected. The heat is supplied externally to a closed loop, which usually uses water as the working fluid.

• Four components of the Rankine cycle:

1. Pump
2. Boiler
3. Turbine
4. Condenser

• Four processes of the Rankine cycle:

1 2: Isentropic Expansion

Turbine (1-2): Superheated steam enters into the Turbine and expands isentropically resulting in the production of work. The shaft of the turbine is connected to the generator. This results in the production of electricity i.e Mechanical energy gets converted into electric energy. Work produced by the turbine,

`W_T = m(h_1 -h_2) K`

2-3: Constant Pressure Heat Rejection

Condenser (2-3): The expanded vapour is then passed through a condenser, where it gets condensed and converts into liquid again. This liquid is again pumped to the boiler.

`Q_r = m(h_2 - h_3) K`

3-4: Isentropic Compression by the Pump

Pump (3-4): The water enters into the pump in a saturated state. Then the liquid is compressed isentropically until it meets the boiler pressure. Work done by the pump is,

`W_P = m(h_3 -h_4) K`

4-1: Constant Pressure Heat Addition

Boiler (4-1): The water enters into the boiler as compressed and leaves as superheated from the boiler. Thus the phase changes from liquid to vapour. The heat supplied by the boiler is

`Q_b = m(h_1 - h_4) K`

Here we take mass flow rate m = 1 for this code.

• The efficiency of the Steam Cycle is given by

`eta = frac{W_n}{Q_1} = frac{W_T-W_P}{Q_1}`

• Applying the Steady Flow Energy Equation (SFEE) to all the process, neglecting the Friction losses and changs in Kinetic & Potential Energy,

  • Q1=h1-h4 @Boiler
  • Wt=h1-h2 @Turbine
  • Q2=h2-h3 @Condenser
  • Wp=h4-h3 @Pump
• The Capacity of the Steam Plant is often expressed interms of Steam Rate (SR) or Specific Steam Consumption (SSC) `S.S.C. = 3600/W_n frac{kg}{kWh}`

Required Inputs:

Turbine Inlet temperature = 400° C

Turbine Inlet Pressure = 30 bars

Turbine Outlet Pressure = 0.05 bars = Condenser Inlet Pressure

MATLAB CODE:

close all
clear all
clc

% Print Process Description
fprintf(\'1-2 Isobaric heat Transfer\\n\')
fprintf(\'2-3 Isentropic Expansion\\n\')
fprintf(\'3-4 Isobaric heat Rejection\\n\')
fprintf(\'4-1 Isentropic Compression\\n\')

%step 1:Enter Inputs
p1 = input(\'Enter the Pressure at the Turbine Inlet (in bar):\');
T1 = input(\'Enter the Temperature at the Turbineinlet (in Degree Celcius):\');
p2 = input(\'Enter the Pressure at the Condensor (in bar):\');

%step 2: Calculate each state point values.
% state point 1
h1 = XSteam(\'h_pt\',p1,T1);
s1 = XSteam(\'s_pt\',p1,T1);

%step 3: state point 2
s2=s1;
sf2 = XSteam(\'sL_p\',p2);
sg2 = XSteam(\'sV_p\',p2);
hf2 = XSteam(\'hL_p\',p2);
hg2 = XSteam(\'hV_p\',p2);   %x2 = (s2-sf2)/(sg2-sf2);
s2 = sg2;
h2 = hg2;                  %hf2 +(x2*(hg2-hf2));
T2=XSteam(\'T_hs\',h2,s2);

%step 4: state point 3
T3=T2;
p3= p2;
s3=XSteam(\'sL_T\',T3);
h3=XSteam(\'hL_T\',T3);
v3 = XSteam(\'vL_p\',p2);

%step 5: state point 4
p4 =p1;
s4= s3;
Cp4 = XSteam(\'Cp_ps\',p4,s4);
Cv4 = XSteam(\'Cv_ps\',p4,s4);
gamma = Cp4/Cv4;
r = (gamma - 1)/gamma;
T4 = T3 *(p4/p3)^r; 

%step 6: Calculate other output values.
Wt = h1-h2;      % Turbine Work      
Wp = v3*(p1-p2)*100;   % Pump Work
h4 = Wp + h3;
W_net = Wt-Wp;     % Net Work unit in kj/kg
Qs = h1 - h4;%heat suppied
N_per = (W_net/Qs)*100;%Efficiency
steam_rate = 3600/(Wt - Wp);%Steam rate per second

%step 7: state point 5 and 6 which help in plotting
T5=XSteam(\'Tsat_p\',p1);
T6=T5;
s5=XSteam(\'sL_p\',p1);
s6=XSteam(\'sV_p\',p1);
h5=XSteam(\'hL_p\',p1);
h6=XSteam(\'hV_p\',p1);

%step 8: print all state poont values to show.
fprintf(\'\\n------------------RESULT------------------\\n\')
fprintf(\'At State point 1:\\nP1 is : %4.2f Bar\\nT1 is : %4.2f Degree Celcius\\nH1 is : %4.2f kJ/kg\\nS1 is : %4.2f kJ/kgk\\n\\n\',p1,T1,h1,s1)
fprintf(\'At State point 2:\\nP2 is : %4.2f Bar\\nT2 is : %4.2f Degree Celcius\\nH2 is : %4.2f kJ/kg\\nS2 is : %4.2f kJ/kgk\\n\\n\',p2,T2,h2,s2)
fprintf(\'At State point 3:\\nP3 is : %4.2f Bar\\nT3 is : %4.2f Degree Celcius\\nH3 is : %4.2f kJ/kg\\nS3 is : %4.2f kJ/kgk\\n\\n\',p3,T3,h3,s3)
fprintf(\'At State point 4:\\nP4 is : %4.2f Bar\\nT4 is : %4.2f Degree Celcius\\nH4 is : %4.2f kJ/kg\\nS4 is : %4.2f kJ/kgk\\n\\n\',p4,T4,h4,s4)
fprintf(\'Wt is :%4.2f kJ/kg\\nWp is : %4.2f kJ/kg\\nWnet is : %4.2f kJ/kg\\nNtherm is : %4.2f percent\\nS.S.C is : %4.2f kg/kWh\',Wt,Wp,W_net,N_per,steam_rate)

%step 9:plot T-S Diagram
subplot(1,2,1)
T_rankine = linspace(T5,T1,5000);
for i = 1:length(T_rankine)
       s_rankine(i) = XSteam(\'s_pT\',p1,T_rankine(i));
end
plot([s1 s2 s3 s4 s5 s6 s_rankine],[T1 T2 T3 T4 T5 T6 T_rankine],\'linewidth\',1.5);
hold on
T_curve = linspace(1,400,500);
for i=1:length(T_curve)
    s_l(i) = XSteam(\'sL_T\',T_curve(i));
    s_v(i) = XSteam(\'sV_T\',T_curve(i));
    h_l(i) = XSteam(\'hL_T\',T_curve(i));
    h_v(i) = XSteam(\'hV_T\',T_curve(i));
end
plot(s_l,T_curve);
plot(s_v,T_curve);
text(s1,T1,\'1\',\'FontSize\',15)
text(s2,T2,\'2\',\'FontSize\',15)
text(s3,T3,\'3\',\'FontSize\',15,\'HorizontalAlignment\',\'right\',\'VerticalAlignment\',\'top\')
text(s4,T4,\'4\',\'FontSize\',15,\'HorizontalAlignment\',\'right\',\'VerticalAlignment\',\'bottom\')
text(s5,T5,\'5\',\'FontSize\',15)
text(s6,T6,\'6\',\'FontSize\',15)
xlabel(\'Entropy in kJ/KgK\');
ylabel(\'Temperature in Degree Celcius\');

%step 10:plot H-S diagram
subplot(1,2,2)
plot([s1 s2 s3 s4 s1],[h1 h2 h3 h4 h1],\'linewidth\',2)
hold on
plot(s_v,h_v,\'color\',\'r\')
plot(s_l,h_l,\'color\',\'r\')
text(s1,h1,\'1\',\'FontSize\',15)
text(s2,h2,\'2\',\'FontSize\',15)
text(s3,h3,\'3\',\'FontSize\',15,\'HorizontalAlignment\',\'right\',\'VerticalAlignment\',\'top\')
text(s4,h4,\'4\',\'FontSize\',15,\'HorizontalAlignment\',\'right\',\'VerticalAlignment\',\'bottom\')
xlabel(\'Entropy in kJ/KgK\')
ylabel(\'Enthalpy in kJ/kg\')

EXPLANATION:

• The Program begins with clear all, close all, clc to erase the workspace and plots..
• Input variables p1,T1,p2 are given by input command whose values are entered in command window while executing the Program.
• @State-1, Values for Enthalpy & Entropy are extracted as a function of Pressure & Temperature.
• h_pT, s_pT, hL_p, sV_p etc.... are the default variables whose value is stored in XSteam file.
• Similarly, all the variables for all states are extracted using a suitable format.[**The Formulae for the State Variables and other depending factors are referred from Power Plant Reference Books.]
• Pressure, Temperature, Enthalpy, Entropy for all the State Variables are Extracted as a function of the dependent variable from the XSteam File.
• @State 2 is a Condenser inlet where the High-Pressure Steam is converted into Low-Pressure Water and hence Dryness Fraction, Enthalpy & Entropy for Saturated Vapour & Saturated Water are considered to Calculate the Specific Enthalpy.
• @State-3 The water is condensed back to its Saturation Temperature and fed to the Pump, This temperature of water at the exit of the Condenser and entry of Pump is the same.
• @State-4 This is Constant Pressure Heat addition, hence pressure is equal to p1, but the temperature increases on heating at Constant Pressure & Constant Volume as our Entropy remains same and hence Cp/Cv=gamma is considered to find temperature T4.
• define two more points 5 and 6 to plot cycle in detail.
• Finally Work done and Heat Evolved & SSC are calculated by basic formulae.
• To plot the Saturation Curve, a Temperature range is defined using linspace command and for the overall length of this Temperature values of Enthalpy and Entropy are calculated at every temperature point. The Break in the Saturation Curve separates the Liquid Phase & Vapour Phase.
• Now all the necessary data is found out, Plotting is done for both T-S & H-S curves using the plot commands. Annotations are assigned using text command.
• Results of the Cycle Simulation is displayed over Comand window using fprintf command.

RESULT:

The Rankine cycle plots have generated by calculating the state points, efficiency and the output is printed in the command window.

COMMAND WINDOWS:

WORKSPACE:

ERROR:

• The error occurs while calling data from Xsteam library. Solve by adding proper syntex.
• The error occurs during the plotting of the Rankine cycle