Project 2 - Rankine cycle Simulator

Rankine Cycle Simulator

Aim:

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

Objective:

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

Description:

The Rankine cycle or Rankine Vapor Cycle is the process widely used by power plants such as coal-fired power plants or nuclear reactors. In this mechanism, a fuel is used to produce heat within a boiler, converting water into steam which then expands through a turbine producing useful work.

The process in Rankine cycle are given as:

1. Isentropic Compression in Pump.
2. Constant pressure heat addition in boiler.
3. Isentropic expansion in a turbine.
4. Constant pressure heat rejection in condenser.

1-2: Isentropic compression in a pump. 2-3: Constant pressure heat addition in a boiler. 3-4: Isentropic expansion in a turbine. 4-1: Constant pressure heat rejection in a condenser.

Code Explanation:

1. The creation of Rankine cycle simulator starts with input value which are required to calculate the other state point in cycle eventually.
2. Then inputs are entered which are inlet pressure for turbine, temperature at turbine inlet and pressure at condenser.
3. 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.
4. 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.
5. 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.
6. 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 Rankine cycle.
7. 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 of output of work done.
8. 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.
9. Then plotting is done respectively for T-s and H-s graph in Rankine cycle and each state point value has been put in command window.

Coding:

%program for Rankine cycle simulator

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 = 50; %Pressure at Turbine Inlet

T1 = 500; %Temperature at Turbine Inlet

p2 = 5; %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,'sow')

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 in Bar\t\t\t\t',p1);

fprintf('P2 = %10f in Bar\n',p2);

fprintf('T1 = %11f in Deg.Celcius\t\t',T1);

fprintf('T2 = %11f in Deg.Celcius\n',T2);

fprintf('H1 = %12f in KJ/Kg\t\t\t',h1);

fprintf('H2 = %12f in KJ/Kg\n',h2);

fprintf('S1 = %9f in KJ/Kg-k\t\t\t',s1);

fprintf('S2 = %9f in 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 in Bar\t\t\t\t',p3);

fprintf('P4 = %10f in Bar\n',p4);

fprintf('T3 = %11f in Deg.Celcius\t\t',T3);

fprintf('T4 = %11f in Deg.Celcius\n',T4);

fprintf('H3 = %12f in KJ/Kg\t\t\t',h3);

fprintf('H4 = %12f in KJ/Kg\n',h4);

fprintf('S3 = %9f in KJ/Kg-k\t\t\t',s3);

fprintf('S4 = %9f in KJ/Kg-k\n',s4);

fprintf('\n')

fprintf('Turbine Work Done = %14f in KJ/Kg\n',W_T)

fprintf('Pump Work Done = %15f in KJ/Kg\n',W_P)

fprintf('Net Work Done = %17f in KJ/Kg\n',W_net)

fprintf('Thermal Efficiency = %13f in percent\n',T_eff)

fprintf('Sp. Steam Consumption = %f in KJ/Kw\n',Sp_S)

PLOTTING :

Plotting graph between Temperature & Entropy .

Above grapgh, heat added in the system the entropy has been increased and similarly as the heat removed from the system the entropy drops with similar rates. From graph itself we can understand the behaviour.

COMMAND WINDOW :

From the bellow graph, the pressure 1 , temperature 1 , pressure 2 are given data as you know already. From these data we arrived the other paramerters.

ERRORS:

The above image are error i faced in command window. This is not the error but i missed the semicolon in work done , v3 and w_p. So that its prints in the results in commands window.

Conclusion:

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

DRIVE LINK :

https://drive.google.com/drive/folders/1MJ6391m-zEWC0UNnKwSul-wssAVo4XiF

References:

1) https://www.nuclear-power.net/nuclear-engineering/thermodynamics/thermodynamic-cycles/rankine-cycle-steam-turbine-cycle/theory-of-rankine-cycle-equations-and-calculation/

2) https://in.mathworks.com/matlabcentral/answers/12855-newlines-and-spaces-in-strings