Challenge

Project 2 - Rankine cycle Simulator

TTivin C Reji19 Jul 2022

HTML MATLAB

The following code gives the Ideal Rankine Cycle Simulator

Aim: To create a ideal Rankine Cycle Simulator using OCTAVE/MATLAB.

PLATFORM USED :-

Software – MATLAB R2019a
Programming Language – C/C++

SYSTEM SPECIFICATIONS :-

Manufacturer - DELL
Model – Vostro 3478
Operating System - Windows 10
Processor - Intel(R) Core(TM) i5-8250U CPU @ 1.60GHz 1.80GHz
RAM – 8 GB

OBJECTIVE :-

To plot H-S and T-S diagram of Ideal Rankine Cycle.
Evaluate the Net Work Done and Cycle Efficiency.

THEORY :-

The Rankine cycle is a model used to predict the performance of steam turbine systems. It was also used to study the performance of reciprocating steam engines. The Rankine cycle is an idealized thermodynamic cycle of a heat engine that converts heat into mechanical work while undergoing phase change. It is named after William John Macquorn Rankine, a Scottish polymath and Glasgow University professor.

There are four process in Rankine Cycle,

Process 1-2 : Isentropic Compression in Pump
Process 2-3 : Constant Pressure Heat Addition by the Boiler
Process 3-4 : Isentropic Expansion in Turbine
Process 4-1 : Constant Pressure Heat Rejection by the Condenser

PROCESS 1-2 :-

In this process the water is pumped to the boiler where the entropies remain constant (S1 = S2).

PROCESS 2-3 :-

In this process the boiler heats the pumped water and the state gets converted into steam at constant pressure (P2 = P3).

PROCESS 3-4 :-

In this process the steam gets expanded in the turbine to generate power where the entropies remain constant (S3 = S4).

PROCESS 4-1 :-

In this process the steam gets converted back into water by removing the heat from the steam at constant pressure (P4 = P1).

NOTE :-

Here I had considered that the Ideal Rankine Cycle starts from Turbine and ends in Boiler for easy calculations and plotting graphs. And also the formulae subject to change as the state points vary.

Energy Analysis

All four componenets of the Rankine cycle are steady-state staedy flow devices. The potentia and kinetic energy effects are neglected. The first law per unit mass of steam can be written as:

Pump	q=0	W(pump.in)=h2-h1
Boiler	w=0	q(in)=h3-h2
Turbine	q=0	W(turbine.out)=h3-h4
Condenser	w=0	q(out)=h4-h1

Governing Equations

GOVERNING EQUATIONS :-

i.Efficiency of Rankine Cycle,

ƞRank=TWDHeat_SuppliedƞRank=TWDHeat_Supplied

Where,

ii.Work Done by the Turbine,

WTurb=H1–H2WTurb=H1–H2

Where,

iii.Work Done by the Pump,

WPump=H4–H3WPump=H4–H3

Where,

iv.Net Work Done,

TWD=WTurb−WPumpTWD=WTurb-WPump

Where,

v.Heat Supplied,

Qadd=H1–H4Qadd=H1–H4

Where,

vii.Heat Rejected,

Qout=H2–H3Qout=H2–H3

Where,

viii.Back Work Ratio,

BWR=WPumpWTurbBWR=WPumpWTurb

Where,

ix.Specific Steam Consumption,

SSC=3600WTurbSSC=3600WTurb

Where,

Main code

%%A program for simulate Rankine cycle

clear all

close all

clc

fprintf('\n RANKINE CYCLE SIMULATOR');

fprintf('\n\n1-2 Isentropic Expansion in Turbine');

fprintf('\n2-3 Constant Pressure Heat Rejection in the Condenser');

fprintf('\n3-4 Isentropic Compression in the Pump');

fprintf('\n4-1 Constant Pressure Heat Addition by the Boiler\n');

%Inputs

p1=30;('Pressure at the turbine inlet (bar):')

t1=400;('Temperature at the turbine inlet (celcius):')

p2=0.05;('Pressure at the condensor')

% @ stage 1 Turbine Inlet

% p1 & t1 are given

h1=XSteam('h_pT',p1,t1);

s1=XSteam('s_pT',p1,t1);

% @ stage 2 Condenser Inlet

%p2 is given

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);

h2=hf2+(x2*(hg2-hf2));

% @ stage 3 Pump Inlet

p3=p2;

h3=XSteam('hL_p',p3);

s3=XSteam('sL_p',p3);

t3=XSteam('Tsat_p',p3);

t2=t3;

% @ stage 4 Boiler Inlet

p4=p1;

s4=s3;

h4=XSteam('h_ps',p4,s4);

cp4=XSteam('Cp_ps',p4,s4);

cv4=XSteam('Cv_ps',p4,s4);

lambda=cp4/cv4;

t4=t3/((p3/p4)^((lambda-1)/lambda));

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);

% Turbine Work

Wt=h1-h2;

% Pump Work

Wp=h4-h3;

% Net Work (kJ/Kg)

W=Wt-Wp;

% Heat in & out of the System

Q_in=h1-h4;

Q_out=h2-h3;

% Thermal Efficiency

ntherm=(W/Q_in)*100;

% Steam rate (kg/kWh)

SSC=3600/W;

% Back Work Ratio

BWR=(h1-h4)/(h2-h3);

% to plot Saturation Curve

T=linspace(1,400,500);

for i=1:length(T)

h_l(i)=XSteam('hL_T',T(i));

h_v(i)=XSteam('hV_T',T(i));

s_l(i)=XSteam('sL_T',T(i));

s_v(i)=XSteam('sV_T',T(i));

end

% plotting TS diagram

figure(1)

hold on

title('T-S Diagram')

plot([s1 s2],[t1 t2],'linewidth',3,'color','b')

plot([s2 s3],[t2 t3],'linewidth',3,'color','b')

plot([s3 s4],[t3 t4],'linewidth',3,'color','b')

plot([s4 s5],[t4 t5],'linewidth',3,'color','b')

plot([s5 s6],[t5 t6],'linewidth',3,'color','b')

xlabel('Entropy (kJ/KgK');

ylabel('Temperature (deg C)');

s_1=linspace(s6,s1,500);

for j=1:length(s_1)'

t_1(j)=XSteam('T_ps',p1,s_1(j));

end

plot(s_1,t_1,'linewidth',3,'color','b')

plot(s_l,T,'linewidth',1.5,'color','r')

plot(s_v,T,'linewidth',1.5,'color','r')

% Annotations

text(s1,t1,'1','fontsize',15);

text(s2,t2,'2','fontsize',15);

text(s3,t3,'3','fontsize',15,'verticalalignment','top');

text(s4,t4,'4','fontsize',15,'verticalalignment','bottom');

text(s5,t5,'5','fontsize',15,'verticalalignment','bottom');

text(s6,t6,'6','fontsize',15,'verticalalignment','bottom');

figure(2)

hold on

title('H-S Diagram');

plot([s1 s2],[h1 h2],'linewidth',2,'color','b')

plot([s2 s3],[h2 h3],'linewidth',2,'color','b')

plot([s3 s4],[h3 h4],'linewidth',2,'color','b')

h_4=linspace(h4,h5,500);

for k=1:length(h_4);

s_4(k)=XSteam('s_ph',p1,h_4(k));

end

h_6=linspace(h6,h1,500);

for m=1:length(h_6);

s_6(m)=XSteam('s_ph',p1,h_6(m));

end

plot(s_4,h_4,'linewidth',2,'color','b')

plot([s5 s6],[h5 h6],'linewidth',2,'color','b')

plot(s_6,h_6,'linewidth',2,'color','b')

xlabel('Specific Entropy (kJ/KgK)');

ylabel('Specific Enthalpy (kJ/Kg)');

plot(s_l,h_l,'linewidth',1.5,'color','r')

plot(s_v,h_v,'linewidth',1.5,'color','r')

% Annotations

text(s1,h1,'1','fontsize',15);

text(s2,h2,'2','fontsize',15);

text(s3,h3,'3','fontsize',15,'verticalalignment','top');

text(s4,h4,'4','fontsize',15,'verticalalignment','bottom');

text(s5,h5,'5','fontsize',15,'verticalalignment','bottom');

text(s6,h6,'6','fontsize',15,'verticalalignment','bottom');

% Results Window

fprintf('\nRESULTS\n\n');

fprintf('At State Point 1 :\n');

fprintf('P1=%f Bar\n',p1);

fprintf('T1=%f Deg Celsius\n',t1);

fprintf('H1=%f kJ/Kg\n',h1);

fprintf('S1=%f kJ/KgK\n\n',s1);

fprintf('At State Point 2 :\n');

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

fprintf('T2=%f Deg Celsius\n',t2);

fprintf('H2=%f kJ/Kg\n',h2);

fprintf('S2=%f kJ/KgK\n\n',s2);

fprintf('At State Point 3 :\n');

fprintf('P3=%f Bar\n',p3);

fprintf('T3=%f Deg Celsius\n',t3);

fprintf('H3=%f kJ/Kg\n',h3);

fprintf('S3=%f kJ/KgK\n\n',s3);

fprintf('At State Point 4 :\n');

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

fprintf('T4=%f Deg Celsius\n',t4);

fprintf('H4=%f kJ/Kg\n',h4);

fprintf('S4=%f kJ/KgK\n\n',s4);

fprintf('Work done by Turbine is : %f kJ/Kg\n',Wt);

fprintf('Work done by Pump is : %f kJ/Kg\n',Wp);

fprintf('Net Work done on the System : %f kJ/Kg\n',W);

fprintf('Specific Steam Consumption is : %f kg/kWh\n',SSC);

fprintf('The Net Thermal Efficiency of the System is : %f\n',ntherm);

fprintf('The BWR of the Rankine Cycle is found to be : %f\n',BWR);

PROGRAM PROCESS :-

The compiler starts the program.
The Rankine Cycle process chart is printed
The values of P1,T1 and P2 are obtained from the user.
Next the H1 and S1 for state point 1 are calculated.
Then H2,T2 and S2 for state point 2 are calculated.
Next P3,T3,H3 and S3 for state point 3 are calculated.
Next P4,T4,H4 and S4 for state point 4 are calculated
Next T5,T6,S5 and S6 values are calculated.
Turbine and Pump work done are evaluated.
Net work done is evaluated.
Heat added and rejected are evaluated.
Thermal Efficiency, back work ratio and specific steam consumption are evaluated.
Next the values of S, T, P and H are displayed for all the four state points.
Also, the Rankine Cycle parameters are displayed in the command window.
Next the H-S and T-S diagram are plotted.
The compiler terminates the program.

Step-wise explanation:

Function X-steam is used, which is the steam table

Clearing the command window, workspace, and closing all plots
Print description of all processes in the command window.
Give the required inputs p1, T1, and p2.
Defining the specific heat(Cp) for values for liquid and vapour using the Xsteam function (steam table).
Defining the saturation temperature Tsat using Xsteam.
Defining saturation properties specific Enthalpy an Entropy at states 1, 2, 3, 4 using the Xsteam function and required inputs.
Starting with the calculation of properties at states 1, 2, 3, 4 using Xstaem and required inputs.
Calculate enthalpies H1, H2, H3, H4 at states 1, 2, 3, 4 using Xsteam.
Calculate entropies S1, S2, S3, S4 at states 1, 2, 3, 4.
Calculate the values of T2, T3, and Wp(pump work), to calculate H and S at different states.
Now define a range of temperature using the linspace command required to plot the graph.
Now define the values of enthalpy and entropy of liquid and vapour lines.
Now coming to plotting, start with the T-S diagram plot all the property lines
Plot the H-S diagram.
Then calculate net work done, thermal efficiency, and SSC.