FINAL INDEPENDENT PROJECT

BRAYTON CYCLE GAS TURBINE

Objectives

• To calculate the values of Brayton cycle gas turbine, heat input, work done on the pump, work done by the turbine, Net work output, gas turbine efficiency and back work ratio.
• To plot the T-S diagram of Brayton cycle with x and y labels and use title of the graph.

THEORY about Brayton Cycle Gas Turbine:-

Gas turbines are used in a wide variety of applications in aviation and electricity generation. It is especially important for aviation as these engines can power huge aircrafts and also are cost-efficient in operation. Today, a great attention has been paid on optimizing the fuel consumption and usability of these engines while minimizing their noise level. This serves the purpose of the smallest possible environmental impact of emissions and low consumption of resources. Thermal and materials engineering play a vital role in designing of gas turbines and improving their performance.

The Brayton cycle is a thermodynamic cycle named after George Brayton that describes the workings of a constant-pressure heat engine. The original Brayton engines used a piston compressor and piston expander, but more modern gas turbine engines and air breathing jet engines also follow the Brayton cycle. Although the cycle is usually run as an open system (and indeed must be run as such if internal combustion is used), it is conventionally assumed for the purposes of thermodynamic analysis that the exhaust gases are reused in the intake, enabling analysis as a closed system.

Gas turbines are also Brayton engines, with four components: a gas compressor, a burner (or combustion chamber), an expansion turbine and condenser.

Ideal Brayton cycle:

1. Isentropic process – ambient air is drawn into the compressor, where it is pressurized.
2. isobaric process – the compressed air then runs through a combustion chamber, where fuel is burned, heating that air—a constant-pressure process..
3. Isentropic process – the heated, pressurized air then gives up its energy, expanding through a turbine (or series of turbines). Some of the work extracted by the turbine is used to drive the compressor.
4. Isobaric process – heat rejection.

The T-s diagrams of an ideal Brayton cycle are shown in the figure. In an ideal Brayton cycle, heat is added to the cycle at a constant pressure process (process 2-3).

q_in = h₃ - h₂ = cp(T₃ - T₂)

Heat is rejected at a constant pressure process (process 4 -1).

q_out = h₄ - h₁ = rp(T₄ - T₁)

Then the thermal efficiency of the ideal Brayton cycle under the cold air-standard assumption is given as

Process 1-2 and process 3-4 are isentropic processes, thus,

Since P₂ = P₃ and P₄ = P₁,

Considering all the relations above, the thermal efficiency becomes,

Where, rp = P₂/P₁ is the pressure ratio and k is the specific heat ratio. In most designs, the pressure ratio of gas turbines range from about 11 to 16.

Using this table we will find entropies using temperatures

MAIN PROGRAM

%BRAYTON CYCLE GAS TURBINE

clear all
close all
clc

%known input values
gamma=1.4;


%state variale
p1=100000; %in pascal
p2=1000000;  %pascal
t1=300; % in Kelvin
t3=1400;   %k
cp=1.005;

rp=p2/p1 ;    %pressure ratio(rp)=p2/p1=p3/p4

%since isentropic compression process(1-2)

%t2/t1=(p2/p1)^((gamma-1)/gamma)    in Kelvin
t2=t1*(rp)^((gamma-1)/gamma);

%pump work (kj/kg)
wp=cp*(t2-t1);

%since process(2-3) heat input (qin) kj/kg
qin=cp*(t3-t2);


%since process(3-4) is isentropic
%since p3=p2 and p1=p4
%t3/t4=(1/rp)^((gamma-1)/gamma)
t4=t3*((1/rp)^((gamma-1)/gamma));

%turbine work ouput (kj/kg)

wt=cp*(t3-t4);

%net work done by the cycle is
wnet=wt-wp;

%the cycle efficiency becomes

n_eff=wnet/qin;

%the back work ratio defines asctime  bwr=wp/wt

bwr=wp/wt;

%from TABLE E7.3-1 the entropy values
s1=s2=6.878;
s3=s4=7.868;



figure(1)
hold on
grid on
plot(s1,t1,'marker','*','linewidth',5)
plot(s2,t2,'marker','*','linewidth',5)
plot(s3,t3,'marker','*','linewidth',5)
plot(s4,t4,'marker','*','linewidth',5)
line([s1,s2,s3,s4,s1],[t1,t2,t3,t4,t1],'linewidth',2,'color','r')
xlabel('Entropy(s) kj/kgk')
ylabel('Temperature (T) Kelvin')
title('BRAYTON CYCLE T-S Diagram')
legend('s1,T1','s2,T2','s3,T3','s4,T4')

%adding state points into the plot
mytext=sprintf('the state point %.2f',1);      %first state point
text(6.878,300,mytext);

mytext=sprintf('the state point %.2f',2);      %second state point
text(6.878,579.21,mytext);

mytext=sprintf('the state point %.2f',3);       %third state point
text(7.868,1400,mytext);

mytext=sprintf('the state point %.2f',4);        %fourth state point
text(7.868,725.13,mytext);

hold off

PROCEDURE:-

• Initially to clear the previously defined values, close any open windows and clear the command window using (clear all, close all and clc).
• First enter all the given inputs (pressure, temperature, specific heat (cp)).
• At state isentropic compression process (1-2) t2=t1*(rp)^((gamma-1)/gamma); using this formula we will calculate temperature of state point of 2.
• Once we know all the parameters we can calculate remaining values of Brayton cycle using the equations.
• After all parameter known then using the plot command, all values are plotted and with the help of text command, the state points are marked.
• Then we can add title of the plot, x-label and y-label.
• After all this we add some more in plot using legend command and using (mytext=sprintf('the state point %.2f',1); this command we denote the state points.
• Finally all the calculated state parameters are displayed onto the workspace.

OUTPUTS:-

• PLOT:- T-S Diagram

• WORKSPACE window

CONCLUSION:-

• Calculated all the values of Brayton cycle gas turbine (heat input, work done on the pump, work done by the turbine, net work output, gas turbine efficiency and back work ratio).
• Plotted the T-S diagram of Brayton cycle.

REFFERENCES:-

• https://en.wikipedia.org/wiki/Brayton_cycle
• https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc&topic=th&chap_sec=09.1&page=theory
• https://in.mathworks.com/matlabcentral/answers/31854-i-want-to-put-a-number-in-plot-function