Question

Design a Matlab program for the Brayton Cycle. The program would be for a standard air cycle. The program should show specific work and thermodynamic efficiency from r=1 to 50, t=1 to 5 , where r is the pressure ratio and t is the temperature ratio,

Answer 1

Brayton cycle.

• The efficiency of the ideal Brayton cycle:-

  

The equation in the form of given data

Efficiency (E) = 1 - t = 1- 1/{r^[(k-1)/(k)]}

Where,

k = γ = Specific heat ratio = 1.4

• specific work output = Turbine specific work - pump specific work

w = (k*(k-1))*R*T1*(r^((k-1)/k)-1) - (k*(k-1))*R*T1*(1-r^((k-1)/k))

*************************************************Matlab script****************************************************

clc
clear all

k=1.4; %specific heat ratio
R=0.287; % Individual gas constant (kj/kgK)
T1= 298; % Surrounding temperature (K)
%E=(1-t)*100; % Efficiency with temperature ratio

fprintf('\n For Pressure ratio')

for r=1:1:50
E=(1-1/(r^((k-1)/(k))))*100; % Efficiency with pressure ratio
  
% Specific work output w (kj/kg)
w=(k*(k-1))*R*T1*(r^((k-1)/k)-1)-(k*(k-1))*R*T1*(1-r^((k-1)/k));

fprintf('\nAt r=%d Efficiency = %0.3f and Specific work = %0.3f kj/kg', r,E,w)
end
fprintf('\n\n\n For Temperature ratio')   
for t=1:1:5
E=(1-t^(-1))*100; % Efficiency with Temperature ratio
r=t^(k/(k-1)); % Temperature ratio to pressure ratio conversion
w=(k*(k-1))*R*T1*(r^((k-1)/k)-1)-(k*(k-1))*R*T1*(1-r^((k-1)/k));
fprintf('\nAt t=%d Efficiency = %0.3f and Specific work = %0.3f kj/kg', t,E,w)
end

*****************************************************************************************************************

Screenshot of Output:-