1.
Idealized Brayton cycle
1
2 3
4 1
2 3
4

2.
Idealized Brayton cycle

3.
The ideal gas turbine cycle equations
𝑊
𝑐 = ℎ1 − ℎ2
𝑊𝑡 = ℎ3 − ℎ4
𝑊𝑛𝑒𝑡 = 𝑊𝑡 − 𝑊
𝑐
𝑄𝑖𝑛 = ℎ3 − ℎ2
𝑄𝑜𝑢𝑡 = ℎ4 − ℎ1
𝜂𝑡ℎ =
𝑊𝑛𝑒𝑡
𝑄𝑖𝑛
𝑃2
𝑃1
=
𝑇2
𝑇1
𝑘
𝑘−1 𝑃3
𝑃4
=
𝑇3
𝑇4
𝑘
𝑘−1

4.
Example 1
compressor Turbine
Combustion
chamber
Heat Exchanger
Input 1
Air
Pressure : 0.1 [MPa]
Temperature : 15 [c]
1
2 3
4
output 2
Air
Pressure : 1.0 [MPa]
Temperature : ?
output 3
Air + exhaust gas
Pressure : ?
Temperature : 1100 [c]
output 4
Air + exhaust gas
Pressure : 0.1 [MPa]
Temperature : 15 [c]
𝑄𝑖𝑛 =?
𝑄𝑜𝑢𝑡 =?
𝑊
𝑐 =? 𝑊𝑡 =?
𝑊𝑛𝑒𝑡 =?
𝜂𝑡ℎ =?

5.
EES Program for Example 1 p[1] = 0.1
t[1]=288
h[1]=Enthalpy(Air,t=t[1])
s[1]=Entropy(Air,t=t[1],p=p[1])
p[2]=1
p[2]=p[3]
p[1]=p[4]
t[2]=t[1]*((p[2]/p[1])^0.286)
h[2]=Enthalpy(Air,t=t[2])
s[2]=Entropy(Air,t=t[2],p=p[2])
t[3]=1373
h[3]=Enthalpy(Air,t=t[3])
s[3]=Entropy(Air,t=t[3],p=p[3])
t[4]=t[3]*((p[4]/p[3])^0.286)
h[4]=Enthalpy(Air,t=t[4])
s[4]=Entropy(Air,t=t[4],p=p[4])
w_c =h[2]-h[1]
w_t =h[3]-h[4]
Q_in =h[3]-h[2]
Q_out =h[4]-h[1]
w_net =w_t -w_c
eta_th=(w_net /Q_in)

6.
Program Result

7.
The actual cycle of the Brayton cycle

8.
The actual gas turbine cycle equations
𝑊
𝑐 = ℎ1 − ℎ2
𝑊𝑡 = ℎ3 − ℎ4
𝑊𝑛𝑒𝑡 = 𝑊𝑡 − 𝑊
𝑐
𝑄𝑖𝑛 = ℎ3 − ℎ2
𝑄𝑜𝑢𝑡 = ℎ4 − ℎ1
𝜂𝑡ℎ =
𝑊𝑛𝑒𝑡
𝑄𝑖𝑛
𝑇2𝑠
𝑇1
=
𝑃2
𝑃1
𝑘−1
𝑘
𝜂𝐶 =
ℎ2𝑠 − ℎ1
ℎ2 − ℎ1
𝜂𝑡 =
ℎ3 − ℎ4
ℎ3 − ℎ4𝑠
𝑇3
𝑇4𝑠
=
𝑃3
𝑃4
𝑘−1
𝑘

9.
Example 2
compressor Turbine
Combustion
chamber
Heat Exchanger
Input 1
Air
Pressure : 0.1 [MPa]
Temperature : 15 [c]
1
2 3
4
output 2
Air
Pressure : 1.0 [MPa]
Temperature : ?
output 3
Air + exhaust gas
Pressure : ?
Temperature : 1100 [c]
output 4
Air + exhaust gas
Pressure : 0.1 [MPa]
Temperature : ?
𝑄𝑖𝑛 =?
𝑄𝑜𝑢𝑡 =?
𝑊
𝑐 =? 𝑊𝑡 =?
𝑊𝑛𝑒𝑡 =?
𝜂𝑡ℎ =?
𝜂𝑐 = 80% 𝜂𝑡 = 85%
𝑃2 − 𝑃3 = 15 [𝑘𝑝𝑎]

10.
p[1] = 0.1
t[1]=288
h[1]=Enthalpy(Air,t=t[1])
s[1]=Entropy(Air,t=t[1],p=p[1])
p[2]=1
t_2s=t[1]*((p[2]/p[1])^0.286)
eta_c=0.80
eta_c=(t_2s-t[1])/(t[2]-t[1])
s_sc=s[1]
h_sc=enthalpy(air,p=p[2],s=s_sc)
eta_c=(h_sc-h[1])/(h[2]-h[1])
p[3]=p[2]-0.015
p[4]=p[1]
t[3]=1373
t_4s=t[3]/((p[3]/p[4])^0.286)
s[3]=Entropy(Air,t=t[3],p=p[3])
s_st=s[3]
h_st=enthalpy(air,p=p[4],s=s_st)
eta_t=0.85
eta_t=(t[3]-t[4])/(t[3]-t_4s)
h[3]=Enthalpy(Air,t=t[3])
eta_t=(h[3]-h[4])/(h[3]-h_st)
w_c =h[2]-h[1]
w_t =h[3]-h[4]
Q_in =h[3]-h[2]
Q_out =h[4]-h[1]
w_net =w_t -w_c
eta_th=(w_net /Q_in)
EES Program for Example 2

11.
Program Result

12.
comparing results

13.
References
1- Wikiwand.com / Accessed 10 July 2017
2- Powergen.gepower.com / Accessed 10 July 2017
3- Siemens.com/ Accessed 10 July 2017
4-Van Wylen Thermodynamics book