1. EGR 334 Thermodynamics Chapter 9: Sections 5-6
Lecture 35:
Gas Turbine modeling with the Brayton Cycle
Quiz Today?

2. Today’s main concepts:
Be able to recognize Dual and Brayton Cycles
Understand what system may be modeled using Brayton Cycle.
Be able to perform a 1st Law analysis of the Brayton Cycle and determine its thermal efficiency.
Be able to explain how regeneration may be applied to a Brayton Cycle model.
Reading Assignment:
Read Chapter 9, Sections 7-8
Homework Assignment:
Problems from Chap 9: 42, 47, 55

3. OK….Quick Matching Quiz
a) Carnot b) Rankine c) Otto d) Diesel p v . 4 1 3 1’ 2 2’ B C D A

4. Today you get to add two more cycles to your cycle repertoire
Today you get to add two more cycles to your cycle repertoire. Dual Cycle Brayton cycle.
Used as a hybrid cycle which includes elements of both the Otto and Diesel cycles. Used to model internal combustion engines
Used as a model for gas turbines (such as jet engines).

5. Heat addition occurs in two steps
Sec 9.4 : Air-Standard Duel Cycle
Neither the Otto or Diesel cycle describe the actual P-v diagrams of an engine
Heat addition occurs in two steps
2 – 3 : Constant volume heat addition
3 – 4 : Constant pressure heat addition (first part of power stroke)
Process 1 – 2 : Isentropic compression
Process 2 – 3 : Constant volume heat transfer
Process 3 – 4 : Constant pressure heat transfer
Process 4 – 5 : Isentropic expansion
Process 5 – 1 : Constant volume heat rejection
To set state 3: Use ideal gas law with V3 = V2.
and

6. Dual Cycle analysis process 1-2: s1 = s2 process 2-3: v2 = v3
Sec 9.4 : Air-Standard Duel Cycle
Dual Cycle analysis
process 1-2: s1 = s2
process 2-3: v2 = v3
process 3-4: p3 = p4
process 4-5: s4 = s5
process 5-1: v5 = v1

7. The thermal efficiency. The cut off ratio
Example (9.38): The pressure and temperature at the beginning of compression in an air-standard dual cycle are 14 psi, 520°R. The compression ratio is 15 and the heat addition per unit mass is 800 Btu/lbm. At the end of the constant volume heat addition process the pressure is psi. Determine,
Wcycle, in BTU/lb.
Qout, in BTU/lb.
The thermal efficiency.
The cut off ratio
State 1 2 3 4 5\
T (R)
p (psi)
u (Btu/lb)
h (Btu/lb) vr Pr
State 1 2 3 4 5\
T (R)
520
p (psi) 14
1200
u (Btu/lb)
h (Btu/lb) vr pr

8. Example (9.38): State 1 2 3 4 5\ T (R) 520 p (psi) 14 1200 u (Btu/lb)
88.62
h (Btu/lb) vr
158.58 Pr
1.2147
State 1 2 3 4 5\
T (R)
520
p (psi) 14
1200
u (Btu/lb)
h (Btu/lb) vr Pr
Given Information:
compression ratio, r = 15
Qin= Q23 + Q34 = 800 Btu
Qout = - Q51
Identify State Properties
State 1: p1 = 14 psi, T1 = 520 R
State 2: s2 = s1 v2 = v1/r
State 3: v3 = v2 and p3 = 1200 psi State 4: p4 = p3 = 1200 psi
State 5: s5 =s4 and v5 = v1
Use Table A22E to fill in many of the other properties.

9. and since 1-2 is isentropic find vr2
State 1 2 3 4 5\
T (R)
520
1468.8
p (psi) 14
594.26
1200
u (Btu/lb)
88.62
260.26
h (Btu/lb)
124.27
361.53 vr
158.58
10.572 pr
1.2147
51.561
State 1 2 3 4 5\
T (R)
520
p (psi) 14
1200
u (Btu/lb)
88.62
h (Btu/lb)
124.27 vr
158.58 pr
1.2147
Example (9.38):
State 1: given T = 520 R
look up u, h, vr, and pr
State 2: use r to find v2
and since 1-2 is isentropic
find vr2
then use Table A22E to look up T2, pr2, u2, and h2:
Pressure p2, can then be calculated using

10. then use Table A22E to look up u3 and h3:
State 1 2 3 4 5\
T (R)
520
1468.8
p (psi) 14
594.26
1200
u (Btu/lb)
88.62
260.26
h (Btu/lb)
124.27
361.53 vr
158.58
10.572 pr
1.2147
51.561
State 1 2 3 4 5\
T (R)
520
1468.8
2966
p (psi) 14
594.26
1200
u (Btu/lb)
88.62
260.26
577.4
h (Btu/lb)
124.27
361.53
780.7 vr
158.58
10.572 pr
1.2147
51.561
Example (9.38):
State 3: given v3 = v2 and
p3 = 1200 psi, use ideal
gas law:
then use Table A22E to look up u3 and h3:

11. State 4: Knowing p4=p3 and the heat in:1 2 3 4 5\
T (R)
520
1468.8
2966
4577.6
p (psi) 14
594.26
1200
u (Btu/lb)
88.62
260.26
577.4
949.7
h (Btu/lb)
124.27
361.53
780.7
1263.6 vr
158.58
10.572
0.2848 pr
1.2147
51.561
5961.6
State 1 2 3 4 5\
T (R)
520
1468.8
2966
p (psi) 14
594.26
1200
u (Btu/lb)
88.62
260.26
577.4
h (Btu/lb)
124.27
361.53
780.7 vr
158.58
10.572 pr
1.2147
51.561
Example (9.38):
State 4: Knowing p4=p3 and the heat in:
Qin= 800 Btu/lb
use the 1st Law: O
Use Table A-22E
to find T4 ,u4, pr4,
and v4r

12. Replace V’s using ideal gas.
State 1 2 3 4 5\
T (R)
520
1468.8
2966
4577.6
2299
p (psi) 14
594.26
1200
61.44
u (Btu/lb)
88.62
260.26
577.4
949.7
431.0
h (Btu/lb)
124.27
361.53
780.7
1263.6
601.48 vr
158.58
10.572
0.2848
2.768 pr
1.2147
51.561
5961.6
305.24
State 1 2 3 4 5\
T (R)
520
1468.8
2966
4577.6
p (psi) 14
594.26
1200
u (Btu/lb)
88.62
260.26
577.4
949.7
h (Btu/lb)
124.27
361.53
780.7
1263.6 vr
158.58
10.572
0.2848 pr
1.2147
51.561
5961.6
Example (9.38):
State 5:
process 4-5 is also isentropic
Replace V’s using ideal gas.
Use Table A-22E to look up T5, u5, h5, and pr5 and then find p5:

13. Example (9.38): Wcycle, in Btu/lb. Qout, in Btu/lb. The thermal eff.
State 1 2 3 4 5\
T (R)
520
1468.8
2966
4577.6
2299
p (psi) 14
594.26
1200
61.44
u (Btu/lb)
88.62
260.26
577.4
949.7
431.0
h (Btu/lb)
124.27
361.53
780.7
1263.6
601.48 vr
158.58
10.572
0.2848
2.768 pr
1.2147
51.561
5961.6
305.24
Example (9.38):
Wcycle, in Btu/lb.
Qout, in Btu/lb.
The thermal eff.
The cut off ratio

14. Example (9.38): Wcycle, in Btu/lb. Qout, in Btu/lb. Thermal efficiency
State 1 2 3 4 5\
T (R)
520
1468.8
2966
4577.6
2299
p (psi) 14
594.26
1200
61.44
u (Btu/lb)
88.62
260.26
577.4
949.7
431.0
h (Btu/lb)
124.27
361.53
780.7
1263.6
601.48 vr
158.58
10.572
0.2848
2.768 pr
1.2147
51.561
5961.6
305.24
Example (9.38):
Wcycle, in Btu/lb.
Qout, in Btu/lb.
Thermal efficiency
The cut off ratio
Cut off ratio: from ideal gas equation at constant pressure:

15. Air-Standard analysis of Gas Turbine Power plants.
Sec 9.5 : Modeling Gas Turbine Power Plants
Air-Standard analysis of Gas Turbine Power plants.
Gas power plants are lighter and more compact than vapor power plants.
Used in aircraft propulsion & marine power plants.

16. Air-Standard analysis: Working fluid is air
Sec 9.5 : Modeling Gas Turbine Power Plants
Air-Standard analysis:
Working fluid is air
Heat transfer from an external source (assumes there is no reaction)
Jet engine:
Suck (intake)
Squeeze (compressor)
Bang/Burn (combustion)
Blow (turbine/exhaust)
Heat Ex
Process 1 – 2 : Isentropic compression of air (compressor).
Process 2 – 3 : Constant pressure heat transfer to the air from an external source (combustion)
Process 3 – 4 : Isentropic expansion (through turbine)
Process 4 – 1 : Completes cycle by a constant volume pressure in which heat is rejected from the air

17. Sec 9.5 : Modeling Gas Turbine Power Plants
Gas Turbine Analysis
process 1-2: s1 = s2
process 2-3: p2 = p3
process 3-4: s3 = s4
process 4-1: p4 = p1
For a gas turbine, the back work ratio is much larger than that in a steam cycle since vair>>vliquid
bwr for a gas turbine power cycle is typically % vs. 1-2% for a steam power cycle.

18. Given T1 & T3  use table to find h1 & h3 .
Sec 9.3 : Air-Standard Diesel Cycle
Gas Turbine Analysis
Given T1 & T3  use table to find h1 & h3 .
Find state 2.
Find state 4.
Compressor
pressure ratio:
For Cold-Air Standard analysis:
For state 2.
For state 4.

19. Effect of Compressor pressure on efficiency.
Sec 9.3 : Air-Standard Diesel Cycle
Gas Turbine Analysis
Effect of Compressor pressure on efficiency.
with
Max T3 is approximately 1700 K

20. The thermal efficiency The back work ratio. The net power developed.
Example : Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 Btu/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate
The thermal efficiency
The back work ratio.
The net power developed.
State 1 2 3 4
T (R)
500
3000
h (BTU/lb)
Similar to 9.41

21. The thermal efficiency The back work ratio. The net power developed.
Example : Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 BTU/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate
The thermal efficiency
The back work ratio.
The net power developed.
State 1 2 3 4
T (R)
500
3000
Since we are given k=1.4, use a cold-air standard analysis.
Temperatures for states 1 and 3 are given.
For state 2.
Similar to 9.41
For state 4.

22. The thermal efficiency The back work ratio. The net power developed.
Example : Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 BTU/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate
The thermal efficiency
The back work ratio.
The net power developed.
State 1 2 3 4
T (R)
500
1063
3000
1411
Similar to 9.41

23. The thermal efficiency The back work ratio. The net power developed.
Example : Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 BTU/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate
The thermal efficiency
The back work ratio.
The net power developed.
State 1 2 3 4
T (R)
500
1063
3000
1411
But need the mass flow rate.
Similar to 9.41

24. The thermal efficiency The net power developed.
Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine
The thermal efficiency
The net power developed.
State 1 2 3 4
T (R)
520
3000 Pr
h (Btu/lb)
Similar to 9.41

25. The thermal efficiency The net power developed.
Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine
The thermal efficiency
The net power developed.
State 1 2 3 4
T (R)
520
1092
3000
1573 pr
1.2147
17.01
941.4
67.24
h (Btu/lb)
124.27
264.12
790.68
388.63
State 1 2 3 4
T (R)
520
3000 pr
1.2147
941.4
h (Btu/lb)
124.27
790.68
Temperatures for states 1 and 3 are given. Relative pressure and enthalpy values from Table A-22E
Find state 2.
Similar to 9.41
Find state 4.

26. The thermal efficiency The net power developed.
Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine
The thermal efficiency
The net power developed.
State 1 2 3 4
T (R)
520
1092
3000
1573 pr
1.2147
17.01
941.4
67.24
h (Btu/lb)
124.27
264.12
790.68
388.63
Similar to 9.41

27. The thermal efficiency The net power developed.
Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine
The thermal efficiency
The net power developed.
State 1 2 3 4
T (R)
520
1092
3000
1573 pr
1.2147
17.01
941.4
67.24
h (Btu/lb)
124.27
264.12
790.68
388.63
But need the mass flow rate.
Similar to 9.41

28. End of Slides for Lecture 35