1.1
ME 200 –Thermodynamics I
Lecture 43: Regenerative Gas Turbines with
Reheat and Intercooling
Yong Li
Shanghai Jiao Tong University
Institute of Refrigeration and Cryogenics
800 Dong Chuan Road Shanghai, 200240, P. R. China
Email : [email protected]
Phone: 86-21-34206056; Fax: 86-21-34206056
1.2
Continue Brayton Cycle
Introduce “regeneration” to boost overall efficiency :
» Idea: reclaim “waste” heat normally exhausted to ambient.
Regenerative open Brayton cycle:
T-s diagram
1.3
Continue Brayton Cycle
» Heat transfer limitations:
l (length of heat exchanger)
“True” counterflow
Limiting states:
Tx ? T4
T2 ? Ty
Usually:
DTHX = 5 K
T T
DTHX
T4
Tx
Ty
T2
Tx < T4
T2 < Ty
1.4
Temperature distributions in counterflow heat exchangers.
(a) Actual. (b) Reversible.
1.5
Continue regenerative Brayton cycle
»Heat exchanger effectiveness:
reg
x 2
4 2
actual heat transfer
maximum heat transfer
h h
h h
y 1out
th,R
in 3 x
Overall cycle efficiency :
h hq1 1
q h h
4 y
4 2
h h
h h
4 1 4 y
3 2 x 2
(h h ) (h h )1
(h h ) (h h )
4 1 reg 4 2
th,R
3 2 reg 4 2
(h h ) (h h )1
(h h ) (h h )
1.6
Continue regenerative Brayton cycle
For a perfect heat exchanger,reg= 1.0
2 1th,R
3 4
h h1
h h
1
p 2 1 22th,R
4p 3 4 3
3
For constant specific heats:
T1
c (T T ) TT1 1
Tc (T T ) T 1T
4 1 reg 4 2
th,R
3 2 reg 4 2
(h h ) (h h )1
(h h ) (h h )
k 1 k 1
k k4 4 1 1
3 3 2 2
Also, assuming ideal gas and isentropic expansion and compression:
T p p T
T p p T
1.7
Continue regenerative Brayton cycle
k 1
k2 1 2 1 2
th,R
3 3 1 3 1
k 1
1 kth,R p
3
T T T T p1 1 1
T T T T p
T1 r
T
Note: for maximum th,R want T3 >> T2!
1
22th,R
43
3
T1
TT1
TT 1T
k 1 k 1
k k4 4 1 1
3 3 2 2
T p p T
T p p T
2p
1
pr
p
1.8
Brayton Cycle with Reheat
Two-Stage Expansion with Reheat: T-s diagram
1.9
Continue Brayton Cycle with Reheat
Continue Two-Stage Expansion with Reheating:
s
T Notes:
-For cycles with regeneration:
qin relatively constant
qin = (h3-hx)+(h3-hx) ~ h3-hxo
wnet increases (by 4-5-6-6o)
Reheater increases th,R
- For cycles without regen.:
qin increases by h5-h4 and
wnet increases (by 4-5-6-6o)
Reheater reduces th,R
3
1
7
x
2
xo
6o
5
T1
4 6
Increase
in work
Increase in temp.
difference available
for regeneration
1.10
Compression with Intercooling
Cooling a gas as it is compressed
would reduce the work
Practical alternative is to separate the
work and cooling
Use the heat exchanger ---- intercooler.
T-s diagram
1.11
Brayton Cycle with Intercooling and Reheating, For an internally reversible, steady flow process:
Notes: - Intercooler
reduces T4 which
improves regeneration.
- Reheater
increases T9 which also
improves regeneration.
T-s diagram
1.12
Continue Brayton Cycle with Intercooling and Reheating
Example :
T1 = 295 K (22oC), p1 = 0.95 bars, rp = p2/p1 = 6, TH = 1100 K
System th 1. Ideal Brayton Cycle 0.385
2.) Brayton cycle with C = 0.82 and T = 0.85 0.233
3.) System 1. with ideal regenerator (reg = 1.0) 0.562
4.) System 2. with real regenerator (reg = 0.7) 0.318
5.) System 4. with ideal intercooler and reheater 0.370
1.13
Continue Brayton Cycle with Intercooling and Reheating
Performance limit for gas turbine engines
Infinite stages of intercooling and reheating with ideal regeneration?
Ericsson Cycle!
s
T
TL
TH
1 2
4 3
1.14
Home work
Review
» All the contents we have learned in this semester
» Contact me or discuss with your classmates if you have any questions.
» Read through all the homework solutions to make sure you can solve
them by your self.
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