EGR 334 ThermodynamicsChapter 9: Sections 7-8

Lecture 36: Reheat and Intercooling of Gas Turbine Systems

Quiz Today?

Today’s main concepts:• Be able to explain the concept and purpose of using

reheat in a gas turbine.• Be able to explain the concept and purpose of using

intercooling in a gas turbine system.• Be able draw and explain Brayton cycles with reheat

and intercooling.

Reading Assignment:

Homework Assignment:

Read Chapter 10

Problem 9:80

3

Last time: Introduced to the Gas Turbine Power Plant

Working fluid is airHeat transfer from an external source (assumes there is no reaction)

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

Sec 9.5 : Modeling Gas Turbine Power Plants

4

http://www.youtube.com/watch?NR=1&feature=endscreen&v=ON0sVe1yeOk

How a Jet Engine Works:

http://library.thinkquest.org/C006011/english/sites/gasturbine.php3?v=2Images from:

Power Station Gas Turbine

Jet Engine

5

Possible Enhancements to the Brayton Cycle:

1) Use of Regenerator to preheat combustion air.

2) Reheating air between successive turbine stages.3) Intercooling of air between successive compressor stages.

6

Brayton Cycle with Regeneration:The exhaust air out of the turbine contains significant waste heat that would normally be discarded to the atmosphere. Use of regenerator can make use of this heat that would be discarded to preheat the air on its way to the combustor, allowing the burned fuel to be used more efficiently.

7Sec 9.8 : Regenerative Gas Turbines with Reheat and Intercooling

To limit the temperature of the gas entering the turbine, air is provided in excess to the primary combustion chamber.

This has the added advantage of having the second turbine run at lower pressure. Processes 2-3, a-b, and 4-1 occur isobarically.

The excess air limits the temperature of the combustion process by providing a heat sink for the heat produced during combustion.

TcmTcmQTcmQ PinertPrxnCombustionPrxnCombustion

8Sec 9.8 : Regenerative Gas Turbines with Reheat and Intercooling

Improved efficiency may also be achieved by decreasing the work required for the compressors.

It is not practice to achieve such cooling within a compressor. Consequently, the compressor is spit with a heat-exchanger in between.

9Sec 9.8 : Regenerative Gas Turbines with Reheat and Intercooling

Putting all three enhancements together, the diagram show a process combining regeneration, reheat, and intercooling.

10

Example (9.74): Air enters the compressor of a gas turbine at 100 kPa, 300 K. The air is compressed in two stages to 900 kPa, with intercooling to 300 K between the stages at a pressure of 300 kPa. The turbine inlet temperature is 1480 K and the expansion occurs in two stages, with reheat to 1420 K between the stages at a pressure of 300 kPa. The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine

(a) The volumetric flow rate entering the cycle.(b) The thermal efficiency of the cycle.(c) The back work ratio.

State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

P (kPa) 100 300 300 900 900 300 300 100

Pr

h (kJ/kg)

11

Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine(a) The thermal efficiency of the cycle.(b) The back work ratio.State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

p (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

300.19

1611.79

1539.44Find state a, Process 1 – a is

11

araS r

pp p

p 158.4

100

3003860.1

From the table haS = 411.26 kJ/kg

Using the isentropic compressor efficiency:

1

1

hh

hh

a

aS

kg

kJhhhh aS

a 42.43284.0

19.30026.41119.3001

1

Isentropic compression

12

Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine(a) The thermal efficiency of the cycle.(b) The back work ratio.State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

P (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

432.42

300.19

1611.79

1539.44Find state a, Process b – 2 is

From the table h2S = 411.26 kJ/kg

22r S rb

b

pp p

p 158.4

300

9003860.1

Using the isentropic compressor efficiency:

b

bS

hh

hh

2

2

kg

kJhhhh bSb 42.432

84.0

19.30026.41119.3002

2

Isentropic compression

13

Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine(a) The thermal efficiency of the cycle.(b) The back work ratio.State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

p (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

432.42

300.19

432.42

1611.79

1275.4

1539.44Find state a, Process 3 – c is

From the table hcS = 1201.5 kJ/kg

33

crcS r

pp p

p 60.189

900

3008.568

Using the isentropic turbine efficiency:

cS

c

hh

hh

3

3

kg

kJhhhh cSc 4.12755.120179.161182.079.161133

Isentropic expansion

State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

p (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

432.42

300.19

432.42

1611.79

1539.44

14

State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

p (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

432.42

300.19

432.42

1611.79

1275.4

1539.44

1216.77

Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine

State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

p (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

432.42

300.19

432.42

1611.79

1275.4

1539.44Find state a, Process d – 4 is

From the table h4S = 1145.94 kJ/kg

44r S rd

d

pp p

p 33.159

300

1000.478

Using the isentropic turbine efficiency:

dS

d

hh

hh

4

4

kg

kJhhhh Sdd 77.121694.114544.153982.044.153944

Isentropic expansion

15

Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine(a) The thermal efficiency of the cycle.(b) The back work ratio.

State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

p (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

432.42

300.19

432.42

1611.79

1275.4

1539.44

1216.77Determine the mass flow rate

1 2 1 2 1.8 /cycle T T C CW W W W W kJ s

badccycle hhhhhhhhm

W 2143

kg

kJ

m

Wcycle 6.394

1.8 /

4.562 /394.6 / 394.6 /

cycleW kJ sm kg s

kJ kg kJ kg

16

Example (9.74): Air enters the compressor of a gas turbine at 100 kPa, 300 K. The air is compressed in two stages to 900 kPa, with intercooling to 300 K between the stages at a pressure of 300 kPa. The turbine inlet temperature is 1480 K and the expansion occurs in two stages, with reheat to 1420 K between the stages at a pressure of 300 kPa. The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine

(a) The volumetric flow rate.(b) The thermal efficiency of the cycle.(c) The back work ratio.

State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

p (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

432.42

300.19

432.42

1611.79

1275.4

1539.44

1216.77

s

kgm 562.4

15 21

1

0.2870 / 300V 4.562 /

(10 / )

kJ kg K KRTA m kg s

p m

3

1V 3.93

mA

s

17

Example (9.74): Air enters the compressor of a gas turbine at 100 kPa, 300 K. The air is compressed in two stages to 900 kPa, with intercooling to 300 K between the stages at a pressure of 300 kPa. The turbine inlet temperature is 1480 K and the expansion occurs in two stages, with reheat to 1420 K between the stages at a pressure of 300 kPa. The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine

(a) The volumetric flow rate.(b) The thermal efficiency of the cycle.(c) The back work ratio.

State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

p (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

432.42

300.19

432.42

1611.79

1275.4

1539.44

1216.77

in

cycle

Q

W

kg

kJhhhhmQ cdin 41.144323

s

kgm 562.4

2734.041.1443

6.394

in

cycle

Q

W

18

Example (9.74): Air enters the compressor of a gas turbine at 100 kPa, 300 K. The air is compressed in two stages to 900 kPa, with intercooling to 300 K between the stages at a pressure of 300 kPa. The turbine inlet temperature is 1480 K and the expansion occurs in two stages, with reheat to 1420 K between the stages at a pressure of 300 kPa. The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine

(a) The volumetric flow rate.(b) The thermal efficiency of the cycle.(c) The back work ratio.

State 1 a b 2 3 c d 4

T (K) 300 300 1480 1420

p (kPa) 100 300 300 900 900 300 300 100

pr 1.3860

1.3860

568.8 478.0

h (kJ/kg) 300.19

432.42

300.19

432.42

1611.79

1275.4

1539.44

1216.77

C

T

Wbwr

W

s

kgm 562.4

43

21

hhhh

hhhh

W

Wbwr

dc

ba

T

C

401.006.659

46.264bwr

19

end of slides for Lecture 36