Gas-turbine Problems with Solution PDF

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####### GAS TURBINE####### 1. The pressure ratio of a####### standard Brayton cycle is 9 and####### the maximum temperature in the####### cycle is 1080 deg. C. Compute for####### the cycle efficiency per kg of air in####### percent?e = 1 − rpk − 1 ke = 1 − 9−1− 1 1.####### e = 0 x 100 = 46%####### 2...

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GAS TURBINE 1. The pressure ratio of a standard Brayton cycle is 9 and the maximum temperature in the cycle is 1080 deg. C. Compute for the cycle efficiency per kg of air in percent? e=1 −r p

k−1 k

− 1.4 − 1 1.4

e=1 −9

e = 0.4662 x 100 = 46.62% 2. A simple brayton cycle which uses helium as the working fluid, has a maximum temperature of 1200 deg K, and a pressure ratio of 3.3. At the start of the compression, the helium pressure and temperature are 90Kpa and 290 deg K. Based upon cold airstandard analysis assumptions, what would be the efficiency of the cycle? e=1 −r p

T2 = 529.95K Q A =m c p [T 3−T 2 ]

350 = m[1][1373 – 529.95] m = 0.42kg/s(3600s/hr) m = 1494.6kg/s 4. A gas turbine utilizing an air standard brayton cycle has a pressure ratio of 10. The air inlet conditions are 100 Kpa and 27 deg C. The maximum allowable temperature is 1300 deg C. calculate the heat added in KJ/kg. T2 ¿r T1 p

k−1 k

1.4 −1 T2 ¿ 10 1.4 27+273

T2 = 579.21K Q A =m c p [T 3−T 2 ]

= m[1][1573 – 579.21] QA = 993.79 KJ/Kg

k−1 k

−5 −1 3 5 3

e=1−3.3

e = 0.3797 x 100 = 37.97%

3. An ideal gas turbine operates with a pressure ratio of 7.5 and temperature limits of 25 deg C and 1100 deg C. The energy input in the high temperature exchanger is 350KW. Determine the air flow rate in kg/hr. T2 ¿r T1 p

k−1 k

1.4 − 1 T2 ¿ 7.5 1.4 25+273

5. Air at 4 bar and 590K is extracted from a jet engine compressor to be used for the generation of auxiliary power for the cabin. The extracted air is cooled in a constant pressure heat exchanger down to 440K. it then enters an isentropic turbine and expands to 1 bar before being rejected into the cabin. If the mass flow is 8 kg/min, determine the temperature of the gas as it leaves the turbine, (b) power developed by the turbine in KW and (c) rate of

heat transfer out the constant pressure heat exchanger. k −1 4 k

¿¯ 1.4 − 1 1.4

k−1 k

=r k

k−1

1.4 −1

15 1.4 =r k r k =6.92

T4 P ¿ T3 P 3 T4 ¿1 440

rp

¿¿

4 ¯¿

T 4=296.1 K

[

k−1 k

e= 1−r p

[

¿ 1−15 e=0

1.4− 1

]−[ 1−r

−1.4 − 1 1.4

k−1 k

]

] −[ 1−6.92

− 1.4 − 1

]

6. A gas turbine working on an air standard Brayton cycle has air enter into the compressor at atmospheric condition and 25 deg C. The pressure ratio is 9 and maximum temperature in the cycle is 1080 deg C. Determine the work of the compressor. k−1 T2 ¿rp k T1 1.4 − 1 T2 ¿ 9 1.4 25+273

T2 = 558.28K W C =mc p [ T 2−T 1 ]

= [1][558.28 – 298] Wc = 260.29 KJ/Kg

7. An air standard Brayton cycle has a pressure ratio of 12. Find the compression ratio. rp

k−1 k

=r kk−1

1.4− 1 1.4

9. An air standard Brayton cycle has a pressure ratio of 11. The air properties at the start of compression are 101kpa and 26°C. The maximum allowable temperature is 1300°C. Determine the network.

1.4− 1

=r k 12 r k =5.9

8. An air standard Brayton cycle has a pressure ratio of 15. Determine the difference from Otto cycle.

k−1 T2 ¿rp k T1

1.4− 1 T2 ¿ 11 1.4 26+273

T2 = 593.21K

k−1 T3 ¿rp k T4

leaving the turbine compression ratio is 9.9. 1.4 − 1 1.4

1300 + 273 ¿ 11 T4

T4 = 792.95K

rk

k −1

if

the

k−1 k

=r p

1.4 − 1

9.9 =r r p =24.77

1.4 −1 1.4 p

W n =W T −W c ¿( [ 1573 −792.82] − [ 593.21−299 ] ) W n =485.95 KJ / Kg

10. An air standard Brayton cycle has a pressure ratio of 11. The air properties at the start of compression are 101kpa and 26°C. The maximum allowable temperature is 1300°C. Determine the head added.

k−1 T3 ¿rp k T4

1200 + 273 ¿ 24.77 T4

1.4 − 1 1.4

T 4=588.77 K T 4=315.77 ° C

Q A =m c p [T 3−T 2 ] Q A =1[ 1573−593.21] Q A =979.79 KJ / Kg

11. An air standard Brayton cycle has an air leaving the high temperature heat exchanger at 1200°C and leaving the turbine at 300°C. Determine the work of a turbine in kcal per kg. W =m c p [ T 3−T 4 ] ¿(1)( 1200−300) W =900 KJ / Kg

13. An air standard Brayton cycle has an air leaving the high temperature heat exchanger at 1200°. Determine the turbine horsepower if the mass of air is 1 kilogram per second with the compression ratio 9.9. rk

k −1

k−1 k

=r p

1.4 − 1

12. An air standard Brayton cycle has an air leaving the high temperature heat exchanger at 1200°. Determine the temperature

1.4 −1 1.4

=r p 9.9 r p =24.77 T3 ¿r T4 p

k−1 k

1200 + 273 ¿ 24.77 T4

1.4 − 1 1.4

T 4=588.77 K W T =m c p [T 3−T 4 ]

W T =(1)(1 )[ 1473−588.77 ] ¿(884.23 KW )

1 HP ( 0.746 KW )

W T =1185.29 HP

14. An air standard Brayton cycle has a compression ratio 9.8. Determine the engine efficiency. rk

k −1

200=m [ ( 950−302 )− ( 371.46 −30 ) ] kg 3600 s m=(0.65 )( ) s hr m=2348.87 Kg / hr

16. The compressor for an actual gas turbine requires 450KJ/kg of work to triple the inlet pressure. The inlet air temperature is 105°C. Determine the compressor air exit temperature in Celsius. W C =mc p [ T 2−T 1 ]

450=( 1)[ T 2−105] T 2=555 °C

k−1 k

=r p

1.4 − 1

1.4 −1 1.4

9.8 =r p r p =24.42 e=1−r p

−k −1 k −1.4−1

e=1−24.42 1.4 e=0.5987 x 100=59.87 %

15. The air standard Brayton cycle has a net power output of 200KW. Air entering the compressor at 30°C, leaving the high temperature heat exchanger at 950°C and leaving the turbine at 302°C. Determine the mass flow rate of air in kilogram per hour. T2 T3 = T1 T4 T2 950 + 273 = 30+273 302 + 273 T 2=644.46 K T 2=371.47 °C W n =m(W T −W c )

17. The compressor for an actual gas turbine requires 450KJ/kg of work to triple the inlet pressure. The inlet air temperature is 105°C. Determine the engine efficiency if the mass flow rate is 5kg/sec. P 2=3 P 1 P2 =3 P1 e=1−r p

−k −1 k

−1.4 −1 1.4

e=1−3 e=0.2694 x 100=26.94 %

18. The compressor for an actual gas turbine requires 350KJ/kg of work to triple the inlet pressure. The inlet air temperature is 110°. Determine the compressor efficiency.

W C =181.28 W BW = C WT 181.28 BW = 400 BW =0.4532 x 100=45.32 %

P2=4 P1 P2 =4 P1

20. An ideal gas turbine operates with a pressure ratio of 10:1 and the temperature limits of 27° and 1200°. The energy input in the high temperature heat exchanger is 220kw. Determine the air flow rate in kilogram per hour.

k−1 T2 k ¿r T1 p 1.4 − 1 T2 ¿ 4 1.4 110+273

T 2=569.14 K W C =mc p [ T 2−T 1 ] ¿(1)[ 569.14−383 ] W C =186.14 W e= a w1 e=

186.14 350

e=0.5318 x 100=53.18 %

19. The compressor in a gas turbine quadruples the inlet pressure. Work generated in the turbine is 400KJ/kg. The inlet air temperature is 100°C. Determine the back work ratio. P 2=4 P1 P2 =4 P1 k−1 T2 ¿rp k T1 1.4 −1 T2 ¿ 4 1.4 100+273 T 2=554.28 K W C =mc p [ T 2−T 1 ] ¿(1)[ 554.28−383 ]

k−1 T2 ¿rp k T1 1.4 −1 T2 ¿ 10 1.4 27+273

T 2=579.21 K W C =mc p [ T 2−T 1 ] 220=( m )[ 579.21 −579.21 ] kg 3600 s m= 0.246 hr s m=886.11 kg / hr

(

)(

)

21. An air standard Brayton cycle has air enter the compressor at 28°C and 100Kpa. The pressure ratio is 13 and the maximum allowable temperature in the cycle is 1450K. Determine the net work. T2 ¿r T1 p

k−1 k

1.4 − 1

T2 ¿ 13 1.4 28+273 T 2=626.37 K T3 ¿r T4 p

k−1 k

1450 ¿ 13 T4

1.4− 1 1.4

T4 =696.78 K W n =m (W T −W c )

¿ [ 1450−696.78 ] −[ 626.37−301] W n =427.84 KJ /Kg

22. An air standard Brayton cycle has air enter the compressor at 27°C and 100Kpa. The pressure ratio is 10 and the maximum allowable temperature in the cycle is 1450K.The compressor and turbine efficiencies are 85% and 80% respectively. If there is a 27kpa drop between the compressor discharge and the turbine inlet, determine the actual air exit temperature. T3 ¿r T4 p

k−1 k

1450 1000 −27 ¿ 100 T4 T 4=756.92 K

1.4− 1 1.4

'

e=

T 3 −T 4 T 3−T 4

'

1450−T 4 0.8= 1450 −756.92 '

T 4 =895.54 K

23. An air standard Brayton cycle has air enter the compressor at 27°C and 100Kpa. The pressure ratio is 10 and the maximum allowable temperature in the cycle is 1450K.The compressor and turbine efficiencies are 85% and 80% respectively. If there is a 27kpa drop between the compressor discharge and the turbine inlet, determine the actual turbine work. e=

Wa w1

0.8=

Wa 1450 −756.92

W a =554.46 KJ / Kg

24. An air standard Brayton cycle has air enter the compressor at 27°C and 100Kpa. The pressure ratio is 10 and the maximum allowable temperature in the cycle is 1450K.The compressor and turbine efficiencies are 85% and 80% respectively. If there is a 27kpa drop between the compressor discharge and the turbine inlet, determine the thermal efficiency of the cycle.

k−1 T2 ¿rp k T1 T2 1000−27 1.41.4−1 ¿ 27+273 100

T 2 =574.7 K

T3 ¿r T4 p

k−1 k

1450 1000 −27 ¿ 100 T4 T 4=756.92 K

e=

1.4− 1 1.4

W T−W L QA 574.7−300 0.85 ( 1450 −574.7)

0.8 ( 1450 −756.92 )− ¿

e=0.2642 x 100=26.42 %

atmospheric condition and 25°C. The pressure ratio 50:4 and the maximum temperature in the cycle is 1088°C. Compute the actual compressor work if the compressor efficiency is 88%. k−1 T2 ¿rp k T1 1.4 − 1 T2 50 1.4 ¿ 25+273 4

T 2=613.22 e=

ideal actual

0.88=

613.22 −298 actual

Wa =358.21 KJ /Kg

25. A gas turbine working on an air standard Brayton cycle has air enter into the compressor at atmospheric condition. If the pressure is increased by 98%, determine the cycle efficiency. P2=1.98 P1 ¿ 1.98 ( 101.325 ) P2=200.62 KPa e=1−r p

−k −1 k

−1 200.62 −1.4 1.4 101.325 e=0.1773 x 100=17.73 %

e=1−

26. A gas turbine working on an air standard Brayton cycle has air enter into the compressor at

27. An air standard Brayton cycle has air enter the compressor at 28°C and 100kpa. The pressure ratio is 13 and the maximum allowable temperature in the cycle is 1450K. Determine the heat added. k−1 T2 ¿rp k T1 1.4 − 1 T2 ¿ 13 1.4 28+273

T 2=626.38 K Q A =m cp [T 3−T 2] Q A =1[ 1450−626.38] Q A =823.62 KJ /Kg

28. 26. A gas turbine working on an air standard Brayton cycle...