Bài giảng hệ thống đẩy trong hàng không phần 2

Kerrebrock, Aircraft engines and gas turbine, The MIT press, 1992 [2] Yunus AC, Michael A.B., Thermodynamics an engineering approach, McGrawHill, 2013... Introduction  Some aspects shou

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Aircraft Propulsion

Introductions to Concepts

March 30, 2014

1

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[1] Jack L Kerrebrock, Aircraft engines and gas turbine, The MIT press, 1992

[2] Yunus AC, Michael A.B., Thermodynamics an engineering approach, McGrawHill, 2013

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Biomimetics and Intelligent Microsystem Laboratory

Introduction

 Describe in simple physical terms the fundamental characteristics

of gas turbines and related flight vehicle propulsion systems

 Control and limit their design and applications

3

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Introduction

 Some aspects should be considered:

• Weight and size

• Takeoff noise (noise per unit of thrust)

• Emission of smoke and gaseous pollutants

 Thermal efficiency

• The laws of thermodynamics  Upper limit on the thermal efficiency

• Carnot cycle (Yunus AC, Michael A.B., Thermodynamics an engineering approach, McGrawHill, 2013)

• 1-2: T=const., reversible isothermal expansion

• 2-3: s=const., reversible adiabatic expansion

• 3-4: T=const., reversible isothermal compression

• 4-1: s=const., reversible adiabatic compression

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T m: Maximum heat addition temperature

85.0

~

c



77.0

~

c



5

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Propulsive efficiency

 Propulsive efficiency

• Linear momentum

• Using Reynolds transport theorem

• Ignore the amount of the fuel flow (2%-4% of the air flow for most aircraft engines)

flowmass

engine to

deliveredpower

mechanicalNet

vehicle to

deliveredpower

u P

&

in flux

momentum linear

the of rate net CV

the within momentum

linear the of change Time

).(

A d u u dV

u t

) ( u u0m

6

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0 2

0 0 2

0 2

22

)(

22

u u

u m

u u u

m u

u m

Fu

e e

ininput power

Total2

2

2 0

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0 0

0

2

2 1

2

1 )

(

u m

F u

u

u u

m

F u

u m F

p e

p

e e

F 

0

and Givenm u

) /(m u0

F 

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F 

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Specific Impulse and Range

F I

I

/

rateflow weight

fuelof

Unit

tunit thrusof

L I dt

D L

W I

I

F dt

dW

)/(

/1

g

W W

W D

L I t



 ( / )ln

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Specific Impulse and Range

 Range

• Overall propulsion system efficiency

 h: energy content of the fuel

11

h

I u h I F

Fu h

dt dW

)/()

g

W W

W D

L I u Range



 0 ( / )ln

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Brayton cycle

 Brayton cycle – The ideal cycle for gas turbine engines

• First proposed by George Brayton in 1870 (reciprocating oil-gas turbine)  Today it is used for gas turbine only

• 1-2: Isentropic compression (in a compressor)

• 2-3: Constant-pressor heat addition

• 3-4: Isentropic expansion (in a turbine)

• 4-1: Constant pressure heat rejection

13 Yunus AC, Michael A.B., Thermodynamics an engineering approach, McGrawHill, 2013

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Brayton cycle

• Energy balance for steady flow, for a unit mass

) (

1 4

2 3

T T

c h

h q

T T

c h

h q

h h

w w

q q

p out

p in

inlet exit

out in

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Brayton cycle

) 1 /

(

) 1 /

( 1

) (

1 ) (

)

( 1

1

2 3

1 4 2

1 ,

2 3

1 4 2

3

1 4

, ,

T T T T

T T

c

T T

c

q

q q

w

B th

p

p B

k

P

P T

T P

P T

T

1

3

4 3

4 1

1

2 1

2

,

4 4

3 1

4 3 1

1

2 1

2

T

T T

T P

P P

P T

k k

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Brayton cycle

• Pressure ratio:

• η th,B vs r p

• k = 1.4, specific-heat-ratio of air at room temperature

• For a fixed T 3 , w net increases with the r p, reaches maximum, and then start to decreases

• In most common designs, r p ~ [11-16]

• Compromise between r p (thermal efficiency) and w net

• Less wnet  larger mass flow rate  larger system to maintain the power output

• Air: combustion of the fuel and coolant, mair/mfuel > 50  treated as air is OK

B th

k

k p k

k

r

r P

P T

T

1 ,

1 1

1 2 2

1

11

1/

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k p p

net

k

k p k

k

k p k

k

p net

p p

out in

net

r

T r

T c w

r

T P

P T

T

r

T P

P T T

T T

c w

T T

T T c w

T T

c T

T c q

q w

1 max

1 min

1 max

1

4

3 3

4

1 min

1

2 1 2

4 2

max min

4 2

3 1

1 4 2

3

1 1

1

/ /

) (

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Brayton cycle

• Net work output per cycle

• Example: The simple ideal Brayton cycle[2]

A gas-turbine power plant operating on an ideal Brayton cycle has a pressure ratio

of 8 The gas temperature is 300K at the compressor inlet and 1300K at the turbine inlet Utilizing the air-standard assumptions, determine (a) the gas temperature at the exits of the compressor and the turbine, (b) the thermal efficiency

T=300K, h = 300.19KJ/kg, pr = 1.386

T=1300K, h = 1395.97 KJ/kg, pr = 330.9

22314

8300

,1000,

4.1

01

min max

) 1 ( 2

max min

) 1 ( 2

max min

) 1 ( 2

max

min /

1 max

p k

k

p p

net

k k

p k

p p

net

r K

T K T

k

T

T r

r T

T dr

dw

r T

T r

T k

k dr

dw

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Example: The simple ideal Brayton cycle[2]

 Steady operating conditions

 The air-standard assumptions

 Ignore changing in kinetic and potential energy

 c p , c v are variable with temperature

• Solution:

(a) Finding T 2 , T 4

T 1 = 300K h 1 = 300.19KJ/kg, P r1 = 1.386 (based on Ideal-gas properties of air data)

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K 770 36

41 9 330 8

1

4

4 3

3

4 4

h

T P

(b) Thermal efficiency of the cycle

Net power output (w net ) = w turb,out – w comp,in

w = (h – h ) – (h – h ) = 362.4 kJ/kg

Example: The simple ideal Brayton cycle[2]

 Example 1:

09 11 386 1 8

1 1

2

P P P

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• Total heat input, q in = h 3 – h 2 = 1395.97 – 544.35 = 851.62 kJ/kg

• Thermal efficiency:

• Note:

%% Cold-air-standard condition (constant specific heat specific values)

% T2/T1=(P2/P1)^[(k-1)/k]=(P3/P4)^[(k-1)/k]=T3/T4

T2=T1*rp^((k-1)/k); % T at the exit of the compressor

T4=T3/(rp^((k-1)/k)); % T at the exit of the turbine

0kJ/kg62

.851

kJ/kg4

q

w



1 4

1

h h

q

q q

out

in

out th

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Ideal jet-propulsion cycles

 Ideal jet-propulsion cycles

cold-air-standard, c p =1.005KJ/kg.̊C, k=1.4; 3 kinetic at the nozzle exit only; 4

turbine work output = compressor work input

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(Assumptions: 1 Steady condition; 2 cold-air-standard,

c p =1.005KJ/kg.̊C, k=1.4; 3

kinetic at the nozzle exit only; 4 turbine work output =

compressor work input

Yunus AC, Michael A.B., Thermodynamics an engineering approach, McGrawHill, 2013

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• Process 1-2: isentropic compression of an ideal gas in a diffuser

kPa T

T P P

K c

V T

T

V T

T c

V V

k k p p

4 56

267 2

2

) (

0

2

h 2

h

m/s 0

m/s 260

) 1 /(

1

2 1 2

2 1 1

2

2 1 1

2 2 2

2 1

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25

• Process 2-3: isentropic compression of an ideal gas in a compressor

K P

P T T

P kPa

P r P

k k p

515

) (

564

/ ) 1 (

2

3 2 3

4 2

T P P

K T

T T

c T

T c

h h

w w

k k

p p

out turb in

comp

281

1125

) (

) 1 /(

4

5 4 5

5

5 4

2 3

5 4

2 3

, ,

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(b) Velocity at the nozzle exit

(c) Propulsive efficiency

K P

P T T

k k

620

/ ) 1 (

5

6 5

803 , 38 )

p in

Q W

kW T

T c m Q

h

V h

/1007

22

6

5

2 5 5

2 6 6

Nozzle exit temperature:

Steady-flow energy equation:

kW 8740 )

 exit inlet Aircraft

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27

Discussion: 100% - 22.5% = 77.5%, where does the 77.5% energy go?

Kinetic energy & increase in enthalpy of the gases

? ) (

? 2

1 6

V m E

K

out

g out



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Problems

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Problems

9-88 Air is used as the working fluid in a simple ideal Brayton cycle that has pressure ratio of 12, a compressor inlet temperature of 300K, and the turbine inlet temperature of 1000K Determine the required mass flow rate of air for a net power output of 70MW Assume constant specific heats at room temperature

9-91 An aircraft engine operates on a simple ideal Brayton cycle with a pressure ratio of 10 Heat is added to the cycle at a rate of 500kW; air passes through the engine at the rate of 1kg/s; and the air at the beginning of the compression is at 70kPa and 0̊C Determine the power produced by this engine and its thermal efficiency Use constant specific heats at room temperature

9-127C What is propulsive power? How is it related to thrust?

9-128C What is propulsive efficiency? How is it determined?

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Problems

9-130 A turboprop-aircraft propulsion engine operates where the air is at 55kPa and – 23 ̊C, on an aircraft flying at a speed of 180 m/s The Brayton cycle pressure ratio is 10 and the air temperature at the turbine inlet is 505 ̊C The propeller diameter is 3 m and the mass flow rate through the propeller is 20 times that through the compressor Determine the thrust force generated by this propulsion system Assume ideal operation for all components and constant specific heat at room temperature

9-131 How much change would result in the thrust of Prob 9-30 if the ropeller diameter were reduced to 2.4 m while maintaining the same mass flow rate through the compressor Note: The mass flow rate ratio will no longer be 20

9-132 A turbofan engine operating on an aircraft flying at 200 m/s at an altitude where the air is at 50 kPa and -20 ̊C is to produce 50,000N of thrust The inlet diameter of the engine is 2.5 m; the compressor pressure ratio is 12; and the mass flow rate ratio is 8 Determine the air temperature at the fan outlet needed

to produce this thrust Assume ideal operation for all components and constant specific heats at room temperature

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Problems

9133 A pure jet engine propels an aircraft at 240 m/s through air at 45 kPa and

-13 ̊C The inlet diameter of this engine is 1.6 m, the compressure ratio is -13, and the temperature at the turbine inlet is 557 ̊C Determine the velocity at the exit

of this engine’s nozzle and the thrust produced Assume ideal operation for all components and constant specific heats at room temperature

9-134 A turbojet aircraft is flying with velocity of 320 m/s at an altitude of 9150

m, where the ambient conditions are 32 kPa and -32 ̊C The pressure ratio across the compressor is 12, and the temperature at the turbine inlet is 1400K Air enters the compressor at a rate of 60 kg/s, and the jet fuel has a heating value of 42,700kJ/kg Assuming ideal operation for all components and constant specific heats for air at room temperature, determine (a) the velocity of the exhaust gases, (b) the propulsive power developed, and © the rate of fuel consumption

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Problems

9-135 Repeat Prob 9-34 using a compressor efficiency of 80% and a turbine of 85%

9-136 Consider an aircraft powered by a turbojet engine that has a pressure ratio

of 9 The aircraft is stationary on the ground, held in position by it brakes The ambient air is at 7 ̊C and 95 kPa and enters the engine at a rate of 20 kg/s The jet fuel has a heating value of 42,700kJ/kg and it is burned completely at a rate

of 0.5 kg/s Neglecting the effect of diffuser and disregarding the slight increase

in the mass at the engine exit as well as the inefficiencies of the engine components, determine the force that must be appliied on the brakes to hold the plane stationary

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Biomimetics and Intelligent Microsystem Laboratory 33 Yunus AC, Michael A.B., Thermodynamics an engineering approach, McGrawHill, 2013

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Biomimetics and Intelligent Microsystem Laboratory 35 Yunus AC, Michael A.B., Thermodynamics an engineering approach, McGrawHill, 2013

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