6 - air breathing engines - turbojet

7/25/2019 6 - Air Breathing Engines - Turbojet

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IIT Kanpur

Turbojet

nozzleintakecompressor

combustorturbine

i 1

2 3 4 e

a a

u, Pa

ui, Pi

Pi< Paui> u

u, Pa ui, Pi

Pi> Paui< u

u, Pa ui, Pi

Pi= Paui= u

before intake (subsonic)

ai: air is brought to intake from far upstream (where pressure

is ambient pressure and relative velocity is flight speed) with

possible acceleration or deceleration

i1: air is decelerated as it passes through the intake (diffuser)and reaches compressor inlet

12: air is compressed in a dynamic compressor

23: air (gases) is heated by burning fuel

34: air (gases) is expanded through a turbine, just enough toobtain power to drive the compressor

4e: air (gases) is accelerated and exhausted through the

exhaust nozzle (if not fully expanded, PePa)

design

point

high

speed

low

speed


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Ideal JetPropulsion Cycle

nozzleintakecompressor

combustorturbine

i 1 2 3 4 ea a

In ideal jet propulsion cycle the gases are expanded in a turbine to a pressure such that the

power produced by the turbine is just sufficient to drive the compressor

Due to flight speed, some compression can be achieved in diffuser, prior to compressor entry

Assume:o compression (diffuser+compressor) and expansion (turbine+nozzle) is adiabatic and

reversible, i.e. isentropic

o Intake entry pressure (Pi) = ambient pressure (Pa), nozzle is fully expanded (Pe= Pa)

o Heat addition (combustor) is isobaric (simple frictionless heaters)

o Velocities through sections 14 (in compressor, combustor and turbine) are negligibleo Working fluid is air (calorically perfect, constant cp) with constant specific heat ratio ()

Ideal Brayton cycle: Isentropic compression

(compressor) and expansion (turbine),

Isobaric heat addition (combustor) and heatrejection (closed cycle)

Open cycleTemperature(T)

Specific entropy (s)

intake

compressor

turbine

nozzle

fully expanded (Pe= Pa)under expanded (Pe> Pa)

a

1

2

3

4

ee

iPican be Pa, depending on

the flight speed and design speed


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Intake

Intake (i1), ambient conditions at i:

o As velocity at 1 (compressor inlet) is assumed 0, P1and T1are the stagnationpressure (isentropic flow) and temperature for conditions a, i and 1

o No shaft work or heat transfer in the intake

1

/

Ambient: temperature (Ta) and pressure (Pa)

Flight speed (u) = /Ma

0, adiabatic 0, neglected 0, neglected

0

0, no shaft

work

i=a 1

Ta, Pa

,

T1, P1

diff

user


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Compressor

Compressor (12):

o Isentropic compression (adiabatic+reversible) with given pressure ratio (rp= P2/P1),

also velocities in the compressor are assumed negligibleo No heat transfer in the compressor (adiabatic), the shaft work done on the

compressor results in the enthalpy rise of air

/

0, adiabatic0, neglected 0, neglected

compressor

1 2

T1, P1

T2, P2


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Combustor

Combustor (23):

o With given fuel air ratio

and heating value of fuel , assuming f


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Turbine

Turbine (34):

o Turbine supplies just enough power to supply the compressor requirement:

o Since the process is adiabatic (no heat transfer), work (shaft) done by the turbine

results in enthalpy drop (assuming same air flow rate, )

o At the end of the turbine we still have high temperature and pressure gas to be

further expanded in the nozzle to generate high velocity stream

3 4

T3, P3

T4, P4

turbine

0, adiabatic0, neglected 0, neglected

equating compressor and turbine work


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Nozzle

Nozzle (4e), fully expanded (Pe= Pa):

o At nozzle inlet we have high pressure (P4) and temperature (T4) gas

o Nozzle inlet is assumed to have near zero velocity, nozzle exit at velocity (ue)

o In the nozzle there is no work or heat interaction, hence stagnationtemperature is constant

o The process is assumed to be isentropic

for fully expanded case

ambient pressure

2

1

using:

2 nozzle4 e

T4, P4

Te, Pe = Pa

0, adiabatic 0, neglected 0, neglected

0

0, no shaft

work


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Example (ideal jet propulsion cycle)

Given:

Turbojet flight speed (u) = 260 m/s

Ambient pressure (Pa) = 35 kPa, ambient temperature (Ta) = 40 C (233 K)

Compressor pressure ratio (rp) = 10, turbine inlet temperature T3= 1100 C (1373 K) Mass flow rate of air ( ) = 45 kg/s

cP= 1.005 kJ/kgK (1005 J/kgK), specific heat ratio (= 1.4)

Heating value of fuel (QR) = 45 MJ/kg

Find:

Velocity of gases at nozzle exit (ue) Propulsion efficiency (p)

Thermal efficiency (th)

Overall efficiency (o)

Solution:

Compressor inlet (diffuser outlet) condition (velocity ~ 0): process a1

233

267

/

35

./ .

56.4

Thrust (Th) Thrust power (Thu)

Rate of addition of kinetic energy

Chemical energy consumption rate

Fuel air ratio (f)


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Combustor inlet (compressor outlet) condition (velocity ~ 0): process 12

10 56.4 564

/

267 10 . /. 515

Turbine inlet (combustor outlet) condition (velocity ~ 0): process 23

1373 564

Nozzle inlet (turbine outlet) condition (velocity ~ 0): process 34

1373 515 267 1125

564

..

281

Nozzle exit condition (fully expanded, Pe= Pa): process 4e

1125

..

620

2 2 1005 1125 620 1007 /

1.4 287 620 500 m/s ~2


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Solution:

//

41%

Propulsion efficiency:

Thermal efficiency:

//

//

55%

Overall efficiency:

0.41 0.55 22.5%

Unusable enthalpy percentage:

45%

Thrust:

45 1007 260 33.6

Thrust power:

33615 260 8.74

Chemical energy consumption rate:

45 1005 1373 515 38.8

Fuel air ratio (f):

Assuming heating value (QR) = 45 MJ/kg:

0.02

Rate of addition of kinetic energy:

/ 2 /2

45 1007/2 260/2 21.30

Fuel flow rate is only 2% of air flow rate

6 - air breathing engines - turbojet

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