Chalmers University of Technology Lecture 6 Turbojet –Optimization –Cycle selection (mission...

Chalmers University of Technology

Lecture 6• Turbojet

– Optimization– Cycle selection (mission dependency)– Indication of thrust– Convergent-divergent nozzles

• Turbofan– Cycle optimization– Mixing

• Increasing thrust (afterburning)• Turboprops• Problem 3.2


Optimization of the turbojet

• Specific thrust is strongly dependent on T03

• At constant pressure ratio an increase in T03 will cause some increase in SFC

• Parameter variation is based on Example 3.1 data with polytropic efficiencies


Recall shaft power cycle behavior

• For a given pressure ratio it is clear that ηcycle increases!

thpnet

pnet

netpnet

net

QfQ

wQ

w

fSFC

,

,,

11

Opposite trend


High specific thrust is still attractive

• High T3 => high specific thrust => small engine

• Reduction in engine size => reduced drag which off-sets this effect– In particular for high speed flight


Optimization of the turbojet

• Same trend in SFC as a function of pressure ratio, when compared with real shaft power cycle

• Note that if pressure ratios where increased considerably above rc=25, SFC would start to increase again.


Cycle selection• High t3 => expensive

alloys, complex (and expensive) cooling

• High rc => many stages. Ultimately multi-spool configurations

• Selection of cycle parameters depend on aircraft mission


Cycle selection

• Business jets:– Low cost (by low

pressure ratios and cheap turbine material)

– Fuel consumption less important

– Range may be important (=>cheap turbojets have been supplanted by cheap turbofans/turboprops)


Lifting engines & long range subsonic

• Lifting engines (VTOL)– Max. thrust per unit weight

(compressor pressure ratio set by what could be achieved by one turbine rotor)

– short life - but run only for short period of time

– Thrust to weight > 20!!! Modern military engines have around 10.

– high cost ok (military)

• Long range subsonic– early - high pressure turbojet

– Today high pressure ratio, high bypass ratio turbofans


Indication of thrust• No direct method for measuring engine thrust

during flight exists!!!• Indirect techniques exist


Theory 6.1 - Indication of thrust

• P04 and T04 can be measured. Pa is known and the nozzle area is assumed to be fixed (assume choked operation and ηj =100%). The thrust is given by (sea level static):

appAmCF 555

pc


Theory 6.1 - Indication of thrustContinuity, the gas law and the first law give:

50425

5

55

555

2 TTcC

RT

P

CAm

p

Which in introduced in the thrust expression yields:

111

2

2

2

04

04

55

5

0404

04

55

55504555

5550455

5

552555

aaa

a

ap

ap

a

P

P

P

PPA

T

TP

p

P

P

PA

PPATTPART

c

PPATTcART

P

PPACAF

Tc


Theory 6.1 - Indication of thrustBut p04/p5 is the critical pressure ratio =>

)(

1111

2

112

1

1

2

1

2

11

21

2

1

1

2

12

041

04

5

104

041

041

5

fKwhere

p

PK

p

P

PA

F

p

P

p

P

p

P

PA

F

aaa

a

aaa


Indication of thrust• In sea level static thrust can thus be directly related

to the engine pressure ratio (EPR)!• When we have ram pressure ratio we have:

RPREPRp

P

p

P

p

P

aa

01

01

0404

• Thus we have an expression also for in flight thrust estimation


Velocity-Area relation for compressible flow

Combining the continuity and momentum equations in differential form for compressible flow gives (Appendix A – Eq. 9):

A

dA

V

dVM )1( 2

What does this tell us?


Convergent divergent nozzles

)1(

)1(

22

2

* 2

11

1

21

MMA

A

It can be shown:


So what was this….

?


• Pe is minutely below Po => small wind. Acceleration in convergent portion and deceleration in divergent

• There will be some value of Pe at which the flow will just barely go sonic at the throat.

• If Pe is reduced further the flow in the convergent portion will remain “frozen”

Lets undertake some back pressure variations


Lets undertake some back pressure variations

• For values below Pe3 but higher than Pperfectly expanded a shock will stand in the divergent part

• It will stand exactly in the exit when the pressure behind the normal shock at the design Mach number is equal to Pe

• For lower pressures the shock will form an oblique shock pattern outside the nozzle which is reduced in strength until the isentropic pressure is attained.


When do we use convergent-divergent nozzles?

• The critical pressure ratio can be estimated with:

853.12

11

2

11

1120

MM

P

P

• For nozzle pressure ratios < 3 the losses incurred are greater in the convergent-divergent nozzles– Even at the isentropic condition!!!


Supersonic flight

• Ram pressure ratio => Exit pressure ratio is increased (EPR)– Pressure ratio for high Mach numbers (2-3) is often 10-20

– Variable exit/throat area has to be allowed for

– Divergence angle less than 30°.

– Exit diameter less than engine diameter to not incur additionaldrag

– Noise suppression and thrustreversing will be harder to implement


Thrust reversing• On icy, wet or snow covered runways the

efficiency of the aircraft brakes may be reduced– Reversing the aircraft engine gas stream may allow for

efficient braking


Thrust reversing


The turbofan engine

• Improve ηp by reducing the mean jet velocity (in comparison with turbojet)

• Reduce noise (in comparison with turbojet)

1

2

a

jp

C

C

• Example 3.2 - homework

– Fan is driven by LP turbine

– If fan and bypass streams are mixed additional equations are necessary


The turbofan engine

hot

cold

m

mbpr


FPR (Fan Pressure Ratio) and specific thrust

• For military aircraft engines mixers are used– Fan exit pressure and turbine exit pressure must be

similar for efficient mixing => FPR and EPR are similar

– EPR sets thrust => – FPR sets thrust


Optimization of the turbofan

Increased T7 => more energy extraction needed before the optimal velocity is obtained

• Four available variables:– FPR = Fan Pressure Ratio– BPR = Bypass Ratio– TIT = Turbine inlet

temperature (T4)

– OPR = Overall pressure ratio

• For a fixed OPR and BPR one obtains:


Optimization of turbofan

• Perform operation for a “grid” of OPR and BPR. – Select the globally best point!

• Optimization should be computerized– Installation losses and weight estimation– Life Cycle Cost– Engine must complete mission!!!

• Take-off• Top of climb• Cruise (most important)


Mixing• For afterburning

turbofans => only one reheat system. More oxygen is made available (compared to an unmixed core flow)

• Subsonic transport – small but valuable reduction in SFC

• An energy balance gives:

070602 TmcTcmTcm pmphhpcc

pm

m

m

hc

hhccm

hc

phhpccpm

c

R

mm

RmRmR

mm

cmcmc

1


Mixing – obtaining p07

A momentum

balance gives:

26

7776622

ppwith

ApmCApCmApCm hhcc

a. M6 (turbine design criteria), T06, P06 are known which gives P6. A6 is obtained from the “X-function”:

b. With p6=p2 we get M2 (p02 is known). mc, Rc, M2, p02 and T02 gives A2 from the X-function. Cc from continuity.

c. mC7+A7P7 is now obtained from the momentum balance.d. A7=A6+A2 and m =ρC7A7 = (P7/RmT7)C7A7

),(2

11 6

)1(2

)1(

266

606

06 MMMAP

RTmhh

h h

h


Mixinge. T07 is known but both P7 and P07 are unknown. Guess M7 =>

T7 from T07 and C7 from Mach number definition. Continuity => p7.

f. Check that momentum equation is satisfied. If not improve guess of M7.

Pooh….


Increasing thrust• Re-design to allow for increased mass flow or

increased T3.

• Temporary increase of thrust (augmentation)– Take-off, acceleration from subsonic to

supersonic, combat maneuvering

• Methods for augmentation– Liquid injection– Afterburning


Liquid injection

• Spray water methanol (lowers freezing point of water

and burns) mixture in compressor during take-off and climb– Equivalent drop in compressor temperature => less

compressor work => more thrust– Secondary effect: thrust increases since mass flow

increases– Partly outdated method


AfterburningBurn additional fuel in the jet pipe– No rotating parts => maximum

allowable temperature is higher. Typically around 2000 K

Accept penalty in SFC– Poor “cycle” (better at high speed –

for fixed momentum drag an increase in gross thurst => considerably greater incerease in net thrust)

21

06

T

RC j


Afterburning

• Speed of sound in the

nozzle exit => variable area nozzle required!• Aim is to maintain gas generator at same condition => variable area necessary to pass the same mass flow at a much lower density.


Turboprop

• Jet and propeller deliver combined propulsion

termsmall

aPR FCSPTP

• Most designs operate with nozzle unchoked and cruise (optimally) around

M=0.6.– Turboprops have lost market share for commuting and airlines to turbofan-powered

aircraft

SAAB-Fairchild 340 aircraft.


Common cores• High pressure core common to

different engines– Cut development cost

– Even from civil to military is possible

Same core


Learning goals• Be able to explain why an increase in T3 may still be

attractive in turbojet cycles, although the SFC is increased– Be able to relate this increase to performance gains of turbofan engines by

considering the propulsive efficiency and designing for higher BPR

• Be able suggest suitable engine cycle parameters (pressure ratio and T3 for different missions)

• Be informed about how the delivered engine thrust is indicated

• Be familiar with– convergent-divergent nozzles, thrust reversing, mixing, thrust

augmentation (ways of increasing thrust)

Chalmers University of Technology Lecture 6 Turbojet –Optimization –Cycle selection (mission...

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