MAE 5380: Advanced Propulsion

GAS TURBINE PERFORMANCE

Mechanical and Aerospace Engineering Department

Florida Institute of Technology

D. R. Kirk

2

AEROENGINE CYCLE ANALYSIS

• Cycle Analysis [What determines the engine characteristics?]– Cycle analysis is the study of the thermodynamic

behavior of air as it flows through the engine without regard for the mechanical means used to effect its motion

– We characterize components by the effects they produce• Actual engine behavior is determined by geometry;

cycle analysis is sometimes characterized as representing a “rubber engine”

– Main purpose is to determine which characteristics to choose for the components of an engine to best satisfy a particular need

3

GAS TURBINE CYCLE ANALYSIS

A gas turbine engine is an example of a thermal engine. A useful conceptual framework to analyze this is through the propulsion chain.

ChemicalEnergy

Heat(ThermalEnergy)

Mechanical Power

Mech.Power to

GasFlow

ThrustPower

The overall efficiency for the propulsion chain is given by:

Combustion Thermal Mechanical Propulsive

[m

f Fuel flow rate; hcomb Heat of combustion (heat of reaction)

= 4.3 x 107 J/kg for jet fuel

uo Flight speed; F = Thrust]

comb

0= overall hf

m

Fu

usage energy chemical of Rate

powerThrust for pay What we

get What we

overallcombustionxthermalxmechxpropulsive

4

INDUSTRY TERMINOLOGY FOR OVERALL FIGURESOF MERIT [Pratt &Whitney]

5

EVOLUTION OF THE AEROENGINE [Koff]

6

SUBSONIC ENGINE SFC TRENDS(35,000 ft. 0.8 Mach Number, Standard Day [Wisler])

71950 1960 1970 1980 1990 2000 2010 2020

Fuel Consumption Trend

JT8D

JT9D

PW4052

PW4084

Fuel Burn

Year

FutureTurbofan

8

9

MAJOR TYPES OF THRUST PROPELLED AIRCRAFT [Walsh and Fletcher]

10

CONCEPTS/TOOLS FOR ENGINE IDEAL CYCLE ANALYSIS

• Concepts of stagnation and static temperature and pressure • Ideal gas equation of state [p = RT] and other attributes

• One-dimensional gas dynamics

• Thermodynamic laws (there are only two that we need!)• Behavior of useful quantities: energy, entropy, enthalpy

• Relations between thermodynamic properties in a reversible (“lossless”) process

• Relations between Mach number and thermodynamic properties (static and stagnation quantities)

• Properties of cycles

11

STAGNATION QUANTITIES DEFINED

• Quantities used in describing engine performance are the stagnation pressure, enthalpy and temperature.

Stagnation enthalpy, ht , enthalpy state if the stream is decelerated adiabatically to zero velocity

ht hu2

2hcpT ideal gas

Tt T u2

2cp

stagnation temperature

Tt

T1

u2

(2cpT)

But cp R 1

; a2 RT (speed of sound)

Tt

T1 1

2u2

a2or

Tt

T1 1

2M2

12

FOR A REVERSIBLE, ADIABATIC (I.E. ISENTROPIC) PROCESS

P

constant

using pRT we findp

T( / 1)

constant

ptp

Tt

T

1

defines the stagnation pressure

(pt is the pressure if the stream is decelerated isentropically to zero velocity)

pt

p 1

12

M2

1

For M2 1, expand using the binomial theorem to get

pt p12u2

"Bernouli Equation" for low speed flow

13

ANALYSIS OF THE LINKS IN THE PROPULSION CHAIN

Examine the magnitudes and behavior of the different efficiencies

is greater than 0.99 for civil aircraft at cruise. It is set by the details of the combustion processes. We will take it to be unity in these lectures

is a measure of the mechanical losses (such as bearing friction). It is also close to unity.

The main figures of merit for gas turbine engines are the thermal and propulsive efficiencies. We can approximate the propulsion chain as

We examine thermal efficiency first

Thermal efficiency:

Heat (actually fuel) is input. An airstream, , mass flow rate, passes through the engine. The mechanical work is the change in kinetic energy, which is, per unit mass,

combustion

mechanical

0 propulsivexthermal

thermalMechanical work

Heat energy

uexit

2/ 2 uinlet

2/ 2

m.

14

THERMODYNAMIC PROCESSES IN THE ENGINE

• How should we represent the thermodynamic process in the engine?

• It is cyclic (the air starts at atmospheric pressure and temperature and ends up at atmospheric pressure and temperature)

• Consider a parcel of air taken round a cycle with heat addition and rejection.

• Need to consider the thermodynamics of this propulsion cycle

• To do this we make use of the First and Second Laws of Thermodynamics

• We will review (one chart each) these concepts

15

RECAP ON THERMODYNAMICS (I)

First law (conservation of energy) for a system: “chunk” of matter of fixed identity

E0 = Q - WChange in overall energy (E0 ) = Heat in - Work done

E0 = Thermal energy + kinetic energy ...

Neglecting changes in kinetic and potential energy

E = Q - W ; (Change in thermal energy)

On a per unit mass basis, the statement of the first law is thus :

e = q - w

16

RECAP ON THERMODYNAMICS (II)

The second law defines entropy, s, by:

ds dqreversible

T

Where dqreversible is the increment of heat received in a reversible process between two states

The second law also says that for any process the sum of the entropy changes for the system plus the surroundings is equal to, or greater than, zero

ssystem ssurroundings0

Equality only exists in a reversible (ideal) process

17

REPRESENTING THE ENGINE PROCESS IN THERMODYNAMIC COORDINATES

First Law: E = Q - W, where E is the total energy of the parcel of air.

For a cyclic process E is zero (comes back to the same state)Therefore: Q (Net heat in) = W (Net work done)

Want a diagram which represents the heat input or output.A way to do this is provided by the Second Law

dqreversibleTds

where ds is the change in entropy of a unit mass of the parcel and dq is the heat input per unit mass

Thus, one variable should be the entropy , s

18

Other variable: look at the control volume form of the first law, sometimes known as the “Steady Flow Energy Equation”

Shaft work

Heat input

Mass flow

Device

1 2

ht2 -ht1 =q-wshaft

q is heat input/unit mass wshaft is the shaft work / unit mass

For any device in steady flow

m

ht2 ht1 Q

W

shaft = Rate of heat in-Rate of shaft work done

The quantity ht hu2 /2 is the stagnation enthalpy defined previously

Per unit mass flow rate:

19

The form of the steady flow energy equation shows that enthalpy, h,

h = e + pv = e + p/

is a natural variable to use in fluid flow-energy transfer processes.

For an ideal gas with constant specific heat, dh = cpdT.

Changes in enthalpy are equivalent to changes in temperature.

To summarize, the useful natural variables in representing gas turbine engine processes are h,s (or T, s).

We will represent the thermodynamic cycle for a gas turbine engine on a T,s diagram

20

Gas Turbine Engine Components:

• Inlet - Slows, or diffuses, the flow to the compressor

• Fan/Compressor (generally two, or three, compressors in series) does work on the air and raises its stagnation pressure and temperature

• Combustor - heat is added to the air at roughly constant pressure

• Turbine (generally two or three turbines in series) extracts work from the air to drive the compressor or for power (turboshaft and industrial gas turbines)

• Afterburner (on military engines) adds heat at constant pressure• Exhaust nozzle raises the velocity of the exiting mass flow• Exhaust gases reject heat to the atmosphere at constant

pressure

21

THERMODYNAMIC CHARACTERISTICS OF THE COMPONENTS(Ideal Components)

Inlet: ht 0

Compressor:ht wshaft wshaft0, work input to compressor

,

s0 adiabatic, lossless

Combustor and afterburner: htqin (heat input)

Turbine: ht wshaft wshaft

>0, work output from turbine

,

s0 adiabatic, lossless

Exhaust nozzle: No shaft work, no heat exchange, s = 0

22

THERMODYNAMIC MODEL OF GAS TURBINE ENGINE CYCLE[Cravalho and Smith]

43

2 5

23

GAS TURBINES: VARIATIONS ON A CORE THEME [Cumpsty]

24

GAS TURBINE ENGINE CORE [Cumpsty]

25

SCHEMATIC CONDITIONS THROUGH A GAS TURBINE [Rolls-Royce]

26

NOMINAL PRESSURES AND TEMPERATURES FOR A PW4000 TURBOFAN [Pratt&Whitney]

27

28

COMMERCIAL AND MILITARY ENGINES(Approx. same thrust, approx. correct relative sizes)

GE CFM56 for Boeing 737

P&W 119 for F- 22

29

SOME TYPES OF GAS TURBINE ENGINES (I) [Rolls-Royce]

30

SOME TYPES OF GAS TURBINE ENGINES (II) [Rolls-Royce]

31

TYPES OF GAS TURBINE ENGINES (III) [Rolls-Royce]

32

SCHEMATIC OF TURBOPROP ENGINE [Kerrebrock]

33

AFTERBURNING ENGINES [Pratt& Whitney]

Lockheed Martin

CTOL STOVL

UK/RNCVimage, courtesy LMTAS

Lockheed Martin Propulsion System

Shaft-Driven Lift Fan Concept

Allison / R-R Lift Fan

Roll ControlDucts

F119 Derivative Engine

Engine Nozzle (Vertical Thrust

Position)

Engine Nozzle (Up-and-Away Position)

image, courtesy PW

[Davenport]

Engines for JSF

Objectives:• Single Engine Safety• Affordability• Improved R&M

IntegratedSub-Systems

Low Observable Nozzle

Matured Control System w/Enhanced Diagnostics

Low Observable Features

Matured F119 Core

F119 Derivative JSF F120 Engine

Enhanced Diagnostics

Lightweight Structures

IntegratedSub-Systems

image, courtesy PW image, courtesy GE

[Davenport]

37

PRESSURE RATIO TRENDS [Jane’s 1999]

38

AEROENGINE CORE POWER EVOLUTION:

DEPENDENCE ON TURBINE ENTRY TEMPERATURE [Meece/Koff]

39

IDEAL CYCLE ANALYSIS

• Our objective is to express thrust,

F, and thermal efficiency, (or

alternatively ) as functions of

– typical design limiters

– flight conditions

– design choices

so that we can analyze the

performance of various engines.

T

Compression

HeatAddition

Cooling

Expansion Isp

40

TURBOJET ENGINE SHOWING STATIONS AND COMPONENTNOTATION [Kerrebrock]

41

CALCULATION OF THRUST AND SPECIFIC IMPULSE IN TERMS OF COMPONENT PERFORMANCE

• If the component performance is known, we can compute the thrust, specific impulse (or TSFC), thermal and propulsive efficiencies

• The procedure will be shown here conceptually for a simple example a turbojet with an ideally expanded nozzle and the contribution of fuel mass to exit momentum flux neglected.

The expression for thrust is

Thrust = F = Ý m 7u7 Ý m 0uo A7(p7 po)

For the conditions described, the mass of fuel is neglected, and the

exit pressure, p7 , is equal to the atmospheric pressure, po.

The thrust expression thus simplifies to

F = Ý m 0(u7 uo )

[station 7 is the exit station]

42

METHODOLOGY

• Find thrust by finding u7/uo (uexit/uo) in terms of q, temperature

ratios, etc.

• Use a power balance to relate turbine parameters to

compressor parameters

• Use an energy balance across the combustor to relate the

combustor temperature rise to the fuel flow rate and fuel

energy content.

43

METHODOLOGY (II)

• Write expressions for thrust and efficiency (Isp)

• That is the easy part. Now comes the algebra...

F m

1f u7 u0 p7 p0 A7

For ideal expansion, p7 p0

F m

u7 u0 F

m

a0

M0u7

u0

1

Isp F

gm

f

F

gf m

44

NOMENCLATURE

= total or stagnation pressure ratio across component (d, c, b, t, a, n) = total or stagnation temperature ratio across component (d, c, b, t, a, n)

Tt T 1 1

2M2 , Pt P 1 1

2M2

1

Tt0

T0

0

Ttt

T0

t

Pt0

P0

0, , ,

45

IDEAL ASSUMPTIONS

1) Inlet/Diffuser: d = 1, d = 1 (adiabatic, isentropic)

2) Compressor or fan: c = cg-1/g , f = f

g-1/g

3) Combustor/burner or afterburner: b = 1, a = 1

4) Turbine: t = tg-1/g

5) Nozzle: n = 1, n = 1

46

THE ALGEBRA (I)

• Working towards an expression for u7 / u0

u7

u0

M7

M0

RT7

RT0

M7

M0

T7

T0

TT7

T7

T 1 12

M27

TT7 TT0

TT2

TT0

TT3

TT2

TT4

TT3

TT5

TT4

TT7

TT5

TT0 dcbtn

T0 1

12

M0

2 cbt

TT7 T00cbt

47

THE ALGEBRA (II)

• Applying a similar procedure for the exit pressure

• Equate this box to the previous box to get

PT7

P0 1 12

M02

1

d c b t n

PT7

p0 0 c t p7 1 1

2M7

2

1

1

12

M72

1

0 c t

M7 2

10 cb t 1 1 2

1

12

M72 0

1 c

1 t

1 0 c bt

TT7

T7

48

THE ALGEBRA (III)

• Continuing on our path to find u7/u0

• Therefore

T7

T0

T7

TT7

TT7

T0

0 c b t

0 c t

b

u7

u0

M7

M0

T7

T0

2 1

M0

0 c t 1 1 2b

0 1

12

M02 M0

2 2

10 1

u7

u0

0 c t 1 b

0 1

49

THE ALGEBRA (IV)

• Now relate temperature ratio across turbine to that across the

compressor

• This can be rewritten as

• So

m

Cp TT3 TT2 m

Cp TT4 TT5 m

hT Q

W

shaft

TT3

TT2

1

TT2

T0

TT4

T0

1

TT5

TT4

TT2

T0

d0 0

c 1 0 t 1 t

t 1

0

t

c 1

;

or

50

THE ALGEBRA (V)

• One more substitution to write the temperature rise across the

combustor in terms of t=TT4/To

• Then substituting everything in

• Thrust per unit mass flow (non-dimensionalized by the

ambient speed of sound) as a function of design parameters

and flight conditions

b

t

0c

F

m

a0

M0

0

0 1

t

0c

1

c 1 t

0c

1 2

1

51

TURBOJET PERFORMANCEEffect of Flight Mach Number

TT4=1600K, PiC=25

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2 2.5 3 3.5Mach Number

Perf

orm

ance

Para

mete

r

Specific Thrust

Overall Efficiency

Thermal Efficiency

Propulsive Efficiency

TURBOJET PERFORMANCE

52

TURBOJET PERFORMANCEEffect of Turbine Inlet Temperature

M=0.85, 12km, TT4=1800K

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50Compressor Pressure Ratio

Perf

orm

ance P

ara

mete

r

Specific Thrust

Overall efficiency

Thermal efficiency

Propulsive efficiency

Spec. thrust, TT4=1400K

Overall eff., TT4=1400K

Thermal eff., TT4=1400K

Propulsive eff., TT4=1400K

TURBOJET PERFORMANCE

Compressor Pressure Ratio

Pe

rfo

rma

nc

e P

ara

me

ter

Effect of Turbine Inlet TemperatureM=0.85, 12km, Tt4=1800K, 1400K

53

The procedure would be similar if the nozzle were not ideally expanded

(and if the flow processes in the inlet and nozzle were not ideal).

For a convergent nozzle we would have Me 1.

This would set pe :

pte

pe(

12

) /( 1) 1.89 ( 1.4)

The rest of the procedure is "the same"

THE ALGEBRA (VI)

54

WHAT DO WE DO WITH THESE EXPRESSIONS?

• How do we interpret the thrust expression?

• Parameters are flight Mach number, Mo, compressor temperature rise, c, and turbine entry temperature (combustor exit temperature), t.

– Flight Mach number set by mission– Turbine entry temperature set by level of technology

and cost (can think of this as a technology limit)– Compressor temperature rise is design parameter

F

m

a0

M0

0

0 1

t

0c 1

c 1 t

0c

1 2

1

55

[Meece]

56

ROLLS-ROYCE HIGH TEMPERATURE TECHNOLOGY [Cumpsty]

57

TURBINE TEMPERATURE PERCEIVED ASA COST DRIVER

58

FOR A GIVEN TECHNOLOGY LEVEL, HOW DOES THRUST VARY WITH c?

• Find maximum thrust/mass flow for given turbine entry temperature

• This is an important condition for an aircraft engine• To do this, take

• Get

• BUT, you already know this from 16.050! The condition for maximum work from a Brayton cycle is

F / Ý m ao c 0.

c maxthrust

t

o

T3

T2

T4

T2

59

OTHER ENGINE CONFIGURATIONS

• For other configurations such as afterburning engines (which we examine next), there are more components to step through.

• There can also be more balances to be made (power to drive the high pressure compressor comes from the high pressure turbine, power to drive a fan or low pressure compressor comes from the low pressure turbine).

• The basic principles, however, remain the same.

• The specific impulse is found from the thrust and the fuel flow, the latter being known from the temperature ratio across the burner. The non-dimensional specific impulse is:

Specific impulse

Isp F

gmf

F

gfm

60

PUT INTO EXPRESSION FOR THRUST PER UNIT MASS FLOW TO GET MAX. VALUE

• Maximum value of thrust

• Upper limit of flight speed is reached when compressor outlet temp. = combustor outlet temp. (no heat can be added)

• But for limit is reached when o = t

F

m

a0

2

1

t 1 2 Mo

2

1 2

M0

c t

o

61

THE AFTERBURNING ENGINE

• There is excess air, compared to fuel, in a gas turbine flow path– Stoichiometric fuel-air ratio is 0.067– Current ratios are less than half of this

• Can add fuel after the turbine exit and thus add heat to the cycle– Larger enclosed cycle area– More work --> increased power and thus increased thrust

• Can add heat and go to high temperatures because the afterburner does not have rotating, highly stressed parts

• High fuel use, but gives military engine high thrust/weight

62

THE AFTERBURNING ENGINE CYCLE(Turbojet; afterburning portion shown dashed [Kerrebrock])

63

AFTERBURNING TURBOFAN ENGINE SHOWING STATIONS [Kerrebrock]

64

CROSS SECTIONS OF PW F100 ENGINES [Jane’s]

65

SPECIFIC FUEL CONSUMPTION FOR AFTERBURNING AND NON-AFTERBURNING OPERATION [Rolls-Royce]

66

ROLE OF AFTERBURNING IN TAKE-OFF AND CLIMB [Rolls-Royce]

67

AFTERBURNER OPERATION FOR A LOW BYPASS RATIO TURBOFAN

From Walsh and Fletcher

68

THRUST PER UNIT MASS FLOW AND SPECIFIC IMPULSE: TURBOJET AT MAXIMUM THRUST CONDITION

(Turbine Entry Temperature 7.5 times Ambient Temperature [Kerrebrock])

(Thrust)

(Specific impulse)

Flight Mach number,

69

SUMMARYAND PREVIEW OF THINGS TO COME

• Introduced figures of merit for aeroengines• Defined ideal thermodynamic cycle for gas turbine engine• Developed a criterion for “optimum” cycle• Introduced methodology to find thrust (TSFC) from component

pressure and temperature changes• Showed application to several different engine types (e.g.,

afterburning engine)

• Analysis so far considered only ideal components and cycles• Need to examine:

– What are the departures from ideal behavior• Physical mechanisms• Magnitudes of the departures

• How do these departures affect the overall engine performance?

70

PROPULSIVE EFFICIENCY AND FAN BYPASS RATIO

• The discussion so far has focused on thermal efficiency and specific power

• For overall efficiency, the propulsive efficiency is a major driver

• The reason is associated with the effect of bypass ratio

• For a given thrust we can impart a large u to a small mass flow (fighter) or a small u to a large mass flow (high bypass ratio civil engine)

• This is shown clearly in the lectures presented by Waitz; two of these charts are given here for reference below

71

Considering jointly the expressions for thrust and propulsive efficiency,

IMPLICATIONS FOR ENGINE DESIGN [Waitz]

Ainlet ; Drag

F Ý m ue uo prop

2

1 ue

/ uo

ueuo

F / Ý m prop

ueuo

1 F / Ý m prop

FÝ m uo

As

As

Also, as

72

PROPULSIVE EFFICIENCY AND SPECIFIC THRUST

For fighter aircraft that need high thrust/weight and fly at high speed, it is typical to employ engines with smaller inlet areas and higher thrust per unit mass flow

However, transport aircraft that require higher efficiency and fly at lower speeds usually employ engines with relatively larger inlet areas and lower thrust per unit mass flow

F16-C, Janes, 1998-9

B777-200, Janes, 1998-9

73

COMMERCIAL AND MILITARY ENGINES(Approx. same thrust, approx. correct relative sizes)

GE CFM56 for Boeing 737

PW F119 for F-22

74

PROPULSIVE EFFICIENCY AND SPECIFIC THRUST

J. L. Kerrebrock, Aircraft Engines and Gas Turbines, 1991

75

PROPULSIVE EFFICIENCY FOR DIFFERENT ENGINE TYPES [Rolls Royce]

76

THRUST HISTORY OF LARGE CIVIL ENGINES [Gunston]

77

OVERALL PROPULSION SYSTEM EFFICIENCY

(After Koff, 1991)

Trends in thermal efficiency are driven by increasing compression ratios and corresponding increases in turbine inlet temperature. Whereas trends in propulsive efficiency are due to generally higher bypass ratio engines

78

BYPASS RATIO DEFINITION [Coons]

79

FAN DESIGN PARAMETERS [Coons]

80

TRENDS IN BYPASS RATIO

(After Koff, 1991)

81

GE90-115B BYPASS RATIO ~ 9

[GE Aircraft Engines]

82

CORE AND BYPASS THERMODYNAMIC STATES [Cumpsty]

83

THRUST PER TOTAL MASS FLOW AND SPECIFIC IMPULSE AS

FUNCTIONS OF TURBOFAN BYPASS RATIO, (Turbine Entry Temperature 7.5 times Ambient Temperature, Ideal Cycle Core and Fan Streams

with Equal Velocities, Condition of Maximum Thrust [Kerrebrock])

Bypass ratio,

84

FAN PRESSURE RATIO AS A FUNCTION OF TURBOFAN BYPASS RATIO,

(Turbine Entry Temperature 7.5 times Ambient Temperature, Ideal Cycle, Core and Fan Streams with Equal Velocities, Condition of Maximum Thrust [Kerrebrock])

Fan pressureratio

Bypass ratio,

85

OPTIONS FOR HIGH BYPASS ENGINES [Koff-1995]

86

AN EXAMPLE OF CYCLE PERFORMANCE IMPROVEMENT