1. 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.
Chemical
Energy
Heat
(Thermal
Energy)
Mechanical
Power
Mech.
Power to
GasFlow
Thrust
Combustion
Thermal
Mechanical
Propulsive
The overall efficiency for the propulsion chain is given by:

4. INDUSTRY TERMINOLOGY FOR OVERALL FIGURES OF MERIT [Pratt &Whitney]

5. EVOLUTION OF THE AEROENGINE [Koff]

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

7. Fuel Consumption Trend
Fuel Burn
JT8D
JT9D
PW4084
Future
Turbofan
Pratt & Whitney introduced the JT8D turbofan engine in the 1960’s on Boeing’s 727 and Douglas’s DC-9, bringing a step-change in fuel economy to commercial aviation.
At the end of the decade Pratt’s JT9D high-bypass ratio turbofan produced the next revolution in fule economy.
With the development and introduction of our PW4000 engines, PW2000 engines, and now our PW6000 engines, Pratt has continued to improve the fuel economy of commercial aircraft.
Our latest technologies will take fuel consumption to new and greater levels of fuel economy - providing longer range, more economical flight.
Principal mechanism for TSFC is the propulsive efficiency, ie BPR
JT8D - EIS 1964 on B727 / 1965 on DC-9 (BPR=1.7, TSFC = )
JT9D - EIS 1969 on B747 (BPR=4.8, TSFC=0.68)
Today’s best PW4000 is around 0.55 TSFC at 6.4 BPR
ATFI at 7.5 BPR
Auxier goal is 17 for the 25% engine
PW4052
1950
1960
1970
1980
1990
2000
2010
2020
Year

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

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

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,

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 - W
Change 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:
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
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
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”
For any device in steady flow
Heat input
Per unit mass flow rate: 2 1
Mass flow
Device
Shaft work
q is heat input/unit mass
wshaft is the shaft work / unit mass

19. The form of the steady flow energy equation shows that enthalpy, h,
h = e + pv = e + p/r
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)

22. THERMODYNAMIC MODEL OF GAS TURBINE ENGINE CYCLE [Cravalho and Smith]3 4 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]

28. COMMERCIAL AND MILITARY ENGINES (Approx. same thrust, approx
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]

34. Lockheed Martin CTOL STOVL UK/RN CV
As you can see, the Lockheed Martin design looks somewhat like a single engine F-22. It uses “a shaft-driven lift fan, two roll ducts, and a swiveling main engine exhaust nozzle [to] provide the vertical lift for the the Marine and Royal Navy JSF variants.”
The main engine for Lockheed, as well as the other two candidates, is being developed by Pratt & Whitney as a derivative of the F119.
“The Allison lift fan is driven by a drive shaft connected to the main engine. Doors open above and below the vertical fan as it spins up. The rest of the vertical thrust is provided by a three-bearing exhaust nozzle on the main engine and two ducts on the wings. The exhaust nozzle, provided by Rolls-Royce, is used for lift and yaw control and can swivel 110 degrees downward from the horizontal. Thrust for the wing ducts, used for roll control, is supplied from the main engine's fan section. This thrust comes from cooler air that normally bypasses the engine's turbine section. The lift-fan approach removes energy from the hot turbine section of the main engine, which, in turn, lowers the main engine's exhaust temperature, producing an even cooler footprint.”
image, courtesy LMTAS

35. Lockheed Martin Propulsion System
Shaft-Driven Lift Fan Concept
F119 Derivative Engine
Roll Control
Ducts
Engine Nozzle (Up-and-Away Position)
Allison / R-R Lift Fan
Engine Nozzle (Vertical Thrust Position)
[Davenport]
image, courtesy PW

36. Low Observable Features Lightweight Structures
Engines for JSF
F119 Derivative
JSF F120 Engine
Low Observable Features
Low Observable Nozzle
Lightweight Structures
Matured F119 Core
Integrated
Sub-Systems
Enhanced Diagnostics
Integrated
Sub-Systems
Objectives:
Single Engine Safety
Affordability
Improved R&M
Matured Control System w/Enhanced Diagnostics
[Davenport]
image, courtesy PW
image, courtesy GE

37. PRESSURE RATIO TRENDS [Jane’s 1999]

38. AEROENGINE CORE POWER EVOLUTION: DEPENDENCE ON TURBINE ENTRY TEMPERATURE [Meece/Koff]

39. typical design limiters flight conditions design choices
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.
Heat
Addition T
Expansion
Compression
Cooling

40. TURBOJET ENGINE SHOWING STATIONS AND COMPONENT NOTATION [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.

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...

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) , , ,

45. IDEAL ASSUMPTIONS
1) Inlet/Diffuser: d = 1, d = 1 (adiabatic, isentropic)
2) Compressor or fan: c = cg-1/g , f = fg-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

47. THE ALGEBRA (II)
Applying a similar procedure for the exit pressure
Equate this box to the previous box to get

48. THE ALGEBRA (III)
Continuing on our path to find u7/u0
Therefore

49. THE ALGEBRA (IV)
Now relate temperature ratio across turbine to that across the compressor
This can be rewritten as So ; 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

51. TURBOJET PERFORMANCE

52. TURBOJET PERFORMANCE Effect of Turbine Inlet Temperature
M=0.85, 12km, Tt4=1800K, 1400K
Performance Parameter
Compressor Pressure Ratio

53. 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

55. [Meece]

56. ROLLS-ROYCE HIGH TEMPERATURE TECHNOLOGY [Cumpsty]

57. TURBINE TEMPERATURE PERCEIVED AS A 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 ! The condition for maximum work from a Brayton cycle is

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

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

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 Du to a small mass flow (fighter) or a small Du 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. IMPLICATIONS FOR ENGINE DESIGN [Waitz]
Considering jointly the expressions for thrust and propulsive efficiency, As As
Also, as
Ainlet  ; Drag 

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
F16-C, Janes,
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
B , Janes,

73. COMMERCIAL AND MILITARY ENGINES (Approx. same thrust, approx
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
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
(After Koff, 1991)

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 pressure
ratio
Bypass ratio,

85. OPTIONS FOR HIGH BYPASS ENGINES [Koff-1995]

86. AN EXAMPLE OF CYCLE PERFORMANCE IMPROVEMENT