Cours de conception aéronautique Dimensionnement · PDF fileDimensionnement mécanique des turbomaréacteurs Introduction au ... Principles of jet propulsion ... Brief review of the

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Introduction au dimensionnement

mécanique et dynamique des

turboréacteurs

Reference :

AERO0015-1 - MECHANICAL DESIGN OF TURBOMACHINERY -

5 ECTS - J.-C. GOLINVAL

Cours de conception aéronautique

2Principles of jet propulsion

Comparison between the working cycle of a turbo-jet engine

and a piston engine

Air intake Compression Combustion Exhaust

Air intake Compression Combustion Exhaust

3

High pressure (HP) turbine

Low pressure (LP) turbine

Low pressure (LP) compressor

Combustion chamber

Exhaust

High pressure (HP) compressor

Principles of jet propulsion

For aircraft propulsion, the thrust is produced by the acceleration

of the air passing through the engine.

4

Fcompressor

(85 kN)Fcombustion

150 kN

Total thrust = 30 kN. Forward.

Fturbine

180 kNFexhaust

25 kN

235 kN 205 kN

For any flow section of the engine, the calculation of the thrust may be achieved using the following formula:

Thrust = Pressure x Area of flow section + Mass flow rate x Velocity of flow

Example of a typical single-pool axial flow engine

Principles of jet propulsion

5

1921 GUILLAUME patent

France

axial-flow compressor

combustor

axial-flow turbine

At that time, these patents clearly described the air-breathing jet

principle but were not executed in practice because of the high

exhaust speed (e.g. 900 km/h) which was not compatible with the

too-slow aerovehicle at that time (e.g. < 300 km/h in the early 1920s)

Brief review of the evolution of turbojet engines

6

United Kingdom

1930 : patent of Frank WHITTLE’s turbojet engine


Multistage, axial-flow compressor

radial compressor stage

combustor

axial-flow turbine

exhaust nozzle

7

United Kingdom

1937: 1st test of Whittle’s engine , the W.U. (Whittle Unit)

May 15, 1941: 1st flight of the Wittle’s engine on the Gloster

experimental aircraft


Turbine

Helicoidal combustion chamber

DiffuserCompressor 1937 Wittle’s engine (WU)

8

• In September 1941, an agreement was signed between Great Britain

and the United States so that the United States could have the

engine W1X and a set of drawings of the Whittle W2B jet engine.

• General Electric was chosen for jet engine development.

• The W2B engine was built and tested on March 18, 1942, under the

name GE 1-A.


United States

9

Germany

1936 : development of an hydrogen turbojet demonstrator (He S-1)

by Hans VON OHAIN in the HEINKEL company

1937 : design of the flight engine (He.S3)

August 27, 1939 : 1st flight of the experimental He-178 airplane

with jet engine He.S3B

Jet engine Heinkel He.S3B

This was the first flight of a turbojet aircraft in the world.


10

Germany

JUMO 004 turbojet engine

First jet engine leading to mass production

Control cone

Combustion chamber

Starter motorCooling air duct


11

Failure was due to the lack of turbine materials capable of withstanding

the high stresses at high temperatures.

Engine life of about 25 hours (above the combat life of a German fighter !)

Start of development Fall 1939

First test run Oct. 11, 1940

First flight in Me-262 July 18, 1942

Beginning of production Early 1944

About 6000 engines delivered May 1945

JUMO 004 development and production schedule

Germany


12

From 1940, design and construction of new turbojets increase drastically.

Advanced concepts appeared very early after the principle of

turbojet engine was discovered but their developments met

two technological problems:

• The complete lack of heat-resistant materials.

• The blade air cooling technology.


13

CertificationRequest

For Proposal

Program Launch

Preliminary Design Review

Definition of the thermodynamic cycle consistent with the specification and of the best structural architecture of the engine

Detailed Design

Industrialization

First Engine To Turn

milestone

Testing Program

Today, the duration of this process is about 3 years (against ~ 6 years in

the 90s)

Development process of the structural design

14

Thrust requirement: for various operating points (limits of the flight

envelope)

Altitude

Speed

Engine maximum power

Aircraft structure maximum temperature

(max Mach)

Aircraft structure maximum pressure

Minimum aircraft

aerodynamic lift

Electric power requirement: increasing need in modern aircrafts

(electric actuators, navigation systems)

This has an impact on the engine architecture and on

the structural design.

Preliminary design

15

Overall efficiency of a jet propulsion engine

overall thermal propulsiveη η η= ×

Thermal efficiency Propulsive efficiency

Overall efficiency

Challenges of turbojet technology

16

0 1 2 3 4 e

Thermal efficiency

3

1

24

e

0Tem

pera

ture

Entropy

Thermodynamic cycle

0

31thermal

T

Tη = −

The thermal efficiency is defined as the ratio of the net power out

of the engine to the rate of thermal energy available from the fuel

According to the T-s diagram of an ideal turbojet engine, the

thermal efficiency simplifies to


17

thrust flight velocity

total power output

exit velocity

Propulsive efficiency

The propulsive efficiency is defined as the ratio of the useful power

output (the product of thrust and flight velocity, V0 ) to the total

power output (rate of change of the kinetic energy of gases through

the engine). This simplifies to

0

0

21propulsive

out e

F V

W V Vη = =

+&


18

Ve / V0

η pr

opul

sive

100

1 42 3

9080

70

605040

If the propulsive efficiency is plotted versus the velocity ratio Ve / V0 ,

it follows that high propulsive efficiency requires the exit velocity to be

approximately equal to the inlet velocity.


19

To progress to the performance capabilities of today, two goals were

(and still are) being pursued:

1. Increase the thermodynamic cycle efficiency by increasing the

compressor pressure ratio.


Trend in compressor pressure ratios

Calendar years Compressor pressure ratio

Late 1930 to 1940 3:1 to about 6:1

Early 1950 About 10:1

1950 to 1960 20:1 to about 25:1

2000 30:1 to about 40:1

20

2. Increase the ratio of power-output to engine weight by

increasing the turbine inlet temperature


Trend in turbine inlet temperatures

Tu

rbin

e i

nle

t te

mp

era

ture

Military

Commercial

Year

°C

21

Depending on the types of applications, different development goals

may be pursued.

Supersonic flight (military engines)

Maximum thrust is sought by increasing the exit velocity (at the

expense of fuel economy) and decreasing the engine inlet diameter

(i.e. of the aerodynamic drag)


Example

SNECMA M88 military engine (used on the RAFALE airplane)

22

If the turbine inlet temperature reaches its limit,

thrust augmentation by afterburning.

0 1 2 3 4 5

Nozzle

Afterburner

6 S

3

1

24

0

6

Tem

pera

ture

Entropy

Thermodynamic cycle


Supersonic flight

23

Example of evolution of military engine performances

Comparison between SNECMA M88 military engine (used on the

RAFALE airplane) against ATAR engine (used on MIRAGE 3 airplane)


ATAR M88

Power/weight ratio base x 2

Fuel Consumption base - 30 %

Engine diameter base - 40 %

Turbine entry temperature (°K) 1210 1850

Pressure ratio 6,1 24

Compressor exit temperature (°K) 600 880

24

Titanium alloy

Nickel base superalloy

600 °C

1580 °C

Disks

∆∆∆∆σσσσr = 1000 MPa

∆∆∆∆σσσσθθθθ = 1000 MPa

θθθθmax = 650 °C locally

SNECMA M88 engine


25

Subsonic flight (commercial engines)

A low thrust specific fuel consumption is sought by increasing the

propulsive efficiency the principle is to accelerate a larger mass

of air to a lower velocity.

Note: to keep a high thermal efficiency, the pressure ratio and

the turbine inlet temperature must remain high.

Drawback: the frontal area of the engine is quite large

more drag and more weight result


Solution: principle of the by-pass engine (called turbofan)

26

Solution: principle of the by-pass engine (called turbofan)

Air flow rate ~ 5 to 7 times the air flow

rate going through the gas generator


27Challenges of turbojet technology

Trend in thrust specific fuel consumption

Year

Propfan

Single-pool axial flow turbojet

Advanced technology (high by-pass ratio)

Twin-spool front fan turbojet

Twin-spool by-pass turbojet

28

Evolution of turbojet engines to the technology level of today

In conclusion,

• new concepts or technological breakthroughs are rare;

• advancements are rather due evolutionary improvements of the

design

To achieve good performances, parallel research and development

effort were undertaken in areas such as in aerodynamics,

aerothermics, acoustics, combustion process, mechanics, metallurgy,

manufacturing, …

Aim of the course

Study the mechanical aspects of the design.


29

Evolution of turbojet engines - mechanical aspects

1. Increasing of the compressor pressure ratio (r)

In the early turbojets: r ~ 6:1 – 8:1

Increasing r « variable » geometry to adapt the compressor

behavior to various regimes

Mechanical challenges of turbojet technology

30

Solution n° 1 : concept of variable stator blades

• Design of reliable airflow control systems

• Prevention of air leakage at the pivots of the vanes at high pressures (temperatures).

Variable stator vanes HP compressor


31

Solution n° 2: concept of multiple rotors (r ~ 20:1 - 30:1)

Example of a dual-rotor configuration

Fan HPC HPT LPT

CFM56

Advantages

• Selection of optimal speeds for the HP and LP stages.

• Reduction of the number of compressor stages.

• Cooling air is more easily taken between the LP and HP rotors.

• The starting of the engine is easier as only the HP rotor needs

to be rotated.


32

Rolls-Royce RB211 engine


33

Mechanical challenges

• Analysis of the dynamic behavior of multiple-rotor systems and

prediction of critical speeds.

• Design of disks.

Example

•2 (or even 3) coaxial rotors require to bore the HP disks to allow

passing the LP shaft

the stress level doubles (hole) and increases with the boring

radius

•To place the first critical speeds above the range of operational

speeds, the LP shaft diameter should be as high as possible.

Opposite requirements


34

2. Increasing the turbine temperature capability

Main technological challenge: the HP turbine temperature is conditioned by the combustion chamber outlet temperature.

SNECMA combustion chamber



Stress distribution in a structural element of the combustion chamber

35

2. Increasing the turbine temperature capability


Rotational velocity

Centrifugal acceleration

Disk load induced by the blades

Example of the SNECMA M88 HP turbine

36

In early turbojet engines: solid blades the maximum

admissible temperature was directly related to improvement of

structural materials (Tmax ~ 1100 °C)

From 1960-70: development of early air-cooled turbine blades

• hollow blades

• internal cooling of blades (casting using the ‘lost wax’

technique)


37

‘Lost wax’ process


HP nozzle guide vane coolingHP turbine blade cooling

Impingement tubes

Film cooling

Internal and film cooling

38

Today: single crystal casting


39Mechanical challenges of turbojet technology

Time (hrs)

Single crystal blades

Comparison of turbine blade life properties

(fixed temperature and stress levels)

Single crystal blades

Conventionally cast blade

Directionally solidified blades

Elo

ngation (

%) *

*

*

Fracture

40

3. Development of high-bypass ratio turbofans

Main technological challenge: mechanical resistance of fan blades

(without penalizing mass).

• Improvement of structural materials such as titanium alloys.

• Design of shrouded fan blades with a high length-to-chord aspect

ratio or of large-chord fan blades with honeycomb core.

• Knowledge of the dynamics of rotors stiffened by high gyroscopic

couples and submitted to large out of balance forces (e.g. fan blade

failure).

• Fan blade-off and containment analysis methods (e.g. blade loss).

• Use of Foreign Object Damage criteria (e.g. bird or ice impact on

fan, ingestion of water, sand, volcanic ashes,...).



41

Example of take-off/landing on a soaked runway


42

New concept: high by-pass engine wide chord fan blade

the weight is maintained at a low level by fabricating the blade

from skins of titanium incorporating a honeycomb core

Prop-fan concept

Wide chord fan blade construction

This configuration is still in an experimental state

Contra-rotating prop-fan


43

In practice:

• rotors usually present more than one disk and a significant distributed

mass of the shaft;

• supports are not rigid and present speed-dependent stiffness and

damping (produced by oil-film bearings) (≠ support of infinite mass);

• rotor-stator interactions may happen.

The Finite Element Method is commonly used in industry.

Dynamic analysis of industrial rotors

44

• 1D-model (beam elements): the most used for pilot-studies.

• 2D-model (plane or axisymmetric shell elements): practical interest

for projects.

• 3D-model (volume elements): used for detailed analyses.

Axisymmetric beam element Axisymmetric

shell element Volume element

Nodes


45

( )S AS+ Ω + ΩK C Kllll

( ) ( ) ( ) ( ), , t+ Ω + Ω + Ω =M q C q K q f q q g&& & &&& & &&& & &&& & &

( )S + Ω + ΩC G Cllll

Structural damping matrix

Gyroscopic matrix

Damping matrix of localized elements

Stiffness matrix of localized elements

Matrix of circulatory forces

Structural stiffness matrix

vector of nonlinear forces (associated to interaction elements)

vector of excitation forces

Mass matrix


Equations of motion

46

Type of analysis

• Stability analysis and determination of critical speeds

(Campbell diagram).

• Forced response to harmonic excitation.

• Forced response to transient excitation (crossing of critical speeds).

Solution methods for the eigenvalue problem

• Direct methods (substructuring techniques for large scale problems).

• Projection methods (pseudo-modal approach).


47

The mission profile consists of several different segments:

• take-off: 100 % ΩN (duration ~ 5 min.)

• maximum continuous: 110 % ΩN (during a very short time,

in case of failure of one of the engines)

• maximum climb: 98 % ΩN (duration ~ 30 min.)

• maximum cruise: 90 à 95 % ΩN

• idle: 75 % ΩN (during descent and diversion when landing)

and 50 % ΩN (warm-up and taxi manoeuvres).

Typical mission profile for a civil aircraft

48

The critical speeds should placed outside two zones:

50 % and [75% - 110%] of the nominal speed.

Typical mission profile for a civil aircraft

Take-off

Cruise

Step climb Continued cruise

Diversion

Hold

Landing

49

Summary of basic steps for the design:

• position the critical speeds outside the range of operational speeds

(e.g. a margin of 10% is usually taken).

• add external damping to lower the resonance amplitude peaks (in

order to keep the rotor-stator gap at the minimum and thus to

optimize engine performances).

• minimize excitation sources (balancing, alignment, optimization of

gaps).

• select low support stiffness (flexible bearing supports) in order to

reduce the dynamic load transmitted through the bearing to the

stator.

Baseline mechanical design of turbojets

50

Twin-spool front fan turbo-jet

(high by-pass ratio)

Take-off thrust of 11 340 daN

The CFM 56-5 jet engine (Airbus A320, A 340)

51

Low-pressure (LP) rotor

(9 nodes, 5 beam elements, 9 disks)

Casings

(15 nodes, 4 beam elements, 4 disks, 6 supplementary mass elements)

High-pressure (HP) rotor

(7 nodes, 3 beam elements, 7 disks)

( )1 25 8750.Ω = ×Ω +HP BP rpm


Schematic model of the jet engine

Bearings

Bearings

Intershaft bearing

52

1000 2000 3000 4000 5000 tours/min.

Campbell diagram Mode-shapes at 5000 rpm

200 –

100 –

ω Hz

1160

2490

3470 4260

5720

HPω = Ω

BPω = Ω

BPΩ

3.9 Hz

19.9 Hz

42.0 Hz

60.7 Hz

71.1 Hz

20803280

3730


53

Response to mass unbalance

on LP rotor (point A)

A B

10

1

0.1

10

1

0.1

1000 2000 3000 4000 5000 1000 2000 3000 4000 5000

At point A At point B

ΩBP ΩBP

1160 2490

3470

4260 5720 11602490

34704260

5720


54

Vibration phenomena are the main cause of failure

of compressor blades and disks.

Requirements

Ability to predict:

• natural frequencies (i.e. to identify critical speeds);

• mode-shapes (i.e. to establish vulnerability to vibrate and

locations of maximum stresses);

• damping levels (i.e. severity of resonance);

• response levels (i.e. fatigue susceptibility);

• stability (i.e. vulnerability to flutter).

Structural dynamics of blades and disks

55

Campbell diagrams

(Natural frequencies vs. Rotation speed)

Standard format for presentation of blade vibration properties in

order to illustrate the essential features and regions of probable

vibration problem areas.

Structural dynamics of blades and disks

56

Structural stiffness matrix

( ) 2S g C C+ − ΩK K σ M

( ) ( ) ( )2C C, t , , ,++ Ω + Ω = ΩM q G q K σ q F g q q&& & &&& & &&& & &&& & &

Gyroscopic matrix

Centrifugal mass matrix

Geometric stiffness matrix

Vector of static centrifugal forces

Vector of external forces

Mass matrix

Equations of motion

Dynamic analysis methods for practical blades

57

Type of analysis and solution methods

Static analysis (in order to determine the stress distribution due

to the centrifugal forces)

( ) ( ) ( )2C C, t , , ,++ Ω + Ω = ΩM q G q K σ q F g q q&& & &&& & &&& & &&& & &

( ) 2S g C C+ − ΩK K σ M

( )( ) ( )2 2S g C C C+ − Ω = Ω +K K σ M q F g

This equation is nonlinear, since σσσσC is unknown a priori the solution

needs an iterative process, such as the Newton-Raphson method.


58

Dynamic analysis

( ) 0C ,+ Ω =M q K σ q&&&&&&&&

As the Coriolis effects can be neglected (this is usually so for radial

blades), the equations of motion reduce to

where K has been determined by a preliminary static analysis.

The solution of this equation for different values of Ω allows to

construct the Campbell diagram.


59

Frequency(Hz)

Rotation speed (rpm)

Engine Order 1

Engine Order 2

Engine Order 3

Engine Order 4

Engine Order 5

Engine Order 6

Engine Order 72nd Bending (Flap)

1st Torsion (Edge)

1st Bending (Flap)

Campbell diagram of a compressor blade

1000

500


60

Supersonic stall flutter

Types of flutter

High incidence supersonic

flutter

Subsonic/Transonic stall flutter (one of the most encountered in practice)

Classical unstalled

supersonic flutter

Choke flutter

Surge line

Operating line

Pre

ssure

ratio

Corrected mass flow rate

50 % 75 % 100 %

Flutter design methodology

61

Shroud or interconnected tip

The design of the first blades of the compressor is governed by

aeroelastic problems.

Criterion: c x f1 > threshold limit

chord

1st natural frequency (torsion or bending)

First solution

Make the chord wider

high weight construction of the blade with a honeycomb core,

which renders the fabrication more complex (high cost).

2( )h c


62

Second solution

Make the first natural frequency f1 higher (and bring damping)

• shrouded blades

• or fixed tip

Take care to the mechanical resistance (high centrifugal effect

at the external diameter).

2 5 3h c .( to )

3 5( )h c .

c x f1 > threshold limit

chord

1st natural frequency (torsion or bending)

Criterion


63

Disks may have different shapes depending on their location into the engine

ring

Drum

HP compressor

Hollow constant-thickness disks

HP and LP turbines

Driving flange

Disks of varying

thickness

FanLP compressor

Mechanical design of disks

64Mechanical design of disks

65

Sources of stresses in a rotor disk

• Centrifugal body force of disk material;

• Centrifugal load produced by the blades and their attachments to

the disk;

• Thermo-mechanical stresses produced by temperature gradients

between bore and rim;

• Shear stresses produced by torque transmission from turbine to

compressor;

• Bending stresses produced by aerodynamic loads on the blades;

• Dynamical stresses of vibratory origin;


66

Damage tolerance philosophy

Initial defect

size

Return to service intervals

cycles

Crack size

Safety limit

Detection limit


Assumed life curves

67

An « optimal » mechanical design requires:

1. The precise determination of physical parameters

(temperature, stress and strain distributions) use of refined

finite element models, thermo-elasto-viscoplastic analyses.

2. The perfect understanding of the material properties and the

conditions which lead to failure this corresponds to the use

of an equivalent safety factor of 1.5 or less.

Mechanical design of turbine blades

68

In summary, the mechanical design of turbojets is challenging.

One of the first challenge is the study of the dynamics of multiple rotor

systems submitted to large gyroscopic couples.

Then, depending on the engine component (blade, disk) and on its

location within the engine, problems are of very different nature:

• In the « cold » parts of the engine (fan, LP compressor, HP

compressor), the mechanical design is based on the solution of

dynamical problems (blade vibrations, aeroelastic flutter, bird

impact).

• In the « hot » parts of the engine (HP compressor, combustion

chamber, HP turbine), the design is based on creep and fatigue

calculations and a damage tolerance philosophy is applied.

Conclusion

Documents

Cours de conception aéronautique Dimensionnement · PDF fileDimensionnement mécanique des turbomaréacteurs Introduction au ... Principles of jet propulsion ... Brief review of the