Dimensionnement mécanique des turbomaréacteurs AERO0015-1 - MECHANICAL MECHANICAL DESIGN OF TURBOMACHINERY - AERO0015-1 - CS-J.-C. GOLINVAL5 ECTS - Reference : Introduction au au Introduction dimensionnement Cours de conception conception de Cours aéronautique mécanique et dynamique des dynamique et mécanique turboréacteurs 2 Principles of jet propulsion

Comparison between the working cycle of a turbo-jet engine

Air intake Compression Combustion Exhaust

and a piston engine

Air intake Compression Combustion Exhaust 3 Principles of jet propulsion

For aircraft propulsion, the thrust is produced by the acceleration of the air passing through the engine.

Low pressure (LP) Combustion Low pressure (LP) compressor chamber turbine

Exhaust

High pressure (HP) High pressure (HP) compressor turbine 4 Principles of jet propulsion

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

Fcompressor Fcombustion Fturbine Fexhaust (85 kN) 150 kN 180 kN 25 kN

235 kN 205 kN

Total thrust = 30 kN. Forward. 5 Brief review of the evolution of turbojet engines

France

1921 GUILLAUME patent combustor

axial-flow axial-flow turbine compressor

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) 6 Brief review of the evolution of turbojet engines

United Kingdom

1930 : patent of Frank WHITTLE’s turbojet engine

combustor radial compressor stage exhaust nozzle

Multistage, axial- flow compressor axial-flow turbine 7 Brief review of the evolution of turbojet engines

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

Compressor Diffuser 1937 Wittle’s engine (WU)

Turbine

Helicoidal combustion chamber 8 Brief review of the evolution of turbojet engines

United States

• 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. 9 Brief review of the evolution of turbojet engines

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 Brief review of the evolution of turbojet engines

Germany

First jet engine leading to mass production

JUMO 004 turbojet engine

Starter motor Control cone Cooling air duct

Combustion chamber 11 Brief review of the evolution of turbojet engines

Germany

JUMO 004 development and production schedule

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

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

Failure was due to the lack of turbine materials capable of withstanding the high stresses at high temperatures. 12 Brief review of the evolution of turbojet engines

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 Development process of the structural design

Industrialization Testing Program

Preliminary Certification Request Detailed Design Design For Review Proposal

Program First Engine Launch To Turn milestone

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

Today, the duration of this process is about 3 years (against ~ 6 years in the 90s) 14 Preliminary design

Thrust requirement: for various operating points (limits of the flight envelope) Engine maximum power Altitude Aircraft structure maximum temperature Minimum (max Mach) aircraft Aircraft structure maximum pressure aerodynamic lift Speed

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. 15 Challenges of turbojet technology

Overall efficiency of a jet propulsion engine

Overall efficiency

η η η = × overall thermal propulsive

Thermal efficiency Propulsive efficiency 16 Challenges of turbojet technology

Thermal efficiency

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

η = − T0 thermal 1 T3 Thermodynamic cycle 3

4 2 1 e Temperature 0 0 1 2 3 4 e Entropy 17 Challenges of turbojet technology

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

thrust flight velocity

η =F V 0 = 2 propulsive & + Wout V e V 0 1

total power exit velocity output 18 Challenges of turbojet technology

If the propulsive efficiency is plotted versus the velocity ratio Ve / V 0 , it follows that high propulsive efficiency requires the exit velocity to be approximately equal to the inlet velocity.

100 90 80 70 propulsive 60 η 50 40

1 2 3 4

Ve / V 0 19 Challenges of turbojet technology

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 Challenges of turbojet technology

2. Increase the ratio of power-output to engine weight by increasing the turbine inlet temperature

Trend in turbine inlet temperatures

°C

Military

Commercial

Turbine Turbine inlet temperature Year 21 Challenges of turbojet technology

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 Challenges of turbojet technology

Supersonic flight

If the turbine inlet temperature reaches its limit,

‰ thrust augmentation by afterburning.

Thermodynamic cycle Afterburner 3 6 Nozzle 2 4 1

Temperature 0 0 1 2 3 4 5 6 S Entropy 23 Challenges of turbojet technology

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 Challenges of turbojet technology

SNECMA M88 engine

Disks ∆∆∆σσσ r = 1000 MPa 1580 °C ∆∆∆σσσθθθ = 1000 MPa θθθ = 650 °C locally 600 °C max

Titanium Nickel base alloy superalloy 25 Challenges of turbojet technology

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.

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

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 26 Challenges of turbojet technology

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 27 Challenges of turbojet technology

Trend in thrust specific fuel consumption

Single-pool axial flow turbojet

Twin-spool by-pass turbojet

Twin-spool front fan turbojet Advanced technology (high by-pass ratio)

Propfan

Year 28 Challenges of turbojet technology

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 Mechanical challenges of turbojet technology

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 30 Mechanical challenges of turbojet technology

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).

HP compressor Variable stator vanes 31 Mechanical challenges of turbojet technology

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 Mechanical challenges of turbojet technology

Rolls-Royce RB211 engine 33 Mechanical challenges of turbojet technology

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 Mechanical challenges of turbojet technology

Evolution of turbojet engines - mechanical aspects

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 Mechanical challenges of turbojet technology

2. Increasing the turbine temperature capability

Example of the SNECMA M88 HP turbine

Rotational velocity

Centrifugal acceleration

Disk load induced by the blades 36 Mechanical challenges of turbojet technology

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 Mechanical challenges of turbojet technology

HP turbine blade cooling HP nozzle guide vane cooling

Internal and film cooling Impingement tubes

Film cooling

‘Lost wax’ process 38 Mechanical challenges of turbojet technology

Today: single crystal casting 39 Mechanical challenges of turbojet technology

Comparison of turbine blade life properties (fixed temperature and stress levels)

* Fracture Directionally * Single solidified blades crystal blades

Conventionally cast blade * Single crystal blades Elongation (%) Elongation

Time (hrs) 40 Mechanical challenges of turbojet technology

Evolution of turbojet engines - mechanical aspects

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 Mechanical challenges of turbojet technology

Example of take-off/landing on a soaked runway 42 Mechanical challenges of turbojet technology

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

Contra-rotating prop-fan

This configuration is still Wide chord fan blade in an experimental state construction 43 Dynamic analysis of industrial rotors

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. 44 Dynamic analysis of industrial rotors

• 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.

Nodes

Axisymmetric beam element Axisymmetric shell element Volume element 45 Dynamic analysis of industrial rotors

Equations of motion Stiffness matrix of localized elements + Ω + Ω KCKS AS lll ( ) Mass matrix Matrix of circulatory forces Structural stiffness matrix

MqC&&+( Ω) qK & +( Ω) qfqq +( , & , Ω) = g ( t ) vector of excitation forces

vector of nonlinear forces + Ω + Ω CGCS lll ( ) (associated to interaction elements)

Damping matrix of localized elements Gyroscopic matrix Structural damping matrix 46 Dynamic analysis of industrial rotors

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 Typical mission profile for a civil aircraft

The mission profile consists of several different segments: Ω • take-off : 100 % N (duration ~ 5 min.) Ω • maximum continuous : 110 % N (during a very short time, in case of failure of one of the engines) Ω • maximum climb : 98 % N (duration ~ 30 min.) Ω • maximum cruise : 90 à 95 % N Ω • idle : 75 % N (during descent and diversion when landing) Ω and 50 % N (warm-up and taxi manoeuvres). 48 Typical mission profile for a civil aircraft

Step climb Continued cruise Cruise

Diversion

Hold

Take-off Landing

‰ The critical speeds should placed outside two zones: 50 % and [75% - 110%] of the nominal speed. 49 Baseline mechanical design of turbojets

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

Twin-spool front fan turbo-jet (high by-pass ratio)

Take-off thrust of 11 340 daN 51 The CFM 56-5 jet engine (Airbus A320, A 340)

Schematic model of the jet engine

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

Bearings Intershaft bearing

Bearings

Low-pressure (LP) rotor High-pressure (HP) rotor (9 nodes, 5 beam elements, 9 disks) (7 nodes, 3 beam elements, 7 disks)

Ω = ×Ω + ( ) HP125. BP 8750 rpm 52 The CFM 56-5 jet engine (Airbus A320, A 340)

Campbell diagram Mode-shapes at 5000 rpm

ω Hz 3.9 Hz ω = Ω HP 3730 19.9 Hz 3280 200 – 2080

42.0 Hz

100 – 60.7 Hz 5720 ω = Ω 3470 4260 BP 2490 71.1 Hz Ω 1160 BP 1000 2000 3000 4000 5000 tours/min. 53 The CFM 56-5 jet engine (Airbus A320, A 340)

Response to mass unbalance A B on LP rotor (point A)

At point A At point B

3470

10 10 5720 4260 5720 2490 1160 1160 3470 2490 4260

1 1

0.1 0.1

1000 2000 3000 4000 5000Ω 1000 2000 3000 4000 5000 Ω BP BP 54 Structural dynamics of blades and disks

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). 55 Structural dynamics of blades and disks

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. 56 Dynamic analysis methods for practical blades

Equations of motion

+σ − Ω2 KKSgC( ) M C

Centrifugal mass matrix Mass matrix Geometric stiffness matrix

Structural stiffness matrix

&&+ Ω & +σ Ω = Ω2 + & M q G q K( C,)q F C ( ) g( t,,, q q )

Vector of external forces Gyroscopic matrix Vector of static centrifugal forces 57 Dynamic analysis methods for practical blades

Type of analysis and solution methods

&&+ Ω & +σ Ω = Ω2 + & M q G q K( C,)q F C ( ) g( t,,, q q )

+σ − Ω2 KKSgC( ) M C

Static analysis (in order to determine the stress distribution due to the centrifugal forces)

+(σ ) −Ω2 =Ω+ 2 (KKSgCMqF C) C ( ) g

σσσ This equation is nonlinear, since C is unknown a priori ‰ the solution needs an iterative process, such as the Newton-Raphson method. 58 Dynamic analysis methods for practical blades

Dynamic analysis

As the Coriolis effects can be neglected (this is usually so for radial blades), the equations of motion reduce to &&&&&& +σ Ω = M q K( C , )q 0

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 Dynamic analysis methods for practical blades

Campbell diagram of a compressor blade

Frequency 1000 (Hz) 2nd Bending (Flap) Engine Order 7

Engine Order 6

Engine Order 5

Engine Order 4

500 1st Torsion (Edge) Engine Order 3

1st Bending (Flap) Engine Order 2

Engine Order 1

Rotation speed (rpm) 60 Flutter design methodology

Types of flutter Supersonic stall flutter High incidence supersonic Surge line flutter Subsonic/Transonic stall flutter (one of the most encountered in practice)

Classical unstalled supersonic flutter

Pressure ratio Pressure 100 % 50 % 75 %

Operating line Corrected mass flow rate Choke flutter 61 Flutter design methodology

Shroud or interconnected tip

The design of the first blades of the compressor is governed by aeroelastic problems.

1st natural frequency (torsion or bending)

Criterion: c x f1 > threshold limit

chord

First solution Make the chord wider (h c 2 ) high weight construction of the blade with a honeycomb core, which renders the fabrication more complex (high cost). 62 Flutter design methodology

1st natural frequency (torsion or bending)

Criterion c x f1 > threshold limit

chord

Second solution

Make the first natural frequency f1 higher (and bring damping) • shrouded blades (h c 2 . 5 to 3 ) • or fixed tip (h c 3 . 5 ) Take care to the mechanical resistance (high centrifugal effect at the external diameter). 63 Mechanical design of disks

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

ring Drum

HP and LP turbines Disks of HP compressor varying thickness

Hollow constant-thickness disks Driving flange 64 Mechanical design of disks 65 Mechanical design of disks

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 Mechanical design of disks

Damage tolerance philosophy

Crack size Assumed life curves

Safety limit

Detection limit Initial defect size cycles

Return to service intervals 67 Mechanical design of turbine blades

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. 68 Conclusion

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.