THE BIRTH OF JET PROPULSION

Working Principle of Propeller m V jet

m Vaircraft

Aerofoil Theory of Propeller

 V jet  Vaircraft  Fthrust  m

Anatomy of Propeller

Capacity of Propeller

 V jet  Vaircraft  Fthrust  m

Engines to drive propeller

Need for Alternative Propulsion Method • Dr. Hans von Ohain and Sir Frank Whittle are both recognized as being the co-inventors of the jet engine. • Each worked separately and knew nothing of the other's work. • Hans von Ohain is considered the designer of the first operational turbojet engine. • Frank Whittle was the first to register a patent for the turbojet engine in 1930. • Hans von Ohain was granted a patent for his turbojet engine in 1936. • However, Hans von Ohain's jet was the first to fly in 1939. • Frank Whittle's jet first flew in in 1941.

Parallel Invention • Doctor Hans Von Ohain was a German airplane designer who invented an operational jet engine. • Hans Von Ohain, started the investigating a new type of aircraft engine that did not require a propeller. • Only twenty-two years old when he first conceived the idea of a continuous cycle combustion engine in 1933. • Hans Von Ohain patented a jet propulsion engine design similar in concept to that of Sir Frank Whittle but different in internal arrangement in 1934. • Hans Von Ohain joined Ernst Heinkel in 1936 and continued with the development of his concepts of jet propulsion.

• A successful bench test of one of his engines was accomplished in September 1937. • A small aircraft was designed and constructed by Ernst Heinkel to serve as a test bed for the new type of propulsion system - the Heinkel He178. • The Heinkel He178 flew for the first time on August 27, 1939. • The pilot on this historic first flight of a jet-powered airplane was Flight Captain Erich Warsitz.

Think Different…. •A Royal Air Force officer. •His first attempts to join the RAF failed as a result of his lack of height, but on his third attempt he was accepted as an apprentice in 1923. • He qualified as a pilot officer in 1928. •As a cadet Whittle had written a thesis arguing that planes would need to fly at high altitudes, where air resistance is much lower, in order to achieve long ranges and high speeds.

• Piston engines and propellers were unsuitable for this purpose. • He concluded that rocket propulsion or gas turbines driving propellers would be required. • Jet propulsion was not in his thinking at this stage. • By October 1929, he had considered using a fan enclosed in the fuselage to generate a fast flow of air to propel a plane at high altitude. • A piston engine would use too much fuel, so he thought of using a gas turbine. • After the Air Ministry turned him down, he patented the idea himself.

• In 1935, Whittle secured financial backing and, with Royal Air Force approval, Power Jets Ltd was formed. • They began constructing a test engine in July 1936, but it proved inconclusive. • Whittle concluded that a complete rebuild was required, but lacked the necessary finances. • Protracted negotiations with the Air Ministry followed and the project was secured in 1940. • By April 1941, the engine was ready for tests. The first flight was made on 15 May 1941. • By October the United States had heard of the project and asked for the details and an engine. • A Power Jets team and the engine were flown to Washington to enable General Electric to examine it and begin construction.

• The Americans worked quickly and their XP-59A Aircomet was airborne in October 1942, some time before the British Meteor, which became operational in 1944. • The jet engine proved to be a winner, particularly in America where the technology was enthusiastically embraced.

The biggest aircraft An-225 Cossack 1,322,750 lb L: 275'7";S: 290' The An-225 Cossack is the largest airplane in the world. Powerplant: 6× ZMKB Progress D-18 turbofans, 229.5 kN each

The popular Biggest Aircrafts in the World

#

Plane Max. Weight Dimensions 1. Hindenburg * 484,400 lb L: 804';D: 135' An-225 Cossack 1,322,750 lb L: 275'7";S: 290' 2. The An-225 Cossack is the largest airplane in the world. HK-1 Spruce Goose 400,000 lb L: 218'6";S: 320' 3. The HK-1 Spruce Goose has the largest wingspan of all aircraft. Airbus A380F 1,305,000 lb L: 239'3";S: 261'8" 4. The Airbus A380F is the largest passenger airliner in the world. 5. KM Caspian Sea Monster 1,080,000 lb L: 348';S: 131' L: 226'8.5";S: 6. An-124 Condor 892,872 lb 240'5.75" 7. C-5 Galaxy 840,000 lb L: 247'10";S: 222'9" 8. Boeing 777-300ER 775,000 lb L: 242'4";S: 212'7" 9. Airbus A340-600 807,400 lb L: 246'11";S: 208'2" 10. Boeing 747

875,000 lb

L: 231'10";S: 211'5"

The world's largest aircraft engine, the GE90-115B

Max. Thrust: 569kN

The fastest Aircraft • X-15 is having a 4,520 mph world speed record. • Fastest manned aircraft. • Not only is the North American X-15 the fastest piloted aircraft ever, it is the highest flying. • Thrust was obtained from one engine that produced 313kN at maximum altitude. • The North American X-15 was produced to explore the limits of sub-orbital supersonic flight. • Three were produced. They flew a total of 199 times. • The X-15 first took to the sky on June 8, 1959. The last flight took place on Oct. 24, 1968. A 200th flight was never made, even after several attempts.

Course Overview

• This undergraduate level course teaches the principles of jet propulsion. • The primary focus of the course is on the teaching of thermodynamics and Gas dynamics in aircraft engines. • The course provides information that will enable the engineering analysis of • ramjets and turbine engines and • its separate components including inlets, nozzles, combustion chambers, compressors, and turbines.

Course Objectives • Students successfully completing MEL 341 will get: • A basic understanding of thermodynamic cycles of jet engines. • A basic understanding of the rational behind several types of jet engines. • A basic understanding of the compressible fluid flow in inlets and compressors and turbines. • A basic understanding of the combustion physics in combustion chambers. • The ability to analyze jet engines; determine propulsion efficiency and design inlets and nozzles.

Course Contents • UNIT- I: PROPULSION • Aircraft Propulsion – introduction -- Early aircraft engines -Types of aircraft engines -- Reciprocating internal combustion engines -- Gas turbine engines -- Turbo jet engine -- Turbo fan engine -- Turbo-prop engine • Aircraft propulsion theory: thrust, thrust power, propulsive and overall efficiencies -- Problems. • UNIT- II: THERMODYNAMIC ANALYSIS OF IDEAL PROPULSION CYCLES • Thermodynamic analysis of turbojet engine – Study of subsonic and supersonic engine models -- Identification and Selection of optimal operational parameters. Need for further development – Analysis of Turbojet with after burner.

• Thermodynamic analysis of turbofan engine – Study of subsonic and supersonic systems -- Identification and selection of optimal operational parameters. Design of fuel efficient engines – Mixed flow turbo fan engine – Analysis of Turbofan with after burner. • Thermodynamic analysis of turbo-prop engine – Identification and selection of optimal operational parameters.

UNIT –III: GAS DYNAMICS OF PASSIVE COMPONENTS OF TURBO ENGINES • FUNDAMENTALS OF GAS DYNAMICS : Energy equation for a non-flow process -- Energy equation for a flow process -- The adiabatic energy equation -- Momentum Equation --Moment of Momentum equation -- Stagnation Velocity of Sound --Stagnation Pressure -- Stagnation Density -- Stagnation State -- Velocity of sound -- Critical states -- Mach number -- Critical Mach number -Various regions of flow. • ANALYSIS OF DIFFUSERS AND NOZZLES: Introduction – study of intakes for subsonic and supersonic engines -- Comparison of isentropic and adiabatic processes -- Mach number variation -Area ratio as function of Mach numbers -- Impulse function -- Mass flow rates -- Flow through nozzles -- Flow through diffusers – Effect of friction -- Analysis of intakes for supersonic engines – intakes with normal shock – oblique shocks – Study of special supersonic nozzles and diffusers.

UNIT –IV: STUDY OF COMPRESSORS • Design and Analysis of compressors – Classification – analysis of centrifugal compressors – velocity triangles – design of impellers and diffusers – analysis of axial flow compressor – analysis of stage – characterization of stage – design of multistage axial flow compressor – Performances analysis of centrifugal and axial flow compressors. •

• UNIT –V: GAS DYNAMICS OF COMBUSTORS • Stoichimetry of combustion – calculation air-fuel ratio – gas dynamics of combustors – thermal loading factors – design and selection of combustors. • UNIT –VI: STUDY OF TURBINES • Concept of gas turbine – analysis of turbine stage – velocity triangles and characterization of blades and stages – Design of multistage axial flow turbine – Performance analysis of turbines. • UNIT –VI: ADDITIONAL TOPICS • Thermodynamic analysis real turbo engine cycles – performance analysis and thermodynamic optimization. • Introduction to ramjets – study of rocket engines – study of missile engines.

Books & References • • • • • • • •

• • •

Jet Propulsion: Flack, R.D.., “Fundamentals of Jet Propulsion”, Cambridge University Press, 2005. Baskharone, E.A., “Principles of Turbomachinery in Air-Breathing Engines”, Cambridge University Press, 2006. Kerrebrock J.L., “Aircraft Engines and Gas Turbines”, MIT Press, 1992. Mattingly, J.D., “Elements of Gas Turbine Propulsion”, McGraw-Hill Inc., 1996. Gas Dynamics: Anderson, J.D., “Modern Compressible Flow: With Historical Perspective”, McGrawHill, 2002. Zuker, R.D., and Biblarz, O.,”Fundamentals of Gas Dynamics”, John Wiley & Sons Inc., 2002. Thompson, P. A. Compressible Fluid Dynamics. Maple Press Company, 1984. Saad, M.A.,”Compressible Fluid Flow”, Prentice-Hall, 1993. Liepmann, H., and A. Roshko. Elements of Gas Dynamics. John Wiley Publishers, 1957.

Propulsion - Overview • • • • • •

What is propulsion? The word is derived from two Latin words: pro meaning before or forwards and pellere meaning to drive. Propulsion means to push forward or drive an object forward. A propulsion system is a machine that produces thrust to push an object forward. • On airplanes, thrust is usually generated through some application of Newton's third law of action and reaction. • A gas, or working fluid, is accelerated by a machine, and the reaction to this acceleration produces a force on the engine.

Classification of Propulsion Systems

Jet Propulsion • Operating principle based on Newton’s laws of motion. – 2nd law - rate of change of momentum is proportional to applied thrust (i.e. F = m a) – 3rd law - every action has an equal and opposite reaction.

Classification of Systems • Only the practical thermo-chemical category will be considered further in this Course. • This may be split into two main sub-categories: • Rockets (Solid or Liquid Propellant);

• Air Breathers (Ramjet, Turbojet , Turbofan & Turboprop); • along with a Hybrid Ram rocket. • The fundamental operating principle common in all these cases is , that of jet or reaction propulsion, i.e. by generating highvelocity exhaust gases.

Jet Characteristics • Quantities defining a jet are: – cross-sectional area; – composition; – velocity. • Of these, only the velocity is a truly characteristic feature and is of considerable quantitative significance.

Jet Characteristics of Practical Propulsion Systems System

Jet Velocity (m/s)

Turbofan

200 - 600

Turbojet (sea-level, static)

350 - 600

Turbojet (Mach 2 at 36000 ft)

900 - 1200

Ramjet (Mach 2 at 36000 ft)

900 - 1200

Ramjet (Mach 4 at 36000 ft)

1800 - 2400

Solid Rocket

1500 – 2600

Liquid Rocket

2000 – 3500

Introduction to Rockets

Solid Propellant Rocket - Basic Operating Features • Four basic components:

– motor case, nozzle, solid propellant charge, igniter. • Propellant charge comprises combined fuel & oxidizer. • Gaseous combustion products fill void at high pressure (70 bar typically) and sustains combustion. • Hot gases vent through convergent-divergent nozzle to provide high-speed (supersonic) propulsion jet. • Gases generated and escape at fixed rate for steady operation by maintaining constant burning surface area.

Solid Propellant Rocket for GW

Rapier

• Jet velocity: 1500-2600m/s • Most widely used in GW

• Short, medium range (< 50 km) • Simple, reliable, easy storage, high T/W

Solid Rocket Features • High propellant density (volume-limited designs). • Long-lasting chemical stability. • Readily available, tried and trusted, proven in service. • No field servicing equipment & straightforward handling. • Cheap, reliable, easy firing and simple electrical circuits.

But • Lower specific impulses (compared with liquid rockets). • Difficult to vary thrust on demand. • Smokey exhausts (especially with composite propellants). • Performance affected by ambient temperature.

Liquid Propellant Rocket - Basic Operating Features • Fuel and oxidant tanked separately and delivered to combustion chamber at specific rates and pressures. • Propellant flowrates (and hence thrust) variable upon demand. • Disadvantages compared with solid propellant rockets: – increased complication; – Storage problems (usually LOX & LH2 which must be maintained at very low temperatures); – more costly; – reduced reliability.

Liquid Propellant Rocket - Space

• Jet velocity: 2000 - 3500m/s. • Highest thrust, can be throttled. • Long sustained flight (5mins+).

Ariane 5

Space Transportation System (STS)

Travel Cycle of Modern Spacecrafts

Rentering Space Craft

Major Knowledge Gains Through Gas Dynamics • Simple principles of Gas Dynamics, it was showed that the heat load experienced by an entry vehicle was inversely proportional to the drag coefficient. • The greater the drag, the less the heat load. • Through making the reentry vehicle blunt, the shock wave and heated shock layer were pushed forward, away from the vehicle's outer wall. • Since most of the hot gases were not in direct contact with the vehicle, the heat energy would stay in the shocked gas and simply move around the vehicle to later dissipate into the atmosphere.

Means to Create A Jet

Jet Characteristics

FT  m jetV jet  m airVac • Quantities defining a jet are: – cross-sectional area; – composition; – velocity.

m jet   jet AjetV jet

FT   jet AjetV jet  m airVac 2

Of these, only the velocity is a truly characteristic feature and is of considerable quantitative significance.

Jet Characteristics of Practical Propulsion Systems System

Jet Velocity (m/s)

Turbofan

200 - 600

Turbojet (sea-level, static)

350 - 600

Turbojet (Mach 2 at 36000 ft)

900 - 1200

Ramjet (Mach 2 at 36000 ft)

900 - 1200

Ramjet (Mach 4 at 36000 ft)

1800 - 2400

Solid Rocket

1500 – 2600

Liquid Rocket

2000 – 3500

Nozzle : Steady State Steady Flow in

jet

First Law :

    V V  Qcv  m  h   gz   m  h   gz   Wcv 2 2  in   jet 2

2

No heat transfer and no work transfer & No Change in potential energy. 2 2

 V  h  2 

  V    h  2 in 

   jet

Combined analysis of conservation of mass and first law 2

 m   m  hin     h jet      jet A jet   in Ain 

2

A SSSF of gas through variable area duct can interchange the enthalpy and kinetic energy as per above equation. Consider gas as an ideal and calorically perfect. 2 2     V Vin   jet  c p Tin    c pT0   c p T jet  2c p  2c p   

How to Create A Jet? in

jet

Isentropic expansion of an ideal and calorically perfect gas.

Tin  pin    T jet  p jet 

 1 

2 2     V Vin   jet  c p Tin    c pT0   c p T jet  2c p  2c p   

How and What to do?

    Vin2  c p Tin    cp  2c p     

Tin  pin     p jet 

 1 

At Design Conditions:

    Vin2  c p Tin    cp  2c p     

Tin  pin  p   

 1 

  2  V jet     c pT0 2c p   

  2 V jet     c pT0 2c p   

Engines to Create a Jet ???

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According To The Evidence

“The heavens cried out, the earth bellowed an answer, lightening flashed forth, fire flamed upwards, it rained down death. The brightness vanished, the fire was extinguished. Everyone who was struck by the lightening was turned to ashes”. And again from the same source: “It was a ghastly sight to see. The corpses of the fallen were so mutilated they no longer looked like human beings. Never before have we seen such an awful weapon, and never before have we heard of such a weapon”.

The Ancient Technique : Ramjets • Only three operating components: – intake (diffuser); – burner (combustion chamber); – nozzle.

Typical Ramjet Schematic

Ramjets - Basic Operating Features • Air decelerated in intake (diffuser) and pressure rises due to ram effect. • Known as ram pressure and significant at supersonic speeds.

• A ramjet therefore needs neither a compressor nor a turbine, simplifying the design and reducing the cost. • Greatest disadvantage is that it has to be accelerated up to very high speed before it produces any useful thrust. • Also complicated supersonic intake required to avoid shock losses - could be nose, side or ventral mounted. 54

Ramjets (Front Intake) for GW

• Jet velocity: 900-2400m/s

• Complex intake • No static thrust (has to be boosted up to speed)

Sea Dart • Mechanically simple, reliable cheap & tolerant of high temperatures. 55

Introduction to Rockets

Solid Propellant Rocket - Basic Operating Features • Four basic components:

– motor case, nozzle, solid propellant charge, igniter. • Propellant charge comprises combined fuel & oxidizer. • Gaseous combustion products fill void at high pressure (70 bar typically) and sustains combustion. • Hot gases vent through convergent-divergent nozzle to provide high-speed (supersonic) propulsion jet. • Gases generated and escape at fixed rate for steady operation by maintaining constant burning surface area.

Solid Propellant Rocket for GW

Rapier

• Jet velocity: 1500-2600m/s • Most widely used in GW

• Short, medium range (< 50 km) • Simple, reliable, easy storage, high T/W

Solid Rocket Features • High propellant density (volume-limited designs). • Long-lasting chemical stability. • Readily available, tried and trusted, proven in service. • No field servicing equipment & straightforward handling. • Cheap, reliable, easy firing and simple electrical circuits.

But • Lower specific impulses (compared with liquid rockets). • Difficult to vary thrust on demand. • Smokey exhausts (especially with composite propellants). • Performance affected by ambient temperature.

Liquid Propellant Rocket - Basic Operating Features • Fuel and oxidant tanked separately and delivered to combustion chamber at specific rates and pressures. • Propellant flowrates (and hence thrust) variable upon demand. • Disadvantages compared with solid propellant rockets: – increased complication; – Storage problems (usually LOX & LH2 which must be maintained at very low temperatures); – more costly; – reduced reliability.

Liquid Propellant Rocket - Space

• Jet velocity: 2000 - 3500m/s. • Highest thrust, can be throttled. • Long sustained flight (5mins+).

Ariane 5

Space Transportation System (STS)

Closure • • • • • • • • • •

Ramjet Advantages: -Low Weight -High Thrust to Weight Ratio. -No moving parts keep initial and maintenance costs down. -Large Thrust to Unit Frontal Area. -Provides best specific fuel consumption of all air breathing engines at supersonic speeds. Ramjet Disadvantages: -Does not work well at off design Mach numbers without a variable geometry diffuser and supersonic spike. -By the nature of air compression, does not provide static thrust. -Fuel consumption at subsonic speeds is very high compared to other air breathing engines.

Unit II Introduction to Jet Propulsion

Global Momentum Analysis

Momentum Equation

Vac

Vjet

pinlet

pexit Newton’s Second Law of Motion

dM cm  Fsurface  dt

Reynolds Transport Theorem: dM cm dM cv   M exit  M inlet dt dt

 Fsurface 

dM cv  M exit  M inlet dt

For a frictionless flight, pressure forces are only the surface forces…

 pinlet Ainlet   pexit Aexit  Fductwall 

dM cv  M exit  M inlet dt

Steady state steady flow

p

inlet

p

inlet

Ainlet   pexit Aexit  Fductwall  M exit  M inlet

 jetV jet  m  airVair Ainlet   pexit Aexit  Fductwall  m

 jetV jet  m  airVair Fductwall   pinlet Ainlet   pexit Aexit  m

 jetV jet  m  airVair Fductwall   pinlet Ainlet   pexit Aexit  m

Pressure Thrust

Momentum Thrust

At design cruising conditions : Pressure thrust is zero.

pinlet  pexit  patm  jetV jet  m  airVair Fthrust  m

Generation of Thrust : The Capacity Thrust

FT  m jetV jet  m airVac  air  m  fuel V jet  m  airVac FT  m

 air 1  f V jet  Vac  FT  m f : Fuel-air ratio

Dynamic Equilibrium : Cruising Vehicle

For a cruising vehicle:

 air 1  f V jet  Vac  drag on Vehicle FT  m 2 ac

V m air 1  f V jet  Vac   Cdrag air Aac 2

Drag on Aircraft

Generation of Lift

Drag Coefficient of an Air Craft

Generation of Lift

Drag Coefficient of an Air Craft

Lift - to - Drag Ratio Flight article

Scenario

L/D ratio

Virgin Atlantic GlobalFlyer

Cruise

37[

Lockheed U-2

Cruise

~28

Rutan Voyager

Cruise[4]

27

Albatross Boeing 747

20 Cruise

17

Common tern

12

Herring gull

10

Concorde

M2 Cruise

7.14

Cessna 150

Cruise

7

Concorde

Approach

4.35

House sparrow

4

Minimum Drag Coefficients Aircraft RQ-2 Pioneer North American Navion

Type Single piston-engine UAV Single piston-engine general aviation

Aspect Ratio 9.39 6.20

CDmin 0.0600 0.0510

Cessna 172/182

Single piston-engine general aviation

7.40

0.0270

Cessna 310

Twin piston-engine general aviation

7.78

0.0270

Marchetti S-211

Single jet-engine military trainer

5.09

0.0205

Cessna T-37

Twin jet-engine military trainer

6.28

0.0200

Beech 99

Twin turboprop commuter

7.56

0.0270

Cessna 620

Four piston-engine transport

8.93

0.0322

Learjet 24

Twin jet-engine business jet

5.03

0.0216

Lockheed Jetstar

Four jet-engine business jet

5.33

0.0126

F-104 Starfighter F-4 Phantom II

Single jet-engine fighter Twin jet-engine fighter

2.45 2.83

Lightning Convair 880

Twin jet-engine fighter Four jet-engine airliner

2.52 7.20

0.0480 0.0205 (subsonic) 0.0439 (supersonic) 0.0200 0.0240

Douglas DC-8

Four jet-engine airliner

7.79

0.0188

Boeing 747

Four jet-engine airliner

6.98

0.0305

X-15

Hypersonic research plane

2.50

0.0950

Propulsive Power or Thrust Power:

Pp  FTVac  Vacm air 1  f V jet  Vac  Measure of compactness of a jet engine:

Specific Thrust S

FT S  1  f V jet  Vac m air

Measure of fuel economy: Thrust Specific Fuel Consumption TSFC TSFC 

m fuel FT

m fuel

f   m air 1  f V jet  Vac  1  f V jet  Vac 

Aviation Appreciation Propulsion Efficiency

Thrust Power  propulsion  Available Kinetic Power of the Jet

 propulsion 



FTVac

m air 1  f V jet2  Vac2 2



m air 1  f V jet  Vac Vac  propulsion  m air (1  f )V jet2  Vac2 2





Jet Characteristics

FT  m jetV jet  m airVac • Quantities defining a jet are: – cross-sectional area; – composition; – velocity.

m jet   jet AjetV jet

FT   jet AjetV jet  m airVac 2

Of these, only the velocity is a truly characteristic feature and is of considerable quantitative significance.

Jet Characteristics of Practical Propulsion Systems System

Jet Velocity (m/s)

Turbofan

200 - 600

Turbojet (sea-level, static)

350 - 600

Turbojet (Mach 2 at 36000 ft)

900 - 1200

Ramjet (Mach 2 at 36000 ft)

900 - 1200

Ramjet (Mach 4 at 36000 ft)

1800 - 2400

Solid Rocket

1500 – 2600

Liquid Rocket

2000 – 3500

Nozzle : Steady State Steady Flow in

jet

First Law :

    V V  Qcv  m  h   gz   m  h   gz   Wcv 2 2  in   jet 2

2

No heat transfer and no work transfer & No Change in potential energy. 2 2

 V  h  2 

  V    h  2 in 

   jet

Combined analysis of conservation of mass and first law 2

 m   m  hin     h jet      jet A jet   in Ain 

2

A SSSF of gas through variable area duct can interchange the enthalpy and kinetic energy as per above equation. Consider gas as an ideal and calorically perfect. 2 2     V Vin   jet  c p Tin    c pT0   c p T jet  2c p  2c p   

Isentropic expansion of an ideal and calorically perfect gas.

Tin  pin    T jet  p jet 

 1 

Parametric Cycle Analysis of Ideal Turbo Jet Engine

Effect of Flight Mach Number on Compactness

Specific Thrust kN.s/kg

t0,cc=4.5 r0p=5 r0p=3

r0p=2 r0p=1 r0p=10 r0p=30

Mac

r0p=20

Effect of Flight Mach Number on Fuel Air Ratio

t0,cc=4.5 r0p

1 2 3 5

f

10 20 30

Mac

Effect of Flight Mach Number on Fuel Economy

TSFC kg/ kN.hr

t0,cc=4.5 r0p=2 r0p=1 r0p=3 r0p=5 r0p=10

r0p=20 r0p=30

Mac

Effect of Flight Mach Number on Fuel Air Ratio

t0,cc=4.5 r0p

1 2 3 5

f

10 20 30

Mac

Effect of Flight Mach Number on Propulsion Efficiency

t0,cc=4.5 r0p = 30

r0p = 5

 propulsion

Mac

r0p =2

Effect of Flight Mach Number on Thermal Efficiency

t0,cc=4.5 r0p

Thermal

Mac

Effect of Flight Mach Number on Overall Efficiency

t0,cc=4.5

O

r0p

Mac

Effect of Pressure Ratio on Compactness Mac=0

t0,cc=4.5 Specific Thrust kN.s/kg

Mac=0.5 Mac=1.0 Mac=1.5 Mac=2.0 Mac=3.0

rp

Mac=2.5

Effect of Pressure Ratio on Fuel Economy

TSFC kg/ kN.hr

t0,cc=4.5

Mac

rp

Effect of Pressure Ratio on Fuel Air Ratio

t0,cc=4.5

f

rp

Effect of Pressure Ratio on Propulsive Efficiency

t0,cc=4.5

 propulsion

rp

Effect of Pressure Ratio on Thermal Efficiency

t0,cc=4.5

Thermal

rp

Effect of Pressure Ratio on Overall Efficiency

t0,cc=4.5

Overall

rp

Effect of Pressure Ratio on Compactness Mac=0

t0,cc=4.5 Specific Thrust kN.s/kg

Mac=0.5 Mac=1.0 Mac=1.5 Mac=2.0 Mac=3.0

rp

Mac=2.5

Turbo Jet with Afterburner

inlet

1

2

3

4

5

6

7

Elevation of Temperature of the Jet: After Burner : More Energy at Same Life  QAB   mair  mfuel ,comb  mfuel ,AB  cpT06   mair  mfuel ,comb  cpT05  mfuel ,abH.V .   mair  mfuel ,comb  mfuel ,AB  cpT06   mair  mfuel ,comb  cpT05  mfuel ,abH.V .   mair 1  fcomb   mfuel ,AB  cpT06  mair 1  fcomb  cpT05 mair 1  fcomb   mfule,AB  c pT06  mair 1  fcomb  c pT05   H.V .  mfuel ,ab

mair 1  fcomb   mfule,AB  c pT06  mair 1  fcomb  c pT05   H.V .  mfuel ,ab

H .V . 

cp

f ab 

cp

f ab

1  f comb  f ab T06  1  f comb T05

H .V .

1  f comb  f ab T06  1  f comb T05

Minimum Jet Temperature Jet Total Temperature :

T07  T06  t0,ab  T0 Jet Static Temperature :  1  

 p7 T7  T06    p05 

T7  T0

t0,ab t0 p,comp

 1  

 p  t0,abT0    p05   1  

 p    p0 

Characterization of AB Jet Maximum obtainable Mach number of Jet T07 T7   1 2 1 M7 2

Performance of Jet FT  m 1  fcomb  fab V7  V1 Propulsive Power or Thrust Power:

Pp  FTV1  V1m 1 fcomb  fab V7  V1

Specific Thrust S S 

1 fcomb  fab V7  V1

Thrust Specific Fuel Consumption TSFC

mfuel mfuel  TSFC  FT m 1  fcomb  fab V7  V1

AB & No AB rp = 10

W/O AB W/O AB

TSFC

Specific Thrust

W AB

W AB

Specific Thrust kN.s/kg

Ideal Afterburning Turbojet Engine Performance : Specific Thrust Vs Compressor Pressure Ratio

2.5 3.0

rp

Ideal Turbojet Engine Performance : Specific Thrust Vs Compressor Pressure Ratio

Specific Thrust kN.s/kg

Maircraft

Compressor Pressure Ratio : rp

TSFC kg/ kN.hr

Ideal Afterburning Turbojet Engine Performance : TSFC Vs Compressor Pressure Ratio

rp

Effect of Pressure Ratio on Fuel Economy

TSFC kg/ kN.hr

Constant TIT

Mac

rp

Ideal Afterburning Turbojet Engine Performance : TSFC Vs Compressor Pressure Ratio

f

rp

Ideal Afterburning Turbojet Engine Performance : Efficiencies Vs Compressor Pressure Ratio

rp

Summary of Turbojet Performance • A high compressor pressure ratio is desirable for subsonic flight for good specific thrust and low fuel consumption. • A special care must be used in selecting the compressor pressure ratio for the supersonic flight Mach number. • Rapid drop in specific thrust with pressure ratio at supersonic conditions. • There exist a pressure ratio for each Mach number of a supersonic flight, that gives maximum specific thrust. • The fuel air ratio decreases with increasing Mach number and compressor pressure ratio. • Propulsive efficiency increases with increasing Mach number.

Rapid fall in specific thrust under supersonic conditions is a serious concern.

Optimization of Turbojet Performance

P M V Subbarao Professor Mechanical Engineering Department

Better Deal for Compactness & Fuel Economy…

Optimum Compressor Pressure Ratio • At supersonic flight conditions, a maximum value of Specific thrust is Exhibited at certain compressor pressure ratio. • The value of pressure ratio to maximize the specific thrust at a given flight Mach number should be found by differentiation of specific thrust equation.





S  1  f V jet  Vaircraft





S  1 f V jet  Vaircraft  F (r0 p,comp , Mac & t0,cc ) For Maximum Specific Thrust: F (r0 p,comp , Mac & t0 p,cc ) S  0 r0 p r0 p

F ( t0 p,comp , Mac & t0 p,cc ) S  0 t0 p t0 p



 1  f V jet t0 p

V jet  c

  F (t0 p,comp ,Mac & t0 p,cc )  0 t0 p

2     1 2  t 0,cc  M ac   t 0 p ,turbt 0,cc 1   2  1   t 0 p ,comp  

V jet  2     1 2  t 0,cc  1 M ac   t t     p turb cc 0 , 0 ,    c 1 2 t    0 p ,comp      2

   21  f      1 2  t 0,cc  t 0 p ,turbt 0,cc 1   M ac       t   1 2  0 p ,comp         t op

2   1  f V  jet 

 

c t op

  t 0 p ,comp  1   t op,turb  1     1  f t 0,cc  

t0cc  t0 p,comp   f  H.V .  t0cc c pT0

Optimum Compressor Pressure Ratio Vs Mach Number

W AB

r0p,opt

W/o AB

Mac

Optimal Turbojet Engine Performance

TSFC kg/ kN.hr

Specific Thrust kN.s/kg

With After Burner

Without After Burner Mac

Energy Flow in Jet Engine Energy input

Long distance travel demands high flight velocity. High flight velocity leads to drop in compactness and fuel economy. A Single Jet is blackmailing the jet engine !!!

Turbos to Create A Jet

The Concept of Turbo Technology • • • •

A control volume based engine to create Jet. Turbo-machinery execute -vdp work. Force or torque is generated with steady flow. Continuous transfer & conversion of energy is possible at steady flow and steady state. • Basic Architecture is:

Open Cycle Using Turbos 3 4

2 T

5 : Jet

1 s 3

2

4

p

5: Jet

1 s

Necessity is the Mother of Invention !?!?!??!

Gas Turbine Technology • 1791: A patent was given to John Barber, an Englishman, for the first true gas turbine. • His invention had most of the elements present in the modern day gas turbines. • The turbine was designed to power a horseless carriage. • 1872: The first true gas turbine engine was designed by Dr Franz Stikze, but the engine never ran under its own power. • 1903: A Norwegian, Ægidius Elling, was able to build the first gas turbine that was able to produce more power than needed to run its own components, which was considered an achievement in a time when knowledge about aerodynamics was limited. • Using rotary compressors and turbines it produced 11 hp (massive for those days). • He further developed the concept, and by 1912 he had developed a gas turbine system with separate turbine unit and compressor in series, a combination that is now common.

• 1914: Application for a gas turbine engine filed by Charles Curtis. • 1918: One of the leading gas turbine manufacturers of today, General Electric, started their gas turbine division. • 1920: The practical theory of gas flow through passages was developed into the more formal (and applicable to turbines) theory of gas flow past airfoils by Dr A. A. Griffith.

THE WORLD‘S FIRST INDUSTRIAL GAS TURBINE SET – GT NEUCHÂTEL

4 MW GT for Power Generation

Gas Turbine Power Generation • Experience gained from a large number of exhaust-gas turbines for diesel engines, a temp. of 538°C was considered absolutely safe for uncooled heat resisting steel turbine blades. • This would result in obtainable outputs of 2000-8000 KW with compressor turbine efficiencies of 73-75%, and an overall cycle efficiency of 17-18%. • First Gas turbine electro locomotive 2500 HP ordered from BBC by Swiss Federal Railways. • The advent of high pressure and temperature steam turbine with regenerative heating of the condensate and air preheating, resulted in coupling efficiencies of approx. 25%. • The gas turbine having been considered competitive with steam turbine plant of 18% which was considered not quite satisfactory.

A Death Leading to New Life • The Gas turbine was unable to compete with “modern” base load steam turbines of 25% efficiency. • There was a continuous development in steam power plant which led to increase of Power Generation Efficiencies of 35%+ • This hard reality required consideration of a different application for the gas turbine. • 1930: Sir Frank Whittle patented the design for a gas turbine for jet propulsion.

Turbojets • As invented by Hans Von Ohain &Frank Whittle.

Typical Turbojet Schematics

Turbojets - Basic Operating Features • Five basic components: – intake: captures air and efficiently delivers it to compressor. – compressor: increases air pressure and temperature. – combustor: adds kerosene to the air and burns the mixture to increase the temperature and energy levels further.

– turbine: extracts energy from the gases to drive the compressor via a shaft.

– nozzle: accelerates the gases further. • High levels of engineering required for efficient operation, especially for compressor and turbine therefore costly compared with rocket.

World's first operational jet engine • • • • •

Dimensions: 1.48 m long, 0.93 m diameter Weight: 360 kg Thrust: 450 kgf (4.4 kN) @ 13,000 rpm and 800 km/h Compression ratio: 2.8:1 Specific fuel consumption: 2.16 gal/(lb·h) [18.0 L/(kg·h)]

World's first Aircraft : He178 • • • • • • • • • • • •

General characteristics Crew: One Length: 7.48 m (24 ft 6 in) Wingspan: 7.20 m (23 ft 3 in) Height: 2.10 m (6 ft 10 in) Wing area: 9.1 m² (98 ft²) Empty weight: 1,620 kg (3,572 lb) Max takeoff weight: 1,998 kg (4,405 lb) Powerplant: 1× HeS 3 turbojet, 4.4 kN (992 lbf) Performance Maximum speed: 698 km/h (380 mph) Range: 200 km (125 mi)

Present Turbojet Engines • The Rolls-Royce/Snecma Olympus 593 was a reheated (afterburning) turbojet which powered the supersonic airliner Concorde. • General characteristics • Type: Turbojet • Length: 4039 mm (159 in) • Diameter: 1212 mm (47.75 in) • Dry weight: 3175 kg (7,000 lb)

• Components • Compressor: Axial flow, 7-stage low pressure, 7-stage high pressure • Combustors: Nickel alloy construction annular chamber, 16 vapourising burners, each with twin outlets • Turbine: High pressure single stage, low pressure single stage • Fuel type: Jet A1 • Performance • Maximum Thrust: 169.2 kN (38,050 lbf)

• Overall pressure ratio: 15.5:1 • Specific fuel consumption: 1.195 (cruise), 1.39 (SL) lb/(h·lbf) • Thrust-to-weight ratio: 5.4

Turbojets for Guided Weapons

Harpoon • Jet velocity: 350 - 1200 m/s.

Teledyne J402-CA-400

• Better propulsive efficiency than rockets (lower than turbofans). • Compact & low weight. • More complex, costly and unreliable than rockets. 139

Harpoon : General Characteristics • Primary function: Air-, surface-, or submarine-launched anti-surface (anti-ship) missile • Contractor: The McDonnell Douglas Astronautic Company - East • Power plant: Teledyne Teledyne J402 turbojet, 660 lb (300 kg)-force (2.9 kN) thrust, and a solid-propellant booster for surface and submarine launches. • Length: – Air launched: 3.8 metres (12 ft) 7 in) – Surface and submarine launched: 4.6 metres (15 ft)

• Weight: – Air launched: 519 kilograms (1,140 lb) – Submarine or ship launched from box or canister launcher: 628 kilograms (1,380 lb) • Diameter: 340 millimetres (13 in) • Wing span: 914 millimetres (36.0 in) • Maximum altitude: 910 metres (3,000 ft) with booster fins and wings

• Range: Over-the-horizon (approx 50 nautical miles) – AGM-84D: 220 km (120 nmi) – RGM/UGM-84D: 140 km (75 nmi) – AGM-84E: 93 km (50 nmi) – AGM-84F: 315 km (170 nmi) – AGM-84H/K: 280 km (150 nmi) • Speed: High subsonic, around 850 km/h (460 knots, 240 m/s, or 530 mph)

• Guidance: Sea-skimming cruise monitored by radar altimeter, active radar terminal homing • Warhead: 221 kilograms (490 lb), penetration highexplosive blast • Unit cost: US$720,000

Teledyne CAE J402-CA-400 • Dimensions: Length 74.8 cm (29.44 in.), Width 31.8 cm (12.52 in. • Physical Description: Type: Turbojet • Thrust/speed: 2,937 N (660 lb) at 41,200 rpm • Compressor: 1-stage axial flow, 1-stage centrifugal flow • Combustor: annular • Turbine: 1-stage axial flow • Manufacturer: Teledyne CAE, Toledo

Micro-turbojets for Weapons

Variation of Jet Technologies

Turbofans • Compromise between turbojet and turboprop with propeller now a fan enclosed within the engine. • Two air streams passing through engine, one of which bypasses internal core.

Turbofans - Basic Operating Features • Similar to turbojet but turbine split into two with low pressure turbine used to drive separate fan ahead of compressor via twin-shaft arrangement. • Bypass effect increases the available mass flow rate and thus reduces the jet velocity needed for a given amount of thrust (improves propulsive efficiency).

149

Turbofan • The Pratt & Whitney F119 is an afterburning turbofan engine developed for the Lockheed Martin F-22 Raptor. • The engine delivers thrust in the 35,000 lbf (160 kN) class, and is designed for supersonic flight without the use of afterburner. • Delivering almost 22% more thrust with 40% fewer parts than conventional, fourth-generation military aircraft engine models, the F119 allows sustained supercruise speeds of up to Mach 1.72.

Specifications F119 • • • • • • •

General characteristics Type: Twin-Spool, Augmented Turbofan Length: 16 ft 11 in (5.16 m) Diameter: Dry weight: 3,900 lb Components Compressor: Twin Spool/Counter Rotating/Axial Flow/Low Aspect Ratio • Combustors: Annular Combustor • Turbine: Axial Flow/Counter-Rotating

• Nozzle: Two Dimensional Vectoring Convergent/Divergent • Performance • Maximum Thrust: >35,000 lbf (156 kN) (with afterburner) • Thrust-to-weight ratio: 9:1

Turbofans for GW

Tomahawk

• Very good propulsive efficiency and

• Jet velocity: 200 – 600 m/s

• Only very long range applications

• Bypass ratio: 0.5:1 (much higher in aircraft applications)

low specific fuel consumption

• Large volume and difficult to design to small scales. 153

Intakes - Turbofan/Turbojet Tomahawk/ALCM

Harpoon/SLAM

Williams F107

Teledyne J402 154

Turboprops • Turbine extracts most of the jet thrust to run a propeller at the front, via a gear box. • Limited GW applications (possibly future UAV’s). • Mainly low-speed aircraft applications (limited to about Mach 0.6). Typical Turboprop Schematic 155

Optimization of Turbojet Performance

Optimal conditions for Compact Turbojet w/o AB  1  f V jet    c     t op 2

  21  f       1 2  t 0,cc  t 0 p ,turbt 0,cc 1  M ac        t 1 2    0 p ,comp      0 t op

  t 0 p ,comp  1   t op,turb  1     1  f t 0,cc  

t0cc  t0 p,comp   f  H.V .  t0cc c pT0

Optimal conditions for Compact Turbojet w AB  1  f comb  f AB V jet    c  0  t op 2

   1 2  t 0, ABT0 M jet   1  2 T jet   T jet

 p  t 0, ABT0  p  0 jet

   

 1 

T jet

  p    t 0, ABT0  r  r p p comp p turb 0 , 0 , 0   

t 0, AB T jet  T t 0,compt 0,turb

 1 

Optimum Compressor Pressure Ratio Vs Mach Number

W AB

r0p,opt

W/o AB

Mac

Optimal Turbojet Engine Performance

TSFC kg/ kN.hr

Specific Thrust kN.s/kg

With After Burner

Without After Burner Mac

Energy Flow in Jet Engine Energy input

Long distance travel demands high flight velocity. High flight velocity leads to drop in compactness and fuel economy. A Single Jet is blackmailing the jet engine !!!

AXIAL FLOW COMPRESSORS

An Option for High Specific Speed • In aero applications, the specific speed is defined as: n m

Ns  4



 p   

3

and the flow coefficient as

Ns 

Q  r2 D22

 Q

h  4 3

Schematic representation of an axial flow compressor

It is easy to design a turbine that will work…. It requires a considerable skill to design a compressor that will work…

Antonov An-225 Mriya • The Antonov An-225 Mriya is a strategic airlift cargo aircraft, designed by the Antonov Design Bureau in the 1980s. • Payload: 250,000 kg (550,000 lb) !!! • Cruise speed: 800 km/h. • Altitude: 11,000 m (36,100 ft). • Thrust Required: 1350 kN • Power plant: 6 × ZMKB Progress D-18 turbofans.

The Progress D-18T ( Lotarev D-18T) • • • • • • • • • • • • • •

General characteristics Type: Three-spool high bypass turbofan engine with a single-stage fan. Fan diameter: 2.33 m (91.73 in) Dry weight: 4,100 kg (9,039 lb) Components Compressor: Seven-stage IP compressor, seven-stage axial HP compressor Combustors: Annular combustion system Turbine: Single-stage HP turbine, single-stage IP turbine, four-stage LP turbine Performance Maximum thrust: 229.77 kN Overall pressure ratio: 27.5 Bypass ratio: 5.7 Turbine inlet temperature: 1,600°K Thrust-to-weight ratio: Approx 5.7:1

Stages of an Axial-flow Compressor

Selection of Pressure Ratio per Stage

The first step in a design of Axial Flow Compressor…..….. Invention of high population element ……

The Aerofoil… A Cascade of Aerofoils…..

Aerofoil Geometry

1: zero lift line 2: leading edge 3: nose circle 4: camber 5: thickness 6: upper surface 7: trailing edge 8: main camber line 9: lower surface

Geometrical Description of NACA 65

NACA 65 Series of Aerofoils

Cascade of Aerofoils

Viscous flow through Cascade

Cascade Geometry λ = stagger angle ( positive for a compressor cascade) a’1 = blade inlet angle a’1 = blade outlet angle

Lift & Drag of a cascade

Selection of Inlet flow angle

Cycling of Kinetic Energy in Axial Flow Compressor

Macro Geometric Specification of An Axial Compressor

The geometry of a compressor can be categorised into 3 main designs types, A Constant Outer Diameter (COD), A Constant Mean Diameter (CMD) or A Constant Hub Diameter (CID),

Specifications of An Axial Compressor • There are several different parameters that can specify a particular compressor. • The first set of input parameters are based on the running conditions for the machine. • These involve mass flow, pressure ratio , rotational speed and the number of stages. • Stage degree of reaction : For controlling the distribution of the load between the rotor and the stator. • If this is not of importance, the outlet flow angle for the each stage must be set instead.

Thermodynamics of An Axial flow Compressor Stage p03 = p02T = T 03 02 p3 Va32/cp

Va22/cp

p2

T

 ωVw2r2  Vw1r1  P  Tω  m p01 p1

T01 Va12/cp

T1 s

Kinematics of An Axial Flow Compressor Stage Inlet Velocity Triangle

Outlet Velocity Triangle

Kinetics of An Axial Flow Compressor Stage Rate of Change of Momentum: 



F  mVw2  Vw1   mVf 2 tanα2  Vf 1tanα1 

Inlet Velocity Triangle

Power Consumed by an Ideal Moving Blade  P  m UVf 2 tanα2  Vf 1tanα1 

Outlet Velocity Triangle

Energy Analysis of An Axial Flow Compressor Stage Change in Enthalpy of fluid Inlet Velocity Trianglein moving blades : 

P  mh02  h01   m c p T02  T01  2 2    Va2 Va1    m c p T2   T1    2c p  2c p    

2  2   Va2 Va1    m c p T2  T1       2c p 2c p    

2 2   Va2  Va1  m    h h 1    2 2   2   

Outlet Velocity Triangle

 Vr12 Vr22  h2  h1      2   2

 Vr12 Vr22  T2  T1       2c p 2c p 

Isentropic compression in Rotor

γ    γ   T2  1  p  p  p  1   2 1 1   Blade   T1    

Degree of Reaction of A Stage,R R :

h2  h1  h02  h01

Vr12  Vr22 R 2 2 2 Vr1  Vr22  Va2  Va1

Compressible Flow Machines • Owing to compressibility of gas in a compressor • The degree of reaction for equal pressure rise in stator and rotor will be greater than 0.5. • The stage total pressure rise will be higher in order to get equal static pressure rise in stator and rotor.

Power input to the compressor : 





Pact  mh03  h01   m c p T03  T01   m c p T02  T01 

Current Practice:

Inlet Velocity Triangle

Vf  Vf 1  Vf 2

U  tan a1  tan 1  tan a 2  tan  2 Vf Theoretical Power input to the compressor: Outlet Velocity Triangle 



Pth  m UVw2  Vw1   m UVf tanα2  tanα1  

Pth  m UVf tanβ1  tanβ2 

For an isentropic compressor: 



Pth  m c p T03  T01   m UVf tanβ1  tanβ2  





Pth  m c p T03  T01   m c p T03  T01   m c p ΔT0S ΔT0s

UVf tanβ1  tanβ2   cp

p03,iso  ΔT0S  1 T01 p01 

  

 γ     γ 1 

ηstageΔT0S p03,act  1   p01 T01 

   

 γ     γ 1 

p03,act p01

UVf tanβ1  tanβ2    η   stage c p   1   T01    

 γ     γ 1 

Vr12  Vr22 R 2 2 2 Vr1  Vr22  Va2  Va1 U  tanα1  tanβ1  tanα2  tanβ2 Vf

Vf tanα1  tanβ1  tanα2  Vr2  cosβ2

DESIGN OF AXIAL FLOW COMPRESSORS

Design Specifications • The different input parameters, used in design Process are: – Main specification – Detailed specification – Inlet specification

Specifications of Axial Flow Compressor • • • • •

Main specification Type of compressor Mass flow Number of stages Pressure ratio of each stage • Rotational speed • Stage reaction

• • • •

Inlet specification Inlet flow angle, Stage flow coefficient Hub tip ratio, rhub/rtip

Parameter variations throughout the compressor • Certain parameters in the compressor will vary in the compressor, namely: • Tip clearance, e/c • Aspect ratio, h/c • Thickness chord ratio, t/c • Axial velocity ratio, AVR • Blockage factor, BLK • Diffusion factor, DF • Stage Loading distribution • A simple linear distribution for the parameters may, for simplicity, be used except for the stage loading.

The stage load distribution throughout the compressor

Mean stream line analysis • The calculations are based on mean line stream analysis i.e. one dimension. • The mean radius is used in the calculations to determine the blade speed. • Normally when calculating with the mean line stream method, the mean radius will not change. • But by changing the mean radius throughout one stage will give a more accurate design. • The mean radius will be kept constant in the space between rotor and stator as well for the space between each row.

• A change in radius in the space between each blade row won’t make a big difference in the end result. • It is more crucial to have a change in radius in the blade them self since this will have a more noticeable effect.

Design Calculation process • Module 0, Inlet geometry • To be able to solve the inlet geometry the inlet flow velocity, Vf, must be known. • If this velocity is unknown, an iterative process must be used. • By approximating the value of Vf, the density can be found. • With help of mass continuity a new inlet flow velocity can be calculated. • This value is then used to start over the calculation until converged.

• The first step is to get hold off the thermodynamic properties in the inlet of the compressor. • The inlet pressure and temperature is known and from these the enthalpy and entropy can be found.

Algorithm: Inlet Geometry • Inlet Parameters: M,p,T ….. • Specify inlet flow angle, ai • Calculate flow area:

 m Area  Vf .BLK

      Area  rtip   2      r    π 1  hub     r     tip     

1/2

rrms

r  

Umean

2 hub

r   2  2 tip

 2πrrmsN     60 

1/2

Blockage Factor The blockage factor is here denoted as, BLK. The geometry is the same for the rotor inlet as for the stator-outlet in the previous stage. A result of this is that the blockage factor should be the same for the rotor-inlet and the stator-outlet at the previous stage.  m Area 1  Vf1.ρ1.BLK From the definition of the cross section area and the mean radius, the hub radius, the mean radius or the tip radius can be calculated depending if the compressor is of the type CID, CMD or COD.

Stage load coefficient

Δh Vw2  Vw1 ψ 2  U U2

Stage flow coefficient

φ

Stage reaction

Vf U

h2  h1 φ h03  h01

de Haller number • Compressor stages both the rotors and the stators are designed to diffuse the fluid. • Transfer and transform kinetic energy into an increase in static enthalpy and static pressure of the fluid. •The more the fluid is decelerated, the bigger pressure rise, but boundary layer growth and wall stall is limiting the process. •To avoid this, de Haller proposed that the overall deceleration ratio, i.e. Vr2 / Vr1 and Va3 / Va2 in a rotor and stator respectively, should not be less than 0.72 (historic limit) in any row.

Module 1: Rotor-inlet Triangle • When starting the calculation, the geometry from the inlet calculations is used. • The calculation for the entire stage is repetative. • Conside the rotor-inlet conditions, i.e. station 1, will have the same velocity and radius as the stator-outlet, i.e. station 3, for the previous stage.

rrms,1  rrms,3(i1) Vf,1  Vf,3(i 1) α1  α3(i 1)

Flow Angles &Velocities

Inlet Velocity Triangle

INLET CONDITIONS

Va1

Vr1 Vr1

Va1

Static Properties Static properties: Now that the velocity is known, the static enthalpy can be calculated. With help from the entropy other fluid dynamic properties like pressure, temperature, density etc. can be found.

To be able to move from the rotor-inlet towards the outlet of the rotor a relationship between these must be used.

Rothalpy Based Design Define the rothalpy which is constant throughout the rotor. 2 r

U2

V  Ih 2 2

The rothalpy is useful for calculating the outlet conditions of the rotor.

Further in to the calculations the relative Mach number and the axial Mach number will be used.

Module 2, Rotor-outlet/stator-inlet •There are two separate modules in module 2. •The first, 2.1, is for the calculation of the entropy rise in the rotor. •The second, 2.2, calculates the mean radius of rotor-outlet. •Both of these are iteration processes where an approximated value is first guessed and then a new value is calculated to adjust the approximated first value. Iteration Loop: Flow angles and velocities : The mean radius at rotor-outlet in unknown so a value for this must be approximates to be able to find out the blade speed. A new value for this will be calculated further on in the calculation.

Since a change in radius throughout the rotor is occurring a modification to the definition of the stage load coefficient must be made. A modification is made based on the blade velocity at the rotor-outlet.

Outlet Velocity Triangle

Design for Performance : Centrifugal Compressors

Blade Nomenclature

Blade Nomenclature

Axial and Radial Flow Turbines Differences between turbine and compressor: Compressor

Turbine Blade 1

Long

Last blade

Short

► Work as diffuser

► Work as nozzle

► Direction of rotation is opposite to lift direction

► Direction of rotation is same as Life

► Number of stages are many

► Number of stages is small Pc, the nozzle is not choked. Thus, Pthroat  P2  2.49 P2 2    2  0.833kg / m3 RT2 m , or , m   2Ca A2 , A2  0.0833m 2 A2   2 Ca m throat area of nozzles; A 2 N   2 C2 or , m   2C2 A2 N  A2 N  0.0437 m 2 , also A 2 cos a 2  A2 N

Axial Flow Turbine Calculate areas at section (1) inlet nozzle and (3) exit rotor. Ca1  C1 , but C1  C3 and C3  C12  T1  1067 K T1  To1  2c p 

 T1   1 P1   P1  3.54bar    Po1  To1  P1 1   1  1.155kg / m3 RT1 m  1Ca1 A1  A1  0.626m 2

Ca3

cos a 3

,  Ca1  276.4m / s

Axial Flow Turbine Similarly at outlet of stage ( rotor) To3  To1  To5  1100  145  955 K , given C3 2 T3  To3   T3  922 K 2c p 

 T3   1 P3   P3  1.856bar    Po3  To3  P3  5  0.702kg / m3 3  RT5

3  P3 / RT5  5  0.702kg / m2 m  3Ca3 A3  A3  0.1047m 2 Blade height and annulus radius ratio

Axial Flow Turbine Mean radius 340  0.216m 2 (250) also for known (A); A  2 rm h

um  2 Nrm  rm 

h

A 2 rm

h h then rt  rm  , rr  rm  2 2

using areas at stations 1,2,3 thus Location

A1 m 2 h1 m rt / rr

1

2

3

0.0626

0.0833

0.1047

0.04

0.0612

0.077

1.24

1.33

1.43

Axial Flow Turbine Blade with width W Normally taken as W=h/3 Spacing s between axial blades

space s   0.25, should not be less than 0.2 W width w r * t should be 1.2  1.4 rr unsatisfactory values such as 0.43 can be reduced by changing axial velocity through  . increasing Ca will reduce rt check has to be made for mach number M v .

Axial Flow Turbine

Vortex Theory The blade speed ( u=r) changes from root to tip, thus velocity triangles must vary from root to tip. Free Vortex design axial velocity is constant over the annulus. Whirl velocity is inversely proportional to annulus.

C a2  cons tan t , C 2 r  cons tan t C a3  cons tan t , C3 r  const , Along the radius.





Ws  u C2  C3   (C2 r  C3 r )  cons tan t

Axial Flow Turbine For variable density, m is given by

m   2 ( 2rr )C a m  2C a2

rt



2

 2 rdr

rr

 C  r  cons tan t  r C 2

but Ca 2 is cosntant,

a2

tan a 2



thus a 2 changes as

 rm  tana 2    tan a 2 m  r 2 similarly  rm  tan a 3    tan a 3m  r 3

(a)

(b)

Axial Flow Turbine u u  Ca2 tan a 2  Ca2 tan  2 , thus, tan 2  tan a 2  Ca2  r  rm     tan a 2 m    r 2  rm

 um (c)   Ca2 for exit of rotor u  Cas tan a 3  Ca3 tan a 3  r  u  rm  (d) thus tan3    tan a 3m     r 3  rm 3 Ca3 Ex: Free vortex Results from mean diameter calculations

a 2 m  58.38,  2m  20.49, a 3 m  10o ,  3 m  54.96, h2  0.0612, rm  0.216, h3  0.077, rr  rm 

h 2

Axial Flow Turbine

 rm   rm   rm  rm     1.164, ( ) 2 0.877,    1.217,    0.849 rt  rr 3  rt 2  rt 3 u m 1 um    1.25, Results are also Ca 2  Ca3

a2

a3

2

3

Tip

54.93

0

8.52

58.33

Root

62.15

39.32

12.12

51.13

mean

58.38

20.49

10

54.96

Axial Flow Turbine U  tan a 2  tan 2  tan 3  tan a3 Ca  c p Tos  m  c p (To1  To3 )  m  UC a (tan a 2  tan a3 )  m  UC a (tan 2  tan 3 ) Wm  UC a (tan a 2  tan a1)  m  UC a (tan 2  tan 1) m To' 3 p Tos  To1  To3  sTo1(1  )  sTo1(1  ( o3 )  /(  1) ) To1 po1 T T where s  o1 o3 To1  To' 3

EES Design Calculations of Axial Flow Turbine Known Information To 1 = 1100 P ratio = DelTs

[K]

1.873

=

145

Etta turbine

=

0.9

Assumptions U = 340 N rps

=

= 3

[m/s]

250

0.8 =

10

Loss nozzle

=

0.05

EES Design Calculations of Axial Flow Turbine cp =

1148

DelTs

=

=

=

1.333

To 1 – To 3

Po 3 C2 · cos (

2

)

Ca U

Gamr =

Epsi

0.287

Po 1

P ratio = Ca =

R =

=

– 1 2 · cp ·

DelTs U

Epsi =

2 ·

Reaction

=

2

· ( tan (

2

· ( tan (

2

) + tan (

3

) – tan (

U =

Ca · ( tan (

2

) – tan (

2

))

U =

Ca · ( tan (

3

) – tan (

3

))

3

))

2

))

EES Design Calculations of Axial Flow Turbine Calculate A2 Loss nozzle

T2 – T2dash

=

C2

2

2 · cp To 2 =

To 1 C2

To 2 – T2 = Po 1

Po 1

Pth = Rho2 =

A2

=

Gamr

T2dash + 1

=

Pc

2 · cp To 1

=

P2

2

Gamr

2 P2 Pth R · T2 m Rho2 · Ca

A2 · cos (

2

) =

A2N

EES Design Calculations of Axial Flow Turbine Calculate A3 Calculate A1 To 1 – T1 = Po 1

To 1

=

P1

A1

=

2

To 3 – T3 =

2 · cp Gamr

T1 P1

Rho1 = C1 =

C1

R · T1

Po 3

=

P3

m Rho1 · Ca

A3

=

2

2 · cp Gamr

T3 P3

Rho3 = C3 =

Ca

To 3

C3

R · T3 Ca m Rho3 · Ca

EES Design Calculations of Axial Flow Turbine Blade height at section 2

Blade height U =

2 ·

A2 =

2 ·

r t2 =

rm +

r r2 =

rm –

· N rps · r m

· r m · h2

Blade height at section 1 A1 = r t1 =

r r1 =

rratio 1

2 ·

· r m · h1

rm +

rm –

=

rratio 2 =

h1 2 h1 2

2 h2 2

r t2 r r2

Blade height at section 3 A3 =

2 ·

· r m · h3

r t3 =

rm +

r r3 =

rm –

r t1 r r1

h2

rratio 3 =

r t3 r r3

h3 2 h3 2

EES Design Calculations of Axial Flow Turbine A1 = 0.06345 3 = 10

C3 = 272 Ettaturbine = 0.9

A2 = 0.08336 2 = 20.49

Ca = 272 = 1.333

A2N = 0.04372 3 = 54.97

A3 = 0.1046

2 = 58.37

C1 = 272

C2 = 518.7

cp = 1148 [J/kgK]

DelTs = 145

Epsi = 2.88

Gamr = 4.003

h1 = 0.04666

h2 = 0.06129

Nrps = 250 [rev per sec]

P1 = 355.1

h3 = 0.07692

Loss nozzle = 0.05

m = 20 [kg/s]

P2 = 248.8

P3 = 186.1

Pc = 215.9

Po3 = 213.6

Pth = 248.8

Pratio = 1.873

R = 0.287 [kJ/kgK]

Reaction = 0.4211

Rho1 = 1.159

Rho2 = 0.8821

Rho3 = 0.7029

rratio1 = 1.242

rratio2 = 1.33

rratio3 = 1.432

rm = 0.2165

rr1 = 0.1931

rr2 = 0.1858

rr3 = 0.178

rt1 = 0.2398

rt2 = 0.2471

rt3 = 0.2549

T1 = 1068

T2 = 982.8

T2dash = 977

T3 = 922.8

To1 = 1100 [K]

To2 = 1100 [K]

To3 = 955

U = 340 [m/s]

= 0.8

Po1 = 400 [kPa]

Axial Flow Turbine

Axial Flow Turbine

Tip Speed & Materials • The precise stress limits of a given impeller material will depend upon factors such as the required cyclic duty (number of start–stop cycles per unit time). • Cast aluminium to be used up to a tip speed of around 200–300 m/s, • forged machined aluminium up to where a maximum of about 500 m/s. • titanium up to around 650–700 m/s. • Titanium aluminides and titanium metal matrix composites are currently being researched for the higher tip speeds.

The balance of factors affecting stage stability, derived from the work factor is to limit impeller stress levels usually results in a backsweep angle of at least 30°

Efficiency of A Centrifugal Compressor • Broadly speaking, two approaches are used for to determining stage efficiency at the preliminary design stage. • An approach that at first sight appears to be less dependent upon empiricism is to formulate a general 1D compressor model that includes some system of loss estimation for the principal flow elements of the stage. • The most comprehensive method includes, models for IGV, impeller, vaneless space and vaned diffuser. The loss models are tuned so that the method obtains reasonable agreement with a representative range of test cases.

Development of Loss Model • A best empirical approach is to correlate efficiency with parameters such as specific speed or the flow coefficient. • In aero applications, the specific speed is defined as: n m

Ns  4



 p   

3

Ns 

and the flow coefficient as

Q  r2 D22

 Q

h  4 3

Rodgers’ efficiency versus specific speed



Impeller Exit Geometry Vs Tip Losses

Losses in Stator Passages

L

Area Ratio

di

L

di

Irreversible Diffuser p03s=p02s

p02a

p03a

T03=T02 Impeller Losses Overall Losses T

Pinput p01 T01

s

Gas Dynamics of A Real Impeller Va2 Vf2

Vr2 Vw2 < U

Vw1

Vr1

Va1 Vf1





Pact   m  Vw2 r2  Vw1r1   m c p T03  T01 

Ur2  Vw1r1  cp

p03,act p01

 T03  T01 

 compUr2  Vw1r1     1    c T p 01  

       1 

Slip Factor, Power Input Factor & Efficiency • Power input factor and slip factor are neither independent of one another nor of efficiency. • The power input factor represents an increase in the work input. • The whole of this increment is absorbed in overcoming frictional loss and therefore degraded into thermal energy. • Power input factor should be as close as possible to unity. • Low values of Power input factor imply that the impeller is very efficient. • However, the value of compressor efficiency also depends on friction losses in the diffuser which does not affect power input factor. • The slip factor limits the capacity of the compressor and this should be as high as possible. • A high value of slip factor requires higher number of vanes. • Higher number vanes will increase frictional losses and hence increase the value of power input factor and decrease the value of efficiency. • A suitable compromise must be found, and present day practice is : • 19 – 21 vanes to get a slip factor value of 0.9. • There is high demand for Compact design of a centrifugal.

Optimum design of a centrifugal compressor inlet • To obtain high efficiencies from high pressure ratio compressors it is necessary to limit the relative Mach number at the eye. • The flow area at the eye can be written as 2  rh1  2 2 2 2   A1   rt1  rh1   rt1 1  2   rt1 K  rt1 

rh1 0.3   0.6 rt1

Optimum ratio: Tip velocity of eye:

U t1  rt1 2

U t 1  A1     K  

With uniform flow velocity the continuity equation is

  1 A1V f 1 m U t1  Vrt1 cos t1  Vat1 cos a t1

V f 1  Vrt1 sin t1

Ut1

t1

2

U t 1  A1     K  

Vwt1

at1

Vrt1 Vat1 Vft1

Selection of Eye Geometry for Centrifugal Compresser

With uniform flow velocity the continuity equation is 2

U t 1  A1     K  

  1 A1V f 1 m

U t1  Vrt1 cos t1  Vat1 cos a t1

V f 1  Vrt1 sin t1

Ut1

t1

Vwt1

at1

Vrt1 Vat1

2

 cot  t1  cot a t1  3 m  K V  sin  t1     3 1 rt1

Vft1

   1 2  M   1  0  2 

1

1    1 2  M1   1   01  2 

 1

1

 1

Va1 M1  RT1

V f 1  Vr1 sin 1  Va1 sin a1

Vrt1 sin  t1 M1  RT1 sin a t1

sin  t1 M 1  M rt1 sin a t1

2   1  1 2  sin  t1  M rt1   1    2 sin a t1    01    

1

 1

2

 cot  t1  cot a t1  3  m  K V  sin  t1     3 1 rt1

m  K 01Vrt31

 cot  t1  cot a t1    

2

  1 2  sin  t1  1  M rt1   2   sin a t1 

2

  

1

 1

sin 3  t1

2    a  cot cot m  2 3 3 t1 t1  sin  t1 f M rt1   M rt1 3 1 3  2  1 2 K 01c1   1  2  sin 1  1  M rt1    2   sin a1  

This equation is extremely useful and can be used in a number of different ways. For a known inlet conditions one can specify values of , R, p01 and T01 and obtain f(Mrt1) as a function of Mrt1 and t1. By specifying a particular value of Mrt1 as a limit, the optimum value of t1 for maximum mass flow can be found. A graphical procedure is the simplest method of optimising as illustrated below.

Ut1

t1 60 &0.9

Vwt1

at1

Vrt1

f(Mrt1)

Vat1 Vft1

60 & 0.8

90 & 0.9

90 & 0.8 80

50

30

10

f(Mrt1)

60

90 



Pact   m  Vw2 r2  Vw1r1   m c p T03  T01  80

50

30

10

Prewhirl at entry to impeller • Introducing positive prewhirl (i.e. in the direction of impeller rotation) can give a significant reduction of the inlet Mach number Mr1 but, reduces the specific work done on the gas. • Prewhirl is obtained by fitting guide vanes upstream of the impeller. • Can we have constant prewhirl from root to tip of the eye?

Constant Pre Whirl • Absolute flow angle is constant from root to tip. • Specific work input at ith radial location

Pact  Vw2 r2  Vw1r1 i  c p T03  T01 i m i 

Ti   mi Vw2 r2  Vw1r1 i Integral specific Power input rop

Variable Pre-whirl • Guide vanes are designed to produce either a free-vortex or a forced-vortex velocity distribution. • For a free-vortex flow the flow velocity Vf is constant with the tangential velocity Vw varying inversely with the radius. • Use of free-vortex pre-whirl vanes leads to a significant increase in incidence angle at low inducer radius ratios. • The use of some forced-vortex velocity distribution does alleviate this problem.

Forced Vortex Guide Vanes:

r  Vw  A   rt1 

n

High  50

70

Low 

80

70

r     rt1 

r     rt1 

Slip factor • Even under ideal (frictionless) conditions the relative flow leaving the impeller of a compressor or pump will receive less than perfect guidance from the vanes and the flow is said to slip. • If the impeller could be imagined as being made with an infinite number of infinitesimally thin vanes, then an ideal flow would be perfectly guided by the vanes and would leave the impeller at the vane angle. • A slip factor may be defined as

 2, flow Vw2    2,blade U The slip factor is a vital piece of information needed by compressor designers, as its accurate estimation enables the correct value of the energy transfer between impeller and fluid to be made.

Stolda Slip Factor

Vr 2 2  U2 Z number of vanes.

Stanitz’s expression for slip velocity is,

Performance of centrifugal compressors • Pressure Ratio

p03,act p01

 compUr2  Vw1r1     1    c T p 01  

The overall or total-to-total efficiency

     1    

Performance of Radial Vane Compressor

Performance of Backward Vane Compressor

2-D Design analysis • The spatial shape of the inter-blades working channel of the impeller is represented by the spatial flow tube defined by the spatial course of its main streamline and the course of the cross section area. • The Indirect design method : • Based on the calculation of the geometry of the stream tube for given inlet and outlet geometric and flow conditions. • Chosen fundamental general flow properties. • Design procedure comprise the calculation of the shape of the impeller blades and the shape of diffuser flow path.

Vf

Indirect Design Method Basic Assumptions Solution is based on the assumptions that 1. pressure gradient p in the normal direction to mean streamline equals zero. 2 f

1 p V  cos    n R Rm 2 w

V

p 0 n

V f2

Vw2 cos   0  Rm R

2. optimum course of the relative velocity Vr and optimum course of the angle β along the streamline are defined

 s     f   1 s  2

 s  Vr   f   Vr1 s  2

Definition of Blade Geometry

Design and Development Procedure : Two Stage Centrifugal Compressor HPC 1D DESIGN PRESSURE RATIO OPTIMISATION

LPC 1D DESIGN

Y/N

FINAL PARAMETERS DEFINITION

INDIRECT METHOD BLADE SHAPE DESIGN

Y/N

FLOW PATH CFD ANALYSIS

TEST CELL COMPRESSOR TEST

Y/N

LPC Design 5,2

Design Parameters Pressure Ratio Efficiency Mass Flow RPM Temperature Rise Preswirl Inlet Tip Mach Number Circumferential Velocity Outlet Blade Angle Main Blades Splitter Blades Specific Speed

4.475 0.824 4.301 kg.s-1 37 600 186.2 K 0 deg 1.26 526.1m.s-1 45 deg 14 14 127.9

 4,8

4,4

4,0

3,6

3,2

GV T1c

n=100%

p1c 2,8 0,00060

0,00062

0,00064

0,00066

Reduced Mass Flow

0,00068

0,00070

0,00072

0,00074

0,00076

LPC Design

Flow Path Calculation

LPC Design

Flow Path Calculation

LPC Design

Flow Path Calculation

LPC Design

Impeller

HPC Design Design Parameters

3,0 2,8

Pressure Ratio 2.407 Efficiency 0.805 Mass Flow 4.301 kg.s-1 RPM 37 600 Temperature Rise 162.0 K Preswirl 0 deg Inlet Tip Mach Number 0.75 Circumferential Velocity 474.6 m.s-1 Outlet Blade Angle 60 deg Main Blades 16 Splitter Blades 16 Specific Speed 76.04





2,6 2,4 2,2 2,0 1,8 1,6

n=100% n= 100%

1,4

n=95%

n=95%

1,2

GV T1c p1c

1,0 0,00010

0,00012

0,00014

0,00016

Reduced Mass Flow

0,00018

0,00020

0,00022

0,00024

0,00026

HPC Design

Impeller

Compressor Instrumentation

LPC and HPC Subassembly

Compressor Instrumentation

Compressor Instrumentation Layout

Test Generator Design

The Layout of the Experimental Gas Generator

Compressor Test Cell