Review AE430Review AE430Aircraft Propulsion SystemsAircraft Propulsion Systems

Gustaaf JacobsGustaaf Jacobs

NoteNote

Bring Anderson to exam for tables.Bring Anderson to exam for tables.

GoalsGoals Understand and analyze gas turbine Understand and analyze gas turbine

engines:engines: TurbojetTurbojet

Turbofan (turbojet + fanned propeller)!Turbofan (turbojet + fanned propeller)!

RamjetRamjet

AnalysisAnalysis

AnalysisAnalysis Energy control volume per engine componentEnergy control volume per engine component

• Pressure and temperature changes for ideal Pressure and temperature changes for ideal engineengine

• With efficiency definitions: pressure and With efficiency definitions: pressure and temperature changes for non-ideal enginetemperature changes for non-ideal engine

Control Volume over complete engine:Control Volume over complete engine:• Momentum balance=> thrust, propulsion efficiencyMomentum balance=> thrust, propulsion efficiency• Energy balance or thermo analysis:Energy balance or thermo analysis:

Brayton cycle: Thermal efficiencyBrayton cycle: Thermal efficiency

AnalysisAnalysis

Detailed component analysisDetailed component analysis InletsInlets

• Subsonic flow analysis in 1DSubsonic flow analysis in 1D Pressure recovery estimatePressure recovery estimate

• Shock analysis in 1D inlet (converging-diverging)Shock analysis in 1D inlet (converging-diverging) Estimate of lossesEstimate of losses External deceleration principlesExternal deceleration principles

• 2D shock external deceleration2D shock external deceleration Oblique shock analysisOblique shock analysis Estimate spillage and lossesEstimate spillage and losses

AnalysisAnalysis CombustorCombustor

Qualitative idea of combustion physicsQualitative idea of combustion physics• Fuel-air ratio (stoichiometric)Fuel-air ratio (stoichiometric)• Flame speedFlame speed• Flame holdingFlame holding

Quantitative: pressure loss with 1D channel flow Quantitative: pressure loss with 1D channel flow analysis + heat addition=> not treated due to time analysis + heat addition=> not treated due to time restrictionsrestrictions

Compressor/TurbineCompressor/Turbine Estimate of pressure, temperature recovery with Estimate of pressure, temperature recovery with

momentum and energy balancemomentum and energy balance Velocity triangles analysis: first order estimate of Velocity triangles analysis: first order estimate of

compressor aerodynamicscompressor aerodynamics

Control Volume Analysis: Control Volume Analysis: Basic IdeaBasic Idea

T

am em

fm

a e e a a e a eT m m v m v p p A

a e a e a eT m 1 f v v p p A

Engine PerformanceEngine PerformanceParametersParameters

Propulsion efficiency, ratio thrust power to add kinetic Propulsion efficiency, ratio thrust power to add kinetic energyenergy

Thermal efficiency, ratio added kinetic energy to total Thermal efficiency, ratio added kinetic energy to total energy consumptionenergy consumption

Total efficiencyTotal efficiency Thrust Specific Fuel ConsumptionThrust Specific Fuel Consumption

a

p 2 2e a

a f a

Tv

v vm m m

2 2

2 2

e aa f a

thf R

v vm m m

2 2m Q

total th prop

fmTSFC

T

Thermodynamic cyclesThermodynamic cycles

Diagram that looks at the change of state variables at Diagram that looks at the change of state variables at various stage of the enginevarious stage of the engine

Ideal gas turbine: Brayton cycleIdeal gas turbine: Brayton cycle

Isentropic compression, constant p heat addition, Isentropic compression, constant p heat addition, constant p heat rejectionconstant p heat rejection

First law of thermodynamics analysis gives expression First law of thermodynamics analysis gives expression for for ηηthth

1

p 4 1 p 3 2in out 1th

in p 4 1 2

c T T c T TQ Q p1

Q c T T p

Ideal RamjetIdeal Ramjet

Analyze each stage using thermodynamic Analyze each stage using thermodynamic analysis with energy balance and analysis with energy balance and isentropic relations to find:isentropic relations to find: P, T, pP, T, p00, T, T00

vvee, T/m, T/maa

ff

Ideal RamjetIdeal Ramjet

ppt,0t,0=p=pt,7t,7, p, p00=p=p7 7 => M => M00=M=M77

TT7 7 > T> T0 0 since heat is added during since heat is added during

combustion, so vcombustion, so v77>v>v00 => Thrust => Thrust

Fuel to air ratio, use first law:Fuel to air ratio, use first law:

Non-isentropic compression and expansion: Non-isentropic compression and expansion: losses lead to lowered total pressure and losses lead to lowered total pressure and temperaturetemperature

Define total pressure ratios before and after Define total pressure ratios before and after components to quantify the efficiency:components to quantify the efficiency: rrcc, r, rnn,r,rdd

Non-ideal ramjetNon-ideal ramjet

Major difference with ramjet pMajor difference with ramjet ptotal total is not constant like in ramjet but is not constant like in ramjet but

increases and decrease in compressor and turbine.increases and decrease in compressor and turbine.

To find these ratios work from front to back through each stageTo find these ratios work from front to back through each stage Specific: compressor and turbine power are the same so (first law)Specific: compressor and turbine power are the same so (first law)

Non-Ideal turbojetNon-Ideal turbojet

Definition of component efficienciesDefinition of component efficiencies

E.g. diffuserE.g. diffuser

Relates actual total temperature increase to an Relates actual total temperature increase to an isentropic temperature increaseisentropic temperature increase

The isentropic temperature can be related to the The isentropic temperature can be related to the total pressure using isentropic relations total pressure using isentropic relations

The total pressure distribution is determined The total pressure distribution is determined from front to back.from front to back.

Each stage has an effiiciency like this.Each stage has an effiiciency like this.

0,2s ad

0,2 a

T T

T T

TurbofanTurbofan

Example on blackboard.Example on blackboard.

Detailed analysis of componentsDetailed analysis of components

IntakesIntakes Convert kinetic energy to pressureConvert kinetic energy to pressure SubsonicSubsonic

External acceleration or decelleration depends on intake design External acceleration or decelleration depends on intake design and speed of aircraftand speed of aircraft

High speed: spillage. Low speed: stall.High speed: spillage. Low speed: stall.

Diffuser design: prevent stall: use computational (XFOIL, MSES) Diffuser design: prevent stall: use computational (XFOIL, MSES) and experimental validation to designand experimental validation to design

Supersonic intakeSupersonic intake

1D: converging-diverging nozzle1D: converging-diverging nozzle Ideal: isentropic decelleration supersonic to Ideal: isentropic decelleration supersonic to

throat, subsonic after throatthroat, subsonic after throat Not possible in practiceNot possible in practice Shocks in nozzleShocks in nozzle Possible design: shock close to throat and M~1 Possible design: shock close to throat and M~1

at throatat throat Need overspeeding to swallow shock in throat.Need overspeeding to swallow shock in throat. Kantrowitz-Donaldson: design condition is shock Kantrowitz-Donaldson: design condition is shock

swallowing condition.swallowing condition.

Supersonic diffuserSupersonic diffuser

2-D nozzle2-D nozzle Use multiple oblique shocks to slow flow down Use multiple oblique shocks to slow flow down

with small losses in total pressurewith small losses in total pressure Use oblique shock analysisUse oblique shock analysis

Combustor + CompressorCombustor + Compressor

Discussed in last classesDiscussed in last classes