L20 AE0637 Combustors Part1 2013

8/12/2019 L20 AE0637 Combustors Part1 2013

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AE0637AdvancedAircraftPropulsion

(Part1)

RandyChue(Assoc.Prof.)

.

Phone:67906399

. .

1


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TheCombustor

Thescramjetcombustorhastwobasicfunctions:

.

2. Tocombustthemixture

Keydesignissues:

Mixinglengthandcombustionlengthgrowwithincreasing

flowMach

number

or

velocity

Thecombustorisahighheatingandhighdragregionandmus eass or asposs e

Fuelinjection,vaporization,mixing

2


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CombustionStoichiometry

Wehaveseenduringourlecturesonengineperformance

. . .

energyreleasedfromcombustionoccurswhenthefuelis

mixedwith

just

enough

air

so

that

all

of

the

hydrogen

atoms

formwatervaporH2O,andallofthecarbonatomsform

carbondioxideCO2

Thiscondition

of

complete

combustion

is

called

stoichiometric

reaction,andforageneralhydrocarbonfuel(CxHy),theideal

Fromp.8,EnginePerformanceMeasures(Part1)

22222 N421

OH2

CON21

O4

HC

xxxyx

Oxidizer Nitrogen

3

Representativeair Assumedinert


4/24

CombustionStoichiometry(Contd)

Thestoichiometricfuel/airratio(massbased)wasderivedto

airfuel/kgkg,

4103

336

yx

yxfst

FromEnginePerformance

Measures

slides,

p.

9

Involumetricormolarbase,thestoichiometricfuel/airratio

productsN2179O

4HC 22

yxyx

moles

21

791

4

y

xmole1

airfuel/molsmols,

4100

84

791

1

yxyx

fst

4

214


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CombustionStoichiometry(Contd)

Anotherparameteroftenusedtodescribecombustion

, ,

definedastheactualfuel/airdividedbythestoichiometry

fuel/airratio:

stf

f

mixturetricstoichiome,1mixturelean-fuel,1

Thechemical

reaction

for

a

eneraloff

stoichiometric mixture

mixturerich-fuel,1

offuelandaircanthenbeexpressedsimplyas:

79

5

pro uc s

21422

xyx


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TheCompleteCombustionAssumption

Notethatthecompletecombustionassumption doesnotim l that inactual ractice astoichiometricmixtureoffuelandairwillonlyyieldH2OandCO2ascombustionproducts

Inreality,

even

when

we

have

astoichiometric

fuel

air

m xture,wemay ave:

Somedissociationofthecombustionproducts(H2OandCO2)

Incom lete combustion insufficient time to burn the reactants

withinthe

combustion

when

the

flow

speed

is

high

Somelevelofnitrogenoxidation(N2isnotinert)

eac ua gases eav ng ecom us ormay nc u e:

Unreactedreactants(fuel&air)

Dissociated

roducts

Incompletelyoxidizedfuelmolecules

Oxidizednitrogen:nitricoxide(NO),nitrousoxide(N2O),andnitrogen

6

2 . x


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OffStoichiometricCombustion

Foroffstoichiometricfuel/airmixtures,asaroughgeneral

,

ratios:

22.0

Foroffstoichiometricmixtures,therewillbeincomplete

combustion,sothattheproductsspecieslistcanbefarmore

thanthose

of

H2O

and

CO2.

The

generalized

chemical

reaction

canberepresentedby:

OHCOCON

21

79O

4

HC 2OHCO2CO22 22

nnny

xyx

whereetc.includesalltheotherpossiblegasspeciesthat

etc.ONNOOO 2ON2NOO2O 222 nnnn

7

mayexistsfromthecombinationsofO,H,C,andNatoms


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OffStoichiometricCombustion(Contd)

Thiscanalsoberepresentedby:NS

where:

i

iiyx nx1

22 N21

O4

HC

NSisthetotalnumberofspeciesthatmayappearontheproductsideofthechemicalequation

Aiis

the

chemical

formula

of

the

ith

species

niisthemolenumberfortheithspecies

Thefullproductspecieslistandtheirmolenumberswillbe.

,

mayassumethatthechemicalreactionswouldreachequilibrium(althoughnotnecessarilycompletereaction)

8

Achemicalequilibriumanalysiswouldcalculatesuchareaction


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FuelAirMixing

Chemicalreactionsbetweenthefuelandtheairtakeplaceat

Fuelandairmoleculesmustcomeincontactwitheachother

(molecularcollisions)

Theyaremixedtonearstoichiometric proportionsforcombustionto

takeplace

Mixingcan

be

considered

to

occur

at

two

levels

Macromixin stirrin event. Fuel and air are forcibl stirred so

thattheyarepresentamongeachother

Micromixing molecular

diffusion.

The

molecules

of

the

fuel

and

the

a rare use an eycome n ocon ac w eac o er

9


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FuelAirMixinginParallelStreams

Considerthemixingoftwoparallelflowingstreams(airand

m

thickness

Streamvelocities:u1(air)andu2 (fuel)(neglectboundarylayer)

= =

10

Fuel

(YA)2=0,

(YF)2=

1


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FuelAirMixinginParallelStreams(Contd)

Forsimplicity,weassume:

Static ressureofbothstreamsaree ualandconstant

Densityofbothstreamsareequalandconstant

Only

the

velocities

are

different

a oun ary ayersonsp erp a ean onou erwa sareneg ec e

Ifthetwovelocitiesaredifferent,ashearlayerisgeneratedatthe interface between the two streams. Lateral trans orts at

theinterface

include

Momentumistransportedlaterallyfromthefastertotheslower

Vorticity

Thermaland

mechanical

energy

Mass(molecules)transport

Itislikeaboundarylayer,butitisnotatthewallboundary.

11

,


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ZeroshearMixingLayer

Onelimitingcaseiswhenthetwostreamshavethesame

Thereisnoshear,butthereismoleculardiffusion

gradientandisgivenbyFicksLaw:

yCDj AFAA

(kmolA/m3)

Molardiffusivefluxofair2

Concentrationgradient

,

Moleculardiffusivity

betweenfuelandair

12Subscripts

&

symbols:

Afor

air,

Ffor

fuel


13/24

ZeroshearMixingLayer(Contd)

Moleculardiffusionisverysimilartoviscousdiffusion

FA

TheSchmidtnumberistheratioofviscositycoefficientto

DFA

.

0.1CS

Forthezerosheardiffusionproblem,themixinglayer

FA

FA

m

xD

8

whereucistheaverageormeanconvectivevelocitydefined

as:

c

13velocityconvectivemean,2

21

uc


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ThetotaldistanceLmrequiredforthemixinglayerboundaryto

m

b1+ b2)

2b=

c

mFA

u

LDb 82

FA

cm

DbuL

16

2

L

Thisisjustanapproximation,andtheactualmixinglengthmay

betwice

as

lon

TheresultsindicatethattheLmrequireddecreaseswithb2. If

brepresentsthefuelinjectorheight,bshouldbeminimizedto

14reduce

the

mixing

length


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Onepossiblewaytoreducetheinjectorheightbisby

, rapidmixingthatisrequiredinramjetsandscramjetengines

15


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LaminarShear/MixingLayer(Contd)

Forlaminarshearmixinglayer,itdoesntdomuchbetterthan

.

approximately=1(i.e.,DFA=)

Alllateral

transport

is

by

molecular

diffusion

(both

viscosity

and

mass

diffusivityareduetomoleculardiffusion)

Thelaminarshearlayerthicknessisbasicallythesameasthe

m x ng ayert c ness

Theincreaseingrowthrateformisverysmall

Inordertosignificantlyincreasethelateraltransportinthe

s ear ayer, snecessary o ncrease eve oc y erenceusothattheshear/mixinglayerisnolongerlaminar

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TurbulentShear/MixingLayer

Whenthe

velocity

difference

uis

sufficiently

high,

the

laminarfloweventuallyundergoestransitiontoturbulentflow

Whenthisoccurs,thestructureoftheshearlayerisdrastically

changed Theshearlayerbecomesunstableandunsteady

Largevorticesareperiodicallyformedbetweenthetwostreams

e u ynam cp enomenon s escr e y e e v n

Helmoholtz instability(flowinstabilityinshearlayers)

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TurbulentShear/MixingLayer(Contd)

Thesequence

of

events

that

occurs

following

the

formation

of

largevorticesis:

Dashedcurves:mixant

boundariesfor

moleculardiffusion

Fullymicromixedregion

Shearstress

causes

the

periodic

formation

of

large

vortices

,frombothstreams,andstretchesthemixantinterface

Further

stretching

of

the

mixant

interface

increases

the

interfacialareaandenhancesmoleculardiffusion

Moleculardiffusionoccursatthestretchedmixantinterface

19

an even ua yresu s n u ym crom xe s a e


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TurbulentShear/MixingLayer(Contd)

Turbulentshearcanincreasemixingdrastically

However,italsoresultsinlosses

Justasinwallboundarylayers,freeshearlayersleadto

viscousdissipationofmechanicalenergytothermalenergy

Entropyincreases

Totalpressureloss

Decreaseincycleefficiency

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TurbulentShearLayerMixing

Wehaveseenthatturbulentshearlayermixingismuchmore

TheratioofmixinglengthtothefuelinjectorheightLm/bis

ordersof

ma nitude

smaller

than

those

of

zero

shear

and

laminarshearlayers

2b=

m

mixingshear-noorlaminar,)1000O(~b

Lm

21mixingshearturbulent,)100O()50O(~ b

Lm


22/24

TurbulentShearLayerMixing(Contd)

However,turbulentshearlayermixingisstillinadequatein

, 2,optimalcombustioncannotbemetbyshearlayermixing

Therefore,shear

layer

mixing,

particularly

turbulent

shear

mixing,isofgreatacademicinterestbutitisimpracticalinreal

combustordesigns

22


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FurtherRemarksaboutShearLayerMixing

Wehaveonlyconsideredtheeffectsofvelocitydifferent

Thedifferenceindensitybetweenthetwostreams

Temperaturedifference

The

Mach

numbers

(compressibility

effects)

Heatrelease(whenincombustion)

Asawhole,thesefactorsarenotstrongenoughtochangethe

Needsomethingstrongertoenhancemixing

23


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References

Textbook:

HypersonicAirbreathingPropulsion,W.H.Heiser&D.T.

Pratt.

Sections6.1.1,

6.2.1,

6.2.2,

6.2.5.

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Documents

L20 AE0637 Combustors Part1 2013