l20 ae0637 combustors part1 2013
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AE0637AdvancedAircraftPropulsion
(Part1)
RandyChue(Assoc.Prof.)
.
Phone:67906399
. .
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TheCombustor
Thescramjetcombustorhastwobasicfunctions:
.
2. Tocombustthemixture
Keydesignissues:
Mixinglengthandcombustionlengthgrowwithincreasing
flowMach
number
or
velocity
Thecombustorisahighheatingandhighdragregionandmus eass or asposs e
Fuelinjection,vaporization,mixing
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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
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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
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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
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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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ZeroshearMixingLayer(Contd)
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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ZeroshearMixingLayer(Contd)
Onepossiblewaytoreducetheinjectorheightbisby
, rapidmixingthatisrequiredinramjetsandscramjetengines
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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
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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
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TurbulentShearLayerMixing(Contd)
However,turbulentshearlayermixingisstillinadequatein
, 2,optimalcombustioncannotbemetbyshearlayermixing
Therefore,shear
layer
mixing,
particularly
turbulent
shear
mixing,isofgreatacademicinterestbutitisimpracticalinreal
combustordesigns
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FurtherRemarksaboutShearLayerMixing
Wehaveonlyconsideredtheeffectsofvelocitydifferent
Thedifferenceindensitybetweenthetwostreams
Temperaturedifference
The
Mach
numbers
(compressibility
effects)
Heatrelease(whenincombustion)
Asawhole,thesefactorsarenotstrongenoughtochangethe
Needsomethingstrongertoenhancemixing
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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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