ramadan youssef sakr moustafa_lecture9-turbulent combsution

7/23/2019 Ramadan Youssef Sakr Moustafa_Lecture9-Turbulent Combsution

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Turbulent CombustionTurbulent Combustion



OutlineOutline

Types of FlamesTypes of Flames

Basic Concept of TurbulenceBasic Concept of Turbulence

Turbulent FlameTurbulent Flame

Flame StabilityFlame Stability



Types of FlamesT

ypes of Flames

Two basic categoriesTwo basic categories – Pre-mixedPre-mixed

– Non-premixedNon-premixed!iffusion"!iffusion"

Bot# c#aracteri$ed asBot# c#aracteri$ed as%aminar or Turbulent%aminar or Turbulent



PremixedPremixed

&esults from gaseous&esults from gaseousreactants t#at are mixedreactants t#at are mixedprior to combustionprior to combustion

Flame propagates atFlame propagates at'elocities slig#tly less'elocities slig#tly lesst#an a few m(st#an a few m(s

&eacts )uite rapidly&eacts )uite rapidly*xample+ Spar, gnition *ngine



Non-premixed !iffusion"

Non-premixed !iffusion"

.aseous reactants.aseous reactantsare introducedare introducedseparately and mixseparately and mixduring combustionduring combustion

*nergy release rate*nergy release ratelimited by mixinglimited by mixingprocessprocess

&eaction $one&eaction $onebetween oxidi$er andbetween oxidi$er and

fuel $onefuel $one

*xample+ !iesel *ngine



%aminar %aminar

PremixedPremixed – *x/ Bunsen Burner *x/ Bunsen Burner – Flame mo'es at fairly low 'elocityFlame mo'es at fairly low 'elocity – 0ec#anically create laminar0ec#anically create laminar

conditionsconditions

!iffusion!iffusion – *x/ Candle Flame*x/ Candle Flame

– Fuel+ 1ax2 Oxidi$er+ 3ir Fuel+ 1ax2 Oxidi$er+ 3ir – &eaction $one between wax&eaction $one between wax

'apors and air 'apors and air



TurbulentTurbulent

PremixedPremixed – 4eat release occurs muc# faster 4eat release occurs muc# faster – ncreased flame propagationncreased flame propagation – No definite t#eories to predictNo definite t#eories to predict

be#a'iorbe#a'ior

!iffusion!iffusion – Can obtain #ig# rates ofCan obtain #ig# rates of

combustion energy release percombustion energy release perunit 'olumeunit 'olume – *x/ !iesel *ngine*x/ !iesel *ngine – 0odeling is 'ery complex2 no0odeling is 'ery complex2 no

well establis#ed approac#well establis#ed approac#



Turbulence + Basic ConceptsTurbulence + Basic Concepts

Turbulent flowTurbulent flow results w#en instabilities in a flow are notresults w#en instabilities in a flow are notsufficiently damped by 'iscous action and t#e fluid 'elocitysufficiently damped by 'iscous action and t#e fluid 'elocity

at eac# point in t#e flow ex#ibits random fluctuations/at eac# point in t#e flow ex#ibits random fluctuations/ T#e random unsteadiness associated wit# 'arious flowT#e random unsteadiness associated wit# 'arious flowproperties is t#e #allmar, of a turbulent flow and isproperties is t#e #allmar, of a turbulent flow and isillustrated for t#e axial 'elocity component in t#e nextillustrated for t#e axial 'elocity component in t#e nextfigure/figure/

One particularly useful way to c#aracteri$e a turbulent flowOne particularly useful way to c#aracteri$e a turbulent flow

field is to definefield is to define

meanmean

andand

fluctuating quantitiesfluctuating quantities

/ 0ean/ 0ean

properties are defined by ta,ing a time-a'erage of t#e flowproperties are defined by ta,ing a time-a'erage of t#e flowproperty o'er a sufficiently large time inter'alproperty o'er a sufficiently large time inter'al

5 5t 6 t7 – t8/t 6 t7 – t8/



T#e fluctuation2 p9t"2 is t#e difference between t#eT#e fluctuation2 p9t"2 is t#e difference between t#einstantaneous 'alue of t#e property2 pt"2 and t#e meaninstantaneous 'alue of t#e property2 pt"2 and t#e mean

'alue2 p'alue2 pa'ga'g 2 or 2 or

pt"6 ppt"6 pa'ga'g: p9t": p9t"

Or2 in general2 we can write+Or2 in general2 we can write+

;t"6 ;;t"6 ;a'ga'g : ;: ;ii9t"9t"

T#is manner of expressing 'ariables as a mean and aT#is manner of expressing 'ariables as a mean and afluctuating component is referred to as t#efluctuating component is referred to as t#e ReynoldsReynoldsdecompositiondecomposition//



3t t#is point2 t#e ,ey )uestion arises + 3t t#is point2 t#e ,ey )uestion arises +

“ “ What is the physical nature of aWhat is the physical nature of a

turbulent flow”? turbulent flow”?



T#e following figure gi'es aT#e following figure gi'es apartial answer to t#ispartial answer to t#is)uestion/ n t#is figure2 we)uestion/ n t#is figure2 we

see fluid blobs and filamentssee fluid blobs and filamentsof fluid intertwining/ 3of fluid intertwining/ 3common notion in fluidcommon notion in fluidmec#anics is t#e idea of amec#anics is t#e idea of a

fluid eddyfluid eddy

3n 3n eddy eddy is considered to beis considered to bea macroscopic fluid elementa macroscopic fluid elementin w#ic# t#e microscopicin w#ic# t#e microscopicelements composing t#eelements composing t#eeddy be#a'e in some wayseddy be#a'e in some waysas a unit/as a unit/



For example2 aFor example2 a vortex vortex imbedded in a flow would beimbedded in a flow would beconsidered an eddy/considered an eddy/

3 turbulent flow comprises many eddies wit# a multitude 3 turbulent flow comprises many eddies wit# a multitude

of si$es and 'orticities2 a measure of angular 'elocities/of si$es and 'orticities2 a measure of angular 'elocities/ 3 number of smaller eddies may be imbedded in a larger 3 number of smaller eddies may be imbedded in a largereddy/ 3 c#aracteristic of a fully turbulent flow is t#eeddy/ 3 c#aracteristic of a fully turbulent flow is t#eexistence of a wide range of lengt# scales2 i/e/2 eddyexistence of a wide range of lengt# scales2 i/e/2 eddy

si$es/si$es/For a turbulent flow2 t#e &eynolds number is a measureFor a turbulent flow2 t#e &eynolds number is a measureof t#e range of scales present< t#e greater t#e &eynoldsof t#e range of scales present< t#e greater t#e &eynoldsnumber2 t#e greater t#e range of si$es from t#e smallestnumber2 t#e greater t#e range of si$es from t#e smallesteddy to t#e largest/ t is t#is large range of lengt# scaleseddy to t#e largest/ t is t#is large range of lengt# scales

t#at ma,es calculating turbulent flows from firstt#at ma,es calculating turbulent flows from firstprinciples intractable/ 1e wilt discuss lengt# scales inprinciples intractable/ 1e wilt discuss lengt# scales inmore detail in t#e next section/more detail in t#e next section/



T#e rapid intertwining of fluid elements is aT#e rapid intertwining of fluid elements is ac#aracteristic t#at distinguis#es turbulent flowc#aracteristic t#at distinguis#es turbulent flow

from laminar flow/from laminar flow/T#e turbulent motion of fluid elements allowsT#e turbulent motion of fluid elements allowsmomentum2 species2 and energy to bemomentum2 species2 and energy to betransported in t#e cross-stream direction muc#transported in t#e cross-stream direction muc#

more rapidly t#an is possible by t#e molecularmore rapidly t#an is possible by t#e moleculardiffusion processes controlling transport indiffusion processes controlling transport inlaminar flows/laminar flows/

Because of t#is2 most practical combustionBecause of t#is2 most practical combustion

de'ices employ turbulent flows to enable rapidde'ices employ turbulent flows to enable rapidmixing and #eat release in relati'ely smallmixing and #eat release in relati'ely small'olumes/'olumes/



%*N.T4 SC3%*S N T=&B=%*NT F%O1S%*N.T4 SC3%*S N T=&B=%*NT F%O1S

n t#e turbulence literature2 many lengt# scales #a'en t#e turbulence literature2 many lengt# scales #a'ebeen defined< #owe'er2 t#e following four scales are ofbeen defined< #owe'er2 t#e following four scales are ofgeneral rele'ance to our discussion and2 in general2general rele'ance to our discussion and2 in general2are fre)uently cited/ n decreasing order of si$e2 t#eseare fre)uently cited/ n decreasing order of si$e2 t#ese

scales are as follows+scales are as follows+1. (L) Characteristic width of flow or macroscale1. (L) Characteristic width of flow or macroscale

T#is is t#e largest lengt# scale in t#e system and is t#eT#is is t#e largest lengt# scale in t#e system and is t#eupper bound for t#e largest possible eddies/ n aupper bound for t#e largest possible eddies/ n a

reciprocating internal combustion engine2 % mig#t bereciprocating internal combustion engine2 % mig#t beta,en as t#e time 'arying clearance between t#eta,en as t#e time 'arying clearance between t#e

piston top and t#e #ead2 or per#aps t#e cylinder bore/piston top and t#e #ead2 or per#aps t#e cylinder bore/



2.2. l l oo) Integral scale or turbulence macroscale) Integral scale or turbulence macroscale

T#e integral scale p#ysically represents t#eT#e integral scale p#ysically represents t#e

mean si$e of t#e large eddies in a turbulentmean si$e of t#e large eddies in a turbulentflow< t#ose eddies wit# low fre)uency and largeflow< t#ose eddies wit# low fre)uency and largewa'elengt#/ T#e integral scale is alwayswa'elengt#/ T#e integral scale is alwayssmaller t#an %2 but is of t#e same order ofsmaller t#an %2 but is of t#e same order ofmagnitude/magnitude/

!. l !. l

" " Taylor microscale Taylor microscale

T#e Taylor microscale is an intermediate lengt#T#e Taylor microscale is an intermediate lengt#scale between t#e integral scale scale between t#e integral scale l l o" ando" and>olmogoro' Scale >olmogoro' Scale l l ,"2 but is weig#ted more,"2 but is weig#ted moretowards t#e smaller scales/ T#is scale istowards t#e smaller scales/ T#is scale isrelated to t#e mean rate of strain/related to t#e mean rate of strain/



#. l$"#. l$" Kolmogorov microscale Kolmogorov microscale

T#e >olmogoro' microscale is t#e smallest lengt# scaleT#e >olmogoro' microscale is t#e smallest lengt# scale

associated wit# a turbulent flow and2 as suc#2 isassociated wit# a turbulent flow and2 as suc#2 isrepresentati'e of t#e dimension at w#ic# t#e dissipationrepresentati'e of t#e dimension at w#ic# t#e dissipationof turbulent ,inetic energy to fluid internal energy occurs/of turbulent ,inetic energy to fluid internal energy occurs/T#us2 t#e >olmogoro' scale is t#e scale at w#ic#T#us2 t#e >olmogoro' scale is t#e scale at w#ic#

molecular effects ,inematic 'iscosity" are significant/molecular effects ,inematic 'iscosity" are significant/ T#e final point we wis# to ma,e concerningT#e final point we wis# to ma,e concerning lk lk is possibleis possiblep#ysical interpretations/ np#ysical interpretations/ n TennekesTennekes model of amodel of aturbulent flow2turbulent flow2 lk lk represents t#e t#ic,ness of t#e smallestrepresents t#e t#ic,ness of t#e smallest

'ortex tubes or filaments t#at permeate a turbulent flow2'ortex tubes or filaments t#at permeate a turbulent flow2w#ile ot#ers suggest t#atw#ile ot#ers suggest t#at lk lk represents t#e t#ic,ness ofrepresents t#e t#ic,ness of'ortex s#eets imbedded in t#e flow/'ortex s#eets imbedded in t#e flow/



D!I"ITI#" #! T$%&$L"T !L'D!I"ITI#" #! T$%&$L"T !L'

*D*D

=nli,e a laminar flame2 w#ic# #as a propagation 'elocity=nli,e a laminar flame2 w#ic# #as a propagation 'elocityt#at depends uni)uely on t#e t#ermal and c#emicalt#at depends uni)uely on t#e t#ermal and c#emicalproperties of t#e mixture2 a turbulent flame #as aproperties of t#e mixture2 a turbulent flame #as apropagation 'elocity t#at depends on t#e c#aracter of t#epropagation 'elocity t#at depends on t#e c#aracter of t#e

flow2 as well as on t#e mixture properties/flow2 as well as on t#e mixture properties/

For an obser'er tra'eling wit# t#e flame2 we can define aFor an obser'er tra'eling wit# t#e flame2 we can define aturbulent flame speed turbulent flame speed 2 S2 Stt as t#e 'elocity at w#ic#as t#e 'elocity at w#ic#unburned mixture enters t#e flame $one in a directionunburned mixture enters t#e flame $one in a direction

normal to t#e flame/normal to t#e flame/



n t#is definition2 we assume t#at t#e flame surface isn t#is definition2 we assume t#at t#e flame surface isrepresented as some time-mean )uantity2 recogni$ingrepresented as some time-mean )uantity2 recogni$ing

t#at t#e instantaneous position of t#e #ig#-temperaturet#at t#e instantaneous position of t#e #ig#-temperaturereaction $one may be fluctuating wildly/reaction $one may be fluctuating wildly/

Since t#e direct measurement of unburned gas 'elocitiesSince t#e direct measurement of unburned gas 'elocities

at a point near a turbulent flame is exceedingly difficult2at a point near a turbulent flame is exceedingly difficult2at best2 flame 'elocities usually are determined fromat best2 flame 'elocities usually are determined frommeasurements of reactant flow rates/ T#us2 t#e turbulentmeasurements of reactant flow rates/ T#us2 t#e turbulentflame speed can be expressed as +flame speed can be expressed as +

St6 m ( 3a'gSt6 m ( 3a'g ρρuu""T#e reason for using t#is time-smoot#ed flame area isT#e reason for using t#is time-smoot#ed flame area is

s#own below +s#own below +



*xperimental*xperimentaldeterminations ofdeterminations of

turbulent flame speedsturbulent flame speedsare complicated byare complicated bydetermining a suitabledetermining a suitableflame area/ 32 for t#ic,2flame area/ 32 for t#ic,2

and fre)uently cur'ed2and fre)uently cur'ed2flames/ T#e ambiguityflames/ T#e ambiguityassociated wit#associated wit#determining t#is flamedetermining t#is flamearea can result inarea can result inconsiderable uncertaintyconsiderable uncertaintyin t#e measurement ofin t#e measurement ofturbulent burning 'elocity/turbulent burning 'elocity/



ST&=CT=&* OF T=&B=%*NT P&*0?*!ST&=CT=&* OF T=&B=%*NT P&*0?*!F%30*SF%30*S

3gain2 referring to t#e pre'ious figure we can say t#at T#e 3gain2 referring to t#e pre'ious figure we can say t#at T#einstantaneous flame front is #ig#ly con'oluted2 wit# t#einstantaneous flame front is #ig#ly con'oluted2 wit# t#elargest2 folds near t#e top of t#e flame Fig/ a"/ T#elargest2 folds near t#e top of t#e flame Fig/ a"/ T#epositions of t#e reaction $ones mo'e rapidly in space2positions of t#e reaction $ones mo'e rapidly in space2

producing a time-a'eraged 'iew t#at gi'es t#e appearanceproducing a time-a'eraged 'iew t#at gi'es t#e appearanceof a t#ic, reaction $one Fig/ b"/of a t#ic, reaction $one Fig/ b"/

T#is apparently t#ic, reaction $one is fre)uently referred toT#is apparently t#ic, reaction $one is fre)uently referred toas aas a turbulent flame brushturbulent flame brush//

T#e instantaneous 'iew2 #owe'er2 clearly s#ows t#e actualT#e instantaneous 'iew2 #owe'er2 clearly s#ows t#e actualreaction front to be relati'ely t#in2 as in a laminar premixedreaction front to be relati'ely t#in2 as in a laminar premixedflame/ T#ese reaction fronts are sometimes referred to asflame/ T#ese reaction fronts are sometimes referred to aslaminarlaminar flameletsflamelets//



3s mentioned abo'e2 spar,-ignition engines operate wit# 3s mentioned abo'e2 spar,-ignition engines operate wit#turbulent premixed flames/ &ecent de'elopments inturbulent premixed flames/ &ecent de'elopments in

laser-based instrumentation #a'e allowed researc#ers tolaser-based instrumentation #a'e allowed researc#ers toexplore2 in muc# more detail t#an pre'iously possible2explore2 in muc# more detail t#an pre'iously possible2t#e #ostile en'ironment of t#e internal combustiont#e #ostile en'ironment of t#e internal combustionengine combustion c#amber/ T#is is s#own in t#e nextengine combustion c#amber/ T#is is s#own in t#e nextslide/slide/

n t#ese flame 'isuali$ations2 we see t#at t#e di'isionn t#ese flame 'isuali$ations2 we see t#at t#e di'isionbetween t#e unburned and burned gases occurs o'er abetween t#e unburned and burned gases occurs o'er a

'ery s#ort distance and t#e flame front is distorted by'ery s#ort distance and t#e flame front is distorted bybot# relati'ely large- and small-scalebot# relati'ely large- and small-scale wrin$leswrin$les//



T#is figure s#ows a timeT#is figure s#ows a timese)uence of two-se)uence of two-dimensional flamedimensional flame'isuali$ations in a spar,-'isuali$ations in a spar,-ignition engine from aignition engine from a

study/study/T#e flame begins toT#e flame begins topropagate outward frompropagate outward fromt#e spar, plug2 as s#ownt#e spar, plug2 as s#ownin t#e first frame2 andin t#e first frame2 and

mo'es across t#emo'es across t#ec#amber until nearly allc#amber until nearly allt#e gas is burned/t#e gas is burned/



T#ree Flame &egimesT#ree Flame &egimes

T#e 'isuali$ations ofT#e 'isuali$ations ofturbulent2 flamesturbulent2 flamespresented before suggestpresented before suggestt#at t#e effect oft#at t#e effect of

turbulence is to wrin,leturbulence is to wrin,leand distort an essentiallyand distort an essentiallylaminar flame front/laminar flame front/

Turbulent flames of t#isTurbulent flames of t#is

type are referred to astype are referred to asbeing in t#ebeing in t#e wrin$ledwrin$led

laminar%flame regimelaminar%flame regime//



T#is is one pole in ourT#is is one pole in our

classification of turbulentclassification of turbulentpremixed flames/ 3t t#epremixed flames/ 3t t#eot#er pole is t#eot#er pole is t#edistributed%reactiondistributed%reactionregimeregime//

Falling between t#eseFalling between t#esetwo regimes is a regiontwo regimes is a regionsometimes referred to assometimes referred to ast#et#e flamelets%in%eddiesflamelets%in%eddies

regimeregime//



&egime Criteria&egime Criteria

&ecall t#at t#e smallest scale2 t#e >olmogoro'&ecall t#at t#e smallest scale2 t#e >olmogoro'microscale2microscale2 lk lk 2 represents t#e smallest eddies in t#e flow/2 represents t#e smallest eddies in t#e flow/T#ese eddies rotate rapidly and #a'e #ig# 'orticity2T#ese eddies rotate rapidly and #a'e #ig# 'orticity2resulting in t#e dissipation of t#e fluid ,inetic energy intoresulting in t#e dissipation of t#e fluid ,inetic energy into

internal energy2 i/e/2 fluid friction results in a temperatureinternal energy2 i/e/2 fluid friction results in a temperaturerise of t#e fluid/rise of t#e fluid/

3t t#e ot#er extreme of t#e lengt#-scale spectrum is t#e 3t t#e ot#er extreme of t#e lengt#-scale spectrum is t#eintegral scale2integral scale2 lolo w#ic# c#aracteri$es t#e largest eddyw#ic# c#aracteri$es t#e largest eddy

si$es/ T#e basic structure of a turbulent flame issi$es/ T#e basic structure of a turbulent flame isgo'erned by t#e relations#ips ofgo'erned by t#e relations#ips of lk lk andand lolo to t#e laminarto t#e laminarflame t#ic,ness2flame t#ic,ness2 δδl/l/



T#e laminar flame t#ic,ness c#aracteri$esT#e laminar flame t#ic,ness c#aracteri$es

t#e t#ic,ness of a reaction $one controlledt#e t#ic,ness of a reaction $one controlledby molecular2 not turbulent2 transport ofby molecular2 not turbulent2 transport of#eat and mass/ 0ore explicitly2 t#e t#ree#eat and mass/ 0ore explicitly2 t#e t#ree

regimes are defined by +regimes are defined by +

1rin,led laminar flames+1rin,led laminar flames+ δδll @@ l l k k

Flamelets in eddies+Flamelets in eddies+ l l oo AA δδll AA l l k k !istributed reactions+!istributed reactions+ δδll AA l l oo



1#en t#e flame t#ic,ness2 is muc# t#inner t#an t#e1#en t#e flame t#ic,ness2 is muc# t#inner t#an t#esmallest scale of turbulence2 t#e turbulent motion cansmallest scale of turbulence2 t#e turbulent motion canonly wrin,le or distort t#e t#in laminar flame $one/ T#eonly wrin,le or distort t#e t#in laminar flame $one/ T#e

criterion for t#e existence of a wrin,led laminar flame iscriterion for t#e existence of a wrin,led laminar flame issometimes referred to as t#esometimes referred to as t#e Williams%&limovWilliams%&limov

criterioncriterion//

3t t#e ot#er extreme2 if all scales of turbulent motion are 3t t#e ot#er extreme2 if all scales of turbulent motion aresmaller t#an t#e reaction $one t#ic,ness2 t#en transportsmaller t#an t#e reaction $one t#ic,ness2 t#en transportwit#in t#e reaction $one is no longer go'erned solely bywit#in t#e reaction $one is no longer go'erned solely bymolecular processes2 but is controlled2 or at leastmolecular processes2 but is controlled2 or at least

influenced2 by t#e turbulence/ T#is criterion for t#einfluenced2 by t#e turbulence/ T#is criterion for t#eexistence of a distributed-reaction $one is sometimesexistence of a distributed-reaction $one is sometimesreferred to as t#e !am,o#ler criterion/referred to as t#e !am,o#ler criterion/



4ence2 in addition to t#e &eynolds Number &e"2 we4ence2 in addition to t#e &eynolds Number &e"2 we#a'e anot#er number t#at t#at c#aracteri$es t#e#a'e anot#er number t#at t#at c#aracteri$es t#e

turbulent flame 'elocity called !am,turbulent flame 'elocity called !am,#ler number !a"/#ler number !a"/T#e fundamental meaning of t#e !am,T#e fundamental meaning of t#e !am,#ler number2#ler number2!a2 used #ere is t#at it represents t#e ratio of a!a2 used #ere is t#at it represents t#e ratio of ac#aracteristic flow or mixing time to a c#aracteristicc#aracteristic flow or mixing time to a c#aracteristic

c#emical timec#emical time//t represents t#e ratio between t#e c#aracteristic flowt represents t#e ratio between t#e c#aracteristic flowtime to t#e c#aracteristic c#emical time/time to t#e c#aracteristic c#emical time/



1#en c#emical reaction1#en c#emical reactionrates are fast inrates are fast incomparison wit# fluidcomparison wit# fluidmixing rates2 t#en !a A 82mixing rates2 t#en !a A 82and aand a fast%chemistryfast%chemistryregimeregime is defined/is defined/Con'ersely2 w#enCon'ersely2 w#enreaction rates are slow inreaction rates are slow incomparison wit# mixingcomparison wit# mixingrates2 t#en !a @ 8/rates2 t#en !a @ 8/

T#is is s#own in t#eT#is is s#own in t#efigure to t#e rig#t/figure to t#e rig#t/



!efinition of t#e t#ree flame regions!efinition of t#e t#ree flame regions

'" WR()&*+, *-()-R%/*-+ R+0(+ '" WR()&*+, *-()-R%/*-+ R+0(+

n t#is regime2 c#emical reactions occur in t#inn t#is regime2 c#emical reactions occur in t#ins#eets/s#eets/

&eferring again to t#e pre'ious figure2 we see&eferring again to t#e pre'ious figure2 we seet#at reaction s#eets occur only for !am,o#lert#at reaction s#eets occur only for !am,o#lernumbers greater t#an unity2 depending on t#enumbers greater t#an unity2 depending on t#eturbulence &eynolds numbers2 clearly indicatingturbulence &eynolds numbers2 clearly indicating

t#at t#e reaction-s#eet regime is c#aracteri$edt#at t#e reaction-s#eet regime is c#aracteri$edby fast c#emistry in comparison wit# fluidby fast c#emistry in comparison wit# fluidmec#anical mixing"/mec#anical mixing"/



2" ,(1R(34+,%R+-5(6) R+0(+ 2" ,(1R(34+,%R+-5(6) R+0(+

6ne way to enter this regime is to require6ne way to enter this regime is to requiresmall integral length scales7 lo 8 l$" 9 '7 andsmall integral length scales7 lo 8 l$" 9 '7 andsmall ,am$ohler numbers ,a 9 '". his issmall ,am$ohler numbers ,a 9 '". his isdifficult to achieve in a practical device7difficult to achieve in a practical device7since these requirements imply that7since these requirements imply that7

simultaneously7 lo7 must be small and vrmssimultaneously7 lo7 must be small and vrmsmust be large7 i.e.7 small flow passages andmust be large7 i.e.7 small flow passages andvery high velocities.very high velocities.

:ressure losses in such devices surely:ressure losses in such devices surelywould be huge and7 hence7 render themwould be huge and7 hence7 render themimpractical. -lso7 it is not clear that a flameimpractical. -lso7 it is not clear that a flamecan be sustained under such conditions.can be sustained under such conditions.



!" /*-+*+1%()%+,,(+1 R+0(+ !" /*-+*+1%()%+,,(+1 R+0(+

T#is regime lies in t#e wedge-s#apedT#is regime lies in t#e wedge-s#apedregion between t#e wrin,led laminar flameregion between t#e wrin,led laminar flameand distributed-reaction regimes as s#ownand distributed-reaction regimes as s#own

in t#e pre'ious figure/ T#is region isin t#e pre'ious figure/ T#is region istypified by moderate !am,o#ler numberstypified by moderate !am,o#ler numbersand #ig# turbulence intensities/ T#isand #ig# turbulence intensities/ T#isregion is of particular interest in t#at it isregion is of particular interest in t#at it is

li,ely t#at some practical combustionli,ely t#at some practical combustionde'ices operate in t#is regime/de'ices operate in t#is regime/



Flame stabili$ationFlame stabili$ation

%ow 'elocity bypass ports%ow 'elocity bypass ports

&efractory burner tiles&efractory burner tiles

Bluff body Flame-#older &ecirculation"Bluff body Flame-#older &ecirculation"Swirl or et-induced recirculating flowsSwirl or et-induced recirculating flows

&apid increase in flow area creating&apid increase in flow area creating

recirculating separated flowrecirculating separated flow

ramadan youssef sakr moustafa_lecture9-turbulent combsution

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