Electron energy exchanges in hydrocarbon flames

COMBUSTIONAND FLAME 19, 237-247 (1972)

237

Electron Energy Exchanges in Hydrocarbon Flames D. BRA DLEY

D, aarrment of Meehamcal Engineer;~tg, The Unwemty, Leed~ 2. England L. F. JESCH

Department of Mechameal b.ngtneer,ng,B:rmingham Umverslty, England and

C. G. W. 5HEPPARD Department of Mechanical Engmeeru~, ~ml,ersttv of Teet~nology,Loughborou~,h,~'ngland

The paper presents a semltheoretlcal, quantitative ".teatment of the lmerreh~tlonshlp between extra equilibrium excttanon c f some speciesand elevanon o| electron temperature above gas temperature, m hydrocarbon-air flames Certain assumptions ale neee,~sary m order to overcome the incompletenessof available data It is suggested that elee~,ron temperatures may be eievated by some hundreds, but not thousands, of degrees as a consequence of colhsmns of the second kind. possibly with vibranonally "warm" OH IX: 11)

1. Introduction Some relatively recent measurements el electron temperatures m hydrocarbon flames, using electrostatic probes, have 'shown electron temperatures e~ther close to gas temperature or elevated above it by some hundreds of degrees [1-5] ]['here is a need to check these values with techmques other thau those which revolve such probes, but ff the existence of some elevation of electron temperature ~s accepted, then the most probable explanation is in terms of electron coll~lons of the second kind !n which electrons gain energy from species m the reactmn zone wMch possess extra equilibrium excitation, as ~uggested by van Engel and Cozen~ [6] It : however, improbable that the electrons are s,.:,rticlenfly energ, tic to coqt71bute a ,,Ip~aficant ,mmber of electron lomzmg colhvon~ [5] The prescr, t work mvol"es so|-~te ~".,enSlOrl- ,, u,c thcoretlcaJ approach o1 Bc~ and B~a.l,e,, '/~ ¢0 c!ect~o|l collisions and ~,.,,!e :r, tcrpre ~ .:ion, ." exp~ ~"ntal obgervatv.0s ,,," hydro, ,coG:, flame" in the l i g h t , these

2. Theory Following Ref 7, the rat* of electro~ energy loss per umt volume per electron per unit volume, due to melastzc colhsions m which e!cctrons rinse molecules of species 'T" from an energy level "x" to a higher energy level "y", ts gtven by

hi(x,y) Nmo A Eitx. yr.~~ where kr( x v) ;'- the rate constant for the lntei'actmn, Nj,.~ ts ~ile number density for sp~.cm "f" m me "'x'" energy level and AEt(x,> ) ts the molecular energy change due to the ~olhsmn ~ : e total rate of electron ener~ Io~ per unit volume per electlroa Or- dnlt voJ=Aille to all species for ',dl ;no]~';,~ar trar~smons mvolvmg energy gmn by ;holecule~ IS g;ven by

tl) ?

#

Publ~.~l~dey ?,met,can blsevler PqV,,sbl~'.,~))'a%

!,le

D BRADLEY. L F JLSCI-[ and C G W SHEPPARD

.'38 where S indicates the summation of all inelas,lc i

l~anslllOnb betwe,,n enerby le'ed', for tile speclos '1" and -.S indicates tile sunlnlatl(..n of tile separate t

spec:es eilergy exchanges over all species under ,mns,deratlon The energy ext.llange *n elastic colhsmns is neghglble compared with thai m melastn, colhslons [7] Colhstons of the secand kind may also occur, in whl,.h electrons gain energy from excited molet.ulcs which make the transition Irom tile energy !¢",q 'l ' to tile lower energy level ":~'" T h e total ~,m. of electron energy gain per amt volume per ,.'let.lion pet unit volumt' horn all ',pecles for all mole,, tla~ lrdIlSltlOnS Iri~OIVl'lg envrgy loss by nlo]ecLIles IS given by

C,

where te/¢~.~,~ r, tile rate constant kit the ~'lectron energy gain mt,'ractlOn, and Nt~v/ ts the nunlber de,lsny l o t st,e~tt-s " ' f ' In the '?,"" energy level Cun,ader ~ondltlons such that all component specl, s o l the gas are in thermal equlhbllam at the bulk gaq ten:peratme, To Z repTesents a sltrnnlatl n over all species Let the 'oral loss rate e,nd gale rate ot e!ec'ron energy per electron in umt volume be Lt, and Gb respectively Tl~e e~ectrons will attain a steady state electron temperature ~.qual tu the bulk gas temperature, wltilln a very ,.hnrt relaxatmn time [8] Under these condmons L~ = Gb

(3)

TItI~ equa,mn provides a means of checking tile v,lhdlty of tho various rate codqanl computations, derived horn electron cnlhslon cross sectmn data Confider tile ~ltUdtlon In which species are presc,,t n, the gas which possess c\frd equl]lbrlunl e'.,t.tt~noll, for example, as a result of chemical re,~,.tlon Such ",pec~es are ~ 1dialled by the super",t.rlpt .... and dr." .o,Jsldered separatel,, ¢roln t]l~ ~e spt ales ~.onlprlsmg the huh,. gas at temperature To Tile effect ol Ihe interaction between ,,old) lhese spet les and the electro.v, WlJl be for tl~e latter to all,m a st~.ady state tenlpelature T* , to b~ called the excited species eleclrc, n tempera-

ture The v21ue ct tl'ns will be greater than T,~ and wdl depend upon the character of: the exoted species and their various degrees of excllatlon ~. m Eqs ( I ) and (2) ~s now a summation soldy oit" the species with extra equilibrium excltal~on, and me corresponding m,ml loss antl gain ,ates of electron energy per electron in unit volume are replesented bv L* and G*, ,~,,,pec~wely The value ol '/"; IS given by L* - G*

(4}

Now ~onslder a fl~me model in which there exist electrons, species m thermal equilibrium at the bulk gas temperatme T o , and some species with extra equilibrium eX.lCation Under these condl. tl~_n~, the steady state electron temperature is T e . m'etme~tate in salue between Tz, and T*~, such th'lt the t ."t rate of loss of electron energy to the sp.~c es in thermal cqulhbrlum at T~ is balanced by t;ae net ~ate of gant of eJectron energy from the species wJ~!, extra equlhbrlum exaltation This condition is expressed by Lo

Gt,

- G*

L*.

t5~

The energy exchange rates ale shown diagrammatically :n Fig l For values of electron temperatureo below T* there is a net rate of gain of elecnon energy flora excited species, (G* - L*), glver~ by the broken curve to flue left ot T* For values o f electron temperatures greater than T* there is a net nite ot loss of electron energy to exe, te J species. (L* G * l , given by the other broke~ curve m the nght ot T,*. The net r,,te of loss ol electron energy to the species in thermal equlhbllun~ at Tb, (Lb - Go). Is given by the full curve I o , values ol electron temperature greater than T~ , whde the other full curve to the left of Zb gl,,e! the net rate or gain of el'.':atron energy from these species for electron temperatures less than "jr'b The steady state electron temperature for the in,xture of bulk gas and species with extra equlhbrlum ex~.ltatlon, To, is gwen by the intersection ot the (L,~ - Go) and (G* - L*) curves The derivation of values of L and G for bulk gasescomposed ot CO2, CO, N2. O2. H2, and H 2 0

ELECTRON ENER(,Y EXCtIANGES IN FLAMES

239

~ { L ~ - G b)

,tO-6") p/ / /

u/ z z o w

/

\\\

1

\

.J L~

/ !

~'E u. m o ~

/

Et.ECTRON

TEMPERATURE

FI~" [ EleL.tronenergy e~ change rate'. ,t%,, tun~?non el elecrrod temperature has been described previously [7,8] The rate constan' for a particular trallsitlOn Is obtained tram tt'e appropriate spectrum at electron colhsloI; cross section, Qlix, yl(~) and tile Maxwelhan energy distribution, Llemg the expression

]?l(x 3) (kT~)-~

28t 2 (6)

(nme)l -JE:,I Eqll':

YI(E) e ' . p ( - E

kTe)dE

where m e is the electron mdsg and ~." the electron energy The present work uses the same sources of data as previously tar cross sections Derivation or values ot G* and L* presepts lormidable difficulties, on tv, o counts First, of the common flame species with ex~'ra equthbrmw excitation, COz, C~., CH, and OH, the ,rely one for which cross section data are available is CO: Thl <. is a consequence of the transient character of th,. other species Second, reformation on the populations of ,, particular species hi each energy level under flame condmons Is incomplete For the~e reasons, in what follows, several a~'~umptlons are made in the derivation of apploxmaate values of (G ~' - L*) This treatment is held to be justffi. able In an explo,arc, ry investigation

Two approaches were employed, m the first, to be described m St.,c 3 I, theorettcal est*mates of energy exchange rates are made and m the second. to b,." described m Sec 3 2, some experimental re~,ults are used to estimate the value at the excited specxes electron temperature, T~, 3 Application to Methane-Air Flames In R e f ":, It was suggested that the elevaUon of electron temperature possibly was attributable to electron co[hslons wrth the excited specms OH* and C ~ . In the methane-alr flame studies which were report~,d, the OH* emission was measured at 3063 Jk [2Z ~ z H (0,0)] and the spatial varlatton of inlellslty of omission was toand to correlate wrth electron temperature elevation in Ref 9, the spatltal variation of electron temperature m oxypropane flames showed a su~ttlar varlatlon to that at the rotauooal temperature of electromcalla, excited hydroxyl. The variation of electron temr~erature elevation m methane-mr flalnes with equwalenee ratio, reported m Ref 5, has been found to correlate with OH* emls:,lon at 3063 A rather than the C~ emlssmn at 5163,~ [3 ll~ - 3 lll~(0 0)1. u,,mg a type at analysis to be ,.ruthned m See 3.2 E×penments suggest ~hat .oneentrahons of OH m hydrocarbon flan~e

D BRADLEY, L F .IESCHand C G W SHE[PARD

240 reaction zones are geI~er,,,lly greater thai those of C~ [I0, I I I For these reasons, ~t is assumed in the tollowmg analyse< of ,nethane-mr flames that tlae principal source ot e'~ergy lot the elevatlor of electron temperature is excess,.vely excited OH This probably arises trom the reaction, suggested by Gaydon [12], CH 4 0 2 -. CO + O H * .

(1)

T'~'re lnI~.USlty of the chemllumlnescent radiation from OH* ~s a measure of the extra-equdlbnum excitation 3.1 Theoretical Denvanon of (G* - L*) In this section, It is ,reuessary to raake assumptions both about the vak, es of electron colhslon cross sections ,or the hydroxyl radical and also about th- populations m the different energy levels In the p,~o.'" ,~),tc~'L there are four tmportam energy levels of the hyaru,xy! radical There are three vibrational ~evels, at 0 45, 0 87, and I 27 e v above the ground level of the grou,nd (2 [11 slate ~nd one I,)w lying electro,,ically excited (~ ~) state a~ 4 02 eV above the ground level [13, 14] There are three vibrational levels alcove the ground level of d,lS latter s~ate Of the six species, whose e'e,zy level and associated cross section data have ~-e,~ used in the pieser.t work, carbon dioxide has energy, levels which are closest to those of hydro~.,,~ .rnese energ! levels for carbon dioxide ~ave been discussed m P.ef 7 The significant levels lot energy exchange are vibrational levels e)f d,c grov.¢ state, at 0 3 , 0 6 and 0 q eV and a )~',J'2r star(, at 3 1 eV The procedure therefore [t.o neon adopted of using tl~,e dat~ on energy le,¢els a, d crgss sJctlons for CO. to constru,.) the net electron ,m, rgy gain rate curve, conl~.'qucnt upon elect)on culhs)ons with excited OH fh~ts probably leads to an overestimate of electron (nergy gain r;,te, clue Io the relatively tugh values of the cross ~ectton~, ul,hough th~s could be partmlly baLJnz,-a by an ur,derestm'mte due to ~be ~mallel rnolecular energy increments of CO2 There are no complete data fo~ the p~pulz, • ": m the dlffe)enl e:~¢tgy ,e ~els of OH m methane-air fla.,~.s Upper ,,tare ~otatlop,l] temperatures grez:er

than 5000°K, ac:ompamed by ground state rotational temperatures clo~ to the equthbnum temperature, have been reported for methane-mr [15], and methal.e-oxygen flames [16]. Bulewtcz, Padley, and Smlta [i 1] have recorded upper state wbratlonal temperatures of 7000°K for both C2(A 3 Hg) and OH (A 2 Z*) in acetylene-oxygen flames and accompanying lower s:ate vibrational temperatures of up to 3000°K for C2(Xallu) and OH (X2,v), the latter figure being some hnndredb of degrees hlghel than the measured sodium D-hne reversal temperatures Number densities were obtained for the ground state, only, but Porter e t a l . [10] have measured hydroxyl number densltlesm the upper state which are approximately seven orders of .'-oagJutude less than m the groultd state Tills concentrat:on corresponds :o that for a hydroxyl radical in equlhbnum at a temperature of 3000°K It was decided to assign a value of 3000°K to the vlbratloqal, rotat.~onal and electronic 'tempera. ture", to represent the: ~.~e~;~¢~.%xtra equdlbrlum e×cll.atlo,,, albeit tha~t th:s most p'obably repre~entq ~. ,;'?-etttraate of the ground electronic state exc,tatlon T~,c t~r*]rz~'nannequation was used to obtain population,, at the different energy levels for this temperature.. Let g* and 1* be the gain and loss sates respectively of electrnn energy per unit volume per electron per unit vollume per excited radical per unit volume, If N* is the number density of e tclted radicals, ,n tills case. hydroxyl radicals, then Eq (5) o~<.,~;~.~. L b - Gb

= N*¢g* -

l*).

(7)

The theoretical net electron er,,ergy gain rate, (g* /*), derived on the basl,; of the abo,'e assumptions, Is ~.,~ ','.', ,n Fig 2 Also shown In Fig 2, by hid broken curve, IS ~ t ,~et gain rate '~zr,at.)Oll on the assumption that the lractton of the OH radicals m the upper state is 10 -3 times t~" t~tal O1-1 population, some four orders of magn]lt ~e greater than that leported expenmen, ,lly ~,v Porter et al [10] in order to oVtam the theoretical curve of net r,.,:.e o! lots ofe~ectron energy (Lb - Gb), agaI,"st ,'~ectron temperature ,n methane-air flames using

ELECTRON ENERGY EXCHANGESIN FLAMES

241

Eqs ( l ) and (2), the gaseous composition at Tb and the appropriate pressure must be known In the absence of experimental data on thls, the composition was taken to correspond ~o the equzhbrtum products of combustion at '/',~ It was found that more than 99 9% of the o3nsmuents consasted of the six gases 02, H2, H20, CO, CO2, and N2, for which electron co]hslon cro$~ section data are avadable Hence, values of (Lt, - Gb) for different values of electron 'emperature were obtained using Eqs (I), (2), and (6) The curve of (Lb - d,O for the equdlbrlum products of a stolchmmetrlc methane-mr flame at a pressure of 38 Tort and a bulk gas temperature of 1223°K is shown by a broken !='ze curve m Fig 3 The gas temperature was that obLamlng at the position of peak electron temperature in an expertmental flame "ihe full line curves show the variation of net rate of gain of electron energy, N*(g* /*) tor proporttons of OH equal to 0 I, 1 0, and 10% m turn These net gum rate curves are based upon

OH IN COMPLETE EQUIUBRIUM ~ 3OOO°LK

'E

the fult hne curve of Fig 2. wtth an excnatton temperature of 3000°K A net gain rate curee based upon the broken curve In Fig 2 is shown by the broken curve for 1 0% OH. With I% of the gas as hydroxyl, a proportion somev,hat higher than that usually recorded m hydro, arbon flames, an elevatmn of electron temperature of 150°K above gas temperature is indicated when the hydroxyl excitation temperature Is 3000°K The greatest elevation of electron temperature above bulk gas temperature occurs at a gas t:inperature below the max,_mum gas temperature and upstream of the position of the latter in this ~ame region, Porter [4] hz.s found that the decrease of electron temperatures was not nearly as rapid as that of gas temperatures as the burner surface was apploached The regior, of electron temperature elevation under consideration Ls a region of only partial o',er#ll chemical reactton For this reason, the assumption that the gases ~omprlse the products of comb,ast~on in

' '~.~

~\ / ~

LOWE R THREE LEVELS (~ :~OOO°K

\'. ~.~,\

UPPER ELECTRONIC STATE FRAC I IONAL POPULA3ION \\

\

~'~ 4J

:

i(5~

\\\

•

m

I'

cJ ~:

1OOO ELECTRON

2000 r:MPEAArURE

3000 (¢K)

Fig 2 "l'heoretleal net deetrorl cner,,y g,l~n ratl,' trol~, .',"1~ d hydroxyl

40~

D BRADLEY. L F JESCH and ( G W SHEPPARD

242

\.r

~" "

't

CH, - AIR

L '

/ I /¢'1 Lb* O~,)

c '~" 'xcc'~,\

w 'E

Q:

x:~,/

'l°-'.°~

///

--

2O00 ELECTRON

'

~--3

"O~

TEMPERATURE

,tOOO ~K)

I'lg 3 I'h't,.on energy e~.ch rage rate~ Item excited hydroxyl In iyiethdne.-,~lrllamd and ,Ill equilibrium at the obselved bulk gas temperature. possibly le~ds to significant error in the construcuon of the (Lb - Gb) ~urves In the absence of complete expertment,d composition plofdes .hrough the flame, an alternative .ssumptxon is made, namely th,it tht. gas at the bulk gas temper,dule, correspoodmg to the peak value of 'P~ , (orh,~lsts el z,tr A curve of net rate el electron enetg/ loss (L ~ - G~,), against electnon temperalure was constJucted lot a~r at 38 Tort and a bulk gas temperature ul 1223°K and this is shown by the t,laaln dotted curvt, in Fig 3 The true net rate of electron energy loss cu, ~'° probably hes somewhere between file two curve~

shown m F~g 3 The curve based upon lhe electron colllSlOp cross sections For dtI shows tt greater elevation of steady state electron tempera ture With 1% of the gas as hydroxyl, with ar~ excttaqon temperature of 3000°K. ar elevation of electrt a temperature of 1010°K above gas temperature 1~ l n d i c d t c d The point of inflection in the chain dottecl curve of (Lb - Gb) for anr m Fig 3 t s o f m t e r e s t At the lower values of electron temperature, the predomznar, t electron energy loss is to oxygen, due to the p esence of a low lying vibratiuna! energy level ,~t 0 I t) eV However, at blghet values of electron temperature, the energy levels it* mtrogen

243

ELECTRON ENERGY' FXCHA,qGES IN FI AMF'~ become more important and the po!rlt of !nl]ect~on is explained by the growm~ significance ,3f the energy loss to nitrogen in fl~:viure~ wlih d greater number of constituents. 1.his effect is smoodic~ out on the energy loss curve

1 rlslng a 3 In diameter Oat flame burner The mas~, flow rate of gas was maintained constant at 0 163 g s -I In ihe interpretation ofexpenmental results which follows, the measured emission intensity,l. is taken as a measure of extra equdibnum excitation The burner .rod experimental techniques emplo/ed .ire described m Ref 5 Some of the results lot a methane-a~r flame of equwalence raho of umJ:y are show. in Fig 4 This shows for &fferent pressures, P, the peak value of Ye, the intensity of the emission at 3063 A at this pos:t.on and the corresponding value of gas temperature,

3 2. Experimental Denvatmn of Excited Species Electron Temperature In the work reported here. measureroents were taken, over a range of pressure bet*'een 40 and IOC Terr of electron temperature, Te. gas temperature Tt,, and lntehsi~y • - ? u _ ~ , ~ o n at 3063 A,

TeI~K) I

3000~ 2800 I

~__

I

2600

1400 ~s

' ~ ~ l

T;

1300

\x

040

I u, 4

| \perlmcpt,d

OH clnlsslon, dn~

~ - - - - 5 ~

--80 PRESSURE (TI~R~R)

10G

v a l u u ~ ot m a x l m u i p clot,ton t~rrlpcrd~ure, 4 n t e n M t y o l gas t~.nlperaturc aL Jltfcrcrd prc~urc~ t~ s;oB.homctnc Itle t ]lJ n C-,,l li" i'ln m .

244

D LIPLADLEY.L

~6'°[.

. . . .

i

' ----T "

~

[

IESCH and C G W '~,HEPPARD

-

,Y

LI 7E

uJ

}

t~ ¢<

2800

3000

ECECTRON TEMPER~/URE t~R) I It~ 5

Net r tte ot ¢lt,Ltt'orl ctl,,rg ~. Io,~

(1 b "Gh) at dttterenl pre,.surcs, ~howmg mea,~utt:d iVdxlmunl cleL.t ton t e m p e r a t u r e ,

'/f, The nater:,,lr~ el C] emiss~o~ ,,t 5163A, ,dthcltlgh el lesse, valll~, show ~, d Mnllld r variation w~th pressure I'~ ese c\pertmental data ,.','ere used to ol,tam part t,I a ((;* L ~) L.urvc, as illustrated m F~g I T0 at.colnph~h t h l ~, It '¢*d~ ilecessary to dative the ,.urvc el (Lt, (b,) agalfr.,t electron te:nperaItlle dnd this "*as dolle lot cqlniibrlutTl products at a ',e,npetatur¢ 1"~, bx the nrethod dest.rlbed m the pre'vlotl~ 5e~.tlOll Such ~.u,wes el net electron elle,g~, Io,,s rate at dtfk, rent pressures and lot the e\pl'rttlIPItld[ c o n d l ~ i o n s Ut ['lg 4 are sho¢¢n in Ftg 5 ~lr ordel to constrtlct :he LLIFVCOt net C] ctron

energy gain, (G* L * ) , it was assumed that the energy galrl Is due to electron colhslotls with excited species, the weasure of the concentr,.t,on of which Is given by ;'re elntsslon ltltenstl2¢, / II \'* h the number 3enstty of excited radicals then

N*

al,

(8)

where "'a" is a numerical constant, dependent upon the expeimtental tend:lions The measured steady ~ate electron temperature at upolnt must sattsly }=qs (7) and (8), namely

Li,

G,,

al(g ~'

l ~)

(0)

245

ELECTROH ENERGY EXCHANGES |lq FLAMES

%

,,

~0~

I0 z

8 o

\

~L___. ~'400

Fig 6

I

~ 2~'0 ELECTRON TEMPERATL~E

i

30OO ('K)

Derived curve of net electron energy gain rate as a function of eleetron temperature

For a particular pressure and assoclateG bulk gas temper~tture, the observed peak value of electron temper~lture is marked on the corresponding c)llwe of (L~, - Gt,) m Fig. 5. As the correspetldmg va)ue c,Cl Is known, values of a(g'* - /*) l~ay be obtained flora IEq (9) Throughout these e~perl ments in which the pressure was var.ed, the experimental eons,'ant "a" remained the same l'he values of a ( g * /*) obtained m this w,By are shown plotted against electron temperature m Fag 6 These represent, on some arbitrary scale, the net electron energy gain rate per tlmt volume 13el electron per Urll~ volume p,.'r excited molecule per umt volume The shape of the curve of

a(g'* - /*) values correspon,]s to 'that to be expected from the reas,3rlmg ~.)fprevious sectIoIIs and extrapolation of the curve suggests a va;ue of ex:lted species electron temperature T~ of .lust over 3000°K Discussion The. influence of the electlomcany excited state of OH m elevating electron temperatures Is showrt by the two etlergy gain curves for 1.0% OH m FEg 3 The lower curve is for vlbrataonal, ~otatlonal and electlomc excitation temperatures of 3000°K whde the upper curve zs for an additional electrcm," excltatlen, with as much as 0 19/o of '.he

!46 ~adlc~l In the higher electronic sta.e This lllcrease in c',.cltatloq results in all ntcrease in the theoretical election temperature ol 50°K, vdten the energy loss curve Lorrestgonds ' o that for air The upper ~tate appems to contribute relatwely little to the energy exc,~mnge rate, thus conflrmu~g tile snggesnon of Padley [17] thai "warm" electrons arise principally from colhslons with vihratlonally excited ground star e radtcals In view tit this thele are lnmtatlons Ill taking tile intensity ol OH emission at 3063 & as the sole paranleter ol extra equlhbrlum excitation, as was done m Se: 3 2 However, Bulewn.z et al [11] have shown in acetvh:ne-oxygen flame ,,tudtes that the population ol the upper electronic state of OH shows a simila r variation with equlvalepce ratio to th' ) of the gmnnd ~tate If CalS similarity were to extend It) pressure variation and I1 the excltrd specle~ electron temperature. Te* . were unchang~ d with pressur then tile derlvatmn ot T*~ m Set 3 2 would stilt be val'td All exp,~'rmtentally ,derived excited spec,:s eiec tron temperature of 3000°1( gwes some support to the lhemet cal computations of See 3 1 These suggest that ele,,atlons ot electron temperatures of son,(.' hundreds ol degrees above gas temper'rture a,e pos';,Ih~,~ In bydlocarbon flames, as a coassquence ol eo]llslOn', ot tile second klno It is more dlJflcult to al+t.ounl lor me.Jsured electron temperature elevatmns ot thousands of degrees It is notewortbv Hi thl~, context that the peak electron temperatures measured Ill f]ames by electrostatic probes, occur in regrons where there are large gradients el bulb electron temperatu,e and ton conccalr,~tlon Tile assumption lmpbclt in most theories lOl the interpretation of probe readings Is that the probe ts nnmersed in a umform plasma Departure lrom till', t.ondttlOU may give rise to elror~ m the coeasulenrent of e[e~.tron temperalure', The Inrttatlons in the present theoretical '.tudy lie m lad~ of da'a on both the populations of excited species I,r the different energy levels and on Ibc values ol cleclron cross ~ctton,, All species with e',.trd eqlnllbrlunl excitation will contrlbuLe towdrds an elevation o[ electron tenlperatnre an,J, as cnrlsston intensity fionr sud: species follows a snlll]al Va~lail(Jllwith pressure 'o th.t lrom 'he OH

D BRADLEY. L F JESCH and C G W SHEPPARD

radical, the derwatton of "/'7 rn Sec 2; 2 is not necessarily t,onfined to the effects of hydroxyl It has already been shown [5], from a consldmatlon of the rate constants for electron tonging eolhstuns, that such colhslons probably have an lns~gmflcant role in hydrocarbon-air flames

5. Conclusions I The use of energy diagrams, applicable to electron energy exchanges in flames, has been demonstrated 2. In the regions where species with extra eqmhbrlum excitation are present, elevation of election temperatures above gas temperatures may be atmbuted to, electron colhsmns of the second kind 3 Some experimental results suggest that flame electrons in the presence ol species with extra equ'),bHum excitation alone would .tiara a temperature of appm'¢~mately 3000"K in a Stolcblometl IC methane-air mixture 4 In methane-air flames evidence has been presented whmh suggests that the principal electron enelgy gain as trom the vrbratlonally excited hydroxyl radical m the lower electronic state 5 'Ihe theory suggests that file magnitude of the elevation of electron temperature in hydrocarbon-air flames may be some hundreds, but not thousands of degrees This supports a previous conclusion that electron ionizing collisions are not slgmflcant AcknowledgTnent ls made to the donors o] The Petroleum Research Fund, admlnrstered by the A mcrwan CTlemlcal So¢ let), .lor partial support oJ tilts researeh The authors also wish to thank tire Selellee Ke~earch CUR?let/Jot support References 1 Taran It N and Tverdokhlcbov. V l . High Tomp {Tepkqtz t wok Temp ) 4. Is0 (19661 2 Sahm O lilt J I.le~tromc~ 25,547 t 1%8) 3 • a,aberla R . and Porter, R P Twelfth Slmposnlm {lmerlt~ttonal) on Combustion. The Combasnon ln~ntute. Pittsburgh Pa (1969). p 423 4 Porter, R P CombustlonandFlamt 14, 275 (1970) ~; Bill J ( . BradDv l) . and Jesd,, L I . Thirteenth ~lttlpt)sllltn [hIH'rnatlonal) on 6omhltsnott Tile ( oelbuMlon l,lsl)I ir~ Pnl,~burgh, Pa I1971L p 345 6 Von Em~el. ' and Cozen.. J R Proc Phvs Sot 82, 85 (1963)

ELECTRON ENERGY EXCHANGES IN FLAME~; 7 Bell, J C , and Bradley, D, Combustion and Flame 14, 225 11970) 8 Bradley. D and Sheppard,C G W ,Cumhustton and Flame 15,323 (1970) 9 Baxendale, D N , Lwese), J B, Roberts, A i . Smllh, D B and Wflham~, ?, , Combustion Scten,'e attd Technolog~ 2, 287 (19711, 10 Porter, R P , Clark, A H , kaskan, W E , ar, d Browne, W E , Eleventh Symposium (International) On Combustlcm, The Combu~t/on In,;t,tute, Pltl~;burgh, Pa 11967), p 907 I 1 Bulewlez, E IV[ , Padlev, P J , and Sm:tb. R E , Proc R~v Soc (LoJ,Edon) A315° 129 (1970) 12 Gaydon ~. G , The Spectroscopy of Flames, Chapm,:n and H dl, London (19Y7), p 160 13 Gaydon. A G and Wollhard, H G ,,r'ro~ Roy Soc fLondon) A203° 63 11951 )

247 14 Shuler. K E , J Chem Phys 18, 122111950) 15 Brol,da, H P , J Chem Phys 19, 1"~83(1951) [6 Gaydon, A G , ~le bpectrosccpv of Flames, Ch,lpman and Hall, Lo,~don 11957), D 146 17 Padley, P J . Tlnrteenth Symposmm (International] on Combustion. The Combu~tlon lhstltute, Plttsb u ~ h , Pa ( 1 9 7 1 L p 352

(Recet red December ~¥ 71, revz~ed vers'on recetvect May 1~72)