Molecular Beam Mass Spectrometric Sampling of Methane Flame

8/9/2019 Molecular Beam Mass Spectrometric Sampling of Methane Flame

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U N I V E R S I T Y O F C A L I F O R N I AL os A ngeles

IA F I B F I S Sampling Study of

Formation of Nitric-Oxide in a PremixedFuel-Rich Methane -A ir Flame

A thesis submitted in partial satisfactionof the requireme nt for the degreeRaster of Science in Engineering

byIvan A . Gargurevich

1980


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The thesis of Ivan A. Gargurevich is approved.

U, D. Van Vorst

Ouen I, Smith

Eldon L . Knuth, Commi ttee Chair

University of California, Los Ang eles1980


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To H o r n and Dad,

Lucia,Cynthia,

Irene,Sergio,

and C armen,


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TABLE OF CONTENTS

P AGEL I S T O F F I G U R E S . . .. ViLIST OFTA BL ES . .. viiiLIST OFSYMBOLS .. ixA C K N O W L E D G M E N T S xiiA B S T R A C T OF THE THESIS xiiiCHAPTER 1. INTRO D UC TIO N .,.",'," iCH AP TER 2. P R E V I O U S STUD IES OF NO F O R M A T I O N IN

H Y D R O C A R B O N F L A M E S . ... 102.1 The Formation of NO in Fuel-Lean Flames . j _ g2.2 Prompt NO Formation ........... 152.3 Formation of NO in Fuel-Rich Flames ... 222.4 Mechanisms of Methane Oxidation ..... 30

2.4.1 Methane Oxidation in Fuel-LeanFlames .............. 30

2.4.2 Methane Oxidation in Fuel-RichFlames ..............34

CH AP TER 3. E X P E R I M E N T A L A P P A R A T U S 443.1 An Introducti on to Sampli ng Techniques

in Combustion Studies ..........443.2 Possible Composition Distortions in MBMS

Sampling of Flames ...........533.2.1 Free-3et Expansion ........54

1


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P A GE3.2.2 Chemical Relaxation in Supersonic

Expansion ............. 593.2.3 Spe cies C on de ns at io n ....... 633.2.4 Pre ssure Di f fu sion ........ 653.2.5 Relaxation Phenomena ....... 693.2.6 Skimmer Interference . . . . .0 . 713.2.7 Mach-Number-Focusing . 723.2.8 Background Scattering ....... 763.2.9 Flame Perturbations by Sampling

Cones 773.3 The U.C.L.A. MB M S Sampling System .... 83

CH AP TER 4. E X P E R I M E N T A L P R O C E D U R E A N D D A T A RE-DUCTION ......... 87

4.1 Composition Measurements ......... 874.2 Temperature Measurements ......... 914.3 Calibration Procedures .......... 93

CHAPTER 5. E X P E R I M E N T A L R E SU L T S ... 965.1 Temperature Measurements in the Flame . . 975.2 Stable Species Profiles .. 1105.3 Formation of Nitric-Oxide in the Flame . . 1125.4 C2H2, C2H6 Profiles .... 1245.5 CH. and H2CO Species in the Flame ....130

C H A P T E R 6. C O N C L U S I O N S . . .. 136R E F E R E N C E S . .....140


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LIST OF FIGURESF IGU R E P AGE1. node of coal formation . 32. The dependence of CH20, C2H4, C2H2, and H2

peak concentrations on flame equivalenceratio ...................40

3. The dependence of peak C2H,, C2H2, and H2on peak J C H - ,} for a range of flames $=0.56 to 1.25 \41

4. The U.C.L.A. MB[*]S sampling system ..... 505. Temperature ratio as function of dimension-

less flou time for free jet gas flows fromorifice 52

6. Free-jet shock structure .......... 557. Schematic diagram of model considered in

Mach-number-focusing 748. Intensity vs. electron energy for A r g o n . . 899. Temperature profile measured using TDF tech-

nique ..... ......... 9310. Temperature profile measured using TOF tech-

niques 10011. Normalized Ox yge n profile (tip dia.= 2.0

mm, d = 0.24 mm) 10412. Normalized O xyg en profile (tip dia.= 0.5 mm,

d . =0.30 mm)...............105


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F IGU R E P AG E.13. C02 normalized profile (tip dia. = 2.0 mm,

d# = 0.24 ram)................IDS14. Normalized C02 profile (tip dia. = 0.5 mm,

d ^ . =0.30 mm) . . . . ..10715. 02, CI-L, and C02 mole-fraction profiles for

CH^-Air flame ................ill16. NO concentration profile ..........11417. N I - U concentration profile ..........11518. HCN concentration profile ..........lie19. Normalized m/e = 30 profile 11720. Normalized m/e = 17 profile .........11921. Normalized m/e = 43 profile .........12322. C2H2 concentration profile .........12623. Normalized m/e = 27profile ........ . 12724. Normalized m/e = 30 profile 12925. C-atom concentration profile ........13126. CM concentration profile ..........13227. CH2 concentration profile 13328. Normalized m/e = 15 profile 134


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LIST OF TA BL ES

TA BL E P A G E

1. Methane oxidation in fuel-lean mixtures ...352. Methane oxidation in fuel-rich mixtures ...36

\M1


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-

LIST OF SYMBOLSa speed of soundC. calibration constant appearing in Eq. (56)d effective source-orifice diameter

d. cone orifice diameterd, skimmer entrance diameterD binary diff usion coefficientE electron energy in ev

C3#E activation energyf mole fraction of heavier speciesh total enthalpyI. ion signal intensity of species iI electron emission in mampDk. foruard reaction rate coefficient for the ith

reactionk _ _ reverse reaction rate coefficient for the ith

reactionK equilibrium constantKn Knudsen's numb er'"Id skimmer entrance - detector distancem mean molecular ueightm . molecular ueight of species im/e mass to charge ration number density


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n , number density a t detectorn, number density at s k i m r a e r entrancep pressurej mass densityRe Reynolds numberS speed ratio

i Sj_ speed ratio perpendicular to jet axisSc Schmidt numberT temperatureTj static temp eratu re perpe ndicul ar to jet axisT,, static te mpe ratur e parallel to jet axist timeu most prob able velocity of moleculesv diffusion velocityX nach disk locationY r - l a c h disk diameterY D diameter of the barrel shockD

thermal diffusivityu ~ ~ t enrichment factor as defined in Eq. (49)n calibration factor appearing in Eq. (56)0 (Fuel/Air) actual/(Fuel/Air) stoich., e q u i v a -

lence ratio0 heat capacity ratio, C /c

'V relaxation time a t constant h,pu n,p


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C relaxation time at constant T.pI PL AB mean time between collisions of A and B m o l e -

cules\ mean free pathc r hard sphere collision cross section

Subscriptseq denotes equilibrium values0 denotes stagnation conditions1 denot es conditions at skimmer entrance

frozen process


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A B S T R A C T OF THE THESISA MBW S Sampling Study of

Formation of Nitric-Oxide in a PremixedFuel-Rich Methane-Air Flame

byIvan A. Gargurevich

Plaster of Science in Engi neerin gUniversity of California, Los Angeles, 1980

Professor Eldon L. Knuth, Chair

The formation of NO in a fuel-rich, premixedmethane-air flame at one atmosphere uas studied usingmolecular-beam-mass-spectrometric (MBMS) sampling tech-niques.

A flat flame of equi va len ce ratio 1.37 uassampled uith particular attention given to NO, HCN, H N C O ,and MB., species. The onset of formation of HCN uasfound to occur prior to the formation of NO, approxi-mately at the same time as the formation of NH,, and verynear the pr im ar y reacti on zone of the flame. Decay ofHCN leads to NH- formation, and, to a lesser extent, to

iJ

NO formation. HNCO is ob serv ed at very lou concentrationsin the post-flame gases, and acts as an intermediate inHCN decay. The peak mole fractions of HCN and NH^about 67 and 44 ppm., respectively,and Nitric-


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Oxide reaches a mole fraction of 56 ppm . after all of theHCN, and NH^ have decayed. The Zeldovich mechanism,taking into account radical over sho ot, accounts, atmost, for 10 ppm. of the NO formed in the flame; therest is the result of HCN decay.

The same flame uas sampled for C, CH} C H , - , ,and C I - U The peak mole fractions of C, CH, and CH-were found to be about 206, 481, and 908 ppm., respec-tively, uith an uncertainty of a factor of approximately2. Because of their greater concentratio ns, CH and CH~are the mo s t likely to lead to HCN fo rmatio n. The con-tribution to the CH., prof ile f rom CH, could not be to-tally elim inat ed, eve n at electron energi es as lou as13.3ev. No effort uas ma de to estimate its mol e frac-tion in the flame. The C H - , profile peaks uithin the pri-mary reaction zone.

The flame uas also sampled for H-CO. Itsformation is ob serv ed to occur befo re the formationof CHr, and upstream from the reaction zone of the flame.

J

The rate of formation CH-, does not reach s ignificantlevels until mos t of the for mald ehyd e has decayed.

A relatively large concentra tion of acetylene

(2100 ppm.) uas f o u n d ; its formation and decay occurredmostly uithin the primary reaction zone. Et h a ne, inmuch smaller concentratio ns, uas also o bs erve d in thesame region. The tuo-carbon species pro vide additional

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paths for the decay of CH- and must be included in thekinetic modeling of fuel-rich hydrocarbon flames,

Visible attachment of the flame to the quartzcone uas observed for the flame of equivalence ratio1.37. Temperature measurements, made using time-of-flight (TOF) techniques, shoued that the effect ofattachment is to decrease the measured temperature gra-dient within the reaction zone. A cone of s mallertip diam eter minimizes this effect. Relative inten-sity profiles shoued also smaller measured gradientsuithin the primary reaction zone for a cone of relative-ly large tip diameter. Attachment of the flame to thecone persisted a ppro ximat ely until the end of the pri-mary reaction zone.

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C H A P T E R 1I N T R O D U C T I O N

In the last d ecade, in order to satisfy anever-increasing demand for energy, and as a result ofcontinuing decline in the domestic production of crudeoil, the United States has been forced to import crudeoil and refined products in increasing amounts. It is

83forecast that, in 1980, thirt y pe rc en t of our totalenergy uill come from the Mid dle East Nations. Fur-thermore, since 1972, the fraction of the energy usedfor p r o d u c i n g the U.S. G i M P u hich has been based oni mport e d oil has dou ble d, increasing from a level ofabout 1 3 o of the U.S. G NP in 1972 to about 26% ofthe U.S. G NP in 1978. Since the end of 1978 the O P E Ccartel has raised the pric e of its exp or ted crude by61j, and it is estimated that by 1985 it uill reach

n A340 per barrel . I n 1985 the U.S. could be im p o r t-8 3ing as mu ch as 15 million barrels per day and, with

an estimated price of $40 per barrel, the cost for1985 would be $220 billion. By c o m pariso n , the valueof oil imports into the U.S.A. in 1972 uas $4.5 billion,

The finite limits of U.S.A. oil and natural84gas r eser ves are fairly well established ; both could


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be exhausted in ten years if they uere w o r k e d to theirfullest capacity. H owe ve r , the estimated resourcesof coal amount to approximately 90,000 x 10 Btu.(o r about 43 0 billion tons) w hich at the present con-sumption rates would last for about 666 years.

In the near future, the U.S.A. will have tofind or exploit altern ative sources of energy if itis to play an important role in the world community.In Duly 1979, Preside nt Carter anno un ced his E n e r g yPlan. The main obje ctive s of the Plan were to dimin -ish oil imp or ts, to accelerate the co nserv ation of oilfuel, and to spend $88 billion over ten years to pro-m o te synthetic-fuel pr od uc ti on from coal and shalerock. A c c o r d i n g to Carter's En erg y Plan for about thenext ten years, oil imports would be kept at the 1977level of 8.2 million barrels per day; 2,5 million bbl./day would be gained b y synthetic fuel prod uc tio n and 2million bbl./day thr o u g h c o nser vatio n and c o n v ersio nmeasures. Carter's Plan would r equi re coal pro duc tionto double by 1985 (i n 1979 coal pr od uc tio n was 625million tons per year) r, in the seven-year period1979-1986, 107 million tons of new capacity would haveto be added e v e r y year.


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ORIGINAL PLANT MATERIAL

FESINGUS MATERIALCUT1CLS,S?OHS

CCA' ?/ACcRA.'(VISUAL MiCHOSCCPY)

RESETS

WOOC, CGnXj

CiRSCNIZATION

V,iCF.CN!TE

RANK F EATL iG N 1 TH US3i~JMN G U SAr-JTH=AC~%C%0

60

Ci!-CR:riC I2CCOVALUE

ra251200 o

KIGH M=D.C5A80 S315 3

I4OCO I SOOa S 5 5GC

Fig, 1. Mods of coal formation . ( Source : Ref. 85.)


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It is clear then that combustion of coal an dp r o d u c ts de ri ve d from coal and shale rock will be play-ing an important role in the U.S. e ne rg y pic tur e for yearsto come. (Nuclear ener gy supplies about 3% of thetotal ener gy pro duc ed in the U.S. today. Its devel-opm ent, howev er, has encountered muc h opposition and itis unlikely that construction of new nuclear plantsuill be started in the 1980's). Coal originates pri-marily from plants. Fig. 1 shows the steps in coalformation. Thr oug h a series of evolutio nary change s,the prim ary pro duc ts of the original de compose d plantmatter bec om es transform ed sequentially into peat,lignite, su b bitu mi n o us coal, b itu mi no us coal, and fi-nally to anthracite. Uith these transformations thecarbon content in creases and the ox ygen content decreases.

n j-Stu dies ' indicate that there is some correlation be-tween coal rank and its aromaticity, 40-50^5 aromaticcarbon content for subbituminous coal and 90% aromaticcarbon content for anthracite. These studies showedno correlation between H/C mole ratio and percent aro-matic carbon. Ox yge n occurs pre dom inan tly as pherolicor etheric g r o u ps in coal. Sulfur found in coal hasa similar function al che mist ry to Oxyge n. Sulfur con-tent in coal varies from 2 to 3 p er ce nt. Nitr o ge noccurs predominantly as p y r i d i n e or pyrrolic type rings,and coal contains typically from 1 to 2 p er ce nt nitr o ge n


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by ueight. Coal structure is consistent with highlyI - 5substituted aromatics uhich are not highly condensed.ICoal unde rgo es primary decom position in the tempera-ture range 400 - 450 C.

The realization of limited and non-reneuablee ne rgy resources and the increasing role of combustionin the years ahead uill require extensive researchin the areas of ener gy conservation and combustionproblems. As a result of President Carter's E n e r g yPlan, there uill be a shift to direct coal burningby the Utilities C om pani es and In dustr y. The healt h,safety and en v ir o n m e n tal threats p osed by m i n i n g andb u r n i n g of coal are severe. In cre ased coal bu rn in guill result in larger emissions of sulfur dioxide,carbon diox ide, and nitric oxid e into the atmosphere.The accumulation of carbon dioxide m i g h t result inthe so called "Greenhouse" effect pre dic ted by manyscientists. The large amounts of ash that uill resultfrom coal burning uill hav e to be disposed of in ane nvi ro nme nt ally safe manner. The p r o d u c t i o n of syn-thetic fuel uill also cause environmental problems.Fur therm ore, the prod uc tio n of synthetic fuel mig htrequire hug e amoun ts of uater for hyd ro gen production.The strain on existing uater supplies migh t be consider-able and one can foresee legal battles for uater rightsbetueen the coal-producing states.


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In 1974, transpor tatio n acco un ted for 54/5n!of the total liquid fuel co nsu mp tio n ' in the U.S.

It is most likely that transportation uill depend pri-marily on liquid fuels in the near future. Most ofthe liquid fuel being consumed today in America islou in aromatics content and has a high H/C content(the average H/C ratio being 1.9). Houever, unlessextensive hydrocracking an d hydrogenation ar e conducted,the properties of synthetic fuels are different fromthose of the fuels bein g used today in transportation.Synthetic fuels are hi gh in aromatic s co nt en t and havea H/C ratio of about 1.2-1.5. Transformation of syn-thetic fuels from coal into m o r e "gasoline-like" fuel

R f iresults in an energy loss of about 2 Q f a of the heatof combustion of the syncrude being pro cessed. Theelimination of restrictions on H/C ratio and boilingrange in fuel manufacture uould result in a consider-able re du ct io n in the cost of the fuel. As a resultof its proper ties, synthet ic fuel comb usti on uould re-sult in the emission of large amo un ts of soot by theinternal combu stion engi ne . Thus, exte nsive researchis ne ed ed to eliminate the ne ed for high levels of hy-drogenation and boiling range conversion in the manu-facture of fuels from coal. Furthermore, more researchis need ed in the chemistry of soot formation and burn-out.


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It is evident that, in the future, ue uillhave to b u r n prime fuels more efficiently with less pollu-tion and ue shall also have to bur n mu ch material thatis not nou considered suitable fuel at all. As Uein-o Yberg points out, progression in com bustio n systemsis in the direction of more controllability. The pro-gression has be en from diffusion flames (the r eactionzone is aluays near stoichiometric, correspon di n g tothe maxim um possible flame temper ature and hence thelargest NO emission) to pr emi xed flames, uhich allowsone to vary flame temp eratu re, bur nin g velocity, ig -nition t emp erat ur e, and stability criteria by con trollingthe fuel/air ratio to the uell-stirred reactor. Uein-berg proposes that the next step should be breaki n g auayfrom this d e p e n d e n c e on initial fuel/air ratio and con-trol the reaction rates in the flame in dep en den tly.To take this desirable step o n co mb ustio n systems, uemust control the reaction rate independently by makingthe tem pe rat ur e in the reaction zone a separate para-mete r, using variable heat recirculation, injectionof free radicals, radiation , etc.

This study is c o n c er ned with the kinetics offormation of nitric ox ide in an atmosp heric , fuel-rich,p r e m i x e d , meth ane-air flat flame, and it is par t of aseries of studies that are being co ndu cted in U.C.L.A.with r e ga r ds to nitric oxide formation from fuel-ni-


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trogen in flames. To give the reader an idea of themag nitu de of this NO formation, in the study of methane-ai r flat flames by R. Gay at U.C.L.A., a concentrationof 140 p p m. uas r ep o r ted in the post-flame gases of amixture of equivalence ratio 1.1. In this same flame,the primary reaction zone uas characterized by therapid formation and decay of f or maldehy de uith a max-imum concentration of 540 ppm., and NO formation uasrestricted to the post-flame region. The primary reac-tion zone uas located uithin the first 5mm. from theb u r ner surface. In the study of NO formation in a fuel-rich flame, the coupling betueen the NO-formation reac-tions and the combustion reactions must be considered.This requ ires a knouledg e of the comb ustion mec hani sm,and for methane com bustion, although extensively studied,there are questions regarding the rate-determiningstep, the f^CO-decay mechanism, the fate of CH~ species,and the role of t^ hydrocarbon s. Nitric oxide abovethat predicted by the Zeldovic h mec han ism is said toform via the formation and decay of H C N . The forma-tion mechanism for this species has been studied butvery little is knoun about its d ecay m o de. Ex pe rimen tsindicate that N H j _ species and OCN -species mi ght playan important role in the decay of H C N.

It is the aim of this study to ansuer orclarify some of the questions regarding the kinetics


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of NO formation in fuel-rich, premixed methane-air flames.It is hoped that this uill be of some value in the studyof NO formation in flames containing fuel-nitrogen.

The study of flames uill be conducted usinga molecular-beam-mass-spectrometer (MBNS) samplingsystem. This system has b e e n shoun to meet all therequirem ents for sampling of high tempe ratur e systemsuith excellent balance. The use of MBFIS sampling sys-tems could u nd ou bte dly play an impor tant role in com-

bustion research in the near future. MBPIS samplingtechniques allou one to follou stable and radical spe-cies uith min imu m distortion. This is valuable helpin the study of (a) o x idatio n mec hanisms and (b) ratecoefficients of elemen tary reactions. As me nt io ne dab o ve, MBNS sampling tec hni ques are bein g used at U.C.L.A.to study the fate of nitrogen-bearing species and,more recen tly, sulfur-containing species in flames.These studies uill n o dou bt help dete rmin e more effi-cien t and mor e clean uays to bu rn fuels such as coalor liquid fuels d er ive d from it.


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tion in lean, premixed hydrocarbon flames. Using re-actions (1), (2), and (3), he derived equation (4)for the rate of NO formation

dt =2k1(D)(N2) 1"(ND)2/K(02)(N2)

k2(02)+k3(OH)(4)

whe re K is the equilibri um constant for the overallreaction Nj + Oj v 1 2ND. In the derivation of equation(4), it is assumed that (i) the reactions occur und erconstant-volume conditions, (ii)d(N)/dt is close tozero; and (iii) eaction (5) is equilibrated in thepost-flame gases.

0 + OH ^ H + 02 (5)The fact that condition (iii) is quickly attained inthe secondary zone of flames has been amply demon-

n T nstrated '. Calculation of the NO formation rateby Equation (4) requires values of the local tempera-ture and concentrations of 02, N2, 0, and OH. Houever,as first suggested by Zeldovich, Uestenberg took finalequilibrium values of the tem per atur e, and of the N2,0~, OH, and 0 concentrations.

Using the equilibrium approximation of I M 2 ,0?, OH, and 0 concentrations, Bowman obtained thefollowing NO formation rate (using data from Ref. 4)

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d ( N O ) 6x10dtmolesc m sec

16T ~"2expf^69,090/T "l x(0 0)eq rk eq/ 2J'eq eq(6)

Elevated temperatures and high 02 concentrations inthe post-combustion gases result in relatively highNO-formation rates. Experimental studies of NO for-mation in the post-combustion zone of laboratory flamessupport this simplified mechanism.

Neuhall and Shaded studied the formationof nitric oxide in the imme diat e vicinity of a flamefront propagating through a high-pressure combust ionvessel in order to investigate the formation of nitricoxide under conditions similar to those occurring ininternal comb ustio n engines. Spectr oscop ic techni quesuere used to determine NO concentrations. Experimentaldata uere obtained for hydrogen-air mixtures at pres-sures of 240, 325, and 340 psia, and 0.7, 0.9 and 1.0equivalence ratios respectively. Temperatures rangedfrom 2000K to 2500K. They found that under theseconditions NO is formed primarily in the post-flamegases, and that the rate of NO formation can be pre-dicted by the Zeldovich mechanism, uith oxygen- andnitrogen- atom concentrations set equal to their chem-ical-equilibrium values.

* >Livesey et al studied the formation ofNO

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Hr -

in atmospheric-pressure, premixed, oxy-propane flames.They used many small diameter stainless steel tubes asflameholders. An outer shield of argon uas used toprevent outside nitrogen from reaching the combustedgases. Gas samples uere taken through a uater-cooledprobe and analyzed for N0v by the Saltzman method.XTemperatures in the burned gas region uere determinedspectroscopically from the temperatures of rotationallyexcited OH. Temperatures uere in the vicinity of 2800K.They shoued that reactions (1) and (2) are sufficientto explain the rate of formation of NO in the post-flame gases.

The effects of combustion -modifications onthe formation of nitric oxide in CH^/air flames uerestudied by England . A 250,000 Btu/hr ring-type burneruas used. Nitric oxide in the flue gas uas measureduith a long-path infrared analyzer at concentrationsfrom 2 to 500 ppm. Gas samples uere uithdraun by auater-cooled quartz probe. He found that nitric oxideemissions could be reduced by 9 Q ? 0 from peak levels byburning very fuel-rich flames, and that by reducingthe air preheat from 650F to 50F, peak nitric-oxidelevels d r o p p e d 67%. The louer NO levels at louer airtemperatures uere due to louer flame temperatures.England also obtained data for NO concentrations uhenu p to 3 2 / o of the combustion gases uere recirculated.


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Nitric oxide in a flame burning uith a combustion airtemperature of 650F uas reduced by B2% from the peaklevels by 32 recirculation. Nitric-oxide productionuas lowered uith product-gas recirculation bec auseof a reduction in the methane-air flame te mperature.These results could have been predicted from Equati on(6); louer flame temperature, TDn, results in a smallereqrate of form ation of nitric oxide. Re duc ti on in theoxygen level has a similar effe ct on the rate of NO

formation.

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2.2 "Prompt" NO FormationThat the formation of NO in the primary re-

action zone might involve a mechanism other than thegZeldovich mechanism uas first indicated by Fenimore

in the Thirteenth Symposium (international) on Combus-tion. He measured the formation of NO in premixedatmospheric flames of ethylene, methane, and pro pan euith N2 " ^2 mixt ures. Post-flame gases were uithdraunby a quartz microp rob e and collected in an eva cuat edflask. NO and N02 concentra tions uere determined bychemical analysis. Tempera tures uere measured by the

20Sodium-line reversal method and uere constant overthe reg ion investigated. Fenimore found that the kin-etics of NO formation in the post-flame region is de-scribed by the Zeldovich mechanism, Houever, extra-polation of the measured NO formation curves back tozero time gav e positi ve inte rcepts , indica ting, as Feni-more su gge ste d, a transient formation of NO in theprimary reaction zone, the growth rate of uhich uastoo fast to be explained by the Zeldovich mechanism.He labeled this intercept NO as "prompt" NO. Sincepositi ve inter cepts uere not f ound in hyd rog en or COflames, Fenimo re suggested reactions such as

CH + N2 ^HCN + N (7)C2 + N2 ^2CN (8)

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to explain the "prompt" NO.Controversy aroused regarding "prompt" NO,

and numerous investigators have made experimental stud-ies to prove or disprove "prompt" NO formation.12Bowman " investigated the formation of NOin shock-induced combustion of H2/02/N2Concentration time-histories of NO, OH, and H?0 ueremeasured during reaction using spectroscopic techniques,,N O formation rates uere found to exceed the rates pre-dicted by the post-flame zone mechanism. It uas shounthat the observed rates uere consistent uith reactions(1) through (3), if 0 and OH concentrations uere cor-rectly determined. In the region of rapid NO formation,observed radical concentrations uere in excess of cal-culated equilibrium values. Hence, the rapid NO forma-tion rates uere found to be the cons equence of non-equil-ibrium combustion chemistry.

Further evidence for non-equilibrium chemistryin the reaction zone of flame uas gathered by Bouman

21and Seery . They studied shock-induced combustionof C H / L - 0? - N 2 mixtures dilutad in argon. Concen-tration histories of NO, OH, and C02 uere measuredusing spectroscopic techniques. Initial temperatureuas in the range 2600 - 3200^, and the initial pres-sure uas 3.5+ 0.5 atm. They found NO-formation ratesto be consistent uith reactions (1), (2), and (3).

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Furtherm ore, discrepancies between observed NO forma-tion rates and those using an "equilibrium" model forNO formation uere explainable in terms of "radicalovershoots" in the reaction zone. They did not findevidence to suggest that other reactions uere of im-portance in the NO-formation mechanism.

Sarafim and Pohl studied NO formation inone atmosphere premixed methan e-air flat flames ofequivalence ratios from 0.89 to 1.15, Gases uere burnedon a water-cooled porous-disk, flat-flame burner.G as samples uere withdrawn through a water-cooled stain-less-steel probe. NO concentrations we re determinedby a modif ied Saltzman me th od ; other species were mea-sured using a gas chromatograph. They found that thepeak rates of NO formation in the flame zone were oneto two orders of magnitude greater than the valuesin the post-flame zone, and to be consistent with themodified Zeldovich mechanism (Reactions (1) - (3)),when free-radical concentrations (of 0, OH, and H)were correctly estimated.

The "Radical Overshoot Theory" requires adetailed consideration of the kinetics of the fuel

combustion, or the use of other suitable ap pr ox im at emethods to compute the non-equilibrium concentrationsof 0, OH, and H near the primary reaction zone in orderto determine NO formation rates. Detailed combustion

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mechanisms are known for only a feu fuels H?, CO,and CFL (methane oxidation will be discussed in a la-ter section), and a simplified appr oach involving the"partial equilibrium" of Reactions (9) - (11) is usedin most cases.

H + 02 OH + 0 (9)0 + H2 ^OH + H (10)H2 + OH H20 + H (11)

In the "partial equilibrium" ap pro ach , the radicalreactions (9) - (11) are considered to be equilibratedin the flame. This is not to say that the radicalconcentrations are equal to their equilibrium values,rather the ratio of the products to reactants concen-trations for each of the reactions (9) - (11) is equalto the reaction equi lib riu m constant. The concentr a-tions of 0 and OH then can be related to the concen-trations of stable species uhich are readily measured.

11Sarofim and Pohl obtained good agreement betueenobserved and calculated "partial equilib rium" NO forma-tion rates in lean and slightly rich hydrocarbon flames,

27Pesters and Flahnen conducted sampling of lean and .stoichiometric CH,/02 flames and observed "partialequilibrium" of Reactions (9) - (11).

13Recently, Gay et al ' studied one-atmospherepremixed methane-air flat flames using a molecular-beam-mass-spectrometer (MBPIS) sampling system. A ua-

18


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ter-cooled, copper porous-plug burner urns used. Thegas temperature immediately dounstream from the primaryreaction zone uas measured using the molecular-beam-time-of-flight technique. For equivalence ratios of0.8, 1.0, 1.1, tuo distinct regions uere found: aprimary reaction zone uhere formation and consumptionof H~CO takes place, and a second ary reaction zoneuhere NO is formed. Their studies shou that contraryto the "pr omp t NO" involved by other investigators,

the formation of NO (if any) in the primary reactionzone is negligible for flames of equivalence ratio


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the sodium-line reversal method and theoretical pro-cedures. Their experiments showed the following:(1) for nonhyd rocarb on flames, the extend ed Zeldovichmechanism is applicable for all fuel-air equivalencerates, (2) for hydrocarbon flames, the mechanism isapplicable, for both in-flame and post-flame regions,for #l,15, and for post-flame region for 01.5), and for regions in the vicinityof the prima ry reaction zone of moder ately rich flames($>1.15), the mechan ism is not tenable because it re-quires improbably high &-atoms concentrations. Theyconcluded that reactions such as (7), (8), and possi-bly (12)

C + N9 CN + N (12)might be responsible for the large rate of NO forma-tion in fuel-rich flames and the primar y reaction zoneof moder ately rich flames (j8>1.15).

2 8Ay and Sichel carried out a numeri cal analy-sis of the combustion of me tha ne in nitrogen-oxygenmixtures in order to clarify the relationship betw eenprompt NO and overshoots in radical concentrations.Diffusion and heat conductio n, which are importantin laminar flames, were neglected in their analysis;nevertheless, their results show the link between rad-

20


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ical overshoot, flame temperature, and the NO forma-tion rate. Their analysis agree s with the exp eri men tsof Iverach et al , namely, "prompt" NO in near-stoichi-ometric and lean flames, w hich is related to the hig hrates of NO formation in the recombination and post-flame zones, can be explained by the Zeldovich mechan-ism provided the appropriate free radical concentrationsare used; for rich mixtures the NO concentrations com-puted using the detailed kinetics were far belou experi-mentally obse rved values, and the Zeldovich mech anis mfails to explain NO production in rich mixtures.


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2.3 Formation of MO in Fuel-Rich FlamesAs indicated first by Fenimo re and later

supported by the experiments of Iverach et al , "prompt"NO formed in fuel-rich hydrocarbon flames cannot beexplai ned by super-eq uilibrium concentratio ns of theradicals 0, OH, and H since the concentrations requiredto explain the observed NO-formation rates uould besignificantly larger than "partial equilibrium" values.The forementioned investi gators pro pos ed that reactionssuch as (7), (8), and (12) played an important rolein the NO formation process

CH + N+ N

H C N + N2C N

C + N2 CN 4 - N

( 7)( 8)(12)

uith subs eque nt reactions of N-atoms-via Reaction (3)to form nitric oxide. The production of NO in theseflames then requi res a detailed combustion mech anis mfor the fuel in consideration. (This is also trueof some leaner flames, see Section 2.2). Met ha ne com-bustion mechanisms are considered in the next section,and as the reader uill find out, there still are un-certainties regarding the rate determining step andthe rate coefficients of reactions involved in themechanisms. The rapid NO format ion rate near the re-action zone of rich flames require s that react ions

22


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such as (7) - (12) be very fast. The experimental29data of Bachmaier et al support this proposal.

Hayhurst and McLean studied a fuel-richflame of unburnt composition H2/02/N2: 3/1/4.75 anda flame of the same composition except that 1% of thehydrogen uas replaced by acetylene. The flame uasburnt at atmospheric pressure on a uater-cooled burnermade from stainless-steel hypodermic tubes. The burntgas temperature reached 2000K. G as samples uere takenthrough a uater-cooled pro be (made of quartz) into achemiluminescent NO analyzer. They found that theamount of NO in the acetylene seeded flame uas overthat formed in the H0/00/N0 flame via the modifiedz z / .Zeldovich mechan ism. Based on ther moche mical dataalone, they prop osed reactions

CH + N2 HCN + N ( 7)CH2 + N2 ^HCN + NH (13)

folloued byN + OH ^NO + H (3)NH + OH N + H20 (14)

to explain the "promp t" NO formation. Furt herm ore,they suggested that HCN is coupled to CN by equilibra-tion of

HCN + H CN + H2 (15)uith NO resulting from one of the tuo exothermic reac-tions

23


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-. - -

CN + 02 CO - f NO (16)CN + OH ^CO + NH (17)

Reaction (17) is followed by (14) and then by reaction(3).

22Haynes et al detected the presence of cyanospecies in fuel-rich hydrocarbon flames. Uarious pre-mixed hydrocarbon-air and nonhydrocar bon-air flames(including a CH, - H2 air flame with equivalence ratioof 1.42) ui th and without the addition of small amountsof pyridine were burnt on a water-cooled Fleker-typeburner. Samples were withdr awn from the post-flamegases via water-cooled pro bes (silica or Alumina), ana-lyzed continuously for CO and C02 (NDIR analyzers),02 (paramagnetic), and NO (chemiluminescent). The con-centrations of cyano species and NH. species in thepost-flame gases were determined chemically, and H-atoms concentrations by the Li/LiOH absorp tion tech-

f~ y * ~f O/inique '. Temperatures uere determined uith Na-linereversal measurements. They found NO, HC N, and NH.concentrations in excess of equi libr ium values. (Themeasured values of NH. concentration are viewed withcaution, ho we ve r, since they were highly susceptibleto sampling conditions). The observed NO formationrates were larger than pred icted by the Zeldovich mechan-ism with 0-atom concentrations inferred from measur edH-atoms concentrations using a partial-equilibrium ap-

24


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proximation for the system H - OH - 0 - H2 - H20. Theformation of cyano-species uas found to be relatedto the decay of hydrocarbons and in very rich flamesoccurs well into the post-flame gases. Furthermore,it uas concluded that HCN decays via CN and the rate-determining reaction

CN + C02 OCN + CO (18)Morley also studied fuel-rich flames, in-

cluding CH, - 02 ~ MO flames with equivalenc e ratiosfrom 1.20 to 1.95. A method involving direct samplingof natural flame ions into a mass spectrometer uasused to calculate the concentrations of HCN, NH 3, andNO. He found that the HCN concentration is proportionalto the N2 concentration independent of the fuel type,that the HCN concentration increases uith increasingequivalence ratio, and that HCN-decay leads to bothI N U a n d NO, the relative proportions depending on theequivalence ratio. Morley suggests the reaction se-quence,

CH + N2


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being the rate-limiting step, and it leaves the nitro-gen from H C I \ 1 as N H - . Nitric oxide and nitrogen areproduced by reactions involving the NH. species andReaction (3)

N + OH , - NO + H17

( 3)("ligauchi et al modeled the combustion of

CH^ - Q j " No f-'-ames using a 40-reaction mechanism.They studied flat flames burning on a cooled stainless-steel porous plate at 0.1 atm. pressure. They used aquartz probe to sample the flame. NO uas detected

Xusing chemiluminescence; H, OH, and 0 using ESR; CN-species using chemic al mea ns, and stable species usinggas chromatography. For eq uiv ale nc e ratios fro m 0.88to 1.42, they concluded tha t the Zeldovich mechanis mis inadequate to predict "prompt" NO formation, andthat HCN is formed prior to NO. They favored Reaction(13) over Reaction (?) on thermochemical grounds andpointed out the violation of the spin-correlation ruleby Re ac ti on (7). Ot he r spe cies like C, C2 did not con-tribute significantly to "prompt" NO formation becauseof their low concentrations in the flame. They sug-gested that

H2CO + M CO + H2 H - M (21)is the rate determining step in methane oxidation.

95Pecters, Blauuens, and Smets measuredthe concentrations of NO, 0, and fuel fragment radi-

26


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icals such as CH, CH2, C2, by means of molecular-beamsampling and mass spectrometric detection in a numberof hydrocarbon/02/N2 flames. The fuel uas ethylene,ethane, or methane. They found that even in hot, fuel-lean flames, the Zeldovich mec hanism cannot acco untfor the rapid NO formation in the flame front. Theyderived an expression for the NO generation rate in theflame front of all flames investigated in terms of theCH2 or CH radical concentrations. They concluded thatboth of the processes

CH + N 2 * HCN + N (7)CH2 + N2 H C M + NH (13)

in each case followed by rapid oxidation of the prod-ucts, may be the principal source of NO in the flamefront, and that other hy dro car bon frag ments , C, C2,C 2H do net contribute to "prompt" N O format ion becauseof their lou concentrations in the flame front.

The actual mechanism of decay of hydrogencyanide in hydrocarbon-air mixtures is uncertain.The studies by Haynes and Morley previously mentionedare in contradiction in regards to uhich reaction isthe rate-determ inin g step in the decay. In order toelucidate the HCN-decay mechanism uhich concludes uith2 fithe formation of NO, Haynes recently conducted astudy of premixed hydrocarbon flames burning on a ua-ter-cooled neker-type burner seede d uith fuel-nitro-

27

'


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gen in the form of pyridine, ammonia, or nitric oxidein amounts up to 2000 ppm. of nitrogen species in thepost-flame gases, A water-cooled silica probe uasused to sample the gases. NO uas dete rmi ned continu-ously by a nondispersive infrared analyser (l\IDIR).Cyano species and total amine species uere determinedusing chemical means. H-atom concent ration in thehot gases uas determined by the Li/LiOH absorption method,Post-flame temperatures were determined by the Sodium-line reversal method. Based on the experimental re-sults, Hayne s pr op os ed two parallel rate-controllingsteps: one which is first order in OH, possibly reac-tion (22)

HCN + OH * HOCN + H (22)the other which is second order in OH:

HCN + OH * CN + H20 (23)CN + OH * OCN + H (24)

The relative contributions of (22) and (24) vary withtemperature, uith Reaction (24) dominating at hightemperatures. The OCN- species decay very rapidlyto form NH.-species1 +HHOCN (cyanic)^HIMCO (isocyanic)^ NH2 - f CO (25)

OCN + H % NH + CO (26)As Haynes points out, measurements of OCN and NH.species are required to confirm the pro pose d mech-anism.

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( " l o r l ey considers the fate of the NH. spe-cies. He indicates that the nitrogen hydrides canbe interconuerted by reactions of the type,

NH V + H N H V , + H9, x=l,2,3 (27)X XX ^-which may or may not be balanced, and the oxidationand the formation of N^ taking place by

N + OH NO + HNHo + NO ^N2 +

* N0 + OH'2

NH + NOH20

N + NO^N2 + 0

(3)(28)(29)(3U)

Furthermore, at relatively lou temperatures, the abovereactions might lead to a build-up of amine species.Experimental measurements are needed.

29


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2.4 Mechanisms of Methane OxidationIn order to predict the formation of nitric oxide

in fuel-rich flames and some lean flames of hydrocarbons(see Sect ions 2.2, 2.3), the concentration histories of thefree radicals are necessary. The kinetics of methane oxygensystems hav e been studied extensively over the years.Nevertheless, many uncertainties rema in, both with respectto the oxidation mechanism and the rates of the elementaryreactions which form part of the mechanism. Furthermore,in the richer methane flames, C^-hydrocarbon decay andformation has to be accounted for, and the mechani sm grousin complexity.

2.4.1 Methane Oxidation in Fuel-Lean FlamesStudies in clude shock-tube exp erim ents by Cooke

3D 31 32and Williams , Bouman , Heffington et al , Brabbs andBrokau , molecular-beam-mass-spectrometer sampling of27flames by Peeters and Mat-men , numeric al analysis and flou

34reactor experiments of Uestbrook et al , the kinetic sur-35 9 6 9 7vey of Engleman , and recent uork by other authors .

In Table 1 (p. 35), the 23 reaction mechanism for31the shock-initiated C H,-oxid atio n pro pos ed by Bouman " is

reproduced. This mechanism has been used extensively byother investigators. Bowman's analysis shows that, in thetemperature range 1900 - 2400K, this mecha nis m correctly

3D


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predicts the time of occurring and ma gni tud e of the radical(0, OH, H) concentration overshoots, and also predicts adeparture from a "partial equilibrium" state during theinitial stages of the radical concentration overshoots.

^ fioni and Penner conducted a sensitivity ana-lysis of the mechanism proposed by Bowman at 2QOOK. Theiranalysis showed that Reactions (Rl), (R7), (R16) and (R25)are the most important reactions for all of the species

CH4 + n CH 3 + H + N (Rl)H + 02 0 + OH (R7)CH 3 + 02 H 2CO + OH (R16)H 2CO + P I HCO + H + M (R25)

In addition Reaction (R15) is important for the major freeradical species, i.e., OH, 0, and CH20. The 0-atom profileis dominated by Reactions (Rl), (R7), (R16), (R25), (R15)(as cited by Bowman) plus Reactions (R24) and (R3)

CH3 + 0 H 2CO + H (R15)HCO + f l CO + H + N (R24)CH4 + H CH3 + H2 (R3)

9 8The mechanism of Reaction (R16) has recently been studied ,and the oxidation of meth yl radicals was show n to occurthrough the steps

CH^ + 0 * CH90 + H\J


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The methoxy radicals produced react by means ofCH3D + M CH20 + H + MCH30 + 02 CH20 + H02

The reaction of CM, uith 02 and the thermal decompositionof C I - U O are the most important pathways of methyl radicaloxidation,

27Peeters and M a i - m e n measured the concentrationof all species, stable as uell as unstable, t hroughout thereaction zone of lou-pressure lean methane-oxygen flames.The results of their analysis shou that (i) CH, reacts 15%uith OH, 15% uith 0, and 10% uith H; (ii) CH, is destroyedOb y 0 atoms; (iii) CH90 disappears 4 Q ? o by thermal decompo-*sition, 40% by reaction uith OH, and 20% by 0 attack; (iv)CHO reacts mostly uith 02; (u) H02 is destroyed 45% by OH,40% by 0, and 15 % by H, Their studies shou that the ratelimiting step is the decomposition of formaldehyde

CH20 + N = CO + H2 + 1 * 1 (31)They argued that Reaction (31) explains quantitatively thefunction of H 9 in the flame, and the activation energy ofzReaction (31) is in good agreement uith the overall "acti-vation energy" of lean-CH^/02 flames (about 40 kcal/mole).On this basis, they rejected reactions such as

CH20 + 0 CO + H + HO (32)

Furthermore, they pointed out that Reaction (R25) of BoumanC H O + N ^ C O + H + N ( R 2 4 )


49/164

may uell be the rate-determining step in shock studies,and Reaction (31) cannot contribute significantly to theremoval of CH20 in shock tubes since the major part of theCH20 is consumed by H atoms in a chain mechanism initiatedby Reaction (R25). Their results also shou that C02 isformed mostly via Reaction (R9)

CO + OH C02 + H (R9)The imp ort ant reactions in Peeters mec hani sm are

CH4 H - OH CH3 + H20

CH4 + 0 CH3 + OHCH3 + 0 CH20 + HCH20 + N $ CO + H2 + MCH20 + OH(0) CHO + H20(OH)CHO + 02 CO + H02H02 + OH(0) * 02 + H20(OH)H02 + H 20HH + 02^OH + 00 + H2 ^OH + HOH + H2 H20 + HOH + OH H20 + 0CO + OH C02 + H

7

(For extensive kinetic data see England ). Furthersupport for Reaction (31) as the rate-determining stepin flames can be found in the investigations of Migauchiet al . They studied premixed CH4/02/N2 flames at 0.1

33


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atm. and equivalence ratios between 0.88and 1.42. Theyfound the rate-controlling reaction of methane oxidationto be Reaction (31) uith a rate constant k31=2.1x!015 exp(-17,620/T) mol"1cm3sec"1.

2.4.2 Methane Oxidation in Fuel-Rich FlamesIn the combustion of fuel-rich hydrocarbon

flames,the -concentrations of hydroc arbon fragments are highenough that their reco mbinati on reactions bec ome impo rtan tand hydro carb ons higher than the original fuel are found asintermediates.

In CH^-oxidation, the chemistry of C 2-hydrocar-bons bec omes importa nt in the fuel-rich mixtures. Ga rdiner

37and Olson have conducted a series of shock tube experi-ments and numerical analysis of fuel-rich CH,/02/Armix-tures. The reaction s o f CH 2 C^H,, and CoH- were found toplay an impo rta nt role in their shock tube exp eriments.The result of their ex pe ri men ts can be mo del ed by a sixty-three-reaction mechanism which is reproduced in Table 2(18000


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TABLE 1,Methane oxidation in fuel lean mixtures

Reaction Rate constant, k f*CH,-i-H+M

2.3.4.5.6.7.8.9.

f l O .11.12.f!3.tH.15.16.f!7.18.19.20.21.22.23.24 .25.26 .27.|2S.f 29 .

t30.

CH4+H-CH,+H,CH,+OCH,+OHH,+OHH+H,OO+HjH+OHH+OjO+OHOH+OHO+H.OCO+OHCO,+HCO+O4-MCO.+MH+OH+ArH,O+krH+OH+H,O-HzO-}-H,OOi+Ar-^O+O+ArH,+ArH+H+ArCH.+O-^HjCO+HCH.+O)H,CO+OHCH.+OHHjCX^+H,H,CO+O HCO+OHH,CO+OHHCO-1-Hr f )H-CO+HHCO+H,HCO+O CO+OHHCO+OHCO+H^)HCO+HCO+H,HCO+MCO+H+MH,CO+M-HCO+H +MH+HO,-*OH+OHH+O.+MHO.+MC,H,CH4+CH,C-H.+OC ^ H ^ + O HHCO+O,CO+HO,

2X1017 exp(-6X10" exp(-2.24X10*7'' ex2.1X10" exp (2.9X10" exp (3.2X10'< exp (2.2X10" e x p (5.5X10" exp (4.0X10U exp(5.9X10"exp(

44 500/77)6290/2 T )p(-4 400/7")-4560/r)-5530/T)-7540/r)-8450/r)-3520/r)-4030/T)-2060/D

7.9X1011 exp(-52770/r)2.2X10" exp(-4S300/r)1X10"2X10"4X10"5X1011 exp(-2300/r)5.4X10" exp(-3 170/r)1.35X10" exp(-l 890/7")1X10"1X10"2X10"5XlOue. xP(-9570/r)4X10U exp(-lS500/r)2.5X10"exp(-950/r)1.5X10" exp(500/r)8X10" exp(-4 500/r)4X10"exp(-32SO/r)4.2X10"exp(-7200/7')

Units : c m , cal, K , m o l e , sec. t Re.iction n o t i n c l u d e d in final m e c n a n i s m .

35


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TABLE 2.Methane oxidation in fuel rich mixtures

Reac t ion(1 ) CH4 + M = CH3 + H + M(2) C H 4 + H = CH3 H - H2(3 ) CH4 + O = CH3 + O H(4) CH4 + O H = CH3 + H2Ob(5) CH4 + CH2 = CH3 + CH3C(6 ) C H 3 + M = C H 2 + H + Mc'd(7) CH3 + O2 = CH2O + O H(8 ) CH3 + H = C H 2 + H2c'e(9 ) CH3 + O = CH2O + H

(10) CH3 + O H = CH2O + H2( 1 1 ) C H 3 + C H 2 = C2H4 + H(12) CH2 +CH 2 = C2H2 + H2(13) CH2 + O2 = C H 2 O + 0(14) CH20 + M = CHO + H + M(15) CH20 + H = CHO + H2(16) C H 2 O + 0 = C H O + O H(17) C H 2 O + OH = CHO + H2O(18 ) C H O + M = H +CO + M(19) CHO + O2 = H O 2 -i-CO(20) CHO + H = CO + H2(21) CHO + O = CO + OH( 22 ) CH O + O H = C O + H 2 O(23) C2H6 + M = C H 3 - t - C H 3 + M / '(24 ) C2H6 + H = C2H5 + H2(25) C2HS + O = C2H5 + O H(26 ) C o H 6 + OH = C2H5 + H20g(27) C2H6 *CH3 = C2H5 -H CH4h(28 ) C2H5 + M = C2H4 + H + M 1(29) C2H5 + O2 = C2H4 + HO2(30) C2H5 + H = CH3 + CH3(31) C2H5 + H = C2H4 + H2(32) C2H4 + M = C2H2 + H2 + M(33) C2H4 + M = C2H3 + H + M(34) C2H4 + H = C2H3 + H2(35) C2H4 + 0 = C H 3 i - C H O(36) C2H4 + O H = CH3 + CH2O( 3 7 ) C2H3 + M = C2H2 *H + M(38) C->H 3 + H = C2H2 + H2C(39) C2H2 + M = C 2 H - H H + M(40) C2H2 + H = CoH + H2;'( 4 1 ) C2H2 + O = C H 2 + CO

IogIOX17.6714.86

7.073.54

13.0016.6711.8414.8613.8312.8713.3013.5014.0016.7013.3013.7015.7014.4712.5313.3013.4813.48

111.2914.1213.2613.8014.7414.6712.1813.5712.2717.3217.4114.8413.3513.0014.9013.0016.62

0.8913-72

Rate Constant0n

002.13.1000000000000000000

-25.300000000000000003.20

046 ,900

7,6003,8401,010

046,9004,5307,600

0000

1,86036 ,235

1,6602,3006,5407,400

0000

80.0204,7153 ,0701,810

10,82013,3902,445

00

39,81048.600

7,3001.360

015,850

053,85025 0

1,860

36

-


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Reaction

(42) C2H2 + OH = CH3 + CO(43) C2H2 +C2H2 = C4H3 + ff(44) C2H2 + C2H = C4H2 + H(45) C 4 H 3 + M = C4H2-|-H + M /(46) C4H2 + M = C4H + H + U >(47) H2 + O2 = O H + O H(48) H + O2 = O H + O(49) O + H2 = O H + H(50) O H + H2 = H2O + H(51) OH + OH = H2O + O(52) H + O2 + M = H O 2 + M/C'i 'V T > _ OU -i- \i TJ f~} 4- \t\,j j ) ti r k jn T jvi rio^-* *"(54) H2 + M = H + H + M(55) O2 + M = O + O + M(56) CO + Oo = CO2 + O(57) CO + O H = CO2 + Hk(58) CO + O + M = CO2 + M(59) H2 + H O 2 = H2O + O H(60) H + H02 = O H + O H(61) H + H02 = H2 + O2(62) O H + H02 = H 2 O + O2(63) O + H02 = O H + O2

Iog10>l

12.0813.0013.6015.9317.5413.2317.08

- 14.3413.7213.7415.4023.8812.35

.11.2711.0812.6013.4511.8614.4013.4013.7013.70

R a t e Constant0

n

000000

-0.910000-2.60.50.500000000

6

25 022,650

030,20040,26024,210

8,3706,8953.2703,520

0046,60048 ,16517,615

4,025-2,285

9,41096035 050 0500

0 R a te c o n s t an ts in the form A X 7" ex p (-6/7"), i n c m , m o l , s, and K u n i t s . T he r ever se r eac t ion ra te c ons tan ts w erec o m p u t e d u s i n g J A N A F th e r m o c h em i c a ! d a t a w h e r e po s si b l e an d local ly c o m p u t e d t h e r m o c h e m i c a l d a t a o the rw ise .b T h e T3 f ac tor m ay e x t r a p o l a t e th e ra te cons tan t l oo h igh at h i g h e r t e m p e r a t u r e s , bu t i s u s e d h e r e b e c au s e thisexpress ion goes t h r o u g h th e h i g h - t e m p e r a t u r e da ta .c E s t i m a t e . N o s en s i t i v i t y to the r a t e of th i s r eac t ion w as observed .^ E s t i m a t e d t o b e e qu a l to f r j /10 .e E s t i m a t e d t o b e eq u a l to J r2.^ This r eac t ion is in the pressure-dependen t fa l l o f f region of a u n im o l e c u l a r decompos i t ion . Th i s rate expression isf r om Olson et al . [9] for exper imen ts over th e range 1330< T < 2500 K and 0.10 < P < 0.50a tm . Care mus t b e takent ha t th i s r a te - co ns tan t expression be u sed on ly f o r the pressure and t e m p e r a t u r e co nd i t i ons f o r wh ich i t i s va l id .

* Th is i s a low - tem pera tu re v a l u e that agrees wi th the f ew h i g h - t e m p e r a t u r e da ta .h S t r o n g l y c u r v ed A r r h en i u s b eh av i o r is observed f o r th i s r eac t ion .1 This r a t e - c o n s t a n t express ion w as obtained by RRK c a l c u l a t i o n s of the f a l lo f f f rom th e ex pe r im en t a l h i g h - p r e s su r el im i t exp je ss ion o f G l a n z e r and Troe[47J.

^ P r e l im in a r y re su l t s .k S ee B a u l c h an d D r y s d a l e [621for a r e v i ew of the l i t e r a t u r e on this reaction.

37


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the CH2 reactions (ll) and (13), and reactions (14) and (2).Literature values for rate constants uere used for Reac-tions (1), (2), (13), (14), (30) and (48). The authorscautioned that the H 2CO-decay mechanism is uncertain andinsufficient experimental data is available. The numeri-cal values for the rate constants of Reactions (7) and (11)uere found by numerical analysis. They believ e their re-sults to give k? to uithin + 5 Q % and k, , uithin a factor of2.

38Harvey and Maccoll studied the formation of C?hydrocarbons uithin m ethane-o xygen flames of equivalenceratios 0.56 to 1.25 at 20 torr. Their expe rime nts shouedthat for their experimen tal conditions the reaction

CH3 + CH3 + N C2Hg + 1 * 1is uell into the fall-off reg io n res ultin g in a lou re-action rate (the max imum mole fraction of ethane in thestoichiometric flame uas 5 x 10 ). Their results enabledthem to propose the following ethylene forming reactions

CH3 + CH2 C2H4 + HThe ChU and CI-U concentrations in these flames are inequilibrium via

H -x p i tv * L M O n / pFigure 2 shows the dependence of CH20, C2H4, C2H2 andH2 peak concentrations on flame equivalence ratio.

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Figure 3 shows the dependence of C 2 H < , C2H2, and hUon peak fCH for a range of flame equivalence ratios.They also pointed out that at higher pressures the rateof the combination of methyl radicals (CH, - f - CH,, + P IO O C2Hg + M) to ethane uill become competitive uith theother sources of C2 hydrocarbons, and acetylene is formedin the flame via

+ CHo x ~ CoHo 4 - HO

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0-4

oo

o

0-3

0-2O5

0- 1

0-5 0-6 O -7 O -8 09 1-0 11 1-2 1-3E Q U I V A L E N C E R A T I O

Fig. 2. The dependence of CH2O ,C2 H2 , and H2peak concentrations on flame equivalence ratio .

40


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( P E A K CH3 M O L E F R A C T I O N ) 210s

Fig. 3. The dependence of peak C_H4 C H and HS on peak2 2 2 2 '( CHS ) for a range of flames Z 0.56 to 1.25 .

41


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Shock-tube studies of the early stages ofpyrolysis and oxidation of metha ne were co nducted by

39Tabayashi and Bauer . Temperatures ranged from 1950to 2770k, total densities (2.37 - 8.91) x ID"6 mol*Zcm , and CH /CU ratios 3.3 and 6.7. From their pyroly-

sis experiments in CH^/Ar mixtures, they concluded thatmethane decomposes mainly via

CH + P i CH, + H + n

C2H5+^*C2H4 *H * NC2H3 + F l C2H2 + H + M

methylene is pr od uce d mostly by the react ionCH2 - r H2 CH3 + H

and con sum ed via reactions with C I - L and species gener-ated during ChL-pyrolysis. Their oxidation studiesshow that ox yg en reacts only with the fragments of meth-ane pyrolysis, and under the met han e rich conditionoxidation starts p red om in an tly via the reaction

CH3 + 02 H2CD + OHrather than

H + 02 OH + 0and the resulting OH radicals react rapidly with meth-ane uhich is present in large excess,

CH4 + OH CH3 + H20thereby gener atin g more methy l radicals, uhich reinforcethe pyroly sis chain. Their calculated speci es prof iles


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best fit the observed profiles if the reaction rateconstant for the meth yl radical-oxygen reaction is givena value of 2.7 x ID12 x exp (-12,000/RT) cm3moi""1s~1.Regarding the fate of formaldehyde, they found thatthermal decomposition of formaldehyde uas in agreementwith their experi mental results and compute r simulations

CH20 + M = CO + H2 + P IHouever, an alternative m echan ism consisting of thefollowing reactions

CH20 + M C H O + H + 1 *1C H O + M ^ C O + H + I V 1C H O + 02 CO + H20C H O -f H C O + H2CH20 + H H2 + HCO

could not be excluded.The role of CH2 in CH^-oxidation uas found

to be ambiguo us. This study also shous that oxidationof CO to CO- occurs mainly via the reaction

CO + OH C02 - f H


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CHAPTER 3EXPERIMENTAL APPARATUS

3.1 An Introduction to Sampling Techniques in Combus-tion Studies

40As Knut h has suggested, specifications forthe ideal instrumentation for flames studies might in-clude the following broad requirements: (a) monitorall chemical species, including intermediate and free-radical species, (b) function in te mpe r atur e , press ureand composition ranges typical of flames, (c) resolvespatial measurements small in comparison uith the flamethickness, and (d) monitor uithout disturbing the (non-equilibrium) t her m o d yna m i c state of the system.

Shock tubes have been shoun to be suitablefor studies of high temp era tu re processes, and excellentrevieus and books are available that describe their ap-plicability in chemistry and physics. The shock-tubemethod of studying high-temperature processes possesses

41at least four major adv anta ges over other metho ds ~:

(1) The equilibrium temperature in the after-shockregi on can be calculated accurately and re-liably from the measu red shock speed andconservation of mass, energy, and momentum


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considerations,(2) The "slug" of gas behind the primary shock

is very uniform in pressure and temperature.Uall effects are negligible because of theshort time scale.

(3) Practi cally any gas mixture can be heatedto any selected temperature by using the ap-propr iate shock str ength.

(4) The heat release by the shock impact is ini-tially in the form of kineti c e ne r gy , i.e.,translational energy of the molecules.The major disadvantage is the short observa-

tion time, which for the after-shock re gio n, is usuallybetueen 1QD and 400 sec, Thus, optical spect rosco pyis by far the most useful method of following the pro-duction and/or consumption of individ ual species behindshock waves. Typically, thr ee or four species are mon-itored. If only one optical path is available, thena oiven set of conditions must be repeated for each ofthe species monitored.

O no of the principal probl ems with spectro-scopic studies is that of dete rmi ning absolute concen-trations, since absorption coefficients are known onlyfor atoms, most diatomic molecules, and a few simplepoly-atomic species. In the absenc e of this knowledgeit is necessary to calibrate the system. This is dif-

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ficult because radical concentrations of knoun valuesare hard to obtain, the p r o d u c t i o n of the radical it-self might be an experimental challenge, and it is neces-

sary to calibrate over the temp era tu re range to be stud-ied since the t em p er a t u r e dep endence of absorption coef-ficients of complex molecules is unknown. O ne alsohas to find absorption lines in the available spectralregions uhich are not obscu red by other species. H encethe use of shock tubes in conjunction with optical spec-troscopy satisfies r e q u i r e m e n t (d) most closely, require-ment (a) least closely.

In a n a l terna t i ve tec hniq ue, g a s sa m p l es a rewi thd r a wn fr o m the fl a m e using a sa m p l ing probs. P r o b esampling is a straig htforw ard process; the sample iswi thd r a wn, qu enc hed , a nd a na l yzed. The chief a d v a nt a g eof this tech niqu e is that a wid e variet y of analyticalinstruments can be used to follow the fates of specieswithin the flame. The mai n di sa dv ant ag e is that compo-sition cha nges due to addit ional ch emic al reactionsdurin g transpo rt from the flam e to the analytical in-strument^) are inevitable. Probes also have perturb-ing effects on the flame that ha ve to be considered:a er o d yna m i c , ther m a l , and catalytic effects. Some ofthese ha ve bee n eliminated by the use of very fine mi-

9croprobes ma de of quartz. The relat ive effects ofseveral different pro be designs on flames ha ve be en studied


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by England , M a l t a , and Allen . The use of samplingprobes meets requirement (a) relatively closely and re-quirement (d) relatively poorly.

S a m p l ing of ions from flames is another tech-nique used by investigators to study the processes oc-curring in the combus ti on mixture. In a typical appa-ratus, the gas is sampled through a small hole at thetip of a cone and e xpand e d into a v a c u u m c h ambe r at10 to 10 torr. The system is des igne d to obtaincritical flow t h r o u g h the nozzle. The ions are formedinto a beam by an electrostatic lens and f ocuse d th ro ugha small hole, typically 2mm. in diameter, into a secondc h ambe r at 10 torr. w h ich h olds a q u a d r u p o l e mass spec-trometer and electron multiplier. B o t h pos itive andn e g a tive ions can be d e t e c t e d by r e v e r s i n g the polari-ties of vari ous voltages. Ideally the e x p a n s i o n of thegas into the vacu um should be fast enough to quench anych e m ica l reactions so th at the e x pand e d gas has a p p r o x -imately the same compos iti on as that in the flame.This is usually the case for neutral molecules, butbecause ion-molecules reactions are typically 1-2 ord ersof magnitude faster than those betueen neutral moleculesconsiderable dis tortion of ion signal can occur .This is particularly important for negative ions becauseof the possibili ty of fast associative reactions. Fur-thermore, the bou nda ry layer t hat exists on the sampling

47


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and quad ru pol e mass spectr ometer detector. Inclusionof an effusive source and a uheel-chopper in the collima-tion chamber allows calibration of gas mix tur es andphase-sensitive detection. The source gas (at pressuresof up to several atmospheres and temperatures of severalthousand degrees Kelvin) ex pands through the samplingorifice into the source chamber (uhere background pres-

3 -1sure is typically 10 to 10 torr.) and the core ofthe resulting jet is skimmed and tra nsferred into thecollimation chamber (uith backgr ound pressure from 10"~to 10 ' torr.). The molecular beam is ch oppe d in thecollimation ch ambe r for ph ase-sens itive de te cti on, andthe collimating orifice admits these molecules flyingalong the system center line into the de te ctor chambe r.The mass-spectrometer detect or generates a signal pro-portional to the species density in the beam at the de-tector.

As uas mentioned in the discussion of ionsampling from flames, the intention here is to lowersuddenly the t e m p e r a t u r e and press ure of the re actionmixture, so that further chemical changes are preventedand the composition of the expanded gas approximates,that of the flame.

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FABR I TEKCOMPUTER

EA I 250 QUAD. BEAMMASS SPECTROMETER CHOPPER

TOP

IONSIGNAL

\

VACUUM PUMP

W A V EGENERATOR

SIGNALEFFUSIVESOURCE

DETECTOR EXCITOR

VACUUM PUMP

LOCK-INAMP.

LSI-11COMPUTER

MOVABLESKIMMER

W A T E R - C O O L E DH E A T S H I E L D

VACUUM PUMP

BURNER POSIT ION SIGNA L

Fig. 4. The UCLA MBMS sampling system.


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Thus, applicability of M B M S sampling techniquesto the study of chemical reactions in flames resultslargely from the rapidity with uhich the gas tempera-ture and pressure decrease during the e xpans ion th rou ghthe orifice in the sampling cone. A plot of the tem-per atu re ratio T/To versus dimensionless time, takenfrom reference 40, is shoun in Figure 5. T is the gast e m p e r a t u r e , a is sound speed, t is flou time (zeroat the throat), x is axial distance (zero at the throat),d is throat diameter, and subscript o refers to source(stagnation) conditions. Fur the rmo re, a point thatshould be stressed is that, uhile in the s amp li ng of ionsone is actually meas ur ing a ver a g e proper ties of thegas that flous t hro ugh the sampling orifice, in MB MSsa m p l ing only that small fraction of the sample d gasthat flous in the vicinity of the orifice centerli nereaches t he q uadr upole mass spe ctrome t e r de te ctor.This results, as uill be explai ned in more detail in thenext section, in the d e t e c t i o n of mole cular-beams thatare muc h mor e represent ativ e of the flame gas.

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Fig. 5 Temperature ratio as function of dimensSonless flow timefor free-jet gas flows from orifice.

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3.2 Possible Composition Distortions i n _ flBNS. Samplingof Flames.

In an idealized model4 of molecular-beamsampling, the sampled gas under g oes an isentropic free-jet expansion through the source orifice and the speci-fic-heat-ratio, ^Tf remains a constant thro ugho ut thisexpansion. Flou remains a cont inuu m upstream from theskimmer entrance and beco mes free-molecular dow n s tre a mfrom this surface. There is assu med to be no bac kgr oun dscattering of the free jet and the mol ecul ar be am.The beam compos ition at the detec t o r is the same asthe source-gas composition.

In the design of a flBHS sampling system, var-ious depa rtu res from the ab ove m o d el m ust be c onsi dered.As the c o m bust i on m i x t u r e flous from the so u r c e to thedetector, the following a re enc o untered : sa m p l ing -p r obe-in duce d distortions of the gas composi tion, chemica lreactions during the expansion of the gas into the vac-uum, species condensa tion , pressure diffusion, freez-ing of vibrational, rotational or translational degreesof freed o m (in this order), skimmer inte rf e rence , Flach-number focusing, and scattering by back grou nd gases(in any one of the lou-pressure chambers). Except forprobe-induced distortions, all of the above considera-tions are t r ea ted in the p a p e r by K n u t h , and the dis-

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cussion is based mostly on this reference and uork byother authors with the U.C.L.A. M B M S sampling system.

3.2.1 Free Ge t Expansion.Before proceeding into the discussion of com-

position distortions in MBMS sampling, the reader mightbenefi t from a brief introducti on to the proble m ofunconfined expansion from a sonic orifice into a lou-pres-sure chamber.

As Sher man indicated, the probl em of trans-onic flou t h r o u g h an orifice or axisymmetric nozzle re-m a ins uns olve d. Houe ver, the supersonic region of theflou is very little influe nced by the t r a nsoni c reg i on,and the met hod of charac teristic s can be appl ied inthe inertia-domi nated regi on of high-Flach-number isen-tropic flou.

The free-jet shock u a v e structure is shounin Figur e 6. As point ed out a b o v e , the met hod of char-acteristics is appli ed to the region inside the bar relshock. O u e n and Thornhill were the first to carryout the comp utat ions for gases uithT7/5 a ssu m ingslightly supersonic flou at the orifice (M = 1 leadsto a singularity). S her m a n a nd Ande rson rep o r tcalculations for other values ofj. The main featureof these calculations is that about one nozzle diameter


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from the orifice the streamlines appear to radiate froma "source" at x . F u r t h e r m o r e , the density decreasesalong each streamline in proportion to the inverse squaredistance from this "source." The isentropic cor e of theflou app ear s to pass from the nozzle exit th ro ug h a bar-rel, the sides of uh ich are the shock u aves gen era te dby the coalescence of comp ress ion uaves origi nate d atthe jet bo un da ry as the reflecti ons of the initial ex-p a nsi on fan. The M a ch disk is form ed by the int ersec-tion of the lateral shock ua ves.

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S O N I CORIF ICE M A C HD I S KB A R R E LS H O C K

Fig . 6. Free-jet shock structure.

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The variation of the mach n u m be r , M , alongthe jet axis with distance x has been carried out bySherman and Ashkenas ' for'"/" = 5/3, 7/5, and by An-derson49 fo r If = 1.30, 1.20, 1.10, and 1.05. They usedthe best fitting fo rmu la

f TlP 1 ~'iM I ^d * x l

w h e r e A, and x are constants which can be obtainedofrom the abo ve references. For other values ofT, onemay use the following equatio n suggest ed by Knu th ,

(34)

Note that Equation (33) has a singularity at x = x ,and therefore it is only applicable if x >1.d* 'It is important to point out effects that arenot considered in the ab'ove analysis of free-jet expan-sion. (1) Boundary-layer grow th on the converging nozzle.The effect of this bo undar y layer will be to changethe effective orifice size (see Ref. 51 for a com pre -hensive analysis) and distort the flow pa tt er n near theorifice. In equations (33) and (34) an effective ori-fice d iame ter then must be used.(2) Freezing of vibrational, rotational, and transla-tional de gr ee s of fr ee do m (always in this order). Freez-ing of d e g r e e s of fre ed om will cause T to change in the

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expansion and not be constant as assumed In Thornhill'sanalysis. Freezing of translational degrees of free-dom causes the flou to transit from continuum to free-molecular. Equations (33) and (34) for the centerlineF l a c h number do not hold in the free-molecular flou re-gion. It should be noted, houe ver , that the densitykeeps decreasing as the inverse square of the distanceas a con sequ ence of the source-point nature of the flou.(3) To the author's knowle dge the d eterm inati on ofjet bounda ries for gas mix tures uith dif f us ive separa-tions (e.g., ba rodif fusion) has not been solv ed theo-retically.

46S h e r m a n d e t e r m i n e d the location of the M a c hdisk empirically,

p = stagnation pressur ep = ambi ent pressureThis is i n d e p e n d e n t of v and hol ds for 15P0/0 17,000.

52Bier and S c h m i d t d e t e r m i n e d , from photo g raphi c studiesof jets, empirical r elations for the nach-disk diametery and the ma xim um diameter of the barrel shock yQm afor 10 p /


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0.591- - 0 316d*

Sometimes, values for the Mach num ber nearthe sonic orifice (upstream of the effective "source"at x ) and upstream of the orifice are needed. As in-dicated above, Equation (33) is restricted to x/d*^l.Values for M in these tuo r eg i ons ha ve be en deter m i nedexperimentally by S her m a n and A s h k e n a s for o = 7/5,and A n d e r s o n ' f or 1) = 5/3. Sh ar ma ar ri ved at ex-pressions for T/T in t er m s of x/d* in these tuo r eg i onsfrom theoretical considerations. His calculated P l a c hnumbers are l a r g er tha n exp er i m ent a l l y d e t e r mi ne d ones.

3.2.2 Chem ical Rel axa tio n in Supersonic ExpansionSuccessful nBHS sampling requires that all

chemica l reactions occurring in the sampled gas mixtureare qu en ch ed , i.e., tha t the y "freeze," as early aspossible in the free jet expansion through the samplingorifice. If the chemic al reacti on is frozen ups tr eamof the sonic orifice, then the s a m p l e d gas is most repre-sentative of the undistur bed gas composition. How e ve r,if the reaction p roc eeds at large rates it uill be ableto follow changes in t e m p e r a t u r e and p ressu re up tothe nozzle throa t, a nd in some cases several thr oa td i a m eters d o w n s t r e a m .

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Hayhurst studied the occurrence of chemicalreactions in the supersonic expansion of a gas intoa vacuum. His investigation focused on the hydrationof HjO4"

H30++ H20 + M # HgQ* + PI (38)in an atmospheric p rem i xed H2/02 flame uith nitrogena dde d as a diluent. Reaction (38) is fast enough tobe equilibrated in the flame. For this purpose it isnecessary to calculate the variation of te mpe rature ,pressure, and density of the gas in the free jet expan-sion. Hayhurst arrived at a complete description ofthe isentropic flou field by the method of character-istics. (The free-jet p r o b l e m has been treated by othera u tho rs ' ). Not e that in the h i g h t e m p e r a t u r e andpressure regions of the expansion, reaction (38) canbe assumed to be equilibrated at all times. Hayhurstconc luded , "The calculations descr ibed above shou thatthere is continuum flou in the expansion of the gas through

-.7the sampling nozzle for about 5 x 10 sec, after uhichthe flou is molecular. Consequently, if the relaxa-tion time of any chemical reaction is muc h gre ate r

_7than 5 x 10 sec at atmospheric pressure, the reactionX

uill not proc eed dur ing the expansion. If such condi-tion holds for all possible chemical reactions, com-position uill not be affected by sampli ng. This repr e-sents the case of ideal sampling. Hou ever, a reaction

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_uith a rela xat ion time less than 5 x 10 sec uill beat equilibrium in the flame, where the time available

_ 3is about 10 s, and uill be able to follow any ch angesof t emper atu re, etc., up to the nozzle throat. Therelaxation time of a reaction similar to (38) uillincrease once inside the nozzle, because of the fallin gas pressure and temperature, so that a point even-tually be reached at uhich equi libr ium can no long erbe maintained and the composition uill b e c o m e "frozen."C onsequent l y , the compos ition obse r ve d uill not neces-sarily be that of the origina l sa np l e, but uill co rres-pond to conditions at some point in the sampling nozzle."

45Ions from flames have also been samp led by f ' l o r l e y .His results are in agre eme nt uith tho se of Hayhurst.

In vieu of the i m p o r t a n c e of che mi cal relax-ation in systems at h i g h t e m p e r a t u r e and press ure ,Knuth studied the chemical relaxation process inflou systems. He i d e n t i f i e d the p rop e r relaxationtime as being^ . , the re laxation time at constantenthalpy a nd press ure , rathe r thariTy p, re laxationtime at constant te mp er at ur e and pressure. (Relaxa-tion time is defined as the time required for the de-

\ viation from equilibriu m to r e d u c e to 1/e its initialvalue if the existing t her m o d yna m i c constraints ueremaintained.) Knut h com bine d Bray's sudden-freezing

57model uith Ph inne y's relaxation-time-freezing p o i n t

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criterion, i .e . ,

tYh>p -C (39)u h e r e D/Dt is the hy d r o d yna m i c deriva tive and C isa constant, to arrive at a chemical relaxation equa-tion, with C g i v e n a value of 0.5. E qu at i o n (54) of

40Knuth pro vid es a criterion for the early freezingof a reaction. This eq uation is characterized by tuoparamet ers; namely, the kinetic p aram eter defined asthe ratio of the chemical a cti vat ion energ y to ther a nd o m the rmal ene rgy, and the scaling par amet er definedas the ratio of the f l o u i time to the collision time.

58Y o ung used a last-activated-collision m o d e lto d e t e r m i n e a crite rion for the freezing of a chemi-cal reaction. In this model, a gi ven chemical reac-tion f reezes approximate ly at the location uhe re thesample molecule encountered its last activated collision,Young studied chemical freezing of bimolecular reac-tions involv ing an activ ation energy. The number ofactivated collisions of a mole cule uas com p ute d alongthe free-jet c enterl ine. The results of this calcula-tion indi cate that chemical freezing in the free jetis characterized by the kinetic and scaling par amet ersas defi ned by Knuth. Furt herm ore , the analysis revealsthat com plete chemical fr eezing in the free-jet isobtained if the ratio of the logar ithmic scaling factor

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divide d by the kinetic parameter is less than 0.5.

0 ~ / E* (40)V" = scaling p a r a m eter = d*/a YR oE* = kinetic parameter = E*/kT .QToo mean time between collisions of A and B moleculesADE* = activation energyd* = , diam. of sonic orifice() denotes stagnation conditionsThese results can be used as a desi gn criterion tode ve l op a sa m p l ing system uhi ch a v o i ds c o m p osi t i ondistortion by chemical reaction in the expansion.

3.2.3 Spec ies Co nd ens at io nSpecies condensation in supersonic molecular

59bea m s uas first observed by Bier et al in 1956.C ondensa t i on uould m a k e the interpretation of measure-me n ts very c o m p l i c a t e d , but fo r t una tel y , as K nu t h con-cludes in his revi eu, the probab ility of co ndensationsin FIBFIS sampl ing of high temp erat ure systems is verysmall.

The classical t heo r y of ho m o g eno us c onden-sation postulates that a critical size nucleus is spon-taneously forme d uhic h has the prope rti es of the bulkphase. Such theory cannot be applied to the rapid ex-

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pansion occurring in a free jet for it leads to crit-ical sizes that are of the same order of m a g n i t u d e asthe molecular diameters . Instead a kinetic theoryapproach ' has been used to predict condensationin the free jet, and the rate limiting step is the form-ation of dimers by termolecular collisions, not onlyfor m ono a t o m i c gases, but also for p o l y a t o m i c gases.O n c e the dim e r i s fo r m ed , tuo bo d y rea c t i ons ca n p r o d u c etrimers and larger clusters whic h lead to the formatio ncf a condensate.

Knu th shows that the ratio of the flou timed*/a to the m e a n time,'f" , b e tw e e n consecutive threebody collisions is the r el ev a nt dimensionless scalingp a r a m eter in di mer forma tion. The smaller the flou tim e,relativ e to the me an time b e tw e e n t er m o l ec u l a r collis-ions, the smaller is the dimer production. This hy-pothesis is supported by experiments conduct ed by several

{ I /-oa u tho rs ' . They found that the excess dimer molefraction (relative to the equilibrium mole fractionin the source) is a p p r o x i m a t e l y a linear function ofp d*. Note that the scalina parameter d*/y a is re-~o o o

r\lated to P by equation (56) of R e f e r e n c e 40. F ur ther-mor e, these exper iment s show that ford*/ a0 0dimer formation is insignificant (see Table I of Ref.40 for example), and that this rate decreases as TQ

.63, 64, 65increases

64

-


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3.2.4 Pressu re DiffusionFo r theoretical tr eat ment of separation ef-

fects in free jets and shocks, the reader is referredF i R fi 7to the continuum analysis by Sherman ', Mikomi and

Takashima , and the kinetic theory approach to a shock-uave structure in binary mixtures by Oberai . Our aimhere is to present the reader with the main resultsof the above experiments and theory.

In his tr eat men t of the free-jet of a bina rygas mixture, Sherma n combines the con tinu um flouconservation equations (Navier-Stokes), uith the bi-nary diffusion equatio n (41) ased on the Cha pma n-Ens ko gtheory of diffusion,fvA f DAB Tf(l-f) fmA"mB V Inp

1 m -7 (41)

Uhere the subscript A refers to the heav ier species;f is the mole fraction of the heavier species, m isthe mean molecular mass g iven by

m = fm ft + (l-f)mQD Q R and(A-are the binary diffusion coefficient andHcjthermal diffusivity, respectively; V. is the diffusionvelocity of the heavier species. Examination of Equa-tion (41)leads to the following conclusions: (1)In the free-jet exp ans io n and in a shock transition,

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the temperature and pressure gradients are in the samedirection. Thermal diffusion opposes barodiffusionunder these circumstances. Houever, an order-of-mag-nitude analysis of Equation (41), as applied to the free-jet or the shock uav e, shou that barodiffusion is thedominant separation mechanism. (2) In the free-jetexpansion, the tempera ture and pressure gradients existin the radial direction outuard from the centerline.The higher pressures and temper atu res occur on theaxis and decrease radially outuard as the Mach n u m b e rincreases. Thus, b a r o d i f f u s i o n in the free-jet uillcause a n enrichment of the heavy molecules along thejet centerline (in barodiffusion the heavy moleculesdiffuse to higher-pressure regions).

Sherma n obtained an expression for f, themole fraction of the heavy species, along the center-line of the jet, by exp an di ng all varia bles in ter msof inverse p o uers of the R eyno l ds number based on stag-nation conditions and orifice dia meter, d*, and solv-ing for the first-order pe rt ur ba ti on term in the molefraction, f, by inte gra ting the equat ion s (the zerothorder approx imat ion leads to isentropic flous, andhomogenous mixtures). This expression can be foundin Ref. 66. The theoretical results of Sherman have

70been validated by the exper iment al results of R o t h e ,

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71 72Sebacker , and Campargue . These results show thatthe heavier species are enriched along the jet center-line as predicted from the diffusion equation and thatmost of the separation occurs over a distance of threethroat diameters from the sonic orifice. Furtherm ore,negligible separation in the free jet was found for

40Knuth considers Sherman's results and shousthat for

CSc m - 1 = o(i) (42)

mass separation due to barodiffusion near the source2orifice is negligible for Re10 . This criterion

is conservative for x/d* >3 due to ordinary diffusion(Sherman neglected or dinary diffusion in his theoreti-cal trea tment. Or dina ry diffusion , houever, may haveto be considered for x/d* ^> 3). In Equation (42),C is a constant, and sub scr ipt o refers to stagnat ionconditions.

Extens ive experi mental studies of the shockstructure in binary gas mix tu res (see Ref. 40 for anextensive literature revi ew) shou the validity of the

Thefollowing features should be noted: (1) Ouing to thefact that barodi ffusion accelerates the heavier mole-cules through the shock, and the light species in the

theoretical treatment of Sherman and Oberai

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3,2.5 Rel axat ion Ph eno men aConsiderations of relaxation effects in the

free-jet e

Molecular Beam Mass Spectrometric Sampling of Methane Flame

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