REPORT 1286

PROPAGATION

SUMMARY

OF A FREE FLAME IN A TURBULENT GAS STREAM’By WILLIAMR. MICKELSDNand NORMANE. ERNSTEIN

E@ectivejame speeds of free twrbdd$anw were meamredby photographic, ionization-gap, and photozwd.tiplia-twbemethoo?t?,and were fownd to have a 8tat&tti dtiti”butionattn”bti to the nature of the turlndtmtjieiii. The efectiveturbtdent$ame peeds for the free j?anie were less than threepreviously meawred for j?am.a w!abi%zd on ?wzz+?eburners,Bunsen burners, and blu$ bodia. The 8ta&tieal qnad ofthe efective turbulent&me epeeok Wa markedly w“der in thelean and rich fuel-air-ratio rqn”onx,which mighi be ~“bw!edto the grealer8&&y of lumhurjhnw speed b~me temper-ature in those region-s. Values caku&2d from the turbwbnifree-jlanw+peed analysis propowd by Tinker apparently formupper limits for the gtutish”calepread of free-j?ame-speed du.ta.Hot-m”re anemometermeawxemem!sof the Lmgitu&nd velociiy@uctuution intensity and longitu.o%n.dcorrela.tim coej%ientwere madeand wtre employed in the compan%onof data and inhe theoreticalcahula-?wnof turbtijihw epeed.

INTRODUCHON

The high volumetric heat-releaae rate required in presentand future je~engine combustors has placed an ever-growingemphasis on turbulent combustion research. The theory ofturbulent flame propagation k as yet in a formative stage,partly because of the lack of reliable experinmntal methodsfor detmmining the effect of turbulence on the rate of flamepropagation. The purpose of this investigation was to ex-plore a new experimental method believed to &’pproximatemoro nearly a theoretical, or ideal, flame model than previousmethods.

The major portion of experimental data on turbulent flamespeeds has been taken in open flames stabilized on Bunsenlmrmm (refs. 1 to 3) or on iMache type burners (refs. 4 and 6).A substantial amount of experimental data has also beeDobtained from flames confined in a duct and stabilized onbluff bodies (refs. 6 to 8). Another experimental methodconsists in measuring the speed of a flame advancin~ into aturbulent fuel-air mixture flowing through a tube (ref. 9).In general, the definition of turbulent flame speed used inthem methods is that given in reference 8:

-J%S,=b ~ (1)

(All symbols are defined in appendix A.) Equation (1) hasbeen used for 100al measurements by the tl.ame-front anglemethod and for over-all flame-speed measurements by the

flame-area method. These two methods are shown in thefollowing sketches:

Flame-frwt angle metlwi Fb3me- area methocl

Turbulent-flame-speed values obtained by these methodsmay be significantly ailected by conditions esternal to theflame ikont itself, such as

(1) Large fluctuations in instantaneous flame-front posi-tion that introduce uncertainty in the determination ofmean position in long-time-exposure photographs ofstabilized flames (ref. 10)

(2) Existence of piloting zones at the rims of Bunsenburnem, immediately downstream of blufl bodies, or inthe boundary layer of flame tubes, which may tiect theburning rate of the flames near such zones (refs. 7 and10)

(3) Large velocity differences between unburned andburned gas flows, which may introduce considerableturbulence in stabilized flames (refs. 2, 6, 7, and 11)

(4) Curvature of unburned-gas stream lines at the flamefront, which may introduce substantial error in flamespeeds measured in stabilized flames by the anglemethod (refs. 7 and 12)

(5) Variations in local flame speeds along the flame enve-lope, which may imtroduce substantial error in averageflame speeds measured by the flame-area method

This investigation was conducted to determine the effectof turbulence on the growth of a free flame. It was thoughtthat the free flame would not be subject to the complicatingconditions present in stabilized flames such as those listed.In addition, the free-flame growth could take place entirelyin a homogeneous, isotropic, turbulent field awa~ fromboundaxy layers and bluil-body -wakes, thus providing nmore nearly fundamental flame model.

The method used in the presant invwtigation is an e..ten-sion of the “soap-bubble” technique (ref. 13) and consistsof the observation of the growth of a free-flame globule asit is carried downstream in a flowing, turbulent, homo-geneous mixture of gaseous fuel and air. The flame globulewas initiated by a single spaxk, and its growth was recordedby three separate methods, high-speed motion-picturephotography, ionization-gap probes, and photomultiplier-tube signals.

ISupcmccksNACIATNW& “Propagationof a Pm Flamein a TurbulentGasStmmL” by NWlaLUR. MiokelsmandNormanE. Ernst@ lW&

773

——. . . —. —— . ....———

774 REPORT 128&NATIONAL ADVISORY COMMIT1’EE FOR AERONAUTICS

The flame-globule growth was characterized by an effec-tive turbulent flame speed &, which is defied by a mass-balance equation similar to that derived in referencp 13:

(2)

Equation (2) can be clariiied by the following sketch:

Lx - -“--;::;rf:f~::”me

‘0-~”---- to mm rcdim r

u— ------..-— - -_L ----- -.~~----&= dr

dt ~ -..-.

The rate of change of the globule radius was measured overperiods of time less than the characteristic time of the tur-bulence. This means that, on the average, the flame fronttraveled through less than one turbulent eddy during thetime of observation. In the past, average turbulent flamespeeds have generally been measured horn photographshaving long exposure times compared with the characteristictime of the turbulence.

The esperimrmt.al work waa carried out in two phases.Th~ first phase was initiated and carried out at the NACALewis laboratory and is reported in reference 14. (Becauseof its limited circulation, comiderable portions of the workreported in ref. 14 are included in this report.) Turbukmt-flame-speed measurements were obtained horn high-speedmoti?n-picture records of the growth of the free-flame glob-ufe as it was swept downstream in an enclosed tunnel.The turbulent field was introduced by means of a wiregrid placed at the tunnel inlet some distance upstream ofthe spark-electrode position. The turbulent field wascharacterized by hot-wire-anemometer measurements.

The effective turbulent flame speeds determined by thephotographic method varied for runs made under identicdfuel-air and mean stream conditions. The variation wasconcluded. to be due to the statistical nature of the turbu-lent field. Statistical analysis of groups of 30 or more runsmade at identicd fuel-air and mean stream conditionsshowed that the data for each group approximated a normalprobability distribution. When plotted on the basis ofcumulative probability of occurrence, the effective turbulent-flame+peed data showed a consistent increase with increasingturbulence intensity.

The second phase of the investigation was carried out ina free jet with a technique whereby the cumulative proba-bility of occurrence of turbulent flame speed could be deter-mined from flame groups consisting of thousands of separateflame globules. This technique utilized ionization-gapprobes and counters, which indicated directly the percent-age of flames reaching or exceeding any given diameter ata series of stations downstream of the spark electrodes.By this method, flame speeds were measured over a rangeof fuel-air weight ratios ~m 0.053 to 0.090 and a range ofmean stream velocities from 35 to 142 feet per second ata stream static pr’txwre. of 1 atmosphere and a stream statictemperature of 85° F. The stream turbulence was varied

by the use of three interchangeable grids, and tho param-. eters of the turbulence were measured with constw t-temperature hot-tie-anemometer instrumentation.

The investigation was carried out at the Lewis laborat oqas a part of the combustion research program.

APPARATUS

AIR-DUCTING, WIND-TUNNEL AND AIIU%OWINSTRUMENTATION

The airducting, wind-tunnel, and airflow instrument ~-tion used in the first phase of the investigation and reportedin reference 14 k shown in figure 1(a). Alterations made tothe apparatus for the second phase of the investigation nroshown in figure 1(b). The alterations essentially convert cclthe system from an enclosed tunnel to a free jot.

IllPlenumchamber

8“ Mom, 12’ long 4 Ag

~.Iabte-areo -’m

Ilt I ~} Prewre taps to mmmmeters

. $ 8“Dlam, 105’ long

I \ 4“Dii ; D3131D-1 I

Preswre- ~.--. —,b.

IIII

4Labo~tary al

air

ExhtCoror -.-’

4“ m-.

AirSJH&f

u

-tShhltgf‘

i

[-----%-rk e!ect&d&

.- UJlmlw GIIUI1lW=

I-Fq‘-Thermocouple rake

~ A$ir$~l‘ro

.603 valve

8“ Dlam, [55’ kmg ~<

(a)

(a) Enclosed-twmel instnhtion.

~} Pressure laps to manometers

Plenumchamber 8“ Diam., 12’ Iang ~ 8“ Diamc,[05’ longa

4~ V ‘W $jo~c:a -*-

, f4“ Dhm “.! -“J,”, ,

r

rxmtroI ~..:

Y

W-tiit iwccl “J&U’- ---~r~ jet 4“ Mom,

G turmelk ebctrcdes

; uierce-germmtlrq grid ~=-

La6utom 1-1 Fau “ K-AlCcqq I-’LJ”-l

--L.Rww Prassure-iF).$ [1 I 1 -Vnlve

-C-- Culming chamiw 1=-1lywrnbsrtian wtion

E-

.+ane gas rnject!m qid .;

G “L Ttwrwwple rake~ “(o

n ${.-/r#/

‘a vatve

8“ Dbm, 15.5’ long ~{

‘-~usim blowout diaptucgm

(b)

(b) Free-jet installation.

FIGUREl.—Air-ductiig, wind-tunnel, and mean airflowinstmmentation.

PROPAGATION OF A FRDE FLAME IN A TURBULENT GAS STREAM 775

Air supplied from the laboratory air facility was meteredwith n standard variable-area oriiice and controlled withthe butterfly and gate valves shown in figure 1. Staticpressures and temperatures were measured with conventionalmanometers and thermocouples.

The ducting approach to the tunnel was designed fromprinciples used in conventional low-turbulence wind tun-nels. The transition section was followed by a honeycomband turbulence-damping screen in the calming section toreduce the turbulence present in the air-supply flow. Theentrance to the enclosed tunnel (or free jet) was a nozzlewith a contraction ratio of 20, and provisions were madeat the tunnel throat for the insertion of turbtience-producinggrids, Three grids were used for the investigation, all hav-ing a mesh to wire-diameter ratio, of 6. The grid wirediametem were 0.0313, 0.063, and 0.125 inch.

The enclosed-tunnel installation was equipped with anadjustable plug and nozzle by which critical flow could bemaintained at the tunnel exit, so that the tunnel flow fieldcould be isolated horn pressure disturbances in the labora-tory exhaust facility. The free-jet installation was equippedwith an exhaust hood into which diluting room air could bedrawn in addition to the free-jet flow.

FUZL SYSTRM

The propane fuel used throughout the investigation hadthe following composition by liquid volume:

Propane, prmnt ---------------------------------------- 97.76

EHhano, percent ----------------------------------------- 1.72Isobutarm, percent --------------------------------------- O.51

The propane fuel system is shown in figure 2 and was iden-tical for both the enclosed-tunnel and free-jet installations.Propane was supplied from a laboratory facility and meteredwith strmdard rotameters. Pressure, temperature, and flowcontrols are shown in figure 2. The propane was injectedinto the airstream through a grid having 60 equally spaced,0.040-inch-diameter holes. The injection grid was installedat CLstation upstream of the cahning chamber as shown infigure 1.

IGNITIONSYSTEM

The flame-globule ignition system consisted of a pair ofspark electrodes protruding into the tunnel stream fromopposing walls and an electrical energy source. The sparkelectrodes used in the enclosed tunnel were carefully stream-lined to a fineness ratio of 5 with a thicknx tapering from0,019 inch at the tunnel center to 0.038 inch at the tunnelwall. The spark electrodes used in the free-jet installationwore of circular cross section with a diameter tapering from0.015 inch at the stub tunnel center to 0.075 inch at the stubtunnel wall. The spark-gap spacing was 0.015 and 0.030inch for the enclosed-tunnel rmd free-jet installations, re-spectively. The spark-electrode positions for the twoinstallations are shown in figure 1.

The spark-energy source was of the capacitive type andproduced single sparks synchronized with the camera opera-tion in the enclosed-tunnel installation or successive sparksat tlm rate of 3 per second in the free-jet installation. Thespark energy could be varied by changing capacitors.

Propane injection grid-? :-1.25-in pipe manifold‘,

‘—”-R ;I ,--Ten Q25-im cwtside diam. Iuks,

+?@

. 4 having S&0.040-in. injector

T-G--<II q Ides equally spaced slang tube

l<J

II J

“+<:t&d\ ,

G3rnem sydwwatsystem Scier-mklvalve ‘$l&M idet ~

Safety-system l=to~ylvt-~1,. ‘ ~- R@omefers

satenoti valve-V

{

“-Service_air

h,Pressurewe I

““m-Safety-systemsokwmld . valve d

tFrom bbomtorypropane facility

FIGURE2.—Fuel system,

FLOTV-FI~ INSTRUMRNTATTON

In general, the flow-field instrumentation was adaptableto point measurements in either the enclosed-tunnel or free-jet streams. lMean-stream-velocity measurements weremade with a conventional pitot-static probe and microma-nometer. Fuel-air ratio was measured directly by a ti~tureanalyzer. Stream samples were drawn through a sharp-edgedO.125-inch-inside-diameter sampling probe to the analyzer,which indicated fuel-air ratio directly by the thermal-conductivity-bridge method.

Turbulence measurements were made with constrmt-temperature hot-wire-anemometer equipment, which isdescribed in append@ B. Sound pressure levels were meas-ured with a conventional microphone and a sound-pressure-level meter, also described in appendix B.

FRRE-FLAMR-GROWTHMRA5SJREMRNT

Photographic instrurnentation,-The growth of the free-flame globule was recorded photographically in the enclosed-tunnel installation with the optical system shown in figure 3.The photographic records were taken with a 16-milhmeter.Fast= camera operated at approximately 3600 frames persecond and located at the end point of the parallel-beamschlieren system. The enclosed-tunnel windows werestriation-free plate glass. The light source was a mercury-vapor BH-6 lamp operated with a high-voltage direct-current power supply.

776

.

—..— .-. —

REPORT 1286—NATIONAL ADVISORY COMMI’17EE FOR AERONAUTICS

ad-c Rwer

%!%’L:;

Va”-Squore wurte=.12” Spherical railmx ‘.

:.’

4“ by 4° tunrm~~

~---llone mirror .: -- ~.. ,

~-t(nife edge ‘-- 12” Spherical rnirrorJ’. .----~~..

‘- Fastex motion--..

‘-~~ “ @ 4“ ~ [4” Pl@e @S Mnrjowspicture camero

FIGURE3.—Photographio instrumentation for measurement of free-flame growth in enclosed-tunnel installation.

Ionization-gap instrumentation.-l%e growth of the free-flame globule was measured in the free-jet installation withan ionization-gap probe, a photomultiplier flame sensingunit, and two flame counters. The physical orientation ofthese instrumentation components is shown in figures 4(a)and (b). The photomultiplier unit and its accompanyingflame counter recorded the total number of flames thatoccurred during any particular run. The ionization-gapprobe and its accompanying flame counter recorded thenumber of flames that grew to a radius of r or greater at theaxial station z during any particular run.

The photomultiplier unit consisted of a 931A photo-multiplier vacuum tube with a fixed-plate voltage supply.The ionization-gap probe is shown in detail in figures 4(c)and (d). The brass fairing along the probe tip prevented

. _J.. _. . —

\

Exhaust tmod

nhdrmutldeW21J21

... -..

1’J._—__.u3ii-.i :>

Dtltition-olr duct-... .— —. .-—.> —,., 3,

. .~

I.-,

Spork electrode-’ \T

.7

/-.

h G3731!~__- .– (01 --- . . . -—

(a) Over-all view of installation. d

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1 I I I

(b)

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--b?’/4,

Flomecwnter

mm!l.

(c)

C-37237

Srass

(d)

(o) Ionization-gap probe.

(d) Construction details of ionization-gap probo.

FmunE 4.-Ionization-gap inetrurnentsition-for measurement of free-flame .gowth in free-jet insta~ation.

PROPAGATION OF A FREE FJJ.0U3 IN A TURRULENT &AS BTRDAM 777

flame seating on the probe both by flame quenching and byelimination of the recirculation zone. Because of the con-voluted form of each flame globule, the voltage signal fromthe ionization gap usually contained multiple peaks, whichcaused spurious counts in the flame counter. In order to

smooth these peaks, resistors, capacitola, and diodes wereincluded in the 360-volt direct-current battery circuit forthe ionization gap.

In order to prevent spurious counts arising from smallfluctuations in the voltage signal horn both the photomulti-plier unit and the ionization-gap probe, a long time constantwas included in the flame-counter design. Th@e flamecounters employed thyratron-controlled relays and solenoidswhich actuated a mechanical counter.

Photomultiplier instrumentation,-sinmhkmeous measurements of the spark light intensity and ensuing fiee-flame-globulo growth were made in the free-jet installation withthe photomultiplier instrumentation shown in figure 5. Thephotornultiplier unit consisted of a 931A photomultipliertube with an adj uetable-plate voltage supply. Light emittedfrom the spark and ensuing flame passed through the narrowslit to the photomultiplier unit. The voltage signal hornthe photomultiplier unit was recorded on 35-millimeter iilmfrom an oscilloscope trace. The photomultiplier instrumen-tation and the assumption required to relate output voltageto flame speed are discussed in appendix C.

PROCEDURE

The test schedule was as follows:

Grid,h. Stremn DIstanm

r ’72 ‘g” ‘%T

Frwjet

O.lm 0.W6 35to m6 &07 l&2t01e.2.126 .d!m 70 .060to. cw m2tolo.2.0%3 .313 70 .06sto. cw m2tol&2.0313 .1E8 Xl .0s2to. w lE.2tol&2

EncIc@dtunnel

am 0.625 36to140 I 0.045(appms.) I 63to 1’5.3

ENCLOSED-TUNNEL INSTALLATION

Room air was supplied to the enclosed tunnel and ex-hausted at critical fl& through an exit choke by means oftho altitude exhaust facihty. Tunnel static pressures andtemperatures were measured by manometers and thermo-couple rakea as shown in figure 1(a). l?uel was injected intothe nimtream and metered through a standard rotameter,after which dilution air was admitted downstremn of thechoke. The tunnel stream velocity was then measured witha Pitot-static probe and micromanometer.

The sequential schlieren photographs of the propagationof the free-flame globule in the fuel-air mixture were obtainedby actuating a single switch which synchronized the followingoperations: fuel shutoff (producing a serni-infinite fuel slug),

sparkelectmdes~

,,

ml.,,, kd~+’’n+d1-~ ,+’notanultiplier unit _J* 5-9”

q Ir .9

Spork electmdes-- 5/

14.4”

Stub tunnel-“

& ‘ ; 1

Iw’

@

Grid----

Recording Nozzle–J, oscikcope:

FIGURE6.—PhotamuMiplier instrumentation for simultaneous meas-urement of free-flame growth and spark light intensity.

camera start, ignition by a single spark, and camera stopafter an appropriate interval.

FEEE!-JIH INSTALLATION

An exhaust airflow rate of approtiately 500 pounds perminute was initiated, and dilution air was admitted to thehood. Laboratory pressurized air and propane were ad-mitted into the stub tunnel, after which the fuel-air ratiowas adjusted to the desired value by means of a probe andthe NACA mixture analyzer; the stream velocity waadeterrnked from Pitot-tube measurements.

The ionization-gap probe was positioned at a station zdownstream of the spark electrodes and at a radial distance rfrom the tunnel centerline. A series of flame globules wasinitiated by the ignition system, iiring at the rate of 3sparks per second. The number of flame globules iVPintercepting the ionization-gap probe and the total number offlame globules ignited iV, were read horn instrumentationshown in figure 4(b).

FLOW-FIELD MEASUREMENTS

In order to check the uniformity of the flow field, velocityprofiles were measured in both the enclosed-tunnel andfree-jet installations. The mean stream velocity for bothinstallations was essentially constant over the core ofinterest, as shown by figure 6. Similar measurements weremade to check the uniformity of the propane-air ratio inboth installations. The propane-air ratio was found to becomtant over the major portion of the enclosed-tunnel flowfield, and typical profiles measured in the free-jet installationare shown in figure 7.

In order to establish the characteristics of the turbulent.field, extensive measurements of the turbulence intensity

@, the spectrum function ~, and the correlation coefficientj were made in both the enclosed-tunnel and the free-jet

— .

.

778 REPORT 128&NATIONAII ADVISORY

0=~

“;&

~m15

0 .5 LO I-5 20 25 3.0 3.5 4.0Distarue from WOI1, y, in

FIGURE‘i’.-Typical fuel-air-ratio proflk in free-jet inetsdlation.16(

14(

12(

la

!4<=b-

“~ 8(

j

s6(

4(

2(

(Tunrd traverse, in

_.—_ _—

COMMITTEE FOR AERONAUTICS05-

\\I\

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r

\a > \ o 0.125

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\-G \s .03= \ao \ Ret 15~

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s .02 b \Observation of

‘\. M 15 (ml &r16* \

— flame grawth— ~..---

.--_, _-1

““’m 100 150 200 250 300Ratio of distance downstream of grid to gdd wire diameter, x/d

FIGURE8.—Longitudinal turbulence intensity rneaeurad in msolosod-tunnel inetdlation.

installations. The definitions of these quantities and theinstrumentation used to measure them are discussed inappendix B.

ENCLOSED-TUNNELTURBULENCEMEASUREMENTS

Longitudinal turbulence intensity measurements mado inthe enclosed-tunnel installation are shown in figure 8. Tlmdata shown in the figure agree well with the von K’irm6n

12

.8

.4

0

1.2

.8

.4

0Distance fmm wall, y, in.

(a) Enclosed-tunnel installation. Measured 10.75 inches dowmtmomof grid of 0.12iXnch-diameter tire by 0.626-hsoh mesh.

(b) Free-jet installation. Reference velocity equals velocity atV=0.5 ~ch ~d z= 1.0 inch downstream of spark eleotrodos,

FIGUEE6.—Typical mean-etream velocity profiles.

PROPAC4ATION OF A FREE FLAME

data quoted in reference 15 and show a substantial decreasein turbulence intensity from the electrode position (x/d= 50)to the end of the flame-growth observation field (x/d= 122).Longitudinal intensity profiles meaaured in the tunnelcenterpkme perpendicular to the observation plane wereewmtirdly flat over the core of interest. Turbulent energyspectra were mensured in the enclosed-tunnel installation wdescribed in appendix B. The scale of turbulence wasestimated by comparison of experimental data with a gridof spectrum density curves based on an exponential form ofthe longitudinal correlation coe.flicient f=exp (f/LJ). Atypical mensured spectrum is shown in iigure 9, and theestimated turbulence scales are listed in table I.

FREEJETTURBULENCEMEASUREMENTS

Conversion of the enclosed tunnel tQ a free jet resulted inan intense sound field originating in the dilution air andexhaust hood and piping. & described in reference 16,velocity fluctuations associated with sound waves contributeto tho hot-wire-anemometer measurements through therelation

G== (3)

with the assumption that no correlation exists between theturbulence and sound velocity fluctuations. In order todetermine the applicability of equation (3) in the free jet,longitudinal velocity fluctuation intensities were measuredboth with and without the intense sound field. These meas-urements are shown in figure 10 for each of the three turbu-Ionco grids used in the investigation. The velocity fluctua-tion intensity was definitely increased with the presence ofthe sound field for each of the three turbulence-generatinggrids,

The sound pressure level in the free jet was measured withthe instrumentation described in appendix B and was foundto be 136 decibels, which corresponds to a sound velocity

IO-286

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2

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8

6

4

I lw\ I 111111112

Ind,“

8

6

4i

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‘“ 10 2 4 68102 2 4 6 8103 2 4 68f04Frequency, n, cps

)?IQUI?E 9.—Typicnl longitudinal energy sprmtrurn of turbulence inonaloacd-tursrrel instnllntion. hlean stream velocity, 60 feet per second.

IN A TURBULENT GAS STREAM 779

fluctuation @of 0.96 foot per second. Values of the sound

velocity fluctuation ~ were also calculated from the data

of figure 10 by the use of equation (3). These values of ~

are compared in table ~ with the value of ~ corresponding

to the sound prmsur@level of 136 decibels; good agreementis shown in every case.

The kinetic-energy spectrum of the sound field alone isshown in figure 11; it has a generally continuous form withpeaks, or periodicities, at 57, 110, 140, 170, 230 to 285, 600to 870, 1050, 1500, 2400, 3000, 4000 to 5600, and 7000 to9006 cycles per second. Periodicities observed in the soundspectrum were generally found again in the longitudinalvelocity fluctuation energy spectxa measured in the free-jetinstallation, as shown by the typical spectrum in figure 12.

Longitudinal double-velocity correlation coefficients Jmeasured in the free-jet installation are shown in figure 13for each of the three turbulence-produtig grids. The irregu-lar form of the correlation-coefficient curw+ is attributed tothe periodic nature of a considerable portion of the velocityfluctuations. The correlation coefficient.s were measured bythe special methods described in appendix B and are definedby the relation

(4)

040 I I I

-it.Y

1

2.015 I I I I ) I 1 ) 1 1 I

3I II 1 Distonce fromI 1 turbulence -~roducing

I I, ,f grid, ~, in -

1I

1- -I

Care of interest - 1

.010 I ;I

I II 1 :: ~~is;; tI I

(a) 1 I o j ~;,1 ,

snundI 1 0. fieti

.0050 I 1I 2 3 4

Distance from stub–tunnel wall; y, in.

(a) Grid: 0.12S-inch-diametir wire, 0.625-inch mesh.FIGURE10.—Longitudinal velocity fluctuation intensity in free-jet

installation.

— ——.

780 REPORT 128~NATIONU ADVISORY

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A 15.2 field

Core of mtwe5t - J, p – v 16.2

1 b 142

I ,1, ,Witi-mt

I 1 - 0 15.2(b)

sound

I 0 16.2 field

.CQ50I

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Dlstcrn~ from stub2 funnei ~al[? YI ‘.

(b) Wld: 0.063-imch_eter wire, 0.313-iich mesh.

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x>025

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=I

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< ! II I

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-G 1= I 1) 1

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I I 1Withg I~.ol o 0 14.2 swnd

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3 v 16.2Core of interest -- 1 n 14.2

I ,1,,-Withaut

I II 0 15.2 sound

(c) I I 0 [6.2 field1

.0050 I ,I 2 3 4

Distance from stub tunnel wall, y, in

(c) Grid: 0.0313-inch&meter wire, 0.15&inch mesh.

FIGURE10.—Concludd. Longitudind velocity fluctuation intensityin free-jet installation.

cOm~E FOR AERONAUTICS

,“.-

Frequency, n, ‘7s

FIGUEII1I.—Longitudinal kinetic-energy spectrum of froo-jot soundiield.

Iu‘“ Frequensy, fl, cPs” -

Ji!Ir.xrrm 12.-Typieal longitudinal -ielocity fluctuation energY spcct rmmeasured in freejet installation. Grid: 0.lZ5-inch-diameter wirt

O.O%-inch mwh; distance ilowrcdmmm of spark electrodes, 4 inche~mean stream -relocity, 6S.5 feet per second; static pressnre, 20 Inchcof mercury absolute; static tempern~re, W 0 R.

“PROPAGATION OF A FRED FLM

whom the symbols me defined by the following vectordiagram:

Tlm longitudinal turbulence scale is usually defined by therehttion

JG=,“f& (5)

Becaum of the periodic nature of the combined turbulenceand sound fields, the longitudinal correlation coefficient didnot opproach zero within the range of measurement. There-fore, equation (6) could not be used to define the turbulencescale. Since the growth of the flame globule was observedover times comparable with t of 0.1 inch, only the firstportions of the correlation c+uves shown in figure 13 wereconsidered relevant to the experiment. As a part of thecalculations involved in the Scurlock-Grover analysis, valuesof the lateral scale of turbulence Lx were calculated asdescribed in appendix D. These calculated values of L. arelisted in the table in the RESULTS section.

DETERMINATION OF FLAME SPEED

PUNDAMZNTAI,CONSIDERATIONS

The rehttion between flame speed and free-fkme-globuleexpansion rate is derived in reference 13 for a constant-pressure laminar free flame propagating in a quiescent fuOl-nir fixture. This relation was obtained by equating themnss flow of the unburned gases entering a flame front ofinfinitesimal thickness to the mass flow of the burned gasesleaving the flame front. In a physical sense, equation (2)accounts for both the flame+ont motion due to flame propa-gation and the motion due to thermal expansion of the burnedgases, The following modiflmtion of this equation to accountfor a finite flame-front thickness 6 is presented in reference 14:

()p~d?’ r—a/2 %‘“=~ dt +$/2

—— (6)

l?or this investigation, the thickness of the flame front wasconsidered negligible compared with the radius r so thatequation (2) was used to analyze the data. The values of

P.) Comwted horn IL aml T., were obtained from measure-ments of tunnel approach-stremn flow. The values of

PF1 computed from RF and l’Ffor each fuel-air ratio, weretaken from references 17 and 18, respectively. The valueof PJ./Pavaried from 0.12 to 0.14 in the present investigation.

A number of assumptions are necessary to the definitionof cfl’ective turbulent flame speed as given by equation (2).The definition requires that—

(1) The free-flame globule grow uniformly in all radialdirections

(2) The combustion proceod in a constant-pressure field

IN A TURBULENT GAS STRJ3AM 781

Spatiol separation of vebdty vech-s, (, in...-

(a) Grid: 0.125-inch-diameter m-ire,0.62.5-inch m~h.

LO 1—. I I 1 I 1 f

\ Au

%- .80

zo\

;60❑

I I l\ I I IIA

I m .

I 22I 3.715.2IG9 M

SPtial seporotion of velodty vectq t, in.

(b) Grid: 0.063-inch-diameter wire, 0.313-inch mesh.

Lo\

,$.8@%ij “=5.4

?

: “2

z430~

.S-~

5-.4

.a .1 LoSpotiol sepmotkm of veloaty vectofs, ~, in

(c) Grid: 0.0313-inoh-diameter tie, 0.153-rnch mesh.FIC+UEE13.—kngitudinal double-velooity correlation mefficiepts

measured in free-jet installation. Mean stream velooity, 68.5 feetper second.

—.—-—— .- .— —...-. —– .

.

782 REPORT 128&NATTONAL ADVISORY COMMIT(’EE FOR AERONAUTICS

(3) The fhm globule be swept downstream at the streamvelocity

(4) No circumferential flow exist about the flame globule(5) Variations in spark energy not a17ect the globule

propagation rateThe vrdidity of the assumptions was established by special

tests described later in this section.

PHOTOGRAPHIC~OD

Photographic data obtained in the enclosed tunnel wereanalyzed by projecting the 16-millimeter motion-pictureb record of each flame-globule expansion onto a iilmviewer. A typical photographic record is shown in figure14(a). The outline of each globule wss traced in orderto permit planimetering its area and calculating a meanrtidius. The mean radius was plotted against time for eachflame globule of the sequence, as shown in figure 14(b).

(o)Finish

(rL)Typical photographic record. Film speed, approximately 3600frames per second.

Ftme-globule grwth time, millisec

(b) Flame-globule expansion history.

‘%%%)!/;;,percent

Assal I

+unnel

122” Itu

T tTo turbulence-generating grid

FIGURElfi—l?lame-globule-growth measurement with ionisation-gap

instrumentation. 8==A ‘“.Mu RITr

#

o

00

___o

—.

—

—--m.6 ..! LO 1,2 1,

Turbulent flame speed, ft&c

o

.—

—.

——-

——

1.

(c) Cumulative probability of turbulent flame speed. Moan streamvelooity, 60 feet per second; propane-air ratio, approximrd oly 0.046by weight; static pressure, 26 irmhes of mercury absolute; tompora-ture, S40° R.

FIGURE14.—Typical turbulent-flame-speed data from enclosed-tunnel installation.

PROPAGATION OF A FREE FLAME

Tlm slope of Q straight line faired through such a series ofexpmirnental points is dr/&. The effective turbulent flamespeed was then calculated by multiplying dr@ by the expan-sion factor PJ’/Pa,as shown in equation (2).

From sets of 30 or more flame speeds obtained in thismanner for identical fuel-air flow conditions, the cumulativeprobability of occurrence of flames having these flame speedswas calculated. In order to illustrate the statistical nature ofthese data, the turbulent flame speeds of a typical set of datahave been plotted against cumulative probability of occur-rcmco in figure 14(c). Each datum point represents theeffective flame speed of a single free flame. Cumulativeprobability of occurrence is defined as the percentage offlames having flame speeds greater than a given value.

IONIZATION-GAP METHOD

In order to obtain a set of turbulent flame speeds for aparticular condition of turbulent approach-stream intensityand fuel-air ratio in the free-jet installation, the ionization-gnp probe was positioned consecutively at two stationsz= 15.2 and 16.2 inches, as outlined diagrammatically infigure 15. For each chosen position r, at least 1000 flamesN, were ignited. The ionization-gap counter recorded thenumber of flames iVp intercepting the probe. The ratioNP/N, was the cumulative probability of a flame globulehaving a rndius at least as great as that indicated by theprobe setting r. The ratio NJN, was then plotted on prob-ability coordinates against r and a curve was faired through

(a) I?uel-air ratio, 0.056; mean stream velocity, 6S 3 feet per second.

~ A TURBUJ.JJNTGAS S!IXEAM

each of the two sets of data asdifference Ar was obtained from

783

shown in figure 16. Thethe curves for the

lative probabilities of 2, 20, 50, 80, and 98 percent.tion (2) was then employed to determine the flamecorresponding to the five probability percentages.

PHOTOMUL’ZTPLIEFSMIWHOD

The photomultiplier method was used to obtain

cumu-Equa-speeds

valuesproportional to the effective flame speed. The methodessentially consists of measuring the free-flame-globulegrowth rate along the axial diameter of the globule. Themethod is described in the APPARATUS section and inappendix C. The instrumentation is shown in figure 5.

.VZRIFICA~ONOF EXPREUMENTALMETHOD

The discussion of equation (2) in a preceding section in-cludes a number of assumptions necessary to the derivationof the equation. Since equation (2) ewentially expressesthe experimental method used in the investigation, theassumptions were verified by tests that are described inthe following paragraphs.

Uniformity of globule grovvth.-Photographic data of theflame-globule growth in the enclosed tunnel were analyzedto determine whether the globules had preferential growthdirections This analysis was made by measuring globule

99.999.8 1 I I I

Disfarce downstreamaf qnd,

Yx, m.

99

y ‘

o I 5.2

\ ❑

9816.2

()

95

- @-~< 90= )--0%~

~; ; c ,=-~&~60 \

“~<% &~=50 Ar

Zz +Io\

~~30 \ P

%--!3~z 20.==~%E: 10~ .~

5

2 \

ILa b

.5

;;(b)

~ , \

.3 .4 .5 .6 .7 .8 .9 1.0Distancs fram bnizatiin gap 10 tunnel axis, c in

(b) Fuel-air ratio, 0.070; mean stream velocity, 69.6 feet per second.

FIGURE16,—Typical cumulative probability of flame-globule size measured with ionization-gap instrumentation in free-jet installation. Grid:O.l%inchdiarneter V&e, 0.626-inoh mesh; static pressure. 29.3 inches of mercu& &mlute. static temperature, 545° R.

—-—— .. .—. ———. .. . ..—

784 REPORT 128&NATIONAL ADVISORY COMbfPITEE FOR AERONAUTICS

diametem (see fig. 17) at four angles of rotation from thetunnel axis. While each globule had different grcnvthrates along the four diameters, no consistent relation be-tween growth rate and direction was found. This obser-vation supports the use of a mean radius in the photographicmethod of flame-sped measurement, the use of a singleradird direction in the ionization-gap method, and the tieof a single diameter in the photomukiplier method of flame-gmwth observation.

Pressure pulsations .—In order to determine whether thefluctuations in flame-globule-growth rates, illustrated byfigure 14(b), were due to pressure fluctuations in the en-closed tunmil, data as shown in figure 17 were inspected forpossible phase- relations between the fluctuations in growthrate along the four diametral directions. Since no frequency-phase relation was found from these data, it was concludedthat pressure fluctuations were not responsible for thefluctuations in glob&-gmvrth rate. Additional measun+ments with a wall-mounted pressure pichwp indicated theabsence of significant pressure pulsations in the enclosedtunnel.

2

IAngulor displomrrent & c60meter

c--n tunnel oxis 1—“. f-lo I I 0 0 1

I 1- Y w- 1 I I I I I 1 10 01” I I I

0

2 Ia =135”

0’ )000 0

IQ cI

Oo 000 00 <)

0 00 <)

o 0( ) o 0

0 10 20 30 40 50 60Film frame number (Woportionol fo time)

FIGURE17.—Typical Ilameglobule-diameter histories measured inenchsed-tmmel installation.

Axial velocity of flame globule,-The effect of buoyancyof the hot flame globule on its axial velocity was determinedby measuring the distance from the spark electrodes to theglobule center on each frame of photographic sequencessuch as shown in figure 14(a). ‘l’he axial velocities calcu-lated from such measurements agreed closely in all caseswith the measured stream velocity, which indicated thatthe buoyancy effect vm.s negligible.

Unburned-gas motion.-b shown by equation (2), thorate of thermal e.spansion of the flame globule is from 7 to8 times as great as the effective turbulent flame speed.In order to determine whether the unburned-gas motionmused by this thermal expulsion waa purely radial (fromthe globule center), simultaneous oscillogmph records weremade in the free-jet installation with the ionization-gapprobe and a shielded hot-wire+memomehr probe as shownby the typical oscillograph and probe position diagmm infigure 18. The ionization-gap trace indicnted the flnme-globule passage, and the anemometer trace was propor-tional to the instantaneous strmm velocity. Inspection of60 such records indicated no axial change in mean strumvelocity and therefore no circumferential flow of unburnedgases about the sphere. The marked decrease in amplitudeof velocity fluctuations at the time of flame-globule passagois interpreted as being due to the radial translation of thefree-jet stream core by the thermal expansion of the flamoglobule.

Effeot of spark energy.-lh order to determine the cflcctoi spark energy on the flame-globule growth, two swies ofruns were mBde in the free-jet installation under ichmticolstream and fuel conditions but with spark sourco energiesdiffering by a factor of 2.5. As shown in figure 19, cumu-lative probabilities of flame-globule sizes were measured nta series of axial positions tvith the ionization-gap instrumm-tation for the two spark source capaoitom of 0.0004 and0.0010 micrcfarads. The data of figure 19 show an incrmmin initial flame-globule size, but no change’ in turbulmLflame speed between the axial positions z=15.2 and 16.2inches.

Effect of spark light intensity.-Additional information onthe relation betmeen the spark characteristics and the flamc-globnle growth v-as obtained with the pho tomult iplior in-

lonizotion-.

_;$k-L._3 “ ~+- “\y;

RSpork ,S probeelectrds

@ =Apprtimotdy LS ftk-m

w~w ~

Iotizath-gcp trmeTime —

FUXJEE18.—Typical oscillo~aph of ionization-gap and hot-wirosignals in free-jet stream at thne of flame-globule paeange. Grid:0.126-inch-distmeter tie, 0.62E-inch m=h; strenm velocity, 70 footper second; static premure, 29 inches of mercury absolute; tomporuture, SOOF.

PROPAGATION OF A FREE FLAMll IN A TURBULENT GAS STREAM 785

strumentation shown in figure 5. With this instrumentation,oscillogmphe were obtained in a free-jet installation show-ing spark light intensity and flame light intensity as afunction of time for 151 consecutive flame globules at con-stant mean stream and fuel conditions. Typical oscillo-gmphs obtained by this method me shown in figure 20.As shown in appendk’ C, the portion of the trace due tothe spark light intensity was proportional to spark current,and statistical analysis of the magnitudes of the peak sparklight intensity indicated that this parameter approximatedD normal probability distribution. The flame speed of theglobule was taken as proportional to the slope of the portionof the+ oscillograph trace due to flame light intensity, asdiscussed in appendix C.

The group of 151 consecutive runs is shown in figure 21,in which peak spark light intensity is plotted against flamespeed for each particular flame globule. The statistical cor-relation coefficient for this data was determined with Pear-son’s product moment formula (ref. 19) and was found tohave an absolute value of 10.17 I for a possible range of zeroto I 1.01. The low value of the statistical correlation coeffi-cient is interpreted to indicate that variations in sparkcurrent had no effect on turbulent flame speed.

Additional verification of statistical variation of turbulentflame propagation,-The cumulative probability of occur-rcnco of slopes measured from the series of 151 photo-

1I I I I I I

HiCumulative probability, percent

o 8050

: 2;A M

H---l -H-iOpen symtwts indicote spmk samecapocltonce of CMO04 #

Sa4id s mlmls i rhte spark sau3?copoc once o ~0010 #

18,2[f - ~~

/

/ ,///

,/’ //

e.- 1 f

4- / / 4

- 17.2/ !’/

.7

;.Gr

~~ 16,2

8/

/1 // ,/~

:#

/

% 15,2

E:=m

! “’2 Jg

13.20.2 .4 .6 ,8 I .0

Change in globule radius, b, in

l?muRD lfl .—Effect of spark source energy on fhme-globufe growth.

multiplier oscillographs is shown in figure 22. The statis-tical distribution of flame speeds measured by this methodis interpreted as additional proof of the randomness of thephenomena.

Validity of oommon-origin assumption.-The ionization-gap method, described earlier in this section, assumes that~ flame globules have a common origin point, as shown infigure 15. In order to determine the error introduced bythis assumption, “origin points” were measued from theseries of 151 photomultiplier traces by extrapolating theslope of the flame light intensity trace to the time axis, asshown in figure 20. The origin points showed a statisticaldeviation in position, and the theoretical error introducedinto flame speeds determined by the ionization-gap method

Florne-grcMh ccme

Yc?

r

Spark electmdes-

1‘Phalomultiptier

_%pnh

1 Stape pqmrticml t/’~~ to tie speed.

r“

u

g r b

o’ Proportional to time — ;

FIGURE20.-Typiaaf osoillographs of photomultiplier probe tracedepicting spark occurrence and growth of flame globule in free-jetstream.

3.4I

1 1

— Statistical mean of

Ipeak s rk hght

$mtensl y——– Statistical mean of

3.2 -I turbulent flame

speedI

I

3.0 I~~ o I‘2 G () ()~ I= 0 0 I~ 2.8 *

o 0, 0

0 &’.._=()-

-E C)0 3n 0

0

m 2.6 u & Ou I ux -o

* j 0 Oc % [& ‘o o o~

:c

ma>

Ql” b ‘=gQf &0

0

g \“l I \ 10 I’-1Q [+J :“ :8 0

D

1° 00 ~:

.-= I I I I I D 1 I0 km

f 2.200 I l-l

Io 1 0

0 Y o>2.0 I

,I 0

‘ “%4 1.6 1.8 2.0 22 2.4 2.6 2.8Propartionol ta turbulent flame speed

FIGURE21.—Correlation betvreen spark light intensity and turbulentflame speed for 151 consecutive flame globs.sk at identical meanstrenm and fuel conditions.

...-— — ...— ——

786 REPORT 128&I?ATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

was c.alculat ed to be &2.5 percent or less, within one standarddeviation of origin positions. The error in flame speed dueto shift in origin point is small compared with the deviationsin flame speed actually measured by the photographic(fig. 14(c)), the ionization-gap, and the photomultiplier-tubemethods (fig. 22).

PXIECMtONOF DATA

Ionization-gap measurements.-Each datum point plotted

as cumulative probability against flame radius, such as shownin figure 16, represents information from at least 1000 flames.As shown in reference 20, samples consisting of 1000 flames

99.9

99.8 ,

u = Standord d~iation calcu-lated on the tmsis of a mrnwl

I ~o

.5

.2

\.o 1.4 2.2 2.6.FToportion’$ to turbu[fflt flame speed

3.0

FIGUED 22.-Statiical variation of flame speed as determined from

photomultiplier osoillogranw

would have the following accuracy in the cumulative prob-ability value:

k-lOumuletive PoMbloProolad&Ili:y, error,

Brent——

M *5% *72 +29

The possible error-s hated correspond to 1.28 standard devia-tions of the error distribution and therefore should hold 80percent of the time. The general consistency of the daLathroughout the lower probability region such as shown infigure 16 seems to justify greater confidence in the lowcumulative probability range than that shown in the preced-ing table.

The reliability of the curves faired through the plottedexperimental data, such as presented in figure 16, may beestimated from the deviation of data points from tho fittmlcurves.

The greatest divergence was found in results for tho 0.126-inch-diameter wire. For the 98-percent probability level,the maximum data scatter from a faired curve was 20 per-cent; for the 50-percent level, 7.8 percent; and for the 2-percent level, 3 percent. The mtium scatter for tho0.063-inch-&meter wire was 5.3 percent at f)8-percenLprobability, and for the 0.0313-inch-diameter wire, it waa 13percent at the 98-percent level.

As discussed earlier in this section, the value of flametemperature used in the equation for turbulent flamo speedwas a calculated theoretical value. It may bo of interest tonote that flame temperature has a much greater effect on LI1OIaminar flame speed than on the calculation loading toeffective turbulent flame speed. As shown by refercmco21, a decrease of theoretical adiabatic flame temperature from4000° to 3900° R would result in a kuninar flame speeddecrease of 43 percent. In contrast, this change in flamotemperature would cause only a 2.5-percent decrease in thoturbulent flame speed calculated from equation (2). Itappears, then, for the purpose of this investigation, that theeffect of a small error in actual flame temperature is nog-I.igible in calculating the density ratio.

Other sources of inaccuracy may be found in tho instru-mentation and equipment. The positioning of the ionization-gap probe involved an error not exceeding 0.6 porcont,Wwmrement of the fuel-air ratio was accurato within 2percent. Flow measurements were made with a precisionof 3 percent.. For the measurements characterizing tlmturbulence parameters, an estimated value of + 5 percent iswggested for the probable limit of error.

Photomultiplier method .—A treatment of the sources oferror present in flame-speed measurement by the photo-multiplier method is presented in appendh C.

Photographic method .—In addition to the errors intro-duced by the equipment and instrumentation, sources oferror peculiar to the photographic method must be con-sidered. Such factors as adjustment of the projectod imagoto one-to-one cm-respondence, timing, optical resolution, and

PROPAGATION OF A FREE FLAME

scrde factor are rdl considered significant and have beenthoroughly treated in referenca 22, which sssigns a relativemaximum error of 10 percent to the photographic-reductionteclmique.

RESULTS

Effective turbulent flame speeds were messured in theenclosed-tunnel and free-jet installations over a range ofpropane-air and turbulence conditions as shown in thefollowing table:

1ana 0.025,126 .6’U.003 ,313,cC13 . L&l

FreeJ?t

I I I

Fro fMrlMbWdgbt I-MO 1Distanca

downstreamofdd, z, la.

wtoloa L18t02WI a 0846 0.07 la.2to Io.270 169 .fwa .056to. o’a l&2t011L270 L24 .0as7 .Mato. w l&2to l&2?0 L 17 .04s7 .063to. w la.2tola.2

Enclcmdtannel I

I 0.1!25 o.02a 35f0140 o.81t0361 aa!itoo.ls 0.046 I &3~wa I1111 I 1 @mrm., , II I I

The lateral turbulence scales Z= for the enclosed tunnelwere obtained from the values of Zf shown in table I byusing equation (BIc) of appendis B. The values of Lg for

the free jet were obtained by fitting an exponential curve

to the lateral correlation coefficient g as described in ap-

pencli~ D. Both methods for evaluation of Lt are baaedon the assumption of isotropy, which was not proven becauseof the luck of turbulence measurements in the lateraldirection.

The effective turbulent flame speeds, plotted in @u.re23, were measured in the free-jet installation at a fixedpropane-air ratio of 0.07 over a range of mean streamvelocities with the O.125-inch wire diameter by 0.625-inchmesh turbulence-generating grid. The data are plotted asa function of longitudinal velocity fluctuation intensity

@ with cumulative probability as a parameter. Sinceturbulence mewurements were made at only one streamvelocity, and since the sound pressure level was inde-

IN A TURBULENT GAS STREAM 787

TABLE I.-SUMMARY OF LONGITUDINAL TURBULENCESCALES

[Estfmatedfrom longftudfrmlenergy _ h endorad-trmnel fnstaflatfon. Meanstrrumveloelty, Ml ft/seq statfo p~ 26 tn. Hg am statfo tamp?rrdare, StOOR. Com~tlvevrdm+scafcmlatd throughthekctroplctarbrdcnearelationML, fromlateralsmleofturbwham data reported fn ref. 15.]

aa 0.16 ..-- . . . .9. a .21 --.-.---

123 .25 a 17lh 3 .2a .21

, I

pendent of stream velocity, the data of table II and thefollowing equation were employed to calculate the longi-tudinal velocity fluctuation intensity:

(7)

The turbulence intensity (@/@) was assumed constantthroughout the range of stream velocity U (see ref. 15),and u: corresponded to the measured sound pressure level of136 decibds.

2.4

#22 – -

/ T rCwnuloti+e probability,. / -

perc# c/ 0

L- r . 0 k VA

3 I I I I I I 1 I I I I I I I

1 d— 1 h I I 1 I h>+- —-3 I ,

@ & 1 1 I I I I 1111151 Illl.%

12 1.6I&itudinol vei~ity fluctuation intensity, -@ ft%c

24

FIGURE23.-Turbulent flame speed aa a function of longitudinal ve-locit y fluctuation intensity With cumulative probabilityy of occur-rence aa a parameter. Propane-air weight ratio, O.O7O;stream statiotemperature, 546° R; static pressure, 29.3 inohes of mercury abso-lute; grid: O.125-inch+liameter wire, 0.625-inch mesh; fre&jetinstallation.

TABLE 11.—COMPARISON OF VELOCITY FLUCTUATIONS IN TURBULENT STREAMWITH AND WITHOUT INTENSE SOUND FIELD

[Velocitytluotuotfonsmeasured along ductaxi% bkmred vrdnoofsoand~rcmurelevd,133db;streammkity, 6S.5ft@.]

arfd,tn. Strenmvclo:olflnchmtfoq Cahfated ~ddm of soundDirianti

Ma ~y:ea cd

3 Y“ : i 4: : :

~d,”~d ‘::t~”d +z>pr %%’:$ ~ ;%b

—

788 REPORT 128 f3--NATIONAL ADVISORY

1.4

I .2

j

= 1.0

&

;- B

~ SL

E .6E=g .41-

2

‘0 .4 .8 L2 1.6 2.0_Z4 2.8 3.2 3.6

Longitudinal rntensily, @, f Vsec

Firms.n 2—L-Turbulent flame speed ae a function of turbulence in-tensity. Propane-air vre&ht ratio, approximately 0.045; streamtempcra~ &40° R; static preseure, 26 inches of mercury absolute;enclosed-tunnel installation; grid: 0.125-iiohdarneter wire 0.626-inoh mesh.

Effective turbulent flame speeds measured in the enclosed-tunnel installation at a fked propane-air ratio of approxi-mately 0.045 are plotted in figure 24 as a function of the

longitudinal velocity fluctuation intensity @ with cumu-lative probabili~ as a parameter. The data show a con-sistent increase of eilective turbulent flame speed withvelocity fluctuation intensity. These data were obtaineddownstream of the 0.125-inchdiameter-wire by 0.625-inch-mesh grid over a range of stream velocities from 30 to 140feet per second. As shown by the data of figure 8, thedecay of the turbulence intensity was quite severe over therange of interest (z/G?=50 to 122). A turbulence int~sity

of (@/U) =0.027 was taken as a representative value and

assumed constant to obtain values of @ over the stream-velocity mnge.

The effects of propane-air ratio and turbulence scale onthe propagation mte of the free flame were investigated inthe free-jet installation by measuring the turbulent flamespeed downstream of the three turbuk.nc~enerating gridsover a range of propane-air ratio from 0.053 to 0.090. (Thevariations in turbulence scale are listed in the table at thebcginnhg of this section.) These data are shown in figure25 along with a dashed line representing laminar flan&peeddata reported in reference 21. TurbuIent flame speedsfrom the enclosed tunnel are included in figure Zs(a) andwere evaluated by interpolating the data of figure 24 at aveloci~ fluctuation intensity equal to that of the free-jetdata in figure 25(a).

(a) Grfd: 0.125-iiohdarneter wire, 0.625-iich mesh.(b) Grid: 0.063-inoh4iarneter wirq O.W!&ch mesh.(c) Wld: 0.03 K3-iiohdiarneter wbq 0.166-inch meeh.

FIGURE Z%.-Turbulent flame epeed aa funotion of fuel-air ratio with

cumulative probability of occurrence as parameter. MeaII streamvelocity, 70 feet per second; stream static preeeure, 1 atmosphere;

statio temperature 85° F. {

CO~D FOR AERONATJTIC8

1 I 1 I 1 1 1 I k 1 1 I /

I I I I /1 I I I I I I I I

2.2

w

1.8

~ 1.6>

J 1.4

-%-

~- I.4

%g 1.2=z+? 1.0ez

.8

.6c-50 m5060c65mu ..075 D80“ .085

Fuel- air weioht roho1.8

!I, !ll

1.6

/6 0

.6 A $3/ ‘ L

98.4 k) ‘ ; s4(re~al.050 D55 ,060 .065 .070 .075 .080 .085

Fuel-air weight mtb

PROPAGATION OF A FREE FLAME IN A TlJIt13ULDNT GAS STREAM 789

DISCUSSIONMEASUREMENTSOF PRESENTINVllSllGATfON

A discussion of the effect of turbulence on flame propaga-tion is generally conceded to rest on the principles of turbu-hmt motion set forth by Taylor in reference 23. Theseprinciples are summarized in the equation relating the meandisplacement X of a fluid particle from its original positionto two pmametera of the turbulent field:

(8)

where D is the turbulent #ifFusion coefficient in the z-direction, Xis the particle displacement in the x-direction, and@ is the Lagrangian double-velocity correlation coefficientdefined by the relation -

It is of particular importance to note that the turbulenceparametem in equation (8) are both mean values, and thatinstantaneous, local particle displacements depend on thestatistical deviations about those mean values. It is sug-gested that the fluid particle displacements have a statisticaldistribution about the mean much the same as the statisticalvariation of velocity fluctuations in the turbulence. Suoh”variations in particle displacements would be particularlynoticeable when observed over times less than the char-acteristic timo of the turbulence, as is the case in the presentinvestigation.

A statistical variation in the particle displacement Xwould probably cause variations in the speed of flames whereflame wrinkling was controlling; a statistical distribution oftlm turbulent diffusion coefficient D would also probablycause variations in the flame speed where the diffusion processaffects turbulent flame propagation. As a consequence of

, I t ,Cumu@iye EquM~oncePyeklbll;ty,

9’ Grid

1--+gjy 1.16 0J25+-dhn.

OX&% %Yesh—–– Ref: 4 1

E ..tizizJ--l I I l_- , 1

n 1(0)I.Uo .4 .8 1.2 1.6 2.0 2.4

Longitudlnol veJo@y fluctwth intentity,—

(a) Free-jet data. Propane-air ratio, 0.070.

this statistical distribution of turbulence velocity and cor-relation coefficients, particular free flames might encounterconditions especially favorable and therefore have highpropagation rates, while others might be subjected to condi-tions that would reduce their rate of growth. This pictureof statistical variation is consistent with the data of thepresent investigation shown in figures 23 to 25 and also agreeswith observations of stabiked flames that show a widebrush of flame tints.

The effect of flame temperature on laminar flame speed hasbeen reported in references 21 and 24, wherein it is shownthat small changes in flame temperature result in largechanges in laminar flame speed. In particular, reference 24shows that this dependence of laminar flame speed on flametemperature is of greater magnitude in the lean and richregions. The lower portions of the flame-speed probabilityband in figure 25 generally show decreases in the ratio of theturbulent to the laminar flame speed ST/5’L in the lean andrich fuel-air regions. This decrease is consistent with theeffect of flame temperature if the lower portion of the proba-bility band is considered to represent flames that have en-countered turbulent conditions sufficiently violent to de-crease the flame temperature by dif7usive action.

Comparison of figures 25(a), (b), and (c) shows thatgreater portions of the flame-speed band fall below thelaminar flame speed as the grid size becomes smaller. As

Cumukqtiye EquFk#ceFKMxlty,

‘f’ Grid

Ht0❑ 25 CU09 0J25+n-diemA 50 vnre byA CKZ5in.-hb %

M

-1a I , , I

w h I I ,

2[>

! l(b)o .4 .8 L2 1.6 2.0 2.4 2B 32 3.6

I 1/! ! I I I

Longlttiinal veJocity fluctuation intensity,

~, ft/sec

(b) Enolose&tunneI data. Propane-air ratio, approximately 0.045.

FIGIJEE2f3.-Comparkn of turbulent-flame-speeddata with those of other investigations.

—— _____ ._ .—— —___ _____

790 REPORT 128&NATIONAL ADVISORY COMMITI!EE FOR AERONAUTICS

shown by figure 13, decreases in the grid size reduce themean turbulent eddy size. Shce the effect of the turbulenceis thought to be increasingly diilusive in character as the tur-bulence scale decreases, this trend might be due to an in-creasing proportion of flames having temperatures less thanthe adiabatic vahe as the turbulence scrde becomes smalIer.

COMPARISONWITH DATA FROM OTHER INVESTIGATIONS

A comparison of the data of the present investigation with

those of references 4,.8, 9, and 22 is presented in @m-e 26.

In order to obtain a basis for comparison, the data are plottedwith the ratio of turbulent to laminar flame speed ST/SL

against longitudinal velocity fluctuation intensity @.The turbulent flame speeds measured in a Ivfache (nozzle)trype burner (ref. 4), a Bunsen burner (ref. 8), and a flametube (ref. 9) fall above those measured by the free-flamemethod in references 14 and 22 and in the present investiga-tion. It should be noted that the S~JSL data from thepresent investigation are plotted against the longitudinalvelocity fluctuation intensity, which includes the contribu-tions from both turbuhmce and sound. A better agreementwith the data of other investigations could be obtained byplotting the ratio STISL against the velocity fluctuation in-

tensity ~ due to turbulence sdone. This procedure isquestionable, since the sound velocity fluctuations mayhave an appreciable effect on turbulent flame speed whencoupIed with turbulence, and also because the magnitude ofthe sound field in the other investigations is unknown.The abscissas of iigure 26 may be converted to turbulenceintensity by the use of equation (3) and the data of table II.

The effect of fuel-air ratio on turbulent flame speed of freeflames is shown in figure 27, in which the data from the free-flame experiment reported in referenca 22 are compared withthose of the present investigation The data horn the presentinvestigation shown in figure 27 were taken 15.2 to 16.2inches downstream of the O.125-inchdiameter-wiro by 0.625 -inch-mesh grid, while the dat~ horn reference 22 were taken14 to 18 inches downstream of a 0.125 -inchdiameter-wire by0.500-inch-mesh .@d. The grid sizes and axial distances areclose enough so that the turbulence scales wem roughly equal.Becnuse of a large di.tference in stream velocity, the two setsof data wero taken under widely difEerent velocity fluctuationintensities. Both sets of data show a general trend of de-creasing turbulent- to laminar-tlame-speed ratio in the leanand rich fuel-air-ratio regions. The considerable deviationhorn mean values exhibited by the data of reference 22 sub-stantiates the statistical deviation of turbulent flame speednoted in the present investigation.

COBIPAIUSON OP DATA WITH VARIOUS THEORIES

The current prevailing concept of turbulent flame propaga-tion is based on references 25 and 26, wherein the proposalsme made that (1) small-scale turbulence (of the order of theflame-front thickness) increases the local flame propagationrate because of increased diflusion rates, and (2) large-scale

2.0

1.8

1.6%“\&_. 1.4

‘

itG

0

HDtince downstream= Cumulative

0,of turbulence-

2 ~rgb~ ty,fi / Sec

prwl:ci~) grid,

.4

0

0

0

A

&

&

n-

Grid.

-H

00 2: 0.125-lrL dbrmA 1.8 15.2 to 16.2

.2 :;! Q&w!~rtb;esh

H

‘A Ret22 .6Q12)-lnbji0rn.-

14 to 18

0 I 0.5~ln mesh

.7 .8 .9 Lo LI 1.2 1.3 [.4 1,5Equivalence ratio, P

FIGURE27.—Comparieon of turbuhm t-flame+peed data with thowof reference 22.

turbulence increases the over-all flame propagation rate by

~g the flame with attendant increased flame-front arm,Although it is well know-n that a turbulent field contains nstatistical distribution of eddy sizes, the complexity of tlloproblem has dictated the assumption of either tile large- orsmall-scale case.

The basic concept proposed by Shelkin (ref. 26) for L11Olarge-scale c~e is that the wrinlchng of the flame front mighLbe approximated by cones having a base proportional to Lhoturbulence scale and a height proportional to tile turbulenceintensity. This concept has been supported cxqxximenLsdhyby Hottel and coworkers in reference 1.

Turbulent flame speeds measured in flames stabilized onbluff bodies in high-velocity fuel-air stremns led Scurlock findcoworkers to postulate the concept of flame-gencratod turlm-[ence (refs. 6 and 7). Theoretical rmalyses to mcounL forflame-generated turbulence were proposed by Karlovitz anclcoworke~ (ref, 2) and by Scurlock and Grover (ref. 11), buLneither analysis conforms to all existing experimental data.A recent analysis by Tucker (ref. 27) predicts thaL litl 10, ifmy, turbulence would be generated by free flames with smallmrface deformations.

Since the Sholkin equation is not only of historical intomstbut is also used w a basis for the Scurlock-Grover theory,

PROPAGATION OF A FRDD FLAMDIN ATURBUIJENT GAS STREAM 791

the data of the present investigation are compared with theShelkin equation in tigure 28, wherein the ratio &/iSL isplotted as a function of longitudinal velocity fluctuationintensity for four cumuhtive probabfi-tia The data includeflame speeds measured with each of the three turbulence-gmmmting grids and are all for the constant fuel-air weightratio of 0.07 (figs. 23 and 25). The Shelkin equation was cor-related with the data at each value of cumulative probabilityby the method of least squares. This correlation was accom-plished by determining tho constrmt B in the Shelkin equation

(lo)

Tlm value of the constant B was estimated to be unity byShelkin but varies from 0.867 for the cumulative probabilityof 2 percent to 0.220 for the curmdative probability of 80percent. The value of the constant B is shown in figure 28

~0 . .

U, [~~ec Di~;.’ %& hz oa

a ~;~ 0.62570 .625:n .: 70 .063 .313

k A 70 ;03~3 :;Is:s b 35z

:1.6 I Ilx

-( )

ST 2

“(’). , // ~.,+ Q55, q2\

q L’

L4., ❑

.

A /<>

12

/ (

(b) / ‘1.OO

.4 .8 1.2 1.6 2.0 2.4Longitudinal velocity fktuaticm intensity,

~, ft/sec

(a) Cumulative probability of occurrence, 2 percent.

(b) Cumulative probability of occurrence, 20 percent.

for each of the cumulative probabilities. The data scatterabout the Shelkin equation but show some aggeement withthe Shelkin theory. A curve plotted through the data ob-tained with the 0.125-inch-diameter-wire grid does not followthe shape of the Shelkin curve, however.

The theoretical expression for turbulent flame speed pre-sented by Tucker in reference 27 was obtained by a waveanalysis of the effect of a low-intensity turbulent field on aninfinitesimally thin flame front having convolutions, or wrin-kles, of low slope. The final equation shows no effect ofturbulence correlation coefficient and is, in the presentnotation.

(11)

where (?(~) is a function of the ratio ~= TF/Ta. The rmalysisincludes the assumption that the second-order terms (~2/@2are negligible, that the flame temperature and laminar flamespeed are dependent only on fuel-air ratio, and that the difEu-sive action of turbulence is negliible.

In order to obtain a comparison with the present data, theTucker analysis was extrapolated well beyond its intendedlimit of the ratio (~/&). The data of the present investiga-tion compare well with the Tucker analysis in the region .of low velocity fluctuation intensity, as shown in iigywe 29,but fall below the theory in the higher-intensity range, wherethe theory cannot be expected to hold. A further comparisonof the turbulent-flame-speed data with the Tucker analysisis made in figure 30, wherein the ratio &/& is plottedagainst fuel-air weight ratio. These data are for each of the

z~ 1.4;

/z0 -5-

.% 1.2 e /a

<- ~

/ - y ()

<%2_

( )-

G2

(d)s~

- I+ 0.220 —s~

LLoo~ I

.4 .8 1.2 1.6 2.0 2.4 2SLangitudrnalve~ty fluctuation intensity,

JJ?, ft/*c

(c) Cumulative probability of occurrence, 50 percent.(d) CurnuIative probability of oocurren~ 80 percent

FICmRE28.— Comparison of turbulenkflame-speed data~tith theory of reference 26. Fuel-air weight ratio, 0.07.

43587u-G7-51

— __ ——.__— .-. _

●

792 REPORT 128&NATIONAL ADVISORY

.

COMMITTEEFOR AERONAUTICS

n-i-i--xll

j%el-air weight ratio

(a) Grid: 0.125-iich-dkmeter wire, 0.62&iich mesh.

Fuel-air vr&ght *

(b) Grid: 0.063-iioh-diameter wire, 0.313-inoh mesh,

FI~URE30.—Comperk.cm of turbulen~flame-epeed data with theories from references 11 and 27.

Longitudinal velo~y fluctuatbn intemity,~~: ft /~c

FIGUEE29.—Comparison of turbuhmtiflame-speed- data with theoriesof references 11 and 27. Propane-air wwight ratio, 0.07; streamstatic pressure, 29.3 inohes of mercury absoluti; temperature,645° R; grid 0.12-5-inch~ameter wir~ 0.626-inch mesh.

three turbulence-generating grids and were taken at the samemean stream velocity. The data in each figure fall below

the theory, but, with the exception of the enclosed-tunneldata (~. 30(a), fuel-air ratio, 0.045), follow the generaltrend of the Tucker analysis in the upper portion of thecumulative probability band. These data suggest that theanalysis might be taken as the limiting value of turbulent

flame speed for the turbulence conditions specified in thefigures.

The turbulent-flrme-speed data are also compared wit hthe Scurlock-Grover analysis (ref. 11) in figures 29 and 30.This analysis assumes that the flames proceed locally at tlmlaminar rate S’L, but that the over-all flame speed i3T isincressed because of flame-front wrhdding caused by hw-bulence. The geometrical model is similar to Shelkin’s,except that the wrinkle height is assumed to be positivelyrdl%oted by turbulent motion and negatively affected bylocal flame propagation. The analysis also accounts forflame-generated turbulence caused by velocity and densitygradients acroes the flame front.

Flame-generated turbulence has been neglected in amodifkd Scurlock-Grover analysis, which was used in thepresent investigation and is discussed in appendi,, D. Themeasured cmdation coefficients, as shown in figure 13, wereused in the analysis, in contrast to the exponential forms-Umed in the Scurlock-Grover report (ref. 11) and thecomparison with free-flame data made in reference 22. Theanalysis predicted that the turbulent flame speed had notyet reached its full value at the axial stations of measure-ment (x= 15.2 and 16.2 in.). Therefore, values of iSJ&were calculated from the theory for flame-growth timescorresponding to both stations and are shown in figures 2~and 30.

PROPAGATION OF A FREE FI.AME

I I I I

I I I I Iq#J&

94~ n 98

I I I I 1

II IIIIL 80

,21 I 9 I I I ,-,. -,

I I I I

-“’1 I I I I I b Ref.II (At:mm5;y$11111 —-wnf77

z: ‘

I I I I I I I I

+LI

1)

.8I I I I

I I I I4 b

.6 1 , ,

n A

.070 .075 .080 .0S5 .090

u!!- 1 I I , , ,

,41(c) I i I.045 .050 .055 .060 .065

Fuel-air we~ht ratio

(c) Grid: 0.03 K34nch+ameter tire, 0.150-inch m~h.

FIGURE30.—Concluded. Comparison of turbulent-fh=u+speed datawith theories from references 11 and 27.

The clat a of the present investigation fall below the valuea

of ST/SL predicted by the moditled Scurlock-Grover ana@is.Tlm data follow the Scurlock-Grover analysis more closelyfor the largest turbulence scale (@. 30(a)), and the agreement

IN A TURBULENT GAS STRDAiU 793

becomes progressively worse as the turbulence scale becomes

smaller (figs. 30(b) and (c)). This type of relation may bc

due to an increasing diilusivo action of the turbulence as tlmscale becomes smaller, as discussed previously in this section.

The data agree somewhat better with the Scnrlock-Groveranalysis than with the Tucker theory in the extremes of t!lelean and rich fuel-air-ratio regions. This probably is due to

the increasing @lS~ in those regions that tend to exceedthe limits of the assumptions made in the Tucker annlysisdiscussed in a preceding paragraph.

In summary, values from both the Tucker and theScnrlock-Grover analysis seem to form an upper limit to thedata of the present investigation, except in the extremes ofthe lean and rich fuel-air-ratio regions.

CONCLUSIONS

From the results of the investigation, the folloting conclu-sions are made:

1. The propagation rate of a bee flame in a turbulent fieldtith intense random sound velocity fluctuations is a statis-tical variable having a probab%~ of occurrence bandbounded by a zero propagation rate and possibly an upperpropagation rate well mbove the laminar flame speed.

2. The propagation rate of a free turbulent flamo is

substantially less than those previously measured for sta-

bilized flames.3. The statistical spread of free-flame propagation rates

is markedly tider in both the lean and rich fuel-air-ratioregions.

4. Values calculated from the Tucker analysis for free-flame propagation rates apparently form an upper limit forthe statistical spread of free-flame propagation rates in theregions vrhere the velocity fluctuation int ensit,y is 10TV.

LEWIS FLIGHT PROPULSION LABORATORYhTATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

CLEVELAND, OHIO, J&y 7, 1966

794

Az

BcDdE

mFf

9iKLrLc9NnR9

;SPLTtuuV,wx

REPORT 12S&NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

APPENDIX A

SYMBOLS

cross-sectional areasmoothed time-avertqge surface area of turbulent

flameconstant in Shelkin equationconstantturbulent diilusion coefficient, sq ft/secwire diameter of turbulence-producing grid, in.d-c voltage, v

rms of a-c complex Wave voltage, vlongitudinal ene~-spectrum density function, seclongitudinal double-velocity correlation coefficientlateral double-velocity correlation coefficienthot-wire current at stream conditions, ampgain of decade amplifierlongitudinal scale of turbulence, in.lateral scale of turbulence, in.Lagrangian scale of turbulence, in.number of flame glob&sfrequency, cpsgas U)nstantLagrangian double-velocity correlation coefEcientradial distance from tunnel axis, in.flame speed, ft./seesound pressure level, dbtemperature, “R

time, sec

mean stream velocity, ft/sec

longitudinal veloci@ fluctuation, ft/sec

lateral velocity fluctuations, ft/sec

fluid particle displacement due to turbulent motion,ft

x distance downstream of turbulence-producingin.

Y distance from tunnel wall, in.angle, deg

; power band width of wave analyzer, cps6 flanwfront thiclmes ft

t spatial separation of velocity vectors comprisingcorrelation coefficient, in.

P density, lb/cu ftu one standard deviationT ratio of flame temperature to unburned-gas tomporw

ture, TF/Ta

P equivalence ratio, fuel-air ratio/stoichiometric fucd-nirratio

$-l hot-wire resistance at stream conditions, ohms

Subscripts:

ambient, or approach stream; flame

f pertaining to correlation coefficient jpertaining to correlation coefhcient g

: lamimu?n pertaining to a frequency intervalo no-flow condition in anemometry, or mf emnce point

in space or time double-velocity correlationcoefEcient9

P pertaining to number of flames of o given radius orgreater

8 soundT turbulentt total, or time

IE at a distance f from zero position

APPENDIX B

TURBULENCE AND SOUND INSTRUMENTATION AND ANALYSIS

THZO12EHCAL BACKGROUND ITurbulent fields are generally defined by the two param- I

eters intensity and correlation ccdicient. The turbukmeintensity is ddlned as the rms value of the turbulent veloci~ Ifluctuations ~~, ~, and w. The doublt+velocity corre- ]lation coefllcient may be represented by a second-ordertensor which for a homogeneous, isotropic field of turbulencecan be reduced to two components w shown in reference 28.These two components are the longitudinal and lateraldouble-velocity correlation coefficients defined as follows:

Longitudinal: f== .2 & ,+ (4)

grid,

(4m)

wherej and g are the longitudinal and the lateral correlationcoefficients, respectively, u is turbulent velocity fluctuation,$ is the spatial separation between the points of measure-ment of the u, and the bar signik a long time average.

Longitudinal and lateral turbulence scales havo boondefined by the relations

LyJ

,“f@ (6)

L.= J~“dt (5aJ

PROPAGATION OF A FRED F’LAW3

These sales me intended to represent a mean turbulenteddy size, and for homogeneous, isotropic turbulence maybe related through the equation (ref. 28)

which, by integration, becomes

@la)

@lb)

()I’or the commordyobserved exponential form of f=exp -~f ,

equation (B lb) becomes

L~2Lg (Blc)

Taylor has shown (ref. 29) that the one-dimensional turbu-lence energy spectrrd density function ~ is the 13’ouriertransform of the longitudinal correlation coefficient f

(J32)

whero l’ is defied by the relations

and

J “Fdn=lo

where ~~ represents the total kinetic energy in the longitudinaldirection, and ~ represents the kinetic energy contained inthe frequency interval n to n+dn.

HOT-WIRE ANEMOMEH3Y

The constant-temperature hot-wire anemometry equip-ment is shown diagrammatically in iigure 31, and for themost part has been described in references 16 and 30. The

equation relating the rms voltage ~ measured by theaverage square computer to the turbulence intensity hasbeen discussed in reference 16 and is as follows:

(B3)

The spectrum density function ~ was metwred from thetape-recorder playback signal by the following equationwhich is given in reference 16:

(B4)

where ~ is the square of the rms voltage reading of thewuvo analyzer.

The double-velocity correlation Coeiiicientywas determinedfrom R double+hannel magnetic-tape recording of the

IN A TURBULENT GAS STREAM 795

%undprcdirq

1~__---- –-_y

11 I

1- ————— —- -!

Test cell

///////zzmmzmzControl rwm

?1+

Ezrl!!!r”‘FIGURE31.—Hot-wire anemometer and au. instrumentation.

instantaneous voltage signal from the hot-wire anemometer.The double-channel tape was played back into a doublecorrelation computer which electronically performed theinstantaneous multiplication of velocity fluctuations indi-cated in equation (4). The variable separation ~ betweenvelocity vectors was attained by the use of a movable and afixed playback head. The separation g between the velocityvectors was equal to the separation between the headsmultiplied by the ratio of the stream velocity to the tapespeed. The equivalence of the correlation coe5cientmeasured by this method and by the two-probe method wasproven as a part of a research program reported in reference31.

SOUND-FIELD INSTRUblENTATION

The sound instrumentation consisted of a standardmicrophone and sound-level meter from which sound-pressurelevel could be determined. The microphone sigrdd was alsoimpressed on the wave analyzer to obtain the sound kineticenergy spectrum through equation (134). The relationbetween sound pressure level S’PL and sound velocity

rfluctuations @is given in reference 32 (for simple harmonicwaves) a9

SPL=20 log (PaG) +74 (135)

—. — ___ .-—

796 REPORT 128~NATIOXAL ADVISORY COMMTIWEE FOR AERONAUTICS

APPENDrx c

PHOTOMULTWLIER INSTRUMENTATION

RmATroN BHWEEN FLAME I.IGHT MENSITY AND FLAME SPEEO

Assumptions .-The conditions assumed in relating flame

light intensi~ as indicated by the voltage output, of a

photomultiplier tube to the surface area of a flame are

treated in reference 33. They may be snnum-wized as

follows:

(1) It is postulated that, if a point source of light is in-creased to a iinite size but the distance from the light sourceto the detector is constant and large in comparison with themaximum dimension of the flame, the light flux impingingon the detector will obey the invelse square law. Under thiscondition, a change in the surface area of the flame will pro-duce an approxirnat ely linear change in the flux intensityregistered by the detector.

(2) The flame must consist of a homogeneous cloud ofnormbsorbing emitters.

If the propagation of a free-flame globule moving in a gasstream ut stream velocity is observed by a detector througha long slit placed axially with respect to globule travel, someadditional requirements are:

(3) The detector must. have an es-sentiallyflat light responseover the entire field of view.

(4) The slit must be narrow- enough in relation to flame-globulo diameter to appro.xirna te n diameter of the projectedspheroid.

(5) The flame-globule center must not suffer any appreci-able radial displacement from the tunnel centerline.

(t3) The flnm~ globule must not have a preferentird growthdirection.

(7) The flame temperature must be constant for nll theflame globules.

Conditions (1) and (4) were met by suitable placement anddimensioning of the nppmatus. For conditio~ (3), it wasdetermined that the photomultiplier unit had a maximumlight response error of 5 percent over the total light accept-rmce angle. Photographic evidence obtained in the pre-Iiminnry phase of the investigation indicakd satisfactoryfulfillment of requirements (5) and (6). Assumption (7)has been previously treated in the section kIEASUREMENTSOF PRESENT IN-WESTIGAmON.

Description of apparatus.-A 931A-type photomultiplier

having “an adjustable-plate voIt.age power supply wasmounted in a lighhtight box behind Q 0.25-inch-diameter

aperture. This detector unit was positioned in nn enclosed

tunnel 4 feet from the free-jet stub tunnel, as shown in

iigure 5. The detector aperture was centndly located with

respect to the slit in the machined aluminum plate, which

replaced an upper portion of one wall of the stub tunnel.

The voltage output of the photomultiplier was amplitied

and fed to an oscilloscope. Oscillogmms were taken by

high-speed, continuous motion-picture technique.

Oscillograms.-As show-n in figure 20, the oscillograph

trace of the ignition and growth of a single flame consists of

two portions, a spark light amplitude decay curve nnd w

flame light amplitude growth curve whose slope nt any point,

is equal to the change of diameter of the flame globule with

time, governed by the considerations listed previously.

This slope Zir/dt is proportional to turbulent flamo speed& a9 given by equation (2).

RBLATIONBETWEENSPARK LIGHT INTENSITY AND SPARK CURRENT

Standring and Looms (ref. 34), using short-durntion

sparks produced by s lightly dnmped oscillatory curren 1,

have shown that the light emitted by a given spark gap

depends on the cmTent in the gap and its time variation.

In order to determine the eflect of a long-duration, direct-

current pulsed spark on the current-spark light relation, on

auxiliary investigation was undertaken in collaboration with

Clyde Cl. %vett, Jr. The spark production and recordingapparatus is fully described in reference 35, The photo-multiplier detector apparatus was as described previouslyexcept that the detector unit was mounted at one encl of nrectangular tube 2 feet in length. The field of view of tb cphotomultiplier tube was limited by a 0.0625- by 2-inchaperture in the other end of the tube. A Polnroid LendCamera was used to make oscillograms.

A series of oscillograms waa taken of sparks ignited in stillair and in an airstream having a velocity of 50 feet per second.Spark duration was ~bout 600 microseconds, spark energywas of the order of 17 millijoules, nnd penk spark curron tapproximated 0.23 amperes. A comparison of spnrk lightamplitud~time curves with the current-time curves obt aimxlin the apparatus designed by Swett showecl n mmkod simi-larity of shape between the sets. It was conducted from thisinformation that, at least for a fksborder approximation,spark light intensity was roughly proportional to sptwlccurrent.

——

PROPAGATION OF A FREE FLAME IN A TURBULENT GAS STRDAM

APPENDIX D

CALCULATION OF FLAME SPEED FROM SCURLOCK-GROVER ANALYSIS

The basic equation in the Scurlock-Grover theory (ref. 11)is obtained by assuming that the increase of flame speed isclue to the minkling of the flame front in the form of rightcircular cones, so that

*=2=[’+”GY (Dl)

Where ~~ is assumed proportional to the ratio of COD.

height to base diameter and 01=4 is a constant. The meansquare particle displacement is nssumed to depend on threeeffects:

(1) Turbulent mising, which increases the flame-front area(2) Lmninar flame propagation, which decreases the flame-

frontl area(3) Flame-generated turbulence, which increases the tur-

bulent mixingThe first effect on ~ is given by

dx$ J—=27 : a?g, atdt(D2)

where @ is the Lagrangian correlation coefficient and gt istho Eulerian correlation coefficient. The second effect isgiven by

=r=c2s~{[1+c@T’-1}dm;

where 02=)4 is a constant. The combtiationtwo etlects is then

(D3)

of the iirst

(D4)

Since the Lagrcmgirm correlation coefficient cannot be meas-ured directly, Scurlock and Grover assumed it to be of theform given in reference 15:

(D5)

where -fZ is the Lagrrmghm scale of turbulence and was as-sumed to be equal to ~ Lz. In the present analysis, ~ wasnssluned to be related to j through the independent variable

797

transformation -.6 @ t (ref. 36). Isotropy N-m ns-sumed, so thnt, g vras obtained from j through the relation(ref. 28)

(D6)

The correlation coefficient g, was then obtained from the inde-pendent variable transformation &&t. The turbulencescale .L~was calculated by matching the curve esp (—&/-LX),g=e-~i’r, in g=Lgt to the g plot pre-kiously calculatedfromf by equation (D6).

All integrations and differentiations were done graphically.and the calculation procedure followed t-he following order:

(1) Calculate g from equation (D6).

(2) Transform~(Q to ~[:/(0.6-@)l(3) Transform g(:) tog, (g/&).(4) Calculate

dz=22 ‘dt s

@g, dt “o

(5) Calculate

(6) C!alcdate

F=F{[’+4WF}(7) Calculate

(8) calculate

@=~’~#dt

(9) Calculate

%=%=[1+4@lln

As mentioned in the DISCUSSION! section, flame-gener-ated turbulence l.ms been assumed negligible, and the h-dform of the Scurlock-Grover theoretical equation is ns givenpreviously.

—. —..—— —.

798 IU3PORT 128~NA~ONW ADVISORY COMMITTEFI FOR AERONAUTICS

REFERENCES

1. Hottel, H. C., WWarns, G. C., and Lavinej R. S.: The Intluence

of Isotropic Turbulence on Flame Propagation. Fourth Sym-

posium (Intimation@ on Combustion, The Williams & WtiUSti. (BalthUoI’0), 1953, pp. 636-644.

2. Karlovitz, B&a, Denniston, D. W., Jr., and Wells, F. E.: Iuveeti-~t,ion of Turbulent Flames. Jour. Chem. ph~., VOL 19, no. 5>

~Iay 1951, pp. 541-547.3. Bollinger, Lovmll M., and lVilliarns, David T.: Effeot of Reynolds

Number in Turbulen&Flow Range of Flame SpeedS of BunsenBurner Flames. NACA Rep. 932, 1949. (Supersedes NACATN 1707.)

4. wright, F. H.: Measurements of Flame Speed and Turbtience inn Small Burner. Prog. Rep. No. 3-21, Jet Prop. Lab., C. I. T.,June 6, 1950.

5. Boditch, F. VJ.: Some Effects of Turbulence on Combustion.Fourth S~m~osium ~tematio~) on ~mbu~ion> ‘he ‘fi-liama & ~h (h (Baltimore), 1953, pp. 674-682.

6. Sourloak, A. C.: Flame Stabilization and Propagation in High-Velocity Gas Strea- Meteor Rep. 19, Fuels Res. Lab.,M. I. T., May 1948. (Contraat NOrd 9661.)

7. RWlirmM,G. C., Hottel, H. C., and Scurlockj A. C.: Flame Stibfl-ization and Propagation in High Velocity Gas Streams. ThirdSymposium on Combustion and Flame and Explosion Ph&nomena,The lViiams & IWlkine Co. (Baltimore), 1949, pp. 21-40.

8. VTobl, Kurt, Show L., von Rosenberg, H., and ‘iVeil, C. W.: TheBurning Velocity of Turbulent Flames. Fourth Syrnp&UIU

(Intematior@ on Combustion, The IWlliarns & Willrins Co.(Baltimore), 1953, PP. 620-635.

9. IXason, D. B.: Turbulence and Flame Propagation in prefixedGases. Fuel, VOL XX% no. 10, Oct. 1951, pp. 233-238; di5cus9ion, pp. 233-239.

10. Caldvrell, Frank lL, Ruegg, Fillmer IV., and Olsen, Lief D.: Com-bustion in hlovimz fi. Paper presented at meeting SAE andAir Transport (N=w York City), Apr. 13-15, 1948.

11. Sourlock, A. C., and Grover, J. H.: Propagation of TurbdentFlames. Fourth Symposium (Intemationd) on C%mbtilon,The JVilliams & wilkius a. (B~timore), 1953, Pp. ’58-

12. Ball, George A.: Combtilon Aerodynamics-A Study of a Two-Dimensional Flame. Dept. Eng. Sci. and Appl. Phys., Harvard

Univ.. JulY 1951. (Army Oral. Dept. Contract No. W–19-020-ORti509.)

13. Stevens, F. W.: A Constant PmEEuroBomb- NACA ReP. 176)1923.

14. Mickelsen, ‘iVilliam R.: The Propagation of a Free Flame Througha Turbulent Gas Stream. M. S. Thesis, Case Inst. Tech., 1953.

15. Dryden, Hugh L.: A Review’ of the Statistical Theory of Turbu-lence- Quart. of Appl. Moth-, vol. 1, no. 1, Apr. 1943, pp. 7-42.

16. Mickelsen, TViiam R., and Laurenc~ James C.: Measurementand Anrdysia of Turbulent Flow Containing Periodic FlowFluctuations. NACA RM E53F19, 1953.

17. Hottel, H. C., ViWliarns, G. C., and Satterfield, C. N.: Thernwdynamio Charts for Combustion Processes, Pt. II. John J’iWey& Sons, In~, 1949.

18. Anon.: Annual Program Report.kmy, Jan. 1, 1949.

Proj. Squid, U. S. Nnvy, U. S.

19. ~orthi-rig, Archie G., and Geffner, Joseph: Treatment. of Experi-mental Data. John Wiley & Sons, Inc., 1943, P. 275.

20. Lusser, Robert: A Study of Methods for Achieving Reliability ofGuided Missiles. Tech. Report No. 75, U. S. Naval Air MissiloTest Cater, July 10, 1960.

21. Dugger, Gordon L.: Ii3Tect of Initial Mi..ture Tomperaturo onFlame Speed of Methanefi, Propane-Afr, and 13thylmm-AirMixtures. NACA Rep. 1061, 1952. (Supersedes NACA TN’s2170 and 2374.)

22. Bolz, Ray E., and Burlagq Henry, Jr.: The Influence of Turbu-lence on Flame Propagation Rates. Jet Prop., vol. 26, no. 6,

June 1955, pp. 265-275.

23. Taylor, G. I.: Diffusion by Continuous Movementi. Proc.London Math. Soo., vol. 20, 1922, pp. 196-212.

24. Botba, J. P., and Spalding, D. B.: The Larninar Flame Speed ofPropane/Air MLxtureEwith Heat Extraction from the Flame.proo. ROY. Sot. (London), mr. A, VOL 225J no. 11601 ‘Ug. 6’1%4, pp. 71-96.

25. Dam!dder, Gerhard: The Effect of Turbulence on the FlameVelocity in Gas Mixtures. NACA TM 1112, 1947.

26. Shelkin,K I.: On Combustion in a Turbulent Flow. A’ACA ‘1’~11110, 1947.

27. Tucker, Maurice: Interaction of a Free Flame Front with aTurbtience Field. NACA TN 3407, 1956.

’28. von K&mAn, Theodore, and HO~~& LEslie: On tho ‘tatisticnlTheory of Isotropio Tqrbulen”ce. Proc. ROY. SOO.(~ndO@~ser. A, vol. 164, Jan. 21, 1938,pp. 192-215.

29. Taylor, G. I.: The Spectrum of Turbulence. Proc. Roy. Sot.(London), ser. A, vol. 164, Feb. W 1938,PP. 47~90.

30. Laurence, Jam@ C., and Landes, L. Gene: AusWnry Equlprnontand Techniques for Adapting the Constant-Temperaturo Hot-Wire Anemometer to Speoifia Problems in Air-FloN’ lMeasurc-ments. NACA TN 2843, 1952.

31. ~urence, James C.: btensity, Scale, and Speotra of Turbulencein Mising Region of Free Subsonic Jet. NACA ROP. 1292) 1~5~,(Supersedes TN’s 3561 and 3676.)

32. Mom, Philip M.: Vibration and Sound. Second cd., McGrn~~’-HiU Book Co., Ino., 1948.

33. Clark, Thomas P., and Bittker, David A.: A Study of tho Radin-tion from Laminar and Turbulent Open Propane-Air Flames nsa Function of Flame Area, Equivalence Ratio, and FUG1FIoN’Rate. NACA RM E54F29, 1954.

34. Standring, TV.G., and Looms; J. S. T.: Light Output from n Spnrk“Point Source”. Nature,, vol. 165, no. 4192, Mnr. 4, 1950, p.368.

35. Swett, Clyde C., Jr.: Effect of Gas Stream Parametcm on thoEnergy and Power Dissipated in a Spark and on Ignition.Third Symposium on Combustion and Flame and ExplosionPhenomena, The Wllfarn6 & Wilkins Co. (Baltimore), 1049,pp. 353-361.

36. Mickelsen, JWlliam R: An Experimental (%rnparfson of thoLagrangian and Eulerian Correlation Coefficients in Homo-geneous Isotropic Turbulence. NACA TN 3570, 1956.