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Blow-Out Stability of Gaseous Jet Diffusion Flames. Part I: In Still AirGautam T. Kalghatgia

a Shell Research Ltd., Thornton Research Centre, Chester

To cite this Article Kalghatgi, Gautam T.(1981) 'Blow-Out Stability of Gaseous Jet Diffusion Flames. Part I: In Still Air',Combustion Science and Technology, 26: 5, 233 — 239To link to this Article: DOI: 10.1080/00102208108946964URL: http://dx.doi.org/10.1080/00102208108946964

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Combustion Scien ce and Technolog y, 19RI, Vol. 26, pp . 233-2390010-2202/R 1/2606·0233506,50/0

© \981 Gordon and Breach Science Publishers, Inc.Printed in Great Britain

Blow-Out Stability of Gaseous Jet Diffusion Flames. Part I: In Still Air

GAUTAM T. KALGHATGI Shell Research l.td.. Thornton Research Centre, PO. Box 7, ChesterCH7 3SH

(Received April 20. /981)

Abstract-v-A universal non-dimensional formula that describes the blow-out stability limit of gaseous jetdiffusion flames in still air has been found experimentally. Its validity has been established over a wide rangeof parameters that affect the blow-out limit. Its extrapolation to cases where the burner exit flow is chokedsuggests that for a given gas there is a critical burner diameter above which a stable flame can exist at anynow rate .

INTRODUCTION

A jet diffusion flame in still air will lift off the tip ofthe burner and form a stable lifted flame when theflow rate through the burner is increased beyond alimiting value known as the lift-off stability limit.If the flow rate is increased further, the flame isextinguished at some limiting rate known as theblow-out stability limit. The lift-offstability and thestructure of the turbulent lifted diffusion flame instill air have received some attention in the past(e.g ., Wohl et al. , 1949; Vanquickenborne and VanTiggelen, 1966; Scholefield and Garside, 1949).The stability of flames of co-flowing streams ofhydrogen and air has been studied by Vranos et al ,(1968). Takeno and Kotani (1975) conductedsimilar experiments but with the aim of under­standing the effect of the temperature of the airstream on the stability of the flame. More recently,Baev and Yasakov (1976) and Annushkin andSverdlov (1979) have published papers that con­centrate on the blow-out stability of diffusionflames. In particular, Annushkin and Sverdlov(1979) propose a semi-empirical formula that canbe used to calculate the burner exit velocity atblow-out for different burner diameters forpropane, methane and hydrogen . However, theexperimental verification provided by them fortheir predictions is rather limited. Moreover, theirformula cannot be used to find the blow-out limitsfor fuels other than those used by them.

This paper describes the results of a systematicexperimental study of the blow-out stability of jetdiffusion flames in still air. The fuel gases used aremethane, propane, ethylene, acetylene, commercial

233

butanes and hydrogen. Burner diameters rangefrom 0.2 mm to 12 mm. From dimensionalanalysis, it is possible to identify non-dimensionalgroupings of the various flow and gas parametersthat affect blow-out. An empirical formula interms of these non-dimensional groupings can befound to describe the blow-out stability limits ofa ll the different gases used. The validity of such a" universa l" formula is further confirmed bystudying the blow-out of flames of mixtures ofmethane/air, rnethane/Co-, propane/air andpropane/C02 , Finally, an attempt is made toextrapolate these results to cases where the flowat the burner exit is choked at blow-out, by takinginto account the expansion of the gases in thesupersonic plume that results from such under­expanded sonic jets.

2 THEORETICAL CONSIDERATIONS

At the base of a lifted diffusion flame, the localturbulent burning velocity, Si, will be equal to thelocal flow velocity, U. If the flow rate through theburner is increased, U will increase and the base ofthe flame will be blown downstream to a newposition where once again S, will equal U. Theflame will blowout when the change in S, cannotkeep up with the change in U anywhere in the jetas one moves downstream from the base of theflame. .

Now let H be the distance along the burner axiswhere the mean fuel concentration falls to thestoichiometric level. It is very unlikely that thebase of the stable, lifted flame will be downstream

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234 G. T. KALGHATGI

where RH = (H· SII/ve) is the Reynolds numberbased on H. We now determine this funct ionalrelationship by experiment.

3 EXPERIMENTS

Each burner is a 65 mm long straight tube mountedat the end of a settling chamber whose internaldiameter is 152 mm . The gases were supplied fromcylinders to the settling chamber through appropri­ately calibrated rota meters. For high flow rates,these rotameters were bypassed and the pressure inthe settling chamber was measured when the flameblew out, using either a water or a mercury mano­meter. Th is pressure was taken to be the stagnationpressure, and the Mach number, M , when the gaswas expanded to atmospheric pressure was calcu­lated from it. The stagnation temperature, To, wasassumed to be equal to the ambient temperature,which was taken to be 290 K . In calculating thevarious flow parameters , the compressibility of thegases was taken into account. The. results ofexperiments us ing pure fuels are described first.

3.1 Resultsfor Pure Fuels

The fuels used , along with their properties, arelisted in Table I. In Figure I, the Mach number,M b , at the burner exit when the flame blows out isplotted against the burner exit diameter, db. fordifferent gases . Of course , M b is the same as M forsubsonic jets. It can be seen that M b increases

(I)

(2)u, ( pe )-- =f RH,-SI/ ' pm

of this point. H is independent of the burner exitvelocity and is given (Birch et al., 1978) by

[fI,: . pc )1 /2 J

H = 4- 1- -5.8 deOs \Poo

where de is the effective burner diameter, Be is thefuel mass fraction at burner exit. Bs is the fuel massfraction in the stoichiometric mixture of the fueland ambient gas, pc is the density of the burner gasat the burner exit and, poo is the ambient density.All things being equal, the larger the value of H ,the more scope there will be fo r the base of theflame to seek a new stable pos ition as the burnerexit velocity is increased, and the more difficult itwill be to blowout the flame. By similar con­siderations the larger the value of the maximumlaminar burning velocity, SIt, of the fuel in amixture with the a m bient gas, the more difficult itshould be to blowout the flame, since the maxi­mum turbulent burning velocity will depend onS" . The turbulent burning velocity will also dependon the local turbulence parameters and the fuelconcentration. These in turn will depend on thekinematic viscosity, "e, of the fuel gas and the ratioof densities, (Pc/Poo) , at the exit plane. Therefore,we can expect Ue, the burner exit velocity a tblow-out, to depend on H, S" , I'e and (Pe/Poo).Simple dimensional analysis (e.g. , Lydersen 1979)now tells us that

TABLE I

Properties of the gases used in the study

MaximumDynamic burning Ratio Mass fraction in

Purity/ viscosity, velocity of stoichiometriccomposition , Molecular 1", a t 0° C, in air, specific mixture with

Gas %v weight rnicropoises SII. m{s heats, y air, O.

Methane 99 16 102.7 0.39 1.31 0.0550.06Propane 99 44 74 0.45 1.13

Ethylene 95 28 91 0.75 1.255 0.063Acetylene 95 26 93.5 1.63 1.25 0.07Hydrogen 99 2 84.2 3.06 1.4 0.028r28 isobutane

42 II-butane1.1 0.06Commercial butanes l 26 propane 54.1 80 0.44

4 otherl hydrocarbons

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STABILITY OF GASEOUS JET DI F FUSION F LAME S 235

o METHANE

6. PROPANE

a COMMERCIAL BUTANES

<J ETHYLENE

x HYDROGEN

~ ACETYLENE

1.0

0.9

0 .8

0 .7

0.6

Mb O.5

OA 0

0 .3

0 . 1

2 3 4 5 6 7 8 9 \0 II 12

db ,mm

FIGURE I Mach number a t the burner exit a t blow-out.

almost linearly with do for all the gases. The samedata are shown in Figure 2 as plots of a non­dimension al velocity,

_ _ u, ( pc ) 1. 5Ue - - -

SII pro

against the Reynolds number, RH. It ca n be seenthat the data for different gases collapse onto asingle curve given by

(3)

The valid ity of thi s " universal" formula to describethe blow-out limit ofjet diffusion flames was furthertested by studying the stability of flames of mixturesof gases . These results are discussed below.

3.2 Results f or Mixtures of Cases

The mixtures used were meth ane/air, methane/Cos,propane/air and propane/Cfrs. For a given burnerdiameter, as the concentration of the diluent in theburner gas is increased , the blow-out velocitydecreases. Thi s is illustrated in Figure 3, where U e

has been plotted aga inst the concentrat ion of thediluent for d ifferent mixt ures , for the 5 mm

FIG URE 3 Th e effect of diluen ts on the burner exitvelocity at blow- ou t. Burn er diameter 5 mm .

o 1,1ETHM JE

t. PROPr.f-JE

'V ETHYLEr·IE

o COMMERCIAL BUTANES

• ,~CE TYL EI'J E

x HYDROGEN

10001900 ,,800 :-

60 0 0 0

FIG URE 2 The uni versal blow-out sta bility curve .

• MET HilNE + CO2

0 MET HA NE + AIR

... PROPANE + CO2

t. PROPilNE t AIR

160

120 ­

1001

Vl I<,

E SOL

~6J

"I20 f-

oL ! t !

o 10 20 30 40 50 60 70DILUENT CONCENTRATION, %v

!

80

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236 G . T . KALGHATGI

50

6000 80 00

AA A {;.(;

• 0o.OI7RH(I- 3 5 x IOGr<H)

BURiJEil DILUENTDIII.,mrn

3

}'"4

5

6

4 }ro,5

6

2000

1'10

130 -

120

11 0

100

~ 9 0

-----~I <€ 80

--- 70:::JQ) Iu? 60

"Q) 50I:::J

4 0

3020 -

10

ool<-- ----=--::'-::--:---'------.J':-:-----'-- ---L-- -'-------'-

' 0

o

,.

4 EXTRAPOLATION OF THE RESULTSTO CASES WHERE THE BURNER EXITFLOW IS CHOKED

It can be seen from Figure I that as the burnerdiameter is increased (beyond 5.3 mm for ethylene,for example) the burner exit flow could be choked

•

FIGURE 5 The non-dimensional blow-out stabili tycurve for mixtures with methane as the fuel.

for C02 concentrations of less than 15 percent. Wecan now express the results such as those in figure3 in terms of Dc and RH. In Figure 5, Dc has beenplotted .against RH for methane/air and methane/CO 2 mixtures, from which it can be seen thatEq. (3) describes the blow-out limit for these cases,where RH varies between 1000 and 9000, reasonablyaccurately. Similarly from Figure 6, where De hasbeen plotted against RH for propane/air andpropane/Cos mixtures, it can be seen that Eq. (3)is valid for 1O,000>RH>40,OOO.

Thus the validity of Eq. (3) in describing theblow-out limit of diffusion flames in still air hasbeen established over a wide range of conditions(Figures 2, 5 and 6).

~~CH4 + C02(FELLS B, , , RUT HERFORD)

CH4 +CO2

I ! t

10 20 30 40 50DILUENT CONCENTRATION, %v

~

~'l2°1100---'------'-------.J'-------'------'---

, ::~r150 ­

140L

1130~3 120['E. 110 .

i 100~ C~H. +C02

90[­

BoLI

70~0 410 do 80 100

DILUENT CO~JC[NTRAT IOr'J . %v

FIGURE 4b Variation of maximum laminar burn ingvelocity (S,,) with diluent concentration.

4 0

diameter burner. Similar experiments with mix­tures were also conducted using the 3 mm, 4 mmand 6 mrn burners.

When air is used as a diluent, the gas propertiesthat change are pc, Be and the dynamic viscosity,J1-c. With CO 2 as the diluent, in addition to theseproperties, Sli also changes. Of these , Pe and Becanbe easily determined as functions of the diluentconcentration. J1-c was calculated using the methodoutlined in Strehlow (1968) and is shown as afunction of the diluent concentration in Figure 4a.SIt was calculated for mixtures with C02 by themethod proposed by Spalding (1956) and Yumlu(1968) and is shown in Figure 4b. Also shown forcomparison in Figure 4b is the straight line withthe slope proposed by Fells and Rutherford (1969)lor methane/C02 mixtures based on their experi­ments, which, it should be pointed out, were done

FIGURE 4a Variation of dynamic viscosity (p.e) withdiluent concentration.

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STABILITY OF GASEOUS JET DIFFUSION FLAMES 237

FIG URE 6 The non-dimensional blow-out stabilitycurve for mixtures with propane as the fuel.

and we could still get a stable flame. The structureof the supersonic plume that results from suchunder-expanded sonic jets has been studiedextensively and is rather complicated . However,we assume, as in Annushkin and Sverdlov (1979),that in such cases the burner can be.simply replacedby an equivalent convergent-divergent nozzle atwhose exit the gas has fully expanded to ambientpressure. The actual burner diameter, db, can berelated to the diameter, de, and the Mach number,M, at the exit of such a nozzle. The result of usingthis equivalent diameter, de, in Eq . (3) is illustratedin Figure 7, where the velocity, Ue, at blow-out atthe exit of the equivalent burner is plotted againstdb for acetylene. The point where sonic velocity isreached at the actual burner exit is also marked onthe plot, which is a stability envelope outside whichstable flames can exist. Thus it can be seen that ifdb is larger than a critical diameter, dcr , which is1.57 mm for acetylene, this extrapolation predicts

(4)

40

",:I\ '

\J

f,.:,/1,-,-

CH.

, 1- '- EON. (3 ) RH < 75000

--- EON,14} RH >75 00 0

~ FLOW AT. BURN~R EXITCHOKED, i.e . Mb - I

. _ . C,He FROM EON, 13OFANNU HKIN S. SVERDLOV

1.0 1.5 2 .0db FOR C2 H2 • mm

db FOR CH4 • C3H a•C2H4 • mm

10 20 30

0. 5

~C2H 4\II

fI

", ,/~ ", C

3He// "

II

I/

/

( /

De = 335 +0.00807 RH

o

70 0

600

800

FIG URE 7 Extrapolation of the stability curve to caseswhere the nozzle exit flow is choked at blow-out.

With this additional assumption, it can be seenfrom Figure 7 that dcr for ethylene, propane andmethane is, respectively, 14.5 mm, 17.2 mm and41.4 mm.

Also shown in Figure 7 is the stability curve forpropane calculated from Eq, (13) of Annushkin and

up to 75,000. Hence we make a further assumptionthat for RH> 75,000, the plot in Figure 2 can beextrapolated by a straight line whose slope is thesame as that of the curve at RH = 75,000, i.e., forRH>75,000

that a diffusion flame would be stable at all flowrates. It also shows that for a burner diameter neardo, stability is restored on increasing the flow ratecontinuously as we cross the upper branch of thestability envelope. These predictions were firstmade by Annushkin and SverdJov (1979) and stemmainly from the fact that the ratio (de/db) increaseswith flow rate once the burner exit flow is choked.

Curves similar to that for acetylene have alsobeen plotted for methane, propane and ethylene inFigure 7. The change in the scale on the abscissa isto be noted. For these cases , the computationbreaks down if we use Eq . (3) for RH>75,000, andin any case, Eq , (3) has only been tested for Rlf

40000

• •o

T •T

~V T

T T

20000 30000HSu PeR - - -

H - fLe

BURNER DILUENTDIA.• mm

0 3 }",V 4

0 5

• :3 },,,T 4

• 5

60 0

500

300

20 0 100 0 0

•

1:3'

:iij';;;---"1:> 400=> cn

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23l! G. T. KALGHATGI

Sverdlov (1979), using the values for the gas para­meters listed in Table I. It can be seen that it differsconsiderably from the stability curve for propane,whose validity has been extensively tested in thepresent work. There is much better agreement formethane between the present work and that ofAnnushkin and Sverdlov (1979) .

It must be emphasized that the extrapolationattempted here is intended to give only a qualitativepicture of what to expect regarding the blow-outstability of diffusion flames for large burners. Itbecomes increasingly difficult to test the curves inFigure 7, especially for methane and propane, afterthe nozzle exit flow is choked. since the flow ratesneeded arc too large for laboratory-scale experi­ments. However, there is some anecdotal evidencein the oil and gas industry that for large burnerdiameters, stable flames can exist for very largeflow rates indeed. For instance, a stable flame wasobserved on top of a 10 em diameter pipe that wasdirectly connected to a natural gas reservoir withan mternal pressure of at least 85 atmospheres.

5 CONCLUSIONS

A universal formula that describes the blow-outstability limit of gaseous jet diffusion flames in stillair has been found experimentally. Its validity hasbeen established over a wide range of parametersthat affect the blow-out limit. Extrapolation of thisformula to cases where the burner exit flow ischoked suggests that for a given gas there is acritical burner diameter, del" beyond which astable flame can exist at any flow rate .

NOMENCLATURE

d,. Burner exit diameter.dc l' Critical burner diameter beyond which

stable flames can exist for all flow ratesd; Effective burner diameter

dr, = d" for subsonic jets

[

2+(y-I)M2 ] (y+ 1l/4(y-1 Id,~ =(!tJ M-I /'l.

y+1for choked jets

If Distance along burner axis at which meanfuel concentration falls to stoichiometriclevel. Equation (I).

M II Mach number at burner exit at blow-out

M Mach number at effective exit at blow-out.M = M b for subsonic jets. For choked jets,M, is the Mach number after expansion ofthe gas to ambient pressure.

R Gas constantRH Reynolds number based on H

- H,Su/Jl eS" Maximum laminar burning velocity for a

mixture of the burner gas with ambientgas (air).

T« Stagnation temperature. Taken to be290 K, i.e., ambient temperature 111 thiswork

Ue _ V(yRTo)·M(I+(y-I)/2M2)-1/2, velocity ateffective burner exit at blow-out.

De - UeISutPe/ Pro) I.S, non-dimensional velocityat blow-out

y Ratio of specific heats!Le Dynamic viscosity at jet exitlie _ !Leipe, kinematic viscosityPe - po(l+(y-I)/2M2), density of jet gas at

effective jet exitpn Dens ity of jet gas at temperature, Tn and

ambient pressurepro Density of ambient gas (air)Oe Fuel mass faction at burner exitOR Fuel mass fraction 111 the stoichiometric

mixture of the fuel and ambient gas

ACKNOWLEDGEMENTS

Thanks are due to M r. R. J. Wade of Shell ResearchLimited , Thornton for building the experimental rig andassisting in the experiments. Mr . D. T. Gray of theDepartment of Chemical Engineering, Cambridge Uni­versity also helped in some of the experiments during hisshort stay in Thornton as a vacation student.

REFERENCES

Annushkin , Y. M., and Sverdlov, E. D. (1979). Stabilityof submerged diffusion flames in subsonic and under­expanded supersonic gas-fuel streams. CombustionExplosion and Shock Waves, 14 (5),597.

Baev, V. K., and Yasakov, V. A. (1976). Stability of adiffusion flame in single and mixed jets. CombustionExplosion and Shock Waves, 11 (2), 143.

Birch, A. D., Brown , D. R., Dodson, M. G., and Thomas ,J. R. (1978) . The turbulent concentration field of amethane jet. J. Fluid Mech., 88 (3), 431.

Fells, I., and Rutherford , A. G. (1969) . Burning velocityof methane-air flames. Combustion and Flame, 13, 130.

Lyder sen, A. L. (1979) . Fluid F10lV and Hear Transfer .John Wiley and Sons , pp. 37-54.

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STABILITY OF GASEOUS JET DIFFUSION FLAM ES 239

Sch olefield, D . A. , a nd Gar side, J. E. ( 1949). The struct urea nd sta bility of diffu sion flames . Third SymposiumUnternat ional ) Oil Combustion, William s and Wilkin s,Ball imore, p . 102.

Spalding, D . B. ( 1956). A mixing ru le fo r lamina r flam espeed . Fuel, 35, 347.

St rehlow, R . A. (1968 ). Fundamentals of Combust ion.Internat ion al Textbook Company. Scranton , PA,·p. 73.

Takeno, T. , and Kotani, Y. ( 197 5). AI' experimental stud yon the stability of je t d iffusion flames. Acta Astro­naut ica, 2, 999 .

Vanquick cnb ornc , L., a nd Van T iggelen , A. (1966). Thesta biliza tion mechanism of lifted diffusion flame s.Combustion and Flame. 10, 59.

Vran os, A., Taback, E. D .• a nd Shipma n. C. W. (I 968) .An exper imental study o f the stabil ity of hydrogen-airdi ffusion flames. Combustion and Flame, 12, 253.

Wohl , K. , Kapp, N. M. , a nd Ga zley , C. (1949 ). Thesta bility of open flames. Third Symposium (Int er­national} on Combust ion, Williams and Wilk ins ,Baltimore, p. 3.

Yurnlu , V. S. (\ 968). The effect s of add it ives on the burningvelo cities of flames and their po ssible pred iction by amixing rule. Combustion and Flame, 12, 14.

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