.. '

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'I '-""• ------------------------~~------------------------~

8 OCT 1948

NATIONAL ADVISORY COMMIITEE FOR AERONAUTICS

TECHNICAL NOTE

No. 1707

EFFECT OF REYNOLDS NUMBER IN THE TURBULENT-FLOW RANGE

' ON FLAME SPEEDS OF BUNSEN-BURNER FLAMES

v' v By Lowell M. Bollinger and David T. Williams

Flight Propulsion Research Laboratory Cleveland, Ohio ·

Washington September 1948

I

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NATIONAL ADVISORY COMUi"l'EE FOR .AERON.Atrl'ICS--

TECmriCAL NOTE NO. 1707

EFFJroT OF :REYNOLDS NUMBER IN TEE TURBULENT -FLOW RANGE

ON FLAME SPEEIB OF BUNSEN -BURNER FL.AMES

By Lowell M. Bollinger and David T. Williams

SUMMARY

The effect o£ flow conditions on the geanetry of the turbulent Bunsen flame was investigated. Turbulent flame speed is defined in terms of flame geometry and data are presented showing the effect of Reynolds number of flow in the range o£ 3000 to 35,000 on flame speed for burner diameters from 1/4 to 1~ inches and three fuels -acetylene, ethylene, and propane.

The normal flame speed o£ an explosive mixture was shown to be an important factor in determining its turbulent flame speed, and it was deduced from the data that turbulent flame speed is a func­tion of both the Reynolds number of the turbulent flow in the burner tube and of the tube diameter.

INTROIUCTION

A flame advancing through an explosive mixture at rest or in laminar flow assumes, at least initially, a smooth combustion front. The speed normal to the front and relative to ;the adjacent unburned mixture with which this front advances is known as the normal flame speed of the mixture (or transformation velocity) • This speed is constant for a given set of physical and chemical conditions.

In turbulent flow, the combustion front !a not smooth,. because it is disturbed by the fluctuating components of' velocity. Yet if a surface sufficiently large in comparison with the scale of tur­bulence is considered, the average position of the combustion front advances with some definite speed normally to itself'. This speed will be called the turbulent flame speed and its value will prob­ably depend upon the aerodynamic as well as the physical and chem­ical conditions of' the explosive mixture.

Because turbulence can greatly increase the rate of burning of fuel-air mixtures, an e7acT. knowledge of the influence of turbu­lence on combustion is highly important to practical applications.

2 lfACA Tlf lfo. 1707

Some information has been gathered :from tests on internal-canbustion engines (reference 1). In these investigations, no attempt was made to relate the rate of' burning to aDY :fundamental measurable property of' the turbulence. The degree at turbulence at the charge in the engine cylinder was varied by changing engine speed or cyl­inder geometry. Two investigators, DamkOhler (ref'erence 2) and Shelkin (reference 3) each have, proposed a theory to relate f'lem.e speed to turbulence. These theories require evaluation with exper­imental data obtained under well-defined conditions.

A possible method of' investigating the relation between tur­bulence and rate of burning is by measurement at rate of :flame propagation in a stea.dy-f'low Bunsen-type burner. It is possible in such an apparatus to create :forms ar turbuJ.ence that have been quantitatively' investigated. Furthermore, it is camnon to deter­mine normal :flame speed as the volume rate at :flow at explosive mixture divided by the sur.race area ar the inner cone at a laminar Bunsen-burner :flame. (See reference 4 :for a discussion ar the method.) This technique :for measuring flame speed can also be used in the range of turbulent :flow. Damkohler (ref'erence 2) carried out some measurements in this manner, but his data are inauf'ficient to establish conclusively a theory.

In experiments conducted at the NACA Cleveland laboratory during 1945, :flame speeds were experimentally' de~erm.ined b;r the Bunsen-burner technique with :fully' developed turbulent :flow in the burner tubes. Data were obtained :for three :fuels, :for burner diameters :fran 1/4 to 1t inches, and :for Reynolds numbers in the

range :from 3000 to :351 000. In order to show the ef'f'ect ar tur­bulence on f'lame speed, these turbulent f'lame speeds were correlated with normal f'lame speed, tube diameter, and Reynolds number. In addition, the data were used to t_est the theories at references 2 and :3.

APPARATUS AND PROCEIXJRE

Equipnent

The apparatus used 1n this investiga.tion is diagrammatically shown in f'igure 1. Fuel and air were metered separately', then thoroughly mixed, and conducted into the Bunsen-burner tube, which was long enough for fully developed turbulent f'low to resul.t at the burner outlet. The burners used were a series of f'our smooth seamless steel tubes, which had the following dimensions:

NACA TB No. 1707

Nominal Inside Length, L Ratio of length diameter diameter, d (om) to inside

(in.) (om) diameter, L/d

1/4 0.626 125 200 5/8 .945 215 228 5/8 1.579 215 156 1!.

8 2.845 215 76

The tubes were cooled to room temperature by water jackets.

In order to prevent blow-off' of the Bunsen flame at high f'lows, it was necessary to surround it by an auxiliary flame. An annular­shaped burner was f'ormed around the lip of the Bunsen burner by surrounding it with a tube of' somewhat larger diameter. A f'uel-air mixture at low velocity flowed through this auxi1iary burner; the fuel in the auxiliary burner was the same as that in the main burner. This mixture burned at the outlet of' the burner and kept the inner Bunsen flame seated to the lip. The a.u.xiliary f'lame was always kept as low as possible so as to reduce the errors caused by this flame to a minimum. The au:rilie.ry f'lame seemed to have had no appreciable ef'f'eot on the main body of the Bunsen f'leme in that, where f'low conditions permitted, no change could be noticed in the Bunsen flame when the auxiliary burner was suddenly shut off'.

Fuels

Measurements were made using three commercial-grade fuels -propane, ethylene 1 and acetylene. Because acetylene is dissolved in acetone in the tank, an appreciable amount of acetone is present in the gaseous fuel. Most of' this acetone was removed by bubbling the acetylene-acetone gaseous mixture through flowing water. The combustion air used came from. the labot"atory service air supply 1 which, when expanded, had a relative humidity. of approximately 15 percent. No temperature control was used; very little variation of temperature, however, was observed.

Method of' Measuring Flame Speed

The ccmbustion zone of a laminar Bunsen flame is thin and clear-out, but :that of' a turbulent Bunsen flame consists of a

KACA Tl' Bo. 1707

"brush" of flame having a roughly conical shape but apparently formed of a rapidly fluctuating, much folded surface (fig. 2 (a)). Nevertheless, certain surf' aces can be identified in the turbulent flame; for example, 1n figure 2(b) an inner and outer envelope of' the fl.ame and a mean surface are indicated. A fl.ame speed cor­responding to each of these surf'aces may be determined. Although Damkohler (reference 2) believed that the inner and outer envelopes are related to the turbulent and normal flame speed, respectively, it is considered herein that the flame front has some average position around which it fluctuates, the degree of' fluctuation determining the position of the inner and outer envelopes. The turbulent flame speed should then be that flame speed corresponding to the surface that is the average position af the flame front, or

(1)

where

ut turbulent flame speed

Q volume rate of flow

S surface area af mean position of burning

The volume rate af flow was obtained by the flowmeter readings. The sur.f'aoe area of any given turbulent flame was determined in the fol­lowing manner: The flame was photogt>aphed on 5- by 7-inch film with an exposure time of' about 2 seconds. An average flame aurf'ace was drawn on the negative of the photograph and an attempt was made to draw the surface halfWay between the inner and outer envelopes of­the flame brush (fig. 2(b)). The surface area was then de'termined by the appro.xima.'te equation for cone-like surf'aoes o:f' revolution

where

L S =A­h

A area of longitudinal cross section of flame as pho'tographed

h height

L length of generating curve, excluding base, of cone-like surf' ace

(2)

This method has been used by others for laminar flames (reference 5).

It) Ol Ol

NA.CA T1i No. 1707 5

The amotmt a£ work required to detennine the surface area was shortened by plotting S/d2 against h/d where d is the burner­tube diameter. Once enough points had been plotted to form a curve, the sur.f'ace area could be found simply by measuring the height of the flame cone. The height was measured directly on the flame by means a£ a horizontal sliding arm mounted on a scale, sishts being placed 18 inches apart on the arm. In this wa:y, the whole flame could be kept within the field a£ view and fair reproducibility was possible.

Sane doubt :tney" exist as to the physical significance a£ a flame speed determined by the method outliD.ed; especially, it ms::r be that, although the idea of an average surface is sound, the positi'on half'wey between the inner and outer envelopes as seen on the photographs is not a tru.e average surf'ace. The data will therefore be presented first in tenns a£ flame geometry and then in terms of flame speeds.

The observations were made on fuel-air mixtures in each case having the maximum flame speed. Each measurement was made by use of a aeries a£ three or four observations in which the fuel-air ratio was varied in the neighborhood of that "ror maximum flame speed. The flame speed observed was taken as the maximum on a curve drawn through the data so taken. By this means e:ny errors due to inaccuracy a£ flow-measuring devices were eliminated.

RESULTS

Geometry of' Turbulent Bunsen Flames

Near the base a turbulent Btmeen flame is almost laminar in appearance. Higher up the flame front develops waviness; and still further up individual peaks a£ flame are observed to shoot up from the interior of. the inner cone. When these peaks of flame appear, the outer envelope begins to bend more sharply inward. These characteristics together with the three dimensionality of the flame make it dif'f'icult or impossible to locate the position of' the inner envelope with certainty.

The ratio a£ mean flame surface area to the square o£ the burner diameter sjd2 is plotted against the ratio of flame height to burne:r;- diameter h/d in figur., 3. The points from various burner sizes for a given fuel fall on a single curve when plotted in this manner. These curves indicate that the flame broadens out as the height becomes greater. For it, in becoming higher, all

6 llACA m Bo. 1707

vertical dimensions a£ a flame were merely stretched, the curve o£ surface area against heisht would be a straight line through the origin, which is obviously not the case.

In figure 4 it is shown that, for a.n::r one fuel, the height at the average position a£ a flame is roughly a function at Re1t1olds number. In every case 1 however, the curves a£ the smaller burners lie higher. The fuel-air ratio is in each case that correspondine to the maximum flame speed.

Same data of the height of the outer envelope a£ the flame brush were recorded. This height minus the height of the average sur.f'ace is one-half' the flame-brush width in the center at the tube. It has been plotted against Reynolds number in-figure 5. Although the scatter is great, the brush thickness seems to vary linearly with Reynolds number. The large scatter is due to the uncertainty­in locating the height af the outer envelope.

Turbulent Flame Speeds

Examples ot the variation a£ flame speed, as previously def'1ned1 with fuel concentration for various Reynolds numbers are shown in figure 6. The data shown were obtained by direct measurement at mean flame height. The fuel concentration for maximum flame speed is observed to be slightly ~icher for turbulent than for laminar flames. This effect is believed to be caused by the turbulent :flame seeming to widen out slightly as it becomes richer so that, for the same mean eur.face area, the height at a rich flame is lees than that of a lean flame •

The variation of flame speed with Reynolds number of pipe flow is shown in figure 7 for fuel concentrations of maximum flame speed. Values of normal flame speed from reference 4 are indicated for the three fuels by points on the ordinate. Reynolds number of flow is not necessarily descriptive, however, ar turbulence at the flame front. The data of' figure 7 were obtained both by photo­graphing the flame and by direct measurement af flame height; in both cases the mean eur.face area was obtained fran the curves in figure 3. The points representing data taken by direct measurement are the maximum flame speeds fran curves like those ot figure 6 and are therefore, in most cases, averages of several measurements. ~:Oat of the pointe represent1ne photographic data are averages of two separate :flame-speed determinations. The large scatter ar the acetylene flame speeds for the 3/8-inch-diameter burner at low Reynolds numbers is believed due to the fact that, because the flame was ema.ll1 a small absolute error in height measurEI!lent resulted in a large relative error.

NACA TN No. 1707 7

The data a£ figure 7 show several consistent characteristics. For arry one explosive mixture, the turbul.ent flame Slleeds are all greater than the normal flame speed and for a given Reynolds number, the flame speed increases with increasins burner diameter. In gen­eral, flame speed increased with Reynolds number but at a decreasins rate, and at the larger values a£ Reynolds number, flame speed approached aa;ymptoticallJ"a linear relation with Reynolds number.

DISCUSSION

Nature a£ Turbulence :i.n Pipe Flow

The fact that the flame speed as def'ined in turbulent flow cannot be determined with very high accuracy is a circumstance that is implicit in the very nature a£ turbulence. The results of' the measurements are principally an identif'ication of' certain trends in turbulent flame speed as summarized. It is thus desirable to iden­tif'y the nature of' the turbulence in which the measurements were made.

The theory of turbulent flow in general is reviewed in ref'er­ences 6 to a. It is concluded in the theory, particularly in reference a, that a scale factor and an intensity of turbulence are suf'f'icient to characterize isotropic turbulence. These two factors have been measured in various weys. The turbulent inten­sity based on lonsitudinal turbulent motion is shown in dimension­less form in figure a, as measured between two infinite planes (ref'erence 9); the distribution is expected to be similar to that in a tube. It is notable that the turbulence in the tube is not completely isotropic so that the mean turbulent intensities are dif'ferent in dif'ferent directions.

The mixing length has also been measured and is shown in figure a as publi.shed in ref'erence 6. It is evident that both mixing lengt;h and turbulence vary widely across the flow. It follows that insof'a.r as the turbulent flame speed is to be asso­ciated with the nature a£ the turbulence, it is a mean flame speed that is associated with an average type of turbulence in the gas issuing from a uniform tube.

In measurements of' flame speed in turbulent flow, the scale a£ the turbulence in the tube is proportional to the size a£ tube and the intensity component is proportional to the mean gas flow velocity, as follows from general similar~ty relation.

8 XACA T1f Ko. 1707

Theories at Turbulent Flame Speed

Damkohler (raf'erence 2) in an attempt to determine the ef'f'ect of' turbulence on :flame speed presents soma data. obtained :from a. Bunsen propane-oxygen flame on a. burner tube tha.t is long enough to have :fully developed turbulent :flow. It was :found that flame speeds corresponding to the outer envelopes were approximately equal to the normal :flame speed of' the mixture. The flame speed corresponding to the inner envelope was assumed to be the turbulent :flame speed. The ratio at the :flame speeds corresponding to the inner and outer envelopes was therefore considered equal to the ratio af turbulent flame speed to nom.al. flame speed. Results :from three burners of' 1.385-1 2.180-1 and 2. 718-millimater diameters were obtained. The :flame-speed ratio was than shown by somewhat limited data to vary linearly with the square root at the Reynolds num-ber ./Re :for the two smaller tubes in the range 2300 < Re < 5000 and linearly with Re :for the two larger tubes in the range 5000 < Ra < 181 000.

In the discussion of' results of' reference 2 1 two conditions of' turbulence are considered that depend on whether the scala af the turbulence is much greater or much less than the thickness of' the laminar f'lame front. Fine scale turbulence was considered to influence the rate o£ d1£f'us ion between the burned and unburned e;as without roughening the f'lame :front and large scale turbulence was considered only to roughen the :flame :front thus increasing its surface area. The theory developed attempted to show that f'or f'ine-scale turbulence,

(3)

and that :for large-scale turbulence

(4)

where

u is kinematic viscosity of explosive mixture

£ is turbulent diffusion coeff'icient

The turbulent dif'f'usion coef'ficient £ is an empirical factor that was devised to develop a theory f'or the turbulent-velocity

liACA TN No. 1707

distribution in a pipe or tube. By analogy with the molecular dif~usion coef~icient, it is written as

where

root mean square ~luctuating component of velocity

~ so-called mixing length, a scale ~actor

9

(5)

In the von KB.rma.n theory of pipe turbulence, the factors canprising £ enter into the theory as empirical parameters evaluated fran the velocity distribution, but equivalent or analogous quantities are directly measurable. It has_ been shown by direct observation that in turbulent pipe flow, Jii2 varies as the mean gas velocity, and that the scale, and therefore presumably l, varies as the pipe diameter. Both quantities are hardly approximately constant across the flow; but in predicting the results of any experiments dependent on €, it is apparent that mean € must vary as the Reynolds nu:oi­ber of the pipe ~low.

In re~erence 2, it was considered that the smallest burner used could be considered to give fine-scale turbulence; whereas the largest burrier gave large-scale turbulence, the difference of which was believed to account ~or the dif~erence in the dependence of ~lame-speed ratio on Reynolds number.

A theoretical analysis of the effect of turbu1ence an f1ame speed is presented in reference 3. The two cases of ~ine-scale and large-scale turbulence are again considered. Based upon the same considerations as in reference 2, the expression for turbulent flame speed tl.t in ~ine-scale turbulence was derived:

(6)

where K is the thermal conductivity due to molecular motion.

For the case of large-scale turbulence, the expression for ut was derived to be

(7)

10 NACA TN No. 1707

where B is a nondimensional coefficient and is approximately unity. It should be noted that flame speed for large-scale tur­bulence is here predicted to be independent of' the scale of tur­bulence ana to be independent of the normal fl~e speed if the

'intensity of turbulence u2 becomes great c~~pared to Un2 •

Test of Theories of Effect of Turbulence on Flame Speed

According to the theories of references 2 and ~' the flame speed in turbulent flow is predicted to depend on the turbulent diffusion coeff'icient e for small-scale turbulence. It has been

shown that E: = ~.fi2- and that E: should- ;ary as the Reynolds number of' flow Re inside the tube. Ii' the change of E: is neglected in the space between the tube outlet and the flame, it follows that the turbulent flame apeed is predicted :for small­scale turbulence (a) in reference 2 to vary as un ../Re', and (b) in reference 3 to vary as Un J1 + kRe where k is· a constant-. Actually the theories as presented were SO!llewhat more specific in their predictions. The predictions of' reference 3, for example,

_ would seem to approximate those of reference 2 because the second - term in the radical is much larger than 1.

Again for large-scale flame speed should -vary as

turbulence, the predictions are that UnR-e {ref'erence 2) and as

I _2 Un \J 1 -1--B ~ 2 (reference 3) • For the range o:f'---e.xperiments,

is approximately 1 foot-per second, and u2 varies in the range of-­magnitude of un2.

Summarizing the results of the flame-speed measurements, fig­ure 7 serves to give some f'airly definite indications as to whether the theories mentioned are accurate.

First, according to the theory of' turbulence in pipes or tubes, the mixing l-ength of __ the turbulent flows used is approximately 0.1 inch, which is definitely greater than the O.Odl inch usually considered to be the approx~te thickness of the laminar flame. The data show that': (a) The Reynolds number is inadequate alone to correlate the turbulent flame ap~ed; and (b) in any case the varia­tion of th-e turbulent flame speed with Reynolds number for a g1 ven tube is nonlinear in the range of large-scale turbulence. Accord­ing to the results of this investigation, it is seen that the theory

.& --

..

HA.CA TN. No. 1707 11

of reference 2 concerning the effect of large-scale turbulence on the flame speed in a Bunsen-burner flame thus appears to be in error as to the dependence on Reynolds number.

The turbulent intensities used are certainly large enough to indicate whether the turbulent flame speeds tend to be independent of the nature or the fuel at large values or u 2. That is, the curves for various fuels are predicted in reference 5 to converge at higher Reynolds numbers; however they show no sign of converging in the range of this investigation. It is concluded according to the results of this investigation that neither of these theories is properly applicable as proposed.

Nature of Variation of Turbulent-Flame Speed

The data af figure 7 obviously require more than one correla­tion variable. The fuel, velocity, and burner diameter are one possible set of parameters; the fuel, Reynolds number, and burner diameter are a possible alternative choice. Reynolds "number rather than velocity is used herein because or the general use af Reynolds number in the analysis or fluid behavior and because previous pro­posed theories used it. In any case, the choice of variables with which to correlate the data ·is arbitrary.

The general appearance af the data suggests ut/Un as a possible variable to express the effect of the fuel.

A second trend is indicated by the fact that ut at any value af Re is greater with larger tube diameter by a factor that varies proportionally with Un·

A third phenomenon is indicated by the curvature of the various graphs, suggesting that Ut might vary as a power af Reynolds num­ber different from 1, for ~ven fuel and burner diamet~r.

The data of figure 7 are used to fix the manner of variation of 1.1.t in the form

(8)

where

turbulent flame speed (om/sec)

c constant, empirically determined from data

12 HACA TN Ho. 1707

'Ltn normal flame speed (em/sec)

d burner diameter (em)

Re burner Reynolds number baaed on mean air speed and burner diameter

a, b, c exponents, empirically determined from. data

The exponent at the normal flame speed Un is chosen by inspection as equal to 1.

The exponent of the diameter d is fixed by cross-plotting the data o:f figure 7. The flame speeds ut taken f'ram the curves for the various tube sizes were compared for given Reynolds number and fuel. The comparison is shown in graphical form in figure 9. Relative flame speeds were compared for 11 different fuel-Reynolds­number choices with relative diam~ter for the 5/8-inch-diameter tube. The log plot is seen to be fairly representable as a straight line, though strictly speaking a alight curvature is noted through the points. The line as shown has a slope equal to 0.26 so that the exponent b a£ the burner diameter in equation (8) is

b = 0.26

The value of' the exponent c a£ Reynolds number in equation (8) is found by making log plots of' the quantity

(9)

as a function of' the burner-tube Reynolds number Re. The data for I

acetylene ethylene, and propane are plotted separately in fig­ures lO(a~, lO(b), and lO(c), respectively. The linea considered by inspection to represent the data moat accurately are indicated on the curves. The three curves are shown on figure lO(d) with the curve obtained by averaging the three. The correlation repre­sented by the average curve is suitable as approximating all the data. The scatter at experimental points is a little greater than would be anticipated f'ram the methods used.

The equation af the average curve (f'1g. lO(d)) 1s

ut 0.18 Re0 •24 u d0.26 ""

n

Is c c

co :0 :n

... NA.CA TN No. 1707 13

or

ut = 0.18 Und0 •26 Re0 • 2~ (10)

.Any uncertainty as to the exa.ot relation among the chosen variables might be removed by an extension of the experiments. It is possible, however, that the same kind of experimental uncer­tainty is to be anticipated in any study of turbulent flames.

The results here shown will suggest some approximate relations for use in future extensions of the theory.· Thus, approximately

The direct dependence of turbulent flame s:peed on laminar flame s:peed is in agreement with reference 2.

Whether these tentative conclusions are valid as a:p:plied to truly isotropic turbulence is an interesting :problem for future investigation.

sm.MARY OF RESULTS

From an investigation to determine the effect of Reynolds number in the turbulent -flow range on flame speeds of Bunsen­burner flames, the following results were obtained:

1. A correlation of the flame speed in a Bunsen burner with several variables has been empirically derived in the turbulent­flow range at sea-level atmospheric conditions in the form

Ut = 0.18 Und0 · 26 Re0 •24 (em/sec)

where

1lt turbulent flame speed

Un normal flame speed (transformation velocity), (em/sec)

BACA TN'lfo. 1707

d burner diameter, {om)

Re Reynolds number based on mean mixture speed and d

The experiments ranged from an Re ~ 3000 to :35, bOO, tube diameters Tram 0.626 to 2.843 centimeters, and the fuels were acetylene, ethylene, and propane. The fuel-air mirtures having maximum Un were used.

2. The theories ~ Damkohler on the effect of large-scale turbulence on the flame speed in a Bunsen-burner flame we~e veri­fied as to the dependence on laminar flame speed, but were found to be erroneous as to the dependence on Reynolds number.

3. The theory of Shelkin was not verified in that no tendency ~s observed of ttirbulent flame speeds ~ different fuels to approach each other at high f'iow rates.

Flight Propulsion Research Laboratory, National Advisory Committee for Aeronautics,

Cleveland, Ohio, June 30, 1948.

1. Burk, R. E., and Grummitt, Oliver: The Chemical Be.okground for Engine Research. Intersoienoe Pub. , Inc. (New York), 194:3, pp. 38; 39.

2 • Da.rakb'b.ler, Gerhard : The Erf'eot o£ 'rurbulence on the Flame Velocity in Gas Mixtures • NACA TM No. 1112, 194 7.

3. Shelkin, K. I. : On Combustion in a Turbulent Flow. NACA TM No. 1110, 1947.

4. Smith, Francia A.; and Pickering, s. F.: Measurements of Flame Velocity by a Mod:tf'ied Burner Method. Res. Paper RP 9001 Jour. Res. Nat. Bur. Standards, vol. 17, no. 1, July 1936, pp. 7-43.

5. Corsiglia, John: New Method for Determining Ignition Velocity­of Air and Gas Mixtures. Am. Gas Assoo. Monthly, vol. XIII, no •. 10, Oct. 1931, pp. 437-442.

6. Bakhmeteff, Boris A. : The Mechanics of' Turbulent Flow. Princeton Univ. Press (Princeton), 1941, p. 53.

,

•

NACA TN No. 1707

7 . Taylor 1 G. I. : Statistical Theory o£ Turbulence. Proc. Roy. Soc. London, ser. A, vol. CLI, no. A873 1 Sept. 1935, pp. 421-478.

8. Dryden, Hugh L.: A Review of the Statistical Theory of Tur­bulence. Quarterly Appl. Math., vol. 1, no. 1, April 1943, pp. 7-42.

9. Prandtl, L.: Beitrag zum Turbulenz Symposium. Proc. Fifth International Congress for Appl. Mechanics (Cambridge), Sept. 12-16, 1943, pp. 340-346.

15

Propane -

ir-

Mixer

Figure 1. - Diagram of burner air-fuel system.

Water jacket

Burner tube

..

z > ~ -1 z z 0

NACA TN No. 1707

~ c-21319 ... 30·<48

(a) ;B'lame •

Boundaries of' tlame brush Location of' tl&llle mean surface

(b) name showing brush and tJ.ame mean surface outlined.

ll'isure 2. - Tllrbulent Bunsen-burner tlame. Nominal diameter of' burner, 3/6 inohj etl:Jylene gas in air.

17

') , ,

NACA TN No. 1707

20

10

0

30

10

0

.(0

30

10

0 0

/

/ ~ Acetylene

~y 11

J~ V'"'

~

/ 1'"'\

/ v

c// ,v

""'~ (~

v Ethylene

0" 2' ~

~ '<::I

--'11

~ ~

f.-Q'

v: <V

0 ,A

/ /0

/ v Propane

/~ l? Nau1nal d1amete~

~ of: burner

...... ~ ~ (in.)

~

~ -~

0 8

A <> ~ 8

~ IP' 0 l!'

8

~ 15 5 Flame hei~t 10

Burner inside a\&mater

Figu~e 3. - Va~lat1on ~f mean fla~e helsht divided by burner inside diameter squared w1th fla~e height divided by burner 1nstde diameter.

19

B 0

i .-1 .. 'o

i ..

20

1 0

• "'lO

5

c

A

0

0 a

-l.nal. d.l.oo.o1;er otbul'ller

(in.)

.!:. ' ~ lJ ~ 8 1

lij

~ A ~ ~

~ ~ v ~ ~ v .....,

~ ~ u k-<: t::-v

s"' ~ v f"

v ~-< c __.f-o

' ~ ~ fJ

'

lq,_ /

/. v ./ v It"\

L ~ v V:: v v

k:: ~ ~ k:: 81 ~ v p.--..--

/ f%: ~ IcY"' 1-

~ r:..o kY: I-' b.-:-" ~--""'"'" v v I-' ~ v

!.a v v ~ v v v

'~

~1...-.o 1-~ ~ v

~ I<Y v ~

-.. ~· "' Re;rnoldo llUllbe1-

Pisur• '· - Taria~n ~ _. t1 ... hol.pj; rtth f\o7DO~ IU.IIIbm-,

PI'Opana v v v 1-

v

Bth;r1ono c:::: f-f-" 1-"

1::::::::

AootJl.eno

iiO

,...v

---cf

.

-

....., ~

'o:uu

:z > (")

> -{ :z: z 0

-..1 0 -..1

NACA TN No. 1707 21

Nominal d.1 ame tar or burner

(in.)

Propane

3 0 8

<> 5 8

0 1 1-8

Acetylene , q_ 3

8

~ 5 -8

30 / Propane

v v.~

0

<> /<>

25

A~ Q Acetylene Q

_) [7 QQ

0 v

0 vc, n ~

0 / ./ 6 ~

~ ~ ~~ "<:

~ ~ ~

~

Q } ~ ( ~~' ~~ ~

/Q; ~q_

~ ~

20

15

10

5

0 30 35 0 5 10 15 20 25 40xlo3

Reynolds number Figure 5. - Varistlon or flame-brush width with Reynolds number.

22 NACA TN No. 1707

'

Reynolds number

130

0.

I - 33,700 0 120

...[J l-9::::o.. 26' 000

A . --:-i. ~18 00

_/' ~·12,500\ I y~ ~ 9,700 ~

7 / \ j <!'!

! / ___;

\ ~7,800

I - 5,940 1~ 17,500 .. 7 ~ \ y ---.~

~- ....... 4, 000 \ .........,;: ~ II y "3,000 \ .)

110

() ll Q'l

~ 100

.J' G) G) p, 90 "' <D

~ r-1 ~

+> 80 1::: G)

~

~ 70

I \.. / \ 60

1

50 ,

40

30

~ 4 5 6 7 8 9 10

Percent fuel Figure 6• - Variation or flame speed with fuel concentration. Burner diamet-er,

3/8 inch; ruel, ethylene iri air, ·

NACA TN No. 1707

~ Acetylene /

300 I/ / v

[7 0 6--' b. ~~ '""

vv ~ v v

/ ~ lA ¢ ~ v/" - / !:if

lo--v

/ vo

~

/ v v 250

..;:: v~

) p/ v~ 0

/ r'

0 .. ., 200 -s

0

/ c

_/

i .. 'c c llo • ., ! .... .. s:: .. 150 ... I r-- "n· acetylene (147 em/sec)

l.--~ Ethylene A l.-- ,..

r '1~ eth_ylene f.- ~ ~.

70 ~~~ec) t,....--: 1---

I ~ V'~ h9- v !--"-' ) '(: lA<

I !« .Cl~ ..... 100

II A v Propane

ri ~b. b .L'. lo-~ 1-

tv-- b __;: ~ ~ ~1:5" i'J'

("' r--' y; ~ - ~-

( Nominal diameter

N ~ ~- o:t burner

95 eX-~ t--- (in.) -, 1

I"- "n· propane (45 om/sec) t::.. "i 3

0 ~

50

0 5 ~

0 1

la

10 20 30 ,.,

40xl0 Reynolds number or pipe :flow .

Figure 7. - Variation o:t :fl11111e speed -.:1 th Reynolds number o:r :flow. (Normal :tlmne speed "n :fran reference 4.)

23

24

.15

~ ~

.. .10 I»

-!.:>

(\ ~

"' oN OJ s::: Q)

-!.:> s:::

oN

-!.:> s::: .05 Q) ..... ~ .c

~

0

.15

.10

I (

0 v 0

~

v

r---t---1--. ~

t---v v /

v

.5 Distance from wall

TUbe radius

NACA TN No. 1707

........... .... 1---

1---1---~

"@? _j

1.0

Figure 8. - R~presentative distribution across tube of turbulent intensity U2;u (reference 9) and mixing length t (reference 6).

..

co co C11

·. NACA TN No. 1707 25

10 I I

8 I I

6 0 Acetylene

0 Ethylene

6. Propane

4

3

2 'C Q) Q) p.

"' Q)

~ ,...., 1..() .....

--A ~ ~

1-~--' Q) ;:. .a or! ...,

J,.....--1 r l.--1

ol ,...., Q) .6 p:: --~

Slope, 0.26 -.4

.3

.2

.1 .1

~ .2 .3 .4 .6 .8 1.0 2 3 4 6

Relative diameter

Figure 9. - Variation or relative rlame speed with relative burner diameter, based on 5/8-inch burner. -

8 10

26

;>rt

10

8

6

4

3

2

1.0

.a

.6

.4

.3

.2

.l 1

EJ

<>

___.. ~

2

Nominal diameter of burner

(in.)

3 8 5 8

- Ali Jl!.o efo

p p ::0......6~ ...,

.....,., [J c

4 6 8 JD 20 Burner~tube Reynolds number

(a) Acetylene in air.

30

NACA TN No. 1707

-.-1--0

~ 40 so eo J.Ooxio~

Figure 10. - Ut as a function of burner-tube Reynolds number. Turbulent u do.M

n

flame speed ut, centimeters pe~ second; normal flame speed ~· centimeters per second; diameter d, centimeters.

•

IS) en en

NACA TN No. 1707 27

10

8 Nominal diameter

o:f burner {in.)

6 3

[J ~

¢ 5 8 4

~ -2

@¢~ ~121 @

~ 0 <:E 1~ 0

0 ...-- ~ [

8

. 3

2

~ 1 1 3 4 6 8 10 20 30 40 60 80 lOOx.ro-3

Figure 10. - Continued.

Burner-tube Reynolds number {b) Ethylene in air.

Undo.2s as a !"unction o~ burner-tube Reynolds number.

Turbulent !"lame speed ut, centimeters per second; normal. !'lame speed Un• centimeters per second; diameter d, centimeters.

28

10 '

8

6 0

4 Cl

<> :5

6.

2

.. r;f 1.0 --.a

.6

.4

.3

• 2

.1 1 2

Nominal diameter o£ burner

(in.)

1 4 3 8 5 a l

l-8

~A~~ pea l ... ~ §l

p

cjQaooE <> !!"

.

'

3 4 6 8 lO 20 Burner-tube Reynolds number

(c) Propane in air.

NACA TN No. 1707

---

. -

j...- 1--

~ 30 40 60 so lOOxlo3

Figure 10. - Continued. ~do.M

as o function or burner-tube Reynolds number.

Turbulent flame speed Ut• centimeters per second; normal flame speed un•

centimeters per second; diameter d, centimeters.

•

NACA TN No. 1707 29

10 I I I I f I I I

8 --Acetylene -----Ethylene

6 ----Propane Ut 0.24

Average curve, = 0.18 Re Und0.26

4

1--I-

~ ~---

~ ~ I; ~.---· ~ . -- ~..;.::::-::: -

1-t:; ~~ 1- --- . 2

~ ~ ~-

r..;...~-"

.-- 1--

___. ~---

.6

.4

.3

.2

~ 2 4 6 8 10 20 30 40 60 80 lOOxW

Figure 10. - Concluded.

Burner-tube Reynolds number (d) Comparison or ruels.

Undo.26 as a function or burner-tube Reynolds number.

Turbulent £lame ~peed ut, centimeters per second; normal flame speed lln• centimeters per second; diameter d, centimeters.

TITLE: Lffect of Reynolds Number in the Turbulent-Flow Range of Flame Speeds of Bunsen-Burner Flames

OTO-35800 OfvnioN

(None) AUTHOR(S):Bollinger, L. M.; Williams, D. T. ORIGINATING AGENCY: Flight Propulsion Research Lab., Cleveland, 0.

OalO. ACEMCT NO. TN-1707

PUBLISHED BY: National Advisory Committee for Aeronautics, Washington, D. C. FUUBKIMO AOXMCV NO.

(Same) OATH

SeDt ' 48 DOC OAS3.

Unclass. COUMIUV

U.S. UNOUAOf

EnK. PAOO 29

ruununoia photo, diaer. graphs

The effect of* flow conditions on the geometry of the turbulent Bensen flame was investi- gated. Turbulent flame speed is defined in terms of flame geometry, and data are pre- sented showing the effect of Reynolds Number of flow in the range of 3000 to 35,000 on flame speed for burner diameters from 1/4 to 1-1/8 in. for three fuels: acetylene, ethylene, and propane. The normal flame speed of an explosive mixture was shown to be an important factor in determining its turbulent flame speed. The .urbulent flame speed is a function of both the Reynolds Number of the turbulent flow in the burner tube and of the tube diameter.

DISTRIBUTION: Request copies of this report only from Publishing Agency DIVISION: Thermodynamics (18) SECTION: Combustion (2)

ATI SHEET NO.: R-18-2-5

SUBJECT HEADINGS: Flame propagation - Effect of turbulence (37313.4)

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