Laminar burning velocity of acetylene-air mixtures by the constant volume method: Dependence on mixture composition, pressure and temperature

Lam&ar Burning Velocity of Acetylene-Air Mixtures by the Constant Volume Method." Dependence on Mixture Composition, Pressure and Temperature C. J. RALLIS, A. M. GARFORZHand J. A. STEINZ Department of Mechanical Engineering, University of the Witwatersrand, Johannesburg, South Africa (First version received September 1962: after further work final version received dul)' 1965)

One o[ the main purposes of this paper has been to provide an evaluation of the spherical constant volume vessel method with particular reference to its use over the full range of the combustion process. To this end basic equations, as well as a variety of corroborative relations, applicable throughout the process are derived. These have been used to obtain results on the e~ects of mixture composition, pressure and temperature on the burning velocity o[ some acetylene-air mixtures. The nature of the pressure and temperature dependence appears to be more complex than has hitherto been found.

Notation

Introduction

M n P r R S t T

molecular weight mass fraction burnt pressure flame front radius radius of sphericalvessel velocity time temperature ratio of mean density of burnt gas to initial density of mixture fl ratio of mean density of unburnt gas to initial density of mixture fl" ratio of density of unburnt gas iramediately ahead of the flame front to initial density of mixture -/ ratio of heat capacities p density

ONE of the intrinsic properties of any combustible mixture is its laminar burning velocity. Evidently this property is a function of the type of fuel, mixture composition, temperature and pressure of the unburnt gas. In the present study, the constant volume combustion method has been used to determine the quantitative effects of these parameters on burning velocity. It appears to be generally conceded that the spherical constant volume technique is potentially one of the most versatile and accurate for determining laminar burning velocities. Two main difficulties are, however, experienced with this method. First, since burning velocity cannot be measured directly, reliable equations are necessary for its calculation. Secondly, extremely accurate measurements are needed (particularly of the flame propagation and the pressure rise during combustion) resulting in complex apparatus. The theoretical relationships used by m a n y previous investigators are only applicable to the early stages of combustion during which the pressure and temperature of the unburnt

Subscripts

b based on burnt gas properties e final condition s spatial 0 initial condition t based on combined burnt and unburnt gas properties u based on unburnt gas properties 345

346

C.J. Rallis, A. M. Garforth and J. A, Steinz

gas do not change significantly. This virtually relegates the method to the status of a constant pressure technique, One of the main purposes of the tests reported herein has been to provide a basis for a critical evaluation of the spherical constant volume vessel method. Only the essential data and results are presented and the reader is referred to refs. 37, 38 and 39 for comprehensive information regarding all phases of the project as well as tabulated test results, The sections in this paper deal briefly with the theory of the method, including recent modifications and a more convenient theoretical relationship, as well as a brief survey of the results of previous investigators. A condensed description of the apparatus is presented, fop lowed by the results on the effect of mixture strength, unburnt gas pressure and temperature on the burning velocity of some acetylene-air mixtures. A consideration of the reproducibility and accuracy of results leads to a confirmation of the potentialities of the constant volume method. Brief Literature Review The literature abounds with information on burning velocity. Much of this, however, must be considered of doubtful reliability because of inherent limitations in the methods used. Also, with the pressure dependence data, the mixture temperature is frequently not reported, This review is not intended to be exhaustive. Only sufficient sources are included to indicate qualitative trends or to illustrate the prevailing confusion,

Effect of mixture composition It is well established that burning velocities v a r y with mixture strength, m a x i m u m velocity generally occurring on the fuel rich side. The position of this m a x i m u m also varies with oxygen concentration ~. Mixture composition studies have been carried out on a variety of fuels with different initial conditions using burner2-% flat flame r,s, soap bubbl& -~2 and constant volume ~:~ methods. Evidently mixture strength also affects the pressure and ternperature dependence of burning velocity",~4, Pressure dependence Confusion apparently exists regarding the

Vol. 9

pressure dependence of laminar burning velocity. This is particularly so with fuel-air mixtures. Earlier results generally indicate an increase of burning velocity with reduction of pressure 15-~". However, positive, negative and no dependence has also been reported =°-22. J. MANTON'S results suggest pressure dependence to be a function of the absolute value of burning velocity 2a,2~. Evidently, a critical velocity exists above which pressure dependence is positive and below which it is negative. D . K . KUEHL has observed the same effect2~. Further illustration of the prevailing confusion is provided by results on ethylene and acetylene mixtures. A negative pressure dependence of the form St 07. P-°":' has been suggested by J. E. GARSlDE, J. S. FORSYTHE and D . T . A . TOWNEND2s, and by P. J. WHEATLEY and J. W. LINNETT27. Others to report a negative dependence, using various methods, are A. C. EGERTON et al. 8,28, L. B. GRAIFFla and M. GILBERT'~. No pressure deoendence was found by J. GRUMER et al. 29 or by G. W. CULSHAW and J. E. GARSIDEa'. W. A. STRAUSS and R. EDSE propose a positive dependenceaL With specific reference to results on acetylene-air mixtures, A. G. GAYDON and H. G. WOLFHARD a'22,~2 and P. J. WHEATLEY and J . W . LINNETT~= report the burning velocity to be essentially independent of pressure over the range 5 m m of mercury to one atmosphere. This conclusion is supported by M. GILBERT'S studies on a range of acetylene-oxygen-nitrogen mixtures'L L. B. GRAIFF confirms this but does not exclude the possibility of a positive pressure dependence between two and ten atmospheres ~3. A . G . GAYDON and H. G. WOLFHARD also indieate that acetylene-air m a y have a m a x i m u m burning velocity at 2(t cm of mercury a. Temperalure dependence Of the three factors affecting burning velocity considered here, probably the least information is available on the effects of temperature. Most of the data indicate a marked increase in burning velocity with increase in unburnt gas temperature. Thus G. L. DUGGER et al. "~3''~4, using a burner method for a range of hydrocarbon fuels, suggest an equation of the form S,( .......) = A T e ( B - 3 . )

December 1965 Laminar burning velocity of acetylene-air mixtures by constant volume method

347

where A , B and n are constants for a particular fuel and ,\ is the mole fraction of oxygen in the mixture. S. HEIMEL and R. C. WEAST ~5 as welt as D. K. KUEHL-'~ have proposed similar relationships for h y d r o c a r b o n fuels, W. C..JOHNSTON '~ concluded that the effect of temperature on burning velocity is marked :and positive.

[8]

rn, = (4v./3) (R 3 -r~,:') p . . . . .

~here -~,,, the mean density of the unburnt gas, is introduced to allow for possible non-uniform properties resulting from pressure gradients :'7. Hence n,,

(rob~m,,)

= 1 - (mu/m,,)

]91

....

= l - /~ + fi(r,,/ R):'

Theoretical Relationships From the equation of continuity, the mass rate

where

of transfer of unburnt gas (of density p,,) across a flame front of area A is evidently (dm,,/dt)=Ao,S . . . . . [1]

Substituting the time derivative of n~ from equatioa 9 into equation 7 yields the unburnt gas equation

where S,, is the velocity, measured perpendicularly to the flame front, with which the unburnt gas crosses this front and is transformed . Now since for constant volume combustion:

S,=

m,, = .z,, - .z, . . . . .

fl=(pu/f'o)

(i~/[Y)I(dr~ldt) . where

.

[10]

{(R:'-r~:')l(ar,,'-'fi)}(did/dt)l

.

[ 11 ]

. /Y= (t,,, / ~,,,)

[ 2]

and consequently

....

112] .

.

.

.

The burnt gas equation

(dm,/dt) = -(dm,,/dt)

....

t3]

it follows that S,,=(1/Ai,,,)(dm~/dt) .... [4] where S,, has been changed to S~, to emphasize the use of the burnt gas formation rate (dm~,/dr). Defining the mass fraction burnt as n = (m,,/m.,)

....

The mass of burnt gas at any instant is mb=(4~/3)rd~pb .... [13] where, as above, t)~,, the mean density of the burnt gas, allows for non-uniformities in the properties of the gas behind the flame front due to pressure and temperature gradients and other possible effects :~. Hence it follows that

[5]

n~ = ( m ~ / m o ) = ~ ( r ~ / R ) '~

....

[14]

where it follows that (d~l dr)

a = (tT,,/t>,,) (1/m,)(dm,,/dt)

=-(1/m:,)(dm,,/dt)

....

[6]

....

]7]

honce S,=S,,--(m./Ap,,)(dn/dt

It is possible to determine three relationships for the mass fraction burnt b y considering the properties of the unburnt and burnt gases separately and then simultaneously as follows,

Substitution of the time derivative ( d n ~ / d t ) equation 7 yields the burnt gas equation

in

S,, = (~//3) [(drb / dr) + (r,,/3~)(d~ / dr)] . . . . [16] The combined

equation

Since equations 9 and 14 represent the same quantity, they can be equated to yield the so-called combined equation for mass fraction burnt, that is

The unburnt gas equation

F o r isotropie flame propagation in a constant volume spherical vessel, A=4~r~ 2 and m..= (4,-./3) R'~p,,. In addition the mass of unburnt gas at a n y instant is

n, = ~ ( f l - 1 ) / ( p - ~ ) . . . . ]17] Substituting the time derivative of n~ into equation 7 yields a combined equation for burning velocity, that is

348

('. J. Rallis, A. M. Garforth and J. A. Steinz

S t = ~ ( B / f l ' ) t (dr~,/dt + {rvfi (1 - ~)/3~ (B - ~)} (d/dt) (~//~)] ....

[18]

This equation, which is one of the possible forms of the combined equation, is particularly convenient for calculating purposes and does not magnify experimental errors. Many of the various forms of burning velocity equations proposed in the literature follox~. directly as special cases of one of the above'~L

Corroborative relationships In addition to the different forms of burning velocity and mass fraction burnt equations already presented, various corroborative tests may be applied to the constant volume method, These help to provide an indication both of the validity of assumptions made and of the reliability of the results obtained, The density ratio ~ yields an assessment of errors involved in using flame front values in place of mean burnt and unburnt gas properties, It also provides an indication of the extent to which equilibrium conditions are attained behind the flame front. The equations available for the calculation of ~ are :

~-(p~/t,,,)-(T,,/M,,)(M,,/T,,)(P,,/P,,)

119]

and since at the end of the process p,.-i)o

~=(m/p,)=(T~/M,)(M~/T~)(p~,/p,.)

120]

A comparison of the observed maximum pressure and the theoretically calculated maximum (equation 21), gives an indication of the validity of the assumption of adiabatic compression,

F,=(Mo/M,.)(T~/To)P,,

....

[21]

The three equations 9, 14 and 17 for mass fraction burnt and particularly their time derivatives, provide an important check on the accuracy of burning velocity, By using an equation for flame front radius,

r~,, in the form 37 rb=R[(/~-l)/(t3-~.)]';

3 ....

[22]

and comparing the values with those observed during combustion, it is possible to ascertain

Vol. 9

the effects of finite pressure wave propagation velocity in the constant volume vessel. A further check on equilibrium conditions behind the flame front is provided by a cornparison of instantaneous observed pressure and the corresponding pressure calculated from the implicit relationshipaL

(P/P,.) (r~,/R) :~+ (P/P,,)'/~,] 1 - (r,,/R) a] .

.

.

.

~

1

[23]

Apparatus The combustion vessel consists of two flanged sections and a ~aindow ring which when clamped together form an internal spherical cavity of 6.306 in. (16-02 cm) diameter. The vessel is provided with a flush diaphragm capacitance transducer unit and associated circuitry for measuring combustion pressures. The output of this transducer is displayed simultaneously on both beams of a double-beam oscilloscope, each beam being set at a different sensitivity. The resulting combined high- and low-range pressure record is photographed via a drum camera on 70 mm film (Figure I). The instantaneous flame radius, as seen through the Perspex slit window, is photographed using another drum camera (Figure 2). Timing marks on both pressure and flame trace records are provided by two neon glow lamos fed by a single oscillator set at a frequency of 1 kc/s. A balanced diaphragm transducer unit is used in conjunction with a U-tube manometer to measure mixture component partial pressures. The initial mixture temperature is measured by thermocouples. Valves are provided to allow mixture components to be fed into the vessel. The bomb is mounted with its slit window in a vertical plane so that any buoyancy effects of the hot flame ball may be observed. Sphericity check ionization gaps together with associated circuitry provide a check on flame front sphericity. The mixture is ignited by a capacitive spark across a 0.040 in. gap centrally situated in the bomb. The soark Dotential is provided by a high-voltage ignition circuit. The voltage for the tests reported was of the order of 6.5 kV. Details of test procedure and transcription of observations can be found in ref. 38.

December 1965 Laminar burning velocity of acetylene-air mixtures b y constant volume method

Figure I. Typical pressure / time record

Figure 2. Typical radius/time record

349

350

C.J. Rallis, A. M. Garforth and J. A. Steinz

Dependence on Mixture Composition, Pressure and Temperature All the tests reported were carried out on acetylene-air mixtures. Burning velocities were calculated using equation 18. The initial condi-

VoI.

dent of both pressure and temperature. Such extrapolation is not possible on the rich side clue to insufficient data being available. Considerably richer mixtures than that of test A were successfully fired in the bomb, but due

Test initial conditions Table 1. Data Jor tests A to F Test o, ,o C 2 H - by volume Po" lb/in2 abs.

10' °R

A

B

C

12.59 12.08 533-9

9-87 12.07 533.9

7.72 12.09 530.8

tions of tests A to F were always ambient (~-~ 12.1 lb/in2 abs. and 535°R). For the G and H series, mixtures were stoichiometric with ambient initial temperatures but varying initial

.

535.0

G3

537-5

540.0

Table 3. Data for tests HI to H6 C H by volume--7"72 per cent 2

PO' l b / i n : abs. T 0, ° R

.

F

4.75 12.10 535-4

3-31 12.10' 539.1

~

1

140

Table 2. Data [or tests G1 to G3 C 2 H by volume--7.72 per cent GI G2

T~ °R

Test

E

5.99 12.08 534-4

to carbon deposition on the slit windows the flame traces were so underexposed as to prevent satisfactory transcription. 160 400

pressures.

Test

D

350

120 60

"~_100

Ib/in2abs.~824°R

/]/

300

[ \ \

,

250 oE

o

% 80 >

.

HI

n2

H3

H4

H5

H6

12"05 538

8-10 540

4'73 540

14'66 547

20"04 544'5

25-76 528

Results

In general a set consisted of two or more successful tests on a given mixture. For tests A to F, means of the observations were first calculated and burning velocities then determined. In the G and H series, burning velocities were calculated for each separate test and the means subsequently found, Comprehensive results are available in ref. 39.

200

~c

~ 60 c2

|50

4o

20

t

/ ¢ t , / / ~20 Ib/in2abs~615° R ~3/~, ~ " ~1~-7 [b/in2 a b s . ~ 5 6 5 o R ,$r/lIb'Z//i -_.~121 Ib/inZabs~535* R / 7~ ' ~ ," l, [. . . . 4 8 10 12 "/o Acetytene (by votume)

l

"~ co

loo 5O

0 14

l.igum~ 3. Burning velocity versus mixture strength 1or acetylene-air mixtures

Mixture composition dependence

The dependence of burning velocity on mixture composition is shown in F i g u r e 3. The temperatures corresponding to each member of this family of curves are average values, since -/,, is not the same for each separate mixture, Extrapolation of these curves on the lean side provides an estimate of the lower inflammability limit as 2"6 per cent of acetylene for acetyleneair mixtures. This limit appears to be indepen-

M e t h o d or obtaining pressure and t e m p e r a t u r e d e p e n d e n c e data

The burning velocity versus pressure curves obtained are shown in Figure 4. The curves representing the almost identical sets of tests G1 and H1, G2 and H4 as well as G3 and H5 are loaded means, that is greater credence has been given to those sets which are believed to be more accurate. This is justified since the

December 1965 Laminar burning velocity of acetylene-air mixtures by constant volume method

/420

,,,,,,

,

,

,

,

,

.

.

.

.

.

.

.

.

.

i

.

.

.

.

.

.

.

.

.

.

.

.

351

.

C,GLHI ~ . 380-"

~

Tests H2

3,0 ~-

"~

~

o Tests 63, H5

W,~~.~K.-_~)z

00!

TestsH6

~

~

O0

--

~J~"

j -

260 es 220 180

I~O 1000

~o~ llllll

] I

I

2.0

I

[

I

4-0

l

l

I

I

I

I

I

I

6-0 8"0 Pressure, atm

I

I

[

l

10"0

I

l

]

l

12"0

J

[

l

l

14"0

I

[:igure 4. Pressure dependence of stoichiometric acetylene-~ir mixtures

results of tests with essentially identical initial conditions are reproducible to well within the estimated error bounds. The effects of oressure and unburnt gas temperature were separated b y superimposing isotherms on the S t / P plot of Figure 4. The pressure corresponding to anv required unburnt gas temperature for a specific test was caleulated from the adiabatic relation °

P = P , , (T,,/T,,)L,."L,-"

The temperature dependence curves of Figure'5 were obtained from Figure 4 b y reading off the values of burning velocity for different temperatures at constant pressures. To conform with accepted practice, burning velocities, pressures and temperatures are expressed in centimetres per second, atmospheres and degrees Kelvin respectively. Pressure dependence Figure 4 shows the pressure dependence of laminar burning velocity of stoichiometric acetylene-air mixtures to be a somewhat com-

plex function of both u n b u r n t gas pressure and temperature. p~- ~

~

~

~

~

~

~

~

:

400~t 360 -

/ ~ 7 ,5

.p. o~ 320 ~;,

/ 9

9 ~1,

g 280 ~> .~ 240 E m 2 200

1601

2 ~/0~.5f'°

120 1 ~- : r r r i I l r r T 00300 340 380 420 460 500 Temperature, °K Figure 5. Temperature dependence oJ stoichiometrie acetylene-air mixtures

352

C.J. Rallis, A. M. Garf0rth and J. A. Steinz

The pressure dependence curves evidently undergo a transition at about 370°K. For temperatures below this value, the curves show both a minimum and a maximum (the latter occurring at a lower pressure), while the higher temperature isotherms only show a maximum, Furthermore, burning velocity apparently tends to become independent of pressure in the region of both high temperatures and pressures, It would seem reasonable to assume that the lower temperature isotherms follow this trend in the higher pressure region although there is no evidence as yet to corroborate this. The general consistency of the isotherms at the lowest pressures where observations were taken, suggests a continuing positive pressure dependence at still lower pressures, Temperature dependence

The temperature dependence of laminar burn-

Vol. 9

ing velocity, shown in Figure 5, appears to be of a strong and varying positive nature. The intermediate isobars (1 to 5 atm) show changes in the rate of rise of burning velocity with increased unburnt gas temperature, passing from concave upwards at lower temperatures to concave downwards for higher temperature values. The remaining isobars are monotonic over the observed regions, No inflection points in these curves are anticipated in the regions outside the area where observations were taken if the pressure dependence curves continue to even out at higher pressures as seems to be suggested. Th~ three-dimensional representation of Figure 6 provides an illustration of the combined effects of unburnt gas pressure and temperature on the burning velocity of stoichiometric acetylene--air mixtures.

Figure 6. Three-dimensional representation o[ combined effects o[ pressure and temperature on burning velocity of stoichiometric acetylene-air mixtures

December 1965 Laminar burning velocity of acetylene-air mixtures by" constant volume method Comparison with literature values

For the purposes of comparison of mixture composition effects, two curves have been extracted from Figure 3 and shown together with values obtained by other methods in Figure 7. These are the curves at 12.1 lb/in 2 abs. ( ~ 535°R) and 14.7 lb/in 2 abs. ( ~ 565°R). In general the agreement with the more reliable literature results is good, both as regards absolute values and variation with mixture strength,

70

Ref 4 180 Ref 5 ~ " \ Ref. 9 ~ef 3 \ ~ ~,,,,,,2%,~tll Ref.~ Th~sstudy .S~.~Z.~..:~.~..\,~ef. 6 160 14.Ttb/~n~ ,,.~ ~ .

60 ~.~ 50 c

This study

~/.It2;; IlZ / y " -- -

12.1 [b/in 2-

~,~ %.

120 >~

Ref. 8 20cm H.

cl~ 20

230

-loo

/ /

;30 c

have been unable to locate literature information on this aspect. The only results, to the authors' knowledge, which bear any resemblance to those of this investigation are due to Wheatley and LinnetW. Although those authors prefer to state burning velocity to be independent of pressure, in view of the fact that they considered their measurement errors too large to warrant any other conclusions, their results do nevertheless indicate a similar general trend in the subatmospheric pressure range, as is shown in Figure 8. The figure also shows that Graiff's observations ~ are in fairly close agreement with the approximately ambient temperature isotherm (300°K) of this study, although he could not have inferred this trend from only three tests.

"~,k'~Ref.2

//

o

>

220

60 N ~

210

80

' ' A

40

f'/ 10

"~ 2 0 0 ~

20

,' Ref.8 (50cm Hg) 0 d~RefTI 4

35"t

I

I 8

I

I

6 10 12 14 % Acetylene by volume Figure 7. Burning velocities of acetylene-air mixtures by various methods Re].

Me:hod

Pressure

2 3 4 5 6 7 8 9 10 11 12 13

Burlier ,.

I aim 1 to 76 c m H g 1 atm ,, 25 c m H 2 1 atm 20' to 50 c m Hg 30 to 76 c m Hg I atm

,,

(?)

Flat "flame . Soal~ b u b b l e

C~'V. b o ' m b

19'3 to 6½[9 c m Hg 1/2 to 2 arm

>', =~

.~ {

O 150

i

~ - --x10% C2H2 - Ar - 0 2 (Ar/02 =79/21)(Ref 12)

i -

. . . . + 10°/o C2Hz-Air(Ref 12) • 7'72% C2H2-Air(Ret 13) ' 7-72% C2H2-Air at 300°14

~ ~ -] ÷

(This study)

_, - ' ,

~

-

',

.,~.

-

I

o~

.~ 140 ~ ca

. '130

- - - - / - -

~ ~

"

/

o

1

"120

110)

0.5

10

1'5

2"0

2"5

Pressure, a t m Figure 8. Comparison with literature data

The results of this study appear to contradict the general opinion that burning velocity is either entirely independent of pressure or negatively dependent on this parameter. A cornparison of pressure dependence data at elevated temperatures is impossible, since the authors

The marked temperature dependence indieated by the results of this study are in accord with the generally held belief that temperature is an important factor. However, these curves are not of the monotonic nature suggested by many other investigators. This is due

384

(7. J. Rallis, A. M. Garforth and J. A. Steinz

to the complex nature of the pressure dependence curves found here. Johnston r who, to the authors' knowledge, is the only one to have reported the effect of temperature on the burning velocity of acetylene-air mixtures, concluded that it was marked and positive. Accuracy of Quantitative Results The accuracy of results obtained using the constant volume method of determining burning velocity is greatly enhanced by employing the various corroborative checks which are available with this technique. These hell) to provide an indication both of the validity of the assumptions made and of the reliability of results obtained. Unfortunately, any discussion of these corroborative methods, other than a comprehensive one, would be trivial and the reader is thus referred to ref. 39 which contains a detailed discussion on this topic. Suffice it to say that these corroborative methods serve to increase the authors' confidence in the accuracy of the results presented. In the same reference estimates of the error bounds, obtained 150 I

!

~/)/ ,Z 17../ ~

140 Error b o u n d s ,

z/

,'~

"7

130---120--

i

! ~

""

u °>,10C

-

51,

cn

"~00 ca 8C

/ @ ~

/

7C

6( 5Cl

2

/'

/¢

J _

~-

i .

.

.

.

.

. . . . . Test c Test el . . . . . . . . Test H1 Estimated error bounds of test H1 l [ [

3 4 5 6 Pressure ratio, P/Po Figure 9. Test reproducibility

with the present apparatus and equations, are also given. These indicate that during the early stages of the process the probable error is _+2 per cent, while the maximum likely error is of the order of + 6 per cent. The reproducibility of results is demonstrated by considering certain tests on stoichiometric atmospheric initial pressure acetyleneair mixtures conducted with different apparatus on three different occasions, each a year apart. These tests together with the estimated error bounds are presented in Figure 9. A numerical data handling process was used in calculating results for tests C while for tests G1 and H1 a more accurate manual and graphical technique was employed~ ". The pressure measurement circuitry was modified after test C and further modifications followed test G1 before the results of test H1 were obtained. Notwithstanding the use of modified apparatus in each case, the correlation between the tests is remarkably good over the regions where they are believed to be accurate (the earlier tests show a marked falloff in the & / P curve towards the end of the burning process--this is believed to be unreal). The discrepancy is generally greatest between tests G1 and H I but is never larger than 3-5 per cent.

./

"/"

/ / / ,,"4/ / / / , ~// )' i~edSf.~,~)~ / . , + rest c-~7,,~//! / j ~ ii,; Test HlI ~ ,,Z/ / i W ' ~ - ~ ,/ ./z"I/l

Vol. 9

~

, 7

.Conclusions

With the exception of the pressure dependence of acetylene-air mixtures the results obtained in this study are generally in agreement with literature values. However, both the pressure and temperature dependence appear to exhibit a more complex character than has hitherto been reported. The fact that (a) individual test results are so consistent with each other, (b) error analyses indicate the tests to be accurate to within + 2 per cent at the early stages of the process and (c) the results of Wheatley and Linnett ~9 and of Graiff" suggest similar trends, all contribute to the belief that the observed effects are real. No claims can be made concerning the quantitative accuracy of pressure dependence data at very high unburnt gas temperatures, except to say that heat loss to the bomb wall m a y serve to counteract heat gain through radiation from the flame. It is, however, believed that the in-

D e c e m b e r 1965 L a m i n a r b u r n i n g velocity of a c e t y l e n e - a i r m i x t u r e s b y c o n s t a n t v o l u m e m e t h o d corporation

of transient

unburnt

gas tempera-

ture measurement a s a feature of the apparatus would yield isotherms in this investigation.

similar to those obtained

References (;AYDOX, A. G. a n d XVOLFHARD, H. G. Flames. ]'heir Structure, Radiation and Temperature, 2nd ed. C h a p m a n a n d H a l l : L o n d o n , 1960 '-' S.~IITH, F. A. ' P r o b l e m s of s t a t i o n a r y flames', Chem. Rev. 1937, 21, No. 3, 389-412 :~ GAVDOX, A. G. a n d \VOLFHARD, H. G. 'Lo,,v pressure flames a n d flame p r o p a g a t i o n ' . Fuel, Lond. 1950, 29, 15-19 .t MORGA.~', G. H. a n d KANE, "VV. R. ' S o m e effects of inert d i l u e n t s on flame speeds a n d t e m p e r a t u r e s ' . Fourth Symposium (International) on Combustion, pp 313-320. W i l l i a m s a n d VVilkins: B a l t i m o r e , 1953 5 BARTHOLOMII:, E. Z. Elehtrochem. 1950, 54, 169. Cited in ref. 1 '; GILBERT, M. ' T h e influence of pressure on flame s p e e d ' . Sixth Symposium (International) on Cornbustion, pp 74-83. R e i n h o l d : N e w York, 1957 7 EGERTON, A. C. a n d THABET, S. t{. ' F l a m e prop a g a t i o n : t h e m e a s u r e m e n t of b u r n i n g velocities of slow flames a n d t h e d e t e r m i n a t i o n of t h e l i m i t s of c o m b u s t i o n ' . Proc. Roy. Soc. A, 1952, 211, 445-471 s EGERTON A. C. a n d SEX, D. ' F l a m e p r o p a g a t i o n : t h e influence of p r e s s u r e on t h e b u r n i n g velocities of flat flames'. Fourth Symposium (International) on Combustion, pp 321-328. W i l l i a m s a n d Wilk i n s : B a l t i m o r e , 1953 ~' LIXNETT, J. \V. ' P r o p a g a t i o n of flame'. Fuel, Lond. 1950, 29, 13-15 1~, IANNLTT, J. W . , PICKERING, H. S. a n d \¥HEATLEY, P. J. ' B u r n i n g v e l o c i t y d e t e r m i n a t i o n s I V - - T h e soap b u b b l e m e t h o d of d e t e r m i n i n g b u r n i n g velocities'. Trans. Faraday Soc. 1951, 47, 974-980 11 PICKI-RING, H. S. a n d LINNETT, J. \V. ' B u r n i n g velocity d e t e r m i n a t i o n V I - - T h e use of schlieren p h o t o g r a p h y in d e t e r m i n i n g b u r n i n g velocities b y the soap b u b b l e m e t h o d ' . Trans. Faraday Soc. 1951, 47, 989-992 1~- WHEATLEY, P. j . a n d LINNETT, J. \V. ' B u r n i n g velocity d e t e r m i n a t i o n V I I I - - S o m e acetylene+ o x y g e n + i n e r t gas m i x t u r e s ' . Trans. Faraday Soc. ]952, 48, 338 i.~ GRAIFF, L. B. ' T h e o r e s s u r e d e p e n d e n c e of l a m i n a r b u r n i n g v e l o c i t y ' . Ph.D. Thesis. P u r d u e U n i v e r sity : I n d i a n a , 1959 J~ J o s T , \V. Explosion and Combustion Processes in Gases. T r a n s l a t e d b y H. O. CROFT. M c G r a w - H i l l : New York, 1946 la UBm':tOHDE, L. a n d KOELLIKER, E . ] . G a s b e l e u c h t . 1916, 49, Nos. 4-7, 49, 65, 82, 98 la K H I T R I N , L. J. tech. Phys. U.S.S.R. 1936, 3, 926 a n d 1028. Cited in ref. 14 lr RIBAUD, G. a n d GAUDRY, H. C.R. Acad. Sci., Paris, 1938, 206, 1648. Cited in ref. 14 is BADIN, E. J . , STUART, J. G. a n d PEASE, R . N . ' B u r n i n g velocities of b u t a d i e n e - l , 3 w i t h n i t r o g e n o x y g e n a n d h e l i u m - o x y g e n m i x t u r e s ' . ]. chem. t)hys. 1949, 17, 314-316

355

J~' GARNER, F. H . , LONG, R. a n d ASHFORTH, G. K . 'Effect of p r e s s u r e on b u r n i n g velocities of b e n z e n e air, n - h e p t a n e - a i r , a n d 2 , 2 , 4 - t r i m e t h y l p e n t a n e - a i r m i x t u r e s ' . Fuel, Lond. 1951, 30, 17-19 '-", KOLODTSEV, K . a n d KHITRIN, L. J. tech. Phys. U.S.S.R. 1936, 3, 1034. Cited in ref. 1, p 75 2~ STEVENS, F. \V. ' T h e g a s e o u s explosive r e a c t i o n - t h e effect of pressure on t h e r a t e of p r o p a g a t i o n of t h e r e a c t i o n zone a n d t h e r a t e of m o l e c u l a r t r a n s f o r m a t i o n ' , Nat. Adv. Comm. Aero., Wash., Rep. No. 372, 1930 '-,2 "~VOLFHARD, H. G. Z. tech. Phys. 1943, 24, 206. Cited in ref. 1, p 45 '-,a MANTON, J. a n d MILLIKEN, B. B. ' S t u d y of pressure d e p e n d e n c e of b u r n i n g veIocity b y t h e spherical vessel m e t h o d ' . Proc. Gas Dynamics Symposium on Aerothermochemistry, p 161. N o r t h w e s t e r n U n i v e r s i t y : E v a n s t o n , Illinois, 1956. Cited in ref. 13 '-'t LEWIS, B. Selected Combustion Problems, pp 176179. A G A R D ; B u t t e r w o r t h s : L o n d o n , 1954. Discussion 2.; KUEHL, D. K . ' L a m i n a r b u r n i n g velocities of prop a n e - a i r m i x t u r e s ' . Eighth Symposium (International) on Combustion, pp 510-520. W i l l i a m s a n d W i l k i n s : B a l t i m o r e , 1962 2~; GARSIDE, J. E . , FORSYTH, J. S. a n d TOWNEND, D.T.A. ' T h e s t a b i l i t y of b u r n e r flames'. J. Inst. Fuel, 1945, 18, 175-185 27 \VHEATLEY, P. J. a n d LINNETT, J. \V. ' T h e effect of pressure on t h e b u r n i n g velocity of e t h y l e n e air m i x t u r e s ' . Trans. Faraday Soc. 1949, 45, 11521158 2s EGERTON, Sir A. a n d LEFEBVRE, A. H. ' F l a m e prop a g a t i o n : t h e effect of p r e s s u r e v a r i a t i o n on b u r n ing velocities'. Proc. Roy. Soc. A, 1954, 222, 2 0 6 223 29 GRUMER, J . , COOK, E. B., RICHMOND, J. K. a n d KUBALA, T. A. ' C o m b u s t i o n a t e l e v a t e d pressures in a spherical vessel'. Rep. Invest. U.S. Bur. Min. No. 5896, 1961 3o CULSHAVV, G. \V. a n d GARSIDE, J. E. Third Syruposium on Combustion, p 204. W i l l i a m s a n d \Vilkins: B a l t i m o r e , 1949 31 STRAUSS, \V. A. a n d EOSE, R. 'Burning v e l o c i t y measurements bv the constant-pressure bomb m e t h o d ' . Sevent}t Symposium (International) on Combustion, pp 377-385. B u t t e r w o r t h s : L o n d o n , 1959 a2 GAYDON, A. G. a n d ~VOLFHARD, H. G. ' T h e influence of diffusion on flame p r o p a g a t i o n ' . Proc. Roy. Soc. ,4, 1949, 196, 105-113 a.~ DUGGER, G. L., ~VEAST, R. C. a n d HEIMEL, S. 'Effect of pre-flame r e a c t i o n on flame v e l o c i t y of p r o p a n e - a i r m i x t u r e s ' . Fifth Symposium (International) on Combustion, pp 589-595. R e i n h o l d : N e w York 1955 "~ DUGGER, ('~,. L . , SIMOx, D. M. a n d GERSTEI.~, M. ' L a m i n a r flame p r o p a g a t i o n ' , Chap. 4, 'Basic cons i d e r a t i o n s in t h e c o m b u s t i o n of h y d r o c a r b o n fuels w i t h air'. Nat. Adv. Comm. Aero., Wash., Rep, No. 1300, 1957, p 127 :~s ]:tEIMEL, S. a n d ~rEAST, R. C. 'Effect of initial t e m p e r a t u r e on t h e b u r n i n g v e l o c i t y of b e n z e n e air, n - h e p t a n e - a i r a n d isooctane-air m i x t u r e s ' . Sixth Symposium (International) on Combustion, pp 296-302. R e i n h o l d : N e w York, 1957 '~(; JOH,'¢STON, W . C. ' F l a m e p r o p a g a t i o n r a t e s a t reduced p r e s s u r e s ' . S.A.E. Jnl, 1947, 55, No. 12, 63-65

356

C . J . Rallis, A. M. Garforth and J. A. Steinz

Vol. 9

~7 I{ALLIS, C. J. 'The determination of laminar burning velocity with particular reference to the constant volume method. Part I - - T h e o r y ' . University

Witwatersrand, Dept of Mech. Engng, Res. Rep. No. 25. January 1965

of the Witwatersrand, Dept of Mech. Engng, Res. Rep. No. 20. July 1964

::' RALLIS, C. J., GARFORTH, A. M. and STEINZ, J. A. 'The determination of laminar burning velocity with particular reference to the constant volume method. Part I I I - - E x p e r i m e n t a l procedure and results'. University of the Wigwatersrand, Dept of Mech. Engng, Res. Rep. No. 26. March 1965

,as RALLIS, C. J., GARFORTH, A. M. and STEINZ, J . A . 'The determination of laminar burning velocity with particular reference to the constant volume method. P a r t I I - - A p p a r a t u s ' . University of the