A survey of recent studies on flame extinction

Pro#. Ener#)ComhJlst. $ci. 1986. Vol. 12. pp. 81 116. Printed in Great Britain. All rights reserved.

0360 1285/8610.00+ .50 Copyright I~ 1986 Pergamon Journals Lid.

A SURVEY OF RECENT STUDIES ON FLAME EXTINCTION JOZEF JAROSINSKI Institute of Aeronautics, Warsaw, Poland

Abstract--A survey of the existing achievements in the domain of problems of extinction and flammability limits is presented, it is shown that the fundamental geometrical proportions between flame thickness and preheat zone for any flame, limit flames being included, are constant and independent of the mixture composition. The behaviour of limit flames under various severe physical conditions of the experiment is described and the influence of various factors on the extinction process is discussed. The conditions of flame quenching by the wall are analysed. Two particular mechanisms of flame extinction are discussed: for a flame moving in a tube in the direction of acceleration and in the opposite direction. The principal aim of the present paper was to describe the physical mechanisms of flame extinction under various initial and boundary conditions. CONTENTS

1. Introduction 2. The Thermal Structure of the Limit Flame 3. A Phenomenological Description of an Adiabatic Laminar Flame and its Properties 3.1. The method used 3.2. Pure thermal flame 3.3. Real flames 4. The Influence of Different Initial and Boundary Conditions on the Behaviour of a Limit Flame 4.1. The extinction of a flame in a standard tube 4.1.1. The extinction of an upward propagating flame 4.1.2. The extinction of a downward propagating flame 4.1.3. Flame propagation from the closed end of a tube 4.1.4. Flame propagation past obstacles 4.1.5. Upward propagating flame with a second flame giving an impulse causing motion of the gas in the opposite direction 4.1.6. Upward propagating flame against a steady downward gas flow 4.2. Flame quenching by a cold wall 4.3. Flame extinction in large vessels. The behaviour of limit flames 4.4. Extinction of near-limit counterflow flames 4.5. The quenching action of turbulenc~ A criterion for quenching by turbulence 4.6. The influence of acceleration on the flammability limits. The behaviour of a flame under conditions of high acceleration and under zero gravity 4.7. Flammability limits in swirling flow 4.8. The influence of pressure on flammability limits 4.9. The influence of the initial temperature on flammability limits 4.10. Flammability limits for different types of fuel. The influence of chemically inert substances 4.11. Flammability limits of dust-gas-air mixtures 4.12. Ignition limits 4.13. The effects of inhibitors on the extinction limits 5. The Use of Experimental Data to Formulate the Limit Conditions for Flame Quenching by a Wall 5.1. Analysis of the simplified model by Williams 5.2. Semi-empirical method of integration of the energy equation 5.3. The results 6. Summary. Two different Mechanisms of Flame Extinction under the Action of Acceleration: Extinction of Upward and Downward Propagating Flames 7. Conclusions Acknowledgements References

I. I N T R O D U C T I O N

91 92 92 94 95 95 97 98 99 101 101 102 104 105 106 106 109 111 111 114 114 114

a n d in i n d u s t r y as well as the need to increase the efficiency o f internal c o m b u s t i o n engines a n d to reduce the toxicity o f c o m b u s t i o n gases. T h e r e is also an increasing tendency to m a k e use of low-grade fuels a n d of waste gases. T h e i m p o r t a n c e of the c o m b u s t i o n of super-rich m i x t u r e s is due, in turn, to the fact that the relevant processes are f u n d a m ~ a t a l

T h e p r o b l e m of c o m b u s t i o n of extremely lean or extremely rich f l a m m a b l e m i x t u r e s a n d the associated p r o b l e m s of f l a m m a b i l i t y limits are objects of c o n s t a n t l y g r o w i n g interest. In the case of lean mixtures this interest is a c o n s e q u e n c e of the necessity to i m p r o v e the safety c o n d i t i o n s in m i n e s JPECS 12:2-A

81 83 84 84 85 86 88 88 89 89 90 91

81

82

J. JAROSINSKI

for the chemical industry. It may also be added that flammability limits are attracting increasing interest for purely academic reasons. A fuel-oxidizer mixture is usually considered to be flammable if external ignition results in the formation of a flame which can propagate through the mixture. It has been found empirically that a flame propagating in hydrocarbon-air mixtures is quenched if its temperature is lowered to about 1000-1200°C and the propagation velocity at the moment of extinction has a finite value of a few centimetres per second. The existence of the flammability limits is a result of heat loss to the surroundings. When a certain relationship between the heat loss rate and the heat release rate is satisfied within the flame front, the flame ceases to propagate and dies out. It has been found experimentally, many times, that the flammability limits depend on the physical conditions under which the experiment is carried out. All previous attempts to define the flammability limits as constants characterizing the flame, in the same sense as the adiabatic burning velocity characterizes a given flammable mixture, have failed. Since flammability limits must be known for practical reasons, an arbitrary definition was introduced by Coward and Jones ~ over 30 years ago. Their work contained the first summary of the empirical studies on flammability limits carried out for more than a century and a half, initiated by Davy 2 and continued by many other scientists. In order to ensure the comparability of data, Coward and Jones proposed that flammability limits should be determined in a standard vertical tube 2 in. (~51 ram) in diameter and 1.8 m long, closed at the top, and open to the atmosphere at the lower end. If, as a result of ignition at the bottom, the flame propagates upwards and reaches the upper end, the mixture is considered to be flammable. If the flame goes out before the upper end is reached the mixture is considered to be nonflammable. If we accept this definition, very convenient for practical purposes, it should be borne in mind that there are cases in which combustion occurs outside the composition limits determined by the method just described. The empirical data compiled by Coward and Jones ~ are very valuable for engineering practice, covering a great variety of flammable mixtures. Their work did not contain, however, any consistent theory which would make it possible to predict the flammability limits and the conditions trader which they should occur. The first attempt to analyse the problem of flammability limits theoretically was made by Zeidovich 3'" over 40 years ago. At that time the foundations of the theory of flame propagation were being laid. As many as three chapters of his book on the theory of combustion of gases were devoted to the problem of the existence of flammability limits." It can be regarded as remarkable that none of his remarks on the subject have as yet lost their validity.

First, Zeldovich relates the occurrence of flammability limits to the phenomenon of heat transfer from the region of chemical reaction, or the adjacent preheat zone, to the surrounding walls, and formulates appropriate equations which can be used to make qualitative and quantitative estimates. Second. he presents an argument to show that all flammable mixtures should have limit compositions, below which flame propagation should be impossible, due to heat loss from the flame to the surroundings. Third, he draws attention to the influence of diffusion, particularly in cases in which the Lewis number differs from unity. At the time of the IVth Symposium on Combustion in 1953 Egerton made an attempt to sum up the then existing state of knowledge in relation to the flammability problem in his survey) A similar review was presented by Linnett and Simpson 6 at the Vlth Symposium on Combustion in 1956. Unfortunately, the ideas of Zeldovich were not mentioned in either of those reviews. Egerton pointed out that the adiabatic flame temperature at the lean flammability limit was approximately the same for different hydrocarbon mixtures and that there was a correlation between the mixture composition and the temperature (or, strictly speaking, the calorific value of the mixture) at the limit. He emphasised the fact that differences between flammability limits for flames travelling upwards and those moving downwards were difficult to explain on theoretical grounds, although it could be supposed that an essential role was played by convection. Finally, he presented a list of problems requiring a theoretical solution. According to Egerton any theory claiming to describe in an exhaustive manner the problem of flame propagation should predict that a flame does not propagate outside a certain composition range. It should also be able to give the limit composition and the burning velocity at the limit. The theory of flammability limits put forward by Spalding 7 was, in a sense, an answer to Egerton's challenge. The same can be said of von Karman's theory described in the book by Williams 8 and Mayer's theory. 9 All these theories propose a simplified, one-dimensional flame model, the extinction mechanism consisting in transferring heat from the flame to the surroundings. Those theories and the ideas involved have, and still are being developed and utilized, t o- 13 although the later papers have not really added any new elements to increase our understanding of the processes involved. Among the various other theories which were put forward there have been numerous ones based on assumptions, such as that flame quenching is due to the effects of convection, ! 4-16 chemical kinetics, t 7 flame stretch as a result of the existence of a velocity gradient, tS't9 preferential diffusion of one of the reactants of the flame, 2° or, finally, the action of factors bringing about instability. 2~ A common

A survey of recent studies on flame extinction drawback of all these theories lies in oversimplification, the real phenomenon of extinction being usually ascribed to the influence of a single factor considered in isolation from all other factors that may influence flame quenching. Most papers written between 1950 and the beginning of the seventies, including some of the theories mentioned above, have been reviewed critically in the detailed survey prepared by Lovachev et al. 22 From this survey it is evident that the present state of knowledge has not yet made it possible to generalize about a large number of known facts or to reconcile the various con.tradictory opinions on the nature of the phenomenon of flame extinction. It appears that the main effort of researchers has been directed towards a detailed analysis of selected single features of the phenomenon, limited in each particular case by the necessary simplifications, rather than towards an attempt at elucidating the mechanism of the complicated phenomenon of flame extinction and formulating generalizations. Some publications which appeared after 1973 added to the information available on the flammability limits and must be mentioned here for the sake of completeness. Thus, Shtessel et al. formulated, in the form of conservation equations the conditions for the effect of natural convection on extinction processes in a gravitational field. 23 Babkin and co-workers made an attempt to generalize the experimental data given by various workers by assuming that the flammability limits of gases were influenced by natural convection. 16 Krivulin and collaborators 24 studied the phenomenon of flame propagation beyond the flammability limits (as normally determined) in large volumes. Bregeon et al. 2° studied hydrogen flames. They attributed flame extinction to the occurrence of a cellular structure in the flame. Work on the influence of cellular structures on the flammability limits is being continued by Williams. 25 Numerical methods for computing the parameters of laminar flames under the quenching action of the wall are being developed.26'27 Additional publications, not mentioned above, will be discussed later in the text. Many of them investigate flame extinction not only in relation to normally determined flammability limits but also under conditions in which the flame can be extinguished by a variety of means far from these limits. In this case one should distinguish the difference between flammability limits and extinction limits. A flame propagating in a mixture of any composition can be extinguished. Furthermore, for a given extinction mechanism, there exist lean and rich extinction limits beyond which the mixture is not combustible. There are different opinions about the physical processes controlling flame extinction. The opinion presented in this paper is that flame extinction

83

always results from heat outflow from the flame, although the triggering mechanisms leading to extinction are different and depend on the physical conditions of the experiment. The mechanisms of flame extinction currently suggested by different authors (i.e. the action of convection, flame stretch, chemical kinetics) are all based on the assumption of a decrease in flame temperature. Until now it has been impossible to formulate a universal theory of extinction limits for the large range of initial and boundary conditions under which limits have been observed. Similarly, in this paper there is no attempt to present such a theory. The theoretical treatment in the present paper is used in two particular cases to shown that fundamental geometrical proportions of the flame are constant independently of mixture composition (also for limit concentrations) and to analyse the relationships between the critical flame parameters for flame quenching by a wall. 2. THE THERMALSTRUCTUREOF THE LIMITFLAME In order to elucidate the mechanisms of flame extinction in limit mixtures, the flame structure, and in particular the flame thickness must be considered. In addition to the burning velocity, the flame thickness is one of the most fundamental parameters characterizing in a global manner the complicated processes occurring in a flame. Unfortunately, experimental data on flame thickness are scarce. Those that can be found in the few existing publications are usually based on different and inconsistent definitions and are thus often questionable. The view that the flame thickness as such is not strictly definable makes matters even worse. Indeed from the point of view of boundary conditions the flame thickness cannot be defined, because of uncertainty both on the upstream side, and on the side of the burnt gases. Against this rather unsatisfactory background, the amount of information that has been collected about flames propagating in homogeneous methane-air mixtures is quite impressive. The flame thickness was determined by Andrews and Bradley, over the entire range of mixture composition, for flames propagating in a closed cylindrical combustion chamber. 2s The basic measurements were made using a Fayhart-Prescott schlieren interferometer. The main advantage of this was that an optical nonintrusive method was used. The entire flame thickness determined by this method is the distance between the beginning and the end of observable temperature variation. The results of Andrews and Bradley are shown in Fig. 1. The lean limit flame thickness obtained is close to the earlier data of Dixon-Lewis and Williams (0.5 cm) who measured the temperature profile of a flat flame on a Powling burner using a thermocouple. 29 Using a LDV, Strehlow and Reuss also found that the thickness of a lean limit flame moving upwards through a standard tube was about 0.5 cm. 3°

84

J. JAROSINSKI

uQ 0

w i..

2

.6

.8

tO

t2

1.4

t6

EQUIVALENCE RATIO- o¢

FIG. 1. Flame thickness, variation with equivalence ratio.

The results can be compared with those obtained by the usual probe methods, such as resistance probes or thermocouples. Those are most commonly employed because of their simplicity. Unfortunately, solid probes interact directly with the flame, and can considerably disturb limit flames. The fact that the thickness of a lean limit flame in a standard tube is quite large has been confirmed by our own measuremerits, employing thermocouples 3! and resistance probes. 3z'3s It has been inferred from temperature profile measurements 33 that the flame thickness as determined in zs is, approximately, 6--2 ( T b - T , ) / (dT/dz)m, where ( T b - T , ) and ( d T / d z ) m are the measured temperature difference and the maximum temperature gradient, respectively. The measured temperatures of limit flames are compared in dimensionless coordinates, with the temperature curve corresponding to a purely thermal model of a flame (Fig. 2). It should be noted that the

,0

/,f

units of the x-axis are related to the "characteristic thickness" Affi 2/cpp, UL.4 One can see that the flame thickness of a real flame, irrespective of its definition, is relatively large compared to A. This is a feature of not only limit flames, but most probably of all other flame types. 3" It would be interesting to test this assumption. Some clue might be provided by the fact that the flame thickness 6 and the laminar burning velocity UL as measured in Ref. 28 are interrelated by the expression 6UL "" const. This is equivalent to the Peclet number which is also constant for flames quenched by the wall. 35"36 To find the relation between the flame thickness and the "characteristic thickness" A, the flame thickness will be defined on the basis of the energy equation.

3. A PHENOMENOLOGICALDESCRIPTION OF AN ADIABATICLAMINARFLAMEAND ITS PROPERTIES 3.1. The Method Used In the present analysis we consider a onedimensional steady-state laminar flame, the temperature of which is governed by the energy equation dT)

dT

d 2-dz -%Po uL-~zz+Qto =0

where z is the co-ordinate normal to the flame front, T - - absolute temperature, 2ffi thermal conductivity, Po ffi density of unburned mixture, % = specific heat at constant pressure, u L f l a m i n a r burning velocity, Q--heat of chemical reaction per unit mass of fuel consumed and to ffi rate of chemical reaction (defined here as the mass of fuel consumed by the chemical reaction per unit volume and time). Equation (1) is the only equation to be considered, since, as in some of the earlier theories of laminar

.6 .4 .2

1 2 X3 4 5 6 Fro. 2. Experimental temperature profiles in z-x co-

ordinates defined by Eqs (2) and (3), for near limit methane-air flames compared with the curve for a purely thermal mechanism of flame propagation, l--The profile obtained for near limit mixture, for upward flame propagation (approximately 5.3% CH,0, 2/cppo=0.41 cme/sec, uL=5cm/sec. 2--The profile obtained for a near-limit mixture for downward flame propagation (approximately 6.1% CH,), 2/%po=0.45 em2/sec, uL=7.5 era/see. 3--The Dixon-Lewis and Williams profile,z9 2/%poffiO.41cmZ/sec, uL=5cm/sec. 4--The pure thermal conductive heating profile, 2/cppo= const.

(1)

Tu

Ii-

t.6A~~

-Z PREI-~AT ZONE 6

REACTION ZONE ~Z

FIG. 3. Temperature variation across the flame front.

A survey of recent studies on flame extinction combustion, the diffusion equations for the mixture components become identical with it, assuming that the Lewis number L e = aid = 1. A typical temperature profile characterizing the flame front is represented in Fig. 3. The axis of the ordinate separates the preheat zone from the region of chemical reaction. The part of the temperature curve T where z is negative corresponds to the region in which the temperature increases as a result of heat conduction only. To the right of the inflection point in the temperature curve, i.e. where z is positive, is the region in which the temperature increases mainly through heat release from chemical reactions. As was done in Ref. 37, the variables can be represented in a dimensionless form dx = %pouz dz 2

T-To T.-To

. . . .

85

1C

.8 6 o.

.t,

•~:.b .2 • .2

.

.4

.6

I "\\ .8

1.0

FIG. 4. Temperature gradient as a function of the temperature in a dimensionless form, a and b--l~ssible limits of variation of the temperature gradients.

(2)

By integrating the Eq. (6) with the boundary conditions (10) and (12) it can be shown that (3)

1

¢ = S P dT,37 therefore, for A¢= 1, ¢ is equal to the 0

dT

p - --dr

(4)

where To and To are the absolute temperatures of the fresh mixture and of the adiabatic flame, respectively. Thus, Eq. (I) is reduced to

¢=PM

d2"c d~ dx ~-

area of the region below the curve p = f(T). In other words, the eigenvalue can be obtained by graphical integration of the p=f(z) curve and a result of integration is equal to some mean dimensionless temperature gradient Pu (where the subscript M denotes the mean value of temperature gradient).

~ = - eF(~)

or

dp Pd~ - p = - eF(z)

(6)

where ~oQfD¢

z = (~_ 222 To)C~PoUL F(T)=

/. 0¢-,0c

(7)

(8)

1 !

mc= 7- S2todzAO 0

(13)

(5)

(9)

The mean temperature gradient can be expressed in terms of, the maximum temperature gradient (Fig. 4), which can be easily measured. In the reaction zone its value must lie below Pu=Pm (1-0.5 Pro) (line a, Fig. 4). Knowing the temperature gradient PM and the temperature rise AT= 1 one can easily calculate the relevant dimensionless flame thickness -I=Ax=Cpp°uL6M=S PM

(14)

where 6u is the flame thickness corresponding to the mean temperature gradient and cff,;t has the mean value for the temperature range considered. The dimensionless number S expressed in terms of the flame front parameters is the Pcclet number based on 6u. The relation PM= I/S is equivalent to

The boundary conditions are 1

z = 0, p = 0

)

ahead of the preheat zone

z= %,, P=Pm z= l, p = 0

¢p=~. (10) (11)

~,

in the reaction zone

(15)

(12)

the index m denoting the maximum value of the temperature gradient.

3.2. Pure Thermal Flame The theory of purely thermal flame propagation assumes that the entire heat of reaction is released in the neighbourhood of the maximum temperature.'* If we assume that the preheat zone extends up to the

86

J. JAROSINSKI

peak temperature without any reaction taking place, the boundary condition (11) becomes

h

(16)

rm = 1 - ~ , P = Pm

wher¢¢.c 1. In the preheat zone, F(r)=0. Making use

b

o f (6), (10) a nd (16) leads to

dp = d~ rg

and

a..,

-z

.z

p~l. FIG. 6. The relationship between the two temperature

In the thermal flame propagation theory it is also assumed that, within the chemical re,action zone, with boundary conditions (12) and (16), the entire heat of reaction is transferred to the preheat zone. Making use of (6), (16) and (12) one obtains p dp +~F(Ocl~ = 0 and, on integrating .,.1

¢ = -

(17)

2

gradients, Pr, and p.~, in r-= coordinates, for a purely thermal mechanism of flame propagation.

on the z axis gives the "characteristic thickness" A=2/CppoUt. '~ In the same figure, the mean temperature gradient corresponds to the line b. This line replaces the temperature curve T. The area under line b is equal to that below the temperature curve T. In the case of purely thermal propagation the flame thickness 6M is twice the "characteristic thickness" A.

1

3.3. Real Flames

because F(O is defined so that S F(O d r = 1. o

Comparing (13), (14) and (17), gives .,.1 p,, = 2

(18)

S~2.

(19)

and

The relationship between the temperature gradients p,, and PM is represented in Figs 5 and 6. In Fig. 6 the maximum temperature gradient pm corresponds to the line a. The intercept of this line

)o~

P~

6

It has for very long been known that, in real flames, the value of ¢p is always less than 1/2, 37 which means that S>2, in agreement with Eq. (15). An estimate of the quantity S in real flames, the structure of which differs from that of flames with a purely thermal propagation mechanism, should be based on experimental temperature profiles. On the basis of the temperature curves presented in Fig. 2, the form of the function p = fir) was determined and shown in Fig. 7. By integrating this function graphically it was found, in agreement with (13) and (14), that ~p= PM = 0.197 and S=5.1. The relationship between the maximum and mean temperature gradients was found to be Pm/PM ~ 1.32 - 1.37.

1.0 .8 .6 Q'.4

2L .2

.4

.6

.8

10

FIG. 5. The relationship between the two temperature gradients, Pm and p~, in p-r coordinates, fdk a purely thermal mechanism of flame propagation.

/, j'p~ .2

.4

.6

.8

1.0

FIG. 7. The relationship between the two temperature gradients, Pm and p~, in p-z coordinates, for the real flame corresponding to curve I in Fig. 2.

A survey of recent studies on flame extinction

determine the dimensionless number S = the entire range of mixture composition, it is possible to utilize the data obtained from experiments on flames of homogeneous methane-air mixtures, carried out under conditions approaching those of adiabatic combustion discussed in the previous chapter and illustrated in Fig. 1. The values of the flame thickness obtained by

87

To

c~,pofi~utJ2, over

x4

Andrews and Bradley are somewhat higher than those which c o r r e s p o n d to the gradient. If they are to be used to S they should be multiplied by 0.66 ( 5 ~ , ( 1 . 3 2 / 2 . 0 0 ) 6 , because

mean temperature o b t a i n the value of a factor of o r d e r diM~l.32 fin, a n d

6."1/26). Finally, c o m p u t a t i o n results for the d i m e n s i o n l e s s n u m b e r S expressed by the relation (14) are s h o w n in T a b l e 1 a n d in Fig. 8 (open squares)~ T h e n u m b e r S h a s also been c o m p u t e d from e x p e r i m e n t a l d a t a o b t a i n e d u n d e r c o n d i t i o n s w h i c h were very far from a d i a b a t i c a n d a p p r o a c h e d l i m i t i n g c o n d i t i o n s in a q u e n c h i n g channel, a6 T h e results are a l m o s t the same as for a d i a b a t i c c o n d i t i o n s (Fig. 8, o p e n hexagons). T w o p o i n t s for h y d r o g e n - a i r a n d p r o p a n e - a i r flames are included. T h e analysis was confined here to t h o s e

o CH4-oir. odiobatsc [28] o CH4.air.t~n~ t f l a m e [36]

,,

o H~ .n~ [18,441

2

•"- C ] H e . a i r [18.44] I

J

i

i

l

|

•

1.0

two points due to a lack of reliable data on flame parameters, a n d o n the flame thickness in particular. F r o m Ref. 36 it m a y be inferred t h a t difference in thickness between an a d i a b a t i c flame a n d a limit flame are at a m i n i m u m for a s t o i c h i o m e t r i c mixture. A s s u m i n g that a q u e n c h i n g c h a n n e l can accomm o d a t e two flame thicknesses as defined in Ref. 28

TABLE 1. Flame parameters Equivalence ratio

UL.

6.

T,, or Tli*,

cm/sec

cm

~C

2/cpp o cm2/sec

ULfCl,po/2

S

8.7 7.9 7.8 8.0 7.8 8.2 8.8 9.3 10.0 10.0

5.7 5.2 5.1 5.3 5.1 5.4 5.8 6.1 6.6 6.6

0.440 0.455 0.470 0.480 0.492 0.487 0.483 0.473 0.467 0.460

8.9 8.4 8.1 7.8 8.0 8.1 8.5 9.6 10.2 11.4

5.9 5.6 5.3 5.1 5.3 5.3 5.6 6.3 6.7 7.5

0.662

7.4

4.9

0.485

7.6

5.0

CH4--air near adiabatic conditions 2a 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

16 23 30 37 45 45 41 34 26 19

0.260 0.170 0.135 0.115 0.100 0.100 0.115 0.145 0.200 0.270

1390 1550 1710 1830 1940 1920 1850 1770 1690 1610

0.478 0.496 0.520 0.535 0.550 0.548 0.535 0.525 0.515 0.505

CH4--air limit conditions 36 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

8.5 18.3 26.2 34.0 37.5 36.0 30.5 24.0 16.5 9.5

0.460 0.210 0.145 0.110 0.105 0.110 0.135 0.190 0.290 0.550

1060 1180 1310 1410 1490 1480 1420 1350 1290 1230 H 2 - - a i r ~ s.

1.0

195

0.025

44

1550 C3Hs--air ~8.`4

1.0

40

0.092

*I~ is assumed that TjI,~=0.8T~ K

1500

t=

12 1.4 EQUIVALENCE RATIO FIG. 8. The dimensionless number S= cppouLfM/2 as a function of the equivalence ratio. .8

88

J. JAROflNS~

(which has been observed for methane-air mixtures 36) and making use of the data of Potter and Berlad *') and those of Lewis and von Eibe ~s S values were computed for stoichiometric mixtures of hydrogen and of propane with air (Fig. 8). Differences between the values of S for the two cases are insignificant. The fact that the values of S vary very little with mixture composition (Fig. 8) and are not sensitive to the amount of heat lost from the system, implies that the fundamental geometrical proportions of a flame are almost constant The knowledge of the number S can be used to examine the character of the heat release function. The gradient (dp/d~)m in Eq. (6) is always zero at the point of inflection of the temperature curve t = t~,, therefore the maximum value of the temperature gradient can be expressed by

On substituting from (15) this gives 1

11i lo I

9i al

2: 2!

I I 2 3 4

6

8

S

FIG. 9. Exponent n as a function of the dimensionless number S, Eq. (25).

measured for a mixture of methane and air, gives n~2.0. This value of the exponent n corresponds to a heat release curve, typical for combustion processes controlled by chain reactions. The character of this function can best be represented by a simple relationship for autocatalytic reactions

Pm= ~PF(tm).

p . = -:F(t,,X

I1 d

(2o1

5

Making use of (7) and (15) the burning velocity can be easily found, provided the heat release function is known. An attempt to describe the character of this function can be made by expressing it in a generalised form, which can assume different shapes, 14. 37 for instance

F(r)= :2i'Tn,n + l)e(l _ 'g'_ i) n-I

(21)

with

dr to = - - = k r ( a - r)e - ~:/R7. dt

(26)

where k is a constant, a and ( a - r ) = t h e number of moles of the reactant per unit volume, at time t = O and at t = t, respectively,a° The analysis presented shows that the combustion process is controlled, to a greater degree than is usually supposed by chain reaction mechanisms with propagation dependent on diffusion of free radicals. The arguments presented above strongly suggest that the structure of a limit flame is similar to that of any other flame.

(22)

p=~l _:-1)

4. THE INFLUENCE OF DIFFERENT INITIAL AND

1 (23)

BOUNDARY CONDITIONS ON THE BEHAVIOUR OF A LIMIT FLAME

and

n, y I

P,n ---- n

(24)

The exponent n can be calculated from (20), (21), (23) and (24): S+2

n ..... S-2

(25)

The theory of Zeldovich a n d Frank-Kamenetzky 3s assumes that q)~ 1/2, which corresponds to S ~ 2 and n~oo(Fig. 9). Taking S = 6 as a typical value

An effective approach leading to an elucidation of the physical process of flame extinction consists of investigating the influence of various boundary and initial conditions on the limit flame, because the behaviour of this flame under different and, often extreme physical conditions makes it possible to learn more of its properties and to assess the role of various factors for flame propagation and extinction.

4.1.

T h e E x t i n c t i o n o f a F l a m e in a S t a n d a r d

Tube

A square tube equivalent to the standard tube was used to study the influence of various initial and boundary conditions on the behaviour of limit flames.4o.4t

A survey of recent studies on flame extinction

4.1.1. The extinction of an upward propagating flame A flame of a limit mixture propagating upwards (Fig. 10) is interpreted as a zone of combustion on the surface of a bubble of preheated gas driven upwards by buoyancy forces. 42 Schlieren films of the flame extinction process show that after extinction the top of the bubble continues to move at the same speed for a distance of about 0.2 m. Then its boundaries become deformed and it fades away. The extinction process always starts at the top of the flame and then an extinction wave moves downwards along its surface. Temperature measurements (Fig. 11) show that the temperature of the moving gas decreases relatively quickly and amounts to only about 200°C at a distance of 500 mm from the leading point of the flame front. In the neighbourhood of the tube axis the temperature profile for a limit flame differs substantially from that for a flame for a mixture considerably removed from the limit

89

composition. Measurements of the instantaneous temperature of the tube walls indicate that the temperature increase begins at the point of contact between the flame and the wall (Fig. 12), therefore the heat flux to the walls cannot account for flame extinction. 31 It has been shown experimentally that, beginning from the moment of extinction, reactants flow only around a centrally rising body of hot gas. 4e

4.1.2. The extinction of a downward propagating flame Free downward propagating flames in non-limit mixtures were convex, the convexity being directed in the sense of motion, and were characterized by propagation velocities along the tube considerably higher than the burning velocity. When the mixture approached the limit composition the curvature of the flame was reduced as well as the propagation velocity (see Fig. 34). The free downward propagating flame in a mixture of a limit composition resembled a plane disc at approximately right angles to the walls of the tube. 42 The propagation vdocity of the limit flame was lower than the adiabatic burning velocity. In every case the flame front slowed down or stopped before extinction and a tongue of low density gas licked the wall moving towards the

..7.r..

a P

,,..¢,.--

FIG. 10. Schlieren photograph of a typical upward propagating flame.

FIG. 11. Temperature distribution in an upward propagating flame, obtained very near the limit composition (5.3 °,o CH4) and for a composition well away from the limit (6.1 ~o CH4). The numbers indicate dimensionless temperatures relative to the maximum temperature of the second flame.

90

J. JAROSINSKI

FIG. 12. Record of wall temperature obtained from a sensor placed on the right-side of the tube at the level of the visible wire. Upward propagation. Time increases from left to right.

FIG. 13. Schlieren photographs of downward propagating flame in a standard tube just before complete extinction. Note the tongue of hot gas ahead of the main flame. Sequence is from left to right. Time interval between frames is 0.018 sec.

Unburned mixture (Fig. 13). As a consequence a sharp temperature gradient between the hot gas and the cold mixture gradually disappeared. The flame survived longest away from the walls, on the axis of the tube, and usually began to lift during the last phase of the process. 4.1.3. Flame propagation from the closed end of a tube When the mixture was ignited at the closed bottom end of the tube, the flame propagated at a speed which depended on the mixture composition. The motion of the flame front was in this case due to the expansion of hot gases. With very lean mixtures, between 5.4 ~o CH,, and the limit composition for downward flame propagation ignition at the upper closed end of the tube,

led to a downward motion of the flame which eventually went out. Flames in mixtures containing above 5.4?/o CH4 propagated for a distance which was a function of the methane concentration and which increased as the mixture became richer (Fig. 14). Before extinction, in the course of its downward propagation, the flame front went through a series of rocking motions (Fig. 15). The flame always went out at the end of an oscillation cycle,-when its mean speed approached zero. When the mixture composition was equal to that corresponding to the flammability limit for downward propagation, the flame became stable after a few oscillations, and moved downwards towards the open end of the tube in its usual way (not smoothly) at a speed typical for a flame propagating downward from the open end of the tube.

A survey of recent studies on flame extinction

z

z

o 20.0:]

SOu. t.0 o

o°

, I,,-.

'°I1 |

5.2

¢¢

53

~

•

i

5.5

5.6

|

5.7

|

5.8

5.9

% CH~

FIG. 14. The distance over which the flame propagates before extinction as function of methane concentration. Propagation from the upper, closed end of the tube.

1.t,

91

The presence of an axially placed copper tube 21 mm in outer diameter, with 0.5 mm wall thickness and 160 mm in length did not change .the flammability limits. For a mixture composition approaching the flammability limits the flame passed easily through the region surrounding the tube. Also a number of evenly-spaced vertical plates did not quench the flame unless the plate spacing was less that 9 ram. The plates were made of plexiglass 1.5 mm thick and 103 mm in length and divided the tube into 2, 3, 4, 5 and 6 channels, with width 24.75, 16.00, 11.63, 9.00 and 7.25 ram, respectively. A 9-ram channel width was found to approach the quenching distance for both lean flammability limit compositions in a standard tube. Similarly to the case of a tube the near-limit flame propagating downwards in a quenching channel was almost plane On the contrary the upward propagating near-limit flame was rounded and made an acute angle with the wall. Channels 7,25 mm in width quenched flames which were leaner than 5.55 ~o of methane for upward propagation and 6.05 ~o for downward propagation (the relevant limit compositions for standard tube were 5.25 ~ and 5.85 ~o of methane, respectively). Reversed flows were observed in some channels but in no case was flame extinction observed if the mixture was richer than the limit mixture and the spacing between plates greater than the quenching distance

1.2 4.1.5. Upward propagating flame with a second flame

giving an inpulse causing motion of the gas in the opposite direction

o,

N,6

0

I0

FRAME

20 30 NUMBER

FIG. 15. The behaviour of a flame in a 5.7 °o methane-air mixture ignited at the closed top end of the tube. Left: successive schlieren images of the flame (55 frames per secondl. Right: the measured downward velocity (maximum downward displacement per frame).

4.1.4. Flame propagation past obstacles Obstacles in the form of concentric tubes or partitions in the form of vertical plates did not cause any change in the observed flammability limits until a certain minimum obstacle spacing was reached.

An upward propagating flame proved to be very resistant to any change of shape under the influence of a gas flow coming from above with variable acceleration. To study this case two sources of ignition were installed in the tube, the first at the lower (open) end of the tube, the second in the upper section, near to the closed end. Ignition in the lower open section of the tube initiated an upward propagating flame. When this flame had reached the lower edge of the observation window the mixture was ignited in the upper part of the tube. The ignition of the mixture at the top of the tube initiated the expansion of gases above the first flame, thus making the gas flow towards the lower (open) end of the tube. As a result the first flame slowed down in its upward motion, stopped and started to move downwards. Its form, however remaining unchanged (Fig. 16). The fact that the shape of the upward propagating flame did not change when it was impulsively pushed from above by another flame in the tube indicates that the flow ahead of the flame is irrotational, and is not influenced by the growth of the boundary layer at the walls. This information was used by yon Lavante and Strehiow in their calculation of flame stretch 43 in an upward propagating flame.

92

J. JAROSINSKI

FIG. 16. Downward movement of an originally upward propagating flame due to secondary ignition of the mixture at the closed top. Although the entire flame system is displaced downwards, the shape of the flame remains identical with that of the ordinary upward propagating att"ame.The shading on the walls of the tube is caused by moisture which has condensed on the walls when the flame had been higher up in the tube (55 frames per second). Time increases from left to right.

4.1.6. Upward propagating flame against a steady

downward gas flow In this case the tube was supplied with a flammable mixture from the top, the lower end being open. The gas velocity profile changed along length of the tube from very flat at the top, near the mixing chamber, to a fully-developed laminar profile in the lower part of the tube. The mixture was ignited at the lower end of the tube. For mean flow velocities higher than 15 cm/secthe flame moved upwards in one comer of the tube only. The length of this flame clearly depended on the mixture composition and on the flow velocity. F o r slightly richer mixtures the flame resembled a long ribbon which had a tendency to become shorter as the mixture become leaner or the flow velocity increased. Below a certain level of fuel concentration or above a certain gas flow velocity, the ribbon disappeared and only a small residual flame remained, propagating in the comer of the tube, decreasing in size as it moved upwards. F o r mixture compositions approaching the limit value the flame moved only in one comer of the tube. These flames disappeared in the upper part of the tube when their length was 5-10 ram. 4.2. Flame Quenching by a Cold Wall Potter and Berlad found nearly 30 years ago that the quenching d/stance of a flame, in the same

mixture, was different depending on whether the flame propagated upwards or downwards.*" This observation was confirmed in the course of an investigation into the passage of limit flames through grids placed in a standard tube used for experiments on flammability limits, carried out by Strehlow and the present author. `*° It was also observed during experiments with grids that when the distance between grid plates was larger than about 9 mm it did not influence the lean extinction limits of methane-air mixtures. For channel distances D > 9 mm the limits for both upward and downward propagation were the same as in the standard tube. This result disagreed with earlier reports, t's According to the theory, complete independence of the limits from the dimensions is possible only for channels or tubes of very large size. In view of the importance of the phenomenon observed, the extinction of flames in a quenching channel was subjected to detailed investigation for both directions of p r o p a g a t i o n ) 6 The measurements were carried out in quenching channels 30cm long, formed by inserting suitable blocks into a standard flammability tub~ The variation in the length of the hot region behind the flame as a function of the spacing between the walls is illustrated in Fig. 17. A length of the quenching channel of 30 cm was sufficient for the ratio of channel length to the region of elevated temperature behind the flame front to be larger than that which one obtains in the case of flame

A survey of recent studies on flame extinction

propagation in a standard tube (the ratio of the length of the standard tube to that of the hot region is, under normal conditions, LT/L=180 cm/50 cm ~4). The curves expressing the relationship between the quenching distance and the mixture composition for both directions of flame propagation, are shown in Fig. 18. The difference between the flammability limits for the two directions increases with increasing deviation from stoichiometry. In the case of lean mixtures it was confirmed that the upward and downward propagation limits are established, for a channel wider that 9.2 mm, at the same level as in a standard tube. For rich mixtures the limits depend on the distance between the walls. The flame speeds within channels are shown, for limit propagation conditions, in Fig. 19. This figure contains also, for comparison, the laminar burning velocity as determined by Andrews and Bradley under conditions approaching the adiabatic case. 2s The Upward flame speed is higher and the downward

1

9 8o

8

--' 70

7

i

Z

oS0

6

BJ

" h 0

50

5

o

40

~ 30 Z

w =J 20 I0 I

!

CHANNEL

WIDTH

D

93

-mm

FIG. 17. The length of the hot region near the quenching limit in channels.

D / OWNWARO l/ L Z

zW

2 % C H 4 /9.48 , , -

0

,

C

,

.

0.7

0.6

.

0~

,

0~9

1.

I

I

I

I

5

0.6

0.7

0J}

0.9

i

1.0

,

1.1

I

1.2

I

13

I

1.4

I

1.0 1.1 1.2 EQUIVALENCE

I

I

1.3 1.4 15 RATIO o o<

1.5 I

_--

16 -

FIG. 18. Quenching distance D for different equivalence ratios, for methane-air mixtures for upward and downward flame propagation.

12G

i

6O

~. 40 2G I

I

0.6

0.7

I

I

I

0,8 0.9 1.0 EQUIVALENCE

I

I

I

1~ 1.2 1.3 RATIO o(

a

T-

14

FIG. 19. Flame speeds for methane-air mixtures in narrow channels. Downward propagation. The number by each curve indicates the channel width in millimetres: A--upward flame speed at the flammability limit: B--downward flame speed at the flammability limit; C--burning velocity as determined in a bomb.2s

94

J. JAROSINSKI

flame speed is lower than the laminar burning velocity as determined in a bomb. This shows that in the case of upward motion of the flame in channels, buoyancy plays an important role. Experimentally-determined temperature profiles and estimates of the Rayleigh number indicate that there is no free convection in the channels to intensify the heat exchange with the walls (Ra < 600). It is only by conduction that heat can be transported from the flame to the walls. Since, however the quenching distances for the upward moving flame differ from those for downward propagation, there must be differences in the heat exchange with the walls in the two cases. By comparing the quenching distance, D.p, for flames moving upward with the flame thickness for flames approaching the adiabatic type 5a (cf. the date of Ref. 28), it is found that the ratio D.~/6o is constant over the entire range of mixture compositions and amounts to D~p ~ 2.0-2.2. 5o

(27)

For a flame moving downwards, for which the Milan and yon K,'irm,'in method can be usedff s calculation results indicate that the ratio Ddo,,./5 should also be constant. Since in the neighbourhood of stoichiometry the flame thickness is nearly the same for either direction of propagation (Fig. 18), it should also be true that Ddo../5~2.0. It follows now that a flame can exist in the channel, in both cases, provided its width is greater than twice the flame thickness. When the flame moves downwards the combustion process is slower, probably because the heat loss is more intense. This is manifested by a flame thickness greater than under adiabatic conditions and a lower burning velocity, which can best be observed in the case of an extremely lean mixture. By expressing the flame thickness as 5 = const. 2/cppouL and making use of relation (27) it can be inferred that the Peclet number expressed in terms of the parameters of the channel and the flame should be constant under the limit condition. For normal

0 29 sec

0 5 0 sec

conditions for flat quenching channels this number is, Pe= 39-41, 30 (compared to P e = 4 6 for tubes35).

4.3. Flame Extinction in Large Vessels. The Behaviour of Limit Flames Most flammability limit studies are carried out in relatively small containers. 1.22 The use of the data obtained to predict the behaviour of limit flames in a large vessel is thus possible only to a limited extent. The propagation of limit flames in a large combustion chamber (8 m a) was studied by Lovachev et al. 24'46"47 who used ammonia-air mixtures, with very low burning velocities. In a standard tube a flame of such a mixture is incapable of propagating downwards. The experiments demonstrated that the behaviour of limit flames under such conditions is different from that in a standard tube. Figure 20 shows photographs of consecutive stages of a flame, which is moving upwards as a result of buoyancy forces. Because of the existence of these a specific velocity field was formed around the flame. Since the velocity of the upward motion of the flame considerably exceeded the burning velocity, the initially spherical flame was distorted. According to Lovachev a free flame finally assumes a toroidal form, and this becomes very stable and may move for a considerable distance. 46 TIle flammability limits of ammonia-air mixtures determined in a large combustion chamber were wider than for a standard tube. For upward propagation they were: 15.8 % and 28 % NH a (ignition at the centre of the combustion chamber), and for downward propagation: 17.4 and 28 % NH a (ignition at the centre) 18.6 and 27.7 % NH a (ignition near the ceiling). Depending on the mixture composition when the flame reached the ceiling, it was either quenched or propagated along the ceiling parallel to its surface. In the latter case the flame spread underneath the ceiling at a constant linear speed of 80 cm/sec. Analysis of the relevant photographs showed that this speed was comparable with the expected speed

0 7P sec

0 . 9 2 sec

FIG. 20. Buoyancy of an a m m o n i a - a i r flame in an 8 m s chamber (2660/0 N H s in air). Ignition at the centre of the chamber. The distance between the marks on the right is 10 cm. 2"*

A survey of recent studies on flame extinction rate due to buoyancy. The spread of the flame under the surface of the ceiling is analogous to the spread along a horizontal tube, the same physical mechanism being in operation. After the flame had spread to cover the whole ceiling, it began to move downwards at a gradually decreasing speed. During the downward propagation of the flame, the flame front had the form of an almost flat continuous surface with down-turned edges. For mixtures with higher burning velocities the flame reached the chamber bottom having thus passed a distance of 2 m. For lower burning velocities the flame stopped and went out at a certain distance from the ceiling. Those flames which reached the bottom of the chamber moved at a speed of the order of 3040 cm/sec. Since the burning velocities of a m m o n i a air mixture are only a few centimeters per second, comparison of the two sets of values leads to the conclusion that heat transfer to the walls during the downward propagation of the flame was insignificant. It should be stressed that the flammability limits for rich a m m o n i a - a i r mixtures in an 8 m a combustion chamber are wider than those for an upward propagating flame in a standard tube (the relevant values for limit mixtures are 28.0 % N H 3 and 26.3 %, respectively). 4.4. Extinction of Near-Limit Counterflow Flames

95

propane mixtures approach each other under nearlimit conditions and that the reaction process was not completed within the stangation region. High non-equilibrium concentrations of hydrogen and carbon monoxide were observed even for lean mixtures. Also the temperatures were rather low within the stagnation point region. On the other hand the distances between flames of rich methane and lean propane mixtures were relatively large under near-limit conditions, the reactions were completed and the temperatures were high. Those flames were extinguished by pure flame stretch. Ishizuka and Law 49 observed a variety of nonsteady, nonplanar flame configurations, including cellular flames, star-shaped flames, groove-shaped flames, and vibrating flames. Their burner was suitable for further studies of flame instability in a diverging flow field. 4.5. The Quenching Action of Turbulence..4 Criterion

for Quenching by Turbulence The influence of turbulence on the quenching of laminar flames was studied using an experimental arrangement represented schematically in Fig. 22, 32 designed in order to be able to observe the effect of isotropic turbulence in its pure form, with zero mean gas flow. The experimental arrangement consisted of a standard tube for flammability tests with a

Burners of several types were developed to study the mechanisms of flame extinction in a stagnation flow of premixed gas (Fig. 21). Tsuji and Yamaoka '*a studied in their experiments the counter flow, premixed, twin flames established in the forward stagnation region of a porous cylindrical flame holder (they had two opposed premixed flames separated by product gases). Ishizuka and Law 49 investigated two flames established in the space formed as a result of interaction of two opposite flows of homogeneous mixture from two parallel porous plates. Sato s° used two identical opposite streams of homogeneous mixture flowing out from two nozzles and observed two flames propagating in the stagnation region. In all these experimental studies the same effects were observed. It was found, in particular, that flames of lean methane and rich

"fWlN

POROUS

/ PREMIXED N G~

FLAMES CYLINDER

.

LENS APERTURE'I~PHOTOMUL TIPLIER PREMIXED GAS

Itl/t

~ ,,'/ MUU:= PLATE

I0

. //,U ~ I1,~

"~ '~'N2..="T'f PREMIXED GAS

FIG. 21. Three types of counterflow flame burners.

ul"

FIG. 22. Diagrammatic representation of the experimental apparatus showing the tube, the turbulence generator (not to scale) and the measuring equipment.

96

J. JAROSINSKI

(a)

(b)

FIG. 23. Schlieren [a) and direct photographs (b) of a flame approaching the region of increased turbulence.

turbulence generator mounted at the top, capable of producing turbulence with the required parameters and the desired root mean square (rms) turbulent velocity. The initially undisturbed flame propagating from the open lower end of the tube entered, in the neighbourhood of the upper end, a region of turbulence of gradually increasing rms turbulent velocity (Fig. 23). Its passage through this region was accompanied by an increase in the propagation velocity. When the rms turbulent velocity was sufficiently high for the given conditions, there was observed a sudden collapse in the propagation velocity and the flame was quenched. The flame was unable to proceed beyond a certain level in the tube, where the rms turbulent velocity reached a critical value. The values of the parameters for which the flame was quenched were recorded. Lean and rich methane-air and propane-air mixtures and a m m o n i a - a i r mixtures over the entire composition range were studied. Two generators of turbulence were used, with turbulence scale,s 2.14 and 6 mm and variability ranges of the rms turbulent velocity of 0.1-1.2 and 0.5-3.4 m/sec, respectively. It was found that the conditions for the quenching of flames of homogeneous gaseous mixtures by turbulence could be correlated by means of the Karlovitz-Kovaszney criterion: u'6 K =-- -L uL

(28)

A survey of recent studies on flame extinction where u' is the rms turbulent velocity, L= the integral scale of turbulence, 6 = the laminar flame thickness and uL~- the laminar burning velocity. This criterion is usually regarded as the ratio of the chemical reaction time to the characteristic "eddy break up" time in turbulent flow. The measured critical values of K ranged from 7 to 20. The quantities appearing in Eq. (28), i.e. the laminar burning velocity and the flame thickness were measured in the same tube and for the same mixture compositions for which the quenching experiments were carried out. In order to estimate K, it is customary to employ the thickness of the preheat zone given by 2/CppoUL. This is considerably less than the real thickness of the flame (this has already been discussed in Section 3) and leads to values of K which are lower by approximately an order of magnitude. On the basis of the results obtained it may be concluded that within the range of conditions studied, i.e. for a scale of turbulence comparable with the flame thickness, the flame is quenched by the turbulence if the time scale of the chemical process is by at least one order of magnitude larger than the characteristic "eddy-break-up" time.

4.6. The Influence of Acceleration on the Flammability Limits. The Behaviour of a Flame under Conditions of High Acceleration and under Zero Gravity The influence of the acceleration due to gravity on a flame (and the adjacent region of hot gases) manifests itself in the effect of buoyancy forces. The upward motion of the flame due to buoyancy exerts in turn a considerable influence on the flammability limits, by controlling the flow field around the flame and the conditions of heat exchange between the flame and the ambient medium. It follows that under the action of an acceleration, flame fronts with different orientation in space must be associated with different flammability limits. The influence of acceleration on flames is usually studied in the case of acceleration due to gravity. The characteristics of the behaviour of different flames under the action of normal gravity forces has already been discussed. 'm'~l It is of considerable interest to study the behaviour of a flame in extreme cases, in which it is influenced by high accelerations or placed under zero gravity conditions. The influence of high centrifugal accelerations on the flammability limits of a mixture of natural gas (98 ~o methane) with air, was studied by Krivulin et al. 51 for a flame propagating through a tube under normal ambient conditions. Figure 24 shows the dependence of the flammability limits on acceleration for a flame propagating in the direction of acceleration (downwards) and in the opposite direction (upwards). It can be seen that the difference between the flammability limits for an upward and J P E C S 12:2-B

97

i/ 6

8

10 112 14 % OF GAS

16

18

FIG. 24. Effect of gravity (relative) on the flammability limits of natural gas-air mixtures (g--acceleration, go-acceleration due to normal gravity); 1--upward propagation, 2--downward propagation.51

downward propagating flame is greater for higher values of the acceleration. If a value G = g/go = 97 is exceeded, downward flame propagation becomes impossible. The bdlaviour of a flame in a standard tube, under conditions of zero gravity was studied by Strehlow and Reuss. 3° Because of the short duration of the experiment (2.2 sec) only the early stages of flame propagation could be observed. The flame was approximately spherical and limit mixture composition was found to approach the lean limit value for a flame propagating upwards under conditions of one g-field. The behaviour of near limit flame, under zero gravity condition was also studied by Krivulin et al.,s2 who used a 20 I. cylindrical combustion chamber, the diameter of which was equal to the distance betwen the end walls. The zero gravity conditions were achieved by conducting the experiment on board an airplane under special flight conditions. The object of the study was the combustion of lean hydrogen-air mixtures and rich propane-air mixtures. It was found that the flammability limits under zero gravity conditions take values which were intermediate betwt~m the limits for an upward and downward propagating flame in one g-field. The results of those tests are given in Table 2. As the duration of zero gravity conditions was sufficiendy long (about 8 see), many interesting observations could be mad~ Thus, it was found that for gffi0 the disappearance of flame luminosity for mixtures outside the flammability limits was five to ten times slower than in the g = I field, which was probably due to much less effective heat and mass transfer. Measurements of the laminar burning velocity and of the pressure increase rate in the combustion chamber near the flammability limits, show that there are differences in these parameters between the cases of zero gravity and that of I g.

98

J. JAROSlNSKI

TABLE2. Flammability limits for lean hydrogen-air-mixtures and rich propane-air mixtures under zero gravity conditions g=go

g=O

Kind of mixture

Upward propagation

Downward propagation

Symmetric propagation with respect to the point of ignition

Concentration of H2 °4 ~

4.0

8.5

6.6

Concentration of C3Hs ~'o°~/o .

9.9

8.0

8.8

Under zero gravity the limit burning velocities were very low (about 2 cm/sec). The pressure increase rates in the combustion chamber were also considerably below those for 1 g. From the behaviour of the limit flames under zero gravity conditions as described in Ref. 52, it is apparent that the length of time over which the observations are made may play an important part in the experim~ts, therefore the times available in free fall may be found to be insufficient.

4.7. Flammability Limits in Swirling Flow Laminar swirling flow can be brought about by making a cylindrical combustion chamber rotate about its axis. Rotating combustion chambers were used by Margolin and Karpov 5a'54 (who used two

combustion chambers, 80 and 200 mm in diameter and 50 mm in height) and, somewhat later, by Babkin et al. 55 (combustion chamber 223 mm in diameter and 25 mm in heighU. A flame, initiated at the periphery of the rotating chamber, moved towards its axis where its form changed from a spherical into a cylindrical one, and then spread outwards at a speed equal to or less than the laminar burning velocity,s3 The change from the spherical flame to the cylindrical one must occur at an early stage of flame propagation because the change of shape is favoured by the distribution of mass forces s6'57 and also because the propagation velocity along the axis of rotation is very high) s The experiments showed unambiguously that for some acceleration the flame propagating outwards grew up to a certain critical radius re, and then died out (Fig. 25). The value of the radius re increased with

FzG. 25. Direct streak photographs of flame propagating from the centre of a cylindrical combustion chamber in a mixture of 8 ~o CH, with air. Initial pressure 0.I MPa: a, t~=0; b, to=748 I/sec.

A survey of recent studies on flame extinction increasing laminar burning velocity and decreasing rotational speed. The velocity of flame propagation decreased with increasing pressure both for stationary mixtures and for swirling flow. For swirling flow the rate of decrease in the flame propagation velocity depended on the speed of rotation--the greater the rotational speed, the more rapid the decrease in the propagation velocity of the flame. Babkin et al. considered the rotational speed gradient of the gas, &o/dr, as one of the possible factors influencing the flame quenching process. They noted that this gradient could cause considerable stretch of the flame along the flame front. They considered, however, that flame quenching as a result of this stretch was less probable than quenching as a result of heat loss from the hot gases to the wall. On the other hand from the work of Zawdzki, s6's7 in which the temperature of the swirling gas was measured, it lollows that under conditions of much more intense swirl and turbulent flow the combustion gases were not cooled during the passage of the flame from the centre of the cylindrical combustion chamber towards its periphery, and the flame was not extinguished, despite the fact that the propagation velocity of the flame was not much higher than the laminar burning velocity. It follows that the heat loss from the hot gases to the walls was not important during the extinction process. Thus, the extinction of a flame in swirling mixture is, under laminar conditions, most probably due to the same mechanisms as in the case of a downward propagating flame as described in Subsection 4.6. In both cases the flame is extinguished under the action of centrifugal acceleration. However, the value of the limit acceleration is by one order of magnitude higher in Babkin's work s5 than the value mentioned in the preceding work. 5~ This discrepancy of data might be caused by the differences in structure of the two combustion systems (different flame speeds relative to the walls) or might result from wrong estimation of the rotational speed of the charge in the cylindrical combustion chamber. The error in estimation may result from possible differences between the rotational speed of the charge and the chamber. The curvature of a flame propagating from the centre in the direction of increasing acceleration is reduced between the walls normal to the rotation axis. The flame straightens and approaches the cylindrical form. Such an interpretation is a result of analysis of two comparable flames in the photographs recorded by a drum camera and shown in Fig. 25. It may be guessed, similarly to the case of a nearlimit downward propagating flame under conditions of gravity acceleration (Subsections 4.1 and 4.2), that the flame front is plane at the moment of flame extinction and makes approximately right angles with the walls normal to the axis of rotation. As already noted, the reduction in the curvature of the flame and the increase in the angle of contact with the wall are probably accompanied by increased heat

, 80 >-

o 60 LU

99

O

O

O0

0

~'

0 0

z

~0

Z

•I , CH~

FIG. 26. Radial turbulent burning velocity in swirling flow as a function of mixture composition. The shaded area belongs to the region of laminar burning velocity of methane-air mixture taken from Ref. 28. The measurement points shown in the diagram correspond to various mean velocities of flow and various turbulence parameter~ 5~

loss from the flame to the wall, The thickness of the cooled flame increases and the burning velocity decreases. In the limit case the flame is quenched at the wall in the same manner as it is in a quenching channd. The flame quenching initiated at the wall, spreads over the entire surface of the flame. Under conditions of intense turbulent swirling flow no flame quenching action was observed. 56,s7 The flame propagated over the entire volume. The burning velocities were independent of the parameters of turbulence and were contained within the same range of values as found by Andrews and Bradley 2s for laminar flames (Fig. 26). 4.8. The Influence of Pressure on Flammability Limits There is only a small amount of material concerned with the influence of pressure on the flammability limits and the information that is available is fragmentary. The influence of pressure is diversified, often specific for the given mixture, but extremely interesting from the scientific point of view. It is manifested, above all, in the effect on the burning velocity and the flame thickness. Typical diagrams illustrating the dependence of the limit mixuture composition on the pressure show that, in the low pressure range (below 0.1 MPa) lean and rich limits of flame propagation depend very little on pressure over a wide pressure rang~ The lower portions of the U-form curves, are determined by the pressure, below which ignition and flame propagation are impossible. The observed limit pressure is not a fundamental property of the given mixture, but rather determines the conditions under which the ratio of the heat release rate to the heat

100

J. JAROSINSKI

loss rate become critical from the point of view of flame extinction. In this sense the influence of the pressure on the flammability limits is analogous to that in the case of self-ignition in a wall-enclosed space, which was considered by Semenov. s9 It may be assumed that the quenching distance is in inverse proportion to the pressure, over a wide pressure range* Thus, for very low limit pressure, the quenching distance may be of the same order of magnitude as the characteristic dimension of the vessel. In most cases when the initial pressure is above atmospheric, several characteristic regions can be identified in the diagram illustrating the relationship between the mixture composition and the limit pressure. They can be studied using as examples methane-air and hydrogen-oxygen-nit rogen mixtures. In the first case the flammability limits of natural gas are presented as a function of pressure (Fig. 27), use being made of the data from the work of Coward and Jones) The natural gas used contained about 85 % of methane and 15 % of ethane. The figure shows that the lower limit depends but sligl~dy on the pressure, the upper one being raised considerably at higher pressures. It was observed that, up to 2.0 MPa, the flammability limits are somewhat narrower for downward propagating flames on both the lean and the rich side and are wider for higher pressures. For upward propagating flames the limits are widened over the entire pressure range There is, for both directions of flame propagation, a large difference between the flammability limits which will probably vary with varying initial pressure. The existence of that difference was confirmed by the detailed studies of Babkin and V'yun 6° for methaneoxygen-nitrogen mixtures, for pressures up to 1.5 MPa. The factor responsible for the existence of two flammability limits dependent on the direction of flame propagation is, as has already been observed, the phenomenon of convection always

present in a gravity field. The experiments of Zawadzki and the present author s: show that, the elimination of this convection by turbulent flow leads to only one flammability limit, which is the same as for an upward propagating flame. The influence of pressure on the flammability limits of a hydrogen-oxygen-nitrogen mixture was studied by Panin et ai. 61 for upward propagating flameg The results obtained are summarized in Fig. 28, which also includes some data from Ref. 1. The diagram shows that if the pressure drops below atmospheric, the region between the two limits of flame propagation becomes at first wider, and then narrower, and finally vanishes completely for very low pressures. The minimum limit value of the pressure changes from about 4 to about 53 kPa as the oxygen content of the mixture decreases. For mixtures with a low content of N 2 the effect of the narrowing d o w n of the flammability interval for higher pressures is very slight. As the concentration of oxygen decreases the two limits approach each other and meet at a 6--6.5 9/o oxygen content. Below 4.8 9/o of oxygen hydrogen-oxygen-nitrogen mixtures were nonflammable under any conditions. The influence of pressure on the flammability limits can be interpreted in a qualitative rather than a quantitative manner due to the fact that, although it is known in what sense all the important parameters influencing the flammability limits depend on pressure, it is not yet possible to produce a quantitative treatment which would take them all into account. Thus an increase in pressure is accompanied by a reduction in the values of two principal quantities characterizing the flame front and influencing the flammability limits, i.e. the laminar burning velocity uL and the flame thickness 6. 62 Since the rate of chemical reaction increases with increasing pressure, 63 a decrease in the thickness must be stronger than laminar burning velocity (so that the duration of the chemical reaction ~= 6/uL is reduced). As a

Id 6C .<

5C

' 4C

Ill ,< J

t/I t~ n,.

3O

o. !o 2

20

z

lO

0

t

8

,2

;6

2o

PRESSURE MPa

FIG. 27. Effect of above atmospheric pressure on the flammability limits of natural gas-air mixtures.

"

20

"

~0

•

60 % H2

•

80

100

FIG. 28. Diagrammatic representation o f the flammability limits as a function o f pressure and oxygen concentration for H 2 - 0 2 - N 2 mixtures. Curve | corresponds to H 2 - O 2 mixtures, curve 2 to 4.8 ~o 02. Increasing numbers correspond to increased nitrogen concentration in the mixture. 6~

A survey of recent studies on flame extinction result, if we consider a flat flame of thickness 6, moving in a tube of a diameter d, a decrease in the flame thickness is accompanied by a decrease in the rate of heat loss to the walls by conduction, according to the relation:

101

then the natural flammability limits with approximately equal concentrations of air or methane respectively, behaving as inert gas. In order to obtain better insight into the effect of pressure on flammability limits more research is clearly necessary.

q ~ ctTtdtS(Tb- To) where ~= Nu Aid and Tb is the mean temperature of the flame, therefore an increase in pressure should result in reduced rate of heat loss by conduction. The problem of the influence of pressure on heat loss by radiation is more complex. This influence can be determined from the expression for emissivity, which can characterize in an indirect manner the rate of heat loss by radiation 64

e=l-e

-kp~

(29)

where k is the absorption coefficient for a pressure of 0.1 MPa, p = p r e s s u r e and s = effective thickness of the radiating layer. Assuming that the thickness of the radiating layer is that of the flame which is approximately in inverse proportion to the pressure,* we find that ps=const, and, finally, e=const. From the above analysis it follows that the pressure has no influence on the rate of heat emission by radiation into the ambient medium. Thus, under comparable conditions, increased pressure results in increased heat release rate and reduced rate of heat loss to the ambient medium. Both agents are expected to widen the flammability rang~ The above argument describes the sense of the variation of specific parameters with pressure but cannot explain the variation in the flammability limits which is different for each mixture, nor certain anomalies in the dependence of the specific parameters as a function of pressure. Conclusions reached in the course of this analysis do not agree with at least part of the experimental data illustrated in Figs 27 and 28. It is, for instance, difficult to use them to account for the fact of a considerable widening of the flammability range as a result of an increase in pressure for very rich mixtures of natural gas with air (Fig. 27). According to Zeldovich 4 the rich flammability limit of a methane-air mixture is influenced, under normal conditions, by the inhibiting action of the excess methane which enters into endothermic reactions with the combustion products. As the pressure increases the excess methane becomes more and more inert and its inhibiting action becomes weaker. For very high pressures (over 12.5 MPa) it behaves as a chemically inert gas. The lean and rich limit are

*A more accurate statement is that the flame thickness varies in proportion to p - " : where n is the order of a reaction.

4.9. The Influence of the Initial Temperature on

Flammability Limits The data obtained by White and quoted in the book by Bone and Townend 65 indicate that an increase in the initial temperature of a mixture results in an apparently linear rise in the flammability limits. An analysis made by Egerton and Powling 66 using White's data, showed that the reduction in the heat of chemical reaction per unit volume of the mixture due to the lowering of the lower limit was approximately compensated for by increased initial enthalpy of the mixture. These data then lead to the inference that, when the flammable mixture is preheated, the temperature of the flame at the lean limit remains approximately the same If higher initial temperatures are considered the experimental data from various sources are usually distorted, because the flammability limits are influenced by the length of time for which the mixture remains in the vessel (oxidation of the fuel in the course of heating). A detailed discussion of this problem can be found in the extensive survey by Lovachev et al. e2 4.10. Flammability Limits for Different Types of Fuel.

The Influence of Chemically Inert Substances Egerton and Powling 66 observed that the limit adiabatic temperature of saturated hydrocarbon fuels increases as the fuel ascends the homologous series. They also found that it is incorrect to relate the limit temperature to the ignition temperature. Their data show that, while the theoretical temperature of the limit mixtures increases for heavier hydrocarbon, the ignition temperature decreases. They concluded 66 that a flame must reach a certain minimum temperature in order for the reaction to be self p r o p a g a t i n g - because an appropriate concentration of free radicals must be maintained in the reaction zon~ Increasing dilution of fuel-air mixtures by inert additives results in a narrowing down of the flammability limits The effect of those diluents is illustrated in Fig. 29. From Fig. 29 it is evident that sufficiently high concentrations of inert additives can prevent the propagation of flames. Egerton and Powling 66 observed that, for the lean flammability limit, theoretical adiabatic temperature of the limit flame increased with increasing content of the additive. They considered this increase only apparent and assumed that, if incomplete combustion was taken

J. JAROStNSKI

102 15

compared with hydrocarbon flames especially under limit conditions.

4.11. Flammability Limits o f D u s t - G a s - A i r M i x t u r e s

10 ~j

Z

5

15

r

25 35 45 INERT GAS . %

55

FXG.29. F]ammabi]ity ]imits of methane-air mixtures with carbon dioxide, water vapour, nitrogen, helium and argon.

u, 1400 I/d

iz w 60(: Ig W I

i

i

.G

.8 10 t2 it, t6 EOUIVALENCE RATIO 0¢ IN M E T H A N E . A R MIXTURE

FIG. 30. Temperature of limit flames measured in methaneoxygen-nitrogen mixtures (at the tube axis). Upward propagation in a standard tube. Limit conditions were approached by introducing nitrogen into methane-air mixture. 67 Numbers against the curve denote the methane concentration.

into consideration, the real temperature of the limit flame would be found to be constant. This assumption has been verified experimentally by measuring the temperatures and upward propagation velocities of limit flames in a 50 mm standard tube for methane--oxygen-nitrogen mixtures. 67 Measurements showed that the temperature of the flame at the lower flammability limit really was approximately constant and increasing slightly on the rich side as the fuel content in the mixture was increased and reached a maximum for extremely rich mixtures (Fig. 30). The velocity of upward propagation of the flame in the tube increased linearly, as the mixture became richer in fuel; from about 23 to about 28 cm/sec and, for downward propagation, from 8 to 13 era/see. In flames of hydrogen--oxygen-nitrogen mixtures z° the behaviour of the flame propagation velocity was different and a distinct minimum was observed in the neighbourhood of stoichiometry. Flames of hydrogen mixtures differ considerably from hydrocarbon flames due above all to differences in diffusion coefficients, of the fuel and oxidizer. For this reason, flames of hydrogen should not be

Although most research on the combustion of coal dust with air is conducted under conditions approaching those found in practice, namely in galleries of experimental coal mines, 6a fundamental research is also being carried out. A detailed account of the research on the combustion of coal dust mixtures can be found in the work of Krazinski et al. 69 and Smoot et al. ~° Usually, there are considerable problems with fundamental research because it is extremely difficult to make the experimental conditions reproducible as a result of differences in the physical and chemical properties of different coal dusts, insufficient accuracy in suspending the dusts, differences in the design of the experimental apparatus, the use of different ignition energies etc. Under such circumstances better standardization of the experimental conditions appears to be one of the most urgent requirements. A few fundamental publications have appeared recently, 7L72 in which attempts were made to establish some quantitative relationships between the principal parameters influencing the flammability limits of coal dust mixtures. The first of these papers describes experiments conducted in a 7.8 1. vessel. The second was concerned with experiments on the combustion of coal dust in a tube. It has been shown that the lean limit of coal dust-air mixtures varies inversely with the content of volatiles in the dust. 71 Although the experimental minimum dust concentration varied from 45 to 450 rag/l, the concentration of volatiles at the flammability limit changed very little, all experimental results falling in the range from 40 to 60 mg/i. For Pittsburgh coal dust the particle size had no influence on the flammability limits for particle diameters up to 40/,tin. 71 The temperature of the limit mixture flames was comparable with the limit temperature for methane mixtures. 7~ Buksowicz et al. 73 made an attempt to determine the structure of the upward propagating flame and the mechanism of flame propagation in limit dustgas-air mixtures, on the basis of experiments made in a tube. They tried to make the shape of the flame regular, rather like the shape of a gas flame. This could most easily be achieved for relatively low dust concentrations, a few seconds after all the supply devices had been turned off, particularly the coal feeder. Temperature measurements on limit flames showed that the thickness of the flame front for a dust-gas-air mixture was higher (depending on the quantity of the dust), than for a gas flame. Records of limit temperatures for gas and coal dust-gas flames

A survey of recent studies on flame extinction

103

{at

lb) FI6.31. Trajectories of burning coal dust particles recorded by drum camera;73 a--slit on the axis of the tube. b--slit 1 cm from the tube wall.

indicated that for the latter flames the limit temperatures were about 20 ~o higher and that the elevated temperature behind the flame front was sustained for a shorter period. The propagation velocity of the limit dust--gas-air bubble shaped flame was about 25 cm/sec, it was therefore close to the velocity of the limit gas flame. The gas dynamic structure of the flame was studied by recording the trajectories of dust particles using the drum technique. Photographs (Fig. 31) show the trajectories of burning particles in two of the most characteristic regions of the tube, at the axis and at a distance of 1 cm from the wall. Near the axis of the tube particles are first lifted up and carried with the flame, then they remain stationary (with reference to the tube walls) and, finally, fall downwards accelerating. Simultaneously it can be seen that their velocity with reference to the flame front increases continuously. In the neighbourhood of the walls the motion of the particles is downward, the velocity increasing gradually relative to the walls. The trajectories of burning particles are also visible in direct photographs (Fig. 32).

It is interesting to compare the thermal structure with the gas dynamic structure of the flame. An attempt was made to determine the relationship between the two structures by using an interferometric method of measurement. The method consisted of superimposing two images: direct image of the burning particles and the interferometric image of the flame (Fig. 33). The use of this method showed that particles begin to emit light on the tube axis already in the region of low rising temperature. The interferometric records appear to show that the flame structure at the tip of the flame is somewnat aifferent from that in the neighbourhood of the walls: near the tube axis the luminous particles reach the boundary of the interferometric fringes, while away from the axis a gap of several milimeters exists between the light emission boundary and the fringe boundary. In the course of this work it was found that the limit dust-gas-air flame propagating in a vertical tube from the lower (open) end to the upper (closed) end of the tube was, despite certain differences, basically of the same character as a flame in a gaseous mixture.

104

J. JAROSINSKI

r.~ ~

~

¢

!

!, L

ib

FIG. 32. Direct photograph of dust-gas flame with trajectories of burning coal dust particles 7a

the development of the reaction, by contrast with a steady combustion process in which the transport of heat and radicals to the fresh mixture is a condition of propagation of the combustion w a v e . 7a A critical review of the present state of the thermal ignition theory has been given by Merzhanov and Averson 75 and by Averson. 76 Despite the more than 40 year long period of developmemt of spark ignition theory the details of the mechanism of that process has not as yet been explained. However, the work on the elements of that mechanism and the mechanism as a whole are continued. Of recent works let us mention the paper of Maly and Vogel, 77 who found that the ignition and the subsequent flame propagation were controlled mainly by the energy introduced during the breakdown phase of the establishment of the spark, and only to a moderate degree by the total energy. Ballal and Lefebvre 7s observed that the duration of the spark in the arc phase and the energy distribution with time had a profound impact on successful ignition. Several other works are devoted to the investigation into the mechanism by which the energy of electric discharge is converted into activation energy. 79- s~ In the subsequent work of Refael and Sher s2 a mathematical model was presented to simulate the evolution with time of a segment of spark channd in a combustible methane-air mixture. This model takes into consideration the physics of plasma and incorporates a detailed reaction scheme coupled with the relevant conservation laws. Before the details of the ignition mechanism are known, let us draw the reader's attention to some relations characterizing the initial flame kernel in the light of the flame properties discussed in Section 3. It has been found by experiment that there exists a critical diameter of the flame or a quenching diameter, which is the minimum diameter to which the flame develops, initiated by a spark with nearlimit ignition energy. Comparison of the data of Lewis and von Elbe for quenching diameters for methane-air mixtures is (Tables 5.6 and 5.8) with those of Andrews and Bradley for the flame thickness in the same mixtures 2s leads to d = 2R "" 26

FIG. 33. Interferometer photograph of dust-gas flame. 73

4.12. Ignition Limits Ignition by an external source of energy occurs when the centre of chemical reaction initiated by, for instance, an electric spark, is capable of forming a propagating flame front. Until the moment of forming the flame, the transport of"heat and radicals from the reaction region to the fresh mixture is a factor which hampers

(30)

therefore at the ignition limit the critical radius of the flame kernel is approximately equal to the flame thickness. From the physical point of view this means that, at the ignition limit, we are also concerned with the limit conditions for flame propagation. In the light of the result obtained let us consider the energy involved during the process of flame formation as a result of spark ignition. Use can be made of the data of Lewis and von Elbe, Is who considered the amount of energy equivalent to the quantity of heat contained in a spherical volume of

A survey of recent studies on flame extinction combustion gases of diameter d, to be the limit amount of energy for which the flame is quenched, assuming that the gases were at a temperature Tb and had a density Pb:

H=-~7t d 3 cppb(Tb--To).

(31)

If, however, we take into account the real temperature profile of a laminar flame (Fig. 2), the amount of ,energy contained in a volume considered will be approximately halved (H,-~0.5 H). Corrected data for the critical parameters of ignition are given in Table 3. It can be seen that the quantity of heat equivalent to the minimum ignition energy Hi, is in all cases less than 39 ~ of the total energy contained in a flame of minimum size. The value of H, is the sum of the energy of ignition and of chemical reaction in the mixture. The minimum energy of ignition is of the same order of magnitude as the thermal energy transferred by conduction to the region outside the reaction zone, i.e. to the pretaeat zone. It is highly probable that, until the flame is formed, the quantity of heat constituting the minimum energy of ignition is necessary to sustain the temperature above the critical level. If we use the Zeldovich estimate of the time of cooling of the critical flame kernel preheated up to the adiabatic temperature, for the characteristic time of reaction a4, then, with the laminar flame temperature profile as assumed here, we shall obtain, as an ignition condition, R>6A--~6 (instead of R>3.7A) which is in good agreement with the result of Ref. 33. The ignition energy used for flammability limit study should be higher than that determined at the ignition limit, to be sure that a combustion wave is present at the beginning of flame propagation. 4.13. The Effects o f Inhibitors on the Extinction Limits

The effect of different inhibitors on flames is to decrease the rate of chemical reaction and thus the burning velocity. This results in a narrowing of the flammability range. The fuel as well as the inhibitor usually consists of

105

a gas, a liquid or solid particles and forms with the oxidizer, a homogeneous or heterogeneous mixture. Inhibitors may influence the combustion process thermally, chemically or both. The thermal influence is due to the cooling of the flame by chemically neutral substances. The chemical influence can be due to the chemical production of neutral gases which extinguish the flame or participate directly in the reaction process. Some chemical agents such as sodium bicarbonate and potassium bicarbonate are decomposed by heating and liberate neutral carbon dioxide. Chemicals containing halogen or alkali metals directly influence the reactions by reducing the radical concentration~ The oldest method still used in mines to prevent flame initiation and propagation consists in the neutralization of coal dust-air mixtures by applying rock dust to the mine passageways. More recently passive and triggered barriers have been developed in which water, rock dust or chemical extinguishers are used. According to Refs 83 and 84 chemical extinguishers which are successful in small scale studies, may only be effective as thermal agents in large scale explosions in mines. Recently, Hertzberg et al. ~5 have been investigating in the laboratory, the effectiveness of some inhibitors as extinguishers. They have found that the measured rates of inhibitor devolatilization are consistent with their measured effectiveness in extinguishing explosions. Relatively large-scale experiments on prevention and suppression of coaldust explosions by bromochlorodifluoromethane and carbon tetrachloride showed that volume concentrations of suppressants of about 1-1.5% prevent ignition. 86 The bulk of the work in the field of flame inhibition is devoted to the investigation of the effects of different chemical extinguishers on flame in order to reach some fundamental understanding of the chemical mechanisms of their interaction with the flame. Because of the complexity of flame systems, the detailed chemical kinetic reaction mechanisms of many known chemical extinguishers are still not fully understood. Recently the influence of halogenated inhibitors has been investigated on hydrocarbon flames (mainly on methane) burning under different con-

TABLE3. Some critical flame parameters for methane-air mixtures at the ignition limit ~8.28 CH4-air mixture, vol. °o

Quenching distance d. cm

Flame thickness 6, cm

d ~

6.84 7.76 8.62 9.50 10.30 11.60

0.29 0.22 0.20 0.21 0.25 0.45

0.16 0.13 0.11 0.10 0.11 0.13

1.82 1.70 1.82 2.10 2.30 3.45

Maximum energy of ignition Hi. 10 - 6 cal

H~ H

Hi H,

180 100 72 72 110 400

0.15 0.17 0.19 0.16 0.14 0.09

0.31 0.35 0.39 0.33 0.29 0.19

106

J. JAROSINSIG

ditions, a7-97 Studies of the inhibition by halon and halagon acides HBr, HI, HCI have been carried out in hydrogen--oxygen flames. 9s- i o, Also the influence of other inhibitors mainly salts and metallic addifives has been studied in many experimental works. I°z-1°9 The structure of inhibited flames has been investigated experimentally by means of spectroscopic and laser Rayleigh scattering measurements.1 ~o- ~: 3 Some modelling of inhibition phenomena in flames has been suggested by Fristrom and Van Tiggelen. 1l,~ In these and many other works the details of the inhibition process have been systematically documented and can be used to search for new and more powerful chemical flame inhibitors.

"•60 )

I

5C

r~

,,ul, ~c e~

, . 30 ",Jr

10 I

I

I

I

I L

.2 .t. .6 ,8 10 PLATE SEPARATION.cm 5. T H E USE O F E X P E R I M E N T A L D A T A T O F O R M U L A T E T H E L I M I T C O N D I T I O N S F O R F L A M E Q U E N C H I N G BY A WALL

In some cases, as described earlier, it is observed that flame quenching is preceded by a reduction in curvature of the flame front and establishment of flame contact perpendicular to the wall. All the above cases were concerned with flame propagation in the direction of gravity acceleration or its multiple in a field of high centrifugal forces and occurred in quenching channels, tubes and also in laminar swirling flow. It is most probable that the extinction of a flame was due, in all those cases, to increased heat loss from the flame to the wall, when the angle between them approached a right angle. In the light of the experimental data obtained let us formulate the limit conditions for plane laminar flame propagation in contact with the wall at right angles. To this aim we shall adapt one of the many existing one-dimensional theories of flame quenching. Unfortunately despite the present degree of development of computer techniques, no multidimensional theory of flame quenching has as yet been developed, the results of which could be made use of here. The only two-dimensional theory of a laminar flame with heat losses to the wall, established by von K/trm~in and Millan 45 and known since the fifties, can only be used to a very limited extent for the estimate of the structure of a flame in contact with the wall. Unhappily, this method cannot be used to determine the limit conditions of a flame, in view of the assumption that the limit burning velocity is a known value determined on the grounds of the onedimensional theory. This limitation was eliminated in the method of Aiy and Hermance. 2T Unfortunately their assumption of a plane flame propagating freely between parallel plates at a speed equal to the burning velocity is unrealistic. Experiments show that the displacement of a plane flame in a quenching channel is possible only in a very narrow range of conditions approaching the limit conditions (Fig. 34). Within the remaining range of conditions the

FIG. 34. Velocity of stoichiometric downward propagating flame in channels as a function of plate separation. 1--Flame speed in methane-air mixture measured in channels, 36 2--burning velocity of methane-air mixture measured in a bomb, 28 3---calculated flame speed based on 1st order kinetics and Le=O for propane-air mixture) v 4-calculated flame speed based on 2nd order kinetics and Le=O for propane-air mixture. 2~

flame is curved and propagates at a velocity which is higher than the burning velocity. It follows, therefore, that this method cannot be used here. No other method being available, of many onedimensional methods we shall select the simplest but most illustrative method of Williams, 8 which will be used to discuss the influence of the mixture composition on the limit conditions in the light of the criteria in Williams' book. Then, since the assumption of a constant reaction profile may raise some doubts as regards the generality of the solution, a semi-empirical method of integration of the energy equation will be used in further study, thus obtaining solutions of tolerable accuracy.

5.1. Analysis of the Simplified Model by Williams 8 The results of the analysis of a simplified onedimensional laminar flame with heat losses, 8 can be used to determine the limit conditions of existence of a flame and the characteristic points on the temperature curve for the limit flame. The form of that curve for such a flame is represented schematically in Fig. 35 and described in terms of a one-dimensional energy equation. d / dT'x

dT

+ Q,o- L =0

(32)

where L is the rate of heat loss per unit volume and time. To minimize the deviations from the onedimensional model let us confine our considerations

A survey of recent studies on flame extinction

107

and

l

2uk ¢=- Co

J

Bearing in mind the fact that, in agreement with Eq. (2), the thickness of the reaction zone as expressed in terms of the dimensionless co-ordinate x is S= (cvpouz,/2u) b and making use of (33) and (37) we obtain the relationship tp = I/S. The solution of Eq. (35) is

I

0 HEALING ZONE

REACTION ZONE

",

COOt.ING ZONE

t=-+A

FiG. 35. Temperature distribution in a flame with heat loss.

to an analysis of a limit flame propagating downwards in a closed from below narrow channel between two infinite parallel plane walls. By the term of "limit flame" we shall understand a flame propagating under conditions approaching those of quenching. A limit flame propagating downwards in such channels is flat. The length of the hot region being small, it may be assumed that a fully developed velocity profile typical of laminar flow will not have time enough to be formed. The temperature distributions which were obtained by measurement in narrow channels a6 showed that the temperature in the core just behind the flame front was almost uniform, confirming this statement. Following Williams let us recall the simplifying assumptions introduced in Ref. 8, that is, those of Lewis number L e = l , c o = 0 for z<0, co=cou for O < z < b , co=0 for z > b and the constants 2 and c r We shall assume for the computation the mean values of 2 and cv for a prescribed temperature range. The width b of the combustion zone is determined by the relationship Qcoub= cv(To - To) Po uL.

(33)

The specific heat loss rate from the flame to the walls may be expressed as L = k ( T - To)

(34)

where k is a constant. Depending on the physical conditions, k assumes values ranging from 0 for an adiabatic flame up to a certain value at the extinction limit. Let us introduce the dimensionless co-ordinates (2) and (3). The Eq. (32) can now be reduced to the form d2z

dz

dx:

dx

0r = - q,

(35)

where tp =

(T~ - To) c~ pg u~

(37)

pg ut"

(36)

e'lX+B e"2~

(38)

aa.2=~ (1 + 41 +4#).

(39)

¢

where I

From the continuity condition of the temperature z and the temperature gradient dz/dx across the boundaries between zones at the points x = 0 and x---$ we find, by performing some algebraic manipulations, similar to those in Ref. 8, the unknown coefficients A and B in Eq. (38). We have, finally, the temperature at the beginning of the reaction zone (x--O). rl=

- -

(1 - e .is)

(40)

~1 ~ ~2

and the temperature at the end of the chemical reaction (x = s) zb-

~0

~1

- -

(1-e"s).

(41)

The maximum value of the temperature can be determined by equating to zero the first derivative of the temperature [Eq. (38)]: z, = ; (1 _ e[.~.za=l _.zfls t , x . - -

al

S.

(42)

The quantities involved in Eq. (38) or obtained from that equation can be computed or appraised on the basis of experimental data, making use of appropriate numerical criteria. A fundamental criterion which determines the conditions for flame quenching by a channel wall is the Peclet number, usually defind a s Pe.~.cpPoULD/~.o,where D is the quenching distance. The heat transfer between the flame and the wall in a quenching channel is expressed by the Nusselt number defined as N u = aD/2 M, where ~ is the heat-transfer coefficient. By assessing, on the basis of Eq. (34) the heat loss from the flame to the channel walls, if the distance

108

J. JAROS/NSK/

between them approaches the quenching distance D, the following expression taken f r o m 23 is obtained

Pe(~)Nu=4

pe(W-d

~c 2~.M Nu D2

2~ D

k. . . .

(43)

There exist rigorous relations between the quenching distance D and the thickness of the reaction zone b which is represented in Fig. 35. In Ref. 36 the following relation between the quenching distance D and the flame thickness defined by Andrews and Bradley zs was established: D ~26. Assuming that the flame thickness ~ is equal to the sum of the thickness of the reaction zone b and that of the preheat zone and assuming in an arbitrary manner that the mean thickness of the preheat zone is equal to a double value of what is referred to as the characteristic thickness, + we find 6~-D/2=b+2 2M/coPoUL therefore, in agreement with definitions of the criterial numbers Pe and S we have 2o/guPe=2S+4. This assumption has been confirmed by an analysis of measured temperature profiles. 33 The parameter ~p can be determined from (33) and (36) as

/,b2e 2)-'

1

The parameter 0 under the limit conditions (43) can be determined from (37) as #

Thus,

=

2(2=~ 2

Nu/ea.

31

o~ 2c

~,~

I(] ¢e ¢e

.2

.6

,4

1.0

.8

~.% RG. 36. Peclet number Pe as a function of the temperature ~+and rb--graphical representation of Eqs (40) and (41).

the Nusselt number Nu. The experimentally determined limit % field is also indicated in the figure. Confrontation of the data shows that for quenching conditions (Pe~40) the Nusselt number must be in the range 4-6. Taking the values Pe--40 and Nu--.4 all the parameters which are of interest from the point of view of this work have been computed. The following values were obtained ¢ p = - 0 . 1 6 7 , ¢,=0.031, ¢p/CJ= 5.333, ~ = 1.030 and ~z= -0.030. These results were then used as a point of departure for a computation of the characteristic points on the temperature curve: ~1=0.153, %=0.862, ~,=0.864 and xm=5.830. The numerical values of t+ depend slightly on the heat loss. Thus, for instance, for an adiabatic flame we have r~=0.167. F o r the quantities of % and ~, this

the ratio ¢p/¢, will be expressed by the relation = % CH t 19.t,8

Pe 2

,p 2 S \ 2 u ]

I 8.7

Nu

gw~

.63

i

.55

•

I

and the coefficient

'( ] +=(=<=.)

~.2=~ 1__

!50

25 1

20

For the flame extinction in a narrow channel it has baen established experimentally that P e r 4 0 . 36 A theoretical estimate for the Nusselt number given in Ref. 115 for the case of laminar flow through a cylindrical tube, yields Nu=3.65. This value corresponds qo a developed flow and is somewhat lower than for the earlier sections of the tube. Comparison of the relevant data has shown that, for narrow channels, the Nusselt number is of the same order of magnitude as for tubes (cf. Table 13 m Ref. 115). The measured values of the limit temperatures of flames are usually about rb=0.80--0.85. 36 The calculated limit Peclet number is represented in Fig. 36 as a function of dimensionless temperatures r~, ~ and

200

,0.

\~0/

i 150

E 15

i

w

g !

i

, lC

L ~

100 O

.2

.4

.6

.8

3

I.(1

D . em FIG. 37. The variation of QcoM, L~ and L, with the equivalence ratio ~bin a narrow channel at flame extinction. Qco~ is the mean heat rdeasc rate, Lc--mean rate of heat Joss by conduction, L,--mean rate of heat loss by radiation and D--the quenching distance.

A survey of recent studies on flame extinction

109

TABLE4. The parameters characterizing heat loss at the extinction limit ~b

0.55

0.63

0.7

0.8

0.9

1.0

~.

cm

0.460

0.230

0.175

0.140

0.120

0.100

b,

cm

0.346

0.173

0.132

0.105

0.090

0.075

UL, cm/sec

12.0

17.5

22.0

29.0

36.0

43.0

(T, -To),

1270

1410

1540

1710

1835

1935

14.7

48.5

88.1

164.0

257.5

390.6

K

QwM, cal/cmasec L,., cal/cmasec

0.73

3.38

6.69

12.21

18.33

28.52

L,, cal/rcm3sec

0.40

0.56

0.76

1.08

1.36

1.80

7.71

8.11

8.46

8. I 1

7.65

7.76

L~+ L, QO~M

100 ~,~

The quantities t~, uL and (T~- To) were determined using the data given in Ref. 28. Qo~u and L~ were evaluated using Eqs (33), (34) and (43). and assuming that b= 3/46 and %=0.85. The value of L, was estimated according to Ref. 115.

dependence is strong. The dimensionless limit temperatures thus obtained are in satisfactory agreement with the measurement results. For mixtures of methane and air, the variability of the heat release rate QtoM and that of heat loss have also been calculated over the composition range from the lean flammability limit to stoichiometry, under conditions approaching the limit conditions for L~. The results are shown in Table 4 and Fig. 37.

By introducing the above temperature dependence of Qto, which will be convenient for future consideration (for any distribution of to over the reaction zone), Eq. (32) can be reduced, making use of dimensionless variables (2) and (3), to the form d2z dr dx----I - ~ - = ~/[ F(z) - E(z)]

(44)

where 5.2. Semi-Empirical Method of Integration of the With this method the eigenvalue of the energy equation is computed by graphical integration, in dimensionless parameters, of the derivative of an experimental temperature profile. Assuming that the variation of the temperature in the flame is represented in a qualitative manner for realistic distributions of Q co and L, by the diagram in Fig. 35, we find that: ----~=0 for the preheat z o n e x < 0 , 0 < r < z ~ ----~= to1 --- fa(z) for the region O z ~ zb ----~=0 for the cooling zone x>S, z
2oW

~/=

Energy Equation

(T.-

(45)

To) "~'p P~O2 .~, L

F(z)=

,~Qo, --

(46)

2oW 2L

E(z)= --

(47)

20W and

I

1

l-Tin Th W= ~oL { ~(Qah - L) d z - 1 2(Qc%- L)dz . (48a) Till

The integral expression W determines the effective heat release rate in the entire flame (preheat zone, reaction zone) defined as the difference between the heat produced as a result of the chemical reaction and the heat loss; 20 is the thermal conductivity of the fresh mixture and the quantities to in Eq. (46), 091 and to2 in the integral expression W and 2 take values appropriate for a given region, % is assumed to be a constant. By treating the temperature gradient dT/dx as a dependent variable and r as an independent one, the

110

J. JAROmNSKI

order of the differential Eq. (44) may be reduced. Thus, by setting dr p----dx

replaced by the following relation for W

(49)

Eq. (44) takes the form dp

- p= -

~[ F ( ~ ) -

E(z)]

(50)

with the boundary conditions z=0, p = 0 z = z,., p =

W ~ 1 z~ , S .J-(Q(Ol- L ) dz. Ao o

In other words the complication due to the nonmonotonic character of the curve z(x), can be avoided by rejecting that part of the reaction zone in which the temperature gradient is negative (for r
(51)

rill

t/= I P dr

(52)

O.

This means that F(O)=F(0)=0 and F(z,,)=E(z,.), therefore Q o . , ( ¢ , . ) = L ( z . , g The solution of the Eq. (50) is illustrated, in a qualitive manner in Fig. 38. the curve p in Fig. 38 can be easily estimated using data obtained by the temperature measurements. The initial part of the curve p follows the relationship p-~ 3, the expression in parentheses in Eq. (50) being close to zero in the preheat zone. Then, the p curve approaches a plateau

~-z ..m"

Eventually it reaches the z-axis at the point zM~0.85. The curve p, which illustrates the case of a flame with heat loss within the temperature interval zb < z < z,., has two branches, the lower of which, with negative gradient, corresponds to the region x,.
because from the definition (46) and (47) of F(z) and E(z), and the definition (48b), of W, it follows that rill

I [F(T)-E(z)]

dz~l.

0

Therefore r/ is equal to the area under the curve

p= f(z), that is to the product

.8 .6

AQ

2 Zm

,1 = - - .

(55)

The mean limit value of the heat loss rate can be assumed with reference to the mean effective heat release rate by integrating the expression (47): r++l

S 2Ld+ j" E(z) d z = o =N. o 2oW

rill

e,,

.t,

(54)

where pu is the mean dimensionless gradient of the dimensionless temperature ~x), which can be obtained by graphical means, for instance (for positive gradients only, if the above simplification has been made). Making use of the mean temperature gradient PM, and the temperature rise Az=z.,, the corresponding dimensionless flame thickness can be estimated to be AX=Z,,dpU=CpPoUL6M/AM=SM where 6M is the flame thickness corresponding to the mean dimensionless temperature gradient. On substituting PM = z,,,/S~< into (54) we find

SM

1.0

(53)

0

t/= PM Z,. P" = ( T . - To) c, P0 ut

(48b)

adiabatic

(56)

Assuming, for the temperature range considered, a mean value of AM and making use of the relations (3), (34), (43), (45), (55) and (56) we find

.2

,.6,FIG. 38. Graphical representation of Eq. (50).

2u Nu 6M N = 2o Pe D"

(57)

A survey of recent studies on flame extinction

111

Besides, direct calculation shows that a solution for r within the range of small Peclet numbers exceeds the region of physically realistic values. Thus, for instance, for N u = 4 and Pe ~ - 10 we find zi> rb. 2. As a result of the quenching properties of the channel walls the flame is extinguished at a defined J' . Peclet number. For a flame propagating in a 0 ~"r.1 homogeneous methane-air mixture we have Pe= FIG. 39. Heat release rate and heat loss rate as a function of 40. 36 The existence in such a mixture of a flame the temperature. characterized by a lower Peclet number is impossible. The critical condition for flame extinction is expressed by Eq. (57), which shows that a flame According to the rough evaluation of Ref. 33, we should be extinguished if the heat loss rate by have 6 u ~ =0,666. Now since 6/D~-1/2, we have all conduction exceeds 8 % of the effective heat release the data necessary to evaluate N, which is N ~0.08. rate. Typical curves of heat release rate and heat loss Table 4 and Fig. 37 show that the mean heat rate are illustrated in a qualitative manner in Fig. 39. release rate Qtou decreases rapidly as the equivalence This form of the function expressing the heat release ratio varies from the value for stoichiometry towards rate towards the end of the reaction process is the lean or rich range. This rapid decrease in Qtou is justified by prolonged combustion of CO. It may also due to a prolongation of the reaction time, measured be used to explain the relatively large difference in terms of 6/uL. The heat loss rate from a limit flame between the measured temperature at the end of the to the walls, as a function of the equivalence ratio reaction and the adiabatic temperature. The charac- varies, in a similar manner, that is, in agreement with ter of the function F(r) in Fig. 39 is also justified by (43) in inverse proportion to the square of the flame the heat release rate curve which has been considered thickness (at the limit D ~ 26). and discussed in Section 3. The passage from stoichiometry to the limit equivalence ratios is accompanied by an increase in the flame thickness and the quenching distance. As 5.3. The Results the mixture becomes leaner or richer the conThe Peclet number Pe (or the associate number S) tribution of thermal radiation to the heat loss from is a measure of the burning velocity in dimensionless the flame increases, the rates Lc and L, becoming parameters. If the relation (41) is considered from a comparable (see Fig. 37). formal point of view, it can be stated by direct computation that, under the condition of ~, ~: 0, each 6. SUMMARY. TWO DIFFERENT MECHANISMS OF FLAME temperature zb located within the region 0 < r < l EXTINCTION UNDER THE ACTION OF ACCELERATION: which is realistic from the physical point of view, EXTINCTION OF UPWARD AND DOWNWARD PROPAcorresponds to two values of the Peclet number. This GATING FLAMES would lead to a conclusion that there are two laminar burning velocities as was the case in Refs 7 and 8. To understand the physical foundations for the Such a conclusion would be erroneous, however, existence of flammability limits it is necessary to for reasons that are illustrated in some measure in bring together all the arguments, based on the Fig. 36. experimental facts which have been discussed above. 1. The lower of the two values, obtained by The existence of flammability limits is a result of computation for the laminar burning velocity would heat loss from the flame to the surroundings. correspond to a range of Pc< 10. From the analysis According to Zeldovich, flame extinction occurs as a made in Ref. 33 it follows that the existence of a result of the intensification of heat loss due to the range of P c < 10 has no physical sense. The thickness burning velocity4 being lowered on lowering the of the thinnest adiabatic flame (for any flammable flame temperature. The same idea is expressed in a mixture) with a purely thermal mechanism of very clear manner by Merzhanov, 116 who treats the propagation is limited to the preheat zone, therefore flame front as a thermal wave: it is equal to the double subtangent of the tem"Heat losses reduce the temperature and the propagation perature curve at the inflection point which is velocity of the wave. Reduced wave velocity leads in turn fi=2(}.M/CppoUL). 33 The physical conditions of existto an increase in the time for which molecules remain in the wave. which increases the heat losses. Thus there is ence of a flame in a channel require that the width of positive feedback resulting in propagation limits for the the channel should at least be equal to double the wave: for a certain level of heat losses the wave cannot flame thickness, therefore D~--4(~.M/CppoUL~ This conpropagate and dies out". dition is equivalent to (2o/2u)Pe~-4. For a limit With laminar flow a flame can loose heat by temperature T~1000°C, ~.u/20 ~ =2.4 and Pe~lO. conduction for by radiation. In an infinite enclosure, Thus, in the extreme case of a pure thermal flame we the role of heat conduction vanishes, and the flame obtain a lowest value of the Peeler number Pc= 10.

'"

~ F

I'J.'}-E(~'}

112

J. JAROSZNS~d

can only lose heat by radiation. Conversely, in an enclosure with cold walls conduction is the principal cause of heat loss. Either of these two types of heat loss may bring about flame extinction, provided that the loss rate exceeds a certain level with respect to the heat release rate. If heat loss is the only cause of flame extinction, the experimental fact that there is a great variety of extinction mechanisms deserves attention. To explain flame extinction, attempts have often been made to find a single principal mechanism or the unique "true" flammability limit. However, these attempts to formulate a general mechanism, capable of operating under different physical conditions have mostly failed. There are many ways of bringing about flame extinction as the flammability limit is approached. It may also be found that the dominant mechanism of flame extinction is different depending on the particular conditions of the experiment. Since the existence and steady motion of a flame are dependent upon the ratio of the rate of heat loss from the flame to the surroundings to the heat release rate as a result of chemical reaction, any increase in the heat loss, affecting the critical value of that ratio, should lead to flame extinction. Usually, the critical value is exceeded not over the entire "surface" of the flame but only a part of it. This often results in gradual extinction of the whole flame. Thus, a fundamental condition for the existence of flammability limits is that the heat fluxes in the flame should approach the critical values. This can be achieved by appropriate modification of the physical conditions (a leaner or richer mixture, lower pres:ure or lower temperature, the introduction of a cold wall etc.) If the flame approaches the critical state, there will always be some factor capable of affecting the critical heat loss rate. This factor will be determined by the physical conditions of the experiment. The above argument can be illustrated by detailed description of two different extinction mechanisms for a flame propagating in a standard tube) ~7 For some fuel-air mixtures there are two distinct flammability limits depending on whether the flame propagates upwards or downwards. A flame of a near-limit mixture propagating through a standard tube from the lower (open) to the upper (closed) end, resembles in its appearance (Fig. 13), structure (Fig. 14) and behaviour an elongated air bubble moving in a heavy liquid. In the field of gravity forces, the density difference between the hot and cold gas, causes the hot gas to rise which is accompanied by "the downward motion of cold gas near the walls. The speed of this motion considerably exceeds the laminar burning velocity, therefore the cold mixture near the flame on the axis of the tube tends to rise as well which results in a downward motion of the mixture in the neighbourhood of the walls, where most of it is burned. The walls of the tube determine the form of the flow field around the flame, the tangential velocity component increasing

as the mixture moves downward along its surface It is this flow pattern which gives the flame front its characteristic shape. In the limit case, the upward velocity of the flame with respect to the tube walls can be found from the expression of Davies and Taylor ~t s u=0.328

(9d)*

(58)

where 0 is the acceleration due to gravity and d = the tube diameter. The surface of the flame adjusts itself to the velocity of the leading point and to the laminar burning velocity in such a manner that SuL=Fu, where S is the flame area and F = the cross-sectional area of the tube. This can be verified empirically by comparing in the same tube, the propagation of limit flames with different limit burning velocities such as, e.g. for propane-air and ammonia-air mixtures. With the buoyancy velocities of the two flame being approximately the same, the ammonia-air flame has a larger surface. By determining experimentally the shape of the flame surface, the field of flow can be easily calculated. Visualization of flow in dust-gas-air mixtures (Section 4.11, Fig. 32) confirms the fact that the mass flow behind the flame front occurs along streamlines directed towards the tube axis and downwards. These observations make it possible to represent the flow pattern diagrammaticaly as shown in Fig. 40. This is a classical case of flow with the flame being stretched. It has been shown 4° that the flow arodnd the flame is potential and does not influence the motion of the boundary layer (Fig. 16). This in turn allows one to reach the conclusion, on the basis of computations, that the stretch is maximum at the leading point of the flame. 43 An attempt can now be made to describe, on the basis of the fundamental observations made and the

t.L .Lt3_

i FIG. 40. Flow field for the gases for a limit flame propagating upward in a standard tube; a--streamlines, b-gas velocity distribution, with reference to the walls.

A survey of recent studies on flame extinction inferences resulting from them, the most probable mechanism of flame extinction. First, consider Xhe phenomena which usually accompany flame extinction as discussed here and which may have bearing on the extinction process. At least two of these can be mentioned here, namely flame stretching and preferential diffusion. Undoubtedly there is a connection between flame stretch and the phenomenon of flame extinction. The flame disappears first in the region where the stretch is at a maximum, i.e. at the top of the flame, and men the decay wave moves downwards along its surface. The heat loss to the wall does not influence the process of flame extinction. This fact is confirmed by temperature measurements made at the wall which show that the temperature begins to rise only at the point of contact between the flame and the wall (Fig. 12), which is about 7 cm below the point at which extinction begins. The effect of preferential diffusion of flammability limits has been observed by yon Lavante. *a In the case of lean methane-air mixtures it is responsible for the rounded tip of the flame becoming richer in methane, which extends the flammability range The smaller the radius of curvature of the flame surface the wider is the flammability range. In the case of lean methane-air mixture the most probable mechanism of flame extinction is, a result of the opposing effects of preferential diffusion (heat flows to the tip of the flame) and flame stretch (heat flows from the tip of the flame downwards), under conditions where the ratio of the heat loss rate to the heat release rate approaches the critical value. Near the flammability limit the flame is thick and is characterized by a very long reaction time and a low heat release rate. As the limit mixture composition is approached, the heat release rate becomes so low that the state of the flame becomes critical from the point of view of heat transfer to the surroundings. Under such conditions even a small heat loss due to flame stretching may bring about criticality and the disappearance of the flame. The mechanism discussed above is in satisfactory agreement with all the experimental facts. It confirms the observation that the flammability limit of an upward propagating flame is time dependent, because the distance travelled by the flame, ignition and going out can be controlled by accurate selection of mixture composition. This mechanism can also be made use of to explain the fact that the flammability range becomes narrower as the diameter of the tube increases, a2 The extinction mechanism of a flame propagating freely from the upper (open) end to the lower (closed) end of the tube is quite different. ]'he quenching process is initiated, in this case, by the wall. It has already been observed above that such a mechanism of flame extinction occurs if the flame propagates in the direction of the acceleration. The extinction of a flame during its propagation towards the closed JPECS 12:2-C

113

lower end of a standard tube is a case of the flame extinction in a field of acceleration due to gravity. It has been observed that the flame is quenched at the wall if it is plane and at approximately right angles to the wall. In this case the quenching of the flame may be explained by the fact that in this position the flame area is minimum while the area of contact with the wall, through which heat is conducted to the walls, is maximum. The flame quenching at the walls is accompanied by cooled, heavy gases in the boundary layer flowing in the direction of flame propagation. The flattening of a flame propagating in the direction of the acceleration may be caused by the action of at least three factors which are the mixture composition (or, which is equivalent, the laminar burning velocity), the acceleration acting on the flame, and the dimension of the channels. Let us consider now a number of particular cases. 1. For a fixed mixture composition and fixed dimensions of the channel, the curvature of the flame can be reduced by increasing the acceleration acting on the flame in the direction of flame propagation (Krivulin's experiments with a centrifugal machine, 5~ Babkin's experiments in laminar swirling flowSS). 2. For a fixed acceleration and fixed dimensions of the channel, a similar effect of reduced curvature may be obtained, if the mixture is made either richer or leaner (experiments with downward propagating flames in standard flammability tubes~ 3. For a fixed mixture composition and a fixed acceleration the curvature of the flame can be effectively reduced by decreasing the distance between the wall~ If it approaches the quenching distance, this should remove the curvature completely (experiments with quenching channels, a6 see Fig. 34). The following mechanism of flame extinction may be assumed for a flame propagating in the direction of the acceleration, for example, in a standard tube. Temperature measurements showed that, at a distance of about 30 cm behind the flame front, the combustion gases have already cooled down. 31 Thus after the contact between the flame and the wall has been broken the hot body of gas can rise. This is impossible as long as the laminar burning velocity is high and the flame touches the walls at an acute angl~ However, if the mixture is made sufficiently lean or rich, or if the acceleration is made sufficiently high, the flame straightens and takes a position at right angles to the walls, as a consequence of which it is quenched in the neighbourhood of the wall~ The remaining portion of the flame together with the hot gases, rises slightly and goes out. At the moment of extinction, as a result of buoyancy effects, cooled

114

J. JA~tOSlN,Srd

combustion gases propagating ahead of the downward propagating flame (Fig. 13) can always be observed near the walls, which results in the extinction of the flame because it would now have to propagate in a partially diluted mixture. Observation of all the cases of extinction of flames propagating freely downwards showed that the motion slows down just before extinction, that the flame first goes out near the walls, that there is a flow of the cooled combustion gases ahead of the flame downwards, the remainder of the flame near the tube axis being slightly lifted. From the point of view of preventing further propagation of the flame its extinction near the walls is of prime importance. Buoyancy effects, due to which the mixture becomes partially diluted ahead of the flame, as a result of which the flame goes out, are only secondary phenomena. In practice, for lean methane-air mixtures, the flame is seldom extinguished over the entire width of the tube. In a tube its surface is usually divided into several cells, their convex sides pointing downwards. Thus, the streamlines behind the convex flame front in each cell may be treated as streamlines behind the convex flame front in a separate channel, t19 Under limit conditions, the extinction process starts in one of the cells. The remainder of the flame in that cell and the adjacent hot gases move upwards, the cooled combustion gases flowing down along the walls. Later the flame goes out in all the remaining cells, and this process may take as long as several seconds. On the basis of information obtained from experiments we can analyse, in a similar manner, all the remaining mechanisms of flame extiction.

5.

6.

7.

8.

9.

10.

11.

12.

velocity gradient at the region between the core flow and the boundary layer. The mechanism of flame extinction in a standard tube for determining the flammability limits is different for different senses of flame propagation: an upward propagating flame is extinguished as a result of flame stretch, and a downward propagating flame as a result of the quenching action of the wall. Gas mixture burned in a large vessel has flammability limits which are wider than under the standard conditions. A flame can be quenched by turbulence if the Karlovitz number, which is defined by the relation (28) exceeds a value of 7-20. An increase in acceleration acting on a flame makes the extinction limits narrower. The influence of zero g is similar. An increase in the initial temperature of the mixture increases linearly the flammability limits. The lean flammability limit of coal dust-gas mixtures varies inversely with the content of volatiles in the dusL The critical radius of the flame formed during spark ignition is of the same order of magnitude as the flame thickness. A flame is quenched if the ratio of the heat loss rate to heat release rate exceeds a value of 8 %.

Acknowledoements--The author is indebted to Professors E. Bulewicz, J. Chomiak and J. H. Lee for critically reading the manuscript and for many helpful discussions. This help is greatly appreciated.

REFERENCES

7. CONCLUSIONS 1. A limit flame of methane-air mixture resembles flame of any other mixture compositions. The constancy of the Peclet number S in Fig. 8 for any mixture composition and the amount of heat losses mean, from the physical point of view, that the fundamental geometrical proportions of flame in these different conditions are almost invariable. 2. A flame in a quenching channel is quenched when the distance between the walls is reduced to about twice the flame thickness. 3. An upward propagating limit flame in a standard tube cannot be quenched as a result of thermal action. Any attempt to quench such a flame by cooling its top part by inserting sets of partitions in the form of vertical plates did not cause any change in the observed flammability limits up to an obstacle spacing equal to the quenching distance. 4. A limit flame propagating upwards in a standard tube against constant downward flow of mixture at a mean velocity of above 15 cm/sec propagates in the boundary layer and its size depends on the

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