The ignition of gaseous explosive media by hot wires

IGNITION OF GAS MIXTURES

2.

3.

4.

5.

6. 7.

8.

9. 10.

11.

12. 13.

E X P / C F 1071 (Exp. Inc. Tech. Memo. No. 65) (July 31, 1948). COWARDAND GUEST: "Ignition of Natural Gas-Air Mixtures by Heated Metal Bars," J.A.C.A., 49, 2479 (1927). DRYDEN: "Aerodynamics of Cooling," Vol. VI, Sect. T., p. 261 et seq., "Aerodynamic Theory," Reprinted Edition, California Institute of Technology (1943). DRYDEN: "A Review of the Statistical Theory of Turbulence," Quarterly of App. Math., 1, 7 (1943). DRYDEN: "The Role of Transition from Laminar to Turbulent Flow in Fluid Mechanics," University of Pennsylvania Bicentennial Conference on Fluid Mechanics and Statistical .Methods in Engineering. The University of Pennsylvania Press, Philadelphia (1941). FENN: Unpublished report. FENN AND IRBY: "Additional Factors Affecting the Precision of Hot Rod Ignition Measurements," Informal Bumblebee Memorandum, E X P / C F 1070, (Exp. Inc. Tech. Memo. No. 64) (July 31, 1948). JOST: "Explosion and Combustion Processes in Gases," P. 27, Croft translation, McGraw-Hill Book Co. Inc., New York (1946). Loc. tit., p. 45. KENNARD: "Temperature Distribution and Heat Flux in Air by Interferometry," p. 685, "Temperature," Reinhold Publishing Co., New York (1941). KNOWLESAND PRUDEN: "On the Drag of Circular Cylinders at High Speeds," Ministry of Aircraft Production, A.R.C. Technical Report, R. & M. No. 1933 (February 1944). LANDAU:"The Ignition of Gases by Local Sources," Chem. Rev. 21,245 (1937). McADAMS: "Heat Transmission," McGraw-Hill Book Co., Inc., New York (1942).

329

14. ~IULLEN,FENN, AND GARMON:"Burners for Supersonic Ramjets, Some Factors Controlling Overall Burner Performance," Paper delivered before Division of Gas and Fuel Chemistry, American Chemical Society, ll2th Meeting, New York (~eptember, 1947). 15. MULLEN, GARMON,BRINCKERHOFF• BARR: "The Ignition of Pentane-Air in High Velocity Flow by Heated Rods," Informal Bumblebee Memorandum, E X P / C F 697 (Exp. Inc. Tech. Memo. No. 24) (June 2, 1947). 16. PATERSON:"The Ignition of Inflammable Gases by Hot Moving Particles, I," Phil. Mag., (7), 28, 1 (1939). 17. PATERSON:"The Ignition of Inflammable Gases by Hot Moving Particles, II," Phil. Mag., 30, 437 (1940). 18. REEF AND SIMMONS: "The Effect of Eddies Generated by the Motion of Circular Cylinders Through a Fluid," Ministry of Aircraft Production, A.R.D. Technical Report, R. & M. No. 917. 19. ~COTT,JONES, AND ~COTT: "Determination of Ignition Temperature of Combustible Liquids and Gases," Anal. Chem., 20, 238 (1948). 20. SEMENOFF: "Chemical Kinetics and Chain Reactions," p. 86, Oxford at the Clarendon Press (1935). 21. ~ILVER:"The Ignition of Gaseous Mixtures by Hot Particles," Phil. Mag., (7), 23, 633 (1937). 22. THORNTON: Reference cited p. 19 of S.M.R.B. Paper No. 36, "The Ignition of Gases by Hot Wires" by Shepherd and Wheeler (1927). 23. WINDINGAND CHENEY: "Mass and Heat Transfer in Tube Banks," Ind. Eng. Chem., 40, 1087 (1948). 24. WOLLNER Am) LEnMANN: Ann. Min. Belg., 6, 9 (1886); also Ber. der preuss, Schlagwetter kommission, Anlagen Zum Haupt-Berichte, Berlin, 3, 193 (1886).

35

THE IGNITION OF GASEOUS EXPLOSIVE MEDIA BY HOT WIRES By H. P. STOUT n~rD E. JONES t Authors' Note: The fusing energies of fine wires in air have since been measured by another method and it appears that, beyond a certain time of current application, which is smaller the thinner the 1 Imperial Chemical Industries Limited, Nobel Division Research Department, Stevenston, Ayrshire, Scotland.

wire, the fusing energy increases linearly with application time. The results suggest the setting up of a.convection current which is a function of the wire temperature and is, thereforel constant at a given wire temperature. Once the convection current has been established,'and this ~ccurs very quickly with fine wires, the heat communicated

330

THIRD SYMPOSIUM ON COMBUSTION, FLAME

to the air becomes an approximately linear function of the time. This convection current, and the heat it carries away, plays an important part in the ignition of gases by hot surfaces. INTRODUCTION The study of the conditions under which explosive media may be ignited by thermal means is of considerable practical and theoretical interest and the use of electrically heated wires as the igniting agency offers a convenient technique for exploring the energetics of ignition and obtaining quantitative data comparatively free from ambiguity. Experiments along these lines (not yet published) have been carried out by the present writers, with the purpose of elucidating the mechanism of operation of "low tension fuseheads" as used in commercial electric blasting caps and the work, though originally designed for solid explosives, has recently been extended to include two particular cases of ~IDGEWIRE

SOLDER

pRESS80ARO BRASS

FOIL

AND EXPLOSION PHENOMENA

and with three explosive media, namely, copper acetylide, a mixture of four parts byweight of lead mononitroresorcinate to one of potassium chlorate and a mixture of five parts by weight of potassium chlorate to one of birchwood charcoal. The results were found to be most readily expressed in terms of the heat, i2Rt, generated in the wire during the period of application of the current and may be summarised as follows: For any one explosive composition, the critical energy for ignition, E, increased linearly with the time of current application and could be represented by the equation E = A + Bt

(1)

where E is the critical energy for ignition corresponding to an excitation time t and A and B are constants. This result confirms that previously obtained by J. D. Morgan (1) in a similar experiment. For a constant excitation time, the critical energy was found to increase linearly with the length, l, of the heating element, the results being represented by the equation

~SOLbs

= C + Dl

"

~

,~RA~S FOIL

Fro. 1. Sketch of hot wire igniter. gaseous explosive media. The object of the present paper is to describe the latter experiments but it is essential for the proper appreciation of the results to indicate briefly the findings in the work on solids. The heating element used for igniting the solid explosives was the same as that used in the present experiments (fig. 1), but was embedded in a bead of solid explosive formed by a dipping an d drying process the solids being bonded together with nitrocellulose. In the experimental procedure, a known current was passed through the heating element, which consisted of a Short length of fine resistance wire, for a predetermined time, which could be varied between 1 and 60 milliseconds, and the mean firing current, or 50 percent ignition current, corresponding to the chosen application time, or excitation time as it may be called, was determined. Experiments were made with nichrome wires of different lengths, 0.087 to 0.285 cm. and varying diameters, 0.0013 to 0.0078 cm.,

(2)

where C and D are constants. By compounding the results represented by equations 1 and 2, it was determined that E = Gl + (H + Jl)t

(3)

when both l and t vary, G, H and J being constants for a particular composition. Experiments with wires of various diameters further showed that G =K+La

(4)

where a is the cross-sectional area of the wire and K and L are constants. Finally, the use of wires of different materials, covering a range of thermal properties, indicated that a = g

+ Mh

(5)

where h is the thermal capacity of the wire per unit length and K and M are constants. The term A in equation 1 represents the limiting energy required for ignition when the heat is generated instantaneously in the wire, i.e., when t = 0, provided, of course, the extrapolation to zero time can be made without introducing Other complications. A simple interpretation of the

331

I G N I T I O N O~" GAS M I X T U R E S

linear form of this equation might then be that a certain critical thermal state, represented by A, must be established in order to bring about ignition and that the term Bt represents heat lost by conduction in attaining this state. In practice, the situation may be more complex and the division of the energy into these two parts may be somewhat idealistic. Equation 3 shows that the factor B may also be resolved into two components, one independent of the length of the wire, and the other directly proportional to it. Again, a simple interpretation is that the first term, H, represents loss of heat from the ends of the wire into the soldered joints etc., and the second term, Jl, the heat dissipated laterally by conduction into and through the surrounding medium, this portion naturally varying with the length of the wire. Equation 3 also shows that A, the limiting value of the energy required for ignition under conditions of instantaneous heat generation, is directly proportional to the length of the bridge wire, thus indicating that the energy per unit length, G, is the critical factor determining ignition. This factor is further shown by equation 5 to vary linearly with the thermal capacity per unit length of the wire. As before, this equation may be interpreted as indicating that the critical enel:gy for ignition may be further sub-divided into two parts, one part, Mh, being retained in the wire and the other, K, being given up to the explosive medium. The constant M thus becomes the temperature of the wire and the conclusion is reached that ignition always occurs at a particular temperature of the wire. The linear variation of G with area of cross-section of wire, as shown by equation 4, is thus to be expected and could have been deduced from equation 5 since for wires of the same material, the thermal capacity per unit length is directly proportional to the cross-sectional area. The technique employed above is based on successive extrapolations to zero and, while such a process can not be carried to its limit in practice, it can be simulated graphically, thereby providing a useful means of analysing the energetics of ignition by hot wires. The results obtained with solid explosives will be described more fully elsewhere and the brief outline given above is intended as an introduction to the present investigation, the customary review of the literature being omitted because little attention appears to have been given to the particular aspect of the problem of ignition considered here.

EXPERIMENTAL

The heating element consisted of a short length of fine resistance wire stretched across the tip of a narrow strip of cardboard sandwiched between two metal foils, the ends of the "bridge-wire" being soldered to the foils which could thus be connected to the source of electric current by inserting the unbridged end of the strip into a simple spring clip in the battery circuit. The bridged end of the strip was stepped so as to control the length of the bridge and also to ensure that the wire stood clear of the cardboard for most of its length and would therefore be completely surrounded by the gas to be ignited. The construction of the device will be apparent from the sketch given in figure 1. The actual length of the bridge-wire was determined in each case by measuring the resistance of the bridge and calculating its length from the known linear resistance of the original wire. The magnitude of the firing current was controlled by means of series resistances and its duration by a Pendulum time switch designed to give times of current application varying from 1 to 60 X 10-8 sec. In each experiment, a few preliminary tests were made to establish roughly the value of the mean firing current for a given time of application of current and then 20 tests, each with a fresh igniter, were made at each of two currents, one slightly above and the other just below the expected mean, the number of ignitions occurring at each current being noted. The true value of the mean firing current for that particular time of application was obtained by interpolating the point at which 50 percent ignitions would occur. The currents required to give 50 percent of ignitions were estimated for a range of application times, and the corresponding energy calculated in each case. The wires used were of nichrome, and the diameters, estimated from the linear resistance of the wire and the specific resistance of nichrome, varied from 0.0043 cm. to 0.0011 crn. In ~ach case the mean length was approximately 0.15 crn. The gas mixtures were made up in a 20 litre bottle, and stored over water, the aspirator being connected to the explosion vessel which consisted of a vertical glass tube 10 cm. long and 2 cm. diameter. The upper end of the tube carried a rubber stopper through which passed two brass rods forming a .clip to hold the igniter, while the lower end was dosed by a second rubber stopper. There were two side tubes, one connected to a water pump and the other to the bottle. The pressure in the vessel was first reduced to

332

T H I R D SYMPOSIUM ON COMBUSTION~ F L A M E A N D E X P L O S I O N P H E N O M E N A

3 cm. of mercury, and gas then admitted from the bottle. A known current was passed through the bridge-wire for a time limited by the pendulum, and the occurrence or non-occurrence of ignition noted. The criterion of ignition was taken to be a definite explosion, generally sufficiently powerful to blow out the lower stopper. Reaction without explosion sometimes occurred, indicated by slight condensation of moisture on the walls of the tube, but such was not regarded as a true ignition leading to an explosive reaction. Two gas mixtures were used, namely, 20 percent hydrogen-air and 11 percent methane-air, the

resistance is much the same no matter whether the wire is heated rapidly or slowly, all the energies in tables 2 and 3 will be too low by a constant factor, and their variation will be similar to the variation of the true energies. I t will be seen that the hydrogen-air mixtures were ignited by all the wires over the complete range of times used, but that ignition of methaneair could not be effected at the longer application times, the time above which ignition did not take place decreasing as the diameter of the wire decreased, and finally becoming less than 4 or 5 milliseconds for the thinnest diameter.

TABLE 1

Ignition energies of 20 per cent hydrogen-air mixture Resistance

(ohm)

Diameter

1.20

4.33 X 10-acm.

Time m. sec. Current amps. Energy m. joules

4.5 1.85

18.4

10.5 1.32 21.7

15.4 1.12 [22.9

26.3 .93 27.3

36.8 .85 31.7

50.1 980 38.5

2.16

2.79 X 10-acm.

Time m. sec. Current amps. Energy m. joules

3.18 1.18 9.57

8.6 .75 10.4

15.2 .626 12.9

26.2 .52 15.5

41.8 .484 21.2

50.1 9 24.8

6.92

1.8

X 10-acm.

Time m. sec. Current amps9 Energy m. joules

3.54 9545 7.28

8.5 .37 8.2

15.1 .318 10.6

25.8 929 15.0

41.7 .28 22.5

50.1 .294 29.9

9.05

1.5

X 10 acm.

Time m. secs. Current amps. Energy m. joules

3.54 ,36 4.16

8.4 .246 4.61

15.1 .214 6.25

23

41.7 .21 16.7

50.1

Time m. secs. Current amps. Energy m. joules

3.54 9231 2.8

8.44

42.2

50.1

14.9

1.14 >( 10-a cm.

percentages referring to the composition after admission to the explosion vessel. Eleven percent methane was chosen because it was found that ignition was often difficult to effect with mixtures weaker than 10-11 percent. CRITICAL ENERGY FOR IGNITION The mean firing currents and corresponding energies for 20 percent, hydrogen-air mixtures and 11 percent methane-air mixtures are given in tables 1 and 2 for the different wires9 The energies were calculated as i2R t, where R is the resistance of the wire when cold, and are" thus too low, because the resistance of the wire increases as its temperature rises9 Assuming that the chan.ge in

16

3.21

[15.1 I

.149

] 4.98

198 8118 23:6 9 8.78

.145

13.3

.195

17.6

.147

16.2

The energy required for ignition is plotted against application time in figures 2 and 3 for hydrogen-air and methane-air respectively, from which it will be seen that the energy decreases with decrease in the time of application, but is still finite on extrapolating to zero time. M o r e o v e r the value of the energy at a given application time decreases as the diameter of the wire decreases. This behaviour is very similar to that found in the case of solid explosive media, except that for the latter the critical energy for ignition increased linearly with application time. I n the present case, the increase in ignition energy with time appears to be greater than linear and the results might be represented by an equation of the form

IGNITION

OF

where E0 is the intercept on the the second term represents the factor. If we assume t h a t extratime is valid then the term E0

E = Eo + f ( t ) , energy axis and effect of the time polation to zero

GAS

333

MIXTURES

hence its thermal capacity, we can vary the amount of heat retained in the wire and, if we then extrapolate to zero diameter of wire, we can in principle eliminate this factor. The values of E0 for bridge-

TABLE 2 Ignition energies of 12 per cent mel,'tane-air mixture

Resistance (ohm) 1.20

2.16

6.92

9.05

14.9

Diameter

4.33 X 10-3 cm.

2.79

X

1.8

Time m. sec. Current amp. Energy m. joules

10-s cm.

X 10 Scm.

1.5

X

10-Scm.

1.14 X 10-a cm.

5.01

9.15 1.43 22.5

1.83

20

17.3 1.08 24.2

Time m. sec. Current amp. Energy ~a. joules

2.05

4.08

1.35

1.05

8.1

9.7

Time m. sec. Current amp. Energy m. joules

2.05 9628 5.58

4.19 9 69

Time m. sec. Current amp. Energy m. joules

2.02 .42 3.2

4.26 9308 3.66

I0

Time m. sec. Current amp. Energy m. joules

2.02

4.26

10

10.2 .72 11.3

27.8 40.6 .898 , .808 i 26.9 i31.8

50.2 .79 37.6

i114.25

50.2

29.2 1 .627; .515 i 12.1 16.7 I

10

L 19.7 .354 ti * J 8.67 II

39.1 *

i

.

.

19.7 * .

.238 5.14

.

.

19.7

.

50.2 * .

.

39.1 * . .

50.2 :::

39.1

50.2

I

* No ignitions. +*~'!*7=o+~t*

, JO" Joutf$

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,..

III

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ii

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/

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"'!!i;!

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!!~

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t/

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ii:il

3 ?14it

[~i4z ,+i

.=r" I .

1 zo EXCITA'r

+ I

~-

I

u

Jo

I

i.+.'"

i~iii

[~- q- ;-4"" . . . . . . . . . Io

, , :

- -t-T-t~ 4O 9 10"15Er

$o

tOM

SO

TIME

I r

] I + I I

.-H'"

-i+lliil

<+

[

,

|/+

1 Iltt

, I0

'

+i+ll+l+l, I I + I Ld+.~2+;t

',--,lllJlll ~I~llllIII I III

"rATION

+:

,+_ , : !!

i;;

iii

I I I II

10

+ [

I

[ i I L-~fl I I I ..--I-rl i i i ii I , !ll ill ii

s

A-"+

30 "rIMr

I II *@ I I0"$14~C,+ $0

FIG. 2. Variation of ignition energy with excitation time for 20 percent hydrogen-air mixture.

I=IG. 3 . Variation of ignition energy with excitation time for 11 percent methane+air mixture.

represents the quantity of heat which, when generated instantaneously in the bridge-wire will cause ignition of the gas mixture. When ignition occurs, a proportion of this heat will have been communicated to the gas mixture and the rest will be contained in the bridge-wire. B y varying the diameter of the bridge-wire, and

wires of different diameters are given in table 3 and are plotted against the thermal capacities of the bridge-wires in figure 5, where (a) corresponds to the hydrogen-air mixture and (b) to the methane-air mixture 9 I t will be seen from this graph t h a t the points lie roughly on straight lines, suggesting that E,, = E,, ~ + kC, where E,, ~ and k are

334

THIRD

SYMPOSIUM

ON

COMBUSTION,

constants and C is the thermal capacity of the bridge-wire. This result is similar to that obtained for solid explosives and the factor k may be regarded as TABLE

3

t

[

l

Area of cross section (sq. i ** cm. X 10-6) 14.7 6.11 2.54 1.77 1.02 Thermal capacity (cal. X ! j I ', 10-~) . . . . . . . . . . . . . . . . . . 2.040.850.350.250.14 .

.

.

.

.

.

.

.

.

.

.

.

~6 :

[

Hydrogen-air . . . . . . . . . . . Methane-air . . . . . . . . . . . .

I

]

4.43 2.18 1.60 .9( .62 ] 4.95 1.91 1.22 .67 - l

14} 9 104~'OU L I | , + l 9

r

--

, i i i i i

t--

it ~-,. +-

_tl+ I,~

__+._ _

+ i i

~'~ I l i r-_ ~. .. i 9+

+ii

a r

: : : t I I

Io

,~.~-

- ~Wf'l

i

,,l

_[

+,iX-, :

~

L -Idt ~ Z ~-4"1~

--VT-] I [ I I I I II

It

II Ill

4~.t045|r

|o 1o EXCIT^TION TIME

FIG. 4. Variation of fusing energy with excitation time for nichrome wires in air.

!ti S,

I I

+11

I1

,!

~

III ilil ]]

I

1 I '

/

9 ,~'/

]

1 J

"1 I I I11 111 III

-5

in TH [RNAL

:!

- l l t l

II

i J" t ~+,r

" I d " i"

~ !I,.-"J-I ,+.,:",,+~ 11 ,

i

]

I I I

9

i1-] II 11111

- " -

] I~/.,

~l!.!ql l l

++ l l l k

i

o|

i-7 i/i II l,'k.)

I

Illi Ill ill I I ] I t i iil

+II :Ii,

ii

1 I

I I

I ]

I ]il I

I I I

L8 CA@AGIT r

FIG. 5. Variation of critical energy with thermal capacity of bridge wire. equivalent to a temperature, in which case it would appear that the temperature of the wire-at ignition is constant irrespective of the diameter, or thermal capacity, of the wire. The value of

FLAME

AND

EXPLOSION

PHENOMENA

this temperature, as given by the slope of the appropriate line in figure 5, is about 2000~ or the hydrogen-air mixture and 2300~ for the methane-air mixture, but these are only rough estimates since the energies were calculated from the cold resistance of the wire, no account being taken of the variation in resistance with temperature, and the thermal capacities were calculated from the specific heat of nichrome at ordinary temperatures, again ignoring changes with temperature. As the two effects act in opposite directions and so tend to neutralise each other, the resultant effect is not likely to be great and the temperature of the wire at ignition would appear to be considerably higher than the melting point of nichrome, which is only 1350~ This suggests that the temperatures involved are sufficient to cause fusion of the wire and that the ignition failures experienced with the methane-air mixture under certain conditions might have been caused by fusion of the wire before sufficient energy had been communicated to the explosive mixture to effect ignition. I t was decided, therefore, to measure the fusing energies of the various wires and compare them with the corresponding ignition energies. CRITICAL ENERGY FOR FUSION The currents required to fuse the wires in air at different application times were first measured in the usual way, and the fusing energies, calculated on the cold resistance, were estimated, the complete results being given in table 4. The fusing energies are plotted against application time in figure 4, from which it will be seen that, for each wire, the fusing energy is lower than the corresponding ignition energy of the gas mixtures, which suggests that fusion should occur before ignition is possible. On the other hand, the thermal conductivity of air is less than that of methane, resulting in a smaller lateral heat loss, so that the fusing energies in air might be expected to be less than in the explosive mixture. A few measurements of the fusing energies in pure methane were made, with the results shown in table 5. It will be seen that these figures are much higher than the fusing energies in air, this effect being consistent with expectations based on thermal conductivity considerations but not necessarily wholly attributable to this cause. The corresponding energies for methane-air mixtures will be intermediate between those for pure methane and pure air, and are presumably greater than the ignition energies of the

335

IGNITION OF GAS MIXTURES

explosive mixture with the thicker wires. As ignition could not be effected with the smallest diameter wire, it would appear that the ignition energy was greater than the fusing energy, and similarly for the intermediate diameter wires at the longer times. As the slopes of the ignition energy vs. excitation time curves for the methane-air mixture are greater than for the fusing energies vs. excita-

perienced in igniting weaker methane mixtures may be partly due to the lower thermal conductivity decreasing the time required to fuse the wire with a given current, and so setting up conditions where fusion occurs before ignition. The fusing energies for the hydrogen-air mixture will be greater than for pure methane, in view of the higher thermal conductivity, and will thus

TABLE 4 Fusing energies of wires in air Resistance (ohm)

Diameter

1.20

4.33 X 10-3 cm.

2.16

6.92

9.05

14.9

2.79 X 10-3 cm.

1.8 X 10-3cm.

1.5 X 10-3 cm.

1.14 X 10-a cm.

Time m. secs. Current amp. Energy m. joules Time m. secs. Current amp. Energy m. joules

2.43 11"2 I 1.26 6.85

917

9575 4.62

0.325

Time m. secs. Current amp. Energy m. joules

2.365 2.42

0.22

Time m. secs. Current amp. Energy m. joules

Application time (m. sec.)

Diameter of wire (lO-S cm.)

4 4 ~ _6

1.5

20 67

Time m. secs. Current amp. EnergT m. joules

TABLE 5

4.33

10 1.2 17.2

Fusing energy in methane (millijoules) Fusing energy in methane (millijoules)

8.1

24.1 4.7.

tion time curves for air, it is obviously possible for the fusing energies to be greater than the ignition energies at short times of application and to be less at long times. This confirms the observation that with a continuous current, a tungsten wire fuses in a shorter time than is required for ignition at low currents, corresponding to long application times, but ignites methane before fusing when the currents are high, corresponding to short application times (2). On this view, the difficulty ex-

2.

.24 1.71

7.3~__

16.7 1.07 23 16.7 .56~ 11.6 16.7 .28! 9.66

4.4

16.7 .17 4.38

0.125 2.0

16.7 .13 4.18

20 93 2018 20 .523 11.9 --

20 12 4128

41.5 .785 30.7

46.6 .78 34.4

41.5 .447 17.9

46.6 .41 16.9

41.5 ~1.o .245 .2 17.2

46.6 .25 20.1

41.5 .167 .1' 10.5

46.6 .17 12.4

~1.5 41.5 .121 9.08

46.6 .13 11.7

tend to be greater than the measured ignition energies of the mixture. It is interesting to treat the values of fusing energy at zero time of application in the same way as the ignition energies, and to see how they vary with area of cross section of the wire. Table 6 gives t~he values of E0 for each wire. Figure 5, curve c, shows the E0 values in calories plotted against the thermal capacities of the bridgewires, also expressed in calories, and it will be noted that the points lie roughly on a straight line. This line represents the amount of heat which must be generated instantaneously in the wire in order to cause it to fuse when surrounded by air. Under conditions similar to those holding over the range of times considered we may assume that fusion is brought about by the melting of the material of the wire and that the fusing energy indudes the latent heat of fusion of the bridge-wire. If this quantity is deducted from the fusing energy,

336

THIRD SYMPOSIUM ON COMBUSTION~ FLAME AND EXPLOSION PHENOMENA

hydrogen-air mixtures, it is interesting to note that, in this case, the calculated values are substantially higher than the melting point of nichrome. If this signifies that the real temperatures are at, or possibly above, these values, it would appear that the temperature of fusion of nichrome wire is much higher in these inflammable mixtures than in air. This might be taken as an indication that the actual rupture of the wire does not coincide with the completion of the heating process but occurs after a short delay during which an opportunity is afforded for conduction losses which are not eliminated by extrapolation to zero time of heating. There is, however, an alternative interpretation arising from the fact that the temperatures are obtained from energy determinations and not by direct measurement. As shown in table 5, the fusion energy of a given wire is much greater in methane than in air but, if the amount of energy absorbed by a gas like methane were to increase with temperature, the quantity retained in the wire would be correspondingly reduced and the real temperature of the wire would be lower than the calculated value. Thus, although the measured igniting energies may be unambiguous, the calculation of the wire temperature from these dat~ requires further information on the effect of temperature on the heat absorbed by the gas, particularly inflammable gases like methane and hydrogen.

we get the figures given in the last row of Table 6 and these are represented graphically in curve (cl), Fig. 5. These figures should now represent the amount of heat required to raise the wire to the melting point and the temperature should be indicated by the slope of this line. This appears to be constant for all diameters of wire, its value being approximately 1200~ TABLE 6

F

Area of cross-section (X i li !2.5411 . . . 6. 1. . . "17,1.O2 10 6 cm3) . . . . . . . .14.7 Thermal capacity (X 10-6 cal.) . . . . . . . . . . . . . . . . . . . Latent heat of fusion (X 10-a cal.) . . . . . . . . . . . . . . . Fusing energy (X 10-s cal.) . . . . . . . . . . . . . . . . . Fusing energy less latent heat (X 10 a cal.) . . . . . . .

2.04t0.85[0.350.250.

i4 ! ! r I ! ! 0.97 0.40 0.1710.1210.07 i i 1 ~ i : 1 3.661.7f0.93!0.670.43! I J I ! ' 2.69 1.320.76:0.5510.36 i I !

In comparing this figure with the melting point of nichrome, approximately 1350~ it should be noted that besides ignoring the temperature coefficients of resistance and specific heat, the calculation is based on the assumptions that the whole of the wire is melted at fusion and that the temperature is uniform. In practice it is improbable that either assumption is strictly true and the calculated temperature will consequently tend to be below the actual value at the point of fusion. Reverting to the calculated wire temperatures corresponding to ignition of methane-air and

REFERENCES

1. MORGAN,J. D.: Phil. Mag. 4 9 (1925). 2. WHEELER, R. V. AND SHEPHERD, %'. (~. F.: S.M.R.B. Paper No. 36.

36

THE SPARK IGNITION OF NITROUS OXIDE-HYDROGEN MIXTURES By J. w. LINNETT AND D. 3I. NUTBOURNE Experiments on the spark ignition of hydrogenoxygen mixtures by Thompson and by Frost, Linnett and Raynor showed that the minimum ignition pressure of a given mixture was lowered by the addition of small amounts of chemically inert gases. The lowering could be correlated with the diffusion coefficients of the inert gases, those with small diffusion coefficients being most effective in lowering the minimum ignition pressure. I t was therefore concluded that the inert gases promoted

ignition by preventing the radicals from diffusing away from the spark and so aiding the uncontrolled increase of radicals in that region. Frost, Linnett and Raynor gave a satisfactory semi-quantitative treatment of this based fundamentally on the ideas of Mole. It was also found that larger additions of the inert gases raised the minimum ignition pressure, and that the order of this effect for the different gases was the order of their heat capacities. The bigger the heat capacity of the added