COMBUSTION OF PLASTICIZED NITROCELLULOSE

A. G. Arkhipov, A. P. Denisyuk, and B. N. Kondrikov

Combustion of mixtures of nitrocellulose (NC) with a plastifier is interesting from a theoretical point of view mainly as an example of complex exothermic reaction proceeding in condensed and gas phases in a thin layer close to the phase interface. The theory of this process has been developed in consJlerable detail. One of the most important results in- volves the fact that with certain relationships between combustion characteristics and ex- ternal conditionsthe process loses stability and changes into a nonsteady vibrating regime or it is extinguished [1-3]. Combustion rate u in a nonsteady regime, similar to the depen- dence of velocity on temperature T and a pressure V, in a general form, cannot be calculated theoretically; this is a theoretical problem which does not have an analytical solution. Experience so far has also not provided an answer to this question and this may be because until now mixtures with a high (up to 60%) content of NC and with a markedly negative oxygen balance have been mainly studied. For these mixtures the u(T 0) dependence is low, combus- tion rate is variable, and correspondingly the phase interface surface temperature is low. In addition, with high oxygen deficiency at the surface a layer -carcass forms of carbonized polymer threads which markedly improves combustion stability [4]. It might be possible to think that with a reduced NC content and use of a plastifier rich in oxygen the stability of combustion is reduced and it will be possible to measure combustion rate in a nonsteady vibrating regime.

In accordance with this in the present work a study was made of dependences u(p) and u<T 0) for binary mixtures of NC and plastifier with an NC content up to 40Z.

Tests were carried out in a massive (4.5 kg) metal block with an opening 12 mm in diam- eter and 160 mm deep. The block together with a cylindrical specimen (7 mm diameter, 12-15 n~m long) placed in the hole was held in a thermostat uns complete levelling in temper- ature in the system, after which they were transferred to constant pressure equipment <volume 5 dm3). Combustion was carried out in a nitrogen atmosphere. Combustion rate was determined from the range of pressure increase, which was measured by a tensomanometer. Maximum pressure p during combustion was 0.5 MPa. The range of change in initial pressure ~as 1.5-14 MPa, and the initial temperature was 220-370~

Prior mixing of NC (colloxylin NKh, 12Z N) with plastifier (propanetriol trinitrate) was carried out by dispersing the components in an aqueous medium at 320~ and finally in laboratory rollers at 370~ Specimens for testing were prepared by through pressing in a hydraulic press, cut into Sections, and clad; the cylinder, easily lubricated with vaseline, was forced into a tube 6 mm in diameter. In each series of tests the temperature of the thermostat and the block was kept constant, and pressure was varied. Mixtures containing 60, 50, and 40% NC were tested; in future they are designated 60/40, 50/50, and 40/60, res- pectively.

The dependence of combustion rate on pressure for all of the mixtures has the usual form (Fig. i):

where p = P/P0; u0 -= u(p0); P0 = 0.98"i0 s Pa. Values u 0 and u for all of the mixtures are independent of pressure.

For a 60/40 mixture the dependences of u 0 and 9 on initial temperature have the form

uo = O , 0 3 1 2 e x p ( T o / l O O , 8 ) , , , m / s e c , ~ = ~,|82 - TJ679,4,

but the temperature coefficient for sensitivity depends only on pressure (Fig. 2a):

= (Oln t z /OTo)p = (9,92 -- 1,4721n ~ ) . 1 0 -a, K -i.

Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 23, No. 3, pp. 88-92, May-June, 1987. Original article submitted August 4, 1985; revision submitted March 31, 1986.

0010-5082/87/2303-0327 $12.50 ~ 1987 Plenum Publishing Corporation 327

lXt ~ - " - ' T .

20

tQ TO=Z73K A

8

4 2.9:~-/7 - ~ F /

4 / 211) 20 40

a)

, .

f x

/ " i z / /

/ /

6'0 80 fO0.

[ _ . ~ _

u,n~/ sec

?~ ._To= 383 K .

22z ~/ 2 ] 0 . 20 40 80 80 7oo y

Fig. I. Dependence u(p) for mixtures 60/40 (a) and 40/60 (b).

TABLE 1 i i i , , , , i

60 223--373

223--293 50 293--323

323--373

223--293 40 293--323

323 --36.%

~.iO', }(with p, MPa

1,5 I 3,o ]

2,9 3,2 I �9 4,2 4,4 ]

�9 I 4,5

6,5 iO i l

3;78 3,14 --

6,0 4,6 3,6 3,5 3,7 3,8 4,7 4,8 5,0-

7,7 6,0 4,7 1,7 i,2 0,9 G,9 5,t ~,3

The derivative of 8 for temperature, the same as of v for the logarithm of pressure, equals zero.

A 50/50 mixture (Fig. 2b) with P0 = 6.5-14 HPa displays weak deviations from the linear path of the dependence log u(T0), lying close to the limit of measurement accuracy. With a lower pressure there is a sharp change in this dependence; with T o = 220-290~ 8 is grea- ter by a factor of 2-2.5 than with T o = 330-370~

With a reduction in NC content to 40% (Fig. 2c) sharp breaks in the curves are noted over the whole pressure range studied, and their left-hand part is steeper, the lower the pressure. Values of 8 are given in Table i.

The main result of this work involves the fact that with low T 0 a mixture with a high plastifier content (50/50 and 40/60) burns markedly slower than a 60/40 mixture, although at room and elevated temperatures the value of u increases with an increase in the content of plastifier rich in oxygen. Simultaneously there is an increase at low temperature in the value of ~, and even more markedly for 8.

It is natural to connect the changes with the changeover of combustion into a nonsteady vibrating regime. According to [2] with r = (eTp/eT) > 0 and Z = S(Tp -To) > 1 combustion stability is governed by the Novozhilov criterion

N = ( Z - - O V ( Z + t ) r .

With N < 1 combustion is stable, in the case of N > 1 it changes over into a vibrating re- gime, and with N > 2 - r/(Z + i) = 2 there is exponential instability. If at the surface there is a layer of inert particles heated to high temperature, the limiting value of N in- creases [4]. For a thin layer (61a ~ i) the limit of vibrating instability increases to a value

Z f l j [ + Z ( i -- 61~ l-i,

328

u, ~n/sec a)

20 :

5."~ i i~. .~"

10 ~ f~

z ~ _ _ _ 2 _ _ _ 223 2FJ dOJ J4J JSJ

40

5"

22J 2~J JO$ J43 JdJ

u, ~ / s e c

// Z2J" 28$ JO3 J4$ To,K

Fig. 2. Dependence u(T o) for mixtures 60/40 (a), 50/50 ( b ) , and 40/60 (c). P0, MPa: i) i0, 2) 6.5, 3) 3, 4) 1.5, 5) 14.

TABLE 2

To, K

373

p, MP, I

1,5 3,0 6,5

t0,0

u.~ml/sec .+ Tp, K

7,5 ] . 679 I0.85 721 17j 776 23,25 8 i l

0,55 0,51 0,46 0,41

Z

1,82 �9 t ,7 t

I+,52 1,38

0,43 0,36 0,24 0,t4

293

i,5 3.0 6,5

lO,O

4,29 7,25

i3,0 i8 ,0

6;:38 682 741 778

0,48 0,46 0,42 0,38

2,04 1,91 t ,69 1,52

0,74 0,62 0,43 0,29

223 1,5 3,0 6.5

lO,O

2,9 5,2

10,,2 +4;5

606 653 7t5 753

0,44 0,42 0,39 0,36

o,97

1,86 1,66

t ,13 0,95 0,67 0,47

TABLE 3

p, MPa

1,5 3,0 6,5

lO i4

N for mixtures

50/50

i ,79/2,33 i ,60/2,04 i ,22/i ,55 0,88/I,15

,0,58/0,79

&O/60

2,i9/2,65 i,99/2,47 1,67/2,04 i,36/!,68 i,07/i,3i

Note. Values of N are given in the numerator for T o = 293~ and in the denominator for T o = 223~

~here ~ = uc p adl /~ is dimensionless thickness of the layer; p is its density; dla is dime~ionle~slthi~kn$ss; Cp and kp are average specific heat capacity and thermal con- ductivity coefficient of the ~uel. For example, with Z = 2 and r = 0.2 the limiting value N, = 1.15.

Calculation of the value of N is carried at first for a 60/40 mixture burning stably. We use an equation obtained in [5]:

u. = t,8-tO~exp(5OOO/Tp)kg/(m=~

Calculated results are given in Table 2. With T o = 223~ combustion occurs close to the limit of vibrating instability: p = 3 and 1.5 MPa, and N = 0.95 and 1.13, respectively. It

329

/ /

8 e

4 / or

os Z X3 10 ' 'za 4o Go 80 1oo~

Fig. 3. Effect of soot on combustion rate for a 40/60 mixture at 253~ i, 2) 1.2 and 2% soot; 3) without addi- tive.

is evident in the latter case that combustion is maintained in a stable regime in view of presence at the surface of a thin layer of carbon particles.

Calculation of parameters governing combustion stability with N > 1 is incorrect [2]. By means of this calculation it is only possible to determine the limit of the region for unstable combustion. Given in Table 3 are data for 50/50 and 40/60 mixtures. The boundary is determined clearly, and it coincides with that obtained by the experiment; for a 50/50 mixture combustion is unstable (N > I) with T o < 293~ p ~ 6.5 MPa; for a 40/60 mixture it is unstable with T o < 293~ p ~ 14 MPa. It is evident that combustion proceeds near the limit, propagating into a regime of vibrating instability. The region of exponential in- stability, in which continued combustion is impossible [6, 7], is probably not reached in this case, i.e., the value of N > 2 (see Table 3) is evidently connected with the fact that measurement of N was carried out in the region of vibrating instability.

The assumption that combustion of a 40/60 mixture With T O < 293~ proceeds in an un- stable regime was proven by tests in which I-2% soot was added to the mixture. According to theory [4] and tests [4, 7] addition of soot leads to an increase in combustion stability as a result of forming a layer of particles heated to a high temperature at the surface of the fuel. The soot itself exhibits a very weak catalytic effect, and therefore its effect on combustion stability is determined by purely physical reasons. Results of the tests are shown in Figs. 2c and 3. At room temperature in the region of combustion stability the combustion rate for mixtures with soot and without it are the same. At low temperature in the region of combustion instability the value of u for a mixture with soot is markedly higher than without it. Simultaneously introduction of soot reduces v; combustion is less stable, the lower the pressure. Correspondingly, the drop in rate in tests without a stabiliz- ing addition at low pressure is more marked.

In conclusion, it is noted that judging from the nature of u(T 0) curves the effect of the degree of thermal instability on combustion rate is more complex (see Fig. 2b, c); the section of a sharp fall in rate with N > 1 is preceded by a small temperature range in which the rate depends weakly on T O . The reason and role of this effect in the process of a change- over from stable to unstable combustion is still not clear.

LITERATURE CITED

I. Ya. B. Zel'dovich, Zh. ~ksp. Teor. Fiz., 12, 11-12 (1942). 2. B. V. Novozhilov, Nonsteady Combustion of Solid Rocket Fuelds [in Russian], Nau~a, Mos-

cow (1973). 3. Ya. B. Zel'dovich, O. I. Leipunskii, and B. V. Librovich, Theory of Nonsteady Combustion

of'Powders [in Russian], Nauka, Moscow (1978). 4. B. N. Kondrikov and B. V. Novozhilov, Fiz. Goreniya Vzryva, 12, No. 3, 333 (1976). 5. A. A. Zeni11, in: Physical Processes in Combustion and Explosion [in Russian], Atomizdat,

Moscow (1980). 6. B. N. Kondrikov and B. V. Novozhilov, Fiz. Goreniya Vzryva, i0, No. 5, 661 (1974). 7. V. E. Annikov and B. N. Kodrikov, Fiz. Goreniya Vzryva, 15, No. i, 57 (1979).

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