interaction of carbonaceous materials with gunpowder gases

become evident until the temperature is reached at which it decomposes with the formation of the catalyzing agents.

LITERATURE CITED

i. A. P. Glazkova and I. A. Tereshkin, Zh. Fiz. Khim., 35, No. 7, 1622 (1961). 2. A. F. Belyaev and S. F. Maznev, Dokl. Akad. Nauk SSSR, !31, No. 4, 887 (1960). 3. Pascal, Krieg, Declerque, Perier and Francois, Mem. Poudres, 35, 335 (1953). 4. A. P Glazkova, Yu A. Kazarova, and A. V. Suslov, Arkhiw. Termodiy. Spalania, 9, No. 4,

591 (1978). 5. H. Watts, Trans. Faraday Soc., 54, 93 (1958). 6. K. K. Andreev, Thermal Decomposition and Combustion of Explosive Substances [in Russian],

Oborongiz, Moscow (1957). 7. A. P. Glazkova, Combustion Catalysis of Explosive Substances [in Russian], Nauka, Moscow

(1976). 8. B. D. Bond and P. W. M. Jacobs, J. Chem. Soc., Ag, 1265 (1966). 9. E. A. Bordyushkova, P. I. Protsenko, and L. I. Venerovskaya, Zh. Prikl. Khim., 40, No.

7-8, 1438 (1967). i0. L. A. Alekseenko, Proc. V. V. Kuibyshev Tomsk State Univ., 126, 20-26 (1954). ii. A. P. Glazkova and Yu. A. Kazarova, Archiwum Combustionis, 6, No.l, 61 (1986). 12. A. P. Glazkova, Candidate!s Dissertation, D. I. Mendeleev Moscow Chem.-Techn. Inst.,

(1952). 13. K. K. Andreev and A. F. Belyaev, Theory of Explosive Substances [in Russian], Oborongiz,

Moscow (1960). 14. G.Kast, Explosive Substances and Ignition Means [in Russian], Gos. Khim.-Tekh. Izd.,

Moscow-Leningrad (1932). 15. N. A. Shilling, Gunpowder Course [Russian translation], Oborongiz, Moscow (1940). 16. F. A. Baum, Tubular Gunpowders and Fuses [in Russian], Oborongiz, Moscow (1940). 17. T. M. Oza and S. A. Patel, J. Indian Chem. Soc., 31, 523 (1954).

INTERACTION OF CARBONACEOUS MATERIALS WITH GUNPOWDER GASES

A. P. Denisyuk and Yu. G. Shepelev UDC 662.311.1

Carbonaceous materials (CM) are used in many gunpowders. They can be carbon black from various ranks, used as components of combined combustion catalysts [I], graphite for the coat- ing of the pyroxylin gunpowder granules [2], or the carbon filament, used as a heat conduction element [3]. The gunpowder combustion energy and temperature as well as the presence of a solid phase in the combustion products, which leads to a reduction in their transparency [4], all depend on the combustion completeness of the CM contained in the gunpowder. Thus, the problem of the combustion of the carbonaceous materials in the gunpowder composition is im- portant from various points of view, yet has remained heretofore practically uninvestigated. In the present work, we have investigated the interaction of various CM's with the gases in the ~unpowder combustion wave.

EXPERIMENTAL PART

The investigations were carried out with gunpowders A and N, which have different explosive transformation heats Qt and oxygen balances. Thus, the oxidizer excess coefficients are a = 0.72 or 0.55, respectively, from which the computed Qt values are 5187 and 3846 kJ/kg. The gunpowder A contains up to 49% of nitrocellulose and nitroglycerine and up to 1% of centralite and Vaseline mass. Added to the gunpowder was carbon black with various dispersivities: PM-15 (Ssp = 15 m2/g) and KGO-250 (Ssp = 250 m2/g), as well as from 1 to 17% graphitized 6-~m-diameter carbonaceous fiber (the fiber length in the finished gunpowder was about i00 ~m). These materials contain from 95 to 99.9% carbon. For comparison, tests were also conducted with a noncombustible silicone dioxide additive.

Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 25, No. 4, pp. 25-32, July-August, 1989. Original article submitted September 1987; revision submitted May i0, 1988.

0010-5082/89/2504-0403512.50 �9 1990 Plenum Publishing Corporation 403

7~ A C

a

~ B C

_1/ b

~i ~ c

Fig. i

Tc~

,3000 " \

2800., \ x ~ 2200 -

NO0 \

", , 7

Fig. 2

Fig. i. Typical oscillograms of the recorded temperature in the combustion wave of gunpowders A and N without additives (a), with CM additives (b), and with silicon dioxide additives (c).

Fig. 2. Variation of the combustion temperature of gunpowders A (1-5) and N (6, 7) with the introduced additive content: I) silicon dioxide; 2) PM-15 carbon black; 3) KGO-250 carbon black; 4, 6) carbonaceous fiber; and 5, 7) carbon (computation).

TABLE I

Gun- powder

A

Carbonace- ous fiber (CF), %

0 4.8 9,1

0 i.O 2,9 4,8

To, ~

computed I exp

3063 2399 2696 2t49 2297 i996

2362 2068 2278 2013 2i17 1893 i957 i824

ATr, "oK

575 355 254

300 265 199 i66

The completeness of combustion of the CM in the gunpowder gas was indicated by the combustion temperature, and in the KGO-250 carbon black also by the solid phase content in the products. In the tests, gunpowder specimens with a diameter d = 7 mm were used, which were press- fitted into a polycarbonate tube, assuring their face-burning. Testing was done at a pressure p = I0 MPa. Under these conditions, complete combustion of the gunpowders A and N is achieved, since at p > 6 MPa their maximum flame temperature is pressure independent [5]. The d = 7 mm value exceeds the limiting di value, above which the combustion temperature T c is independent of d [5]. For example, for the gunpowder N, dl = 5.8 mm at p = 5.5 MPa. The combustion temperature was determined with microthermocouples in a constant pressure bomb having a volume V = 2000 cm 3. Three to five tests were conducted for each gunpowder composition, from which average values were computed. The temperature measurement error was 2.5%.

The amount of the solid phase was determined by the collection of the solid residue after burning the specimen in the bomb. A stainless steel bomb with a volume V = 300 cm ~, provided with a special insertion piece for the collection of residue, was used for this purpose. Spe- cial tests had shwon that in order to avoid particle entrainment in the gas, its release from the bomb must proceed slowly (taking no less than 30 min).

The T c value was measured with K-shaped ribbon tungsten--rhenium thermocouples following the method of [6]; moreover, the thermocouples were fastened to the specimen with glue (the cartridge halves were joined with clamps during heating). The minimum thermocouple thickness, which can be practically used in the measurement of the temperture profile, is about 5 ~m [6]. With such thermocouple thickness, the determination of a complete temperature profile is possible with satisfactory accuracy, when the combustion velocity of the specimen is less than i0 mm/seco

404

At p = i0 MPa the combustion velocities u for gunpowders N and A were 10.8 and 18 mm/sec, respectively. Thus, it seems that, in general, at the indicated pressure it is impossible to find the true temperature distribution in the combustion wave in gunpowder A. Therefore, to determine only the maximum combustion temperature, a 15 ~m thick thermocouple, that is more suitable for the application, was used. However, the recording of the temperature profile even with such thermocouples made it possible to clarify on the oscillograms some of the combustion features of the specimens containing CM and silicon.

Typical oscillograms of the recorded temperature in the combustion wave are shown in Fig. i. It is evident that with the introduction of carbon black, or silicon dioxide, into the gunpowder, significant temperature fluctuations appear, whose amplitude increases with the solid residue content in the combustion products. If the gunpowder produces no solid residue, the temperature fluctuations are absent. It can be assumed that the fluctuations are related to the low rigidity and stability of the thermocouples in the gas flow stemming either from the endothermal reactions of the carbon particles with CO 2 and H20 on the thermocoupie, or from the adherence on the thermocouple of solid particles, which reduce its heat losses and the subsequent break of the formed crust by the gas flow. The latter appears to be more con- vincing, since no fluctuations are observed in the combustion of a gunpowder without additives and are encountered in the case of the combustion of gunpowder With a silicon dioxide additive, which does not react with the gunpowder gases.

Once a carbonaceous material is introduced into the gunpowder, the oscillograms show (see Fig. Ib) a segment B, having a duration between 50 and i00 msec, preceded by a segment A with a temperature gradient, as in the original gunpowder (for example, in the gunpowder A, on the average, it equals about 6~ These segments are followed by a constant temperature (T c) segment C. The B zone is divided into two parts: B', where the temperature rises, while the temperature gradient is between 6 and 15 times smaller than in the segment A, and B", where the temperature drops. (The temperature profile shape in the segment B in the case of the gunpowder N is less clearly defined than in the combustion of the gunpowder A.)

Comparing the experimental and computed T c values for the gunpowders without additives, one observes a significant difference between them caused by the heat losses from the radiation AT r [6], Which can be confirmed by appropriate computations. Henceforth, in the discus- sions of the results, we shall use the experimental T c values with a correction &Tr, evaluated using the method and some data of [6]. The combustion temperature for gunpowder N, including the radiation correction, agrees well with the calculated value, while for gunpowder A it is somewhat lower than that obtained from the thermodynamic calculation (Table i). This is evi- dently related both to the inaccuracy in extrapolating the data from [6] to the considered conditions here (thermocouple thickness, temperature) and the presence of up to 1% of moist- ure in the sample.

We now consider the effects of various additives on the gunpowder combustion temperature (Fig. 2) and compare these to the calculated values. The thermodynamically maximum possible amount of the CM, reacting with the gunpowder gases, depends on the gunpowder composition, in particular, on ~. For the gunpowders N and A it amounts to i0 and 17%. The lowering of T c with the introduction of CM's up to the limiting amount is related both to the gunpowder dilution and to their endothermic interaction in the combustion wave. As the n value is increased further, the temperature drops only due to the system dilution and to the heat consumed in the phase transitions. It is for this reason that a break point occurs on the computed Tc(n )

curves. The locations (in the CM concentration) of the break points in the experimental and computed curves are noticeably different. These differences depend on the gunpowder composition and the CM types.

For the gunpowder N the computed and experimental T c data agree up to a carbonaceous fiber content between 4 and 5%, i.e., about 50% of the thermodynamically possible carbonaceous material burns up in the combustion wave. This is in good agreement with the data on the amount of solid residue in the combustion products. A perceptible amount of residue is observed when the CM content in the gunpowder exceeds 4.5%. Thus, in the specimen with 5, 9 and 13% fiber the amount of solid phase is 0.6, 4.4 and 8.5%, rspectively.

For the gunpowder A the location of the break poinn depends on the CM type. In this case, the experimental Tc(n) variation is close to the computed one. For the highly dispersed carbon black KGO-250, the breaks are observed when its content in the gunpowder is between 8-9%. An analogous result was obtained from the determination of the solid residue (Fig. 3). The carbonaceous fiber, having a relatively low specific surface (s s = 0.35 m2/g), nevertheless behaves

405

as the KGO-250 carbon black with s s = 250 m2/g. This probably can be explained by the inclusion into the process of a significant (about 200 m2/g) surface of the carbonaceous fiber cavity [7]. Thus, between 8 and 9% of the mentioned highly dispersed CM's, which constitutes about 50% of the thermodynamically possible amount, burns up in the combustion wave of the gunpowder A. The low-dispersion carbon black PM-15 burns up to a lesser extent; the break in the curve is observed at 5%.

When an amount of carbon black introduced into the gunpowders A and N exceeds the thresh- old value, the solid residue rises in proportion to the additionally introduced carbon black.

The break point in the Tc(n) curves divides them into two segments: in the first the reduction inT c is 85K/%, while in the second it varies between 6 and 15%o The latter values are lower than those for silicon dioxide, which reduces T c by 27K/%. The silicon dioxide apparent- ly has enough time to melt (T m = 1986~ thereby leading to an additional lowering of the temperature at a time when the carbonaceous material does not undergo any phase transitions up to the sublimation temperature T s = 3800 to 3900~

Thus, it follows from the experimental data on the combustion temperature and on the presence of a solid residue in the combustion products that, depending on the material's specific surface, between 30 to 50% of the thermodynamically possible CM amount reacts in the combustion wave. The probable reasons for this are kinetic impediments.

DISCUSSION OF RESULTS

We now address the following questions: in which zone and by what reactions does the carbonaceous material burn. To this end, we analyze in detail the character of the oscillogram (see Fig. ib) of the temperature record in the combustion wave of gunpowders, containing CM.

If one assumes that the interaction of the CM with the combustion products of the gunpowder proceeds at an appreciable rate starting already on the combustion surface, then the temperature profile should be analogous to the profile of a gunpowder without any additive, yet with a lower temperature gradient, a smaller T c value and without the segment B", wherein the temperature drops. In reality, one observes a peculiar temperature profile shape with a characteristic segment B, starting at T = 1200 to 1500~ which consists of parts B' and B". The temperature drop in the B" zone can be caused by the occurrence of only endothermic interaction reactions of the carbon with CO 2 and H20:

C + C O 2 = 2 C 0 , A H = 1 7 1 , 8 kJ/mole , C + H 2 0 = C O + H2, AH = ~29,9 kJ/mole

At atmospheric pressure, the equilibrium of these reactions is displaced practically fully towards the generation of CO at T > 1500~ (for the C + C02 reaction the degree of carbon con- version reaches 99.9% [8]). An increase in pressure leads to an opposite shift in the equilibrium; however, in the case of the C + CO 2 reaction at p = i0 MPa and T = 1500~ the CO/CO 2 ratio remains considerable (~i0)o The gunpowder combustion develops a temperature of up to 2000 to 3000~ Approximate calculations made on the basis of the data in [9] indicate that under these conditions even at p = 300 MPa the value of C0/C02 is about i0.

Endothermic reactions also occur in the zone B', whose temperature interval is between 200 and 500~ (depending on the type and amount of the CM and also on the gunpowder type). This follows from the fact that taking into account the system dilution, the maximum temperature in the regime B' is below T c. Moreover, the temperature interval of the segment B", which is between 70 and 200~ is overlapped by the interval of the region B', which also points to the occurrence of the indicated reactions.

On the segment A, which precedes the B segment in the oscillogram, the value of the temperature gradient (6~ is the same, as in a gunpowder without any additive, i.e., in this zone, there are no endothermic reactions with a noticeable rate taking place. The upper temperature bound of the zone A is between 1200 and 1500~ i.e., it corresponds to the maximum temperature of the flue gas zone, in which an interaction reaction between NO 2 and the gunpowder decomposition products takes place. In the B segment, the temperature remains constant until the combustion of the specimen ends (the particle residence time in this zone varied between 7 and I0 msec, which is i0-20 times longer than in zone B). This indicates a virtual absence of endothermic reactions, in spite of the fact that in the zone B, CO 2 and H20 are still found in the combustion products. However, the reductions of their concentrations (in

406

view of the fact that a portion of CO 2 and H20 had reacted in zone B) at a relatively low temperature results in a marked decrease in their interaction rate with the CM.

The temperature interval of the segment B (200 to 500~ is rather narrow, as compared to the mean temperature level in it (of the order of 2000~ This indicates that the basic reaction taking place there has a high activation energy. According to Arrhenius' theory, the reaction rate constant drops by a factor of ten in the temperature interval AT = 2.3 RT2/E. The C + CO 2 reaction has a high activation energy (356 kJ/mole), and in the present case its rate drops by an order of magnitude in the 2150K interval and by more than a factor of 200 in the 500~ interval, which confirms the possibility of the indicated reaction occurring in the stated zone.

Thus, the B segment, in which the C + CO 2 and C + H20 reactions take place, is found within a temperature interval ranging between 200 and 50~ (which corresponds to the portion B', whose temperature interval overlaps the entire B zone).

We shall now estimate the time required for a complete interaction between the carbon particles with CO 2 and H20, and shall compare it with the residence time of these particles in the gunpowder combustion products. We shall do this, using the C + CO 2 reaction as an example, assuming to a first approxiamtion that the reaction rates of carbon with CO 2 and H=O are close to each other.

The specific interaction rate K s of the carbon particle with gases is described by the equations [ii]

+ , c~ d c,.

NudD K = K o e x p ( - E / R T ) , c~ d = d~ '

iN, Ud = 0,7 " ] / -~ 1 - exp ( - o,a5 V~7) '

where c o is the concentration of the oxidizing gas in the flow, $ is the stoichiometric factor (for the 2C + C02 + H20 = 3C0 + H 2 reaction we computed the relationship to be 2.12:(44 + 18) = 0.387 kg of carbon for 1 kg of oxidizer), ~d is the transport constant of the medium in the gas phase, Nu d is the diffusion analog of the Nusselt number, D is the diffusion coefficient of the reagent in the gas phase, d c is the characteristic particle dimension, Re is the Reynolds number, ~ is the reactive gas exchange coefficient, which is an analog to the chemical reaction rate constant for a porous body, characterizing the intensity of transport processes on the phase interface, K is the reaction rate constant, K 0 and E are the pre-exponent and the activation energy, S i is the internal surface per unit particle volume (pore surface), and S a is the total particle surface (internal and external). For the C + C02 reaction, Ko = 1.6"109 cm/ sec, and E = 356 kJ/mole [12].

Under the conditions p = i0 MPa, T = 2000~ and d c = 0.012 to 6 pm, a gas flow velocity of 1-2 m/sec, S i = 200 m2/g (for carbonaceous fiber) the computations produced the following parameter values: K = 0.95 cm/sec, ~ = 1-556 cm/sec, D = I.i cm2/g, Re =0.023-2.3, and Nu d = 2-2.6, ~d = ( 5-2000)'103 cm/sec. Thus, because of the small carbon black and carbon fiber particle dimensions, one observes the relationship ~ << ed, which indicates that the process occurs in a quasikinetic regime, where the gas phase diffusion is not a limiting factor. The specific interaction rate is found from the equation K s = ~c0~.

The initial (prior to the start of carbon combustion) CO= and H20 concentrations produced in the flue gas zone are unknown. The carbonic acid gas and water are also produced in the higher temperature zone of the combustion wave by the CO + 2N0 and 2H 2 + 2NO reactions. The kinetic parameters of the third order reaction CO + 2NO have been determined in [13]: K 0 = 2.10 I~ liter2/(mole.sec), E = 207,7 kJ/mole. At T = 2000~ the reaction rates for CO + 2NO and C + CO 2 are of the same order of magnitude, therefore, within the temperature interval between 1500 and 2000~ they run in parallel. Therefore, in the specific rate calculations for the interaction between the CM and gases, the final equilibrium CO 2 concentration in gunpowder gases at the mean temperature within the segment B has been used (see Fig. ib), which makes it possible to estimate the maximum possible rate under the given conditions and the minimum time, required for the complete combustion of the CM. Taking into account the concurrent

407

m,%

G-i, / ' / /

Fig. 3. Amount of solid phase m in the combustion products for gunpowder A as a function of the content of KGO-250 carbon black

introduced into it.

TABLE 2

Gun- % powder n, (T), ~ ~, msec t, msec

A

2.0 4,8 6,5 9,i

t0.5 t3.8 t6,0

3.0 4,8 6,5 9,i

10,5 i3.8 i6,0

4.8 6,5 9.i

i0.5 i3.8 i6.0

KGO-250 2660 0,004 2330 0,02 2120 0,i6 2070 0,37 2020 0.89 1980 2,9 t960 14,3

PM-15

2490 0,14 2320 0,50 2310 0.52 2310 0,87 2300 t.4 2240 4,3 2050 99,6 Carbon fiber

2330 0.02 2120 0,t4 2100 0,25 2080 0,43 2050 1.2 2030 6.0

0,25--0,5

0,25--0,5

0,25--0,5

i.0 2.9 4.8 6.5 9.1

t0,5

Carbon fiber

2280 0.08 2050 0.37 t910 2.3 1880 4,8 t870 t5,7 t860 >200

0,22--0,45

Note. <T> is the mean temperature in the reac-

tion zone.

presence of CO 2 and H20 in the combustion products, in the equation for K s the sum of the con-

centrations of these reagents has been used.

The time needed for a complete burnup of the carbon particles having a radius r and density p with a mass combustion rate K s can be found from the equation [ii]:

= ~ / x ~ . r (~),

where ~(~) is the excess-oxidizer coefficient function, which equals the ratio of the mass contained in a unit oxidizer volume to the mass of the oxidizer, required for the combustion of all carbon particles in that volume. The function characterizes the reduction of the oxidizer concentration in the combustion process, since it does not occur in an unbounded medium but for a defined oxidizer excess. The curve of this function for q > 1 has a hyperbolic shape.

The results of computations for a carbon fiber and carbon black PM-15 and for KGO-250 in the compositions of gunpowders A and N are presented in Table 2. The computational accuracy is governed basically by the accuracy of the values of the activation energy in the process E and the temperature, at which it takes place. It follows from a literature survey [12] that for the C + CO 2 reaction, E = 343-377 kJ/mole, with a mean of 356 kJ/mole. The calculation

408

shows that for simultaneous variation of • (• kJ/mole) about the 356 kJ/mole value for E and of the temperature by • (•176 about the 2000~ value, the calculated value of the residence time required for the interaction can change up and down by no more than a factor of 5, i.e., the calculation correctly determines the order of magnitude of ~.

The residence time of the carbon particle in the reaction zone of the combustion wave t was determined from the transition time through this zone using a thermocouple (from the oscillogram), from the gunpowder combustion rate and from the gas efflux. Inasmuch as the osciliograms contain considerable pulsations, it was found to be impossible to make apparent the time difference for specimens with different CM content. For this reason, in Table 2 data are listed for the particle residence time in the reaction zone, which are averages over all specimens. The residence time is found from the obtained oscillograms as the sum of the residence times in the segments B' (0.1-0.4 msec) and in B" (0.4-0.6 msec), amounting to between 0.5 and 1.0 msec. However, the thermocouples, used in the temperature measurement, have an elevated inertia, which, compared to the actual temperature distribution, leads to a stretch-out in the time of the measured profile [6]. For example, for gunpowder A in the case, when the temperature is close to T c at p = i0 MPa, the temperature gradient ~p = 6~ Using a 2-3 ~m thick thermocouple in gunpowder NB, which is similar to gunpowder A in terms of energy and combustion rate, it was found that at p = I MPa (u = 3.9 mm/sec) @P = 5.5~ ~m, while at p = 5 MPa (u = 11.2 mm/sec), ~p= 13~ The ~D(p) variation has a saturat- ing charcter, and at p > 5 MPa, ~p increases insignificantly. Thus, the use of thick (15 ~m) thermocouples leads to an approximately twofold increase in the characteristic times for the combustion zone. Consequently, the CM particle residence time in the B zone is evaluated as being twice the smaller value, namely 0.25-0.5 msec.

It follows from a comparison of the computed time, required for complete interaction, and the particle residence time in the reaction zone within the combustion wave, as experi- mentally determined, that regardless of the approximate nature of these values, the kinetic impediments actually limit the possibility for the combustion of the carbonaceous materials in the gunpowder gases and they constitute the reason for the discrepancy between the experimental CM combustion data and the data obtained by a thermodynamic computation.

CONCLUSIONS

We have investigated the completeness of the interaction of various carbonaceous materials with gunpowder gases in the ballistite gunpowder combustion wave. We have shown that the limit in the carbonaceous material content, above which a change occurs in the interaction of the CM with the gunpowder combustion products, depends on the material's specific surface and is independent of the oxidizer-excess coefficient of the gunpowder.

For the highly dispersed (200-250 m2/g] materials (carbon fiber and KGO-250 carbon black) this limit is about 50% of the thermodynamic value, which equals 10% for the gunpowder N (~ = 0.55) and 17% for gunpowder A (~ = 0.72), while for the carbon black PM-15, which has a lower specific surface (15 m2/g) it is about 30%.

The incomplete combustion is explained by the presence of kinetic impediments in the interaction of the carbon with carbon dioxide and water.

LITERATURE CITED

i. A. P. Denisyuk, A. D. Margolin, N. P. Tokarev, et al., Fiz. Goreniya Vzryva, 13, No. 4, 576 (1977).

2. M. E. Serebryakov, Internal Ballistics of Barrel Systems and of Gunpowder Rockets [in Russian], Oborongiz, Moscow (1962).

3. US Patent 4,072,546, "Application of garphite elements to increase the TNT combustion rate. "

4. S. A. Loser, Gasdynamic Lasers [in Russian], Nauka, Moscow (1977). 5. V. M. Mal'tsev, M. I. Mal'tsev, and L. Ya. Kashporov, Basic Combustion Characteristics

[Russian translation], Khimiya, Moscow (1977). 6. A. A. Zenin, Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 125 (1963). 7. A. A. Konkin, Carbonaceous and Other Heat-Resisting Fiber Materials [in Russian], Khim-

iya, Moscow (1974). 8. N. V. Lavrov, V. V. Korobov and V. I. Filippova, Thermodynamics of Gasification and Gas

Synthesis Reactions [in Russian], Izd. Akad. Nauk SSSR, Moscow (1960).

409

9. F. Yoker, F. Rusinko and G. Austin, Carbon Reactions with Gases [Russian translation], IL, Moscow (1963).

i0. A. A. Zenin, Physical Processes in Combustion and Explosion [in Russian], Atomizdat, Moscow (1980).

ii. L. N. Khitrin, Physics of Combustion and Explosion [in Russian], Moscow State Univ. ( 1 9 5 7 ) .

12. N. V. Lavrov, Physical-Chemistry Fundamentals of the Fuel Combustion Process [in Russian], Nauka, Moscow (1971).

13. C. P. Fenimore, J. Am. Chem. Soc., 69, No. 12, 3143 (1947).

THE NEGATIVE-EROSION MECHANISM IN SOLID-FUEL COMBUSTION

V. K. Bulgakov, A. M. Lipanov, V. N. Vilyunov, and A. I. Karpov

UDC 536.46

Negative erosion has been observed [i] in tests on the effects of an incident flow on the combustion rate for ballistic powder N, i.e., the burning rate was reduced by the flow. The view has been taken that this effect is a consequence of systematic error and is not a real physical phenomenon, so in [2], a decisive experiment was performed, which directly confirmed negative erosion in low-explosive combustion. Certain suggestions have been made on the phenomenon [i, 3]. Here we report a numerical experiment that theoretically confirms a mechanism analogous to that proposed in [3].

The physical essence is that negative erosion is not associated with turbulence. When the surface is blown, the transverse velocity component in the gas-phase combustion wave is increased, i.e., the gas convection effect is increased relative to normal combustion, which means that the reaction zone is displaced into the gas from the fuel surface and the temperature profile is stretched, so there is a reduction in the heat flux to the fuel and thus a reduction in the burning rate.

The numerical experiment was as follows. The complete Navier-Stokes equations were used in calculating the combustion of a fuel in a planar channel formed by combustion surfaces. The treatment is more complicated than the method based on bou.ndary-layer equations [4] and is used because it is possible to consider more correctly the processes occurring near the channel input, where the negative erosion is most prominent.

The assumptions are: I) the gas reaction is described by a single overall one: 2) the thermophysical characteristics for the initial reagent and the final product are the same; and 3) laminar flow is involved. The model is

a~ , au 4 a c)u O au ap 2 a Ov , a au P u - j T ~ PU-~y = ~ ~-z ~-5-/z + - ~ ' y ~ -~-y - - a-7 -- ~ ~ ~ ~-~ ~-5~ z ,

O~" ~ # v 4 0 O~ ~ 0 Ov Op 2 0 Ou , 0 au pu ~ -7- pu-~y ---- ~ ~ ~ ay ~ az ~ ~ ay 3 ay ~ az ? ax ~ ay '

aT aT O k aT_~ a ~ aT i ~

Oa pv o0.~.~ = O Le~.Oa , O Le~. aa 9u--f'fx - r ~ Oz % O'-f ~ 0--'] % a] -- 9 W '

Opu T Opv O, Ox L Oy

p = 9 f i T .

(i)

Here x and y represent the coordinate system linked to the combustion surface, u and v are the velocity components in the x and y directions, T temperature, a concentration, ~, ~, Cp, and p dynamic viscosity, thermal conductivity, specific heat, and density for the gas, W = ank0 exp(-Ea/RoT) and Q being the reaction rate and heat produced.

Khabarovsk and Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 25, No. 4, pp. 32- 35, July-August, 1989. Original article submitted December 17, 1987; revision submitted April 8, 1988.

410 0010-5082/89/2504-0410512.50 �9 1990 Plenum Publishing Corporation

interaction of carbonaceous materials with gunpowder gases

Documents