CONVECTIVE COMBUSTION OF GAS-PE~ABLE FUELS

V. G. Kirostelev and Yu. V. Frolov UDC 536.463;662.612.3

In certain conditions, the laminar combustion of gas-permeable fuels is disrupted [i], and there arises perturbed combustion [2, 3], which then is accelerated and turns into con- vective combustion. The region of existence of perturbed combustion is bounded in pressure: below by the pressure of laminar-combustion disruption Pd' at which combustion begins to pene- trate into the fuel pores; and above by the value Pup, corresponding to the onset of sharp acceleration of the process, from which the onset of convective combustion is sometimes deter- mined. The features of the development of Perturbed combustion have been investigated mainly in conditions of spontaneous penetration of the combustion products in the fuel pores. In the present work, the dynamics of this process are considered in the presence of an initial pressure drop at the entrance to the pore.

The laws of combustion were investigated in the conditions of a constant-pressure bomb, according to the scheme of an "immured" charge [i]. The dependence of the combustion rate on the external pressure uc(Po) was determined for the mixed stoichiometric system PCA + PM~. The samples used were of diameter and length 15 mm, composed of tablets of height 5 mm, and placed inside a strong shell (Fig. i). The rate of combustion was determined from the combus- tion of wires placed between the tablets. The pressure in the bomb and at the closed end of

the charge Pt was measured. To eliminate the influence of gas compression in the pores, a free volume approximately eaual to the pore volume in the whole sample was provided at the end behind the supporting grid.

The results of measuring the combustion rate at pressures of 2-150 atm are given in Fig. 2. Within the limits of scatter of the experimental points, the combustion rate did not de- pend on the position of the measuring base in the sample, and was determined solely by the external pressure. This indicates that neither transient processes associated with the forma- tion of characteristic regions nor the boundary conditions (the limited~ of the charge) have a significant effect on the combustion.

The curve of uC(po) has three characteristic regions. At the lower end, the rate is close to the normal value (UN). This section corresponds to laminar combustion conditions. With rise in the initial pressure drop Apo at the entrance to th~ pore, laminar combustion transforms to perturbed combustion: a pressure dependence of the power index vC in the com- bustion law appears; the difference in level of the rates of perturbed and normal combustion becomes steadily more pronounced. Finally, after reaching Pup, the dependence uc(Po) is con- siderably intensified. The acceleration of combustion occurs relatively smoothly and therefore Pup may be determined only approximately. With further rise in po, the relation uC(Po) becomes weaker (Fig. 2), and the value of v C stabilizes. This action corresponds to the development of convective combustion.

The appearance of three characteristic regions on the curve of uc(Po) was also observed in the combustion of gas-filled (Apo = 0) samples of hexogen and PETN [4].

Thus, in different experimental conditions, for melting and "nonmelting" systems, uC(Po) may have the same form. A dependence of this kind is not always observed [i]. In particular, in investigating the combustion of hexogen (Fig. 3) in the same conditions as for the mixed system, the combustion rate sharply increased at po ~ 50 atm (according to estimates, to not less than 20 m/sec). Judging from the form of disruption of the supporting grid, the pressure in the combustion region reached several hundred atmospheres.

The character of the change in pT(t) depends on the external pressure. Typical pressure curves at the end of the charge are shown in Fig. 4, and oscillograms corresponding to the section of greatest gradient duc/dpo in Fig. 5. The form of the curve in the region to the left of point 1 (Fig. 4f) is shown in Fig. 4a, while Fig. 4a-c corresponds to the section between points 1 and 3 of the curve of uc(Po) and Fig. 4d-e to the region to the right of

1982. Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 18, No. 2, pp. 3-10, March-April,

Original article submitted May 27, 1981.

0010-5082/82/1802-0127507.50 �9 1982 Plenum Publishing Corporation 127

I

4

9

Fig. i. Scheme of charge: i) igni- tion charge (gas permeable); 2) armor layer (epoxy resin); 3) sample; 4) steel shell; 5) supporting grid; 6) combustible wires; 7) free volume; 8) seal; 9) fluid transmitting pres- sure to the sensor.

point 3. For the mixed system and for hexogen, in the perturbed-combustion region, the form of the curve is identical on the whole, and is determined solely by the position of the point on the curve uc(Po ). On passing from point 1 to 2, the maximum pressure at the peak (Fig. 4a, b) rapidly rises, reaching, according to estimates, a value approximately corresponding to point 3.

Existing concepts do not allow all the experimental data obtained to be explained. In particular, the weakening of the dependence uC(Po ) in the region of convective combustion cannot be associated with dilution of the combustion products [4], since there was no initial gas filling in the pores.

In order to explain the features of the change in PT and the courseof the curve uc(Po), processes of perturbed combustion must be analyzed. Literature data [i], photorecording [3],

and also the investigation of the character of the emergence of combustion at the end of the sample [4] indicate nonuniformity of ignition front motion in the form of the predominant propagation of combustion along individual pores (passage of combustion). The pressure in these pores exceeds the external presssure, as indicated by the intense dispersion of the fuel. There are direct measurements ~5] according to which the acceleration of the process is associ- ated with increase in the amount of disperse material, which indicates a growth in the scale of combustion penetration into the pores. These data allow the appearance of pressure peaks on the traces of the end sensor (Fig. 4a, c) to be related to the emergence of combustion

along individual pores to the ends of the sample. Release of combustion products into the free volume occurs here (Fig. i), which is associated by conditions of pressure growth in the pores. The combustion products are then rapidly cooled; some condense, and the pressure falls.

On the basis of the foregoing, a model of the processes has been formulated, taking the interaction of passage of the combustion in individual pores with gas filtration over all the pores into account. It is assumed that in the gas-permeable and strong (for example, pressed) system there is a size distribution of the pores. In some of the pores, the pressure in the pores increases with increasing distance of the ignition front of these pores into the depth of the charge (Fig. 6b). At a definite depth of passage, the pressure difference in the pores and external volume at which disruption of the fuel occurs is reached.

On dispersion, the passage of combustion ceases; the external pressure is transmitted to the rupture cross section, where previously the gas pressure was determined by its filtration over all the pores, and therefore was less than the external pressure (the rupture cross sec- tion is formed by the bottom of the cavity appearing after passage at the surface of the fuel, and the influence of burnup of the surface inhomogeneities on the pressure in the rupture cross section is assumed to be insignificant). The pressure difference Ap~ appearing at the inlet to the pores (Fig. 6c) creates a new filtration front, which propagates into the depth of the charge. After dispersion (within the holding time), passage of combustion in the pores again occurs. At this time, the pressure difference Apl is spread out, forming a region of gas transfer [6]. Beyond the limits of this region, in the filtration region, the gas "follows" only the change in mean velocity of the end of the charge (the combustion rate uc).

128

u C , c m / s e c

100-I

lot!

f,0

0~

. ,q.

i d r ~ - - i i ~ l i I i t - - - ~ - ' P "

lO I00 p, atrn

Fig. 2

ti C cm/$~

~oof + f ,

�9 ,5

A 4

1C

+

/ O) f ~--r--~c--r-rm- j j , ~--

0 10 ~ob p, a t m

F i g . 3

Fig. 2. Dependence of the combustion rate on the pressure for the composition 85Z PCA + 15% P~,IMA. The open porosity of the fuel mo = 0.14; the gas permeability K = 7.10 -12 cm2; 1-4) com-

bustion rate at the first (from the ignition charge), second, third, and first two measuring bases.

Fig. 3. Dependence of the combustion rate of hexogen on the pressure; mo = 0.14; K = 8.10 -11 cm 2 (notation as in Fig. 2).

On the basis of the given model, the multiplicity of pressure-wave traces may be explained in that they fix different phases of the process. For example, Fig. 4a, c corresponds to the moments directly after and before dispersion. The traces in Fig. 4b may be observed before

the onset of passage of combustion in the pores. Note that the pressure recordings correspond- ing to the region of convective combustion (Fig. 4d, e) indicate the absence of passage of combustion. In these conditions, the given model is inapplicable.

The absence of passage of combustion is most concisely explained in that the pore diam- eter dp and the external pressure in the given experiment are too small for combustion to

penetrate into the individual pores with purely convective perturbations affecting them.* Therefore, passage of combustion may only appear at higher pressure. In the perturbed-com-

bustion region, where a heated layer is created mainly as a result of conduction, the pres- sure necessary for passage of combustion to appear is evidently much decreased. This may

explain the presence of passage of combustion in low-pressure regions.

In perturbed combustion, judging from plots of pT(t), the most favorable conditions for the passage of combustion exist in regions with a strong dependence uc(Po). In fact, even a

small growth in the pressure pp in the pore in this region facilitates a sharp (by an order of magnitude or more) increase in the rate of passage. In the lower section of the uc(Po) curve, the development of passage of combustion occurs sluggishly: the rate of appearance of combustion in the pore is little different from the rate of normal combustion, and therefore ignition of the pore, which limits the rise in pp, is possible.

The region of transfer into the filtration region is distinguished by high gas velocity [6]. From Darcy's law u ~ 3p/3x and the filtration equation (assuming that the pressure pro- file is linear) 3p/Dt ~ (~p/Dx) 2, it follows that u ~ r and therefore, as the transfer

region approaches the end of the charge, the rate of rise in PT must increase. Hence, point

A in Fig. 5 corresponds to the leading edge of the transfer region. The pressure at this boundary is less than the external pressure and therefore in the given case combustion condi- tions with alternation of the leading pressure is realized, the variety of which was con-

*For Fig. 2, d% ~ 4-i0 -s cm, while from the data of [i] it follows that a pressure p > I00 atm is necessary for combustion to penetrate into the pores even to the order of a large diameter.

129

P a 1 b ' / Fig. 4.

t % 9 p Characteristic form of oscillogram recording the pres-

sure in the free volume.

sidered earlier [6]. With passage of combustion, the maximum (leading) pressure is moved into the pore.

From plots of PT(t) it follows that passage of combustion occurs over the whole length of the transfer region. This feature is not random, and may be regarded as the result of the really acting mechanism of stabilization of the mean rate of perturbed combustion. In fact, if the strength of the fuel corresponds to the load which arises with passage of combustion into the depth of the transfer region, the latter is completely disrupted on dispersion. As a result, the accumulation of gas in the filtration region is eliminated and, at constant pressure po, the combustion is stabilized.

If the strength of the fuel is too small for passage of combustion to occur over the whole width of the transfer region, then part of this region will be retained after disper- sion. This leads to decrease in the rate of gas influx into the pores, because of their gradual accumulation in the filtration region. Hence, after a time tg between the passagesof combustion (which is constant for given po), the penetration depth of gas in the pores de-

creases. Ultimately, the width of the transfer region becomes equal to the depth of passage, i.e., comes to correspond to the strength of the fuel, and the rate of combustion stabilizes.

And, finally, if the passage of combustion may occur at a depth exceeding the dimension of the transfer region, not only the transfer region but also part of the compression region is disrupted on dispersion [6] (Fig. 7). The difference Apl at the inlet to the pore (Fig. 6c) is increased after the passage of combustion, which leads to rise in the rate of inflow of gas and increase in its penetration depth in the pore after a time tg. This continues until the dimension of the transfer region becomes equal to the depth of passage or until all the pressure difference is used in the filtration region.

Thus, perturbed combustion (and, in the presence of passage of combustion, also convec- tive combustion) is regulated and stabilized by passage of combustion in pores. However, rigid requirements in the homogeneity of the strength properties of the charge and the con- stancy of po (in regions with a strong dependence of u C on po) in real conditions hinder stabilization by the passage mechanism.

The time of existence of elevated pressure in the pore with passage of combustion in it is very small, and therefore the depth of passage must be determined by the dynamic strength of the fuel. This strength, as is known, is not a parameter solely of the material, but is determined to a considerable extent by other factors [7]. For a porous fuel, the supply of heat in the gas entering the pore is significant. The depth of heating of the condensed phase along the pore and the rate of ignition, and hence also the rate of pressure increase in the pores with passage of combustion, are directly related to this quantity. With increase in the rate of loading, the resistance of the material to disruption rises (for times of order 10 -3 sec, the breaking stress o is associated with the time of load application ~ by the dependence T = A exp (--eo), where A and ~ are constants), and therefore the store of heat in the gas must affect the strength of the fuel and the depth of passage.

Considering the possible consequences of the passage of combustion in the pores, and taking into account that its development is influenced by the pressure profile in the filtra- tion zone and the amount of heat transmitted to the condensed phase up to the onset of the passage of combustion, it will be assumed that the qualitative features of perturbed combus- tion are determined by the stages preceding the passage of combustion, which itself only in- fluences the rate of combustion. For filtration and conditions of heat transfer, certain assumptions are made.

130

t Fig. 5. Oscillograms of the ex- perimental parameters: i) signal from the combustible wires; 2) external pressure; 3) pressure in the free volume.

i. Gas filtration is quasisteady in character, i.e., the pressure profile in the filtra- tion zone may be fine-tuned under the changes in external pressure.

2. From a consideration of the conditions for the penetration of combustion into a single pore [8, 9], it follows that there is a range of pore diameters in which ignition is determined by the time of creation of a heated layer of condensed phase, the. Compari-

son with experimental data shows ~i] that, for nonmelting materials with pores of diam- eter less than 40-100 Dm, and for melting materials (obviously, regardless of pore size), this is in fact so. In this region, the formation of a heated layer does not depend on the rate of gas flow. Therefore, in the first approximation it may be assumed that the in the given conditions is the same as in normal combustion

tg~ ~e ~ ac/u~, (1 )

while the width of the heated layer of the condensed phase corresponding to the combustion rate Ic = acuc/u~, where ac is the thermal diffusivity of the condensed phase..

The above-noted theoretical and experimental data on pore ignition indicate that ignition criterion usually used in the theory of convective combustion [10-12] -- heating of the pore surface to a definite temperature -- may be justifiably adopted only in the case of nonmelting fuels with large pores. This criterion is also applicable, in certain condi- tions [13], for fuels whose ignition is described by solid-phase theory.

3. It is assumed that isothermal filtration occurs, for which the gas temperature in the filtration zone is averaged [14].

An approximate solution of the filtration equation is known [15], giving a linear pressure profile for the case where the initial pressure in the pores PN = 0. Its applicability in real conditions (PN = 1 atm) has been verified experimentally [i]. This solution is used to deter- mine the time to of filtration-zone formation corresponding to the combustion rate uc, the zone dimension l, and also the position of the filtration front Lf a �9 tg after the onset of

gas filtration in the pore

t o 0'656Kp~ Lf ~ ~.62 | / K p ~

l = i.312KPo/mogUc = 2tou C,

where K and mo are the gas permeability and open porosity of the fuel; ~ is the mean gas viscosity in the filtration region.

The process of filtration-zone formation and the features of combustion will not be con- sidered as a function of the ratio of the characteristic times of filtration to and heating tg. Depending on the parameters determining these times -- see Eqs. (i) and (2) -- one of

three possible variants may occur.

I) In the case where to > tg, calculation on the basis of experimental dependences uc(Po) and uN(Po) (see Fig. 2) shows that this condition corresponds to the region of uC(Po) lying

to the left of point 3 in Fig. 4.

In the given case, at the moment of ignition (a time tg after the onset of filtration), the rate of gas inflow into the pore uf > u C. This means that the rate of heat transfer established in the system which is necessary for fuel ignition (u C) does not correspond to

131

c

o0 Fig. 6. Dynamics of pressure-profile formation in the filtra-

tion region: a) from the onset of filtration to the ignition of the condensed phase; b) before dispersion, and after the pas- sage of combustion in individual pores; c) directly after di- spersion; d) before dispersion after a new passage; the dashed curve corresponds to the pressure in the pores along which pas-

sage occurs and the continuous curve to the mean pressure in

all the pores.

the potential possibility of mass transfer (if this is estimated from the mean rate of inflow of gas into the pore under the action of pressure difference Apo after a time tg). The in-

complete use of the filtration potential is a consequence of the fact that, after a time tg, the gas cannot independently transmit the required heat supply to the condensed phase. In these conditions, heat transfer in the system is determined not solely by convection but also

by conduction, and therefore at the onset of combustion (before a filtration zone is formed) the rate of mass transfer exceeds the rate of heat transfer. This leads, in the course of

combustion, to the gradual filling of the pores by gas and to decrease in the already small contribution of convection to the total heat transfer.

However, a time to after the onset of filtration, the rates uf and uc equalize, the growth in the filtration zone (filling of the pores) ceases, and equality of the rates of mass and heat transfer is established in the system. The intensity of convective heat transfer in these conditions also determines the increment in steady combustion rate in comparison with normal conditions. After the formation of the filtration zone ends, the rate of combustion is

stabilized by the passage of combustion (see above) or, in its absence, by discrete dispersion [6].

With rise in external pressure, the ratio of the times tg and to varies, in a nonmono- tonic manner. In fact, tg ~ p72~N and to ~ p~-2~C, while vC > UN and rises continuously.

Therefore, as long as ~C < ~N + 0.5, tg decreases more rapidly than to with rise in Po, there- by increasing the disagreement between the rates of combustion and of filling of the pores by gas. This sustains the rise in u C with increase in po.

In the region where ~C > ~N + 0.5, the decrease in to occurs, conversely, more rapidly than decrease in tg as po increases, and the loss in u C due to pore filling rapidly decreases.

Convective heat transfer and the dependence uC(Po) are intensified.

The pressure Pup, at which ~C = ~N + 0.5, may be regarded as the pressure of breakdown of perturbed combustion for nonmelting systems, since it determines the conditions for the onset of rapid increase in rate of the process and its transition to convective conditions.

Up to the breakdown pressure, tg/to decreases, and thereafter it increases. Hence, the break- down of perturbed combustion occurs when the condition d/dp-(tg/to) = 0 is satisfied. Since the inequality to > tg diminishes with rise in pressure above Pup, equality of these times

will be established at a certain pf.

2) In the case where to = tg, the end of filtration-zone formation coincides with the moment of ignition. From Eq. (2), the relation Lf = 21 = 21 C is obtained. Hence, the mean rate of gas inflow into the pore uf = Lf/tg > u C. This means that, until the onset of com- bustion, the rate of mass transfer in the system is much larger than the rate of heat trans- fer. With convective combustion, these rates must coincide (it is assumed that conduction and

convection are the only competing sources of condensed-phase heating).

Thus, in the given case, the onset of satisfaction of the condition uf = u C or tg = 4to determines the boundary between the perturbed and convective conditions of combustion.

3) The condition to < tg is satisfied to the right of point 3 in Fig. 4 (at pressures above pf). It follows from the inequality that, at the moment of ignition, uf < u C. In these conditions, filtration-zone formation consists of the following process: after ignition the

132

~ . . I _ , _ 2 _ , . 3

i 4 15 rTc=TI rlTC~-rN tn=PN

?'= T N . -

F i g . 7. C h a r a c t e r i s t i c zones and r e g i o n s i n t he combus t i on o f gas - pe rmeab le f u e l s . Reg ions : i ) o u t - flow; 2) transfer; 3) compression; zones: 4) precombustion; 5) combus-

tion; 6) heating; 7) filtration.

gas, the velocity of which is less than u C, is compressed by the arrival of the combustion zone, filling the transfer region and decreasing the pressure gradient there. This is a pos- sible explanation of the plateau preceding the pressure peak in Fig. 4e. The pressure gradi- ent preceding the transfer region, on the other hand, increases until the filtration-front velocity becomes equal to the combustion rate.

In the given region (with po = p,), the condition of onset of convective combustion is satisfied (see above). In these conditions, heat transfer occurs at the mean rate of penetra- tion into the pores of the gas volume containing all the heat supply necessary for ignition.

Therefore, it is possible to speak of a filtrational constraint on the combustion rate here.

The mass and velocity of the gas in the compression region (Fig. 7) with steady combus- tion are constant, on average [6]. Therefore, the momentum of the forces acting on the gas in this region is zero. Taking into account that the mean velocity of the gas participating in heat transfer and periodically (in the time of existence of the transfer region) inter- acting with the compression region is equal to the combustion rate, it may be concluded that the mass of gas entrained into the compression region is equal to the mass of gas participating in convective heat transfer.

Assuming that the gas is entrained over the length of the heating region, the following relations are satisfied in the case of a linear pressure profile

1 c AI = Ap/Apo. , l >~ Lf(to ~ ~), (3)

~fLf=Ap/Apo, l<Lf(to<t~, where Ap is the pressure difference at the boundaries of the entrainment region, which allows a judgement to be formed as to the degree of use of the filtration possibilities. For example, in convective conditions, Lf = ~C, and hence Ap = Apo, which indicates complete use of the pressure difference in the filtration zone.

Taking Eq. (2) into account, it follows from Eq. (3) that Ap may be very small, even when the combustion rate is several times larger than u N. It is also evident that the rise in Ap lags behind po when po < Pup(VC < VN + 0.5), but leads it when po > Pup"

Since the possibilities of filtration are completely utilized in convective conditions, it becomes impossible to increase (as in the case of perturbed combustion) the intensity of convective heat transfer more rapidly than is allowed by the rise in Apo due to increase in the fraction of Ap which it contains. Therefore, when Po > p,, the rise in combustion rate is retarded, and the power index v C in the dependence uC(Po ) is stabilized.

LITERATURE CITED

i. A. F. Belyaev, V. K. Bobolev, et al., Transition of Combustion of Condensed Systems to Explosion [in Russian], Nauka, Moscow (1973).

2. K. K. Andreev, Dokl. Akad. Nauk SSSR, 53, 237 (1946). 3. V. K. Bobolev, A. I. Karpukhin, and S. V. Chuiko, NTPGV, i, No. I, 44 (1965). 4. K. K. Andreev and S. V. Chuiko, Zh. Fiz. Khim., 37, 1304 (1963).

133

5. S. Ya. Kurakin, V. G. Korostelev, and Yu. V. Frolov, in: Kinetics of Physicochemical Reaction [in Russian], Chernogolovka (1977).

6. V. G. Korostelev and Yu. V. Frolov, Fiz. Goreniya Vzryva, 5, No. 2 (1979). 7. L. V. Al'tshuler, S. A. Novikov, and I. I. Divnov, Dokl. Akad. Nauk SSSR, 166, 67 (1966). 8. A. D. Margolin and S. V. Chuiko, Fiz. Goreniya Vzryva, i, No. 3 (1965). 9. Ya. B. Zel'dovich, Zh. Eksp. Teor. Fiz., 12, 498 (1942).

I0. K. Kuo, R. Vishnevetsky, and M. Summerfield, AIAA J., ii, No. 4, 444 (1973). Ii. V. F. Dubovitskii, V. G. Korostelev, et al., Fiz. Goreniya Vzryva, iO, No. 6, 841 (1974). 12. B. S. Ermolaev, B. A. Khasainov, et al., Fiz. Goreniya Vzryva, Ii, No. 5, 720 (1975). 13. A. ~. Averson, in: Heat and Mass Transfer in Combustion Processe-~ [in Russian], Cherno-

golovka (1979). 14. Kokh, Datton, et al., Teploperedacha, 99, No. 3 (1977). 15. G. I. Barenblatt, Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 6, 97 (1954).

TRENDS IN THE SPIN COMBUSTION OF THERMITES

A. V. Dvoryankin, A. G. Strunina, and A. G. Merzhanov

UDC 662.581

A combustion front as a focus moving along a spiral was first observed [i] in the com- bustion of heterogeneous systems of metal--gas type. The phenomenon was called spin combus- tion. A detailed experimental study [2] revealed the main trends. In [3-5], the theory of spin combustion was vigorously developed. It was shown to be possible for combustion to occur in gas-free systems. This is confirmed by experiment in [6] on intermetallic systems.

Below we present results on the main laws of spin combustion for thermite compositions. Particular attention is given to aspects not previously considered.

We examined the combustion in various thermite systems with various degrees of component dilution with reaction products in order to choose the objects. Visual observations on the combustion and analysis of the products were used (the Cylindrical surfaces of the pressed specimens showed tracks characteristic for each condition), and it was found that in most of the systems the limiting combustion mode was oscillatory (there were parallel ring recesses after the combustion). The spin mode (a spiral track around the surface of the cylindrical specimen) occurs only in certain systems (Table i). Subsequently we considered the combus- tion in these systems.

The execution of the experiments and the preparations for them were analogous to those of [7]. The combustion was recorded with a Konvas cinecamera. The rate of movement of the combustion front was determined with an FR-II photographic recorder, while the combustion temperatures were determined with tungsten--rhenium thermocouples placed in the specimen.

Effects of External Factors

Table 2 indicates the width of the combustion region for chromium-zirconium and iron-- zirconium thermites (in various media), wherethe combustion is characterized by luminous foci. The width of the region was affected by the dilution of the initial components with reaction products. At low degrees of dilution, there was steady-state or oscillatory com- bustion, while at high speeds the combustion died out. Combustion with foci occurs most readily in an inert medium (the widest range), but the upper limit in air was somewhat higher than in an inert medium. Evidently, the redox reaction occurring in the system is accompanied by a secondary interaction with atmospheric oxygen. This is also evident from the ratio of the combustion rates in air and in argon (Table 3).

The width of the spin-mode region is also influenced by the sense of displacement of the combustion front (from above downwards or vice versa in the cylindrical specimen). The experiments with iron--zirconium thermite (Fe203 + Zr) showed that luminous points occur at the front in combustion moving from below upwards at higher dilutions (in less calorific

Chernogolovka. Translated from Fizika Goreniya i Vzryva, Vol. 18, No. 2, pp. 10-16, March-April, 1982. Original article submitted April 29,1981.

134 0010-5082/82/1802-0134507.50 �9 1982 Plenum Publishing Corporation