Thermal stability of the burning of the base subsystem of components of a composite propellant

236

ISSN 1990-7931, Russian Journal of Physical Chemistry B, 2007, Vol. 2, No. 3, pp. 236–244. © Pleiades Publishing, Ltd., 2007.Original Russian Text © S.V. Chuiko, F.S. Sokolovskii, G.V. Nechai, 2007, published in Khimicheskaya Fizika, 2007, Vol. 26, No. 6, pp. 48–57.

The problem of attaining the limiting burning rates,both the lowest and highest, of a composite propellantand of regulating its ballistic characteristics within theframework of the concept of interacting subsystems ofcomponents, which we continue to develop, involvesthe determination of the thermal stability of burning ofthe base subsystem, more specifically, its response tothe introduction of heat absorbers and burning rate cat-alysts.

The regulation of the burning rate of various systemsby introducing in them certain amounts of burning ratemodifies has received much attention, see, e.g., [1, 2].

While catalysts enhance the burning rate of propel-lants due to increases in the intensity and completenessof the chemical reactions involved, inhibitors, as a rule,slow down the chemical reactions and, consequently,the burning rate. Note, however, that inhibitors may actlargely through heat absorption, not only by suppress-ing chemical reactions.

Generally, a composite solid propellant (CSP) con-sists of a fuel binder (FB) doped with burn rate modifi-ers and dispersed fillers, such as an oxidizer, metal fuel,energetic additives, etc. Heterogeneous CSPs can bethought of as consisting of elementary cells containingthe minimum amount of propellant whose compositionis identical to that of the propellant sample as a whole.The size of the cell is given by

H

i

=

d

i

+

d

il

, where

d

i

isthe particle size of the coarsest filler fraction and

d

il

isthe FB interlayer thickness for the base subsystem. Thedynamic heterogeneity of a CSP is defined as

G

=

H

/

L

[3], where

L

=

˚

/

U

is the heated layer thickness (

˚

isthe thermal diffusivity of the CSP, and

U

is the burn-ing rate).

Let us define the base subsystem as a primary matrixcapable of self-sustained burning and continuouslyspreading throughout the propellant sample.

For SCPs containing an FB capable of self-sus-tained burning (active binder), this matrix can be iden-tified with the FB matrix; its characteristic size is equalto the thickness of the interlayers between the smallestfiller particles.

For CSPs containing an FB incapable of self-sus-tained burning (passive binder), this primary burnablematrix can be thought of as comprised of a set ofdomains with the highest degree of homogeneity quasi-continuously spreading through the propellant sample.Such domains are characterized by the smallest ele-mentary cell or, at equal cell sizes, by a higher burningrate. Several dispersed components can be consideredto form a single subsystem if

—they experience an intense chemical interactionwith each other in the reaction layer during burningand if

—the structures of adjacent fractions are not sepa-rated, being combined into one subsystem because ofnonoptimal packing.

For example, when the filler is polydisperse ammo-nium perchlorate (AP), the base subsystem is com-prised of the FB and the finest AP fraction. Generally,for any CSP composition, it is possible to specify a setof its components that, when combined, form a quasi-continuous base subsystem capable of self-sustainedburning. The rest of the dispersed components shouldbe considered as inclusions (fillers) that interact, to acertain extent, with the combustion wave propagatingthrough the base subsystem [4].

We believe that the ballistic characteristics of a pro-pellant as a whole are determined by the characteristicsof the base subsystem and the specificity of their inter-action with each other. Of the possible interactions, wewill consider the following:

COMBUSTION AND EXPLOSION

Thermal Stability of the Burning of the Base Subsystem of Components of a Composite Propellant

S. V. Chuiko, F. S. Sokolovskii, and G. V. Nechai

Semenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow, 119991 Russia

Received April 10, 2006

Abstract

—The problem of the thermal stability of the base subsystem of components of a composite solid pro-pellant with respect to the introduction of heat-absorbing agents, inhibitors, and burning rate catalysts was con-sidered. It was demonstrated that the response of the base subsystem to the introduction in it of additives isequivalent to a change in the initial temperature of the propellant, i.e., is determined by its burning rate temper-ature sensitivity. The competition of the fuel components for oxidative species and the role of this phenomenonin the formation of the structure of the combustion wave were examined. Extensive experimental data on theeffect of heterogeneous fillers of various natures on the burning rate of the composite system were obtained.

DOI:

10.1134/S1990793107030074

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B

Vol. 1

No. 3

2007

THERMAL STABILITY OF THE BURNING OF THE BASE SUBSYSTEM 237

(1)

A strong thermophysical interaction

of a com-bustion wave propagating through a base subsystemcontaining a chemically inert filler capable of releasingor absorbing heat.

(2)

A weak thermophysical interaction

of a combus-tion wave propagating through the base subsystem con-taining a filler producing no other effects except chang-ing the geometry of its propagation.

1. MONODISPERSE BASE SUBSYSTEM

In the first series of experiments, we used base sub-systems prepared from monodisperse AP powders withparticle sizes of

d

AP

≈

1

and 4

µ

m (75 wt %) and a plas-ticized carboxylate rubber FB (25 wt %). The burningrate law for these base subsystems reads as

U

d

=

1

µ

m

=5.4

P

0.31

and

U

d

=

4

µ

m

= 1.0

P

0.76

(

U

and

P

, in mm/s andatm, respectively). These quasi-homogeneous sub-systems with a stoichiometric coefficient close to unityare capable of self-sustained burning, the characteristicof which are determined by near-surface reactions [5, 6].

To understand how the dependence of the burningrate on the pressure and temperature can be modifiedbased on the concept of interacting subsystems of com-ponents, it is necessary to determine the thermal stabil-ity of burning of various base subsystems, more specif-ically, their response to the introduction of heat absorb-ers and burning rate catalysts.

1.1. Catalysis of the Base Subsystem

We studied how the burning of the base subsystemwas promoted by a liquid ferrocene catalyst (FC). Thepressure exponent in the burning rate law,

U

=

B

0

P

ν

(

B

0

is a coefficient), was found to decrease with theweight content

C

FC

of the catalyst as

ν

(

C

FC

) = 0.76 –

0.29

C

FC

+ 0.05 (

C

FC

= 0–5.8 wt %). The observeddecrease in the exponent

ν

can be attributed to adecrease in the efficiency of the catalyst,

Z

=

U

c

/

U

0

(

U

c

and

U

0

are the burning rates of the catalyzed anduncatalyzed subsystems, respectively). The higher theburning rate of the uncatalyzed system, the larger theconcentration of the catalyst is required to markedlyincrease the burning rate. At

U

~ 40 mm/s,

Z

= 1 irre-spective of

C

FC

. Under these conditions, the AP particlesize, ~4

µ

m, and the heated layer thickness,

˚

/

U

0

~ 3–4

µ

m, are similar. This means that, in this case, the lim-iting factor in the catalysis of burning is the conversionof the oxidizer into active intermediate products. Thelimiting rate changes linearly as the size

d

0

decreases. The burning rate is inversely proportional tothe oxidizer particle diameter,

/ ~

d

0

/

d

1

. For thesystem under study, the

Z

(

C

FC

) curve levels off onto aplateau, a behavior that can be qualitatively explainedby the catalyst having no time to produce its full effectin the reaction zone. Clearly, the onset of the leveling-

CFC2

U0*

U1* U0*

off must shift to higher catalyst concentrations as theAP particle size decreases.

1.2. Inhibition of the Base Subsystem

An inhibitor, colloidal strontium carbonate (SC)with a particle size of less than

50

Å, was introducedinto the same basis system. The relative efficiency ofthe inhibitor,

ϕ

= 1/

Z

=

U

bs

/

U

SC

, was found to bedescribed by

ϕ

= 1 +

C

SC

within

C

SC

= 0–2.25 wt %,where

C

SC

is the weight concentration of the inhibitorin the mixture. In line with the above analysis of the cat-alytic action, we explained this result by the absence ofthe limiting effect of diffusion (no influence of theinhibitor particle size was observed); i.e., the efficiencyof the inhibitor is determined by its action on a certainreaction zone. When the reactions in this zone are com-pletely suppressed and, hence, their influence on theburning rate, a further increase in the concentration ofthe inhibitor makes the system unburnable. The conclu-sion that the character of the inhibition is thermal issupported by a simple theoretical estimate. Let

Q

and

∆

Q

≈

k

C

SC

be the heat effect of burning and thedecrease in this quantity associated with the presence ofthe inhibitor, respectively. Then, in the first approxima-

tion,

U

bs

≈

and

U

SC

=

; if

Q

�

∆

Q, then

ϕ = Ubs/USC ≈ = 1 + k2CSC, where k, k1,and k2 are coefficients [7]. It is this form of the ϕ (CSC)dependence that was obtained experimentally (Fig. 1).

When both the catalyst and inhibitor were intro-duced, the result could be presented as the algebraicsum of the effects of the FC and SC (at CSC = 0.5 wt %and CFC = 2.25 wt %, U100 = 13.2 mm/s and ν = 0.28).

Q Q ∆Q–

1/ 1 k1CSC–( )

2

0 0.51

1.0 1.5 2.0

3

4ϕ = U0/U

CSC, wt %

Fig. 1. Inhibition effect at pressures of (�) 40 and (�)100 atm as a function of the strontium carbonate concentra-tion.

238

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 1 No. 3 2007

CHUIKO et al.

This result can only be obtained if the thermal decom-position of the catalyst occurs at a relatively low tem-perature near the burning surface and in subsurface lay-ers of the condensed phase [2] while the inhibitor has ahigher temperature of decomposition and, therefore,can produce an effect in hotter zones of the gas phase(relatively far from the burning surface). For the exper-iments performed, these conditions are met. A compar-ison of the results on the effects of the catalyst andinhibitor and the joint effect thereof on the burning ofthe base propellant is indicative of the independentaction of these two modifiers of burning characteristics,since the resultant effect is equal to the sum of theeffects of each.

1.3. Thermal Stability of the Burning of the Base Subsystem

To directly evaluate the stability of the process ofburning with respect to a heat-absorbing filler (its sec-ond role, as an oxidant, can be disregarded here), weintroduced a coarse-grained spherical aluminum pow-der (~250 µm) into the base subsystems (initial anddoped with the catalyst and inhibitor) and measured theburning rates of these mixtures. The initial subsystemwas composed of 25 wt % FB and 75 wt % AP (with aspecific surface area of 8000 cm2/g).

The modified compositions were obtained by mix-ing 100 wt % initial composition with 1.5 wt % FC(composition BS–C) and 1.0 wt % SC (BS–I). The burncharacteristics of these mixtures are summarized inTable 1.

Although the experiments were performed over apressure range from 10 to 100 atm, only the dataobtained at pressures below 40 atm were processed(Figs. 2–4); at higher pressures, the main tendencieshold but the magnitudes of the effects under studydecrease to become comparable with the experimentalerror.

Figures 2–4 display the experimental results in the Zversus C/(1 – C) coordinates, where Z is the ratio of theburning rates in the presence and absence of the addi-tive and C is the additive concentration. Figure 5shows the dependence of Z on the interlayer thicknessdil at a pressure of 20 atm, which is given by dil =

dfil(1.24/ – 1), where dfil is the filler particle size, Cox =(α × 10–2/ρÓx)/{(α × 10–2/ρÓx) + [(1 – α × 10–2)/ρfuel]} isthe volume fraction of oxidant, ρÓx = 1.96 g/cm3 is theoxidant density, ρfuel = 0.93 g/cm3 is the fuel density, andα is the content of oxidant in the propellant (wt %). Ananalysis of the above results led us to the following con-clusions.

Base subsystem. The lower the pressure, the steeperthe decrease of the burning rate with increasing heatabsorber content at C ≥ 0.3 (Fig. 2).

The inhibited system exhibited the classical behav-ior: the higher the pressure (burning rate), the higherthe coolant concentration is needed to produce a givendecrease in the burning rate (Fig. 3). Let us comparethese curves with the analogous curves for the base sys-tem. At C ~ 0.27 and pressures of 10, 20, and 40 atm,Z = 0.74, 0.79, and 0.84, respectively, for the base sub-system and Z = 0.74, 0.86, and 0.95, respectively, forBS-I; i.e., the inhibitor enhances the relative stability ofthe burn-rate-controlling processes with respect to the

CÓx1/3

Table 1. Burning characteristics of base subsystems(u = BPν)

Subsystem B ν

Burning rate, mm/s

P, atm

10 20 30 40

BS 1.194 0.625 5.0 7.8 12.0 21.3

BS-C 6.356 0.262 11.6 13.9 16.7 21.3

BS-Increase 1.447 0.368 3.4 4.4 5.6 7.9

0.6

0 0.10.4

0.2 0.3 0.4 0.5 0.6C/(1–C)

40

20

10

0.8

1.0Z = W/U

P, ‡tm

Fig. 2. Processing of data on the characteristics of the basesubsystem (BS).

0.6

0 0.10.4

0.2 0.3 0.4 0.5 0.6C/(1–C)

40

20

10

0.8

1.0Z = W/U

P, ‡tm

Fig. 3. Processing of data on the characteristics of the inhib-ited base subsystem (BS–I).



effect of the heat absorber (a similar behavior wasobserved at larger C values).

Catalyzed system. As the amount of heat absorberintroduced was increased, the burning rate of the cata-lyzed system first decreased sharply (Fig. 4), but then itdecreased even more slowly than that of the inhibitedmixture. The most likely explanation is that the fillerinhibits the gas-phase reaction, which is known to beresponsible for 10 to 20% of the overall burning rate ofthe catalyzed system. The filler particles prevent thisreaction from occurring in the space between them, i.e.,push it off from the burning surface. The rest of the pro-cesses controlling the burning rate can occur betweenthe filler particles. For the catalyzed system, these pro-cesses are less sensitive to the presence of the filler thanin the case of the base or inhibited mixture. We believethat the influence of the near-surface gas phase is essen-tially eliminated, while the main contribution comesfrom the condensed phase, the second reaction zone.

The results obtained are summarized in Fig 5, whichshows how the burning rate depends on the thickness ofthe interlayers between the particles. As can be seen,the inhibited system exhibits the highest stability: it isessentially insensitive to the introduction of filler parti-cles if the interlayer thickness between them is largerthan 250 µm. The highest sensitivity is observed for thecatalyzed system, while the base subsystem occupiesan intermediate position. These distinctions are mostmarked at large interlayer thicknesses. These results ledus to conclude that, for the inhibited system, the gas-phase reaction within hundreds of microns from thesurface is very slow, and, therefore, its being cut offfrom the condensed phase produces no appreciableeffect. By contrast, the gas-phase reaction within anear-surface zone more than 500 µm in width contrib-utes substantially (~15%) to the burning rate. Note thatthe above conclusion concerning the inhibited systemlends an independent support to our opinion that thestrontium carbonate inhibitor acts largely in the gasphase.

Note that a heat-absorbing filler produces the sameeffect on the burning rate as a decrease in the initialtemperature of the propellant, that is, the response ofthe propellant to the introduction of the filler reflects thetemperature sensitivity of its burning rate. At the sametime, filler particles perturb the combustion wave bydisrupting the formation of a normal temperature distri-bution and preventing the gas phase from influencingthe processes in the condensed phase.

Thus, a given burning rate may reflect the interplayof various physicochemical processes differing inintensity and location. As a result, the combustion wavestructure and, hence, the sensitivity of the system toexternal perturbation also differ. This can only beexplained by variations in the contributions from thegas-phase and condensed-phase processes.

2. POLYDISPERSE COMPOSITE SYSTEM

We studied a composite propellant containing16 wt % FB, 16 wt % aluminum (dÄl = 15 µm), and68 wt % two-fraction AP (oxidizer) with the propor-tion between the fine (f) (df ~ 4 µm) and coarse (c)(dc ~ 240 µm) fractions of 53 : 47. For this propellant,the characteristic size of the elementary cell and theinterlayer thickness between coarse AP particles wereHc ~ 400 µm and dil ~ 150 µm. Since coarse AP parti-cles are much larger than Al and fine AP particles, thestructure of the binder–Al–fine AP mixture that fills thespace between the coarse AP particles is not affectedby the presence of large particles: it contains 25 wt %binder, 25 wt % Al, and 50 wt % fine AP. The char-acteristic size of the elementary cell for this mixturewas found to be HÄl ~ 30 µm (ρÄl = 2.7 g/cm3). SincedÄl > df and Hf ~ 6 µm (the interlayer compositionexcluding Al), coarse AP particles are separated by fineAP–binder interlayers with a thickness larger than thecharacteristic sizes of the corresponding elementarycells, Hf and HÄl, by factors of ~25 and ~5, respectively.Thus, the fine AP–FB elementary cells constitute theprimary (base) matrix.

0.6

0 0.10.4

0.2 0.3 0.4 0.5 0.6C/(1–C)

40

20

10

0.8

1.0Z = W/U

P, ‡tm

Fig. 4. Processing of data on the characteristics of the cata-lyzed base subsystem (BS–C).

1.0

0.9

0.8

0.7

0.6

0.5100 200 300 400 500

dil, µm

Z = W/U

BS–I BS–C

BS

Fig. 5. Dependence Z(dil) for all the base subsystem studiedat 20 atm.

240


CHUIKO et al.

In the absence of an appreciable heat flux from thegas phase to the propellant surface, the propagation ofthe combustion wave through an inert barrier can onlyoccur due to an exothermic reaction in the subsurfacelayer of the condensed phase, which should begin at atemperature T∗ < Ts, where Ts is the temperature of theburning propellant surface. At L > ˚/U0, the role of bar-riers to the combustion wave propagating through aCSP is played by binder interlayers between fine APparticles, interlayers that, nevertheless, are capable ofundergoing oxidative pyrolysis under the action of theoxidant decomposition products. The combustion frontcan propagate at T∗ ≈ Ts if the thickness ∆l of the binderfuel layer is smaller than the distance between the neigh-boring oxidant particles. At dAP ~ 4 µm, the mixture isunburnable at oxidant concentrations of Cf < C∗ ~ 60–68 wt % (on the average, 63 wt % or 44 vol %). There-fore, the FB interlayer thickness is given by ∆l∗ = dil =d[α(C–1/3) – (2/3)1/2] ≈ 0.5df, an estimate indicativeof the diffusion character of the oxidation of FB. Atdil > df/2, the flame consists of flamelets attached toindividual oxidant particles, since the distance of theexpansion of the jet of oxidant gasification productsd/U0 within the period of its existence is shorter than dil;as a result, the combustion front decays into separateweakly interacting domains (Fig. 6). This process is ofspecial importance for CSPs composed of an FB and anoxidant incapable of self-sustained burning individually.

Upon introduction of the catalyst and broadening ofthe particle size distribution, the limiting value of ∆l∗/dat d = 1.5 µm was found to be ~1.7, i.e., it increasedmore than threefold; at d = 11 µm, it did by a factor of~2. In this case, the process of burning appeared as

flameless smoldering accompanied by the formation ofa carbonaceous residue. In the presence of a catalyst,the temperature of onset of condensed-phase reactionsof the fuel and oxidant is lower, a factor that broadensthe reaction zone. The effect of the specific surface areaof the AP is obvious, since the heat release rateincreases with the specific surface area of the AP–FBinterface d. At d = 600 µm, the value of C∗ is lower than10–15 wt %. A catalyst capable of promoting gas-phasereactions acts so as to shift the onset of the combustionof the fuel and oxidant jets to earlier stages of their mix-ing with each other, i.e., makes the flamelets over indi-vidual particles support each more effectively, a factorthat diminishes the influence of diffusion on the burn-ing rate. Thus, a catalyst makes it possible to decreasethe limiting value C∗ for oxidant–fuel mixtures. Thismeans that the stability of burning of the base sub-system of a CSP can be enhanced by using as fine anoxidant as possible in conjunction with a catalyst capa-ble of promoting the oxidant–fuel interaction.

The characteristic dimension can be identified with∆l' ~ ω0τ (ω0 ~ Pn; kinetic regime of oxidation of FB)

or with ∆l ~ (diffusion regime, contact burning);here, τ is the duration of the action of the oxidativeproducts, D is the coefficient of diffusion of these prod-ucts to the FB, and ω0 is the oxidation reaction rate.Note that the condition of absence of combustion wavepropagation, ∆l' < dil = dF(C), leads to the inequalitiesω0/U0 < F(C)const or ω0d < F(C)const. This means that,in the kinetic regime, the burning of a propellant ismore effective if the oxidant particles burn more slowly.Physically, this means that, to burn out a large amountof adjacent FB, the oxidant particle should decomposeslowly.

Let us derive an expression for the burning rate W ofan elementary cell of size H containing a particle of sized surrounded by an FB layer (of thickness ∆l) undergo-ing oxidation at a rate ω0 (the pyrolysis of the FB resi-due occurs at the rate ωp). Given that the ∆l-sized layersof neighboring particles overlap, we can write [6]

Let Ψ = ωp/W; then,

where ζ = and k1 and k2 are constants.

The amount of dispersed or pyrolyzed FB is ϕ = 1 –

Dτ

W H/Στ;=

Στ d il ∆l+( )2/˚FB d/U0 ∆l/ω0+ +=

+ H ∆l d––( )/ωp.

Ψ 1 1ωp

ω0------⎝ ⎠

⎛ ⎞ 1 e ζ––( )–⎝ ⎠⎛ ⎞– C

k1----3

ωp

ω0------ 1

ωp

U0------–⎝ ⎠

⎛ ⎞ ,–=

Ck1----3 1 k2

∆ld-----+⎝ ⎠

⎛ ⎞

Fig. 6. Interaction of AP particles (d ~ 500 µm) with thecombustion front of a slowly burning matrix at 40 atm.



(1 – Â–ζ) = Â–ζ (valid at C ≤ k1). For volatile FB, whichis gasified simply by heating, we have

Στ = ∆l/ω0 + (dil – ∆l)2/(4˚FB) + d/U0

or

ω0/W = 1 – η + d(ω0/U0 – 1)/H + Hω0η2/˚FB,

where η = exp(–ζ); for the rest of the notations, seeabove. At 1/η � 1 and ω0 � U0, ω0/W = [1 – (C/k1)1/3 – η].

Thus, the replacement of a coarse oxidant by a finerone results in a decrease in the concentration limit ofburning of base subsystem mixtures. This can be attrib-uted to the fact that fine oxidant and FB are effectivelyconsumed in condensed-phase transformations, and,therefore, large-sized components introduced in such amatrix experience deficiency in active reactants andproduce, as a result, only a slight effect on the burningrate of the system as a whole. In addition, a catalystintroduced into the system (for example, of ferrocenetype) not only intensifies the condensed-phase reac-tions but also consumes oxidative components. Thisappears as the competition of various fuel componentsfor oxidative species. The character of this competitionis strongly dependent on the behavior of the fuel com-ponents during their transformations in the reactionzone. As a result, the extents of chemical conversion ofthe components at the surface of a burning compositesystem and, hence, the degrees of their participation inthe formation of the combustion wave, differ substan-tially. The thermodynamically equilibrium temperatureand product composition are attained in the gas phasefar from the burning surface. In particular, this impliesthat the combustion temperature of the propellant pro-duces no marked effect on its burning characteristics.

3. INTERACTION OF THE BASE SUBSYSTEM WITH AN INERT INCLUSION

The burning rate of a CSP can be considered asbeing determined by the interaction of the constituentsubsystems, each of which produces a different effecton it. The coarse oxidant and metal fuel, the rates oftransformations of which in the combustion wave aresubstantially lower than the burning rate of the basesubsystem, can be considered to be inert with respect tothe latter. These components absorb heat from the zoneof burning of the interlayer between their large-sizedparticles, an effect that may cause a decrease in theburning rate of the base subsystem and the propellant asa whole.

Let us now examine the mechanism of action of aninert inclusion. For the sake of simplicity, let us assumethat the base system is homogeneous. The introductionof a homogeneous inert additive results in additionalenergy expenditures for heating of the system. Thedecrease in the heat release in the reaction zone can beidentified with a decrease of the initial temperature T0

by a value of (T0 – ) = rC(T∗ – T0) where is theeffective initial temperature, r is the ratio of the heatcapacities of the additive and the system, C is the vol-ume concentration of the additive, and T∗ is the effec-tive burning temperature of the base subsystem. Defin-ing the burning rate temperature coefficient as β =∂lnU0/∂T0, one can estimate the decrease in the burningrate from the formula

Ψ = W/U0 = Âıp(β )/Âıp(βT0).

Expanding the exponential function into a series yields

Ψ ≈ 1 – β(T0 – ) = 1 – βrC(T∗ – T0) = 1 – γC. (1)

The problem of describing the heat transfer from theburning front into heterogeneous filler particles isessentially more complex. The minimum thickness ofthe fuel interlayer between neighboring filler particlesof diameter dfil is dil = dfilF(C), where C is the volumeconcentration of the filler. Since the interaction of thecombustion front with a filler particle is a substantiallynonstationary process, an important role is played byvarious time characteristics, such as the characteristic

time of heating of the interlayer τil ≈ /˚ and the dura-tion of contact of the combustion front with the fillerparticle τc ≈ dfil/U0. Let us introduce the followingdimensionless parameters:

µ = τil/τc = UbsdfilF2(C)/˚, (2)

which characterize the conditions of heat exchange dur-ing the interaction of the combustion front with fillerparticles, and

ε = dilUbs/˚ = HF(C), (3)

which characterizes the sensitivity of the combustionfront to heat loss (H = dilUbs/˚ is a measure of thedynamic heterogeneity of the filler).

The parameters µ and ε make it possible to take intoaccount the nonstationarity and nonuniformity of theinteraction of the combustion front with the filler with-out solving a multidimensional nonstationary problem.Therefore, the above formulation admits the solution ofone-dimensional problems of temperature relaxationduring heat transfer into the wall and of the effect of theheat sink on the burning rate of condensed systems [8].

The influence of the filler on the base subsystem wasdetermined by using the dependence of the burning rateon the initial temperature, U = Âı(βT0), with consider-ation given to Eq. (1):

Ψ = U/U0 = ≈ 1 – βT0 = 1 – γm(1 – e–A/µ), (4)

where γ = ωβ(TS – T0), m is the concentration of filler par-ticles, A = ξ2, and ξ is the root of the characteristic equa-tion, the value of which depends on the value of the Biot

T0' T0'

T0'

T0'

d il2

eβT0–

242


CHUIKO et al.

criterion, which characterizes how the temperature field isrelated to the parameters of the heat exchange at theboundary. Explicitly expressing µ, we recast Eq. (4) as

(5)

Experimental dependences Ψ(C) in the coordinatesof Eq. (5) must be straight lines with a slope propor-tional to ˚/U0d. Expression (5) is the dependence of theefficiency of an inert filler on its concentration, particlesize, the burning rate of the base subsystem U0, and anumber of thermophysical parameters.

The relationships obtained needed further verifica-tion and refinement. For this purpose, we performeddetailed experimental studies on how inert fillers influ-ence the burning rate of propellants.

The object was a propellant composed of fine AP(d ~ 1–5 µm, 78 wt %) and SK synthetic rubber(22 wt %) plasticized with a ferrocene-containing cat-

1 1 ψ–γC

-------------–⎝ ⎠⎛ ⎞ln A

˚

U0d---------- C 1/3– 1–( )–2

.–=

alyst (FC) in an SK : FC = 10 : 12 (wt %) ratio. The fill-ers were aluminum powders of various dispersities withmean particle sizes of 20, 60, 100, and 200 µm. Suchlarge particles can be considered inert, since they burnout far from the propellant surface and, therefore, can-not produce an appreciable effect on the burning rate.The experiments were performed at a pressure of 1 atm.Aluminum particles were ignited at a distance of 1 cmfrom the surface. A relatively low burning rate: made itpossible to decrease it substantially by adding alumi-num filler (Fig. 7).

A qualitative analysis of the experimental data dem-onstrated that

(1) the introduction of aluminum results in adecrease in the burning rate of the system;

(2) the magnitude of the inhibition effect increaseswith the concentration of filler and its dispersity;

(3) the burning rate begins to decrease with increas-ing concentration of aluminum of given dispersity afterit exceeds a certain critical value;

(4) the critical concentration increases with the fillerparticle size; and

(5) at higher filler concentrations (~40–60 wt %),the disruption of stable burning and quenching areobserved.

Since the value of β for catalyzed compositions islow (β = 1.5 × 10–3 K–1), the value of γ in (5) can be setequal to 1 according to (2) and (4). As can be seen fromFig. 8, the experimental curves are indeed straightenedin the coordinates of Eq. (5) with the slope being propor-tional to ˚/Ubsdil. The effective filler particle sizes calcu-lated from the slopes are close to the nominal particlesizes of the aluminum powders listed in Table 2. That theexperimental points deviate from the linear dependencesat high concentration of aluminum particles is likelyassociated with the disruption of stable burning near thequenching threshold.

Table 2 also lists the critical volume concentrationsbelow which no inhibition action of the inert filler isobserved and the corresponding values of the meanthicknesses of the interlayers in the base subsystem dcalcand of the parameter ε∗. The parameter ε∗ is virtuallyindependent of the filler dispersity within 20–200 µmwith variations being of unsystematic character. Themean value of ε œ∗ was found to be 3.3 ± 0.5.

Processing the experimental data, we derived thefollowing expression for the efficiency of the action ofthe filler:

(6)

Ψ = 0 at ε > ε∗.

As can be seen from Fig. (9), when presented in thecoordinates of Eq. (7), the experimental points tend to

at ε ε* Ψ U/U0=<

= 1 γm 1 A/µ–( ) 1 ε2/ε*2–( )[ ]exp–

⎩ ⎭⎨ ⎬⎧ ⎫

.–

U, mm/s8

6

4

2

0 20 40 60 80C, wt %

1

2

3

4

Fig. 7. Dependence of the burning rate of a composite propel-lant on the concentration of aluminum fillers of various dis-persities: (1) 20, (2) 60, (3) 100, and (4) 200 µm; P = 1 atm.

Table 2. Effect of aluminum powders of various dispersitieson the burning rate of a composite system

dm, µm dcalc, µm tanαi �∗, µm ε∗20 19 0.9 50 3.0

60 47 0.354 60 3.6

100 97 0.174 48 2.9

200 270 0.061 66 3.9



group around a straight line with a slope (calculated bythe least-squares method) corresponding to Bi ≈ 1:

(7)

The correlation coefficient was found to be 0.97.

1 1 ψ–γC

-------------–⎝ ⎠⎛ ⎞ln A

1 ε/ε*( )2–µ

--------------------------.–=

As pointed out above, many components of a pro-pellant can be considered inert if the rate of their gasifi-cation in the combustion wave is substantially lowerthan the rate of conversion of the base subsystem. For afiller particle to be considered inert, it is sufficient thatthe rate of the heat release at its surface during interac-tion with the combustion wave be not higher than therate of heat absorption from the heating zone of thecondensed phase of the base subsystem. For catalyzedbase subsystems, along with metal fuel particles, large-sized oxidant and slowly burning explosive particlescan be considered inert fillers. In these cases, the effectof the filler should be described by the above relation-ships.

To establish how general this conclusion is, we stud-ied the action of components of different chemicalnatures. Figure 10 and Table 3 contain the results ofprocessing of the experimental data on the action ofvarious components on the burning rate of the base sub-system in the coordinates of Eq. (4). We used the fol-lowing fillers:

(1) Powdery iron and iron oxide, a heterogeneouscatalyst of burning of condensed systems. Under ourexperimental conditions, these additives produced nocatalytic effect since the base subsystem already con-tained another catalyst.

(2) A coarse AP powder with a particle size ofd ~ 500 µm.

(3) A powder of octogen, an explosive that burnsmore slowly than the base subsystem.

As can be seen from Fig. 10 and Table 3, the basicregularities of action of these components are similar tothose observed for aluminum. The slopes of the corre-sponding linear dependences correlate with the particle

0 244 8 12 16 20(C–1/3 – 1)–2

12 3 4

0.2

0.4

0.6

0.8

1.0

1 1 ψ–γC

-------------–⎝ ⎠⎛ ⎞ln

Fig. 8. Dependence of the burning rate of a composite pro-pellant on the concentration of aluminum fillers of variousdispersities ((1) 20, (2) 60, (3) 100, and (4) 200 µm) plottedin the coordinates of Eq. (5).

1

0 1 2 3 4

2

1 1 ψ–γC

-------------–⎝ ⎠⎛ ⎞ln–

1 ε ε*⁄( )2–

µ---------------------------

Fig. 9. Dependence of the burning rate of a composite pro-pellant on the concentration of aluminum fillers with disper-sity of 20 to 500 µm plotted in the coordinates of Eq. (7).

0.2

0 5 10 15 20

1

2

34

5

(C–1/3 – 1)–2

0.4

0.6

0.8

1.0

1 1 ψ–γC

-------------–⎝ ⎠⎛ ⎞ln

Fig. 10. Dependence of the burning rate of a composite pro-pellant on the concentration of fillers of various natures inthe coordinates of Eq. (5): (1) Fe2O3 (d ~ 1 µm), (2) octogen(d ~ 100 µm), (3) Fe (d ~ 100 µm), (4) octogen (d >600 µm), and (5) AP (d ~ 500 µm).

244


CHUIKO et al.

size within a range from 1 to 500 µm for the differenttypes of fillers studied.

Thus, a comparison of the quantitative estimates andexperimental data suggests that the adopted approach israther efficient over wide ranges of various parameters,such as the concentration and dispersity of the filler.Universal as they are, the derived expressions can beused to evaluate the effect of dispersed components onthe burning rate of composite systems.

CONCLUSIONSWe examined the thermal stability of the base sub-

system of components of a composite propellant withrespect to the introduction of burning rate modifiers(catalysts and inhibitors). The new results obtained areindicative of the combustion wave structure producinga significant effect on the burning rate.

The previously developed model of action of a het-erogeneous heat absorber, which is based on the con-cept of local heat absorption in the combustion wave,was borne out by the experimental results obtained. Themodel correctly reproduces the basic regularities of het-erogeneous inhibition.

Given that the base subsystem of components deter-mines the main physicochemical processes controlling

the burning rate, the effect of components–fillers can bedescribed by analogy with the influence of rapidlyburning components or chemically inert fillers capableof absorbing heat from the combustion zone of the basesubsystem. It was demonstrated that this approach isapplicable to typical components of propellants, suchas oxidants, metal fuels, and explosives.

The experimental data obtained suggest that propel-lants differ in sensitivity to the introduction of fillers. Itwas found that this sensitivity decreases sharply whena catalyst is added or smaller oxidant particles are usedin the base subsystem.

Under certain conditions, the coarse oxidant frac-tion in the propellant can act as an inert heat-absorbingfiller, producing an appreciable effect on the base sys-tem.

REFERENCES

1. V. Z. Annikov, B. N. Kondrikov, and A. A. Polyakova,Fiz. Goreniya Vzryva, No. 5, 60 (1969).

2. S. V. Chuiko, F. S. Sokolovskii, and G. V. Nechai, Khim.Fiz. 16 (2), 54 (1997).

3. F. S. Sokolovskii, S. V. Chuiko, and G. V. Nechai, Khim.Fiz. 23 (7), 51 (2004).

4. S. V. Chuiko, F. S. Sokolovskii, and G. V. Nechai, Khim.Fiz. 24 (9), 66 (2005).

5. V. K. Bobolev, A. L. Breiter, V. M. Mal’tsev, et al., Dokl.Akad. Nauk SSSR 208 (6), 1375 (1973).

6. B. Delmon, Introduction a la cinetique heterogene(Technip, Paris, 1969; Mir, Moscow, 1972).

7. Ya. B. Zel’dovich, Theory of Combustion of Gun Pow-ders and Explosives (Nauka, Moscow, 1982) [in Rus-sian].

8. G. V. Nechai, F. S. Sokolovskii, V. N. Smirnov, andS. V. Chuiko, Khim. Fiz. 22 (7), 65 (2003).

Table 3. Effect of various inclusions on the burning rate ofa composite propellant

Inclusion dm, µm dcalc, µm tanαi

Fe2O3 1 19 3.9

AP 500 47 0.047

Octogen 80 97 0.38

Octogen 630 270 0.041

Documents

Thermal stability of the burning of the base subsystem of components of a composite propellant