Indian Journal of ChemistryVol. 28A, June 1989, pp. 452-457

Pressure dependence of catalysed and inhibited burning rate of compositesolid propellantsR P Rastogi" & V Syal

Chemistry Department, Banaras Hindu University, Varanasi 221 005

and

Haridwar Singh & K A Nerlekar

Explosive Research and Development Laboratory, Pashan, Pune 411 021

Received 5 September 1988; revised and accepted 27 January 1989 e-./

Data on ambient temperature burning rates for an aluminized HTPB composite propellant family withbimodal AP and a total solids loading of roughly 80% over the pressure range from 35 to 105 kg! cm 2 havebeen reported. Data are also reported for the additive free base line formulation and formulations with indi-vidual rate modifying additives (Fe203, copper oxide, CaC03, SrC03) at 2% level. Results have been corre-lated with rate expressions of Summerfield, Rice, Rastogi and several other empirical relations and relativemerits of different equations have been assessed. Further, the experimental data of Blair on pressure andtemperature dependence and of Singh on formulation dependence of burning rate have also been anal ysed.The results show that burning rate is directly proportional to (T, )1/4, in agreement with the prediction basedon burning rate expression of Rastogi et al. (T, is the initial temperature in kelvin).

Understanding of the mechanism of catalysis andinhibition of burning rate of composite solid propel-lants is important from the view point of solid-propel-lant rocket technology'<. A knowledge of pressuredependence of burning rate in the presence ofcatalyst/inhibitor is also equally important. Pheno-menon is know to be complex and technologists havemainly relied on empirical knowledge alone. Al-though several empirical relations between burningrate and pressure have been suggested+', only a fewhave theoretical justification based on specific mod-els. The recently suggested equation due to Rastogi etal", is based on a tubular reactor model which in-vokes the pressure dependence of some of the com-ponents of the combustion reactions. The model wasclarified- subsequently in response to the criticism ofNelson et al.6 The predictions of the model werefound to be in agreement with experimental data. foruncatalyzed propellants with erosive and non-ero-sive burning? based on the data of King" and Girdharet al". The present investigation was undertaken totest whether the above model holds good forcatalyzed/inhibited combustion of composite solidpropellants and to interpret the results in terms of themodel. Burning rate data at different initial tempera-tures 10 and for different percentages of solids load-ing" have also been analysed.

Materials and MethodsPropellant formulations were made by casting

4S2

technique using 99% pure ammonium perchlorate(AP)(WIMCO, Ambernath), Hydroxy terminatedpolybutadiene (HTPB) having viscosity of SOOOcp(2S°C) (ARCO; R-4SM, USA) and 99% pure alumi-nium (Al) (particle size 37 fl; Metal Powder Co.,Madurai, India). Bimodal AP (SO% coarse; 200 fl)and SO%fine(1O to 12 ,u)was used. Emolein(diethyl-2-ethylhexylazelate) was used as a plasticizer. Ballis-tic modifiers (CaCO" SrCO" Fe20, and copper ox-ide, all BDH) of particle size 1.5 fl were used.

Propellant ingredients were mixed in a sigma BladeIncorporator for 2 hr and grain was cast in aluminiumcasting fixture (110 mm int. diam). Cast propellantswere cured at 7SoC for 8 days.

Burning rates at various pressures were deter-mined employing Strand burner method (Crawfordbomb). Propellants of 6 mm diameter were used forburning rate determination. Propellants (i)and (ii)hadthe compositions: (i)AP, 68%; HTPB, 20%; Al, 10%;and modifiers, 2%;and(ii)AP, 69.4%; HTPB, 20.4%;AI,1O.2%.

Results and DiscussionIt is evident from the data in Table 1 that at all pres-

sures the burning rate (r) for composite propellants isthe highest for propellant containing copper oxide asmodifier while it is the lowest for SrCO,-containingpropellant. Burning rate increases with increase inpressure in all the cases. The magnitude of effect ofpressure on r is smaller in the case of propellants-

\

RASTOGI et al.: PRESSURE DEPENDENCE OF BURNING RATE OF SOLID PROPELLANTS

Table I -- Burning rates of composite solid propellants(HTPB + AP+ AI + modifiers)atdifferent pressures.

Modifier Burning rate (mm/s) at pressures (kg/crn-)

:15 5() 7() 9() 105

Nil 4.11 5.4 5.0 t» 7.0CaCO, 4.0 4.:1 4.0 5.1 5.3SrCO, :1.7 4.1 -u 4.5 4.6Fe,O, 6.7 7.0 X.X 9.4 10.4Copper 11.5 D.X 14.X 16.6oxide

containing the inhibitors such as SrCO, and CaCO\and higher in the case of propellants containing catal-ysts like copper oxide and Fe10J- The experimentaldata have been analysed by least square method usingEqs(1-5)_

(t)2 _ a" "- ---bP p

. - - (1)

In r = a *+ b * In P

P/r= al + b, P

P/t=a+bp21\

In r= m, P+ c,

_.. (2)

... (3)

... (4)

... (5)

The constants ofEqs ( 1) and are given by Eqs (6) and(9)

2 Ag,(Tf'-TJk2f, (T)a" -1I~R[C,(T, -TO)-Qh]x (Tj'-T)n (CfjCk)l

b"> 2Ag,(T,-TJk2~ V* f2(T)1I~,R2[C,(T, -TO)-Qh]x (Tj' -~) In (CfjCk)l

_ ll,RT/Mg][C,(T, -To)-QJ' C

a= 12[A~(TI- TJ] [A cxp (- E/RT~)]

... (6)

... (7)

... (R)

1/31 [RT./M,J5/6[c (T -"[ ) - Q JII2b=fl " g g s s 0 s

[Ag(TF-T,lJ'/2[PDgf2It may be noted that Eqs( 1)4 and (4 )12 have theoreticalbasis (for significance of the terms, reference may bemade to original papers'"!"). The values of the con-stants of Eqs (1) to (5) alongwith correlation coeffi-cients are given in Table 2. Figure 1 provides the gra-phical test of Eq. (1).

Table 2 shows that all theEqs( 1)to(5)fitthedataal-most equally well, since correlation coefficients areclose to unity. However, since Eq. (1)due to Rastogi etal.' and Eq. (4 )due to Summerfield et al.'? have sometheoretical basis, the results have been examined fur-

... (9)

110

100

90

.. 80~s: 70

Eu

N

'", 60"N'~ 50..N

EE 40-

N~IQ.30

20

10

•

•o

o 4 8 12 16 20 24 28 32p-' (kll-'cm2) .103

Fig. 1-Dependence of burning rate of composite propellants onpressure 10 - Nil: .f', -:-CaCO,: x -SrCO,: 0 - Fe20,: and

® +copper oxide]

Table 2 - Correlation coefficients and constants of Eqs ( I )10 (5)

Modifiers Correlation coefficients h" a" (/1 a C a" h" b, b mlI(rum-s , (kgem ' (kgcm

, (rnrn-s , (mm IS) (kgl.' (kg " 'crn ')Eq. I Eq. ~ Eq.:I Eq. 4 Eq. 5 kg 'cm") mm IS) mm IS) kg-Icm') cm-21.1

mrn t ls)

Nil O.9X O.9'i 0.95 0.96 0.97 0.002 :I (U)2 4.XO I.X9 1.:12 0.72 0.4:1 0.09 0.55 0.007CaCO, 0.99 0.99 I .00 I .00 I .00 0.00 :10 0.45 :I.6X - 1.21 1.25 055 0.26 0.16 0.93 0.004SrCO, 1.00 O'}9 I .00 1.00 0.90 (U)02X 0.04 2.70 - 3.23 1.24 0.49 0.19 0.19 1.14 0.003Fe,O, o.'n 0.97 O.9X 0.99 O.9X O'()O44 0.:19 :I.2X 1.15 1.66 1.36 0.41 0.07 0.40 0.007Copper I .00 (l.9X 0.99 0.99 0.99 0.0210 1.:1:1 1.47 - 0.02 2.26 4.53 0.31 0.05 0.29 0.005oxide

453

INDIAN J. CHEM., SEe. A, JUNE 1989

ther in terms of Eqs (1)and (4 ), in order to discrimin-ate between the two equations. Perusal of data inTable 2 further shows that; (i) values of a" are higherfor propellant (HTPB + AP+ AI) + catalyst than thatfor propellant without the catalyst; (ii) values of a" forpropellant + inhibitor are lower than that for propel-lant without the inhibitor; and (iii) values of b" arehigher for propellant + catalyst as compared to thatfor propellant + inhibitor. It is also clear from Table 2that for the additives CaCO" SrCO, and copper ox-ide ais negative and there is no orderin the values of a.All the terms on the right hand sideofEqs (8) and (9),except [C, (T, - To) - QJI:~ and [Ag(Tr- TJ]I/2, are al-ways positive. Since, T, is always greater than Ts' theterm [Ag(Tr- TJ]I'2 will always be positive. Followingargument shows that [C,(T, - To) - QJIi2 would alsobe positive. It is clear that, if [C,(T, - To))> Q" both aand bwould be positive. However, if] C,(T, - To)]< Qs>both a and b would become imaginary since[C,(T, - To) - QJ would be negative. Hence, accord-ing to Eq. (4), both a and b should always be positive.Blair!" has also mentioned that if the empirical valuesof a and b are to retain their physical meaning both aand b must be positive. On the other hand, in the caseof Eq. (1) it is clear that both the constants a" and b"can be negative when [C,(T, -To)]<Q, [see Eqs (6)and (7)] or ~ V* is negative. From the above argu-ments, it follows that Eq. (4) does not fit the data foradditives since a is negative contrary to the require-ment of the theory. On the other hand, there is no suchinconsistency in the case of Eq. (1 ).

Eq. (7) suggests that b" is related to ~ V*. Now bydefinition, ~ V*=volume of activated complex-vo-lume of reactants. Hence, ~ V*will have a larger valuewhen a loose activated complex is formed while it willhave a smaller value when tight complex is formed.The results suggest that volume of activation in thecase of propellants containing catalysts is more dueto formation of a loose activated complex as compar-ed to the case of propellants without a catalyst or withan inhibitor. On the other hand, a tight activated com-plex is probably formed in the case of inhibitors on ac-count of which ~ V*is small in comparison to catalyst.

Broadly speaking, the most probable chemicalreactions which take place during the combustion ofcomposite solid propellant arc: (a) AP decomposi-tion; (b) polymer degradation;(c) HCIO.j decomposi-tion.and (d) reaction ofHCIO.j or HCIO.jdecomposi-tion products with polymer and polymer degradationproducts. The processes (a) to (d) have been studiedseparately by various workers 13 - Ih and their resultssuggest that the combustion process of AP decompo-sition is the rate-determining. Therefore, ~ V*may besupposed to he related to AP decomposition. It is wellestablished that AP decomposition takes place ac-

cording to the sequence of reactions shown in Scheme117

NH4CI04 ~ NH3(a) + HCI04 (a) -> Products1~ 1~

Sublimate +- NH, (g) + HCI04 (g) -> Products

The primary step in AP decomposition is protontransfer process. However, it seerns difficult to correl-ate ~ V* and b, particularly in view of the fact that in-hibiting action also involves a change in the path ofdecomposition IXof complex since water and carbondioxide are also released in the reaction between APand inhibitor.

The values of a * are related to the function f I(T),which in turn is essentially a function of energy of acti-vation which is smaller in the case of catalysts andlarger in the case of inhibitors. Since, fl (T) is a func-tion of e " E/RT, it is obvious that fl (T) would be largerfor propellants containing catalysts and 'smaller forthose containing inhibitors. Hence, the magnitude ofa" would be larger for propellants containing catal-ysts as compared to propellants without the catalysts.Similarly a" would be smallerfor propellants contain-ing inhibitors in comparison to those without it. Thisis in accord with experimental data.

The effect of initial temperature (TI) on the burningrate (r) of composite solid propellant has been experi-mentally studied by Blair!". The model of Rastogi etal: suggests that both a" and b" are directly propor-tional to k2 [(see Eqs (6) and (7)]. Since, ~ is the fre-quency factor and known to be directly proportionalto square root of temperature Ill,we can write.

"- CTI 2(/ - I i ... (10)

. .. (11)

where CI and C2are constants. Inserting the values ofa" and b" from Eqs ( I ()) and (11) in to Eq. (1), we get

(!)2 _ C I 2 I 2- T· -CT·P P I _ I... (12)

At constant pressure Eq. (12) can be rewritten as

( . )2 = C r'. 2 - C TI 2 ( )r .' I .j I ••• 13

where C, and C, are another set of constants. There-fore, according to Rastogi model a" and b" should bedirectly proportional to Tilnand (r)2 should be direct-ly proportional to T! 2 at constant pressure.

Accordingly, the data of Blair was analysed usingEq.( 1).The values of a", b", a" / b" and correlation co-efficients are recorded in Table 3 and the plots of a"and b" against T! 2 are given in Figs 2 and 3, respect-ively. The values of r for different initial temperaturesat the same fixed pressure have been estimated from

RASTOGI et al: PRESSURE DEPENDENCE OF BURNING RATE OF SOLID PROPELLANTS

Table 3-Correlation coefficients and constants' of Eq. I

Initialtemperature

(0C)

89.4-94.4 1.32 x 10-4 -3.83xlO-H

35.5-44.4 1.18 x 10-4 1.81 x 10-"

1.1-3.3 1.09 x 10-4 3.28 x 10-"

-74.4--65 0.90xlO-4 4.5IxlO-H

"For evaluation of constants the data have been taken from ref. 10.

a"(in2s - 2Psia -')

b"(in2s-2Psia-2)

a"lh"(Psia)

Correlationcoefficient

- 3.46 X 11)3

65.27 X 103

3.33 x 10'

2.00 x 10'

0.99~

0.999

0.99<)

0.<)97

Table 4- Correlation coefficients and constants' of Eqs ( I ), (3) and (4)

Loading Eq.(I) Eq.(4) Eq. (3)%

a" b" a"l b" CorreI- a b alb CorreI- a, b, a,/ll, Correl-(rnm-s - 2 (mrn-crn" (kgcm " ") ation (kgcm - 2 (mm t+s (kg2!1 ation (kgcm - , (mm "s) (kgcm 2) arionkg- 'em") s - 2kg - 2) coeffi- mrn t Is) kg';' cm -4'3) coeffi- mm 'x) coeffi-

cient cm -213) cient cient

80 0.60 1.53 x 10-1 0.39 0.998 1.55 0.61 2.53 0.997 4.75 0.10 47.3~ 0993

82 0.72 1.68 x 10-) 0.43 0.999 1.50 054 2.75 0.997 4.35 0.09 4~.69 0.<)<)3

84 0.94 2.29xlO-1 0.41 0.999 1.21 0.49 2.47 099~ 3.77 O.O~ 46.90 0.995

86 1.34 4.22 x 10-' 0.32 0.998 0.73 0.44 1.67 0.999 304 0.07 42.00 0.<)96

88 1.92 7.08 x 10-) 0.27 0.998 0.35 0.40 0):;9 0.99<) 2.42 0.06 37.21 0.<)97

"Fos evaluation of constants the data has been taken from ref. II.

19 /18

17

~ 16~0<

•.. 15

14

13

12 ~0.6 0.8 10 12 140' (in2 s~c-2P510-') x 104

Fig. 2- Dependence of a" on initial temperature.

the plots of (UP)2 versus liP drawn for different in-itial temperature. The plots of (j-)2 versus Tin at con-stant pressures are shown in Fig. 4. The linear plotsobtained in Figs 2 and 4 show that a" is directly pro-portional to TI/2 and at constant pressure (t)" is direct-ly proportional to TI!2 as predicted by the model pro-posed by Rastogi et a1.4• The only weak point is thatthe linear dependence of b" on TI12 is not clearly esta-blished (see Fig. 3), although it can not be taken as suf-

20

19

18

- 17~x:~•.. 16

lS

14

13

L---L__-L__-L__-L__-L__-L__-L__-L__~-4 -3 -2 -1 0 1 2 4

b" (in2 50(-2 P.io-2) X 108

Fig. 3- Dependence of b" on initial temperature.

ficient ground for rejection of the model. From Eqs (())and (7)it follows that

a"/b"=-~- f,(T)~ V* f2(T)

It should be noted that a" / b" is not independent of in-itial temperature since both T, and T, would dependon initial temperature and the functional dependenceof f, (T) on T, and f2(T) on T, is not the same.

... (14)

INDIAN J. CHEM., SEe. A. JUNE 1989

1400

1200

-# 1000~)(_ 800 Q)..'uco•.•••600.5

•••..400

.:

o~~;;;;;~.12 13 14 15 16 17 18 19 20

(Ti,k)1I2

Fig. 4 - Dependence of burning rate on initial temperature [0- Atpressure 1000 Psia; x - at 500 Psia; f:;- at 250 Psia; @ - at 125

Psia; 13 -at 50 Psia]

4.8

2.0

4.5

4.0

'0 1.2

uco.•

'EE

';'E 0.8v01x

o

0.4

80 8482ParCQntogQ Solids Loading

Fig. 5-Dependence of a", a and a, on percentage solid loading[-0-0- -a",--f:;--f:;- -a;-G--D--- -a,l

The burning rate data II for aluminized AP/HTPBhaving different percentages of solid loading at differ-ent pressure and ambient temperature was smooth-ened and then analysed in terms ofEqs (1 ),(3) and (4).The correlation coefficients alongwith the constantsof these equations recorded in Table 4, show that allthe equations fit the data equally well. The values ofa", a, al; b", b, b.; a"/ b", aib and alibi are plotted

456

11

~"i 0.7

E

Sf'Eu

;:~O.5 •

a

1.1

0.11

.0.10

0.09

007

0.06

88

Fig. 6-Dependence of b", band b, on percentage solid loading[-0-0- - b";--f:;--f:;- -b;--D--':D-- -b,l

v.•OIl

'EE

3.5";,,Eu

'"s: ~"4.0 2.0

3.0:0IE

• u

~3.5 ~ 1.5co.>t.'0

2.5

5.0

4.5 2.5

3.0 1.0

0.9

so

0.3

.0..••

40 <;

2.5 0.5~80;;-----:8:!:.2-~--:l84:----8,L6-----8L8-1

PQrcentoge Solids Loading

0.1

0~----L---~--~---~~0580 82 84 86

Percentage solids Loading

Fig. 7- Dependence of a"l b", u/b and a,l b, on percentage solidloadingl-O-O- -a"lb";--f:;--f:;-- -alb,--D-

-D---ul/h,1

~..•.o

_---0---..0''''' ....''"''

-,"- -, -,

"\"\

'~,,,"'

against solids loading percentages in Figs 5-7. Theda-ta appear to fit smoothly, However, the data could nothe analysed further in view of the difficulty in estimat-ing the various parameters in Eqs (1) and (4).

RASTOGI et al.: PRESSURE DEPENDENCE OF BURNING RATE OF SOUD PROPELLANTS

Acknowledgement

The authors thank the Ministry of Defence for sup-porting the investigation.

Abbreviations

T,i,

R~V*

burning ratepressureaverage thermal conductivity of flame gas at the surfacetlame temperature at the end of the chemical reactionzonesurface temperature of the burning propellant (average)propellant densitygas constantvolume of activation i.e. difference in the volume of acti-vated complex and the reactants.T~xp (- E/RTF)-T, exp (- E/RT,)- exp ( - E/RT) EIRT dTIn T~xp (- E/RTF)-ln T, exp (- E/RT,)specific heat of solid (average of fuel and oxidizer)equilibrium concentration of fuel species f at the end ofchemical reaction zoneconcentration of species f near the propellant surfacenet heat release ( + ve) for gasification of the propellantambient temperaturefrequency factorammonium perchlorate

Hydroxy terminated polybutediene

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1965.2 Barrere M, Jaumotte A, Veabeka B D F & Vandenkerchkhove

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(1979) 223.6 Nelson CW,AdamsGeorgeF & WardJ Richard,AIAAJour-

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205.8 KingM K,JSpace Craft and Rockets, 15(1978) 139.9 Girdhar H L & Arora A J, Combust Flame, 34 (1979) 303.

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K P, Prog Aeronaut Rocket, I (1960) 141.13 Solymosi F, Structure and stability of salts of halogen oxyacids

in the solid phase (John Wiley) 1977.14 Levy J B, J phys Chem, 66 (1962) 1092.15 Rabinvitch B, Tenth Symposium (International) on Combus-

tion, The Combustion Institute, Pittsburgh, 1965, pp. 1395-1404.

16 Pearson G S & Sutton D, AIAA Journal, 5 (1967) 344.17 Jacobs P W M & Russell-Jones A, AIAA Journal, 5 (1967)

829.18 Schumacher J C, Perchlorates, their properties, manufacture

and uses, (Rheinhold, New York) 1960, p. 39.19 Berry R S, Rice S A & John Ross, Physical chemistry, (John

Wiley, New York) 1980, 1146.

457