The relationship between plateau burning behavior and ammonium perchlorate particle size in HTPB-AP composite propellants

235

COMBUSTION A N D F L A M E 67:235-247 (1987)

The Relationship between Plateau Burning Behavior and Ammonium Perchlorate Particle Size in H T P B - A P Composite Propellants C. W. F O N G and R. F. S M I T H Weapons Systems Research Laboratory, Defence Research Centre Salisbury, Adelaide, South Australia

The burning rates of series of bi- and trimodal AP-HTPB propellants have been incorporated into an empirical statistical model which describes a hypothetical pentamodal polydisperse AP pseudopropellant. This pseudopropellant is the linear summation of five unimodal polydisperse AP pseudopropellants. The five AP particle size distributions cover the range from 400 to 20 #m weight median diameter). The experimental propellants have been further subdivided into plateau burning and nonplateau burning propellants. The statistical model has been used to generate a plateau burning and a nonplateau burning pentamodal AP pseudopropellant. Plateau burning behavior in this propellant system (when compared to nonplateau burning behavior) appears to result from an enhanced burning rate at low pressures and a reduced burning rate at high pressures for the unimoda120 #m AP pseudopropellant. It is speculated that such behavior is consistent with the presence of a binder melt on the burning surface. The larger AP unimodal pseudopropellants also show low burning rates and plateau burning behavior. Such behavior appears to be the result of variations in the importance of the AP monopropellant flame as a function of pressure and AP particle size. A melt layer on the AP particle surface during combustion may be the cause of the plateau burning behavior in the larger AP unimodal pseudopropellants. The temperature sensitivity of the unimodal pseudopropellants increases as a function of the AP particle size. Plateau burning behavior is maintained over the temperature range from 0* to 55"C.

1. I N T R O D U C T I O N The modeling of composite propellant burn rate has been an intensive area of activity in recent times [1]. Much of this work has been aimed at developing predictive mathematical models of the burning rate of ammonium perchlorate (AP) oxidizer-polymeric fuel binder composite propellants. The Beckstead-Derr-Price (BDP) model [2] was the most successful of the early models, and introduced the concept of the multiple flame structure for an AP particle burning in a binder. The BDP model has been continually evolving [1, 3], with the recognition of the importance of the binder phase, as well as the AP particle size, in controlling combustion. The BDP model has also been incorporated into a more comprehensive statistical formalism to allow for polydisperse AP particle size distributions. The method is referred Copyright © 1987 by C. W. Fong and R. F. Smith Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017

to as the petite ensemble model (PEM) in its final form [4, 5]. A different approach has been taken by Miller and coworkers [6, 7], who have developed a statistical method to correlate AP particle size distribution effects with experimentally determined propellant burning rates. Their objective has been to determine an effective particle size parameter which can be used to predict accurately the burning rate of a proposed propellant formulation. The approach is quite different from the true modeling efforts reviewed by Cohen [1], and is more aptly described an empirical statistical method. The approach taken in this paper also uses an empirical statistical method to analyze the effect of different AP particle size distributions on the

236 burning rates of a family of hydroxy-terminated polybutadiene (HTPB)-AP propellants. The principal objective is to identify these factors which control the magnitude of the propellant burning rate pressure exponent. This family of metal catalyzed HTPB/AP propellants includes certain formulations which exhibit plateau burning characteristics; i.e., in a certain pressure range, the burning rate does not increase as the pressure rises (the burning rate pressure exponent, n, is zero). Since plateau burning is a much sought after characteristic for certain rocket applications, it is important to understand those factors which are responsible for such behavior, and differentiate them from those factors which result in nonplateau burning behavior (n > 0). An empirical model which can predict the behavior of other members of this family of propellants will also be developed. 2. EXPERIMENTAL The propellants used in this study were produced in 500 g batches using a vertical anchor blade mixer equipped with breaker bars. After curing, the propellant was machined into 5 mm square strands 170 mm long. The strands were coated with an inhibitor and burned in a nitrogen pressurized bomb at pressures from 2 to 14 MPa. Fusion wires embedded in the propellant and connected to a timing circuit enabled the linear burning rate of the propellant to be determined. Previous experience with the mixing and strand burning procedure on similar propellants has shown that the burn rates from the same propellant mix are reproducible to between 1 and 2 %, and for different batches of the same formulation, between 2 and 3 %. The formulation of the propellant was varied by using different lots of AP in differing ratios. The five lots of AP used were identified by their nominal weight median diamater; they were 400, 200, 90, 55 and 20/xm. Of the five batches of AP, four were used as received from the manufacturer, Kerr McGee. The 20 /~m material was produced locally by grinding the 400/~m material in a rotary pin-disk (KEK) mill. Each propellant contained the same HTPB binder cured with a diisocyanate. The binder

C. W. FONG and R. F. SMITH content was 17% with 0.5% of a metal catalyst added as a ballistic modifier. The oxidant size distribution was varied by using the AP lots in bimodal or trimodal blends. The bimodal blends used two coarse/fine ratios, 80/20 and 70/30. There were two series of trimodal blends, one using the 400, 90 and 20 #m material and the other 200, 55, and 20 #m. All permutations of 60/30/10 were used in both series. A low angle light scattering technique, the Malvern Instruments 3000 Particle Size Analyzer, was used to determine the particle size distribution of each oxidant batch. The results are shown in Fig. 5. The weight median diameter is defined as the diameter which just exceeds 50% of the particles by weight. Comparison of the predicted burning rates from Eq. (1), when applied to experimental burning rates of the propellants represented by Eqs. (2) and (3), indicate that the accuracy of the predicted burning rates from Eq. (1) is 5-7% [as determined by comparing the residuals between the calculated and predicted values from Eq. (1)]. 3. RESULTS Details of the oxidant composition for all formulations are shown in Table 1. Burning rates are shown in Figs. 1-4. The burning rate data in Fig. 1-4 have been analyzed in terms of the following general model: ~p= a400AP400+ a200AP200+ a90APgo + a55AP55 + aEoAP2o,

(1)

where AP400, AP200, AP90, AP55, and AP20 represent the experimental AP particle size distributions characterized by their 400, 200, 90, 55 and 20/~m weight median diameters (Fig. 5). The constants a4oo, a200, a9o, a55, and a20 represent the relative contributions of the various AP distributions to the total burning rate of the pentamodal propellant. The burning rate at a particular pressure, p, is represented by ?p. Individual propellant burning rates from the bi- and trimodal AP formulations (Table 1) were fitted to Eq. (1) by a least squares regression model. Thus Eq. (1) is the best fit equation for the 22 bi- and trimodal AP propellant

PLATEAU

BURNING

OF COMPOSITE

PROPELLANTS

237

TABLE 1 Propellant Formulations Composition of Oxidant (#m) Cast No.

400

4002 4003 4014 4015 4024 4025 4041 4048 4049 4054 4062 4068 4083 4092 4100 4105 4106 4108 4184 4185 4190 4191

200

90

55

80 30 80 30 30 80 30

20

Plateau Burning"

20 70 20 70 70

PB PB

20 70 70

30 60 30 30 10

PB

30 60 10 30 60 60 30 10 10

10 10 60 60 10 30 60 30 60 30 20

30 10 10 60 30

10 80

60 80

PB PB

PB PB

PB PB PB

20

60

10 30

30 10

60

° A plateau burning formulation is identified by PB.

26 24 22 20

r1404g 4-4190 O 4O54 A 4062

X4108

18

\ E

18 14 12

|

I0

m

IS 8 42 0

I

I

4

I

I

8

I

!

8

i

I

10

I

I

12

PRE3SUR~ (UPQ)

Fig. 1. Burning rates at 20°C for trimodal AP 400/90/20tzm) propellants.

14

238

C. W. F O N G and R. F. SMITH

28 24

1240e3 +4O92

22 20 18 18 14 12 z I:

I0

O

8

I

2

!

I

4

I

I

6

!

I

8

I

!

10

!

14

12

PmZSSUmZ (MPa)

Fig. 2. Burning rates at 200C for trimodal AP (200/55/20 #m) propellants. 26 124184 ÷4025 O4002 &4185 X4014

24 22 20 IB E

E

16 n

14 12

Z :) m

10

I

2

I

4

I

I

6

I

I

8

A aE

a;

i

7

.L

J-

|

I

10

B !

JL

|

I

12

PRESSURE (UPo) F i g . 3. B u r n i n g rates at 2 0 " C f o r b i m o d a l A P [ c o a r s e ( 8 0 ) / f i n e ( 2 0 ) ] p r o p e l l a n t s .

I

14

239

PLATEAU BURNING OF COMPOSITE PROPELLANTS

24 | 22 '-~

]

O4015 +4003 O 4024

A4041

18 E

16

|z

10

i

2

4

6

8

10

12

14

PRESSURE (MPo)

Fig. 4. Burning rates at 20"C for bimodal AP [coarse(30)/fine(70)] propellants.

"

Ira70-

÷ 2~ o 9op

f

AS.~v x 20p

805o 4o

2O

" Z 10 0

•

• 10

' ~ 100

LOG SiZE (mlmm.)

Fig. 5. Individual experimental AP particle size distributions.

1000

C. W. FONG and R. F. SMITH

240 formulations, which can formally be represented by #p' = axAPx + ayAPy

(2)

and i'p" = axAPx + ayAPy + azAPz,

(3)

where x, y, and z may be any of the five AP particle size distributions (Table 1). The values of x, y, and Z in Eqs. (2) and (3) were chosen to cover a wide range of compositional space for Eq. (1). In order to confirm that the general model represented by Eq. (1) is statistically a good fit of the total data set, an examination of residuals [8] was undertaken. The residuals were plotted against the predicted values for t~p, resulting in horizonal scatter bands of comparable width for all formulations. The residual analysis indicated that Eq. (1) was a good fit of the experimental data. There was no evidence of the need to incorporate other terms. The goodness of fit for Eq. (2) or (3) when separately compared with Eq. (1) also indicated that the general model was a valid and precise representation of the total data set. As the overall burning rate of composite propellants is predominantly controlled by the AP particle size [1-7], Eq. (1) can then be taken to represent the burning rate behavior of a hypothetical pentamodal polydisperse [4, 10] AP pseudopropellant. The burning rate at a particular pressure is the weighted summation of a number of independent AP particle size burning rates. The burning rate of an individual AP particle size distribution when incorporated into a propellant can be considered as a subfamily of burning rates. That subfamily of burning rates is the same (when appropriately weighted), whether incorporated into a bi- or trimodal propellant (as determined experimentally), or when incorporated into the pentamodal AP pseudopropellant [as represented by Eq. (1)]. Equation (1) assumes there are no interactions between different particle size distributions during combustion. The individual particle size distributions (as represented by their weight median diameters) utilized in this study are considered to be independent variables of ~p. The

physical description of the model, in terms of the BDP multiple AP flame [2], implies that there are no interactions between adjacent multiple flames. Each AP flame has its own fuel binder region, whose pyrolysis products contribute to the primary flame. The burning rates, t:p, from 2 to 14 MPa at 20°C, of the general pseudopropellant family, calculated from Eq. (1) are shown in Fig. 6. The figure displays the theoretical burning rates of five unimodal AP pseudopropellants, each containing only the 20, 55, 90, 200 or 400/~m AP particle size distribution. The effect of temperature t~p of the pentamodal AP pseudopropellant has also been examined at 0 ° and 55"C, to complement the 20* data. Figure 7 illustrates the burning rates at 0", 20", and 55°C over the pressure range 6-10 MPa. From an inspection of Figs. 1-4, it is apparent that certain propellant formulations exhibit plateau burning (PB) characteristics. Plateau burning behavior is exhibited when a region of the ?p versus pressure curve shows a zero slope for the di'p/dp relationship. The distinction between PB and nonplateau burning (NPB) propellants lies in the ratio of coarse (greater than 55 #m) to fine (less than 55 #m) AP particle sizes. PB propellants generally have a 60 : 40 (or greater) coarse to fine AP particle size ratio. In order to gain a clearer understanding of the mechanism of plateau burning behavior in these propellants, we have divided the 22 propellants into PB propellants and NPB propellants. The possession of a substantial PB region, regardless of where that plateau exists, is the sole criterion for classification as a PB propellant. Table 1 lists the two types of propellants. The distinction between the 10 PB and 12 NPB propellants is visually obvious from Figs. 1--4. Equation (1) has again been used to produce a PB pentamodal AP pseudopropellant and a NPB pentamodal AP pseudopropellant from the 10 PB and 12 NPB experimental propellants (Table 2). Figure 8 illustrates the burning rates from 2 to 14 MPa at 200C for these two pseudopropellants. Miller et al [5-7] have published burning rates over a wide pressure range for a series of HTPBAP (12.6 : 87.4) propellants. Multimodal blends

241

PLATEAU BURNING OF COMPOSITE PROPELLANTS

30

x 2o~

28

A~

o 9011 + 200~

26 24 22 20

£

£

18 18 14

i

12

st

I08-

f 6

_

~

-

i

i

_

-

4-J ;tO

i

i

2

0

i

r

4

i

i

6

8

i

i

1O

i

i

12

i

i

14

le

Fig. 6. Burning rates at 20"C for pentamodal AP pseudopropellant.

30 28-

X 20p

26242220-

£

181614-

z E

m

12108 jb,,~'-

~

e' 4-

- •

-

-

201:;

20

i

0

!

2

i

i

4

i

i

6

i

i

8

i

!

10

i

!

12

i

i

14

PRESSURE (MPa)

Fig. 7. Burning rates at O°C, 20°C, and 55°C for pentamodal AP pseudopropellant.

i 16

242

C. W. FONG and R. F. SMITH

30 211

---PB

222426 --NPB

"x~

'°

•

~

- - - X ' ~ ~ ._)x 20p

Y-

, -- - -- "& 5.~

zp

-

12 10 8

90p

.

4 2 0

I

0

!

2

I

I

4

I

I

I

I

6 8 PRESSURE(MPo)

I

I

I

10

I

12

I

I

I

14

16

Fig. 8. Burning rates at 20°C for plateau burning (PB) and nonplateau burning (NPB) pentamodal A P pseudopropellants.

of AP (ranging from 400 to 0.7/x weight median diameter) were incorporated into the formulations. Miller's propellants are defined to be NPB propellants by our criteria, and have been similarly analyzed by Eq. (1). Nine bi- and trimodal AP propellants incorporating the 400, 200, 90, 50 and 20 #m weight median diameter AP particle size distributions were chosen for analysis, since these distributions are very close to the distributions used in our study. Figure 9 illustrates the burning rates from 0.7 to 20.7 MPa at 20"C for Miller's NPB pentamodal AP pseudopropellant. The data selected from Miller's work are not as extensive as our NPB propellant data base, nor do the AP particle size distributions cover as wide a range of compositional space as do our own formulations. Miller's propellants may also have slightly different AP particle size distributions. Consequently the data in Fig. 9 are not quite as accurate or exactly comparable to our data shown in Fig. 8. It should also be noted that Miller's propellants do not contain a metallic burning rate catalyst, and the total AP content is higher (87.4% compared to 82.5% in our propellants). However, it can be

seen that the same qualitative trends are apparent in both Figs. 8 and 9. 4. D I S C U S S I O N

Effect of AP Particle Size on Pseudopropellant Burning Rate The use of Eq. (1) as a model for the burning rate of the pentamodal polydisperse AP pseudopropellant allows the dissection of the experimental data into the component burning rates for the individual unimodal AP pseudopropellants. Figure 6 indicates that the 20 and 55 #m unimodal AP pseudopropellants show pressure dependent burning rates, with the former pseudopropellant showing the higher pressure exponent at all pressures. It is notable however, that the 90, 200 and 400 #m AP pseudopropellants show pronounced plateau burning regions above about 7 MPa, with the 200 and 400/~m distributions having virtually identical burning rates at all pressures. This unexpected outcome may well be a statistical consequence of the mixing of two classes of propellants, i.e., two

243

PLATEAU BURNING OF COMPOSITE PROPELLANTS

i

[] 400~

j

A 5~

E

| i

'°it, I

0

I

2

I

I

I

I

4

I

8

I

8

P~SU~

I

I

10

I

I

12

!

14

(MPo)

Fig.9. Burningratesat 200Cfor literature[6, 7] HTPB-AP(12.6:87.4)nonplateauburning pentamodalAPpseudopropellants. fundamentally different populations of PB and NPB propellants. However, it is apparent from Fig. 8, when the separate PB and NPB propellants have been analyzed, that apart from some minor changes, the overall trends are similar to those shown in Fig. 6. A further complicating factor in our study is the presence of a metallic burning rate catalyst. We have previously produced evidence [9] to show that various transition metal catalysts in this propellant system are active in the condensed phase, especially at low pressures, where chemical kinetics can affect pressure exponents. However, an examination of our analysis of Miller's uncatalyzed HTPB-AP propellants in Fig. 9 reveals qualitatively similar trends to those seen in Figs. 6 or 8. While Miller's propellants contain 87.4% AP compared to 82.5% AP in our propellants, evidence from the literature [1, 5, 6, 7, 10] on unimodal and multimodal propellants does not suggest that small changes to the overall AP concentration will drastically alter n. If it is accepted that the results shown in Figs. 6, 8, and 9 are real, then an unexpected result is the plateau burning behavior of the larger AP pseudo-

propellants. It has been previously demonstrated that current models of composite propellant burning, such as the BDP or PEM models, cannot predict the burning rate of large AP particle sizes in unimodal propellants [1-5]. Using the PEM model, Renie [11] has calculated the theoretical proportional contributions of the primary flame (PF), final diffusion flame (FF), and oxidizer monopropellant flame (AP) for a series of unimodal HTPB-AP (12 : 88) pseudopropellants as a function of AP particle size at 6.9 MPa and 21 *C. Renie shows that the PF and FF rapidly diminish in importance for particle sizes greater than 100 /zm, whereas the AP flame rapidly increases in magnitude. In terms of the BDP model [2], BE (the fraction of the oxidizing reactants that reacts in the PF) is much less than one for large AP particle sizes. King [12] has incorporated a pressure dependent AP heat release process into his model for the burning of large AP particles to obtain agreement with experimental results. Our data for the larger unimodal AP pseudopropellant burning rates suggest that the situation for multimodal polydisperse propellants is far more complicated than for unimodal propellants, since

244 the latter do not show plateau burning behavior for large AP particle sizes [1, 5]. Binder effects are also expected to be less important for larger AP particle sizes [1-4]. A plausible explanation for our results may lie with the competition between the PF, FF, and the opposing effect of the AP flame. In multimodal polydisperse AP propellants, the various "cross-over" points (when the AP flame will dominate the PF and the FF) will be some function of the AP particle size distribution [5], and the pressure response of this variation could also vary in an inverse but corresponding fashion. A physical mechanism which could be invoked as an explanation is the presence of an AP melt layer [13, 14] which would be more dominant on larger AP particle sizes. Thus it is conceivable that a pressure range may exist where the burning rates of large AP particle size propellants will not vary with pressure. In BDP terminology [2], ~F will be pressure dependent, being smaller at low pressures for larger particle sizes [1], and vice versa. Thus in a polydisperse AP propellant, a distribution of pressure dependent/~F shifts needs to be considered. The object of dividing our 22 experimental propellants into two classes of propellants, PB and NPB propellants, was to elucidate those factors responsible for PB behavior. A comparison of the PB and NPB pseudopropellants in Fig. 8 reveals several major features: a. The ~p value of the unimodal 20 #m AP PB pseudopropellant is greater than that for the NPB pseudopropellant at low pressures (2--9 MPa), but the situation is reversed at high pressures (9-14 MPa). b. The Pp values of the unimodal 55 /zm AP PB and NPB pseudopropellants are identical at all pressures. c. The Pp values of the unimodal 90 /xm AP PB and NPB pseudopropellants are fairly similar at all pressures. d. The p values of the unimodal 200 and 400 #m AP PB pseudopropellants are identical at all pressures. e. The Pp value of the 400 #m AP NPB pseudopropellant is statistically slightly greater than the Pp of

C. W. FONG and R. F. SMITH the unimodal 200 #m AP pseudopropellant at all pressures. Overall from (a) to (e), it would appear that the major cause of PB behavior in this propellant system lies with the phenomena described in (a). The most likely explanation lies in an enhanced binder melt-fine AP interaction at low pressures. It has been suggested [9, 15] that condensed phase binder chemistry, in the form of binder melts on the propellant surface, can be important at low pressures. We have presented evidence which suggests that in this propellant system, various transition metal catalysts enhance binder decomposition (by catalyzing the breaking of the weak link urethane linkage in the binder), and PB behavior is a result of increased binder melt-AP chemistry in the pressure region from 2 to 7 MPa [9]. Remembering that PB behavior is usually only observed in this system when the coarse to fine AP ratio is greater than 60:40, then if the fine AP proportion is increased, the overall Pp increases and heat feedback to the burning surface also increases. When the overall burning rate is low, and consequently heat feedback to the burning surface is low, a binder melt on the burning surface has a longer residence time than it would have for faster burning propellants. Consequently catalyzed condensed phase reactions in that melt have a greater chance of occurring. Polybutadiene binder melts have been observed to be thicker at lower pressures than at higher pressures [16, 17] in the combustion of similar composite propellants. When compared to the NPB 20 #m AP unimodal pseudopropellant, it can also be seen that above 9 MPa, the burning rate for the PB 20/~m AP pseudopropellant is depressed. Binder melts have been observed to flow over the AP crystals which are recessed below the burning surface of composite propellants at high pressure [16]. It has been speculated that such a process can lead to intermittent extinction of the AP flame, thereby depressing the overall burning rate [16-19]. Our observation also seems to support such a hypothesis for high pressure combustion. At low pressures, the AP particle is observed to protrude above the burning surface [ 1, 2, 16-18], indicating

PLATEAU BURNING OF COMPOSITE PROPELLANTS that the binder surface is regressing faster than the AP surface. Our postulate of an increased binder melt-AP interaction, which increases the contribution of the PF over those of the FF and AP flames, would result in the binder surface regressing faster than the AP surface at low pressures, exactly, as observed experimentally. The shape of the burning rate curve for the unimoda120/zm AP PB pseudopropellant supports the above hypotheses. The pronounced change in burning rate pressure exponent at 9 MPa is indicative of a nondiffusion controlled process [9, 15, 18, 19]. In a polydisperse propellant, the binder is distributed disporportionately, so that the fine AP is relatively fuel rich and the coarse AP is relatively fuel poor. Thus it might be anticipated that a metal catalyzed binder decomposition process will have a greater chance to contribute to the PF in the relatively fuel rich environment surrounding the fine AP particles. Also binder melts would be more likely to be significant in a relatively fuel rich environment. It has been suggested that decreasing the AP content, or particle size, or using a more readily meltable binder will enhance PB behavior [18, 19]. The other points worthy of comment in Fig. 8 are the small but significant changes in the burning rates of the 200 and 400 /~m AP unimodal pseudopropellants. It appears as if f3r shifts can occur which are functions of the overall burning rate or heat feedback to the surface. The NPB propellants generally have higher ?p than the PB propellants (see Figs. 1-4). If the small shifts in #p for the 200 and 400/zm AP pseudopropellants are a consequence of different heat feedback to the burning surfaces, then the data in Fig. 8 [as discussed in (d) and (e) above] are consistent with an increased AP melt layer as the AP particle size increases. The slight (negative) exponent break at about 7 MPa for both the 200 and 400/~m AP NPB pseudopropellants may indicate that condensed phase AP chemical processes are occurring in the AP melt layer from 2 to 7 MPa. However, while the slight changes in exponent may not be outside experimental error, the generally greater ?p for the 400/zm AP NPB pseudopropellant over that of the 200/zm AP NPB pseudopropellant is statistically significant. This latter observation is also consist-

245

ent with an expected increase in the AP melt layer for the larger particle size. It is difficult to speculate on the effect of the metallic catalyst on such processes, if they do indeed occur. The catalyst resides in the binder phase, so any catalytic activity from the AP melt layer would have to occur via the PF, from an overflowing of the melt layer from the AP crystal. Miller's data, analyzed in Fig. 9, for uncatalyzed NPB propellants, shows the same general features of Fig. 8. However, the burning rate order for the larger AP particle sizes is 90 > 200 > 400/zm, which is different from that found in our NPB propellants (90 > 400 > 200/~m). The difference may be a result of the absence of a burning rate catalyst in Miller's propellants, or the use of slightly different AP particle size distributions in his propellants, or the difference in precision between the data sets. It is worth pointing out that while Miller's AP particle size distributions may not be exactly comparable to our own, and hence cloud any exact comparison of the data in Figs. 8 and 9, the comparison of our PB and NBP propellants in Fig. 8 is rigorous, since the same AP particle size distributions were used for all our 22 experimental propellants.

Burning Rate Temperature Sensitivity The burning rate temperature sensitivity (defined as d In i'p/dTo at constant pressure, where To is the initial temperature) for unimodal [4] and bimodal [2] AP propellants, has been calculated as a function of particle size. It is generally found that the temperature sensitivity increases with increasing pressure and with increasing particle size [2, 4]. Renie et al. [4] have noted that AP flame is more sensitive to changes in the initial propellant temperature than the PF. The temperature sensitivity for the pentamodal AP pseudopropellant is typically of the order of 0.05-0.2%/*C at 6-10 MPa. From the data shown in Fig. 7, it can be seen that the PB behavior persists over the temperature range 0-55"C. There is an increase in temperature sensitivity as the particle size increases, ranging from 0.05%/*C for the 400 #m AP unimodal pseudopropellant to

246 0.2%/*C for the 20 #m AP unimodal pseudopropellant over that pressure range (6-10 MPa). The temperature sensitivity does not increase as the pressure increases from 6 to 10 MPa, largely a result of the PB behavior being maintained in the range 0-55"C. 5. CONCLUSIONS The burning rates of 22 bi- and trimodal AP composite propellants can be accurately fitted to Eq. (1): rp = a400AP400+ a200AP200+ a90AP90 + a55AP55 + a20AP2o. Equation (1) describes a pentamodal polydisperse AP pseudopropellant, which is the linear summation of five unimodal polydisperse AP pseudopropellants. The burning rate behavior of these unimodal pseudopropellants indicates that the 20 and 55 #m AP pseudopropellants have quite different combustion characteristics from 90, 200, and 400/zm AP pseudopropellants in terms of the burning rate pressure sensitivity. Above 7 MPa, the latter pseudopropellants burn at rates which are invariant to changes in pressure, whereas the former pseudopropellants always burn faster as the pressure increases. The experimental propellants can be subdivided into plateau burning (PB) and nonplateau burning (NPB) propellants. These two sets of propellant burning rates have been also analyzed by Eq. (I). PB behavior seems to be largely the result of enhanced burning rate of the fine (20 #m) AP particles at low pressures (2-9 MPa), and reduced burning rate at higher pressures ( > 9 MPa). The enhanced burning rate at low pressure is attributed to increased binder melt-fine AP chemical interaction in the primary flame, whereas the depressed burning rate at high pressure is possibly due to binder melt flowing over the recessed AP particles, thereby resulting in intermittent burning and a lower overall burning rate. PB behavior is generally only observed in this propellant system when the coarse (90-400 /~m) : fine (20-55 #m) AP ratio is greater than 60 : 40. The pressure independent burning rates of the

C. W. FONG and R. F. SMITH coarse AP pseudopropellants are probably due to variations in the importance of the AP monopropellant flames (the /3F shift) when compared to competing primary and final diffusion flame, as a function of pressure and particle size. The presence of a melt layer on the coarse AP particles, in which condensed phase chemistry can occur at low pressures, could provide a mechanism by which the primary and AP flame can vary in importance as a function of pressure. The polydisperse nature of the AP in the unimodal pseudopropellants must also be considered when seeking explanations of such behavior. The temperature sensitivity of the unimodal AP pseudopropellants increases from 0.05%/*C for the 400/~m pseudopropellant to 0.02%/*C for the 20 #m pseudopropellant over the 6-10 pressure range. The PB behavior is maintained over the temperature range 0-55"C. Accordingly the temperature sensitivity does not increase as the pressure increases from 6 to 10 MPa.

REFERENCES 1. 2. 3.

4. 5.

6.

7.

8.

9. 10.

11.

12.

Cohen, N. S., A I A A J. 18:277-293 (1980). Beckstead, M. W., Derr, R. L., and Price, C. F., A1AA J. 8:2200-2207 (1970). Beckstead, M. W., Eighteenth Symposium (Int.) on Combustion, The Combustion Institute, Pittsburgh, 1981, pp. 175-185. Renie, J. P., Condon, J. A., and Osborn, J. R., A I A A J. 17:877-883 (1979). Renie, J. P., Ph.D. Thesis, Purdue University, 1982. (University Microfilms International, Ann Arbor, Michigan, 1984.) Miller, R. R., Donohue, M. T., and Martin, J. R., Thirteenth J A N N A F Combustion Meeting, CPIA Publication 281, Vol. II, September 1976, pp. 1-18. Miller, R. R., Donohue, M. T., and Petersen, J. P., Twelfth J A N N A F Combustion Meeting, CPIA Publication 273, Vol. II, Dec. 1975, pp. 371-388. Davies, O. L., and Goldsmith, P. L. Eds., Statistical Methods in Research and Production, 4th ed., Longman, London, 1980, Chapter 8.54. Fong, C. W., and Hamshere, B. L., Combust. Flame, 65:61-69 (1986). Glick, R. L , and Condon, J. A., Thirteenth J A N N A F Combustion Meeting, CPIA Publication 281, Vol. II, September 1976, pp. 313-345. Renie, J. P., Ph.D. Thesis, Purdue University, 1982. (University Microfilms International, Ann Arbor, Michigan, 1984, p. 152). King, M. K., AIAA Paper 78-216, Jan. 1978.

PLATEAU 13.

BURNING

OF COMPOSITE

PROPELLANTS

Boggs, T. L., Derr, R. L., and Beckstead, M. W., A I A A J. 8:370-372 (1970). 14. Hightower, J. D., and Price, E. W., Eleventh Symposium (lnt.) on Combustion, The Combustion Institute, Pittsburgh, 1967, pp. 463-472. 15. Kishore, K., and Gayathri, V., Progress in Astronautics and Aeronautics (K. K. Kuo and M. Summerfield, Eds.), Academic Press, New York, 1984, Vol. 90, pp. 53-119. 16. Boggs, T. L., and Zurn, D. E., Combustion Science and Technology 4:279-292 (1972).

17. 18.

19.

247

Handley, J. C., and Strahle, W. C., A I A A J. 13:5-6 (1975). Lengelle, G., Brulard, J., and Moutet, H., Sixteenth Symposium (Int.) on Combustion, The Combustion Institute, Pittsburgh, 1976, pp. 1257-1269. Steinz, J. A., Stang, P. L., and Summerfield, M., AIAA 4th Propulsion Joint Specialist Conference No 68-658, Cleveland, 1968.

Received l l February 1986; revised 26 September 1986