STEADY AND TRANSIENT BURNING OF MICROALUMINIZED SOLID ROCKET PROPELLANTS

A. Bandera*, L. Rossettini*, G. Colombo*, S. Cerri*, L.T. DeLuca*,

V.A. Arkhipov**, S.S. Bondarchuk**, A.B. Vorozhtsov**and A. Korotkikh**

* SPLab, Dipartimento di Energetica, Politecnico di Milano, I-20156 Milan, Italy

** Tomsk State University, 634050 Tomsk, Russia

ABSTRACT

The present paper reports the state of the art of a joint effort between Politecnico di Milano and Tomsk State University to characterize the transient burning properties of solid rocket propellants, based on micrometric Aluminum powders as fuel. Fast depressurization tests on highly energetic compounds of this kind were conducted at Tomsk State University, while Pressure Deflagration Limit (PDL) tests on industrial propellants meant for space applications were carried out at the Space Propulsion Laboratory of Politecnico di Milano.

NOMENCLATURE

• AP: Ammonium Perchlorate • ASD: Micrometric Aluminum Powder • HEM: High-Energy Material • HMX: Cyclotetramethylene-

tetranitramine; • IPIB: Inverse Problem of Internal Ballistic • nAl: Nano-sized Aluminum • PDL: Pressure Deflagration Limit • SF: Shape Factor • SKDM-80: Binder • SPLab: Solid Propulsion Laboratory • µAl: Micron-sized Aluminum

INTRODUCTION

Despite the great rise in interest towards nanoAl (nAl) undergone during the recent years in propulsion laboratories all around the world, microAl (µAl) powders still represent the totality of the metal powders used as fuel in real motors. In fact, nAl seems to be a very promising ingredient, because of the short ignition time, decrease of two-phase losses and augmentation of aluminum combustion completeness, but the knowledge of its combustion properties is still largely incomplete to permit its safe use in operational motors. That is the reason why a great interest in the properties of µAl is still alive: it will probably be the only metallic fuel used in full scale motors at least in the near-medium term future. In particular, if the steady state ballistic properties of compositions

based on µAl have been largely investigated in the past, some black holes still remain in our knowledge of their unsteady properties; this work aims at filling this gap. For this purpose a quite energetic propellant based on µAl was investigated in Tomsk State Technical University, in terms of extinction by fast depressurization, with an auxiliary nozzle opening after the complete burning of a plug made of the investigated propellant. The subsequent pressure gradient leads to an unsteady condition, whose burning rate was determined by solving the inverse problem of internal ballistic with the help of direct search technology, or by the method of high-speed combustion recording. The experimental results thus obtained were compared with the theoretical predictions of ZN theory. At the same time, four different industrial propellants (labelled A, B, C, D) were investigated in terms of PDL by the group of Milan: they had different compositions both in terms of Aluminum and Ammonium Perchlorate (AP) mass fraction and grain size distribution, thus permitting to analyze the effects of different propellant formulations on the unsteady combustion properties. These two different approaches will be merged in future in a common research topics and facilities for the two international groups.

FAST DEPRESSURIZATION

A high-energy material (HEM) of new composition was exposed to unsteady burning conditions provoked by a sudden pressure drop. The exact composition of the propellant and the dispersion of the µAl powders (labelled ASD) used as fuel are summed up in Table. 1.

Component Mass, % AP 41

HMX 30 Binder, SKDM-80 14 Aluminum, (ASD) 15

Diameter, µm D10 D20 D30 D32 D43

ASD 1.23 1.,66 2.28 4.34 7.34 Table 1: Fast Depressurization Propellant

Formulation.

To provide low-temperature hardening, a 0.5 % amount of hardener was added in excess, with the hardening process taking place in 36 hours at room temperature. The propellant manufacture procedure comprised 2 stages: the first one, lasting 2 hours in total, in which several mixing cycles were carried on, and the secondary stage where through-feed pressing of the samples of given form and size took place. To grant high quality and reproducibility of burning rate measurements, the density of each lot produced was measured, permitting to disregard samples whose density was more than ±0.02 g/cm3 far from the average of 5 samples of the same lot. Inverse Problem of Internal Ballistic (IPIB) As a first step, a steady state ballistic characterization was gained for this propellant, using armored samples with end face burning. Steady state burning rate measurement was performed using standard methods in a closed vessel under nitrogen atmosphere. The corresponding Vieille’s law is expressed by the following dependency on pressure (with ug in mm/s and P in bar):

4.014.1 Pug = (1) Unsteady burning rate measurements were performed in a microsized solid rocket motor with a cylindrical combustion chamber, whose sizes were 50 mm in diameter and 100 mm axially, endowed with two nozzles, indicated as main and auxiliary. The main nozzle was designed in order to assure a steady state combustion pressure (p0) of 40 bar. The auxiliary nozzle diameter was adjusted in order to provide various pressure drop gradients, and is originally tapped with a T-shaped propellant plug (see Fig. 1). When the plug of the cap burns out the outlet is rapidly opened by the high pressure in the chamber, thus unblocking the auxiliary nozzle. An overall sketch of the experimental set-up is reported in Fig. 1. Pressure in the combustion chamber is measured by means of a strain gauge with an error of ± 0.15 %, and a full-scale value of 200 bar. After the

ignition of the HEM under investigation, a steady-state regime (p0 = const) sets up in the combustion chamber, governed by the joint contribution of both propellant and plug combustion: when the plug is burned out, the pressure inside the chamber exhibits a heavy drop. Unsteady burning rate ug(t) is gained from the pressure curve obtained during fast depressurization, using the methods of inverse internal ballistic problem. The schemes used to identify the burning rate curve versus time, arise from considering the following set of equations, where W is the combustion chamber volume, P and ρ pressure and density of the combustion gases, Φ1,2 e F1,2 flow coefficients and nozzle throat areas for main and auxiliary nozzle, S the burning surface and Tp the solid propellant temperature:

( )

( )

( )11

2211

00

0

12

11

−+

+

+=

−−=

−

−=

γγ

γργϕϕ

γργρ

γ

ρρ

PFFG

GPuSTCPWdtd

GuSWdtd

gpp

g

(2)

From the previous set one can obtain the law ug(t) in nondimensional variables:

11

22

213

1

)(

FF

Pdt

dPPpdt

dPtug

ϕϕ

σ

σγρ

σγ

γγ

+=

+=+=−

(3)

using as scaling values the steady state value of pressure, density and burning rate, while the relaxation time of the combustion chamber free volume was taken as the scaling factor for time. It comes out immediately that P(0) and ug(0) are equal to 1. The ultimate value of burning rate is obtained from the experimental succession of pressure points Pj curve using a direct search method in the second modification of the inverse ballistic problem. The succession of experimental pressure points pressure Pj is split into N time intervals Δti (i=1,...,N). For each time interval the following linear burning rate function is built, ug

i being the previous temporal step value of the variable

( )ii

ig

igi

gg ttt

uuutu −

∆

−+=

+1

)( . (4)

The problem is subsequently reduced in terms of pressure by means of the equation set (2): for each time interval Δti the problem is reduced to finding the minimum of the following function:

Fig. 1: Fast Depressurization Experimental Set-Up

Secondary Nozzle

,)(1 1

∫ ∫+ +

−=℘i

i

i

i

t

t

t

tj dtPdttP (5)

The calculation scheme is depicted in Fig. 2. Another aspect quite important to take into account when implementing this approach, is the effect of the auxiliary nozzle opening, which results in the pressure drop, on the flow coefficient: if the assumption of φ1 being constant with time is adequate for the primary nozzle, where the flow rate modifications are slight, the same is not absolutely true for the auxiliary one. The unsteadiness of the flow coefficient φ2(t) can be estimated as:

( ) [ ]nttet −−= 10,22 ϕϕ (6) on the condition that the characteristic time interval tn since nozzle opening respects Eq. 7:

( )pn RT

FF

Wt

+

+

⟨⟨−

+1

1

21 12 γ

γ

γγ

(7)

with R gas constant of the combustion gases. It can be immediately inferred that φ2(0)=0, with the value rapidly increasing to its steady state value φ2,0.

Results The results of unsteady burning rate investigations for the composition analyzed, based on ASD, is shown in Fig. 3, together with an alternative way of solution of the inverse problem of internal ballistic (labelled first approach); this is based on the numerical differentiation of the experimental curve P(t) obtained approximating the experimental points Pj with a smoothed cubic spline. One can immediately note the low accuracy of the first approach near the beginning of depressurization compared to the direct search solution (second approach). After about 300 ms both the burning rate curves were coincident with the theoretical quasi-steady behavior. The same happened for the pressure curve. The oscillatory behavior of the burning rate obtained is evident. Moreover, the comparison with the theoretical results of the ZN-model (surface temperature Ts not varying with time) evidences deviations from the quasi-steady behavior up to near 30%. The frequency of oscillations is recognized to be 4Hz. However, it has been already pointed out by Arkhipov et al[1] that very similar trends can be obtained when dealing with nAl based propellants: that makes the effect of aluminum powders size and dispersion on the unsteady burning rate still obscure, even if a slight stabilizing effect of nAl was visible. To provide a definitive comparison analysis of aluminum dispersion effect, one should compare two compositions with the same steady ballistic properties; moreover, also the surface temperature can have an important role, being a determinant criterion of ZN-theory. Further investigations on this subject are taking place at this moment at Tomsk State Technical University. High-Speed Recording The high-speed recording technique for evaluating the burning rate of a propellant is a nonintrusive technique, very easy to set up. The experimental set-up used is very similar to that for the solution of the inverse problem of internal ballistic, and is depicted in Fig. 4: the combustion chamber has a quartz glass window through which the high-speed camera gains access to the chamber (3). The propellant sample under examination (labelled 4) is a semicircle whose diameter is 100 mm and 10-30 mm thick, inhibited along the circumference and glued to the chamber wall. The vessel is endowed of two nozzles, with the secondary being initially tapped with a cap of the propellant under examination: after ignition the primary and secondary propellant charges burn simultaneously, and the pressure level is determined by the ratio of the combustion surface and cross section of the main nozzle, that is to say by the balance between

Fig. 2: Calculation Scheme

Fig. 3: IPIB results

the mass flux produced and expelled. After complete combustion of the secondary plug, opening of the auxiliary nozzle and the start of a transient regime leading to a secondary stationary one takes place. The pressure level of this regime, obviously, depend on the increased discharging area. The high-speed camera (whose working frequency spreads from 50 to 2000 Hz) is synchronized with a pressure transducer in order to start recording after the complete burning of the auxiliary plug. Localization of the combustion surface, frame-by-frame, was carried out through an IMI-100 microscope, with indication of coordinates of 3 points on the burning surface for each frame. It was necessary to take into account the sample deformation due to the reduced load during depressurization, which is quite remarkable for high pressure drops. Special tests were conducted on non-burning samples to quantify this effect: an amplitude of oscillation up to 10-25mm was found, because of the deformation. This effect was rapidly disappearing after 2-10 ms, and an artificial negative burning rate due to samples deformation was summed up to the burning rate results. In the end the burning rate measurement procedure error was in the order of 5-8 % for a time resolution of 3ms. Results In the following Fig. 5 typical results obtained for the ASD-based propellant are expressed in terms of experimental ug(t); on the same figure the theoretical quasi-steady curves for ug and P are reported: the experimental ug(t) exhibits an oscillatory behavior, with frequency of oscillation close to 150 Hz and displacement from the quasi-steady solution higher than 50 %. Frequency and amplitude of oscillations decrease with a lower pressure gradient.

In the following Fig. 6, instead, the results obtained with solution of the inverse problem of internal ballistic method for a similar initial pressure gradient are reported: the direct comparison of Fig. 5 and 6 immediately show a considerable disagreement of the two methods: this is probably due to the high-speed recording being a localized method, while the inverse problem of internal ballistic method gives ug averaged on all the burning surface. A comparison between the experimental data and calculations within the Zel’dovich-Novozhilov [2] model has shown the inverse problem of internal ballistic method offering data in closer agreement with theory. The high-speed recording method records local burning rate values, which, according to the site-pulsating combustion hypothesis, may differ significantly from the surrounding points’ values.

Fig. 5: High-Speed Recording Results

Fig. 6: IPIB Results

Fig. 4: High-Speed Recording Experimental Set-Up

PRESSURE DEFLAGRATION LIMIT The Milan group focused its efforts on the pressure deflagration limit (PDL), of four different compositions of microaluminized industrial solid rocket propellants: by definition, PDL is the pressure value where combustion becomes no more self-sustained and extinguishment of combustion occurs. It is an important parameter for propellants, as it gives an idea of the resistance of the combustion to extreme conditions: usually, in a few words, the lower is the PDL, the better is the propellant. The compositions of the four propellants investigated (labelled A (reference), B, C and D), together with their density are summed in Table. 2. AP (%) Al

(%) HTPB

(%) Density (g/cm3)

A 68 bimodal

18 30 μm 14 1.729

B 69 trimodal

19 30 μm 12 1.779

C 69 trimodal

19 30 μm 12 1.788

D 69 trimodal

19 15-30 μm 12 1.775

Table 2: Solid Propellants Compositions

The steady state ballistic properties were acquired in SPLab as a first stage of experimentation, burning 5x5x30 mm samples under an inert atmosphere of nitrogen. The pressure was kept strictly constant by a system composed of pressure transducer, control software and electrovalves; the ignition was given by means of a hot-wire and the measuring technique was optical, recording the combustion videos with an high-speed camera. As far as the PDL experimentation is concerned, the propellants were parallelepiped in shape with the sizes 5x5x50, 10x10x50 and 15x15x50, thus permitting us to study three different shape factor values. The shape factor, in fact, defined as the ratio between the cross section area and the cross section perimeter of the strand, has a great influence on the PDL value: it has been widely reported [1][3][4] that a high shape factor pushes the combustion to continue to lower pressure levels. The PDL tests were conducted in a 40 liters vessel in order to damp the pressure oscillations typical of near PDL zones. A photodiode is placed on one optical access of the chamber; the pressure is monitored by a pressure transducer whose signal, together with the photodiode’s one, is acquired by a digital oscilloscope for analysis. The pressure inside the chamber is regulated by means of a void pump directly controlled by the operator, and the ignition was hot-wire based. The

propellants strands were long enough to permit depressurization with a typical gradient of 1-0.2 mbar/s, in order to avoid any possible fast depressurization effects. Strands were ignited at a pressure slightly higher than the expected PDL; the pressure was then smoothly reduced till complete extinction was reached. The shape of the curves of the photodiode and the pressure transducer seem to suggest the following succession of event during depressurization: while moving toward PDL one can see the signal of the photodiode becoming weaker and weaker, with oscillations with lowering frequencies and increasing amplitudes. When the complete extinction is reached the signal from the photodiode falls to zero, while the pressure curve changes its slope because of the disappearing of the combustion gas production. The pressure level, where one can note these phenomena on the curves, is the searched PDL level. This trend is clearly visible in Fig. 7: note the change in slope of the pressure curve. The final output of a PDL experimentation is a curve linking PDL to shape factors for each propellant. Results The steady state burning rate results on the interval 12-70 bar are summed in Fig. 8 and in the following Table. 3.

Fig. 1: Typical near PDL curves.

B: ug: (1.100±0.036)*P(0.402±0.009)

D: ug: (1.352±0.029)*P(0.479±0.006)

A: ug: (1.402±0.052)*P(0.422±0.001)

C: ug: (1.432±0.037)*P(0.426±0.007)

u g

PDL

Fig. 7: Typical Near-PDL Burning Curves

Fig. 8: Steady Burning Rate Results

One can see that the propellant D, the only one bimodal in Aluminum distribution, is the fastest and also shows the largest pressure dependency. The propellants C and the reference A have very similar trends, while the propellant B is, by far, the slowest, probably because of its heavy load of coarse ammonium perchlorate.

Table 3: Steady Burning Rate Results During combustion, moreover, the propellant B exhibited a continuous expulsion of huge agglomerates from the burning surface (Fig. 9). A similar behavior was evident in the propellant C as well, but only for low pressure values. The results of the PDL experimentation are summed in Fig. 10 and Table 4, as a function of the Shape Factor (SF) for each propellant under investigation.

From the direct analysis of the results reported one can immediately conclude that the reference propellant A is able to withstand combustion up to

very low pressure for all Shape Factor values: in particular the difference from the other propellants is evident for the lowest Shape Factor value.

The Propellant D, instead, tends to have the same behavior of propellant A for higher values of the Shape Factor, but different at lower ones. The propellant B features the higher PDL for every Shape Factor, besides having the lower burning rate at every pressure. The propellant C curve exhibits a very peculiar shape: at lower Shape Factor it follows the trend of propellant B, while at highest it joins the behavior of A and D propellant. This fact, together with the expulsion of agglomerates limited to lower pressure, seems to suggest that Propellant C is a propellant whose combustion quality is strictly depending on burning conditions, spreading from poor to good according to some factors. In particular under all the conditions that tend to increase the combustion robustness and steadiness, such as high pressure and high Shape Factor, C propellant can be easily compared with A and D; otherwise, it is similar to B, which was the lowest performance and quality propellant. This is probably due to different coarse to fine AP fraction ratio of propellant C with respect to B (note that propellants A and D are bimodal in AP distribution and do not have coarse fraction). It is already known [3][4] that a reduction in aluminum powders size, at least moving from µAl to nAl, leads to a reduction of PDL: this tendency seems to be only partially reproduced here; at higher SF, in fact, D propellant has slightly lower PDL compared to A, but this is not true at lower SF. Anyway, considering that also the AP grain size distribution is different between the two propellants, no definitive insight on the role of different sized µAl powders on PDL can be gained, and further experimentation is required on the coupling of AP and Al powders size. Extinguished surfaces visualizations The combustion surfaces appearance after having provoked the flame extinguishment have been analyzed optically with a digital microscope (Eclipse® 10x-1000x) and compared with unburned surfaces. This approach, spread to all the propellants investigated, permitted us to light the

a n A 1.402 ± 0.052 0.422 ± 0.001

B 1.100 ± 0.036 0.402 ± 0.009

C 1.432 ± 0.037 0.426 ± 0.007

D 1.352 ± 0.029 0.479 ± 0.006

PDL (mbar) SF = 1,25 SF = 2,5 SF = 3,75

A 62.3 ± 3.9 33.8 ± 2.8 25.0 ± 1.0 B 108.7 ± 35.2 45.0 ± 5.0 37.0 ± 2.6 C 117.0 ± 32.5 30.4 ± 3.5 27.0 ± 1.7 D 86.3 ± 3.2 30.7 ± 1.2 23.3 ± 0.6

Table 4: PDL Results dependency on shape factor

Fig. 9: Agglomerate Ejection from Burning Surface

0

10

20

30

40

50

60

70

80

90

100

110

120

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5

"Shape Factor", (Cross Section Area / Cross Section Perimeter), mm

PDL,

mba

r

A D B C

Fig. 10: PDL Results for micro-Al propellants

modifications that different AP and Al sizes generate on the burning surface. A direct comparison between reference propellant A and D is presented in Figs. 11 and 12: no clear differences can be observed either in the burned or in the un-burned surface; in particular, in the burned surface images, the same grain size and morphology is observed, and the same goes after combustion. The comparison of propellants B and A infers a very different situation: the different size distribution of AP grains is clearly visible on the unburned surface (Fig. 13); the large size of AP grains lead to a subsequent very large size of

pockets and to the presence of zones with very different properties, thus making B propellant quite more inhomogeneous. Moreover, on the burned surfaces images, large unburned Ammonium Perchlorate grains are clearly visible (Fig. 14). This relates properly with the poor steady and unsteady ballistic properties experimentally evidenced for this propellant. The same characteristics, even if at a minor extent, are visible for the propellant C (Fig. 15 and 16): in particular one can note web-like structures all around oxidizer crystals, which might belong to skeleton layer.

A: Unburned Surface

D: Unburned Surface

A: Burned Surface

D: Burned Surface

A: Unburned Surface

B: Unburned Surface

A: Burned Surface

B: Burned Surface

Fig. 11: Comparing Propellants A and D Unburned Surfaces

Fig. 12: Propellants A and D Burned Surfaces Comparison

Fig. 13: Propellants A and B Unburned Surfaces Comparison

Fig. 14: Propellants A and D Burned Surfaces Comparison

CONCLUSIONS

Two different approaches (IPIB and high-speed recording) to fast depressurization problems have been considered by the Tomsk group: the results gained while measuring the transient burning rate have clearly shown the different characteristics of the two, the first being averaged over the burning surface while the latter is local. The IPIB method seems to be in closer agreement with theoretical predictions.

The PDL experiments of Milan group, instead, have pointed out the importance of aluminum and ammonium perchlorate grain size distribution in modifying the transient behavior of the propellants close to extinction and the surface appearance.

FURTHER DEVELOPMENTS

A more complete analysis on the joint influence of aluminum and ammonium perchlorate sizes is planned by the Milan Group, extending the efforts to nanometric powders. Particular emphasis will be laid on the modification of the ballistic coefficient and a strengthening of the resistance to pressure modifications. Besides of this a new interest in fast depressurization effects will allow to increase our knowledge background [5][6].

REFERENCES

[1] Arkhipov, V.A., Bondarchuk, S.S., Vorozhtsov, A.B., Bandera, A., Colombo, G., Galfetti, L., DeLuca L.T., Transient Burning of Nanoaluminized Solid Propellants, EUCASS 2007, Brussels, Belgium. [2] Novozhilov B.V., Unsteady Combustion of Solid Rocket Propellants, published by Nauka M., Moscow 1973, Russia. [3] DeLuca, L.T., Bandera, A., Galfetti, L., Colombo, G., Maggi, F., Orsini, D., Donde, R., Meda, L. and Marra, G. Micro And Nano Aluminized Solid Propellants Behavior Under Transient Burning Conditions. International Astronautical Conference, Valencia, Spain, 2006. [4] Capelli, Bonvini, “Caratterizzazione sperimentale di propellenti solidi innovativi per la propulsione aerospaziale”, Tesi di Laurea in Ingegneria Aerospaziale, SPLab, Politecnico di Milano 2005, Milan, Italy. [5] Dondé, R., Riva, G., and DeLuca, L.T. Experimental and Theoretical Extinction of Solid Rocket Propellants by Fast Depressurization. Acta Astronautica, Vol. 11, No. 9, 1984, pp. 569-576. [6] Jensen, G.E. and Brown, R.S., An Experimental Investigation of Rapid Depressurization Extinguishment, AIAA J., Vol. 9, 1971, pp. 1667-1673.

A: Unburned Surface

C: Unburned Surface

A: Burned Surface

C: Burned Surface

Fig. 15: Propellants A and C Unburned Surfaces Comparison

Fig. 16: Propellants A and C Burned Surfaces Comparison