Effects of the Diffusion Processes in the Modelling of Composite Propellant Ageing
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1 Processes in the Modelling of Composite Propellant Ageing S.CHEVALIER E.LIEBENS R.NEVIERE SNPE Centre de Recherches du Bouchet, Vert-le-Petit, FRANCE SNPE Etablissement de St Médard, 33 St Médard-en-Jalles, FRANCE 1.0 INTRODUCTION During their service life, the operational integrity of solid rocket propellant grains may be greatly affected by the surrounding conditions of storage. The material degradation is more precisely related to a mechanical properties loss which is known to be mainly controlled by the molecular structure of the synthetic rubber binder. It is well established that the good quality of polybutadiene binder is due to the presence of the unsaturation of the polymer chains which, in consequence to this potential reactivity, may be affected by a long term oxidative crosslinking process. Obviously, due to this process, atmospheric oxygen and moisture are governing ageing factors. For CTPB binder propellants, previous studies have shown the evidence of two competitive reactions involved in the ageing process: oxidative hardening and moisture softening. Many works have shown that this competition in CTPB propellants is won by softening due to long term moisture diffusion with an accelerating effect by temperature [1]. The result is an effective decrease of the propellant stiffness which reveals at the macroscopic scale the breaking of ester crosslinks. This chemical ageing is dependent on the rate at which the binder ester groups which control the structural strength of the propellant are broken. Considering the diffusion and chemical reaction as the governing ageing process in CTPB propellant grains, a numerical simulation methodology was built up upon experimental results of moisture diffusion and its consequent impact on mechanical properties. This paper describes the methodological approach used to estimate the service life of CTPB propellant and preliminary work to HTPB propellant transposition. It should be emphasis that in HTPB propellant, crosslinking is the result of urethane bonds formation and that these urethane groups are known to be quite insensitive to hydrolyze attack. It is thus expected that binder s breaking will not be the controlling factor of ageing but that oxidative crosslinking of HTPB could cause hardening and loss of the flexibility. Keeping in mind this molecular background, the present paper discusses the moisture effect for HTPB propellant. 1.1 Methodology Approach Several inputs need to be known to model by a numerical process the composite propellant ageing and to predict the service life time. From our work, we have identified the following inputs: service surrounding solid rocket motor design ( thermal insulator, adhesives materials, ) chemical and physical ageing process of composite propellant and rate expression moisture effect oxidative crosslinking additives migrations Paper presented at the RTO AVT Specialists Meeting on Advances in Rocket Performance Life and Disposal, held in Aalborg, Denmark, September 2002, and published in RTO-MP-091. RTO-MP
2 2.0 EXPERIENCE OF AGEING IN CTPB PROPELLANT GRAINS 2.1 Environmental Conditions of Storage It is obvious that humidity is the principal cause of the degradation of CTPB propellant mechanical properties. Indeed, valuations of CTPB grains back from operational service have demonstrated that propellant mechanical properties were more degraded than expected and especially along the combustion chamber and close to the composite structure. These observations suggest that humidity diffuses both from the combustion chamber and through the composite structure during the whole life of the grain. As a consequence, to assess the ageing process in solid rocket motors due to humidity one has to assume these two sources of water and quantify them as boundary conditions. Figure 1 shows a schematic view of the situation to be described in a service life simulation process. Diffusion of humidity through structure Propellant Diffusion in combustion chamber Humidity released by composite material Figure 1: Environmental Conditions of Storage or Propellant Grain. An indirect evidence of this situation is revealed by the measured mechanical properties, especially close to the structure, where it is found that the propellant is highly deteriorated. Hence, it can be drawn from this work on CTPB propellant grain, that the knowledge of the environmental life conditions in terms of temperature and relative humidity, is an essential input to the prediction of the service life duration in solid rocket motors. 2.2 Evolution or Mechanical Characteristics of CTPB Propellant Many studies of the influence of these ageing parameters have been achieved for these propellant grains during the past decades. As a summary, one may state the following results: for low RH ( RH10%), mechanical properties do not fluctuate with ageing, in a dry environment mechanical properties increase up to 40%: propellant hardens, for high relative humidity (over RH35%), mechanical properties collapse down to 70% of their initial values: propellant softens. Mechanical properties RH < 10% + 40% 1 RH = 15% RH = 35% - 70% Propellant age Figure 2: Evolution of Mechanical Properties of CTPB Propellant RTO-MP-091
3 2.3 Modeling and Simulation As a well established knowledge from the experience gathered on CTPB propellant grain ageing studies, it points out that to succeed in a service life numerical simulation, it is of capital importance to cumulate information on the solid rocket motor environmental conditions and to link these conditions to the state of degradation of the material properties. Once this stage is achieved the following step is to model both the humidity diffusion in propellant grain and the impact on mechanical properties Diffusion through Propellant By analogy to a heat transfer phenomenon, the Fick s law may be assumed to control humidity diffusion: [ grad( C f ] C = div D t ) + where C is the water concentration, D the diffusion coefficient and f the source term. It is of course of a preliminary study to identify the material properties involved in this fundamental relation. The basic experiments to assess these values are described in section 2. Once these are available, a diffusion simulation may be run by the mean of a finite element code to produce a concentration mapping of humidity inside the grain at each time of interest. An example is shown for long term ageing on figure 3. Figure 3: Simulation of Relative Humidity Concentration in a Propellant Grain. It can be seen on this figure that the affected locations are, as expected, around the central bore up to quite an important thickness (the blue zone) and to an non negligible level underneath the structure (green zone) Modelling of the Ageing of Propellant Mechanical Properties The last step to predict the service life duration of solid rocket motors consists in the evaluation of the safety coefficient of the aged propellant grain. To achieve this operation and considering the one-to-one relationship between humidity and mechanical properties, the missing connection consists in a mechanical properties modelling as a function of humidity and temperature. From the results of figure 2, an empirical time dependent relation is fitted for each property P as: P P(t 0 = 1 ) [ 1 K (RH)] 1 e age tau(rh) where K(RH) and tau (RH) are material constants extracted from experiments. 2.4 Validation by Expert Valuation Obviously the return back at the end of their service life of propellant grains offers the opportunity to confront prediction and observed reality. Some of these grains, selected as different as possible in terms of size, life time and boundaries conditions were thus cut out and series of tensile experiments were RTO-MP
4 performed for propellant and bond line of different locations. The figure 4 shows by comparison the level of the measured properties using the same color map as the grain calculations. In this figure, the value of the mechanical parameter measured in the post-life expertise is represented in a little square at the location where it was taken. bond fracture tests uniaxial tensile tests Figure 4: Agreement between Predicted and Observed Material Properties (Failure Stress). As it can be seen clearly on this figure, there is a good agreement between the predicted state of material properties as a result of the entire simulation process and the experimentally observed reality. 2.5 Conclusion The results gathered for CTPB propellant grains have brought to the fore that the ageing of these structures are mainly controlled by the humidity diffusion process in the propellant. It comes clear from this valuable experience that the long term service life prediction of propellant grains has to take into account for the diffusion process of humidity among all its aspects: boundaries conditions, diffusion modelling and impact on the mechanical properties. It has been demonstrated that a correct evaluation of all these separated aspects may be joined together for a throughout simulation of the long term ageing prediction using finite element calculation code with some success. As an obvious consequence, this methodology described by the synopsis of figure 5 was maintained to assess the HTPB propellant ageing study RTO-MP-091
5 REQUIRED DATA Boundaries conditions Diffusion characteristics Mechanical properties STEPS Modelling of humidity diffusion through the propellant grain "Ageing law" of mechanical properties of propellant Modelling of the ageing of propellant mechanical properties inside the grain Mechanical solicitation calculation (S) Mechanical properties of aged propellant (C) Safety coefficient estimation K = C / S Figure 5: Synopsis of Long Term Ageing Assessment Methodology. 3.0 EXPERIMENTAL TESTS 3.1 Characterization of Diffusion Phenomena in a HTPB Propellant Grain The first step to achieve is to run a numerical simulation of the transfer through the propellant grain of each component involved in the ageing process. For this purpose, two main types of information are required: Since several components may control the propellant ageing, it is necessary to identify both the physical laws governing their diffusion rate inside the grain and the associated material constants (diffusion coefficient and balance curve). A clear knowledge of the location where the diffusion process initiates and is sustained such as free surfaces of the propellant grain itself, thermal insulation and composite structure. As a consequence the diffusion models should be checked for this different couples of materials Diffusion Phenomena through Materials As mentioned earlier, the humidity diffusion phenomena take place in different locations of the propellant grain, it is thus necessary to evaluate each diffusion property of the materials present in the rocket motor. For this evaluation, two types of tests are of common use: Humidity diffusion Permeability RTO-MP
6 The humidity diffusion test provides the diffusion coefficient D and the solubility property S, while the permeability test allows to evaluate the permeability coefficient P of the tested material. With the assumption that the balance curves are linear, these properties are simply related by: P = D S The permeability test consists in a relative humidity gradient controlled on both sides of a thin sample (1 mm) of the material to characterize while the diffusion test consists in a succession of desorptionsorption-desorption of water along with a continuous measurement of the sample mass Diffusion Phenomena through Propellant Depending on the grain size a finite or infinite assumption for the humidity supply inside the propellant may be considered: The material of the rear motor part contains a great amount of water inherent to its composition (this quantity as to be compared to the grain size). The combustion chamber volume itself traps a finite quantity of water available for diffusion in the propellant. Two types of elementary tests are realized to simulate the humidity diffusion through HTPB propellants: Unsealed container test: this is a test of sorption-desorption with a constant external humidity rate. The basic principle assumes an infinite amount of water is available in an infinite surrounding environment. This test target is to characterize the humidity diffusion through the propellant. Sealed container test: a piece of propellant is placed in a closed container and the kinetic evolution towards equilibrium of the propellant with the atmosphere of the sealed box is measured. On the opposite of the previous test, the test assumes a finite amount of water in a finite environment. This test is pertinent to study the water transfer between different materials and especially between the material of rear motor and HTPB propellant. "Unsealed" test "Sealed" test 1 mm propellant sample 5 mm propellant sample T = constant %RH = constant T = constant - %RH = RH(t) Continuous measurement of sample mass Continuous measurement of relative humidity inside the enclosure Figure 6: Description of Sealed and Unsealed Tests. The unsealed test analysis is supported by the diffusion theory in a thin layer (one dimension is very small compared to the others) while the sealed test is a bulk material characterization for which the propellant samples are larger due to the humidity conditions (large amount of water provided by composite material for instance) RTO-MP-091
7 3.1.3 Diffusion Phenomena between Several Materials Since a significant supply of humidity in the grain is identified as coming from the presence of quite a large amount of water in the rear rocket motor part (nozzle and surrounding parts) some specific sealed container tests where performed to model the humidity transfer from this material to the propellant. For these tests a sample of propellant and a sample of material containing water are enclosed together and the relative humidity in the container is then continuously recorded. It is recommended to choose a larger size of the propellant sample to compensate the poor air and propellant sorption capability compared to the other material one Numerical Simulation of Diffusion Phenomena inside a HTPB Propellant Grain Once the experimental informations are available, a numerical calculation of the component diffusion through the propellant may be performed using a finite element code. The diffusion model implemented is a Fick s law for which the required material constants where identified from the results of the above characterizations. The model has been improved to have a satisfactory fit to the experimental results as shown on figure 7. C (g/kg) calculation Experimental result t (min) Figure 7: Comparison between Calculation and Experiment: Opened Enclosure Test on a 1 mm Propellant Sample. 3.2 Characterization of HTPB Propellant Mechanical Properties Experimental Tests Protocols HTPB propellant tested: HTPB/isocyanate binder with 88% of AP/Al fillers, copper chromite as burning catalyst and others additives. Ageing conditions: Standard samples (dogbones) were machined before exposure to ageing conditions in the range of 20 to 60 C and various relative humidity content (5<RH<76%) in sealed cases containing neutral or oxidative atmosphere (air or nitrogen). Salt saturated solutions were chosen to have a well control of relative humidity over the temperature range. Physicochemical tests: Measurements of the soluble fraction (binder sol/gel fractions) are made by swelling extraction in a suitable solvent (toluene or dichloroethane). The method is described in the STANAG 4581in preparation [2] Uniaxial Tensile Tests In order to quantify the influence of the ageing process on the material mechanical integrity, many tests are available but among them the simplest one is obviously the classical uniaxial tension test. Since the material behavior is viscoelastic in nature, these tests may be run for different conditions of strain rate and RTO-MP
8 temperature. This procedure allows both to have an insight on the ageing influence on the viscoelastic properties which are mainly controlled by the macromolecular movements in the network and on the specific mechanical properties required to assess the mechanical integrity of the grain for the different loading conditions in the grain service life (namely the pressurization and the long term storage). The uniaxial tensile tests are performed using the AFNOR NF T standard. The specimens are machined in the standard JANNAF geometry as depicted on fig. 8 and loaded at a constant strain rate and isothermal temperature conditions. The measured properties after the test are mainly the modulus in the linear portion of the response, the maximum stress and the associated strain at that point and finally the fracture strain which is generally larger to the previous one due to the presence of a plateau region and a smooth fracture process. A typical result on which the characteristic points are defined is also shown on figure 8. JANNAF Sample typical tensile test S m 12 R E tg e m e r 95 Figure 8: Uniaxial Tension Test Definitions. The tensile properties give foreground informations on the crosslink density and the network backbone strength since the modulus is a direct measure of the first and the stress capability an indication of the second. As an example, figure 9 presents the uniaxial response of an HTPB propellant aged in different conditions of relative humidity at ambient temperature in a neutral atmosphere (Nitrogen) and the same material aged at different temperatures in dry air. Stress (MPa) Ageing program 6 duration in dry air - Influence of temperature +60 C +50 C +40 C initial +20 C Ageing program 6 duration: +20 C in N² Influence of moisture dry Hr35% Hr55% Hr76% initial Strain (%) Strain (%) Figure 9: Tensile Response of Aged HTPB Propellant for 6 Months Duration in Different Ageing Conditions of Temperature, Moisture and Atmosphere RTO-MP-091
9 For the material aged in dry air, the analysis of such results is described as a material stiffening which is revealed by a modulus and maximum stress increase associated to a fracture strain decrease. This stiffness augmentation is related to a crosslink densification of the network which is suspected to be due to an oxidation process of the elastomer chains. On the contrary, a stiffness decrease is observed when the water concentration is elevated during the ageing process at ambient temperature. This behavior is assigned to the network bonds fracture probably at the particles-binder interface since the HTPB elastomer is known to be rather insensitive to hydrolysis. This assumption may be supported by the fact that the response shape for high moisture concentration (see RH76%) is strongly affected by the ageing process with a typical softening in the fracture region known to be controlled by adhesion. Reminding that the presented results concerning the humidity influence where gathered in an inert gas ambience, indicates that the oxidation process finds another oxygen source than the simple surrounding atmosphere even if this source is not clearly identified. Finally, it should be pointed out that the ageing condition of +20 C and RH35% gives the closest response to the initial time response and it is thus recommended to approach these conditions for grains storage Dynamic Mechanical Analysis The tensile experiments are obviously meaningful to provide valuable information on how the ageing process modifies the molecular structure of the material but such experiments which requires a series of JANNAF samples for each isothermal observation, are material and time consuming. To obtain a more global overview of the material mechanical behaviour on a wide temperature domain using very small samples, it is convenient to turn towards the DMA technique. Though this technique essentially provides informations in term of rigidity, the associated analysis of the dissipation spectrum (the loss tangent) is a powerful tool to yield information in close relation to the molecular structure. Once again the rigidity information is related to the crosslink density while the dissipation level is sensitive to any material structure transition such as glass transition, crystallization processes or any other physical modification on the molecular level. The figure 10 gives a schematic representation of the experimental arrangement and a typical result for an HTPB propellant. displacement sensor Electro-dynamic generator Sample E' glassy modulus tgδ glass soluble fraction transition peak Sample Temperature chamber Load sensor towards equilibrium Figure 10: Schematic Description of the DMA Technique and Typical Results for an HTPB Propellant. The results of figure 10 is the typical response of a strongly viscoelastic material with a rubbery elasticity region (high temperatures) where the material is near thermodynamic equilibrium (low level of the loss tangent and thus no viscoelastic effects). As the temperature is cool down, both the apparent modulus and the loss tangent increase due to viscoelastic friction in molecular movements. It is worth noting that a peak in the loss tangent is observed in the +10 C temperature domain which as been demonstrated to be in closed relation with the solute species behavior (plasticizer and free chains included in the network). RTO-MP
10 The molecular movements of this volume fraction of the polymer network plays an important role in the material macroscopic behaviour and is more precisely suspected to be responsible of the strain capability. This second peak domain is thus seen as a revealing criteria of the material behavior and particular attention is paid to the ageing process impact on this property. As the temperature approaches the glass transition, a net change in the rate of modulus increase is observed combined with the main peak of the loss tangent. This behaviour is typical of a glassy material with a relatively high modulus and once again a low loss tangent characteristic of an elastic material. As an example, figure 11 shows the influence of different temperatures of ageing in dry air on both the real modulus and the loss tangent over a range of temperature from +60 C to -80 C. HTPB Ageing Program - 18 duration Temperature influence in dry air HTPB Ageing Program - 18 duration Temperature influence in dry air 1.E Real Modulus (MPa) 1.E+03 1.E+02 1.E+01 tg δ T= C C C C C C C 1.E température ( C) température ( C) Figure 11: Typical Response of Aged HTPB Propellant to Mechanical Spectroscopy. As could be guessed from the tensile tests experiments, the material shows a global stiffness increase with ageing duration which is amplified by the ageing temperature. It is of principal importance to note that this stiffness increase affects mostly the high temperature domain of the real modulus where the cross-link density and the long range molecular movements of the free portion of the network governs the overall response of the material. On the opposite side of the temperature domain covered by the test, i.e. by the glass transition temperature region, the initial and aged materials tends to have the same modulus but differs by their loss tangent. This is coherent with the existence of a limiting value of the material modulus in this domain where the cross-link density no longer governs the material stiffness. Along with this stiffness information on an extended temperature domain, this simple test provides a useful picture of the material behavior from the analysis of the dissipation spectrum. Obviously it is demonstrated from figure 11 that this mechanical property is strongly affected by the ageing conditions and duration, and as expected the behavior is modified specially in the second peak region. It is observed that the material stiffening is systematically accompanied with a global loss tangent decrease on the whole temperature domain and that clearly appears a displacement of the second peak characteristic temperature. It should be emphasis that this portion of the dissipation spectrum exhibits the behavior of the macromolecules which are not linked to the main network and that a strong correlation is found between the height of the peak and the volume fraction of the solvent extractable species. The drop in this region of the dissipation spectra may thus be interpreted as a material embrittlement consecutive to an excessive amount of cross-linking of the elastomer and loss in the molecular mobility. It is finally to be pointed out that the glass transition temperature is not significantly affected by the ageing process though the height of the peak also shows an important decrease which confirms the material brittleness RTO-MP-091
11 4.0 DISCUSSION The ageing program was completed with attention paid to provide the influence of the each individual ageing parameter on the propellant properties. Figure 12 shows the influence of the ageing temperature in dry conditions for neutral (N 2 )and oxidative (air) atmospheres. E (MPa) strain at failure (%) 60 C dry air 60 C dry Nitrogen 50 C dry air 50 C dry Nitrogen 40 C dry air 40 C dry Nitrogen 20 C dry air 20 C dry Nitrogen Figure 12: Influence of Temperature on Mechanical Properties. The strong hardening of the propellant behavior during ageing is obvious on these figures along with accelerating effect of temperature. It should also be emphasis the lack of influence of the atmosphere oxidative nature which suggests that the oxidative hardening is probably not the only mechanism involved in ageing. In addition, the influence of relative humidity was observed and as an example, for the ambient temperature, figure 13 shows the variation of the mechanical properties during ageing. E (MPa) DRY 35%HR 55%HR 76%HR strain at failure (%) DRY 35%HR 55%HR 76%HR Figure 13: Influence of Relative Humidity at Ambient Temperature. From the analysis of these results, the following comments appeals: the evidence of a quick stabilization of the mechanical properties in relation with the RH content. the hardening in dry conditions can be simply due to the natural drying of the propellant sample. the strong softening under high RH level while the content of water sorption recorded is very low (from 4 to 500ppm). It is suspected that this behaviour may not be explained by a plasticizer effect of the binder with a so low water content but rather by a damage development in the binder-fillers bonding. no significant evolution is noticed in the RH range of 35 to 55% which near the ambient room moisture content. RTO-MP
12 The coupled influence of temperature and humidity during ageing have also been studied. In these experiments, a quick softening of the propellant in relation with the RH concentration is detected before stabilization of the properties at a level dependent of the temperature (figure 14). Once this stabilization period is reached, the propellant hardens. E (MPa) strain at failure (%) 60 C dry 60 C 35%HR 50 C dry 50 C 35%HR 40 C dry 40 C 35%HR 20 C dry 20 C 35%HR Figure 14: Influence of Coupled Temperature-Humidity Ageing Conditions on the Tensile Properties. It is worth noting that the same behavior has been obtained after an ageing duration of 22 at +40 C which suggests the phenomena to be temperature activated. The DMA results, confirms and completes this responses which exhibits an increasing of the propellant stiffness during ageing (the loss tangent is shown on figure 15). Ageing program 22 :+40 C - influence of RH% 0.7 loss tangent Temperature ( C) 6 Rh20% 6 Rh35% 6 Rh55% 22 Rh20% 22 Rh35% 22 Rh55% Initial time Figure 15: Loss Tangent from DMA Results. This evidence of a vanishing of the viscoelastic behaviour suggests that high moisture content and temperature accelerate the increase of the binder cross-link density. This behaviour is well correlated with the measurement of the solvent extractable of the binder (sol fraction Fs shown fig.16) RTO-MP-091
13 Ageing ambiance : Nitrogen - Rh=35% Ageing at +40 C Fs (%) 60 C 50 C 40 C 20 C Fs (%) Nitrogen dry Nitrogen Rh35% Nitrogen Rh55% Figure 16: Volume Fraction of Extractable Species. The soluble fraction (Fs) data shows a slight increase in the first of ageing thus revealing a necessary chains fracture mechanism in the binder which produces extractable molecules. This result is coherent with tensile tests and DMA results which exhibits a softening effect during the same ageing period. Work is in progress to identify the particular mechanism responsible of this soluble production, but, as it is suggested by D.D. Davis [3], the phenomena is likely to be due to the break of binder fillers bonding since the elastomer itself is reputed hydrolysis insensitive. Continuing the ageing duration leads a sol fraction decrease. In this state, the free chains of the polymer have disappeared and is included in the main binder network. Surprisingly, several authors have reported rather a hardening of HTPB propellant during moisture ageing thus no valuable information is available about the chemical process encountered here. On another hand, some authors have suggested that ammonium perchlorate in the presence of moisture is able to produce perchloric acid (HClO4) which acts as a cross-linking agent for the HTPB double bonds [4]. Others suggest that moisture hardening is probably the result of recrystallization of fine particles of ammonium perchlorate [5]. Up to now our observations by electronic microscopy do not correlate this point of view. 5.0 CONCLUSIONS Taking support on previous results issued from a CTPB grains service life simulation program, transposition has been made to HTPB propellant. The support is essentially a methodology which was built up and verified to study the humidity diffusion impact on mechanical and physic and chemical properties of the propellants. The obtained results show a very different feature of the ageing behaviour for HTPB propellant and especially towards humidity influence. As an outstanding result it is found that coupled influence of humidity and temperature produces a hardening effect on the HTPB properties which is observed after a relative softening period. It is suspected that this hardening reveals a sudden acceleration in the binder cross-inking reaction to progressively include the free chain molecules in the main network. Unfortunately, available literature informations does not propose a satisfactory explanation to the observed phenomena and work is of course in progress to identify the chemical mechanism responsible of this concerning situation. 6.0 ACKNOWLEDGEMENTS The authors are grateful to DGA/DSPNuc Service for support of this work. RTO-MP
14 7.0 REFERENCES [1] S.T Chang, S. Han and Bobby Malone: Numerical Analysis of Moisture propagation and Chemical Reaction in a Solid Propellant, 36th AIAA Joint Propulsion Conference July 2000 Huntsville Alabama. [2] NATO Standardization Agreement STANAG 4581, Assessment of Ageing Characteristics of Composite Propellants containing an Inert Binder. [3] D.D. Davis: Use of Dilatation Understanding composite Propellant Aging, 37th AIAA Joint Propulsion Conference 8-11 July 2001 Salt Lake City Utah. [4] Schdelbaur, F.: Report on the Problems Concerning the Determination of the Life of Composite Solid Propellants and Recent Experimental Results, ICT Annual conference Karlsruhe, 1975, pp [5] Simon Torry, Anthony Cunliffe: Humid Ageing of Polybutadiene Based Propellant, ICT Annual conference Karlsruhe, 2001, 25, pp; RTO-MP-091
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