Studies of rheological properties of suspension of heterogeneous rocket propellant based on HTPB rubber

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1 Studies of rheological properties of suspension of heterogeneous rocket propellant based on HTPB rubber Bogdan FLORCZAK Institute of Industrial Organic Chemistry, Warsaw, Poland; Ewelina BEDNARCZYK, Andrzej MARANDA Military University of Technology, Warsaw, Poland Please cite as: CHEMIK 2015, 69, 3, Introduction The initial stage of the technological process of manufacture of solid heterogeneous rocket propellants involves a mixture of liquid and solid chemical substances of semi-solid consistency, which as a result of mixing in specific time and defined temperature becomes dense liquid mass that can be classified as a highly-filled suspension of non- Newtonian fluid properties. Viscosity of such a suspension depends on a number of factors including time, temperature and shear rate. This means that under given experimental conditions only its apparent viscosity ( ) can be determined. This property depends on liquid phase viscosity (η c ) and structural viscosity (η s ) [1]. + η s (1) η s (Φ) [2.5Φ+ 10.5Φ 2 + exp(a+ bφ)] (2) η s (Φ) KΦ/(1/Φ 1/Φ m ) (3) which gives: [1+ 2.5Φ Φ 2 + exp(a+ bφ)] (4) [1+ KΦ/(1/Φ -1/Φ m )] (5) Φ relative volume fraction of solid phase in suspension Φ m maximum relative volume fraction of solid phase in suspension a, b, K constants determined experimentally. The most important factors affecting rheological properties of rocket propeller suspension are following: time, temperature and shear rate. Dependence of shear stress on shear rate is usually described by means of Ostwald-de Vaele rheological model in the form of power law [2]: τ = kd n (6) τ shear stress, N/m 2 k constistency coefficient n flow index D shear rate, 1/s. Consistency coefficient in the formula (6) is a measure of apparent viscosity, while flow index is a dimensionless parameter that is a measure of fluid deviation from non-newtonian fluid. In order to describe rheological properties of the rocket propeller suspension, the following formula is used [2]: η = kr n (7) η viscosity, mpa s k constistency multiplier n flow index R rotational speed, rpm and formula [3]: η(t)= η 0 e kηt (8) η viscosity, mpas η 0 viscosity for t = 0, mpas t time, s k η rate coefficent for viscosity increase (consistency multiplier). Relationship between viscosity and rotational speed in model representing viscosity change (η) with time (t) can be obtained by measurement of propellant suspension viscosity as a function of time [3]. Relationship of viscosity change versus time and temperature can be described using the following formula [4]: lnη(t, T) = lna(t)+ b(t)t (9) where a, b constants determined experimentally. Slope b(t) and lna(t) change linearly with the inverse of temperature (1/T), i.e. lna(t) = m a /T+ c a and b(t) = m b /T+ c b (m a, m b and c a and c b are slopes and free terms of these functions, respectively) [4]. Substitution of the formulas of these functions in the equation (9) gives: lnη(t,t) = m a /T+ c a + (m b /T+ c b )t (10) Differentiation of the equation (10) with respect to time and temperature gives, respectively: (11) (12) The presented relationships (11), (12) allow determination of temperature at which viscosity does not change (by maintaining this suspension temperature cross-linking reaction is stopped, which increases the life-time of the suspension). and (13) (14) Corresponding author: Bogdan FLORCZAK Ph.D., Eng., Associate Professor, florczak@ipo.waw.pl as well as time after which suspension loses its usefulness for processing: nr 3/2015 tom

2 and then: (15) (16) Based on the experimental data from viscosity measurements of rocket propellant suspension one can determine also its thermodynamic parameters, i.e. activation energy (E a ), entropy ( S η ), enthalpy ( H η ) and free enthalpy ( G η ) from Arrhenius and Eyring equations [4]: (17) Preparation of propellant suspension Initial semi-liquid propellant mass without curing agent DDI was produced in ZPS GAMRAT Sp. z o. o. Such a prepared mass was dosed into NETZSCH planetary mixer (Fig. 1) of 0.5 dm 3 capacity. After introducing appropriate amount of DDI (ratio of equivalent weights for HTPB and cross-linking agent DDI was 0.9), the mass was mixed subsequently for 30 min. under atmospheric pressure and for 30 min. under reduced pressure. The propellant suspension obtained in such a manner was poured in vacuo (Fig. 1) into the viscosity measurement vessel of approx. 115 cm 3 capacity. (18) T- temperature, K -1 R universal gas constant, J mol-1 K k reaction rate constant h Avogadro constant, 6.02x10 23 N Planck constant, 6.62x10 34 S η entropy, J/K H η activation enthalpy, J. The values of enthalpy and entropy can be calculated from curve slope and free term of equation (18), respectively, while free enthalpy can be determined using the following relationship: G η = H η - T S η (19) Experimental part The propellant of the following compositions was studied (Tab. 1). Composition of rocket propellant suspension Table 1 Component Content, % Fig. 1. Station for propellant pouring under reduced pressure (on the left) and NETZSCH mixer (on the right) (equipment of the Institute of Industrial Organic Chemistry in Warsaw) Preparation of cross-linking systems For the measurements of viscosity of studied rocket propellant suspensions new generation Brookfield DV-II + Pro Viscometer with T-D spindle and TC-550 thermostat (Fig. 2) were used. The viscometer is a rotational measuring instrument and the measurement is performed by rotation of a measuring tip (spindle) immersed in suspension (Fig. 2). The spindle is coupled with calibrated spring. Drag force resulting from the viscosity of studied material retards the rotating spindle and causes deformation of the spring, which is measured electronically. Ammonium chlorate(vii) 70.0 Aluminum dust 15.0 BEFP 0.2 Liquid components (HTPB R45M + DDI + DOA) + additives 14.8 The propellant suspension was prepared using rubber R45M (manufacturer IPI), as well as the following substances: dioctyl adipate (DOA) (manufacturer Boryszew Erg S.A.) as a plasticizer, ρ= g/cm 3, boiling point: 690 K, acid value: mg KOH/g, volatile substance content at 373 K of not more than 0.08%, water content of not more than 0.05%, 2-heptyl-3,4-bis(9- isocyanatononyl)-1-pentylcyclohexane (DDI) (manufacturer IPI) as a curing agent, % NCO = 13.79, 2,2 -bis(ethylferrocenyl) propane (BEFP) (manufacturer Neo Organics) Fe content approx. 23%, H 2 O content 0.03%, insolubility in chloroform below 0.02%, ammonium chlorate(vii) (manufacturer IPI), above 0.4 mm 2%, above 0.25 mm 38%, above mm 55%, above mm 3%, below mm 2%, aluminum dust (manufacturer Benda Lutz), D 10 = 3.14 μm, D 50 = 6.30 μm, D 90 = μm. Fig. 2. Equipment for viscosity measurement Viscometer was mounted on Helipath drive. The viscometer with appropriately mounted T-shaped measuring spindle, thanks to such a solution, can be slowly lowered and lifted during the measurement. This allows spindle motion (while maintaining its rotation) along a spiral path inside the studied sample (Fig. 3). This eliminates the error related to the formation of a kind of channel along the spindle [6]. The sample of studied propellant suspension was placed in the teflon measuring vessel of 115 cm 3 capacity (height 70 mm, diameter 142 nr 3/2015 tom 69

3 46 mm) placed in a smaller thermostat equipped with temperature sensor. The smaller thermostat was connected to a bigger one using silicone hoses. The measurements were carried out with Brookfield s Rheocalc software and T-D measuring spindle. The Helipath drive was lifting and lowering viscometer with speed of 2.6 cm/min. Initially, the measuring spindle was immersed in the propellant suspension at depth of 8 mm. The studies of rheological properties of the rocket propellant suspension involved recording value of viscosity as a function of time and rotational speed of the spindle at the following temperatures: 313 K, 318 K, 323 K, 328 K, 333 K and 338 K. Moreover, average values of viscosity were determined for each thirty-minute measurement period (15 th minute of each thirty-minute measurement period). They are presented in Figure 5, while values of constants η 0 are shown in Table 3. Table 3 Values of η 0 versus temperature of the studied propellant T, K η 0, mpas k η, h-1 R Fig. 3. Scheme of spindle motion during the measurement using Helipath drive [6] Determination of cross-linking reaction rate constant The viscosity of propellant suspension during cross-linking was measured at equal time intervals at six different temperatures (313 K, 318 K, 323 K, 328 K, 333 K and 338 K) with spindle rotational speed of 4 rpm. Experimental data was approximated by exponential function (8) η(t) = η 0 e kηt by means of least square method with determination of constants η 0. Relation viscosity vs time for different temperatures is presented in Figure 4, while values of constants are shown in Table 2. Fig. 5. Graph of averaged viscosity change versus time Determination of thermodynamic parameters The value of activation energy (E a ) was determined from Arrhenius equation (15), which describes relationship of reaction rate and temperature. The activation energy was determined from the curve slope of the relationship ln k η = f(1/t) presented in Figure 6. Fig. 4. Graph of relation viscosity (η) vs time (t) Table 2 Values of η 0 as a function of temperature of the studied propellant T, K η 0, mpas k η, h -1 R Fig. 6. Graph of functions ln k η = f(1/t) and ln k ηav = f(1/t) The value of enthalpy ( H η ) and entropy ( S η ) of the crosslinking of rocket propellant was determined using Eyring formula (16) based on slope and free term of the curve representing fuction ln k η /T= f(1/t) (Fig. 7), respectively. Using the equation (17) the values of free enthalpy at measurement temperatures were determined. The values of determined thermodynamic parameters are presented in Tables 4 and 5. nr 3/2015 tom

4 Fig. 7. Graph of linear functions ln k η /T= f(1/t) and ln k ηav /T= f(1/t) Values of determined thermodynamic parameters Table 4 Table 6 Values of lna, b and coefficient R 2 for η T, K ln a B R 2 ln a b R E a, kj/mol H η, kj/mol S η, J/(K mol) for η 36,15 ±4,84 33,44 ±4,83-158,92 ±14,84 37,11 ±4,03 34,41 ±4,02-155,44 ±12,37 Values of free enthalpy Table 5 T, K G for η, kj/mol G, kj/mol Determination of cross-linking inhibition and maximum technological usefulness time Based on the slope and free term of curve lnη = f(t) obtained after logarithmization of the equation (8), the values of lna = lnη 0 b = k η were determined. The presented relations (Fig. 8) of these parameters and temperature lna = f(1/t) and b = f(1/t) allowed determination of the following coefficients m a, m b, c a and c b. Table 7 Values of coefficient and cross-linking inhibition temperature, as well as maximum time of technological usefulness m a c a m b c b T, K t, h for η Effect of shear rate on the viscosity of rocket propellant suspension Measurements aiming to verify if the propellant suspension has thixotropic or anti-thixotropic properties were also carried out. To this end, relationship of viscosity vs spindle rotation speed changing in range of rpm, with 0.5 rpm step, was studied. The results of measurements are presented in Figures Fig. 9. Graph of η changes as a function of increase and decrease in R at T = 313 K Fig. 8. Graphs showing linear relationship lna and b vs inverse temperature (x = 1/T) Substitution of numerical values corresponding to m a and m b gives the value of time t=4.4 h, while for the average viscosity this gives a result of t=4.6 h. After this time the viscosity increases rapidly and the suspension is no longer useful for processing. By proceeding in a similar manner, substitutions of values m b and c b in equation (14) give the value of temperature T = 303 K, while for the averaged viscosity it is T=302.5 K. This is a temperature at which cross-linking reaction in propellant is inhibited. The detailed calculated values are presented in Tables 6 and 7. Fig. 10. Graph of η changes as a function of increase and decrease in R at T = 318 K 144 nr 3/2015 tom 69

5 Fig. 11. Graph of η changes as a function of increase and decrease in R at T = 323 K Fig. 12. Graph of η changes as a function of increase and decrease in R at T = 328 K cross-linking reaction for the studied propellant suspension in 36 kj/mol. The calculated positive value of free enthalpy ( G η ) at all temperatures of measurements proves that the cross-linking reaction cannot proceed spontaneously. While the positive value of enthalpy confirm the endothermic nature of cross-linking reaction. Moreover, the measurements allowed also calculation of the temperature at which the reaction is effectively inhibited, so the life-time of such a propellant suspension can be prolonged. The measurements allowed also to determine the time after rapid increase of viscosity is observed and the suspension stops being technologically useful. Conclusions The study leads to the following conclusions: 1. The cross-linking reaction of the studied rocket propellant suspension is weakly time-dependent. This is shown by the low values of reaction rate constants (k η ), which vary in range from h -1 up to h -1, depending on temperature. 2. The technological time limit for processing of propellant suspension determined based on experimental data is quite long (t = 4.4 h), which indicates its good technological usefulness. 3. Experimental data was also used to determine temperature, at which curing of the propellant is almost inhibited is equal to approx. 303 K. This value compared with the literature value T = 264 K [4] is preferable. Research project funded from science funds for the years as a development project. Fig. 13. Graph of η changes as a function of increase and decrease in R at T = 333 K Fig. 14. Graph of η changes as a function of increase and decrease in R at T = 338 K The hysteresis loops recorded during the measurement indicate that the studied propellant suspension shows thixotropic properties. The graphs showing relationship viscosity vs time prove that as the temperature increases the suspension viscosity decreases for a given time interval. Moreover, the increase in the value of this viscosity with time is observed, which shows the progress of cross-linking reaction in rocket propellant. The reaction rate constants calculated using experimental results are increasing with temperature. This shows the obvious dependence of this reaction on temperature. The constants determined for averaged viscosity and ones obtained directly from experimental results show small differences. Based on the conducted measurement, the values of the following thermodynamic parameters were determined: activation, enthalpy, entropy and free enthalpy. The obtained activation energy value for Literature 1. Florczak B., Stokowski P., Maranda A.: Badania właściwości wytypowanych lepiszczy stałych paliw rakietowych niejednorodnych. Przemysł Chemiczny 2013, 92, 6, Brookfield DV-II+ Pro Viscometer. Manual, com/download/files/dv2pro_manual.pdf ( ). 3. Mahanta A. K., Goyal M., Pathak D. D.: Empirical modeling of chemoviscosity of hydroxy terminated polybutadiene based solid composite propellant slurry. Malaysian Polymer Journal, 2010, 5, 1, Mahanta A. K., Goyal M., Pathak D. D.: Rheokinetic analysis of hydroxy terminated polybutadiene based solid propellant slurry. E-Journal of Chemistry, 2010, 7, 1, Muthiah R. M., Manjari R., Krishnamurthy V. N., Gupta B. R.: Rheology of HTPB propellant: effect of mixing speed and mixing time. Defence Science Journal, 1993, 43, 2, Viscosity, texture, powder, Labo Plus Sp. z o.o., 2012, pl/ ( ). Bogdan FLORCZAK Ph.D., Eng., Associate Professor of the Institute of Industrial Organic Chemistry has graduated from the Faculty of Chemistry and Technical Physics of the Military University of Technology (1976). He has obtained his Ph.D. from the Faculty of Chemistry and Technical Physics of the Military University of Technology (1990). Currently he works at the Institute of Industrial Organic Chemistry. Scientific interests: chemistry and technology of energetic materials, especially solid rocket propellants; materials science and engineering. He has authored or co-authored 70 papers in scientific and technical journals, as well as 60 oral presentations and posters at national and international conferences. He has co-authored 26 patents and 9 patent applications. florczak@ipo.waw.pl, phone: Ewelina BEDNARCZYK - has completed (2014) full-time B.Sc. course at the Faculty of Advanced Technologies and Chemistry of the Military University of Technology with specialization in dangerous materials and chemical rescue. Currently she is a student of the M.Sc. course at the aforementioned faculty. Andrzej MARANDA Professor (Sc.D., Eng) is a graduate of the Faculty of Chemistry, Warsaw University of Technology (1971). Currently, he works for the Military University of Technology and the Institute of Industrial Organic Chemistry. Research interests: chemistry, technology and the use of explosives, protection of the environment. He is the author of 5 monographs, 20 patents, over 500 articles, papers and posters at national and international conferences. amaranda@wat.edu.pl, phone: nr 3/2015 tom