Jtam-A4.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 52, 2, pp. 313-321, Warsaw 2014 ODDITIES IN DETERMINING BURNING RATE ON BASIS OF CLOSED VESSEL TESTS OF SINGLE BASE PROPELLANT Zbigniew K. Leciejewski Military University of Technology, Faculty of Mechatronics and Aerospace, Warsaw, Poland e-mail: zbigniew.leciejewski@wat.edu.pl Theproper determination of parameter values defining the dependence of the burning rate r of smokeless propellant on gas pressures p surrounding the burning grains constitutes one of the goals of experimental pyrostatic (closed vessel) testing. The aim of the hereby paper is the analysis of results of experimental closed vessel tests realized in the context of isolating possible oddities in determining the relation r(p). During the experimental tests, a single base propellantwith grains of different or similar combustible layer thickness e1 was burned while implementing identical or various loading conditions. Identical ignition systems were used in both instances. The results of experimental tests and theoretical analysis performed permit a more complete verification of the assumptions with regard to proper realization of pyrostatic comparative tests and prove additionally that closed vessel tests should be focused in the direction of “dedicated” tests. Keywords: internal ballistics, closed vessel test, smokeless propellant, burning rate law 1. Introduction The burning rate of the smokeless propellant within high-pressure environments (magnitude of tens or hundreds of MPa) within the barrel during firing is one of the significant ballistic characteristics permitting proper theoretical analysis of barrel propellant systems. The mathematical model widely used for purposes of this analysis, within the thermody- namic aspects established by Serebryakov (1949) and Corner (1950), clarified by Baer (1979), Tuomainen (1996) andMilitary Agency for Standardization in STANAG 4367 (2000), does not provide direct correlations between properties of the igniting material and the ignition mecha- nism of propellant grains and the intensity of the formation of propellant gasses released from the propellant being subjected to combustion. In this model, assuming the simultaneous and instantaneous ignition of all grains of the propellant charge, the rate of propellant burning r is (for its standard initial temperature) only a function (linear or exponential) of the gas pressure p surrounding the burning propellant grains. Toobtain a complete picture of the internal ballistic cycle, theburningrate law r to calculate the mass fraction burning rate of the propellant is needed. In the case of geometric, regular shape of propellant grains with smooth unburned surface S1 and unburned volume V1, the mass fraction burning rate (one of the interior ballistics governing equations) may be expressed as dz dt = S1 V1 Φ(z)r(p) (1.1) Accurate knowledge on the form of the propellant burning law r(p) and values of its coeffi- cients (and also form function Φ(z), specific energy and covolume) plays the fundamental role in the determination of the burning rate of propellants and simulation of internal ballistics. The 314 Z.K. Leciejewski proper determination of the parameter values describing the function r(p), by combustion of a specific propellantmass in adiabatic and isochoric conditions, constitutes one of themain goals of experimental pyrostatic (closed vessel) testing. The conditions of realization of such tests do however differ with regard to the process of firing from a real barrel propellant system. The following constitute significant differences: a) combustion of a propellant in pyrostatic testing takes place in closed volume conditions, while duringfiringwithin abarrel propellant system–within thevariable volume resultant fromthemotionof theprojectile,with thepropellantgassesperformingtheworkassociated with propelling the projectile within the barrel; b) the initial loading density within the propellant system (∆ ≈ 1000kg/m3), meaning the ratio of the propellantmass to the initial volume of the cartridge chamber ismuch greater than during the standard pyrostatic testing (∆=100-200kg/m3); c) the propellant ignition system used during pyrostatic testing is not adequate (in terms of, among others, the mass and type of the igniting material) to the ignition system used in real ammunition. The above represents that the values of the r(p) function parameters, obtained by way of the standard pyrostatic testing, must be – within the process of modelling the firing effects – quite often corrected bymeans of adjusting coefficients. The problematic aspects of describing the r(p) function have been the subject of numerous works which analysed both the results of experimental pyrostatic testing using different igni- tion systems as well as theoretical models of the ignition process and propellant combustion. The results of investigation of ignition time and propellant combustion rate after ignition were presented in detail especially by Zel’dovich (1982), Assovskii et al. (1983, 1986) and Eisenrich et al. (2002). The modelling of thermal boundary layer due to igniter material flowing over a propellant surface was presented by Woodley et al. (2007). Some problems connected with the ignition process and unsteady combustion behaviour of smokeless propellants was mentioned and discussed by Khristenko (2001) and Khomenko and Shirokov (2006). The presented above problemwas first discussed inPoland bySmoleński (1979) and examined byTorecki et al. (1997) and Papliński (2002). The author of the hereby article had also joined these efforts by undertaking pyrostatic testing of propellants in non-standard loading conditions and with the use of non-standard ignition systems.The limitations with regard to the application of the linear formof the burning rate r(p) were noted (2007, 2008). It was also shown that such a form, meaning r = r1p, may not be used directly as part of ballistic analysis of propellant systems, especially those making use of fine grain propellants. The results of tests performedbyLeciejewski and Surma (2011) within a conventional closed vessel (CCV) and within a micro closed vessel (MCV) indicated that for a propellant of a specific chemical composition and thickness of the combustible layer e1, when using during the tests identical loading conditions but different ignition systems, it is possible to obtain different values of the r1 coefficient for the linear r(p) function aswell as a different value of the dynamic characteristics of the propellant combustion process (relative quickness, dynamic vivacity). The aim of the hereby paper is the analysis of the results from experimental closed vessel tests of a single base propellant characterized by: a) varied thickness of the combustible layer (used during testing with identical loading con- ditions); b) the same thickness of the combustible layer (while applying varied loading conditions during testing). Oddities in determining burning rate on basis of closed vessel tests... 315 The same ignition systemwas used in both instances. The analysis performed should permit a more complete verification of the assumptions with regard to proper realization of the closed vessel comparative testing in the future. 2. Method and materials The aim of work has been realized on the basis of closed vessel tests carried out inside a conven- tional closed vessel (CCV)with a volume of W0 =200cm 3 andwithin a specialized closed vessel with a membrane safety valve (VCV – Vented Closed Vessel) described and used by Torecki et al. (1997), in which the interruption of the propellant burning takes place after the propellant gases reach a predetermined pressure level. A black powder ballast with a mass of ωign = 2g was placed in a small sack made of a combustible material and used for igniting the propellant being subjected to testing. The ignition of the black powder was initiated by means of a thermal impulse emitted from the igniting head activated by an electrical impulse. During realization of the experiments, both the loading conditions as well as the pressure measuring system met the requirements of the standardization agreement STANAG4115 (1997), used not only for industrial propellant testing but also commonly in the field of scientific tests. The pressure was measured with a HPI 5QP 6000M piezoelectric transducer, whose signal was amplified by TA-3/D amplifier and recorded on a Keithley DAS-50 12-bit analog-to-digital converter at a frequency of 1MHz. The maximum systematic error of the pressure indirect measurement systemwas 1.1%. The subject of these tests constituted a single base propellant which varied mainly only in terms of its combustible layer thickness e1 (half ofweb size). Single-perforation propellant grains were combusted in theCCVchamber,with a single determined loadingdensity (∆=100kg/m3) and the total web size thickness which equalled 0.33mm, 0.37mm and 1.52mm respectively. The average web size dimension of grains – declared by the manufacturer – was verified by direct measurements of groups of 150 granules using NEOPHOT 21metallographic microscope and LUCIA software. Tests of this type have hereinafter been designated as A type tests. The multi-perforation propellant grains with a constant combustible layer were burned in the VCV chamber (Fig. 1), but in the conditions of a broad range of loading densities (∆=75-700kg/m3). Fig. 1.Main parts of Vented ClosedVessel: combustion chamber (in the middle), ignition plug equipped with pressure gauge and blow-off valve Tests of this type have in turn been designated as type B tests. Such an arrangement of the test program enabled evaluation of the influence of the propellant grain burning surface 316 Z.K. Leciejewski (in type A tests) as well as the loading density (in type B tests) on the dynamics of the bur- ning process of the single base propellant, especially in its initial burning stage of the powder grains. 3. Results In Fig. 2, the experimental changes of pressure p in time t, resulting from type A tests during combustion of the propellant with a mass ωp, density ρp and containing N propellant grains with a perforation volume Wh are presented. Fig. 2. Experimental plots of the function p(t) resulting from combustion of the single base propellant with grains of different combustible layer values Significantdifferences in timeare observablebetween the timeof the start of theblackpowder ignition (with energy characteristics: force fbp and co-volume αbp) until the time of the powder gases reaching the established ignition pressure pign resulting from the relation established by Serebryakov (1949) pign = fbpωbp W0− ( ωp ρp −NWh ) −αbpωbp (3.1) The graphs of the rate of change of combustion r(p)were calculated using the below formula r= de dt = de dz dz dp dp dt (3.2) taking as the basis the registered experimental curves p(t), while the method and the relations necessary for calculation of the variability in the thickness of the combustible layerwith a change in the relative mass of propellant burnt (de/dz) as well as variability of the relative mass of the propellant burnt with a change in pressure (dz/dp) were assumed as described by Military Agency for Standardization in STANAG4115 (1997). The r(p) function curves are presented in Fig. 3. From the calculations realized in accordance with relation (3.2) and Fig. 3, it results that the rate of combustion of the tested single base propellant is not identical within the initial combustion stage. Clearly observable are in this stage the differences in the combustion rate depending on the size of the propellant grains. It is possible after this stage to observe levelling of theburningrate values alongwithan increase of gaspressureswithin the combustion chamber. The influence of intensity of the initial burn of propellant grains is also reflected during the determination of the coefficient r1 for the linear form of the relation r(p). Oddities in determining burning rate on basis of closed vessel tests... 317 Fig. 3. The course of variability of the combustion rate r(p) for the single base propellant with grains of different combustible layer thickness values Its value may be established either on the basis of the total Ipt pressure impulse according to the relation below r1 = e1 Ipt = e1 tpmax ∫ tpign p dt (3.3) or on the basis of a limited pressure impulse Ipa−b according to the relation r1 = ea−b Ipa−b = ea−b tb ∫ ta p dt (3.4) Relation (3.3) takes into account the total course of the variability of gas pressurewithin the combustion chamber from the time of propellant ignition (from pign and e=0) until the time of its complete combustion (meaning until pmax and e = e1), while relation (3.4) eliminates from further calculations the period of initial burning (from e = 0 until the moment of the combustion of the layer e = ea) and the afterburning (from the time of combustion of layer e= eb until complete combustion, meaning e= e1) of the propellant grains. The value of the coefficient r1 calculated according to relation (3.3) is presented in Fig. 4a, while those calculated according to relation (3.4) are presented in Fig. 4b. Fig. 4. Values of the coefficient r1 for the single base propellant with grains of varied combustible layer thickness, calculated while taking into account the total pressure impulse: (a) the total pressure impulse – formula (3.3), (b) a limited pressure impulse – formula (3.4) These figures indicate that the values of the coefficient r1 calculated according to relation (3.3) may suggest significant differences in combustion rates of the tested propellant depending 318 Z.K. Leciejewski on the size of the propellant grains (thickness of the combustible layer e1) which definitely contradicts the presentation of the coefficient r1 calculated with the omission of the ignition time and after-burning time. Type B tests permit the comparative analysis of the combustion rate, however only within a limited section of the z parameter. It is not possible for tests realized in such a manner to calculate the values of the coefficient r1 from relation (3.3), in which the entire impulse of the propellant gas pressure is utilized while the possibility of comparing the values r1 calculated according to relation (3.4) is very limited. Tests realized within the VCV chamber do however enable comparative analysis of the propellant burning rate calculated from relation (3.2) within the initial period of its combustion for different loading conditions (loading densities). The diagrams illustrating the rate of change in combustion of the tested propellant in refe- rence to the applied loading densities (75, 225 and 700kg/m3) are presented in Fig. 5. Fig. 5. The change of combustion rate r(p) of the single base propellant (with grains of equal combustible layer e1) depending on the loading densities applied in the tests Distinctly visible are the discrepancies in the designated propellant combustion rate (in the initial stage of combustion) depending on the loading density, while maintaining the same ignition system. 4. Discussion Taking into account the conclusions made by the author in previous papers, the results of tests in closed vessels at high loading densities published by Grune and Hensel (1993) and Wang (1993) as well as the results of tests and calculations realized for purposes of the hereby paper, valid becomes the statement that one of the fundamental assumptions of the geometric combustion model (established by Serebryakov (1949) and Corner (1950) in their fundamental works), which states that in the initial propellant combustion stage the ignition of the propellant is instantaneous and covers the entire accessible burning surface of the grains fails to function. Such a state of affairs may present itself by obtaining from the pyrostatic (closed vessel) tests of different (depending on the loading and ignition conditions) coefficient values of the function r(p) for the same propellant. This further results in: • lack of basis for realization of proper comparative analysis of the propellant burning rate as a characteristic of the material, • necessity of applying corrected values for the coefficients of the function r(p) during ana- lysis of the effectiveness of propellant systems (solving themain problem of internal balli- stics). A well founded basis exists to improve the above mentioned areas by applying a different approach to the conditions for realizing pyrostatic testing. In the case of realizing comparative Oddities in determining burning rate on basis of closed vessel tests... 319 tests of propellants (with the same test sample mass but of different propellant grain geometry or different chemical composition) combusted within a closed chamber of the same volume, establishing the conditions for experimental testing should be preceded by an analysis of the heat exchange conditions between gases of the igniting material (in the case of black powder, also of the hot solid particles) and varied surface of the propellant grains. In accordance with the thermal model of ignition for solids, the decisive factor influencing the ignition of the solid state (propellant grain), is the generation of an appropriate area of temperature on its surface layer. The time for reaching such an area of temperature determined by Taylor et al. (2008) by the relation tign ∼= 1 4 πλpρpcppT 2 pptt 2S2pQ −2 ign (4.1) is a function of the material properties (density ρp, thermal conductivity λp, isobaric specific heat cpp, thermal decomposition temperature Tppt) and time t of the effective action of igniting gases energy Qign on the initial surface Sp of the propellant grains. Inorder to establish theproperconditions for realization ofpyrostatic comparative testswhile taking into account technological difficulties (Cieślak et al., 2011) associatedwithmanufacturing of single base propellant grains of minimal surface coarseness (porosity) as well as repeatable shapes and sizes (pertaining especially to the fine grained single base propellant), relation (4.1) should include the real value of the grain surface area. Attention to this problemwas brought by Leonov (2008) where the relation for the burning rate of the porous single base propellant rpor was presented in the following form rpor = r0 1 1−η0 (1+∆S) (4.2) where r0 is the burning rate of a nonporous single base propellant, η0 – porosity of condensed phase, ∆S – relative increase in the burning surface due to combustion in the pores. The obtaining of proper values of the coefficients of the function r(p) permitting direct application into simulation of propellant systems operation (without the requirement of correc- tive verification on the basis of realistic firing results) requires realization of pyrostatic tests, in which the possibility exists for application of loading and ignition system conditions similar to a real propellant system. Such possibilitiesmay be provided by specializedMCVandVCV type manometric chambers. It seems that all propellant grains are probably ignited uniformly, with all exposed surface areas of the grains performed by a gaseous ignition system presented by Jeunieau et al. (2002). The ignitionmixture (for exampleCH4-02) allows one to treat the ignition process of the propel- lant according to the geometrical model of propellant ignition and, additionally, to discriminate the combustion properties of two parts of the particles (in deterred propellants). 5. Conclusion The experimental pyrostatic (closed vessel) tests still remain the fundamentalmethod for deter- mining the formof the function r(p) and thevalueof its coefficients.Theconditions of realization of such tests however, especially the method of ignition, should evolve in such a direction as to obtain more credible experimental data. The current approach to the issue of ignition during pyrostatic testing (established ignition mass and loading density) results in the fact that: • in comparative tests of propellants with different chemical compositions or grain shape and size, the comparability of heat exchange conditions is entirely omitted, 320 Z.K. Leciejewski • in identifying tests, realized for the purpos of propellant systems simulation, no possibility is being considered for the application of igniting systems found in real munitions. The results of the experimental tests and theoretical analysis aswell as literature information indicate that closed vessel tests should progress in the direction of “dedicated” tests, that is towards comparative tests where the ignition should take into account the principles of heat exchange, while the identification tests should incorporate the ignition systems similar to those found in real-life propellant systems. The specialized closed vessels ofMCV andVCV typemay prove a very useful tool in this aspect. Acknowledgements The author gratefully acknowledges the assistance of Mr Zbigniew Surma, Ballistics Laboratory of Military University of Technology inWarsaw in providing the measurement data presented here. References 1. Assovskii I.G., Zakirov Z.G., Leipunskii O.I., 1983, Effect of ignition on fuel combustion, Combustion, Explosion, Shock Waves, 19, 1, 37-42 2. Assovskii I.G., Zakirov Z.G., Leipunskii O.I., 1986, Ignition and combustion of propellant in a radiating gas flow,Combustion, Explosion, Shock Waves, 22, 6, 658-663 3. Baer P.G., 1979, Practical interior ballistic analysis of guns,Progress in Astronautics and Aero- nautics, AIAA, 66, 37-66 4. CieślakK.,OstaszewskiD.,KsiążczakA., 2011,Analysis of the structureof seven-perforation propellant grain for medium-calibre ammunition and single-perforation for small-calibre ammuni- tion (in Polish), Proceedings of 18th International Conference on Development Production and Maintenance of Weapons Systems, Pułtusk, Poland, 439-445 5. Corner J., 1950,Theory of the Interior Ballistics of Guns, JohnWiley & Sons, Inc., NewYork 6. EisenrichN., FischerT.S., LangerG.,KelzenbergS.,WeiserV., 2002,Burn ratemodels for gun propellants,Propellants, Explosion, Pyrotechnics, 27, 3, 142-149 7. Grune D., Hensel D., 1993, Burning behavior of high energy solid propellants in closed vessels at high loading densities, Proceedings of the 14th International Symposium on Ballistics, Quebec, Canada, 223-229 8. Jeunieau L., Lefebvre M.H., Papy A., Pirlot M.C., Guillaume P., Reynaud Ch., 2002, Closed vessel test: influence of the ignition method on the combustion rate, 33rd International Annual Confernce of ICT, Karlsruhe, Germany 9. Khomenko Yu. P., Shirokov V.M., 2006, Determining the unsteady combustion behaviour of propellants from results of closed-bomb testing, Combustion, Explosion, Shock Waves, 42, 2, 149-157 10. KhristenkoYu.F., 2001,Experimentalmethods for studying the combustionof granularpowder in a broad range of process parameters,Combustion, Explosion, Shock Waves, 27, 1, 72-77 11. Leciejewski Z.K., 2007,Singularities of burning rate determination of fine-grained propellants, Proceedings of 23rd International Symposium on Ballistics, Tarragona, Spain, Vol. I, 369-376 12. Leciejewski Z.K., 2008a, Criticism of linear form of burning rate law with reference to co- nventional fine-grained propellants, Proceedings of the 7th International Armament Conference SAAT’2008, Pułtusk, Poland, 191-200 13. Leciejewski Z.K., 2008b, Experimental study of possibilities for employment of linear form of burning rate law to characterise the burning process of fine-grained propellants,Central European Journal of Energetic Materials, 5, 1, 45-61 Oddities in determining burning rate on basis of closed vessel tests... 321 14. Leciejewski Z.K., Surma Z., 2011, Effect of application of various ignition conditions in closed vessel tests on burning rate calculation of a fine-grained propellant, Combustion, Explosion and Shock Waves, 47, 2, 209-216 15. Leonov G.N., 2008, Some aspects of the effect of the porosity of the condensed phase on the combustion of nitrocellulose propellants,Combustion, Explosion, Shock Waves, 44, 5, 547-551 16. Papliński A., 2002, Numerical analysis of initiation of transient combustion process in granu- lar beds of propellant, Proceedings of the 4th International Armament Conference SAAT’2002, Waplewo, Poland, 87 17. Serebryakov M., 1949, Internal Ballistics (in Russian), Oborongiz,Moscow 18. Smoleński D., 1979,Combustion of Explosives (in Polish), MoD,Warsaw 19. STANAG 4115 LAND (Ed. 2), 1997,Definition and Determination of Ballistic Properties of Gun Propellants, Military Agency for Standardization, Brussels 20. STANAG 4367 LAND (Ed. 2), 2000, Thermodynamic Interior Ballistic Model with Global Para- meters, Military Agency for Standardization, Brussels 21. Taylor M.J., Woodley C.R., Fuller S.R., Gilbert S., Gransden J.I., 2008, Considera- tion of the ignition delay of gun propellants,Proceedings of the 24th International Symposium on Ballistics, NewOrleans, USA, Vol. I, 59-66 22. Torecki S., Leciejewski Z.K., Surma Z., Ciepielski S.,Wójcik R., 1999, Complex investi- gation of thermodynamic properties of propellant gases and real burning rate of propellants and revision of internal ballistic formulas,ReportNo.OT00A00811,MilitaryUniversity ofTechnology, Warsaw 23. TuomainenA.H., 1996,The thermodynamicmodel of interiorballistics,Thesis, ActaPolytechnica Scandinavica, Applied Physics Series, 205, University of Helsinki 24. Wang G., 1993, Experimental research on porous propellant with high burning rate,Proceedings of the 14th International Symposium on Ballistics, Quebec, Canada, 399-405 25. WoodleyC., Taylor M., Wheal H., 2007, Boundary layermodelling of the heat transfer pro- cess fromigniters to energeticmaterials,Proceedings of 23rd International SymposiumonBallistics, Tarragona, Spain, Vol. I, 295-302 26. Zel’dovichYa.B., 1982,Theory of Combustion of Propellant andExplosives (inRussian),Nauka, Moscow Manuscript received July 19, 2013; accepted for print September 17, 2013