INTERIOR BALLISTIC PRINCIPLE OF HIGH/LOW PRESSURE CHAMBERS IN AUTOMATIC GRENADE LAUNCHERS

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1 XXXX IB08 19th International Syosiu of Ballistics, 7 11 May 001, Interlaken, Switzerland INTERIOR BALLISTIC PRINCIPLE OF HIGH/LOW PRESSURE CHAMBERS IN AUTOMATIC GRENADE LAUNCHERS S. Jaraaz1, D. Micković1, Z. Zivković and R. Ćurcić 1 Faculty of Mechanical Engineering, 7.arta, Belgrade, Yugoslavia Coany Sloboda, Ratka Mitrovića b.b., 3000 Cacak, Yugoslavia Autoatic grenade launchers renew the interest for the interior ballistic rincile of high/low ressure chabers which is alied in the. For the sake of rincile otiisation in the secific autoatic grenade launcher the theoretical and exeriental investigations are carried out. In theoretical odelling secial attention is aid to flow of two-hase ixture of roellant gases and unburned roellant fro the high-ressure chaber to the low-ressure chaber, and to continuation of roellant cobustion in the low-ressure chaber and the launcher barrel. Through exeriental investigations the influence of roellant tye, relation of chaber volues, nuber, diensions, and osition of holes in wall searating chabers, and tye of liner across the holes are studied. All these influences the code based on theoretical considerations siulates correctly. INTRODUCTION Autoatic grenade launchers are the best answer to a very concrete oerational requireents which justify their introduction as an additional weaon tye at coany (or equivalent) level. Current autoatic grenade launchers exhibit technical characteristics linking the to the other area weaons deloyed at the sae echelon level, in articular to achine guns and ortars. When one roerly considers the three basic criteria obility, fireower and self-sustainability according to which infantry cobat units are organised, it becoes evident that each level ust be given the tools to raidly and effectively solve the ost critical situations in which it could find itself, without having to rely on fire suort fro uer levels. Autoatic grenade launchers are intended to solve that roble [1,]. Current autoatic grenade launchers renew the interest for the interior ballistic rincile of high/low ressure chabers which is alied in the. In order to irove ignition of roellant charge and unifority of grenade velocities we alied the interior ballistic rincile of high/low ressure chabers instead of classical one in 30 autoatic grenade launcher. Through theoretical odelling and exeriental investigations we consider influence of different factors on the interior ballistic characteristics of odified concet. 73

2 Interior Ballistics THEORETICAL MODEL Interior Ballistic Cycle The scheatic resentation of interior ballistic cycle in the autoatic grenade launcher using the high/low ressure chabers rincile is given in Fig. 1. Figure 1. The interior ballistic cycle starts with initiation of ignition cu and ignition of roellant charge laced in the high-ressure chaber (see Fig. 1-a). The roellant charge burns in the constant volue of high-ressure chaber until the oent when the roellant gas ressure achieves the value e at which the roellant charge covering and additional liner are enetrated. Then starts flowing out of roellant gases and ignited roellant grains through holes on the searating wall between the high-ressure and low-ressure chabers (see Fig. 1-b). The art of roellant charge burns on high ressure achieved in the high-ressure chaber, and the art of roellant charge which asses through holes continues to burn in the low-ressure chaber. When the ressure in the low-ressure chaber achieves the grenade start value s the grenade starts to ove in the launcher barrel (see Fig. 1-c). During firing the roellant cobustion first ends in the high-ressure chaber. Then through holes flow only roellant gases, and the roellant cobustion in the low-ressure chaber is near the end (see Fig. 1-d). After the end of roellant cobustion the grenade is further accelerated due to roellant gases exansion. Basic syste of equations Using the usual interior ballistic assutions the syste of equations which describes hysical rocesses in the syste with high/low ressure chabers gets the following for: 74

3 Interior Ballistic Princile of High/Low Pressure Chabers in Autoatic Grenade Launchers a) High-ressure chaber equations of roellant burning e w = ; e 0 energy equation n dw a + b = ; dt e 0 = W 0 fi ω 3 1 w + C w C3 w z = C + ωi + f ω( ξ η) ( 1 z ξ) ωα( z η) flow out equations of roellant gases and roellant through holes dη dξ = ; b = 3) dt ω dt ω In revious equations the following sybols are used: ean ballistic ressure in high ressure chaber, ω roellant charge ass, ω i igniter ass, f roellant force, f i igniter force, δ roellant density, W 0 volue of high-ressure chaber, z roellant ass share burned in high-ressure chaber, η roellant gases ass share flowed out through holes, ξ roellant ass share flowed out through holes, α covolue, w relative burnt web of roellant grain, e 0 roellant web, e roellant burned web, t tie, a, b, n burning law constants, C 1, C, C 3 shae coefficient of roellant grain, ass flow rate of roellant gases through holes, roellant ass flow rate through holes. b) Low-ressure chaber equations of roellant burning e n 1 w 1 = dw ; 1 a 1 + b = ; 3 z (4) e 1 = C1 w1 + C w1 + C 3 w 1 0 dt e0 energy equation Vgr f ωξ z1 + f ωη ( κ 1) ϕgr 1 = ωξ( 1 z (5) 1) W1 ωα( η + ξz1) + s X δ equations of grenade oving dvgr dx 1 s = ϕgr ; V (6) dt gr = dt In revious equations is: 1 ean ballistic ressure in low-ressure chaber and launcher barrel, ϕ coefficient of fictitious grenade ass, W 1 volue of low ressure chaber, z 1 roellant ass share burned in low-ressure chaber, κ coefficient of roellant gases adiabatic exansion, gr grenade ass, V gr grenade velocity, s surface of barrel cross-section, X grenade ath in barrel, w 1 relative burned web of roellant grain in low-ressure chaber, e 1 roellant burned web in low-ressure chaber. δ (1) () 75

4 Interior Ballistics For the sake of deterination of ass flow rates of roellant gases and grains ( and ) we consider two-hase flow through holes between chabers. This flow is treated as hoogeneous ixture of gas and solid hase. In that case the ixture adiabatic coefficient is defined by relation: ( 1 ε) c + ε c r 1 ξ z κ = ; ε = 1 ε c + εc 1 ξ η (7) ( ) υ r where: c, c υ secific heats of roellant gases at constant ressure and at constant volue, c r roellant secific heat, ε ass share of solid hase in ixture flowing through holes. c) Characteristic iortant odel relations The flow of hoogeneous ixture through holes in the searation wall between chabers is deterined by relation between ressure in the high-ressure chaber and ressure on the botto of low-ressure chaber. The critical ressure value on the botto of the low-ressure chaber is given by relation: 1 (8) 1,crit + 1 We analyse two cases: 1 0 1,w 1,crit In this case the ass flow rate and flow velocity of ixture through holes are given by exressions: ( ) + 1 = ( ) 1 1 (9) = µ Sh ; Vfi = ( 1 ε)f + 1 ( 1 ε)f + 1 where: S h total surface of holes cross-sections, µ flow out coefficient through hole. 0 1,w 1,crit The ass flow rate of ixture through holes is deterined by relation: + 1 1,w 1,w κ κ κ = µ Sh ( κ )( ) (10) 1 1 ε f ( ) ( ) The flow in velocity of ixture through holes in this case is given by exression: κ 1,w V (11) fi = ( 1 ε) f 1 1 The ass flow rate of roellant gases ( ) and the ass flow rate of roellant grains ( ) are given by following relations: = (1 ε), = ε. In systes with high/low ressure chabers during firing the characteristic ressure rofile is established in the low-ressure chaber and launcher barrel. For deterination of that ressure rofile we use the coon Lagrange assution and the linear velocity flow rofile of two-hase ixture V x = K X + V fi (see Fig. ). ( ) 1 76

5 Interior Ballistic Princile of High/Low Pressure Chabers in Autoatic Grenade Launchers Figure. Through further develoent (detailed develoent is given in [3]) we get the relation between the ressure on grenade base 1,gr and the ean ballistic ressure 1 : 1,gr ρλ V ( = ω 1+ 3ϕ V fi gr 1 V ) fi In the eq. (1) the ass ω' and density ρ λ of two-hase ixture in the sace behind the grenade are given by relations: ω' =ω (η + ξ) ρ λ = ω'/(w 1 + sx). The ressure on the botto of low-ressure chaber 1,w is given by exression: ω ρλ V V fi gr 1,w = 1,gr ( 1+ 1 (13) ϕ ) ( V ) 1 gr fi d) Couter code The syste of equations which describes the interior ballistic cycle of the syste with high/low ressure chabers is coosed of the first order ordinary differential equations and algebraic ones. Solving of the syste of ordinary differential equations by the fourthorder Runge-Kutta ethod is done. For coutation of firing in the autoatic grenade launcher with high/low ressure chabers HILOP code is fored. In Fig. 3 couted ean ressures in high and low ressure chabers, and 1, resectively, as functions of tie t are shown (roellant charge is coosed of.7 g of nitrocellulose roellant NC1). 1 gr (1) 77

6 Interior Ballistics 500 ressure (bar) Figure tie (s) EXPERIMENTAL INVESTIGATIONS AND MODEL VERIFICATION Exeriental investigations erfored in 30 autoatic grenade launcher had two ain goals: otiisation of design and roelling characteristics of concet of high/low ressure chabers, and verification of resented theoretical odel. Through exeriental investigations the influence of roellant tye, relation of chaber volues, nuber, diensions, and osition of holes in wall searating chabers, and tye of liner across the holes are studied. Boundaries of range of studied influence araeters were liited by the existing syste configuration. The influence of roellant tye on basic interior ballistic characteristics is resented in Table 1. Table 1 Proellant charge [bar] 1,w [bar] V 0 [/s].7 g NC1 Exerient Coutation g NG1 Exerient Coutation Rearks: axiu ressure in high-ressure chaber, 1,w axiu ressure on the botto of low-ressure chaber, V 0 grenade uzzle velocity. Data given in Table 1 show good corresondence between exeriental and calculation results. According to ballistic requireents the nitrocellulose roellant NC1 gives better results then the doublebase roellant NG1. All further exeriental investigations are carried out with the roellant NC1. 78

7 The influence of relation of chaber volues on basic ballistic characteristic is given in Table. Data given in Table show good corresondence between exeriental and calculation results. Table Interior Ballistic Princile of High/Low Pressure Chabers in Autoatic Grenade Launchers W 0 /W ,w V 0 [bar] [bar] [/s] Exerient Coutation Exerient Coutation The roellant charge is laced in the celluloid covering. In desire to increase the interior ballistic cycle unifority additional brass liners of different thickness were laced across the holes in the wall searating chabers. Results of this investigations are given in Table 3. Table 3 The rogra HILOP adequately estiates the influence of the roelling charge covering and the additional liner on holes on the wall between chabers. For deterination of influence of nuber and diaeter of holes in the wall between chabers exerients with 6 holes of 3.0 diaeter, 6 holes of 3.3 diaeter and 9 holes of.1 are carried out. Results of this investigation are resented in Table 4. Table 4 Proellant charge Liner 1,w V 0 [bar] [bar] [/s] celluloid Exerient Coutation celluloid + Exerient brass Coutation celluloid + Exerient brass Coutation Holes (nuber x diaeter).7 g NC1 6 x g NC1 6 x g NC1 9 x.1 Data given in Table 4 show good corresondence between exeriental and calculation results. The choice of otial design and roelling characteristics of the syste with high/low ressure chabers deends on the concrete ballistic requireents. [bar] 1,w [bar] V 0 [/s] Exerient Coutation Exerient Coutation Exerient Coutation

8 Interior Ballistics CONCLUSIONS Based on revious considerations we can ake the following conclusions: Autoatic grenade launchers are conteorary systes which alications is actualised last years. In the interior ballistic sense autoatic grenade launchers renew the interest for the concet of high/low ressure chabers. The atheatical odel for syste with high/low ressure chabers is develoed and the couter code HILOP is established. The atheatical odel is verified through coarison with data of exeriental investigations of influence of different factors on interior ballistic characteristics. Exeriental investigations and verified theoretical odel enable otiisation of design and roelling characteristics for the syste with high/low ressure chabers. REFERENCES 1. J. Lenearts, Autoatic Grenade Launchers and their Role, Military Technology, 48 53, No. 10, S. Jaraaz, Between achine guns and ortars ( in Serbian), Reort, 30 31, No. 3, S. Jaraaz, D. Micković, Investigations of autoatic grenade launcher roelling syste otiisation (in Serbian), Technical Reort TR-8/000, Faculty of Mechanical Engineering, Belgrade,