Modelling of pressure gradient in the space behind the projectile

Transcription

1 Moelling of reure graient in the ace behin the rojectile Luěk JEDLIČKA, Stanilav BEER, Mirolav VÍDEŇKA Deartment of weaon an ammunition Univerity of Defence Kounicova 65, BRNO 5 Czech Reublic Abtract: -The article eal with moelling of reure itribution of roellant gae in the ace behin the rojectile of orinary ballitic ytem. The number of exiting moel ecribing the reure graient i analyze an confronte with reult of exerimental firing carrie out on the high erformance anti-aircraft cannon of calibre of 30 mm. Key-Wor: - ballitic, interior ballitic, reure graient, rojectile bae reure, breech reure Introuction During the movement of a rojectile inie a barrel i create a reure graient between the barrel breech an the rojectile bae ue to the ifference in velocitie of roellant gae at the breech an the rojectile bae, Fig.. Thi reure graient belong among factor that ignificantly affect not only interior ballitic calculation but alo the eign of rojectile. The reure graient i uually characterize by the ratio of the breech reure an the rojectile bae reure. Moel of reure graient From above mentione literature four the mot wierea moel ecribing the reure graient in the ace behin a rojectile were choen an were marke for nee of thi article a Moel 4. The fifth reure itribution moel i ue in the interior ballitic moel ecribe in [3] an wa marke a moel STANAG Generally, it can be ai, that baic element of all analye moel of reure graient i the ratio, ma of roellant charge, m q ma of the rojectile. m q. Moel Thi moel i etermine for ballitic ytem with a cylinrical cartrige chamber of the ame area of cro-ection a area of cro-ection of barrel, Fig.. Fig. Preure graient in the ace behin a rojectile... ballitic reure, v... velocity of rojectile, l... rojectile trajectory The literature [], [7] contain number of moel ecribing the reure graient but without any comarion with exerimental reult. Mot of the moel are relatively ol an were create for ballitic ytem of lower erformance, e.g. howitzer. There i not any tuy analying the uitability of thee moel for moern meium calibre an high erformance ballitic ytem that till atify the conition / m q <. Fig. Schema of cylinrical cartrige chamber (l kom = l 0 ) l kom length of cartrige chamber, l 0 length of initial combution volume In thi moel i the ratio of breech reure to the rojectile bae reure exree a ISSN: ISBN:

2 = +, () ϕ m... breech reure,... rojectile bae reure,... ma of roellant charge, m q... ma of rojectile, φ... loe coefficient (uually between.0 (howitzer an cannon) an. (mall arm.05.), [7], [8]). In thi moel the ratio / trongly een only on ratio / m q an remain contant uring the rojectile movement inie the barrel, i.e. the ratio i ineenent of the rojectile trajectory. The eenency for common extent of value / m q i hown in Fig. 3. Ratio of reure / [] Ratio / m q [] Fig. 3 Deenency of / on ratio / m q φ =. From the Fig. 3 i clearly een that accoring to the Moel i the reure ratio / irectly roortional to the ratio / m q.. Moel A real cartrige chamber ha uually bigger iameter than the iameter of the barrel. Thi moel i bae on the Moel an extene by an effect of cartrige chamber hae. The effect of the cartrige chamber hae i ecribe by the coefficient of cartrige l0 chamber hae χ =, Fig. 4. l kom q Fig. 4 Schema of real cartrige chamber (l kom l 0 ) The ratio of breech reure to the rojectile bae reure i, in thi moel, ecribe by following emirical relation k = +, () ϕ m χ q χ... coefficient of cartrige chamber hae, k... exonent (recommene value 0.3,[]). For calculation of exemlary coure of / were choen tyical extent of ratio / m q from 0. to.0, exonent k = 0.3 accoring to recommenation from literature, an coefficient φ =.. The obtaine eenencie of / are hown in Fig. 5. Preure ratio / [] / m q = 0. / m q = 0.8 / m q = Cartrige chamber hae coefficient χ [] Fig. 5 Deenency of / on cartrige chamber hae coefficient χ φ =., k = 0.3 The ratio / i again ineenent of the rojectile trajectory an remain contant uring the rojectile movement inie the barrel. Generally, the ratio / ecreae with increaing cartrige chamber hae coefficient χ an with ecreaing ratio / m q. Further the figure how that there are, accoring to thi moel, certain combination of cartrige chamber hae coefficient χ an ratio / m q that give / ISSN: ISBN:

3 maller than ; in other wor the breech reure woul be lower than the rojectile bae one. Thi fact i, in cae of claical ballitic ytem atifying the conition / m q <, unexlainable..3 Moel 3 The Moel 3 i alo bae on the Moel. Thi time the Moel i extene not only by the effect of the hae of cartrige cae chamber χ but alo by the effect of increaing volume of the ace behin the rojectile exree by the rojectile trajectory l an the reure graient i written a = + χ ϕ m q l χ + c0... cro-ectional area of barrel, c 0... initial volume of cartrige chamber. 3, (3) The ratio / wa calculate again for tyical value an i hown in Fig. 6. From the figure i clearly een that / increae with the trajectory of the rojectile an alo with ratio / m q. The increae of / i the teeet in the beginning of rojectile movement an later become nearly contant. Preure ratio / [] / m q = / m q = 0.8 / m q = Fig. 6 Deenency of / on rojectile trajectory φ =., c 0 / = 0.4, χ =.75.4 Moel 4 A a lat of the mot ue moel of the reure graient in the ace behin the rojectile that take into account excet an m q, alo χ an relative rojectile trajectory Λ. The ratio / i given by following relation χ = + (4) ϕ m q ( +Λ) l Λ=. c 0 For calculation wa again choen the tyical extent of ratio / m q from 0. to.0. The obtaine eenencie are hown in Fig. 7. The figure how that / increae with the trajectory of the rojectile an alo with ratio / m q. The increae of / i again the teeet at the beginning of rojectile movement. Preure ratio / [] / m q = / m q = 0.8 / m q = Fig. 7 Deenency of / on rojectile trajectory φ =., c 0 / = 0.4, χ =.75.5 Moel STANAG 4367 In the Moel STANAG 4367 that i a art of the interior ballitic moel ecribe in [3] i the ratio / given by the following relation R g = +, (5) m q R... reitance reure againt rojectile motion, g... reure of gae ahea of rojectile. It can be een that the ratio / een not only on an m q but alo on ratio R / an /. All variable, with excetion of an m q, are time eenent, an o the ratio / i not contant uring ISSN: ISBN:

4 rojectile movement inie the barrel. Tyical coure of ratio / on rojectile trajectory i hown in Fig. 8. reure wa rea when the rojectile ae the iniviual reure gauge. For the exeriment the ballitic teting weaon of caliber of 30 mm bae on anti-aircraft gun 30 mm PLDvK M 53 wa ue. For the tet firing wa ue ractice ammunition 30 mm JNhSv, v 0 = 000 m. -. The chema of ue ballitic barrel with oition of iezoelectric reure gauge i hown in Fig. 9. Fig. 8 Deenency of / on rojectile trajectory All reviouly analyze moel were ue for calculation of ratio / for a ballitic ytem of calibre of 30 mm that wa later alo ue for exeriment. It ballitic characteritic were = 0.85, m q = kg, χ =.9, φ =.03, c 0 =.39e-4 m 3, = 7.364e-4 m. Obtaine theoretical reult are ummarize in Table. Ditance of iniviual reure gauge from back of barrel are hown in Fig. 9. Fig. 9 Schema of ballitic barrel with oition of reure gauge Examle of meaure reure on all reure gauge i hown in Fig Gauge No. Gauge No. Gauge No. 3 Gauge No. 4 Gauge No. 5 Gauge No. 6 Table Reult of calculation of / from iniviual moel Gauge No Moel Moel Preure [MPa] Moel Moel Moel STANAG Exeriment For the valiation of all reviouly mentione moel of the reure graient in the ace behin the rojectile it i neceary to know the breech reure an the rojectile bae reure. The exeriment wa focue on the meaurement of the reure of roellant gae at the breech an at the bae of the rojectile. The meaurement of the rojectile bae reure wa realize by mean of five iezoelectric reure gauge lace along the barrel, Fig. 9. The rojectile bae Time [] Fig. 0 Examle of meaure reure 4 Reult of exeriment their analyi From obtaine exerimental ata were etermine reure at iniviual gauge (Gauge No. - 6) at intant of rojectile arrival an their correoning breech reure (Gauge No. ). The evaluate value of both reure together with correoning reure ratio / are ummarize in Table. ISSN: ISBN:

5 Table Reult of exerimental firing Gauge No [MPa] [MPa] / [] Calculate an exerimentally obtaine ratio / are comare in Fig.. At exerimentally obtaine ratio / are alo hown their correoning tanar eviation. Preure ratio / [] Exeriment Moel Moel Moel 3 Moel 4 Moel STANAG Fig. Comarion of exerimental an calculate / From comarion of reult of calculation an exerimentally obtaine / follow that the reult of calculation are in goo agreement with exeriment ata, eecially in the mile art of the barrel. The only excetion i the Moel whoe reult o not agree neither with reult of exeriment nor with reult of other moel. Thi iagreement i caue by inaroriate value of the exonent k. From the comarion can be further een that at the beginning of rojectile motion an near the muzzle i the ifference between reult of calculation an exeriment more ignificant. Common iavantage of all the analye moel i the fact that none of them take into account the leakage of roellant gae. In other wor, ue to wear of the riving ban i change the contact reure between the riving ban an the barrel wall. The Moel require more uitable value of the exonent k to get into better agreement with exerimental reult. Reference: [] SEREBRJAKOV, M. E. Interior ballitic. n Eition. Mokva: Oborongiz, 949. [] VENTCEL, D. A. Interior ballitic. Praha: Státní naklaateltví technické literatury, 953. [3] STANAG 4367 Interior ballitic moel with global arameter. [4] Interior ballitic of gun. eitor KRIER, H. New York: American intitute of aeronautic an atronautic, 979. ISBN [5] Gun roulion technology. eitor STIEFEL, L. Wahington DC: American intitute of aeronautic an atronautic, 988. ISBN [6] Textbook of ballitic an gunnery. eitor LONGDON, L. W., Lonon: Her Majety' tationery office, 987. [7] PLÍHAL, B., JEDLIČKA, L. Ue of hyroynamic rincile in thermoynamic interior ballitic moel. [Textbook]. Brno: Military acaemy in Brno, 003. [8] PLÍHAL, B., BEER, S., JEDLIČKA, L. Interior ballitic of barrel weaon. [Textbook]. t Eition. Brno: Univerity of Defence, ISBN [9] GUBAREV, A., VILJUNOV, V., N., MEDVEDĚV, Ju., J. Thermoynamic baic of interior ballitic of barrel weaon. Penza: PVAUI, 974. [0] ČURBANOV, Je., V. Interior ballitic. Leningra: VAA, Concluion The bigger ifference between meaure an calculate ratio / near the muzzle of the barrel can be exlaine by the leak of roellant gae between barrel wall an riving ban that i at thi tage of rojectile movement worn. Barrel wear uually alo grow towar the muzzle of barrel. ISSN: ISBN: