Giải bài toán cơ bản thuật phóng trong bằng mô hình khí động

NGHIEN CU'U-TRAOeOl GIAI BAI TOAN CQ B A N THUAT PHONG TRONG BANG Md HINH KHi£)ONG SOLVING THE FUNDAMENTAL PROBLEM OF INTERIOR BALLISTICS BY USING GAS-DYNAMIC MODEL ThS Nguyin Quang Tii^n Hpc vien Ky thuat Qum su TOM TAT Bdi bdo trinh bdy phuang phdp gidi bdi todn ca bdn thugt phong cua sung phdo bdng cdch su dung mo hinh dQng He phuang trinh md td cdc qud trinh thugt phong duac xdy difng tren ca sa ly thuyit mdi truamg lien t^ic vd dugrc gidi bang phuang phdp "hgt lan" (hay cd duac goi la phuang phdp Davudov) Md hinh tinh todn dugc dp dung de gidi bdi todn ca bdn thugt phong cho phdo chong tdng nong tran 100 mm T12 vai dan duai ca EM2 Cac kit qud tinh todn dd khdng dinh tinh dung dan cua md hinh Tu khda: Thugt phdng trong, md hinh dong, md hinh cd dien, phuangphdp hat l&n, dgn du&i ca ABSTRACT The article describes a method of solving the fundamental problem of interior ballistics by using gas-dynamic model The system ofequations describing the interior ballistics processes in gu barrels is built on the basis ofcontinuum theory and solved hy using the method of "large particles (also known as Davydov's method) The calculation model is applied to solve the fundamental problem of interior ballistics for Soviet smoothbore 100-mm anti-tank gun T12 with BM~2 APFSD projectile Calculated result gives us confidence in the correctness of the model Keywords: Interior ballistics, gas-dynamic model, the method of "largeparticles", APFSD projectile, the classical model DAT VAN DE Viec giai bdi todn ca ban thudt phdng Uong (TPT) cd y nghia quan trpng Uong thidt kd, cai tien, khai tiidc va su dung cac loai vii CO ndng Hien nay, vdn sii dung md hinh cd didn (md hmh nhiet dgng) de giai bdi ca bdn TPT Thuc td dd chi ring, md hmh cd didn cho ket qud Idid chinh xac ddi vdi nhimg loai dan cd so tdc khdng Idn lam, nhien ddi vdi nhimg loai dan cd so tdc Idn thi md hmh cho sai sd tuong ddi 1cm so vdi thuc nghiem Nguyen nhdn la md hinh cd didn bd qua nhiSu hien tupng tiiang ddi quan trpng xdy ti-ong qud tiinh ban Dd gidi quyet vdn dd ndy hien ngudi ta su dung md hinh ddng ISSN 0866 - 7056 TAP CHI CO KHl VIET NAM, Sd 1+2 nam 2017 www.cokhivietnam.vn NGHIEN CO'U-TRAODOI HE PHXrONG TRINH VI P H A N CUABAI TOAN CO BAN TPT CtA SUNG-PHAO Bdn chat cua phuang phap la su dung ly thuyet mdi trudng lien tuc dd md td su bidn ddi cua cdc tham s6 thudc long ndng BB thidt lap he phucmg trinh toan hpc md ta hien tugng ban md hinh ktii ddng ta ch^ nhan mgt so gid thidt nhu sau: - Cac tiiam sd ciia thudc cd gia tri nhu tai mgi diem cua ciing mgt mat cat long ndng; - Phuang trinh bdo todn ndng lugng: d{pE)^ dt +• divipEW) + div{pW) = 0; e tim dp suat thudc ta sii dung jdnrang liinh trang Ihai dudi dang p = £p(k-\), d6£ = E-u chat 12 la ndi nang rieng cua Cdc phuong trinh md ta qua trinh ehdy va tao cua thudc phong: - Thanh ndng dugc coi la cimg tuydt ddi; - Thudc phdng khdng nen dugc; dz _ p - Khi thudc cd the ndn dugc, bd qua luc quan tinh vd luc cdn nhdt cua Idii thudc; - Bd qua cac phdn ijmg hda nhiet xdy Uong qua trinh taotiianh,dan nd vd ngudi thudc; - Thdnh phdn thudc, luc thudc phdng, hang sd chdt va chi sd miz doan nhiet coi nhu khdng ddi toan bd thai gian xdy hidn tugng bdn Gid su rang khdng va cac sdn pham chay Id mdt hdn hgp ddng nhdt Khi dd, su bien ddi ciia ddng thudc Idng ndng dugc md td bdi he phuang trinh vi phan sau: Cac phuang trinh md ta chuyen ddng cua dan: dl^_ dv _Sp dt ' dt tpm FHirONG PHAP "HAT LCfN" DE GIAI HE PHlTONG TRINH VI P H A N CUA BAI TOANCOBANTPT Trong phucmg phap mdi trudng lien tuc dugc mo hinh hda bdi mpt hd cdc hat Idn, cdc hat tai thdi diem ddu tien trimg vdi cac d mang cua ludi Ole (hinh 1) rU'7""T - Phuang trinh bdo toan khdi lugng: dt + div(pW) = 0; (Say - Phuong trinh bao toan dong luong: ^^^^divipu-W)+^ dt dx = 0; ' - m^g (W- "ff^I" (aw Hinh Cdu true luditinhtodn Ole Qua trinh tinh toan gdm nhieu budc lap di lap lai ve thdi gian Mdi budc tinh bao gdm ba giai doan nhu sau: ^ ISSN 0866 - 7056 TAP CHi CO KHf VIET NAM, Sd 1+2 ndm 2017 NGHIEN CO'U-TRAODOI 1) Giai doan Ole: Trong giai doan nay, ta se bd qua cdc hieu img lien quan tdi su dich chuyen ciia d mang (mdi trudng vat chdt dugc coi nhu tam thdi dung j^en), chi tinh tdi cac lii?u ling tang tdc ciia chat nhd vao luc ap suat Trong giai doan se xac dinh cac gia tri trung gian ciia cac tham sd cdn tim ^{U,E) cho mdi d mang: r.n _ ,,n pf+\l2 'p"-\n Af"+i=M"+2;AM|;+AM3„ d day AMj - Kh6i lugng dich chuyen qua mgt bien nao ciia mang , Af khoang thai gian At,XAWj- T6ng kh6i lugng dich chuyen qua tit ca cac Men cua A p.- O day, nhung dai luong voi chi so khong nguyen la gia tri cua cac tham s6 tai bien cac mang: "Mn^ ""+""+1 ^"^'; n uf+uU ""-1/2 = ^ ' '; 2) Giai doan Lagrange: Trong giai doan se tmh toan cac dong v§t chit di chuySn qua bien cac mang Ole: P'^MIlSAt, khiS?n,2>0, mang Cac dai lugng Alf va AE^ dugc hiSu tuong tu nhu d6i vai AM^ Cac dai lugng voi ky hieu "ch" la khoi lugng khi, dgng lugng va nang lugng ma mang nhan dugc tu su chiy ciia thuoc phong Khi tinh toan nang lugng thuoc cac m ^ g ta can phai tinh toi ca cong ma thuoc da thirc hien d6 dich chuyin dan long nong, cong dugc ky hieu 11 AE^ Ta nhin dugc cac biju thiic ii xac dinh gia tri cudi cung cua cac tham s6 cua dong t^ thoi diSm mai t"*' = t" + At co dang nhu sau: ^«+i ' A"+1«J°+1/2'5A(, khiii?^,/2