doi: 10.18698/2309-3684-2017-2-3964
The study deals with a one-dimensional analytical model for computing the loads on the body of an aircraft caused by water entering the annular space of a launch canister. We used potential theory to solve the "external" hydrodynamic problem. Solving Lamé equations for the static case accounts for the strain in the walls of the aircraft and the launch canister.
[1] Nigmatulin R.I. Dinamika mnogofaznykh sred [Dynamics of multi-phase media]. In 2 vols. Moscow, Nauka Publ., 1987, vol. 1, 464 p.; vol. 2, 360 p.
[2] Nakoryakov V.E., Pokusaev B.G., Shreyber I.R. Volnovaya dinamika gazoi parozhidkostnykh sred [Wave dynamics of gas-liquid and vapour-liquid media]. Moscow, Energoatomizdat Publ., 1990, 248 p.
[3] Yakovlev Yu.S. Gidrodinamika vzryva [Hydrodynamics of explosion]. Leningrad, State Publishing House for Shipbuilding Literature, 1961, 316 p.
[4] Prikhodko N.A., Siryy V.S. Gidromekhanika — Hydromechanics, 1980, no. 43, pp. 85–93.
[5] Cole R.H. Underwater explosions. Princeton University Press, 1948, 437 p.
[6] Leighton T.G. The acoustic bubble. London, Academic Press, 1994, 613 p.
[7] Grumondz V.T., Zhuravlev Yu.F., Paryshev E.V., Sokolyanskiy V.P., Shorygin V.P. Gidrodinamika i dinamika vysokoskorostnogo dvizheniya tel v zhidkosti [Hydrodynamics and dynamics of high-speed motion of bodies in fluid]. Moscow, Nauka Publ., 2013, 574 p.
[8] Rozhdestvenskiy V.V. Kavitatsiya [Cavitation]. Leningrad, Sudostroenie Publ.,1977, 247 p.
[9] Abramovich G.N. Teoriya turbulentnykh struy [Theory of turbulent jets]. Moscow, Nauka Publ., 1984, 716 p.
[10] Yakimov Yu.L. Sbornik statey [Collected publications]. Moscow, Moscow State University Publ., 2013, 536 p.
[11] Kutateladze S.S., Nakoryakov V.E. Teplomassobmen i volny v gazozhidkostnykh sistemakh [Heat and mass transfer and waves in gas-liquid systems]. Novosibirsk, Nauka Publ., 1984, 301 p.
[12] Alemasov V.E. Teoriya raketnykh dvigateley [Theory of rocket engines]. Moscow, State Publishing House for the Defense Industry, 1962, 476 p.
[13] Vaulin S.D., Kirillov V.V., Feofilaktov V.I. Matematicheskaya model gazodinamicheskikh protsessov v nizkotemperaturnom gazogeneratore s kameroy okhlazhdeniya [Mathematical model of gas-dynamic processes in a lowtemperature gas generator with a cooling chamber]. Raketno-osmicheskaya tekhnika. Ser. XIV [Aerospace technology. Series 14], 2004, no. 1 (50), vol. 1, pp. 181–190.
[14] Yakimov Yu.L., Eroshin V.A., Romanenkov N.I. Modelirovanie dvizheniya tela v vode s uchetom ee szhimaemosti [Simulating motion of a body in water, considering its compressibility]. Nekotorye voprosy mekhaniki sploshnoy sredy [Certain problems in continuum mechanics]. Moscow, Moscow State University Publ., 1978, pp. 29–33.
[15] Lohse D., Schmitz B., Versluis M. Nature, 2001, no. 413, pp. 477–478.
[16] Scorer R.S. Environmental aerodynamics. New York, Halsted Press, 1978, 551 p.
[17] Aleksandrov A.A., Dimitrienko Yu.I. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 1 (1), pp. 3–4.
[18] Perot B., Nallapati R. Journal of Computational Physics, 2003, vol. 184, no. 1, pp. 192–214.
[19] Peregrine D.H. Journal of Fluid Mechanics, May 1981, vol. 106, pp. 91–119.
[20] Jürgens H., Peitgen H.-O., Saupe D. Scientific American, 1990, no. 263, pp. 60–67.
[21] Apalkov Yu.V., Mant D.I., Mant S.D. Otechestvennyye ballisticheskiye rakety morskogo bazirovaniya i ikh nositeli [National sea-launched ballistic missiles and their carriers]. St. Petersburg, Galeya Print Publ., 2006, 216 p.
[22] Morskiye strategicheskiye raketnye kompleksy [Marine strategic missile system]. Moscow, Voyennyy parad Publ., 2011, 268 p.
[23] Degtyar V.G., Pegov V.I. Gidrodinamika podvodnogo starta raket [Hydrodynamics of the submarine missile takeoff]. Moscow, Mashinostroeniye Publ., 2009, 448 p.
[24] Efremov G.A., Strakhov A.N., Minasbekov D.A., Gorlashkin A.A., Plyusnin A.V., Sokolov P.M., Bondarenko L.A., Govorov V.V. Otrabotka gazodinamiki podvodnogo starta na nazemnom gazodinamicheskom stende predpriyatiya [Underwater launch gas dynamic tests on the ground gas dynamics ground test bench of the enterprise]. Raketnye kompleksy i raketno-kosmicheskie sistemy — proektirovanie, eksperimentalnaya otrabotka, letnye ispytaniya, ekspluatatsiya. Trudy sektsii 22 im. akad. V.N. Chelomeya XXXVIII Akademicheskikh chteniy pokosmonavtike [Rocket and space-rocket systems — designing, experimental tests, flight tests, exploitation. Proc. of the 22nd section acad. V.N. Chelomei of XXXVIII Academic Space Technology Readings]. Reutov, 2014, pp. 65–74.
[25] Plyusnin A.V., Bondarenko L.A., Sabirov Yu.R. Analiz gazogidrodinamicheskikh protsessov i metodov ikh rascheta na osnove opyta predpriyatiya v otrabotke podvodnogo minometnogo starta Analysis of gas and hydro dynamic
processes and their calculating methods on the basis of the enterprise experi-
ments in underwater mortar launch tests]. Raketnyye kompleksy i raketno-
kosmicheskiye sistemy — proyektirovaniye, eksperimentalnaya otrabotka,
letnyye ispytaniya, ekspluatatsiya. Trudy sektsii 22 im. akad. V.N. Chelomeya
XXXIX Akademicheskikh chteniy po kosmonavtike [Rocket and space-rocket sys-
tems — designing, experimental tests, flight tests, exploitation. Proceedings of
the 22nd section named after acad. V.N. Chelomei of the XXXIX Academic
Space Technology Readings]. Reutov, 2015, pp. 74–83.
[26] Dergachev A.A., Bondarenko L.A., Sabirov Yu.R., Lobzov N.N., Plyusnin A.V. Sposob starta raket s podvodnoy lodki, nadvodnykh korabley i nazemnykh nositeley iz nezatoplennoy puskovoy ustanovki i puskovaya ustanovka dlya ego realizatsii [A way for launching rockets from a submarine, surface combatants and ground vehicles using a non-submerged launcher and a launcher to implement
it]. Patent RU2536961, bulletin no. 36, Dec 27th, 2014.
[27] Plyusnin A.V. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2016, no. 3 (11), pp. 53–78.
[28] Zhukovskiy N.E. O gidravlicheskom udare v vodoprovodnykh trubakh [On water hammer in water plumbing pipes]. Moscow, LIBROKOM Publ., 2011, 104 p.
[29] Plyusnin A.V. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 3 (3), pp. 55–73.
[30] Plyusnin A.V. Issledovanie zavisimosti maksimalnoy raschetnoy otsenki davleniya “gidroudara” pri podvodnom gazodinamicheskom vybrose LA ot vybora fizicheskoy modeli yavleniya [Investigating how the maximum estimated value of fluid hammer pressure during submarine gas-driven aircraft ejection depends on the physical model selected to describe the phenomenon]. Sbornik tezisov XLI
Akademicheskih chteniy po kosmonavtike, posvycshennykh pamyati akademika V.N. Chelomeya i drugikh vydayushcihsya otechestvennykh uchenykh — pionerov osvoeniya kosmicheskogo prostranstva [Abstracts XLI Academic readings on cosmonautics, dedicated to the memory of academician S.P. Korolev and other outstanding domestic scientists — pioneers of space exploration]. Moscow, Bauman Moscow State Technical University, 2017, p. 516.
[31] Plyusnin A.V., Bondarenko L.A. Vestnik MGTU im. N.E. Baumana. Ser.Yestestvennyye nauki. Spets. vypusk “Matematicheskoye modelirovaniye” — Herald of Bauman Moscow State Technical University, Series Natural Sciences. Special iss. “Mathematical Modeling”, 2012, no. 4, pp. 111–122.
[32] Zarubin V.S., Kuvyrkin G.N. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 1, pp. 5–17.
[33] Grigolyuk E.I., Gorshkov A.G. Vzaimodeystvie uprugikh konstruktsiy s zhidkostyu (udar i pogruzhenie) [Elastic structure interaction with fluids (impact and submerging)]. Leningrad, Sudostroenie Publ., 1976, 200 p.
[34] Dimitrienko Yu.I. Mekhanika sploshnoy sredy. V 4 tomakh. Tom 4. Osnovy mekaniki tverdykh sred [Continuum mechanics. In 4 vols. Vol. 4. Fundamentals of mechanics of solid mechanics]. Moscow, BMSTU Publ., 2013, 624 p.
[35] Eroshin V.A., Plyusnin A.V., Romanenkov N.I., Sozonenko Yu.A., Yakimov Yu.L. Izvestiya Akademii nauk SSSR. Mekhanika zhidkosti i gaza — Fluid Dynamics, 1984, no. 3, pp. 15–20.
[36] Dimitrienko Yu.I. Mekhanika sploshnoy sredy V 4 tomakh. Tom 2. Universalnye zakony mekhaniki i elektrodinamiki sploshnykh sred [Mechanics of Continua. In 4 vols. Vol. 2. Universal Laws of Mechanics and Electrodynamics of Continuous Media]. Moscow, BMSTU Publ., 2011, 560 p.
[37] Plyusnin A.V. Inzhenernyy zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovations, 2013, no. 7 (19), Available at: http://engjournal.ru/ catalog/hmodel/aero/847.html (дата обращения 03.10.2017).
[38] Loytsyanskiy L.G. Mekhanika zhidkosti i gaza [Fluid mechanics]. Moscow, Nauka Publ., 1987, 840 p.
[39] Sobolev S.L. Uravneniya matematicheskoy fiziki [Equations of mathematical physics]. Moscow, Nauka Publ., 1966, 444 p.
[40] Sedov L.I. Mekhanika sploshnoy sredy [Continuum mechanics]. In 2 vols. Vol. 2. St. Petersburg, Lan Publ., 2004, 560 p.
[41] Lamb H. Hydrodynamics. Cambridge, Cambridge University Press, 1932, 928 p.
[42] Lavrentyev M.A., Shabat B.V. Metody teorii funktsii kompleksnogo peremennogo [Complex variable theory methods]. Moscow, Nauka Publ., 1987, 688 p.
[43] Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integraly i ryady [Integrals and series]. In 3 vols. Vol. 3. Spetsialnye funktsii [Special functions]. Moscow, Nauka Publ., 1983, 752 p.
[44] Plyusnin A.V., Bondarenko L.A., Sabirov Yu.R. Raschet nestatsionarnoy gidrodinamicheskoy nagruzki, deystvuyushchey na deformiruemuyu panel opereniya LA [Computing unsteady hydrodynamic loads on a deformable empennage panel]. Raketnye kompleksy i raketno-kosmicheskie sistemy — proektirovanie, eksperimentalnaya otrabotka, letnye ispytaniya, ekspluatatsiya: Trudy sektsii 22 imeni akademika V.N Chelomeya XL Akademicheskikh chteniy po kosmonavtike [Rocket and aerospace systems — design, experiment-based refinement, flight
testing, operation: Proc. of the section 22 of V.N. Chelomey 40th Academic readings in cosmonautics]. Reutov, 2016, pp. 185–196.
[45] Bateman H., Erdélyi A. Higher Transcendental Functions. In 3 vols. Vol. 2. McGraw-Hill Book Company, 1953, 396 p. [In Russ.: Bateman H., Erdély A. Vysshie transtsendentnye funktsii. In 3 vols. Vol. 2. Funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny [Bessel functions, functions of the parabolic cylinder, orthogonal polynomials]. Moscow, Nauka Publ.,
1974, 296 p.].
[46] Batchelor G.K. An introduction to fluid dynamics. Cambridge, Cambridge University Press, 2000, 615 p.
[47] Plyusnin A.V. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 2, pp. 77–100.
[48] Plyusnin A.V., Dodenko I.A. Inzhenernyy zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2013, no. 7. Available at: http://engjournal.ru/catalog/mathmodel/aero/841.html (accessed October 3, 2017). [49 Idelchik I.E. Spravochnik po gidravlicheskim soprotivleniyam [Handbook on friction loss values]. Moscow, Mashinostroenie Publ., 1992, 672 p.
[50 Siov B.N. Istechenie zhidkosti cherez nasadki [Fluid flow through attachments]. Moscow, Mashinostroenie Publ., 1968, 140 p.
[51] Timoshenko S.P., Goodier J.N. Theory of Elasticity. McGraw-Hill Education, 1970, 608 p. [In Russ.: Timoshenko S.P., Goodier J.N. Teoriya uprugosti. Moscow, Nauka Publ., 1979, 560 p.].
[52] Polilov A.N. Etyudy po mekhanike kompozitov [Studies in composite mechanics]. Moscow, FIZMATLIT Publ., 2016, 320 p.
Plyusnin A.V. Mathematical simulation of the process of water entering the annular space of a canister during submarine gas-driven aircraft ejection. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 39-64