Mathematical model of cavitational braking of a torus in the liquid after impact

The process of cavity formation under vertical impact and subsequent braking of a torus of an elliptical cross-section semisubmerged into a liquid is investigated. The solution of the problem is constructed by means of a direct asymptotic method, effective at small times. A special problem with unilateral constraints is formulated on the basis of which the initial zones of a separation and contact of liquid particles are determined, as well as perturbations of the internal and external free boundaries of the liquid at small times. Limit cases of a degenerate and a thin torus are considered. In the case of a thin torus, the flow pattern corresponds to the 2D problem of cavitation braking of an elliptical cylinder in a liquid after a continuous impact.

Keywords

ideal incompressible liquid, torus of elliptical section, hydrodynamic impact, cavitation braking, asymptotics, free border, cavity, small times, Froude's number

Received

26.09.2018

Publication date

04.10.2018

Number of characters

711

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GOST	Norkin M. Mathematical model of cavitational braking of a torus in the liquid after impact // Matematicheskoe modelirovanie – 2018. – V. 30. – Number 8 C. 116-130 [Electronic resource]. URL: http://ras.jes.su/mmod/s207987840000005-4-2-en (circulation date: 04.05.2024). DOI: 10.31857/S023408790001179-0
MLA	Norkin, M. "Mathematical model of cavitational braking of a torus in the liquid after impact." Matematicheskoe modelirovanie 30.8 (2018):116-130. DOI: 10.31857/S023408790001179-0
APA	Norkin M. (2018). Mathematical model of cavitational braking of a torus in the liquid after impact. Matematicheskoe modelirovanie 30(8), pp.116-130 DOI: 10.31857/S023408790001179-0

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1. Sedov L.I. Ploskie zadachi gidrodinamiki i aehrodinamiki. – M.: Nauka, 1966, 448 s.

2. Norkin M.V. Obrazovanie kaverny pri naklonnom otryvnom udare krugovogo tsilindra pod svobodnoj poverkhnost'yu tyazheloj zhidkosti // Sibirskij zhurnal industrial'noj matematiki, 2016, t.19, №4, s.81-92.

3. Norkin M.V. Kavitatsionnoe tormozhenie krugovogo tsilindra v zhidkosti posle udara // Prikl. mekhan. i tekhnich. fizika, 2017, t.58, №1, s.102-107.

4. Norkin M.V. Kavitatsionnoe tormozhenie tverdogo tela v vozmuschennoj zhidkosti // Nelinejnaya dinamika, 2017, t.13, №2, s.181-193.

5. Reinhard M., Korobkin A.A., Cooker M.J. Cavity formation on the surface of a body entering water with deceleration // Journal of Engineering Mathematics, 2016, v.96(1), p.155-174.

6. Kochin N.E., Kibel' I.A., Roze N.V. Teoreticheskaya gidromekhanika. Ch.1. – M.: Fizmatgiz, 1963, 583 s.

7. Yudovich V.I. Odnoznachnaya razreshimost' zadachi ob udare s otryvom tverdogo tela o neodnorodnuyu zhidkost' // Vladik. matem. zhurnal, 2005, t.7, №3, s.79-91.

8. Zhukov M.Yu., Shiryaeva E.V. Ispol'zovanie paketa konechnykh ehlementov FreeFem++dlya zadach gidrodinamiki, ehlektroforeza i biologii. – Rostov n/D: Izd-vo YuFU, 2008, 256 s.

9. Dvorak A.V., Teselkin D.A. Chislennoe issledovanie dvumernykh zadach ob impul'sivnom dvizhenii plavayuschikh tel // Zhurn. vychisl. matem. i matem. fiziki, 1986, t.26, №1, s.144-150.

10. Rvachev V.L., Protsenko V.S. Kontaktnye zadachi teorii uprugosti dlya neklassicheskikh oblastej. – Kiev: Nauk. dumka, 1977, 235 s.

11. Vabischevich P.N. Chislennye metody resheniya zadach so svobodnoj granitsej. – M.: Izd-vo Mosk. Univ., 1987, 164 s.

12. Lions Zh.L. Optimal'noe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi. – M.: Mir, 1972, 416 s.

13. Norkin M.V. Smeshannye zadachi gidrodinamicheskogo udara. – Rostov n/D: Izd-vo Tsentra valeologii vuzov Rossii, 2007, 136 s.

14. Vorovich I.I., Yudovich V.I. Udar kruglogo diska o zhidkost' konechnoj glubiny // Prikl. matem. i mekhan., 1957, t.21, №4, s.525-532.

15. Uflyand Ya.S. Metod parnykh uravnenij v zadachakh matematicheskoj fiziki. – L.: Nauka, 1977, 220 s.