531.6.011.32:532.582.4 Modeling of subsonic separation flow around bodies by the method of discrete vortices based on the concept of an equivalent surface with cubic splines

Timofeev V. N. (Bauman Moscow State Technical University)


doi: 10.18698/2309-3684-2020-4-2743

For mathematical modeling of subsonic separation flow around axisymmetric bodies with a bottom section, a technique with a partial implementation of the concept of visco–inviscid interaction was used. A flow scheme with an equivalence semi-infinite surface was used. Numerical simulations were carried out according to the algorithms of the method using the method of discrete vortices and approximation by smoothing cubic splines. Data on the influence of the shape of the tail section of an equivalent surface on the velocity and pressure distribution during axisymmetric flow around bodies with a bottom section are presented. The proposed recommendations make it possible to apply this technique more universally.

[1] Fletcher K. Vychislitel'nye metody v dinamike zhidkostej. T. 2. Metody rascheta razlichnyh techenij [Computational methods in fluid dynamics. Vol. 2. Methods for calculating different flows]. Moscow, Mir Publ., 1991, 552 p.
[2] Patankar S.V. Chislennye metody resheniya zadach teploobmena i dinamiki. [Numerical methods for solving problems of heat transfer and dynamics]. Moscow, Energoatomizdat Publ., 1984, 152 p.
[3] Kalugin V.T., Sobolev V.Yu. Mathematical simulation of processes of subsonic turbulent flow around stabilizing devices of flying vehicles under condition of flow separation. Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, 2005, no. 2, pp. 20–30.
[4] Golovkin M.A., Golovkin V.A., Kalyavkin V.M. Voprosy vihrevoj gidromehaniki [Questions of vortex hydromechanics]. Moscow, Fizmatlit Publ., 2009, 264 p.
[5] Saffman P.G. Vortex Dynamics. Cambridge, Cambridge University Press, 1992, 311 p.
[6] Andronov P.R., Guvernyuk S.V., Dynnikova G.Ya. Vikhrevye metody rascheta nestatsionarnykh gidrodinamicheskikh nagruzok [Vortex methods of calculation of nonstationary hydrodynamic loads]. Moscow, Institute of Mechanics Lomonosov MSU Publ., 2006, 184 p.
[7] Lewis R.I. Vortex element methods for fluid dynamic analysis of engineering systems. Cambridge, Cambridge University Press, 2005, 592 p.
[8] Kuzmina K.S., Marchevskii I.K., Moreva V.S. Vortex sheet intensity computation in incompressible flow simulation around an airfoil by using vortex methods. Mathematical Models and Computer Simulations, 2018, vol. 10, iss. 3, pp. 276–287.
[9] Kocur O.S., Shcheglov G.A. Implementation of the particle strength exchange method for fragmentons to account for viscosity in vortex element method. Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2018, no. 3, pp. 48–67.
[10] Dergachev S.A., Scheglov G.A. Vortex element method simulation of flow around bodies using closed vortex loops. Civil Aviation High Technologies, 2016, no. 223, pp. 19–27.
[11] Belotserkovskiy S.M., Nisht M.I., Kotovskiy V.N., Fedorov R.M. Trekhmernoe otryvnoe obtekanie tel proizvolnoy formy [Three-dimensional detached flow of the bodies of arbitrary form]. Moscow, TsAGI (Central Aerohydrodynamic Institute) Publ., 2000, 265 p.
[12] Gogish L.V., Stepanov G.Yu. Otryvnye i kavitatsionnye techeniya. Osnovnye svoiystva i raschet modeli [Detached and cavitational flows. Basic properties and model calculation]. Moscow, Nauka Publ., 1990, 384 p.
[13] Timofeev V.N. Mathematical modeling of separated subsonic flowaround axially symmetrical bodies with base pressure. Engineering Journal: Science and Innovation, 2014, no. 10. Available at: http://engjournal.ru/ catalog/mathmodel/aero/1246.html (accessed October 17, 2017).
[14] Timofeev V.N. Construction of a semi-infinite equivalent body in mathematical modeling of subsonic separated axisymmetric flow. Маthematical Modeling and Computational Methods, 2016, no. 4, pp. 67–83.
[15] Rjgers D.F., Adams J.A. Mathematical elements for computer graphics. New-York, McGraw–Hill Science, 1989, 512 p.
[16] Dimitrienko Yu.I. Tenzornoe ischislenie [Tensor calculus]. Moscow, Vysshaya shkola Publ., 2001, 576 p.
[17] Lifanov I.K. Metod singulyarnykh integralnykh uravneniy i chislennyy eksperiment (v matematicheskoi fizike, aerodinamike, teorii uprugosti i difraktsii voln) [The method of singular integral equations and numerical experiment (in mathematical physics, aerodynamics, theory of elasticity and diffraction of waves)]. Moscow, LLP Yanus Publ., 1995, 520 p.
[18] Timofeev V.N. Mathematical simulation of the subsonic flow around the lengthening bodies with the flow separation in the region of ground shear with the use of an equivalent body. Journal of Physics: Conference Series, 2018, vol. 1141, art. no. 012095.
[19] Timofeev V.N. Special features of vortex diagram in simulation of subsonic detached flow around the semi-infinite equivalent body. Mathematical Modeling and Computational Methods, 2017, no. 4, pp. 73–91.
[20] Aubakirov T.O., Belotserkovskiy S.M., Zhelannikov A.I., Nisht M.I. Nelineinaya teoriya kryla i ee prilozheniya [Nonlinear wing theory and its applications]. Almaty, Gylym Publ., 1997, 448 p.
[21] Timofeev V.N. Simulation of the subsonic detachable body with a bottom cut on the current pattern with an equivalent half-infinite surface at small angles of attack. Маthematical Modeling and Computational Methods, 2019, no. 4, pp. 31–49.

Тимофеев В.Н. Моделирование дозвукового отрывного обтекания тел методом дискретных вихрей на основе концепции эквивалентной поверхности с кубическими сплайнами. Математическое моделирование и численные методы, 2020, № 4, с. 27–43.

Download article

Количество скачиваний: 188