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 Nelin. Dinam., 2018, Volume 14, Number 4, Pages 473–494 (Mi nd626)

Nonlinear physics and mechanics

Dynamics of a Body with a Sharp Edge in a Viscous Fluid

I. S. Mamaevab, V. A. Tenenevb, E. V. Vetchanincb

a Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S. Kovalevskoi 16, Ekaterinburg, 620990 Russia
b Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia
c Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: This paper addresses the problem of plane-parallel motion of the Zhukovskii foil in a viscous fluid. Various motion regimes of the foil are simulated on the basis of a joint numerical solution of the equations of body motion and the Navier – Stokes equations. According to the results of simulation of longitudinal, transverse and rotational motions, the average drag coefficients and added masses are calculated. The values of added masses agree with the results published previously and obtained within the framework of the model of an ideal fluid. It is shown that between the value of circulation determined from numerical experiments, and that determined according to the model of and ideal fluid, there is a correlation with the coefficient $\mathcal{R}=0.722$. Approximations for the lift force and the moment of the lift force are constructed depending on the translational and angular velocity of motion of the foil. The equations of motion of the Zhukovskii foil in a viscous fluid are written taking into account the found approximations and the drag coefficients. The calculation results based on the proposed mathematical model are in qualitative agreement with the results of joint numerical solution of the equations of body motion and the Navier – Stokes equations.

Keywords: Zhukovskii foil, Navier – Stokes equations, joint solution of equations, finitedimensional model, viscous fluid, circulation, sharp edge

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.2405.2017/4.6 Russian Foundation for Basic Research 15-08-09093-a18-08-00995-a The work of V. A. Tenenev (Sections 2 and Conclusion ) was carried out within the framework of the state assignment given to the Izhevsk State Technical University 1.2405.2017/4.6. The work of E. V. Vetchanin (Introduction and Section 1) and I. S. Mamaev (Section 3) was supported by the Russian Foundation for Basic Research under grants Nos. 15-08-09093-a and 18-08-00995-a, respectively.

DOI: https://doi.org/10.20537/nd180404

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MSC: 37Mxx, 65Nxx, 70Exx, 76Dxx
Accepted:07.09.2018
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Citation: I. S. Mamaev, V. A. Tenenev, E. V. Vetchanin, “Dynamics of a Body with a Sharp Edge in a Viscous Fluid”, Nelin. Dinam., 14:4 (2018), 473–494

Citation in format AMSBIB
\Bibitem{MamTenVet18}
\by I. S. Mamaev, V. A. Tenenev, E. V. Vetchanin
\paper Dynamics of a Body with a Sharp Edge in a Viscous Fluid
\jour Nelin. Dinam.
\yr 2018
\vol 14
\issue 4
\pages 473--494
\mathnet{http://mi.mathnet.ru/nd626}
\crossref{https://doi.org/10.20537/nd180404}
\elib{http://elibrary.ru/item.asp?id=36686069}

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This publication is cited in the following articles:
1. Ivan S. Mamaev, Evgeny V. Vetchanin, “The Self-propulsion of a Foil with a Sharp Edge in a Viscous Fluid Under the Action of a Periodically Oscillating Rotor”, Regul. Chaotic Dyn., 23:7-8 (2018), 875–886
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