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

2018, Vol. 14, no. 4, pp.  473-494

Author(s): Mamaev I. S., Tenenev V. A., Vetchanin  E. V.

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
Citation: Mamaev I. S., Tenenev V. A., Vetchanin E. V., Dynamics of a Body with a Sharp Edge in a Viscous Fluid, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 4, pp.  473-494
DOI:10.20537/nd180404