Abstract
A general formulation of the plane coupled dynamical and aerodynamical problem of the motion of a rigid body with a rotational degree of freedom in a viscous incompressible fluid flow is given. A computation technique for solving the Navier-Stokes equations based on the meshless viscous vortex domain method is used. The autorotation of a single plate and a pair of plates is investigated. The effect of the reduced moment of inertia and the Reynolds number on the angular rotation velocity is determined. The time dependences of the hydrodynamic loads are compared with the corresponding instantaneous flow patterns. The increased the autorotation velocity of two plates in tandem is detected.
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References
N.E. Joukowski, “Air Fall of Light Elongated Bodies Rotating about Their Longitudinal Axis (the First and Second Papers),” in Complete Collected Works, Vol. 4 (Gostekhizdat, Moscow, Leningrad, 1949) [in Russian], 41–68.
P.R. Andronov, S.N. Barannikov, S.V. Guvernyuk, A.F. Zubkov, Kh. Isvand, and A.F. Mosin, “Problems of Aerodynamics of Weather Vanes, Pendulums, and Propellers,” in Abstracts of the 11th School-Workshop “Modern Problems of Aero-and Hydrodynamics” (Moscow State University Press, Moscow, 2003), p. 12.
S.N. Barannikov, “Experimental Identification of Unsteady Vortex Structures in Flow past an Autorotating Finned Cylinder,” in G.G. Chernyi and V.A. Samsonov (Eds.) Proceedings of Conf.-Competition of Young Scientists (Moscow State University Press, Moscow, 2004), 20–27.
T. Sarpkaiya, “Computational Vortex Methods. Freeman Lecture (1988),” Sovremennoe Mashinostroenie, Ser. A, No. 10, 1–60 (1989).
S.M. Belotserkovskii and A.S. Ginevskii, Simulation of Turbulent Jets and Wakes on the Basis of the Discrete Vortex Method (Fizmatlit, Moscow, 1995) [in Russian].
L.A. Barba, A. Leonard, and C.B. Allen, “Advances in Viscous Vortex Methods—Meshless Spatial Adaption Based on Radial Basis Function Interpolation,” Intern. J. Numer. Meth. Fluids 47,No. 5, 387–421 (2005).
Kh. Isvand, “Simulation of a Vortex Layer of Finite Thickness Using the Discrete Vortex Method,” Aeromechanics and Gas Dynamics, No. 1, 51–56 (2003).
P.R. Andronov, S.Ya. Gertsenshtein, G.Ya. Dynnikova, and Kh. Isvand, “Effect of the Thickness of a Vortex Layer on Its Stability,” Vestn. Khar’k. Un-ta, Ser. “Mat. Modelirovanie. Informatsionnye Tekhologii. Avtomatizirovannye Systemy Upravleniya,” No. 590, Issue 1, 3–8 (2003).
P.R. Andronov, “Numerical Identification of Unsteady Vortex Structures in Flow Past an Autorotating Finned Cylinder,” in G.G. Chernyi and V.A. Samsonov (Eds.) Proceedings of Conf.-Competition of Young Scientists (Moscow State University Press, Moscow, 2004), 12–19.
V.A. Aparinov, M.I. Nisht, and G.N. Strelkov, “Mathematical Simulation of an Infinite-Span Plate Falling in a Fluid,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 179–184 (1989).
A.J. Chorin, “Numerical Study of Slightly Viscous Flow,” J. Fluid Mech. 57, Pt. 4, 785–796 (1973).
S. Shankar and L. van Dommelen, “A New Diffusion Procedure for Vortex Methods,” J. Comp. Phys., 127, No. 1, 88–109 (1996).
Y. Ogami and T. Akamatsu, “Viscous Flow Simulation Using the Discrete Vortex Model. The Diffusion Velocity Method,” Computers and Fluids 19, No. 3 4, 433–441 (1991).
G.Ya. Dynnikova, “Vortex Motion in Two-Dimensional Viscous Fluid Flows,” Fluid Dynamics 38(5), 670–678 (2003).
G.Ya. Dynnikova, “Lagrangian Approach to the Solution of Time-Dependent Navier-Stokes Equations,” Dokl. Ros. Akad. Nauk 399, No. 1, 42–46 (2004).
S.V. Guvernyuk, G.Ya. Dynnikova, P.R. Andronov, S.N. Barannikov, A.I. Gircha, D.A. Grigorenko, and A.F. Zubkov, “Simulation of Unsteady Loads in the Motion of Bodies in a Viscous Fluid,” Report No. 4775 of the Research Institute of Mechanics of the Moscow State University (2005).
S.V. Guvernyuk and G.Ya. Dynnikova, “Modeling the Flow Past an Oscillating Airfoil by the Method of Viscous Vortex Domains,” Fluid Dynamics 42(1), 1–11 (2007).
L.G. Loitsyanskii, Mechanics of Liquids and Gases, Pergamon Press, Oxford (1966).
N.E. Kochin, Vector Calculus and Foundations of Tensor Analysis (Nauka, Moscow, 1965) [in Russian].
D.A. Grigorenko, “Questions Concerning the Programming of Lagrangian Vortex Methods,” in 17th Intern. Internet-Conference of Young Scientists and Students on Problems of Engineering Science (MIKMUS-2005), Collected Works (Izd-vo IMASh RAN, Moscow, 2006) [in Russian], 121–124.
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Original Russian Text © P.R. Andronov, D.A. Grigorenko, S.V. Guvernyuk, G.Ya. Dynnikova, 2007, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2007, Vol. 42, No. 5, pp. 47–60.
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Andronov, P.R., Grigorenko, D.A., Guvernyuk, S.V. et al. Numerical simulation of plate autorotation in a viscous fluid flow. Fluid Dyn 42, 719–731 (2007). https://doi.org/10.1134/S0015462807050055
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DOI: https://doi.org/10.1134/S0015462807050055