Magnus effect and dynamics of a spinning disc in a rarefied medium

• Autorzy: Mishuris G. , Plakhov A.
• Języki publikacji: EN

Abstrakty

EN

Magnus effect consists in deflection of the trajectory of a rotating body moving in a gas. It is a direct consequence of the interaction between the body surface and the gas particles. In this paper, we study the so-called inverse Magnus effect which can be observed in rarefied gases. We restrict ourselves to the two-dimensional case, namely a spinning disc moving through a sparse zero-temperature medium. We consider general non-elastic interaction between the disc and the particles depending on the incidence angle. We give a classification of auxiliary parameters with respect to possible dynamical response. In the absence of other forces, three kinds of trajectories are possible: (i) a converging spiral, (ii) a curve converging to a straight line and (iii) a circumference, the case intermediate between the two first ones. A specific 2-D parameter space has been introduced to provide respective classification.

Słowa kluczowe

EN

inverse Magnus effect; free molecular flow; non-elastic interaction

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2009
• Tom: Vol. 61, nr 5
• Strony: 391--406
• Opis fizyczny: Bibliogr. 30 poz.

Twórcy

autor

Mishuris G.

autor

Plakhov A.

• Wales Institute of Mathematical and Computational Sciences Institute of Mathematics and Physics, Aberystwyth University, UK,

Bibliografia

• 1. J. ASHENBERG, On the effects of time-varying aerodynamical coefficients on satellite orbits, Acta Astronautica, 38, 75-86, 1996.
• 2. J. ASHENBERG, Dynamical characteristics of a tethered stabilized satellite, J. Guid. Control Dyn., 20, 1268-1271, 1997.
• 3. H.M. BARKLA, L.J. AUCHTERLONIE, The Magnus or Robins effect on a rotating sphere, J. Fluid Mech., 47, 437-447, 1971.
• 4. K.I. BOR.G, L.H. SODERHOLM, Orbital effects of the Magnus force on a spinning spherical satellite in a rarefied atmosphere, Eur. J. Mech. B/Fluids, 27, 623-631, 2008.
• 5. K.l. BORG, L.H. SODERHOLM, H. ESSEN, Force on a spinning sphere moving in a rarefied gas, Physics of Fluids, 15, 736-741, 2003.
• 6. S.G. CHADWICK, S.J. HAAKE, Methods to determine the aerodynamic forces acting on tennis balls inflight. Tennis Science and Technology, S.J. HAAKE, A. COE [Eds.], Proceedings of the 1st International Conference on Tennis Science and Technology. Blackwell Science, Oxford, UK, pp. 127-134, 2000.
• 7. A.J. COOKE, An overview of tennis ball aerodynamics, Sports Engineering, 3, 2, 123-129, 2000.
• 8. P.S. EPSTEIN, On the resistance experienced by spheres in their motion through gases, Phys. Rev., 23, 710-733, 1924.
• 9. S.G. IVANOV, A.M. YANSHIN, Forces and moments acting on bodies rotating around a symmetry axis in a free molecular flow, Fluid Dyn., 15, 449-453, 1980.
• 10. M.N. KOGAN, Rarefied gas dynamics, Plenum, New York 1969.
• 11. R.D. MEHTA, Aerodynamics of sport balls, Annu. Rev. Fluid Mech, 17, 151-189, 1985.
• 12. R.D. MEHTA, J.M. PALLIS, The Aerodynamics of a Tennis Ball, Sports Engineering, 4, 1-13, 2001.
• 13. P. MOORE, The effect of aerodynamic lift on near-circular satellite orbits, Planet. Space Sci., 33, 479-491, 1985.
• 14. I. NEWTON, Netu theory of light and colours, Philosophical Transactions of the Royal Society London, 1, 678-688, 1672.
• 15. A.Yu. PLAKHOV, T.V. TCHEMISOVA, Force acting on a spinning rough disc in a flow of noninteracting particles, Doklady Math., 424, 26-30, 2009.
• 16. L. PRANDTL, Application of the "Magnus Effect" to the wind propulsion of ships, Die Naturwissenschaft, 13, 93-108; transl. NACA-TM-367, June 1926.
• 17. L. RAYLEIGH, On the irregular flight of a tennis ball, Messenger of Math., 7, 14-16, 1877.
• 18. V.V. RIABOV, The Magnus effect in rarefied gas near a spinning cylinder, [in:] 15-th AIAA Applied Aerodynamics Conference, Atlanta, GA, June 23-25, 1997, Technical Papers, Pt. 2 (A97-31695 08-02).
• 19. V.V. RIABOV, Numerical simulation of kinetic effects in low-density hypersonic aerodynamics, [in:] Proceedings of the 25th International Congress of the Aeronautical Sciences, 3-8 September 2006, Hamburg, Germany.
• 20. B. ROBINS, New principles of gunnery, C. HUTTON, F. WINGRAVE [Eds.], London, 1805 (originally published in 1742).
• 21. S.I. RUBINOV, J.B. KELLER, The transverse force on a spinning sphere moving in a viscous fluid, J. Fluid Mech., 11, 447-459, 1961.
• 22. S.A. SCHAAF, Mechanics of rarefied gases, [in:] Handbuch der Physik, Springer, Berlin, vol.VIII/2, 591-625 1963.
• 23. J.A. STORCH, Aerodynamic disturbances on rapidly rotating spacecraft in free-molecular flow, [in:] Proceedings of the 9th Biennial ASCE Aerospace Division International Conference on Engineering, Construction, and Operations in Challenging Environments, March 7-10, 2004, League City/Houston, TX, pp. 429-436.
• 24. G.A. TOKATY, A history and philosophy of fluid mechanics, Foulis, Henley on Thames 1971.
• 25. C.-T. WANG, Free molecular flow over a rotating sphere, AIAA J., 10, 713, 1972.
• 26. R.G. WATTS, R. FERRER, The lateral force on a spinning sphere: Aerodynamics of a curveball, Am. J. Phys. 55, 40-44, 1987.
• 27. P.D. WEIDMAN, A. HERCZYNSKI, On the inverse Magnus effect in free molecular flow, Physics of Fluids, 16, L9-L12, 2004.
• 28. K. MOE, M.M. MOE, Gas-surface interactions and satellite drag coefficients, Planet. Space Sci, 53, 793-801, 2005.
• 29. P.D. FIESELER, A method for solar sailing in a low Earth orbit, Acta Astronautica, 43, 531-541, 1998.
• 30. E.D. KNECHTEL, W.C. PITTS, Normal and tangential momentum accommodation for Earth satellite conditions, Astronautica Acta, 18, 3, 171-184, 1973.