Aerodynamic coefficients of a spinning sphere in a rarefied-gas flow
- A. N. Volkov
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A three-dimensional rarefied-gas flow past a spinning sphere in the transitional and near-continuum flow regimes is studied numerically. The rarefaction and compressibility effects on the lateral (Magnus) force and the aerodynamic torque exerted on the sphere are investigated for the first time. The coefficients of the drag force, the Magnus force, and the aerodynamic torque are found for Mach numbers ranging from 0.1 to 2 and Knudsen numbers ranging from 0.05 to 20. In the transitional regime, at a certain Knudsen number depending on the Mach number the Magnus force direction changes. This change is attributable to the increase in the role of normal stresses and the decrease in the contribution of the shear stresses to the Magnus force with decrease in the Knudsen number. A semi-empirical formula for the calculation of the Magnus force coefficient in the transitional flow regime is proposed.
- S.I. Rubinow and J.B. Keller, “The Transverse Force on a Spinning Sphere Moving in a Viscous Fluid,” J. Fluid Mech. 11 Pt 3, 447–459 (1961). CrossRef
- S.A. Morsi and A.J. Alexander, “An Investigation of Particle Trajectories in Two-Phase Flow Systems,” J. Fluid Mech. 55 Pt 2, 193–208 (1972). CrossRef
- N.A. Zarin, Measurement of Non-Continuum and Turbulence Effects on Subsonic Sphere Drag (NASA Report NCR-1585, 1970).
- W.R. Lawrence, Free-Flight Range Measurements of Sphere Drag at Low Reynolds Numbers and Low Mach Numbers (Arnold Eng. Development Center. Report AEDC-TR-67-218, 1967).
- A.B. Bailey and J. Hiatt, Free-Flight Measurements of Sphere Drag at Subsonic, Transonic, Supersonic, and Hypersonic Speeds for Continuum, Transition, and Near-Free-Molecular Flow Conditions (Arnold Eng. Development Center. Report AEDC-TR-70-291, 1971).
- A.B. Bailey and J. Hiatt, “Sphere Drag Coefficients for a Broad Range of Mach and Reynolds Numbers,” AIAA J. 10(11), 1436–1440 (1972). CrossRef
- C.B. Henderson, “Drag Coefficients of Spheres in Continuum and Rarefied Flows,” AIAA J. 14(6), 707–708 (1976). CrossRef
- L.E. Sternin, B.N. Maslov, A.A. Shraiber, and A.M. Podvysotskii, Two-Phase Mono- and Polydisperse Gas-Particle Flows [in Russian] (Mashinostroenie, Moscow, 1980).
- P.P. Brown and D.F. Lawler, “Sphere Drag and Settling Velocity Revisited,” J. Environment. Eng. 129(3), 222–231 (2003). CrossRef
- Ch.-T. Wang, “Free-Molecular Flow over a Rotating Sphere,” AIAA J. 10(5), 713–714 (1972). CrossRef
- S.G. Ivanov and A.M. Yashin, “Forces and Moments Acting on Bodies Rotating about a Symmetry Axis in Free Molecular Flow,” Fluid Dynamics 15(3), 449 (1980). CrossRef
- H. Niazmand and M. Renksizbulut, “Surface Effects on Transient Three-Dimensional Flows Around Rotating Spheres at Moderate Reynolds Numbers,” Computers and Fluids 32(10), 1405–1433 (2003). CrossRef
- Y. Tsuji, Y. Morikawa, and O. Mizuno, “Experimental Measurements of the Magnus Force on a Rotating Sphere at Low Reynolds Numbers,” Trans. ASME. J. Fluids Eng. 107(4), 484–488 (1985). CrossRef
- B. Oesterle and T. Bui Dinh, “Experiments on the Lift of a Spinning Sphere in a Range of Intermediate Reynolds Numbers,” Experim. Fluids 25(1), 16–22 (1998). CrossRef
- J.H. Maccoll, “Aerodynamics of a Spinning Sphere,” J. Roy. Aeronaut. Soc. 32 777–798 (1928).
- V.A. Naumov, A.D. Solomenko, and V.P. Yatsenko, “Effect of the Magnus Force on the Motion of a Rigid Spherical Body at a High Angular Velocity,” Inzh. Fiz. Zh. 65(3), 287–290 (1993).
- N. Chegroun and B. Oesterle, “Etude Numérique de la Trainée, de la Portance et du Couple sur une Sphere en Translation et en Rotation,” (Actes 11éme Congrés Francais Mecanique, Lille-Villeneuve d’Ascq, France, 1993. V. 3), 81–84.
- S.C.R. Dennis, S.N. Singh, and D.B. Ingham, “The Steady Flow due to a Rotating Sphere at Low and Moderate Reynolds Numbers,” J. Fluid Mech. 101 Pt 2, 257–279 (1980). CrossRef
- K.I. Borg, L.H. Soderholm, and H. Essen, “Force on a Spinning Sphere Moving in a Rarefied Gas,” Phys. Fluids 15(3), 736–741 (2003). CrossRef
- P.D. Weidman and A. Herczynski, “On the Inverse Magnus Effect in Free-Molecular Flow,” Phys. Fluids. 16(2), L9–L12 (2004). CrossRef
- A.N. Volkov, “Numerical Modeling of the Magnus Force and the Aerodynamic Torque on a Spinning Sphere in Transitional Flow,” (Proc. 25th Int. Symp. Rarefied Gas Dynamics, St. Petersburg, Russia, 2006) (Eds. M. Ivanov and A. Rebrov, SBRAS Press, Novosibirsk, 2007), 771–776.
- M.N. Kogan, Rarefied-Gas Dynamics [in Russian] (Nauka, Moscow, 1967).
- G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, 1994).
- F.C. Hurlbut, “On the Molecular Interactions between Gases and Solids,” in: Dynamics of Manned Lifting Planetary Entry (Wiley, New York, 1963), 754–777.
- V.P. Shidlovskii, Introduction to Rarefied Gas Dynamics [in Russian] (Nauka, Moscow, 1965).
- G. Kirchhoff, Vorlesungen über Mathematische Physik: Mechanik (Teubner, Leipzig, 1876).
- O.M. Belotserkovskii, A.I. Erofeev, and V.E. Yanitskii, “Nonstationary Method of Direct Statistical Simulation of Rarefied Gas Flows,” Zh. Vych. Matem. Mat. Fiz. 20(5), 1174–1204 (1980).
- M.S. Ivanov and S.V. Rogazinskii, “Comparative Analysis of the Algorithms of the Direct Statistical Simulation Method in Rarefied Gas Dynamics,” Zh. Vych. Matem. Mat. Fiz. 28(7), 1058–1070 (1988).
- A.N. Volkov, “The Aerodynamic and Heat Properties of a Spinning Spherical Particle in Transitional Flow,” (Proc. 6th Int. Conf. Multiphase Flow, Leipzig, ICMF’2007, CD, Paper S2 Mon C 6).
- V.V. Riabov, “Aerodynamics of a Spinning Cylinder in Rarefied Gas Flows,” J. Spacecraft and Rockets 36(3), 486–488 (1999). CrossRef
- Aerodynamic coefficients of a spinning sphere in a rarefied-gas flow
Volume 44, Issue 1 , pp 141-157
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- spinning sphere
- transitional flow regime
- drag force coefficient
- Magnus force
- aerodynamic torque coefficient
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