The planar motion of a slightly distorted sphere around a fixed sphere in an unbounded fluid is investigated by a perturbation approach. An approximate velocity potential is derived in terms of sets of singularities by using the successive potential method. In a relative coordinate system moving with the uniform stream, the kinetic energy of the fluid is expressed as a function of 15 added masses. Approximate analytical solutions of added masses in series form are obtained and applied to determine the trajectories of the slightly distorted sphere around a fixed sphere. The hydrodynamic interaction between two bodies is computed based on the dynamical equations of motion. It is found that the presence of a sphere generates an effect on the planar motion of the slightly distorted sphere and the initial configuration of the slightly distorted sphere has a decisive influence on the development of its subsequent rotational motion.
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Received 24 August 2000 and accepted 8 February 2001
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Sun, R., Chwang, A. Hydrodynamic Interaction Between a Slightly Distorted Sphere and a Fixed Sphere. Theoret Comput Fluid Dynamics 15, 11–22 (2001). https://doi.org/10.1007/s001620100040
- Coordinate System
- Kinetic Energy
- Dynamical Equation
- Rotational Motion
- Planar Motion