Wall-induced forces on a rigid sphere at finite Reynolds number

By Lan Zeng, S. Balachandar, Paul F. Fischer. Journal of Fluid Mechanics, 2005

275 citations recorded by the source corpus.

We perform direct numerical simulations of a rigid sphere translating parallel to a flat wall in an otherwise quiescent ambient fluid. A spectral element method is employed to perform the simulations with high accuracy. For $Re\,{<}\,100$, we observe the lift coefficient to decrease with both Reynolds number and distance from the wall. In this regime the present results are in good agreement with the low-Reynolds-number theory of Vasseur & Cox (1977), with the recent experiments of Takemura & Magnaudet (2003) and with the simulations of Kim et al. (1993). The most surprising result from the present simulations is that the wall-induced lift coefficient increases dramatically with increasing $Re$ above about 100. Detailed analysis of the flow field around the sphere suggests that this increase is due to an imperfect bifurcation resulting in the formation of a double-threaded wake vortical structure. In addition to a non-rotating sphere, we also simulate a freely rotating sphere in order to assess the importance of free rotation on the translational motion of the sphere. We observe the effect of sphere rotation on lift and drag forces to be small. We also explore the effect of the wall on the onset of unsteadiness.

Subfields: Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/7cf3c537e8b7eae45955fbefafb287f45d9762a6

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Citations in the corpus

Particle focusing in microfluidic devices (2010, background): “This so-called ‘‘tubular pinch effect’’ is a result of competition of inertial lift forces acting on particles (Saffman 1965), of which the two dominant ones are the wall lift and the shear-gradientinduced lift (Asmolov 1999; Zeng et al. 2005).”
Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime (2008, methodology): “Similar behavior is reported by Zeng, Balachandar, and Fischer (2005) who have investigated the drag force on a single sphere translating in a channel with quiescent fluid.”