Unsteady flow about a sphere at low to moderate Reynolds number. Part 2. Accelerated motion

TLDR: In this paper, a full numerical simulation based on spectral methods is used to investigate linearly accelerating and decelerating flows past a rigid sphere, and the authors find that the viscous force on the sphere decays in a power law manner after acceleration or deceleration ends, followed by rapid convergence at later times to the steady state.

Abstract: A full numerical simulation based on spectral methods is used to investigate linearly accelerating and decelerating flows past a rigid sphere. Although flow separation does not occur at Reynolds numbers below 20 for a steady flow, in the linearly decelerating flow separation is observed at much lower Reynolds numbers with complete detachment of vorticity possible in certain cases. The existence of a large recirculation region contributes to the result that a negative viscous force on the sphere is possible. The contribution of the pressure to the force includes a component that is well described by the inviscid added-mass term in both the accelerating and decelerating cases. The force on the sphere is found in general to initially decay in a power law manner after acceleration or deceleration ends followed by rapid convergence at later times to the steady state. For the cases examined this convergence is found to be exponential except for those in which the sphere is brought to rest in which case the convergence remains algebraic. This includes the special case of an infinite acceleration or deceleration where the free stream velocity is impulsively changed.