UNSTEADY-FLOW ABOUT A SPHERE AT LOW TO MODERATE REYNOLDS-NUMBER .2. ACCELERATED MOTION

A full numerical simulation based on spectral methods is used to inves tigate linearly accelerating and decelerating flows past a rigid spher e. Although flow separation does not occur at Reynolds numbers below 2 0 for a steady flow, in the linearly decelerating flow separation is o bserved at much lower Reynolds numbers with complete detachment of vor ticity possible in certain cases. The existence of a large recirculati on region contributes to the result that a negative viscous force on t he sphere is possible. The contribution of the pressure to the force i ncludes 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 a fter acceleration or deceleration ends followed by rapid convergence a t later times to the steady state. For the cases examined this converg ence is found to be exponential except for those in which the sphere i s brought to rest in which case the convergence remains algebraic. Thi s includes the special case of an infinite acceleration or deceleratio n where the free stream velocity is impulsively changed.