Journal of Fluid Mechanics

Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion

Eugene J.  Chang a1p1 and Martin R.  Maxey a1
a1 Center for Fluid Mechanics, Turbulence and Computation, Brown University, Box 1966, Providence, RI 02912, USA

Article author query
chang ej   [Google Scholar] 
maxey mr   [Google Scholar] 


A direct numerical simulation, based on spectral methods, has been used to compute the time-dependent, axisymmetric viscous flow past a rigid sphere. An investigation has been made for oscillatory flow about a zero mean for different Reynolds numbers and frequencies. The simulation has been verified for steady flow conditions, and for unsteady flow there is excellent agreement with Stokes flow theory at very low Reynolds numbers. At moderate Reynolds numbers, around 20, there is good general agreement with available experimental data for oscillatory motion. Under steady flow conditions no separation occurs at Reynolds number below 20; however in an oscillatory flow a separation bubble forms on the decelerating portion of each cycle at Reynolds numbers well below this. As the flow accelerates again the bubble detaches and decays, while the formation of a new bubble is inhibited till the flow again decelerates. Steady streaming, observed for high frequencies, is also observed at low frequencies due to the flow separation. The contribution of the pressure to the resultant force on the sphere includes a component that is well described by the usual added-mass term even when there is separation. In a companion paper the flow characteristics for constant acceleration or deceleration are reported.

(Published Online April 26 2006)
(Received July 19 1993)
(Revised April 6 1994)

p1 Present Address: Naval Research Laboratory, Code 6410, Washington, DC 20375, USA