A direct-forcing immersed-boundary (IB) pressure correction method is used to investigate numerically the total hydrodynamic force for a solid sphere in normal approach to a plane wall. For constant approaches, Cox and Brenner's classic asymptotic formula in the lubrication regime was extended to cover particle Reynolds number Re. ≤. 50. An explicit force formula was proposed by fitting the current simulation results. We also consider gravity-induced decent of an immersed sphere towards a wall and an equation of motion was proposed containing quasi-steady viscous drag and two unsteady components-added mass force and history force. Possible effects from liquid inertia at finite-Re and wall at small gaps are described by least-square fitting of the simulation results. The proposed formula agrees to existing low-Re theories.
|Number of pages||14|
|Journal||International Journal of Multiphase Flow|
|Publication status||Published - 2013 Jul|
All Science Journal Classification (ASJC) codes
- Mechanical Engineering
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes