Fluid velocity fluctuations in a collision of a sphere with a wall

Abstract

A study of thermal counterflow using particle tracking velocimetry Phys. Fluids 23, 107102 (2011) Particle accumulation on periodic orbits by repeated free surface collisions Phys. Fluids 23, 072106 (2011) We report on the results of a combined experimental and numerical study on the fluid motion generated by the controlled approach and arrest of a solid sphere moving towards a solid wall at moderate Reynolds number. The experiments are performed in a small tank filled with water for a range of Reynolds numbers for which the flow remains axisymmetric. The fluid agitation of the fluid related to the kinetic energy is obtained as function of time in the experiment in a volume located around the impact point. The same quantities are obtained from the numerical simulations for the same volume of integration as in the experiments and also for the entire volume of the container. As shown in previous studies, this flow is characterized by a vortex ring, initially in the wake of the sphere, that spreads radially along the wall, generating secondary vorticity of opposite sign at the sphere surface and wall. It is also observed that before the impact, the kinetic energy increases sharply for a small period of time and then decreases gradually as the fluid motion dies out. The measure of the relative agitation of the collision is found to increase weakly with the Reynolds number Re. The close agreement between the numerics and experiments is indicative of the robustness of the results. These results may be useful in light of a potential modelling of particle-laden flows. Movies illustrating the spatio-temporal dynamics are provided with the online version of this paper.

Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes

“…The governing equations (1)-(2) are discretized on a staggered grid with the velocities at the faces and all the scalars in the center of the computational cell; the resulting system of equations is solved by a fractional-step method. The finite-difference solver is based on that described by [34] and has been tested in a wide variety of enclosed cylindrical flows [18,20,24,25,32,33], establishing resolution requirements over a wide range of parameters.…”