Terminal velocity of porous spheres

TLDR: In this paper, the authors experimentally measured the terminal velocity of porous spheres for a Reynolds number range of 0.2 to 120 and found that the porous sphere terminal velocity was less affected by the container walls than for the case of an impermeable sphere.

Abstract: Terminal velocity of porous spheres was experimentally measured for a Reynolds number range of 0.2 to 120 for a normalized sphere radius, β = R/R of 15.6 to 33, where R and k are the sphere radius and permeability, respectively. The drag coefficient for 15 < β < 33 was found to be CD = 24Ω/Re [1 + 0.1315 Re(0.82 - 0.05w)] for 0.1 < Re ≤ 7 and CD = 24Ω/Re [1 + 0.0853 Re(1.093 - 0.105w)] for 7 < Re < 120 with w = log10Re where Re is the sphere Reynolds number and Ω=2β2 [1 - (tanh β/β)] / 2β2 + 3[1 - tanh β/β)] At high Reynolds numbers, it was found that the porous sphere terminal velocity was less affected by the container walls than for the case of an impermeable sphere. However, at very low Reynolds numbers, the wall effects were found to be similar for both the permeable and the impermeable spheres. On a mesure experimentalement la vitesse de chute libre de spheres poreuses, pour des nombres de Reynolds variant entre 0.2 et 120, et pour un rayon normalise de sphere( β = R/k) de 15.6 a 33; R et k sont respectivement le rayon et la permeabilite de la sphere. On a trouve que le coefficient de frottement, dans le cas ou 15 < β < 33, etait: CD = 24Ω/Re [1 + 0.1315 Re(0.82 - 0.05 w)] lorsque 0.1 < Re ≤ 7 et CD = 24Ω/Re [1 + 0.0853 Re(1.093-0.105 w)] lorsque 7 < Re < 120 w = log10ReRe est le nombre de Reynolds de la sphere et Ω = 2β2 [1 - (tanh β/β)]/2β2 + 3[1 - (tanh β/β)] On a trouve que, pour des nombres de Reynolds eleves, la vitesse limite de la sphere poreuse etait moins affectee par les parois du contenant que lorsqil agissait d'une sphere impermeable; toutefois, pour des nombres de Reynolds faibles, les effets des parois etaient les měmes, dans le cas de spheres permeables et impermeables.