Wall effect for the fall of spheres in cylindrical tubes at high reynolds number

Abstract

New experimental results on the wall effect for sphere motion in cylindrical tubes are presented and discussed for the conditions dlD 5 0.9 and Re,,, I 2oooO. Extensive comparisons with previous studies have been carried out to evaluate their predictability and to demonstrate the utility of the present results.The wall factor, defined as the ratio of settling velocity in an unbounded medium to that measured in a cylindrical tube, is found to depend on sphere-to-tube diameter ratio and on sphere Reynolds number. However, for small values of the Reynolds number (Re 0.5), as well for large values (Re 2 loOO), the Reynolds number dependence of the wall factor disappears; in these regions, only the dependence on diameter ratio remains. De nouveaux rksultats exHrimentaux sur l'effet de paroi pour le dtplacement des sphbres dans des tubes cyclindriques sont prtsentks et analyds pour les conditions dlD s 0,9 Re,,, S 2000. On a effectue des c o m p s o n s ~OUS&S avec les ktudes antkrieures afin d'tvaluer la caractbre praictif du modble et de dtmontrer I'utilitk des prtsents r6sultats.On a trouvt que le facteur de paroi, dtfini c o m e le rapport entre la vitesse de dkantation dans un milieu infini et la vitesse dans un tube cylindrique, dtpendait du rapport de diamktre sphkres-tube et du nombre de Reynolds des sphtres. Cependant, pour le petites valeurs du nombre de Reynolds (Re s 0.5) c o m e pour les grands (Re I IOOO), la dtpendance du facteur de paroi par rapport au nombre: de Reynolds disparait; dans ces rkgions, seule subsiste la dkpendance par rapport au rapport des diambtres.Keywords: sphere drag, wall effect, terminal velocity. onfining walls are well known to exert a retarding C effect on a sphere in free fall. A knowledge of the wall

An approach for particle sinking velocity measurements in the 3–400 μm size range and considerations on the effect of temperature on sinking rates

“…At Reynolds numbers below 0.5, such wall effects only depend on the distance of the particle to the wall (Uhlherr and Chhabra 1995). In this study, sinking velocities were measured in glass cuvettes of different dimensions (Table 2).…”

NMR Imaging of Falling Water Drops

“…Apart from being of fundamental interest, the falling drop is the simplest model for studying extraction phenomena. Nevertheless, the dynamics of moving drops remain a challenge for scientists [1][2][3][4][5][6][7]. Falling drops are investigated, e.g., by optical methods, where the shape is interpreted in terms of fluid dynamic models [8,9].…”

Empirical Relationships for the Terminal Settling Velocity of Spheres in Cylindrical Columns

“…In evaluating the optimum values of the two parameters, experimental results obtained by Francis [3], Fidleris and Whitmore [4], McNown [7], Uhlherr et al [8] and Barr [9] were used in addition to those obtained in this work.…”

“…Such profile can be approximated with a logic function described by (8) With the physical limiting conditions for l = 0 and l = 1 discussed above, (8) becomes (9) Thus, the wall factor can be described with only two parameters namely l 0 and p.…”