An experimental study of motion of cylinders in newtonian fluids: Wall effects and drag coefficient

Abstract

The terminal velocity of several cylinders (of glass, perspex and stainless steel) falling with their axis parallel to the direction of motion has been measured in a series of Newtonian fluids embracing a 40-fold variation in liquid viscosity. The measurements have been carried out in fall tubes of four different diameters to elucidate the importance of wall effects. The experimental results encompass the following ranges of conditions: cylinder to fall tube diameter ratio: 0.08 to 0.4; length to diameter ratio: 0.05 to 2 and Reynolds number varied from 0.2 to 180.The wall effects are discussed in a manner analogous to those for spherical particles. Terminal velocity data are analysed using two approaches, namely, drag coefficient-Reynolds number relationship and a dimensionless velocity ratio denoting the departure from the behaviour of an equivalent sphere. Predictive equations have been developed using both schemes.LA vitesse terminale de plusieurs cylindres (de verre, de Plexiglas et d'acier inoxydable) tombant de telles sorte que leur axe principal est confondu avec la direction de chute, a Cte mesurC dans une serie de fluides newtoniens dont la ganime de viscosite varie d'un facteur 40. Des mesures ont 6tC effectuees dans des tubes de quatre diametres differents pour comprendre I'importance des effets de parois. Les resultats experimentaux englobent les conditions suivantes: rapport cylindre-diambtre du tube entre 0.08 et 0.4; rapport longueur-diamktre entre 0.05 et 2 ; et nombre de Reynolds conipris entre 0,2 et 180.Les effets de parois sont examines comme dans le cas des particules spheriques. On a analyse les donnees de vitesse terminale par deux approches, a savoir, la relation entre le coefficient de trainee et le nombre de Reynolds et un rapport de vitesse sans dimension representant I'Ccart par rapport au comportement d'une sphere Cquivalente. On a mis au point des modeles prCdictifs en utilisant ces deux approches.

Drag on non-spherical particles in power law non-Newtonian media

“…This finding is consistent with that of . Similarly, except a very few points relating to the sedimentation of thin needles (Unnikrishnan and Chhabra, 1991;Venumadhav and Chhabra, 1995), the maximum and average deviations for all other shapes are less than 100% and 35%, respectively, which are well within the limits of predictions of most such correlations available in the literature Yow et al, 2005). Finally, the predictions of various correlations themselves differ by varying amounts.…”

“…Cylinders (Both orientations) 0.63-0.87 10 À 6 -143 et al (1994) for spheroidal particles (Re PL V 100), of Sharma and Chhabra (1991) and Borah and Chhabra (2005) for cones in power law fluids (10 V Re PL V 110), and of Unnikrishnan and Chhabra (1991) and of Venumadhav and for cylinders, needles and prisms ( Table 2). All these results display similar deviations and for the entire population (both Newtonian and power law fluids) of 1437 data points, the overall mean deviation is 30%.…”

“…Furthermore, bearing in mind that the experimental determination of drag coefficient for non-spherical particles can easily entail an error of 10%-15% or even more, both these predictions are regarded to be satisfactory and acceptable. Included in this figure are also the results of Borah and Chhabra (2005) and of Sharma and Chhabra (1991) for cones, the numerical predictions of Tripathi et al (1994) for spheroidal particles, data for cylinders falling in vertical orientation (Unnikrishnan and Chhabra, 1991;Venumadhav and Chhabra, 1995) and of prisms (Venumadhav and Chhabra, 1995) as summarized in Table 1. Combined together, these results encompass the following ranges of conditions: 0.33 V W V 0.98 and 10 À 5 V Re V 400 (based on d s ).…”

A new shape dependent drag correlation formula for non-spherical rough particles. Experiments and results

“…Some authors use the ratio between the volume-equivalent-sphere and the surface-equivalent-sphere diameters (d n /d A ), where the surface is that of the projected area [2,[12][13][14]. Other authors, in order to focus on the effects of particle elongation, define particles shape in terms of the aspect ratio (particle length along the symmetry axis over the largest diameter of the cross section) [15,16].…”

Revisit of the Wall Effect on the Settling of Cylindrical Particles in the Inertial Regime

“…It is in agreement with the literature that corrections developed for spherical particles can reasonably predict to the settling of cylindrical particles having an aspect ratio less than 2. 20,35,36 Effect of particle size with constant aspect ratio A comparison of the wall effect on the settling of cylindrical particles having a constant l/d ratio of 4 but various diameters and lengths is shown in Figure 9. It can be seen that U t /U t,∞ is only a function of l/d and independent of the actual d and l when the particle settling orientation is essentially constant at low d/D and high d/D.…”