The pipeline flow of capsules part 6 - numerical analysis of some variables determining free flow

Four specific factors, concerned with the geometry and frictional effects of a cylindrical capsule flowing freely in a liquid-filled pipe in which the liquid is in laminar flow, have been investigated numerically. The factors are: axial displacement of the capsule from the concentric position, end configuration and length of capsule, deformed circular cross-section and frictional effect between the bottom of the capsule and the inside pipe surface. The effect which axial displacement has on any dynamic variable, e.g. capsule velocity, was found to be a uniformly increasing one for up to 90% of the total possible displacement. Beyond 90% displacement the effect was relatively much more pronounced. Friction was found to decrease capsule velocity uniformly: as the friction force was increased a critical value was reached for larger capsules which resulted in a rapid decrease to zero. The effect of end shape on velocities and flow rates was found to be negligible, although there was a considerable change in flow pattern. Deformation of the capsule, i.e. deformation through a vertical cross-section, caused little effect for 10–20% deformations, beyond which there was almost a linear increase of percentage deformation with pressure gradient required to maintain the same capsule velocity. The rate of increase itself increased with the proximity of the capsule to the pipe wall. Nous avons etudie quatre facteurs specifiques en relation avec la geometric et la friction d'une capsule cylindrique s'ecoulant librement dans un tuyau rempli d'un liquide dont le regime est laminaire. Ces facteurs sont: le deplacement axial de la capsule, la geometric et longueur de la capsule, la deformation de la section circulaire de la capsule et la friction entre la portion inferieure de la capsule et la surface interieure du tuyau. Le deplacement axial a un effet sur les variables dynamiques, telle que la vitesse. Cet effet croit uniformement jusqu'a 90% du deplacement total possible mais est plus prononce au-dela de cette limite. La friction diminue uniformement la vitesse de la capsule mais cause une diminution rapide au-dela d'une valeur critique. Le patron d'ecoulement est grandement affecte par la geometrie des capsules mais L'effet sur la vitesse et le taux d'ecoulement est negligeable. La vitesse de la capsule est peu affectee par une deformation variant de 10 a 20% de la section perpendiculaire.