Entrance Lengths for Fully Developed Laminar Flow in Eccentric Annulus

Abstract

We study the entrance length in eccentric annular geometries, where the axes of the inner and outer pipes forming the annulus are offset from each other. Such geometries are considered relevant for several industrial applications, such as drilling of wells for hydrocarbon production or geothermal energy recovery, as well as biomedical research involving annular vessels. Previous studies have shown that eccentricity increases the entrance length in annular geometries, and this has been attributed to azimuthal redistribution of fluid between the wide and narrow sides of the annulus. The present computational study aims to increase the understanding of entrance lengths in eccentric annuli for laminar flow with Reynolds numbers spanning the range from the creep limit and up to intermediate laminar values, below the regime of annular gap instabilities. We find that the entrance lengths in eccentric annuli generally increase for narrower annular gaps (higher aspect ratios). Moreover, the entrance lengths in the annuli with higher aspect ratios are also more sensitive to the degree of eccentricity compared to wider annuli (lower aspect ratios). We report empirical correlations for the dimensionless entrance length using the same form as earlier studies (Le=[C0n+(C1Re)n]1/n). We find that eccentricity, which breaks the axial symmetry of the annulus and causes azimuthal flow in the entrance region, impacts the value of the exponent n, which has been assigned the value of 1.6 in previous studies of axisymmetric conduits.