Numerical study of the flow in an eccentric cylindrical gap with a feed hole

Abstract

A numerical investigation on the flow of eccentric Taylor-Couette system with rotating inner cylinder and fixed outer cylinder is presented. The flow between eccentric rotating cylinders is of interest in the fluid dynamic community, for instance, in the lubrication technology due to the strong effect of both the Reynolds number (Re) and eccentricity. Here, Re is defined as Re = UcLc/ν where Uc is the rotational speed of the inner cylinder, Lc is the mean value of the gap width and ν the kinematic viscosity of the fluid. The main flow field has been examined, the topology of its streamlines and the transition region from the laminar Couette-flow to the Taylor-vortex-flow in different eccentric arrangements of the cylinders. The effect of the eccentricity on flow patterns was studied for three different values of the eccentricity ε relative to the medium gap width 0.25, 0.5 and 0.75, respectively. For the classical Taylor-Couette system with rotating inner cylinder and fixed outer cylinder, the fluid flow passes through stable circular Couette flow for Re < Recr and steady axisymmetric Taylor vortex flow for Re > Recr. The value of Recr was found to increase by increasing the eccentricity. However, if one of the cylinders is displaced to an eccentric position, the rotational symmetry is broken and a fully three-dimensional flow can be observed. Typically, the Reynolds equations, which are an idealized form of the Navier-Stokes equations, are used to compute the flow in journal bearings yielding a pressure distribution in relation to mean clearance and eccentricity. This pressure distribution, which can be calculated analytically, is compared with computed data by solving the Navier-Stokes equations directly. For small clearances an outstanding agreement of the pressure distribution is obtained for low Re however, for a larger gaps between inner and outer cylinder a substantial deviation can be found. Furthermore, a feed hole is applied to the external cylinder to model the flow in journal bearings. The fluid flow, which is fed through the hole in the outer cylinder, generates a cross flow mixing with the circumferential main flow of the system and exits at both ends of the system, equally. In this case the pressure distribution differs essentially from the idealized distribution given by the Reynolds equations