COMPARISON OF VARIOUS NUMERICAL DIFFERENCING SCHEMES IN PREDICTING NON-NEWTONIAN TRANSITION FLOW THROUGH AN ECCENTRIC ANNULUS WITH INNER CYLINDER IN ROTATION

Abstract

Flow through annulus is a widely solved problem in fluid mechanics because of its practical applicability in many areas. In oil well drilling, cuttings generated are of non-Newtonian nature which flows through an eccentric annulus with inner cylinder in rotation, considering the real drilling situations. In the present work, a comparison have been done amongst three differencing schemes, the second order upwind, the Power law scheme and QUICK scheme used in computational fluid dynamics solution algorithms, so as to find the best amongst them to solve transition flow for this case as well as in general. A three dimensional orthogonal hexahedral mesh with suitable boundary conditions & input parameters was taken as computational domain for eccentric annulus. This was solved with standard k-ω turbulence model and SIMPLE algorithm. Results were validated against the published experimental work of J. M. Nouri, et. al [1]. Radial velocity, axial velocity and tangential velocity of fluid were plotted along chosen planes and contours of molecular viscosity as well as turbulence kinetic energy were observed for comparison amongst the solutions obtained by three differencing schemes. Although in most of the cases close agreement have been observed between computational data, but as far as prediction of radial velocity is concerned there was surprising difference amongst the three schemes.