STABILITY OF ECCENTRIC CORE-ANNULAR FLOW

Perfect core-annular flows are two-phase flows, for example of oil and water, with the oil in a perfectly round core of constant radius and the water outside. Eccentric core flows can be perfect, but the centre of the core is displaced off the centre of the pipe. The flow is driv en by a constant pressure gradient, and is unidirectional. This kind o f flow configuration is a steady solution of the governing fluid dynam ics equations in the cases when gravity is absent or the densities of the two fluids are matched. The position of the core is indeterminate so that there is a family of these eccentric core flow steady solution s. We study the linear stability of this family of flows using the fin ite element method to solve a group of PDEs. The large asymmetric eige nvalue problem generated by the finite element method is solved by an iterative Arnoldi's method. We find that there is no linear selection mechanism; eccentric flow is stable when concentric flow is stable. Th e interface shape of the most unstable mode changes from varicose to s inuous as the eccentricity increases from zero.