The flow between two coaxial cones

This thesis provides a study of the flow between two coaxial cones, a geometry with many interesting features and of practical importance. We consider the flow for different driving mechanisms and start by studying the highly viscous flow when the fluid is driven by rotation of the cones or a spherical lid. The solution is found through a low Reynolds number e)...pansion expressed as a combination of forced modes and geometric eigenmodes. The latter may cause an infinite sequence of counter-rotating vortices at the apex of the cones, we study the flow topology for a wide range of parameter values and specify when an infinite sequence of eddies occurs. We also cons.ider the non-axisymmetric Stokes flow where each wave number m gives rise to infinitely many eigeninodes. We map the spectra for different wave numbers and study the relative dominance between the eigenmodes. In contrast to the axisymmetric flow and the flow in one cone, no infinite sequence of eddies occur except in special cases. The solutions to the Stokes equations can be expressed as a symmetric and anti-symmetric part and we consider the response from a moving nonrigid lid, where the .flow exhibits a transition from a flow with closed streamlines to what appears to be a completely chaotic flow. in the second part we consider the flow which results from a point sink situated at the apex of the cones. The problem is reminiscent of the classical Jeffery-Hamel flow. We study the flow in the Stokes limit and find that the similarity solution experiences a break-down for certain cone openings. For a general Reynolds number the governing equations do not admit separable solutions so we consider asymptotic expansions of the flow in a narrow gap limit. In the far field the viscous forces dominate and the flow assumes a parabolic profile, the influence of inertia increases as we move downstream and by computing solutions of a PDE we find the resulting boundary layer flow. In the final chapter we consider the same flow for a slightly different cone geometry where there is a constant gap between the cones. We compare the solutions between the two geometries and discuss their qualitative differences.EThOS - Electronic Theses Online ServiceGBUnited Kingdo