Bistability of buoyancy-driven exchange flows in vertical tubes

Buoyancy-driven exchange flows are common to a variety of natural and engineering systems, ranging from persistently active volcanoes to counterflows in oceanic straits. Laboratory experiments of exchange flows have been used as surrogates to elucidate the basic features of such flows. The resulting data have been analysed and interpreted mostly through core–annular flow solutions, the most common flow configuration at finite viscosity contrasts. These models have been successful in fitting experimental data, but less effective at explaining the variability observed in natural systems. In this paper, we demonstrate that some of the variability observed in laboratory experiments and natural systems is a consequence of the inherent bistability of core–annular flow. Using a core–annular solution to the classical problem of buoyancy-driven exchange flows in vertical tubes, we identify two mathematically valid solutions at steady state: a solution with fast flow in a thin core and a solution with relatively slow flow in a thick core. The theoretical existence of two solutions, however, does not necessarily imply that the system is bistable in the sense that flow switching may occur. Through direct numerical simulations, we confirm the hypothesis that core–annular flow in vertical tubes is inherently bistable. Our simulations suggest that the bistability of core–annular flow is linked to the boundary conditions of the domain, which implies that is not possible to predict the realized flow field from the material parameters of the fluids and the tube geometry alone. Our finding that buoyancy-driven exchange flows are inherently bistable systems is consistent with previous experimental data, but is in contrast to the underlying hypothesis of previous analytical models that the solution is unique and can be identified by maximizing the flux or extremizing the dissipation in the system. Our results have important implications for data interpretation by analytical models and may also have interesting ramifications for understanding volcanic degassing

INTERFACE ADVECTION AND JUMP CONDITION CAPTURING METHODS FOR MULTIPHASE INCOMPRESSIBLE FLOW

In this work, new numerical methods are proposed to efficiently resolve interfaces occurring in multiphase incompressible flows. Multiphase flow problems consist of a large class of physical phenomenon from bubbles to bow waves in ships. Over the recent decades, numerical methods are becoming an important tool in addition to pure analytical and experimental methods. However, there is still large room for improvement in existing numerical methods. Contributions are made in the field of interface advection and the jump conditions for pressure. In the case of advection, a method is developed specifically for implicit interfaces that evolve with the Eulerian advection of a scalar field. The new method is validated by comparison with the interfaces that evolve with Lagrangian advection using a connected set of marker particles. To accurately capture the jump conditions, a second order accurate method is proposed for solving the variable coefficient Poisson's equation in the discretized Navier-Stokes formulation. This new method assumes both phases exist in the interface cell and that their collective effect can be expressed by a volume fraction weighted average value. The new capabilities have been integrated to build a dynamic Navier-Stokes equation solver. The new advection scheme scheme is also associated to track the interface. The new solver is tested by applications in several two phase flow problems