Diffuse Solid-Fluid Interface Method for Dispersed Multiphase Flows

Abstract

Industrial chemical engineering processes such as bubble columns, reactors and separators involve multiphase flows of two or more fluids. In order to improve the design and operation of these processes, an understanding of their multiphase hydrodynamics is essential. An emergent tool in studying multiphase flow systems that is becoming readily accessible to researchers is computational fluid dynamics (CFD) simulation. CFD simulations of multiphase flow systems enable researchers to explore the effect of different combinations of operating conditions and designs on pressure drop, separation efficiency, and heat and mass transfer without the cost and safety issues incurred by experimental design and pilot studies. Consequently, CFD simulations are increasingly relevant for the design and optimization of chemical process equipment. The multiphase hydrodynamic model that is often used to study chemical engineering processes is the two-fluid (Euler-Euler) model. In this model, the fluids are treated as inter-penetrating continua and fluid phase fractions are used to describe the average spatial composition of the multiphase fluid.

Generally, the physical boundaries (e.g. vessel walls, reactor internals, \textit{etc.}) in numerical simulations using the two-fluid model are defined by the mesh or grid, i.e. the mesh/grid boundaries correspond to an approximation of the physical boundaries of the system. The resulting conformal mesh/grid could potentially contain a large number of skewed elements, which is undesirable in numerical simulations. One approach to address this issue involves approximation of solid boundaries using a diffuse solid-fluid interface approximation. This approach allows for a structured mesh to be used while still capturing the desired solid-fluid boundaries. The diffuse-interface method also allows for the simulation of moving boundaries without the need for manipulation of the underlying mesh/grid or interpolation of boundary variables to the nearest node. This allows for the geometry of the domain of interest (i.e. process equipment) to be easily modified during the process of simulation-assisted design and optimization.

In the two-fluid model, phase fractions are used to describe the composition of the mixture and are bounded quantities. Consequently, numerical solution methods used in simulations must preserve boundedness for accuracy and physical fidelity. Firstly, a phase-bounded numerical method for the two-fluid model is developed in which phase fraction inequality constraints are imposed through the use of an implicit variational nonlinear inequality solver. The numerical method is verified and compared to an established explicit numerical method. The effect of using separate phasic pressure fields as opposed to the commonly used single-pressure assumption is also found to be non-negligible in dilute dispersed flows (less than 3% gas fraction).

Subsequently, the phase-bounded numerical method is extended to support a diffuse-interface method for the imposition of solid-fluid boundaries. The diffuse-interface is used to define physical boundaries and boundary conditions are imposed by blending conservation equations from the two-fluid model with the solid boundary condition. Simulations of two-dimensional channel flow and flow past a stationary cylinder are used to validate the diffuse-interface method. This is achieved by comparing the bubble plume width and time evolution of the overall gas hold-up from the diffuse-interface simulations with results obtained using boundary-conformal meshes. The results from the channel flow simulations are found to be in agreement with the boundary-conformal mesh solution when the interface width is sufficiently small. In the case of flow past a stationary cylinder, similar flow features are observed in both diffuse-interface and reference simulations.