Study, Analysis, and Validation of a Specific Two-fluid Model for Dispersed Two-Phase Flow

Abstract

Multiphase flows are commonly found and have a significant role in different processes in the energy, environmental, biological, and pharmaceuticals industries. The behavior of multiphase flows is very complicated due to their multiphysics nature and the fact that they involve more than one simultaneous physical field. An understanding of this behavior is vital for designing and operating process equipment in the aforementioned industries. While experimentation can be a useful method of acquiring this information, its limitations make it impractical in many cases. Specifically, experimental approaches can be time-consuming, expensive, and, in some cases, are infeasible.

Computational fluid dynamics (CFD) can be a more feasible option. However, the accuracy of CFD simulations relies heavily on the model used to represent the underlying physical phenomena, closures introduced, and numerical methods employed to solve the model. As a result, considerable effort has been put into developing multiphase flow models in the literature. In general, the validity of different variations of the two-fluid model could be examined from two points of view: (i) physical fidelity of the canonical form of the model and (ii) accuracy of the closures used to describe the interphase momentum exchange term. In the two-fluid model canonical form, a key point to consider is whether or not molecular fluxes (stress, etc.) appear in the dispersed phase momentum equation. Furthermore, many different closure terms are used in the literature for performing simulations without conclusive efforts to validate them.

In this research, most of the effort has been devoted to addressing these issues. First, a less-studied variation of the two-fluid introduced by Brennen, which has a more physically-informed mathematical derivation is introduced and discussed. Having established the canonical form of the Euler-Euler model, the interphase momentum exchange term is studied. Three closures supported by theoretical derivations are analyzed through scaling analysis and simulation. This analysis involves three different multiphase flow regimes present in industrial processes: bubbly flow, particulate flow, and flow of microorganisms in liquid. Finally, based on these analyses, the dispersion force was determined to be the most significant of the three closure terms, and as a result, added to the model. Eventually, the final form of the Brennen two-fluid model and the dispersion force as momentum exchange term is formulated and used for simulation and validation.

While not conclusive, simulation results are promising where, for a bubbly flow test case, the Brennen model with dispersion achieved better accuracy than the well-known standard version of the two-fluid model, especially in areas with high velocity magnitude. Additionally, using the dispersion force, the nonphysical behavior in the regions with high gradient in volume fraction is removed, and smoother results for the volume fraction of dispersed phase are obtained.