Multi-Dimensional Verification of the Two-Fluid Momentum Equation on Dispersed Flows

The standard two fluid model treats the dispersed phase, such as bubble or mist flow, as a materially-connected phase (continuous phase), and thus there is a difficulty in modeling stress terms in the averaged momentum equations. Ansderson and Jackson and Prosperetti formulated the averaged momentum equations for dispersed flow in a different manner. They averaged the equation of a solid/fluid particle motion that includes various force terms such as the drag, lift, added mass, and history forces. The approach might be more reasonable for dispersed flow. Recently, Kim et al showed theoretically that the different momentum equations can predict the motion of the fluid particle against the surrounding fluid correctly. This approach is validated through one-dimensional simulations in a pipe, contraction and expansion. In this study the averaged two-fluid momentum equations based on the equation of a fluid particle are investigated with a multi-dimensional thermal hydraulic code, CUPID. The CUPID code has been developed in Korea Atomic Energy Research Institute (KAERI) for the analysis of transient two-phase flows in nuclear reactors. It employs a two-fluid three-field model. The governing equations are discretized by the finite volume method (FVM) and uses unstructured mesh. The validation of CUPID can be found in Yoon's paper. Since CUPID is a multi-dimensional code, it does not need any wall friction partitioning terms used in one dimensional thermal hydraulics codes but solves the shear stress directly. The validity of the momentum equations is checked by solving a simple two dimensional turbulent channel flow without gravity including the parameter variations, such as inlet velocity, Reynolds number, mesh, inlet void fraction. In this study, the conventional and fluid particle based two-fluid momentum equation were investigated with the multi-dimensional two-phase code, CUPID. The conventional two-fluid momentum which assumes the shear forces of the dispersed phase as the matter of continuum showed unphysical momentum increase on disperse phase. This issue in laminar flow cases was solved by the modified momentum equation which uses the shear forces as the form of the partitioned viscous force of surrounding fluid according to void fraction of each phase