Numerical Modeling of the Two-Phase Flow of Water with Ice in the Tom River

A new mathematical model and a numerical method were constructed for numerical investigation of a two-phase turbulent flow in an open channel. Solid particles with a density close to that of water were considered a continuous phase with effective properties. This new model is based on a continuum-mechanics approach, a hydrostatic assumption, and equations averaged by the flow depth. Turbulent closure of the equations was done with a two-parameter k − ε turbulence model modified by Pourahmadi and Humphrey to account for the influence of the particles on the turbulent structure of the flow. The new numerical method is based on partial elimination algorithm for computing areas of the two-phase flow free of ice particles and uses semi-implicit approximation in time. The influence of the dynamic parameters of the dispersed phase on the structure of the flow was also investigated by computing several scenarios of the flow in an open channel with a 90-degree bend. Applications of the approach to the modeling of riverside flooding due to sudden increase in the river depth after a release of an ice jam illustrate the capabilities of the model.