Mathematical modeling of frazil ice formation and evolution

In cold regions the production of frazil ice in supercooled turbulent water has a profound impact on the design, operation and maintenance of water resources infrastructure. Studies on frazil ice formation are therefore important and imperative for ice engineering. This study mainly focuses on the development of mathematical models for frazil ice formation and evolution, which is an important part of modeling ice formation in a river.; A general mathematical model is formulated that includes the modeling of flow and turbulence, heat transfer, and frazil ice transport in open channel flow. In addition the methodologies to model the physical processes of ice formation are described. Three mathematical models to simulate the supercooling process and frazil ice evolution were developed based on the general mathematical model and frazil ice dynamics. A zero-dimensional mathematical model was able to simulate water temperature history, frazil ice number evolution in the well-mixed water and the varied size distribution of frazil ice during the supercooling process. A vertical one-dimensional mathematical model was able to simulate water temperature variation with time at the different water depths, velocity and turbulent intensity distribution over the water depth, and the vertical distribution of frazil ice number concentration. The variation of mean size of frazil ice particle is also simulated. An extended one-dimensional mathematical model was developed from the vertical one-dimensional model by including the size distribution of frazil ice and the complicated physical processes. The three mathematical models developed are calibrated and verified using experimental data.