Abstract
The flow of a pseudoplastic fluid with a free surface realized during the filling of a channel at a constant flow rate in the entry section is modeled. The fluid flow direction coincides with that of gravity. The mathematical problem is formulated on the basis of the complete equations of motion. A numerical technique for solving the problem in the two-dimensional formulation is developed on the basis of the SIMPLE algorithm and the method of invariants. A parametric investigation of the free surface evolution is carried out for different values of the governing criteria and rheological parameters. Three filling regimes are found to exist, namely, a complete filling regime, a transitional regime characterized by air cavity formation, and a jet regime. Criterial dependences separating these regimes are presented.
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