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Applied mathematics, Fluids and plasma physics, Applied mechanics
The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of a two-roll mill is also given. Photographs confirm the salient features predicted by our theoretical study.
Hills, C. (2002). Flow Patterns in a Two-Roll Mill. Quarterly Journal of Mechanics and Applied Mathematics. vol. 55, part 2, pg. 273-296. doi:10.21427/q4ax-sg57