ISSN:
0271-2091
Keywords:
pre-metered
;
metered
;
free boundary condition
;
free surface flow
;
viscous
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
In a forward-roll coating gap or nip, steady laminar flow of liquid between counter-rotating cylinders or rolls is used to split the flow into a coated layer on one roll and a rejected layer on the other. Both layers have free surfaces in contact with air. Liquid may be carried into the gap as a layer on one or both rolls. If the arriving layer is not too thick, all of the liquid flows through the gap, a situation called pre-metered. If the arriving layer is too thick, part of the liquid is rejected and runs back down the lower roll. The flow rate through the gap is said to be metered and is not known a priori.The transition from a pre-metered regime to the metered situation was examined by solving the Navier-Stokes system for steady, two-dimensional flow in a domain bounded by free surfaces, two rigid roll surfaces and chosen inflow and outflow surfaces. The free boundary condition, as described by Papanastasiou et al. (Int. j. numer methods fluids, 14, 587 (1992)), was explored and proved to accommodate both the pre-metered and metered regimes. A run-back flow state across the synthetic inlet plane was obtained, provided a condition on the thickness of the arriving layer was replaced by a kinematic condition at a certain stage.The coupled equation system was solved by Galerkin's method with finite element basis functions. The resulting non-linear algebraic system was solved by Newton's method with initialization by pseduo-arc-length continuation and automatic parameter step adjustment.Results show the existence of multiple solutions which can lead to hysteresis. Flow regime maps were constructed to portray the operating parameter range in which a coating bead can exist and the ranges in which a coating gap operates in either the pre-metered or the metering regime. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 813-831, 1997.
Additional Material:
18 Ill.
Type of Medium:
Electronic Resource
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