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Three-dimensional flow through forming fabrics and the motion of flexible fibres in flow Vakil, Ali

Abstract

This dissertation addresses the 3D flow through forming fabrics. In the first part of this thesis, the single phase 3D flow through certain specific fabrics was modeled. In practice, the Reynolds number of the fabric flow, based on paper-side filament diameter, is around 100. Consequently, it is not too surprising that the permeability of the fabrics was found to vary approximately as Re ⁻⁰˙⁴, which is intermediate between the expected low Re (Re⁻¹) and high Re (Re⁰) limits. The resistance of a multilayer fabric was found to be nearly equal to the sum of the resistance of each layer considered in isolation. The effect of filament-scale and weave-scale flow non-uniformity on the fiber distribution in the finished paper was considered. For one specific fabric, there was 3 times more chance for short fibers to accumulate initially over openings than blockages of the fabric. Jet-to-wire speed ratio was found to have an insignificant effect on permeability results, but a marked effect on the Machine Direction shear stress in the vicinity of the paper-side filaments. In an attempt to model sheet formation, numerical simulations of the motion of a single fiber in the flow field of a cylinder was carried out as a canonical test case of the fiber/filament interaction system. Seven dimensionless groups govern the problem. A range of dimensionless groups were found for which the fiber hung up on the cylinder, whereas for other values of the dimensionless groups the fiber slid over the cylinder. In general, longer and more flexible fibers had a greater likelihood to be caught by the filament. Yawed finite aspect ratio cylinders at moderate Reynolds numbers are approximate representations of fibers in the flow field of forming fabrics. No analytical solution or any experimental data are reported in the literature to predict the drag and lift force on such particles in such flows. Computational Fluid Dynamics (CFD) simulations were conducted to find the drag and lift coefficients of inclined finite circular cylinders at Reynolds numbers in the range 1-40. The simulations showed that the Independence Principle was highly inaccurate for low inclination angles.

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