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Numerical simulations of flow through model paper machine forming fabrics Huang, Zhaolin

Abstract

In the manufacture of high quality paper, it is of vital importance that the fiber distribution in the web be as uniform as possible so that the best formation is attained. In order to provide for uniform dewatering and uniform fibre distribution, a uniform velocity profile is desired upstream of the paper side fabric layer. To understand the factors that affect the flow upstream of the forming fabric, a computational model has been applied to study the flow details through paper machine forming fabrics. The flow through the forming fabric is three-dimensional and involves interaction with wood fibers and fines, and is therefore extremely complicated to model in full. To avoid these difficulties, simplified model was proposed. The flow through forming fabrics was modeled as two-dimensional laminar water flow around cylinder arrays of unequal sizes. All calculations are done using FLUENT™, a commercially available CFD software. A systematic study on both an existing forming fabric i.e., the commercial 73 x 75 mesh triple-layer fabric, and a hypothetical triple-layer fabric was performed. Under their current configurations, there is little variation of the flow upstream of the fabric caused by the machine side mesh. The effect of several design parameters of the two fabrics were investigated, such as the z direction separation between the paper side and machine side layers, the diameter ratio of two-row cylinders, the second row spacing between two adjacent cylinders, and variable second row spacing between two adjacent cylinders. The simulations showed that upstream flow was non-uniform and may cause formation problems for several conditions. First, when the forming fabric has fine mesh in both paper and machine sides, changes in z direction separations of the two layers, diameter ratios, or offsets between two layers appear to have little impact on the velocity profiles upstream. Second, when the fabric has a fine mesh in the paper side and a coarse mesh in the machine side, the z direction separation between the paper side and machine side layers has the most significant effect on the flow non-uniformity. When this separation is greater than approximately 2d, where d is the diameter of filaments on the paper side layer, the variations on the velocity profile are negligible. Third, the steady simulation gives the same trend of the impact on flow upstream as the unsteady simulation. Fourth, the unequal cross-machine direction (CD) separations of the machine side layer also have a significant impact on the flow upstream. The CD separation of the machine side layer should be kept as constant as possible; otherwise a larger z direction separation between the two layers is required to eliminate the impact on flow upstream. As a rough rule of thumb, provided the fine layer is more than L upstream of the coarse layer, where L is the scale of the largest irregularity in the downstream fabric (e.g. the width of two grouped filaments), then the flow above the fine layer is unaffected by the coarse layer. This two-dimensional model can only address the wire marks in the cross direction, not in the machine direction. It cannot distinguish double-layer fabrics from single-layer ones or different triple-layer fabrics among many configurations of CD filaments. Developing a three-dimensional model is thus recommended for future work.

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