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Modelling of jet impingement and early roll forming Dalpke, Barbara


Twin-wire paper machines have gained great importance in the production of printing paper and other paper grades. The two major former types used are roll and blade formers, with each having fluid dynamics that significantly influence the quality of the final paper. While many aspects of these forming hydrodynamics are well understood, the first part of the drainage section, where the flow impinges between the two fabrics, has been largely neglected, although it is known that certain paper properties are strongly influenced in this zone. The objective of this study was to model the hydrodynamic details of jet impingement and drainage in the early part of roll forming in twin-wire paper machines. A theoretical approach based on computational fluid dynamics was chosen to model the free jet and impingement zone. For the first time, a two-dimensional, viscous model was employed using a Volume of Fluid method. The first step modelled jet impingement on a single fabric. This case represented jet impingement on the outer fabric in twin-wire formers. In addition, with slight modifications, it applies to Fourdrinier papermaking as well. Computations were carried out for cases with or without fibre mat build-up for different machine settings (jet velocity, impingement angle and jet rush or drag). It was shown that both the inertial and viscous component of resistance are important. It was further shown that forces from jet impingement influence flow over only a short distance around the impingement point, causing most of the drainage to occur over a distance of about one or two jet thicknesses. This force on the fabric is mainly influenced by the jet velocity and the impingement angle, while drainage depends mainly on the fibre mat resistance. Rush or drag affects the shear stress at the fabric, but has little influence on pressure and drainage. To validate the computations, drainage velocity profiles were measured for impingement on a stationary single fabric. Agreement with computations was reasonable over the first centimetre after impingement, but was less good further downstream. Probable causes are inaccurately measured fabric resistances at low flow velocities and a dependence of the re sistance on the flow angle. The fabric roughness also might have an important effect on drainage in single-fabric-impingement. The model was then extended to include the wedge of roll formers. The outer fabric curvature was calculated based on a force balance. Findings by other researchers regarding the dependence of the forming zone length on machine variables were confirmed. The pressure distribution in early roll forming takes on a more complex form than that given by P = T/R (pressure = fabric tension/roll radius). It is lower than T/R at the wedge entry, and then increases. In some specific cases, it increases to local pressures exceeding T/R. The increase depends on the jet velocity, wrap angle, and fibre mat resistance. Higher fabric tensions cause overall higher pressures. The forming zone geometry, which is partly influenced by the impingement forces, affects the pressure distribution, but the impingement position does not affect the flow in the wedge.

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