The rapidly converging section of a paper-machine headbox carries a dilute concentration of pulp fibers to the wire mesh where the fibers are dried to become paper. Ideally, the mean velocity distribution in the fluid mixture leaving the converging section (or slice as it is called) should be uniform over the paper thickness direction and across the entire span of the slice exit. Non-uniformities in this distribution can result in defects in the paper being produced by the machine. A complete computer simulation of a typical headbox, reported here, identifies two important sources of mean velocity defects as the re-circulation rate and the design shape of the manifold, which initially spreads the pulp into the several hundreds of tubes which deliver it, in turn, to the converging section. As emphasized in the present report, it is critically necessary for the proper identification of defects, that there be a single simulation of the complete headbox, correctly locating individual tubes and other major components. The turbulence which occurs in the converging section does not affect the mean flow distribution significantly but it is critically important in preventing unwanted fiber flocculation and in providing a degree of dispersion for the fibers, which would otherwise be strongly oriented in the flow direction under the action of the mean rate-of-strain field created by the rapid convergence. A detailed knowledge of this turbulence is therefore essential in order to model the fiber motion and the effectiveness of the paper-machine, and to predict the quality of the paper produced. LDA measurements of the three turbulence components have been made in a laboratory scale paper-machine converging section, and corresponding measurements have also been made of the statistical orientation of short pieces of nylon thread, representing pulp fibers, carried by the flow. CFD simulations of this rapidly converging flow are reported here. Results using the usual k-ε and Reynolds stress turbulence models are compared to the appropriate experimental measurements, and found to be inaccurate. A large eddy simulation (LES) computation of the converging section is next reported. The calculated time-averaged turbulence components are compared to the measured values along the centerline of the converging section. Qualitatively, the calculated and observed turbulence distributions follow similar trends. Differences occur because of the significantly different initial conditions for the measured and calculated cases. A Lagrangian tracking scheme capable of simulating the motion of flexible or rigid individual fibers in a computed flow field has been devised and is used in the LES representation of turbulence (and other simpler flow field representations) in the convergence to predict the statistical orientation of nylon “fibers”. Two different schemes to couple the LES flow field calculations with the fiber model are reported, one using a fixed or “frozen” 3D flow field from the LES calculations and the other using the complete unsteady LES flow field. Both these give similar (but not identical) statistical results for the fiber orientation. This suggests that the much simpler “frozen field” technique can be used in future computations, making the numerical prediction of statistical fiber orientations in a diffuser (or other complex geometries) practical with the realistic LES scheme and present computational resources.
Brief Review and Mathematical Modelling of Air Cushioned Pressurized Paper Machine Headbox