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Expermental and mathematical modeling of flow in headboxes Shariati, Mohammad Reza

Abstract

The fluid flow patterns in a paper-machine headbox have a strong influence on the quality of the paper produced by the machine. Due to increasing demand for high quality paper there is a need to investigate the details of the fluid flow in the paper machine headbox. The objective of this thesis is to use experimental and computational methods of modeling the flow inside a typical headbox in order to evaluate and understand the mean flow patterns and turbulence created there. In particular, spatial variations of the mean flow and of the turbulence quantities and the turbulence generated secondary flows are studied. In addition to the flow inside the headbox, the flow leaving the slice is also modeled both experimentally and computationally. A Plexiglas scaled-down model of a headbox was constructed and LDV measurements of mean and turbulence velocities in the model were made. The numerical models used in Computational Fluid Dynamics (CFD) simulations were based on finite volume Reynolds-averaged equations and included turbulence representations with the standard k-e model, quadratic and cubic algebraic turbulence models and the Reynolds stress model (RSM). The "volume of fluid" method was used to model the free surface of the jet leaving the slice. The CFD investigation showed that the turbulence generated secondary flows in the headbox are much smaller than previously thought and that they are confined to a very small region close to the wall. Comparison of the experimental and numerical results indicated that streamwise mean components of the velocities in the headbox are predicted well by all the turbulence models considered in this study. However, the standard k-e model and the algebraic turbulence models fail to predict the turbulence quantities accurately. Standard k-e model also fails to predict the direction and magnitude of the secondary flows. Inaccuracies in the numerical prediction of turbulence quantities increase as the contraction ratio increases. This is due to the incorrect representation of the production of the turbulence kinetic energy by the k- e model and the algebraic turbulence models. Significant improvements in the k-e model predictions were achieved when the turbulence production term was artificially set to zero. This is justified by observations of the turbulent velocities from the experiments and by a consideration of the form of the kinetic energy equation. A better estimation of the Reynolds normal stress distribution and the degree of anisotropy of turbulence was achieved using the Reynolds stress turbulence model. Integral length scales were measured from the LDV velocity observations in the plexiglass scale model and were compared to the length scales obtained computationally using both standard k-£ and Reynolds stress turbulence models. Although similar magnitudes were found for the measured and computed length scales, different trends between numerical and experimental results were observed. Measured integral length scale and computed length scales have been reported to be similar only in decaying grid turbulence, so that the differences observed in this rapidly distorting flow are not surprising. The trends measured here, and their contrast to the calculated values of length scale, should be kept in mind when discussing turbulence characteristics in a rapidly converging section such as the headbox contraction. Careful examination of the measured turbulence velocity results shows that after the initial decay of the turbulence in the headbox, there is a short region close to the exit, but inside the headbox, where the turbulent kinetic energy actually increases as a result of the distortion imposed by the contraction. The turbulence energy quickly resumes its decay in the free jet after the headbox. The turbulence quantities obtained using the k-e model in the free jet have the same trend as the results from RSM model. However, the results using the k-e model are at unrealistically high compared to those found from the RSM turbulence model in the free jet. This is due to the error that is made in the k-e results from computations inside the converging section of the headbox. The RSM model gives more realistic values for the turbulence quantities in the free jet region when the R S M model is used throughout the contraction region as well. The overall conclusion from this thesis, obtained by comparison of experimental and computational simulations of the flow in a headbox, is that numerical simulations show great promise for predictions of headbox flows. Mean velocities and turbulence characteristics can now be predicted with fair accuracy by careful use of specialized turbulence models. Standard engineering turbulence models, such as the k - e model and its immediate relatives, should not be used to estimate the turbulence quantities essential for predicting pulp fiber dispersion within the contracting region and free jet of a headbox, particularly when the overall contraction ratio is greater than about five.

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