Flow in contractions with application to headboxes

by Parsheh, Mehran

The hydraulic headbox used in paper manufacturing machines has a two-dimensional contraction. It is believed that some of the mechanical properties of the produced paper depend on the ow inside this contraction. Problems as non-homogeneity and streaky structures of paper sheets are related to this ow. In order to determine the performance of di erent turbulence models in two-dimensional contractions, the turbulence characteristics along the contraction centreline were measured and compared to computational results using di erent turbulence models and to results from analytical methods in the literature. This study showed that the Reynolds stress model qualitatively predicts the ow well. However, the results were dependent on the upstream boundary condition for the rate of dissipation. Besides, it was observed that the performance of the K ; model is very poor for this kind of ow. In some applications of hydraulic headboxes turbulence producing vanes are mounted in the contraction zone. Also, in a special kind of paper manufacturing, by mounting separation vanes in the contraction zone, it is possible to put di erent components into separate layers of the paper sheet and thereby improve the sheet quality. However, the commercial introduction of forming of multi-layer printing and writing papers is held back due to large layer mixing in the jet of the headbox. This mixing is believed, to a large extent, to be the result of turbulent uctuations in the wake behind the separation vanes. The turbulence level and characteristics of these wakes depend, among other things, on the boundary layer that separates from the vanes. The development of this boundary layer was studied experimentally using the hot wire anemometer technique and it was found that because of the favourable pressure gradient the turbulent boundary layer relaminarises and becomes self-similar, before it reaches the end of the vane. Moreover, the turbulent wake behind the vane was investigated. It was observed that the wake can become self-similar although a universal velocity and length scale was not found. In addition, the mixing in the wake behind the vane was studied experimentally by heating the ow above the vane and measuring the temperature pro les downstream. It is a de nite possibility that for any headbox con guration, there is an optimum vane length which leads to the lowest mixing. The layer mixing in the strati ed liquid jet of a headbox was modelled by a simple model using a commercial Navier-Stokes solver. A passive scalar was put in one of the uid layers and its transport to the other layers was investigated. It was observed that the relative di erence of the vane length and the contraction length was one of the most important factors. It was also shown that avane shorter than the contraction gives unexpectedly low mixing. A quasione-dimensional model was developed to determine the shape of the separation vanes subjected to the uid ow in a strati ed headbox. It was observed that the results were dependent onvane bending sti ness, the relative velocity di erence at the contraction inlets, contraction geometry and the relative length di erence of the vaneandthecontraction. This model was tested by comparing its results to the results of a Navier-Stokes solver using the commercial code CFX, and it was observed that they agree well. v vi Preface This thesis studies the ow inside a two-dimensional contraction, in which the ow is contracted only in the vertical direction. This investigation consists of boundary layer, wake, and mixing inside the wake and is applicable to ow inside the hydrodynamic headbox of paper manufacturing machines. Paper I. Parsheh M. & Dahlkild A. A. 1997 Numerical modelling of mixing in strati ed headbox jet. Presented at TAPPI engineering & Papermakers Conference Nashville, 1997 and a modi ed version to be submitted. Paper II. Parsheh M. & Dahlkild A. A. 1999 Modelling the ow around elastic guiding vanes in the converging zone of a headbox. Presented at TAPPI Engineering/Process and Product Quality Conference Trade Fair at Anaheim 1999, and a modi ed version is submitted to the Journal of Pulp and Paper Science. Paper III.Parsheh M., Dahlkild A. A. & Alfredsson P. H. 1999 Relaminarisation of a turbulent boundary layer in a two-dimensional contraction. To be submitted. Paper IV. Parsheh M., Talamelli A. & Dahlkild A. A. 2000 Turbulence characteristics of ow through two-dimensional contractions. To be submitted. Paper V. Parsheh M. 2000 Development and mixing of a two-dimensional contraction. To be submitted. at plate wake ina