Abstract
Basic equations describing steady, two-directional, isothermal and fully developed drag-pressure flow of generalized Newtonian fluid between parallel plates assumed as the appropriate flow model in flat, shallow screw channel, are given. It is shown that the flow output for any generalized Newtonian fluid in the two-directional case can be described by a simple expression with a few parameters depending in a complicated way on pressure gradient, channel geometry and constants of the constitutive model. The expression is also valid for unidirectional flow as the limiting case of the two-directional flow. The parameters must be determined as a rule with numerical methods. To simplify the practical calculations, a few (semi)analytical methods of parameters determination for unidirectional power law flow are discussed first. These methods make possible to calculate analytically the pressure gradient for known output that is typical of screw flow characterization. The results obtained for the unidirectional flow 1-D were generalized to describe the two-directional flow 2-D, which takes into account both longitudinal and transverse velocity components. The generalization is based on translation and dilation of the 1-D flow characteristics by introducing a few additional parameters, which are only dependent on the helix angle and power law exponent. It was found a very good agreement between exact numerical and approximate ( semi)analytical characteristics for both flows.
References
Agassant, J. F., Avenas, P., Carreau, P. J., Vergnes, B. and Vincent M.: Polymer Processing. Principles and Modelling, Hanser, Munich (2017), DOI:10.3139/9781569906064.fm10.3139/9781569906064.fmSearch in Google Scholar
Baird, D. G., Collias, D. I.: Polymer Processing. Principles and Design, Wiley, Hoboken (2014)Search in Google Scholar
Chung, C. I.: Extrusion of Polymers. Theory and Practice, Hanser, Munich (2011)Search in Google Scholar
Griffith, R. M., “Fully Developed Flow in Screw Extruders. Theoretical and Experimental Study", Ind. Eng. Chem. Fundam., 3, 180– 187 (1962), DOI:10.1021/i160003a00410.1021/i160003a004Search in Google Scholar
Hirshberger, M.: Flow of Non-Newtonian Fluids in Rectangular Channels, M.S. Thesis, Dept. of Chem. Eng., Technion, Israel Institute of Technology, Haifa (1970)Search in Google Scholar
Marschik, C., Loew-Baselli, B. and Miethlinger, J., “A Network-Theory-Based Comparative Study of Melt-Conveying Models in Single-Screw Extrusion: A. Isothermal Flow", Polymers, 10, 929–950 (2018), DOI:10.3390/polym1008092910.3390/polym10080929Search in Google Scholar PubMed PubMed Central
Marschik, C., Roland, W., Loew-Baselli, B. and Miethlinger, J., “A Heuristic Method for Modelling Three-Dimensional Non-Newtonian Flows of Polymer Melts in Single Screw Extruders", J. Non-Newtonian Fluid Mech., 248, 27–39 (2017), DOI:10.1016/j.jnnfm.2017.08.00710.1016/j.jnnfm.2017.08.007Search in Google Scholar
McAskill, B., Watt, W., Balzarini, E., Johnson, B., Kennedy, R., Melnyk, T. and Zarski, Ch.: Chapter1 Function Transformations, Pre-Calculus 12, McGraw-Hill Ryerson, Toronto, p. 6–55 (2012)Search in Google Scholar
Pachner, S., Loew-Baselli, B., Affenzeller, M. and Miethlinger, J., “A Generalized 2D Output Model of Polymer Melt Flow in Single-Screw Extrusion", Int. Polym. Proc., 32, 209–216 (2017), DOI:10.3139/217.332610.3139/217.3326Search in Google Scholar
Potente, H., “Approximationsgleichungen für Schmelzeextruder", Rheol. Acta, 22, 387 –395 (1983), DOI:10.1007/BF0133376910.1007/BF01333769Search in Google Scholar
Rauwendaal, C.: Polymer Extrusion, Hanser, Munich (2014), DOI:10.3139/9781569905395.fm10.3139/9781569905395.fmSearch in Google Scholar
Steller, R. T.: “Generalized Slit Flow of an Ellis Fluid", Polym. Eng. Sci., 41, 1859 –1870 (2001), DOI:10.1002/pen.1088310.1002/pen.10883Search in Google Scholar
Steller, R., “Flow of Generalized Newtonian Liquids in Screw Channel of Extruder Plasticating System (in Polish)", Polimery, 54, 288 – 295 (2009) (in Polish), DOI:10.14314/polimery.2009.28810.14314/polimery.2009.288Search in Google Scholar
Steller, R., “Theoretical Model for Flow of Polymer Melts in the Screw Channel", Polym. Eng. Sci., 30, 400–407 (1990), DOI:10.1002/pen.76030070410.1002/pen.760300704Search in Google Scholar
Steller, R., Iwko, J., “Generalized Flow of Ellis Fluid in the Screw Channel Part 1 Parallel Plates Model", Int. Polym. Proc., 16, 241– 248 (2001), DOI:10.3139/217.164910.3139/217.1649Search in Google Scholar
Steller, R., Iwko, J., “Generalized Flow of Ellis Fluid in the Screw Channel Part 1 Curved Channel Model", Int. Polym. Proc., 16, 249–256 (2001), DOI:10.3139/217.165010.3139/217.1650Search in Google Scholar
Tadmor, Z., Gogos, C. G.: Principles of Polymer Processing, Wiley, Hoboken (2006)Search in Google Scholar
Tadmor, Z., Klein, I.: Engineering Principles of Plasticating Extrusion, Van Nostrand, New York (1970)Search in Google Scholar
Torner, R. V.: Grundprozesse der Verarbeitung von Polymeren, VEB Deutscher Verlag für Grundstoffindustrie, Leipzig (1973)Search in Google Scholar
White L. J., Potente, H.: Screw Extrusion. Science and Technology, Hanser, Munich (2003), DOI:10.3139/9783446434189.fm10.3139/9783446434189.fmSearch in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston, Germany