Abstract
Given a reference extruder with a certain geometry and operating point, the aim of scale-up is to define the geometry and operating conditions of a target extruder (generally of significantly different size) in order to subject the material being processed to the same flow and heat transfer conditions, thus yielding products with the same characteristics. Since existing scale-up rules are crude, as they usually consider a single performance measure and produce unsatisfactory results, this work approaches scale-up as a multi-criteria optimization problem, where the aim is to define the geometry/operating conditions of the target extruder that minimize the differences between the values of various performance criteria for the reference and target extruders. Some case studies are discussed involving individual and multi-criteria scaling-up in terms of operating conditions, geometry, and both together, the usefulness of the approach being demonstrated. A few experiments are also performed in order to validate the concept.
References
Broyer, E., Tadmor, Z., Solids Conveying in Screw Extruders – Part I: A Modified Isothermal Model, Polym. Eng. Sci., 12, 12–24(1972).10.1002/pen.760120103Search in Google Scholar
Carley, J. F., McKelvey, J. M., Extruder Scale-up Theory and Experiments, Ind. Eng. Chem., 45, 985–989(1953).Search in Google Scholar
Carneiro, O. S., et al., Experimental and Theoretical Study of Twin Screw Extrusion of Polypropylene, J. Appl. Polym. Sci., 78, 1419–1430(2000).10.1002/1097-4628(20001114)78:7<1419::AID-APP130>3.0.CO;2-BSearch in Google Scholar
Chung, C. I., On the Scale-up of Plasticating Extruder Screws, Polym. Eng. Sci., 24, 626–632(1984).10.1002/pen.760240904Search in Google Scholar
Coello Coello, C. A., et al.: Evolutionary Algorithms for Solving Multi-Objective Problems, Kluwer, Amsterdam(2002).10.1007/978-1-4757-5184-0Search in Google Scholar
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms, Wiley, New York(2001).Search in Google Scholar
Elbirli, B., et al., Mathematical Modelling of Melting of Polymers in a Single-Screw Extruder, Polym. Eng. Sci., 24, 988–999(1984).10.1002/pen.760241208Search in Google Scholar
Elemans, P. H. M., Meijer, H. E. H., Scale-up of the Mixing Process in Continuous Mixers, in Mixing and Compounding of Polymers, Manas-Zloczower, I., Tadmor, Z. (Ed.), Carl Hanser Verlag, Munich, p. 457–470(1994).Search in Google Scholar
Fenner, R. T., Williams, J. G., Some Melt Flow and Mechanical Design Aspects of Large Extruders, Polym. Eng. Sci., 11, 474–483(1971).10.1002/pen.760110606Search in Google Scholar
Ferreira, J. C., et al., A New Methodology to Select the Preferred Solutions from the Pareto-optimal Set: Application to Polymer Extrusion, 10th Esaform Conference on Material Forming, Zaragoza(2007).Search in Google Scholar
Gaspar-Cunha, A., Modelling and Optimization of Single Screw Extrusion, PhD Thesis, University of Minho, Guimarães, Portugal(2000).Search in Google Scholar
Gaspar-Cunha, A., Covas, J. A., The Design of Extrusion Screws: An Optimisation Approach, Int. Polym. Proc., 16, 229–240(2001).Search in Google Scholar
Gaspar-Cunha, A., Covas, J. A., RPSGAe – A Multiobjective Genetic Algorithm with Elitism: Application to Polymer Extrusion, in Metaheuristics for Multiobjective Optimisation, Lecture Notes in Economics and Mathematical Systems, Gandibleux, X., Sevaux, M., Sörensen, K., T'kindt, V. (Eds.), Springer, Berlin, Heidelberg, 221–249(2004).10.1007/978-3-642-17144-4_9Search in Google Scholar
Gaspar-Cunha, A., et al., Defining the Configuration of Co-rotating Twin Screw Extruders with Multiobjective Evolutionary Algorithms, Polym. Eng. Sci., 45, 1159–1173(2005).10.1002/pen.20391Search in Google Scholar
Goldberg, D. E.: Genetic Algorithms in Search, Optimisation and Machine Learning, Addison-Wesley(1989).Search in Google Scholar
Hyun, K. S., Spalding, M. A., Bulk Density of Solid Polymer Resins as a Function of Temperature and Pressure, Polym. Eng. Sci., 30, 571–576(1990).10.1002/pen.760301003Search in Google Scholar
Kacir, L., Tadmor, Z., Solids Conveying in Screw Extruders – Part III: The Delay Zone, Polym. Eng. Sci., 12, 387–395(1972).10.1002/pen.760120511Search in Google Scholar
Lindt, J. T., Pressure Development in the Melting Zone of a Single Screw Extruder, Polym. Eng. Sci., 21, 1162–1166(1981).10.1002/pen.760211708Search in Google Scholar
Machado, A.V., Covas, J. A., van Duin, M., Chemical and Morphological Evolution of PA6/EPM/EPM-g-MA Blends in a Twin Screw Extruder, J. Polym. Sci.: Part A: Polym. Chem., 37, 1311–1318(1999).10.1002/(SICI)1099-0518(19990501)37:9<1311::AID-POLA11>3.0.CO;2-YSearch in Google Scholar
Maddock, B. H., A Visual Analysis of Flow and Mixing in an Extruder, Society of Plastics Engineers Journal, 15, 383–394(1959).Search in Google Scholar
Maddock, B. H., Extruder Scale-up by Computer, Polym. Eng. Sci., 14, 853–858(1974).10.1002/pen.760141208Search in Google Scholar
Pearson, J. R. A., Scale-up of Single Screw Extruders for Polymer Processing, Plastics and Rubber: Processing, 1, 113–118(1976).Search in Google Scholar
Pinto, G., Tadmor, Z., Mixing and Residence Time Distribution in Melt Screw Extruders, Polym. Eng. Sci., 10, 279–288(1970).10.1002/pen.760100505Search in Google Scholar
Potente, H., Fischer, P., Model Laws for the Design of Single Screw Plasticating Extruders, Kunststoffe, 67, 242–247(1977).Search in Google Scholar
Potente, H., Existing Scale-up Rules for Single-screw Plasticating Extruders, Int. Polym. Proc., 6, 267–278(1991).Search in Google Scholar
Rauwendaal, C.: Polymer Extrusion, Hanser Publishers, Munich(1986).Search in Google Scholar
Rauwendaal, C., Scale-up of Single Screw Extruders, Polym. Eng. Sci., 27, 1059–1068(1987).10.1002/pen.760271406Search in Google Scholar
Schenkel, G., Extruder Series with Variable L/D Ratios, Kunststoffe, 68, 155–162(1978).Search in Google Scholar
Spalding, M. A., Hyun, K. S., Coefficients of Dynamic Friction as a Function of Temperature, Pressure, and Velocity for Several Polyethylene Resins, Polym. Eng. Sci., 35, 557–563(1995).10.1002/pen.760350702Search in Google Scholar
Stevens, M. J., Covas, J. A.: Extruder Principles and Operations, Springer, Berlin, Heidelberg(1995).10.1007/978-94-011-0557-6Search in Google Scholar
Tadmor, Z., Broyer, E., Solids Conveying in Screw Extruders-Part II: Non Isothermal Model, Polym. Eng. Sci., 12, 378–391(1972).10.1002/pen.760120510Search in Google Scholar
Walker, D. M., An Approximate Theory for Pressures and Arching in Hoppers, Chem. Eng. Sci., 21, 975–997(1966).10.1016/0009-2509(66)85095-9Search in Google Scholar
Wang, W., Manas-Zloczower, I., Temporal Distributions: The Basis for the Development of Mixing Indexes for Scale-up of Polymer Processing Equipment, Polym. Eng. Sci., 41, 1068–1077(2001).10.1002/pen.10807Search in Google Scholar
Wang, C., et al., Frame Indifference, Fluid Flow in Single Screw Pumps and Extruders, Int. Polym. Proc., 11, 199–207(1996).Search in Google Scholar
Yi, B., Fenner, R. T., Scaling-up Plasticating Screw Extruders on the Basis of Simular Melting Performances, Plastics and Rubber Processing, 1, 119–123(1976).Search in Google Scholar
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