A scaling-up methodology for co-rotating twin-screw extruders

Transcription

1 A scaling-up methodology fo co-otating twin-scew extudes A. Gaspa-Cunha, J. A. Covas Institute fo Polymes and Composites/I3N, Univesity of Minho, Guimaães , Potugal Abstact. Scaling-up of co-otating twin scew extudes is studied as a multi-objective optimization poblem whee the aim is to define the geomety/opeating conditions of the taget extude that minimize the diffeences between the values of the pefomance citeia that depict the efeence and taget extudes. Thee computational expeiments ae discussed. These peliminay esults seem encouaging. Intoduction Scale-up and scale-down ae two impotant opeations in co-otating twin scew extusion, as vey often one needs to tansfe the pocessing settings fom laboatoy to poduction plant units o vice-vesa, while maintaining the same poduct chaacteistics [1]. Cuently, most extude manufactues offe a ange of machines with diffeent sizes, but having constant extenal to intenal scew diamete atio (this detemines the fee volume) and, in some cases, identical specific toque. Although the idea is to guaantee simila shea histoies, extudes of diffeent sizes have inheently diffeent suface-to-volume atios, thus affecting the heat tansfe efficiency, with consequences on flow, mixing and viscous dissipation [2]. Thus, geometical similaity between extudes is not enough fo adequate scale-up. Consequently, seveal authos deived powe-type elationships, usually applicable to the fully filled sections of the machine and based on simplified flow analyses, that scale machines of diffeent sizes in tems of simila degee of fill, mean esidence time, thoughput, mixing quality, melt tempeatue, etc [2-6]. One obvious difficulty is that scaling fo one paamete will povide diffeent esults than scaling fo anothe paamete. This means that choices have to be made [2]. The situation becomes moe poblematic when both the efeence and taget extudes exist, so that scaling-up consists in defining the scew pofile and/o the opeating conditions of the latte. Indeed, most existing ules focus on the diamete atio. Ideally, a scaling-up method should: - conside simultaneously the vaious elevant pocess paametes and povide infomation on the degee of satisfaction of each that was achieved by the solution poposed; - ely on accuate desciptions of flow and heat tansfe along the machine; - take in the vaious scew geometical paametes and opeating vaiables. The authos attempted to apply such an appoach to the scaling up of single scew extudes [7]. They egaded scaling-up as a multi-objective optimization poblem whee the aim is to define the geomety/opeating conditions of the taget extude that minimize the diffeences between the values of the pefomance citeia that depict the efeence and taget extudes. Simila stategies wee adopted to design single and cootating twin scews [8,9]. The pesent wok aims at applying the same pinciples to the moe complex case of scaling- 1

2 up o scaling-down co-otating twin scew extudes. Scale-up as an Optimization Poblem Optimization methodology. The aim of extusion scale-up is to guaantee identical themo-mechanical conditions in both the efeence and taget extudes. This is done hee though solving the optimization poblem whee the aim is to obtain the opeating conditions and/o the geomety of the taget extude that minimizes the diffeences in pefomance between both extudes [7]. The coesponding pocedue involves five sequential steps: i) compute flow and heat tansfe in the efeence extude (using an appopiate modelling outine) fo a specific geomety and opeating condition; ii) define the pocess paametes that should be consideed fo scale-up; iii) select the geometical and opeational paametes of the taget extude to be defined, as well as thei ange of vaiation; iv) pefom the optimization; v) select the best solutions poposed. Two basic outines ae needed, one fo pocess modelling, anothe fo multi-objective optimization [10,11]. The latte is based on a Multi-Objective Evolutionay Algoithm (MOEA) developed peviously by the authos [12]. Modelling. The modelling outine used consides the entie path of the mateial fom hoppe to die [13]. The following individual steps ae modelled: 1) solids conveying without pessue, 2) solids conveying unde pessue, 3) melting; 4) melt conveying unde pessue and 5) melt conveying without pessue. Thei sequence depends on the scew pofile and opeating conditions. Computations ae pefomed fom the scew entance to the die exit. The fist estictive element is identified. Then, an iteative pocedue spots the location upsteam whee the channel becomes fully filled. The calculations poceed along small channel incements. In the fist estictive element solids conveying, melting and melt conveying ae included, while in the emaining only melt conveying is assumed. The pogam computes the evolution along the scew of pessue, aveage and maximum tempeatue, shea ate, viscosity, mechanical powe consumption, degee of fill, defomation, esidence time and specific mechanical enegy. Moe details can be found elsewhee [13]. Scale-up objectives. The objectives to be selected must conside the pedicting capabilities of the modelling outine. They can assume two shapes: a value, eflecting the global extude esponse (e.g., maximum o aveage melt tempeatue at die exit, aveage esidence time, aveage defomation, specific mechanical enegy), o a function descibing the evolution along the scew of, fo example, melt tempeatue, pessue, shea ate, viscosity, o degee of fill. These objectives ae incopoated in the methodology via the following equations: F F j j j C j C = (1) C K C j, k K C k= C j k j = 1, j, k (2) whee F j is the fitness of citeion j, C j and C j ae the values of citeion j (single values) fo the taget and efeence extudes, espectively, and C j,k and C j,k ae the values of citeion j on location k (along the extude) fo the taget and efeence extudes, espectively. The aim is to minimize F j, which vaies in the ange [0;1]. 2

3 Optimization uns A Clextal twin scew extude was used as efeence (see scew configuation in Table 1), while a Leistitz LSM was selected as taget extude (Table 2 pesents the geometies of the 16 elements available). A polypopylene (ISPLEN PP030 G1E, fom Repsol, see popeties in [13]) is being pocessed in the Clextal machine with a flat bael tempeatue of 220ºC, a feed ate of 8 kg/h and a scew speed of 200 pm. Table 1. pofile fo the efeence extude (Clextal 21.25). denotes a block of kneading discs with a staggeing angle of º KB KB KB Thee diffeent optimization (scale-up) uns ae epoted hee: - assuming that the 16 elements of the taget extude poduce a meaningful pofile, define the opeating conditions; - fo the efeence and taget extudes opeating unde identical conditions, define the best sequence of the scew elements of the latte (elements 1 and 2 will be kept in thei initial positions); - as in the pevious un, fix the opeating conditions and define the scew pofile, but now allow also the staggeing angle of the two kneading blocks to be also optimized. Moe specifically, the angles can take the following values: 90º, 60º, 45º, 30º, -30º, º, -60º. In all cases, thee objectives wee included: i) aveage melt to bael tempeatue atio - a measue of viscous dissipation (T/Tb), ii) aveage stain and iii) specific mechanical enegy (SME). Table 2. elements of the taget extude (Leistitz LSM 30.34) Results and Discussion Figues 1 to 3 pesent the Paeto fonties fo the 3 uns. The Paeto fontie is a suface epesenting the tade-off between the thee objectives, shown hee as two 2D plots. As seen in Figue 1, it is easy to minimize the T/Tb objective, as the diffeences between the two extudes ae always lowe than 10%. Convesely, the diffeences fo the othe two objectives main each 40%. 3

4 When compaing uns 2 and 3 (figues 2 and 3), it becomes evident that vaying the geomety of the kneading blocks bings on moe flexibility to the optimization, since the ange of vaiation of the objectives becomes much highe. The best scew configuations minimizing each of the objectives in un 3 ae pesented in Tables 3 to 5. The coesponding objective function values ae gatheed in Table 6. The scew minimizing the T/Tb objective is simila to that of the efeence extude, with the estictive elements distibuted along the axis. The aveage stain objective is minimized fo a scew with a longe kneading block (the two estictive elements ae adjacent to each othe), but at the cost of lage diffeences in SME. Finally, the SME objective is minimized when the kneading blocks have positive staggeing. Fig. 2. Paeto fonties fo un 2. Fig. 1. Paeto fonties fo un 1. Fig. 3. Paeto fonties fo un 3. 4

5 Table 3. configuation minimizing T/Tb (un 3 1) Table 5. configuation minimizing SME (un 3 3) Table 4. configuation minimizing the aveage stain (un 3 2) Table 6. Objective function values fo un 3. F(T/Tb) F(AvgSt) F(SME) Conclusions Scaling-up o scaling-down of co-otating twin scew extudes is appoached as a multiobjective optimization poblem, instead of using coelations coveing individual pocess pefomance paametes. Thee computational expeiments illustate the potential of the method. Futhe developments ae equied to convet the method into a useful tool fo pactical application. Refeences 1. K. Kohlgube, Co-Rotating Twin- Extudes, Hanse,Munich (2008) 2. H.E.H. Meije, P.H.M. Elemans, The modelling of continuous mixes. Pat I: The 5

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