Numerical Simulation of Viscoelastic Extrudate Swell Through Elliptical Ring Die

›› 2011, Vol. 19 ›› Issue (1): 10-17.

Numerical Simulation of Viscoelastic Extrudate Swell Through Elliptical Ring Die

许星明^1,2, 赵国群², 秦升学³, 王威¹

1. College of Mechanical and Electrical Engineering, Shandong University of Science and Technology, Tai’an 271019, China;
2. Engineering Research Center for Mold&Die Technologies, Shandong University, Jinan 250061, China;
3. College of Mechanical and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China

收稿日期:2009-12-13 修回日期:2010-12-12 出版日期:2011-02-28 发布日期:2011-02-28
通讯作者: ZHAO Guoqun, E-mail: zhaogq@sdu.edu.cn
基金资助:
Supported by the National Science Foundation for Distinguished Young Scholars of China(50425517);the Shandong Province Natural Science Foundation(Y2007F59)

Numerical Simulation of Viscoelastic Extrudate Swell Through Elliptical Ring Die

XU Xingming^1,2, ZHAO Guoqun², QIN Shengxue³, WANG Wei¹

1. College of Mechanical and Electrical Engineering, Shandong University of Science and Technology, Tai’an 271019, China;
2. Engineering Research Center for Mold&Die Technologies, Shandong University, Jinan 250061, China;
3. College of Mechanical and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China

Received:2009-12-13 Revised:2010-12-12 Online:2011-02-28 Published:2011-02-28
Supported by:
Supported by the National Science Foundation for Distinguished Young Scholars of China(50425517);the Shandong Province Natural Science Foundation(Y2007F59)

摘要/Abstract

摘要： The numerical simulation of extrudate swell is significant in extrusion processing.Precise prediction of extrudate swell is propitious to the control of melt flow and the quality of final products.A mathematical model of three-dimensional(3D)viscoelastic flow through elliptical ring die for polymer extrusion was investigated.The penalty function formulation of viscoelastic incompressible fluid was introduced to the finite element model to analyze 3D extrusion problem.The discrete elastic viscous split stress(DEVSS)and streamline-upwind PetrovGalerkin(SUPG)technology were used to obtain stable simulation results.Free surface was updated by updating the streamlines which needs less memory space.According to numerical simulation results,the effect of zero-shear viscosity and elongation parameter on extrudate swell was slight,but with the increase of volumetric flow rate and relax time the extrudate swell ratio increased markedly.Finally,the numerical simulation of extrudate swell flow for low-density polyethylene(LDPE)melts was investigated and the results agreed well with others’work.These conclusions provided quantitative basis for the forecasting extrudate swell ratio and the controlling of extrusion productivity shape.

关键词: viscoelastic fluid, extrudate swell, finite element method, polymer extrusion

Abstract: The numerical simulation of extrudate swell is significant in extrusion processing.Precise prediction of extrudate swell is propitious to the control of melt flow and the quality of final products.A mathematical model of three-dimensional(3D)viscoelastic flow through elliptical ring die for polymer extrusion was investigated.The penalty function formulation of viscoelastic incompressible fluid was introduced to the finite element model to analyze 3D extrusion problem.The discrete elastic viscous split stress(DEVSS)and streamline-upwind PetrovGalerkin(SUPG)technology were used to obtain stable simulation results.Free surface was updated by updating the streamlines which needs less memory space.According to numerical simulation results,the effect of zero-shear viscosity and elongation parameter on extrudate swell was slight,but with the increase of volumetric flow rate and relax time the extrudate swell ratio increased markedly.Finally,the numerical simulation of extrudate swell flow for low-density polyethylene(LDPE)melts was investigated and the results agreed well with others’work.These conclusions provided quantitative basis for the forecasting extrudate swell ratio and the controlling of extrusion productivity shape.

Key words: viscoelastic fluid, extrudate swell, finite element method, polymer extrusion

许星明, 赵国群, 秦升学, 王威. Numerical Simulation of Viscoelastic Extrudate Swell Through Elliptical Ring Die[J]. , 2011, 19(1): 10-17.

XU Xingming, ZHAO Guoqun, QIN Shengxue, WANG Wei. Numerical Simulation of Viscoelastic Extrudate Swell Through Elliptical Ring Die[J]. , 2011, 19(1): 10-17.

参考文献

1 Sombatsompop, N., O-Charoen, N., “Extrudate swell behavior of PS and LLDPE melts in a dual die with mixed circular/slit flow channels in an extrusion rheometer”, Polym. Adv. Technol., 14, 699-710 (2003).
2 Sombatsompop, N., Intawong, N., “Extrudate swell and flow analysis of polystyrene melt flowing in an electro-magnetized die in a single screw extruder”, Polym. Adv. Technol., 16, 505-514 (2005).
3 Carneiro de Araujo, J.H., Ruas, V., “A stable finite element method for the axisymmetric three-field Stokes system”, Comput. Methods Appl. Mech. Eng., 164, 267-286 (1998).
4 Tome, M.F., Grossi, L., Castelo, A., Cuminato, J.A., McKee, S., Walters, K., “Die-swell, splashing drop and a numerical technique for solving the Oldroyd-B model for axisymmetric free surface flows”, J. Non-Newt. Fluid Mech., 141,148-166 (2007).
5 Tome, M.F., Castelo, A., Ferreira, V.G., McKee, S., “A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows”, J. Non-Newt. Fluid Mech., 154, 179-206 (2008).
6 Huang, X., Phan-Thien, N., Tanner, R.I., “Viscoelastic flow between eccentric rotating cylinders: Unstructured control volume method”, J. Non-Newt. Fluid Mech., 64, 71-92 (1996).
7 Eleni, T., Georgios, C.G., Evan, M., “Numerical simulation of the extrusion of strongly compressible Newtonian liquids”, Rheol. Acta,47, 49-62 (2008).
8 Beris, A.N., Armstrong, R.C., Brown, R.A., “Spectral finite-element calculations of the flow of a Maxwell fluid between excentric rotating cylinders”, J. Non-Newt. Fluid Mech., 22, 129-167 (1987).
9 Fan, X.J., Phan-Thien, N., Zheng, R., “A direct simulation of fibre suspensions”, J. Non-Newt. Fluid Mech., 74, 113-135 (1998).
10 George, K., John, T., “Steady extrusion of viscoelastic materials from an annular die”, J. Non-Newt. Fluid Mech., 154, 136-152 (2008).
11 Mitsoulis, E., Heng, F.L., “Extrudate swell of Newtonian fluids from converging and diverging annular dies”, Rheol. Acta, 26, 414-417 (1987).
12 Garcia-Rejon, A., DiRaddo, R.W., Ryan, M.E., “Effect of die geometry and flow characteristics on viscoelastic annular swell”, J. Non-Newt. Fluid Mech., 60, 107-128 (1995).
13 Mitsoulis, E., “Annular extrudate swell of pseudoplastic and viscoplastic fluids”, J. Non-Newt. Fluid Mech., 141, 138-147 (2007).
14 Ganvir, V., Lele, A., Thaokar, R., Gautham, B.P., “Prediction of extrudate swell in polymer melt extrusion using an Arbitrary Lagrangian Eulerian (ALE) based finite element method”, J. Non-Newt. Fluid Mech., 156, 21-28 (2009).
15 Intawong, N-T., Sombatsompop, N., “Experimental studies on radial extrudate swell and velocity profiles of flowing PS melt in an electro-magnetized die of an extrusion rheometer”, Polym. Eng. Sci., 44 (12), 2298-2307 (2004).
16 Guo, J.L., Zhou, G.F., Zhou, Y.F., Yan, L., “The full three dimensional isothermal viscoelastic numerical simulation on the extrusion die swell of polymer profile”, Journal of Nanchang University (Engineering & Technology), 29 (1), 4-8 (2007). (in Chinese)
17 Siddiqui, A.M., Mahmood, R., Ghori, Q.K., “Some exact solutions for the thin film flow of a PTT fluid”, Phys. Lett. A, 356, 353-356 (2006).
18 Takehiro, Y., Masakazu, I., Masaki, N., Kiyoji, N., Noriyasu, M., “Three-dimensional viscoelastic flows through a rectangular channel with a cavity”, J. Non-Newt. Fluid Mech., 114, 13-31 (2003).
19 Paulo, G.S.de, Tome, M.F., McKee, S., “A marker-and-cell approach to viscoelastic free surface flows using the PTT model”, J. Non-Newt. Fluid Mech., 147, 149-174 (2007).
20 Mitsoulis, E., “Annular extrudate swell of pseudoplastic and viscoplastic fluids”, Journal of Non-Newtonian Fluid Mechanics, 141,138-147 (2007).
21 Ki, B.S., Seung, J.P., Seong, J.L., Kyung, H.A., Seung, J.L., “Numerical simulation of three-dimensional viscoelastic flow using the open boundary condition method in coextrusion process”, Journal of Non-Newtonian Fluid Mechanics, 99, 125-144 (2001).
22 Beverly, C.R., Tanner, R.I., “Numerical analysis of three-dimensional Newtonian extrudate swell”, Rheol. Acta, 30, 341-356 (1991).
23 Gifford, W.A., “A three-dimensional analysis of coextrusion”, Polym. Eng. Sci., 37 (2), 315-320 (1997).
24 Qin, S.X., Zhao, G.Q., Mu, Y., Xu, X.M., “Numerical simulation of driven and pressure flow in compound shaped part of co-extrusion process of polymer with metal insert”, Key Eng. Mater., 392-394,299-303 (2009).
25 Sun, J., Smith, M.D., Armstrong, R.C., Brown, R.A., “Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method: DAVSS-G/DG”, J. Non-Newt. Fluid Mech., 86, 281-307 (1999).
26 Sun, J.S., Phan-Thien, N., Tanner, R.I., “An adaptive viscoelastic stress splitting scheme and its applications: AVSS/SI and AVSS/SUPG”, J. Non-Newt. Fluid Mech., 65, 75-91 (1996).
27 Huang, S.H., Jiang, T.Q., Lu, C.J., Huang, J., “Experiments and numerical simulation of die swell for LDPE melt”, Journal of Shanghai Jiaotong University, 37 (4), 535-640 (2003). (in Chinese)

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Numerical Simulation of Viscoelastic Extrudate Swell Through Elliptical Ring Die

Numerical Simulation of Viscoelastic Extrudate Swell Through Elliptical Ring Die

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