Numerical simulation of coextrusion process of viscoelastic fluids using the open boundary condition method

Seung Joon Park; Kyung Hyun Ahn; Seung Jong Lee

Korea-Australia Rheology Journal, Vol.13, No.1, 37-45, March, 2001

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Numerical simulation of coextrusion process of viscoelastic fluids using the open boundary condition method

Seung Joon Park, Kyung Hyun Ahn , and Seung Jong Lee^†

School of Chemical Engineering and Institute of Chemical Processes, Seoul National University, Seoul 151-742, Korea

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Numerical simulation of coextrusion process of viscoelastic fluids within a die has been carried out. In the coextrusion process velocity profile at the outflow boundary is not known a priori, which makes it difficult to impose the proper boundary condition at the outflow boundary. This difficulty has been avoided by using the open boundary condition (OBC) method. In this study, elastic viscous stress splitting (EVSS) formulation with streamline upwind (SU) method has been used in the finite element method. In order to test the validity of the OBC method, comparison between the results of fully developed condition at the outlet and those of OBC has been made for a Newtonian fluid. In the case of upper convected Maxwell (UCM) fluid, the effect of outflow boundary condition on the interface position has been investigated by using two meshes having different downstream lengths. In both cases, the results with the OBC method showed reasonable interface shape. In particular, for the UCM fluid the interface shape calculated with OBC was independent of the downstream length, while the results with the zero traction condition showed oscillation of interface position close to the outlet. Viscosity difference was found to be more important than elasticity difference in determining the final interface position. However, the overshoot of interface position near the confluent point increased with elasticity.

Keywords:Open boundary condition;Coextrusion;Upper convested maxwell model;Finite element method

[References]

Debae F, Legat V, Crochet MJ, J. Rheol., 38(2), 421 (1994)
Dheur J, Crochet MJ, Rheol. Acta, 26, 401 (1987)
Dheur J, Crochet MJ, J. Non-Newton. Fluid Mech., 32, 1 (1989)
Griffiths DF, Int. J. Numer. Methods Fluids, 24, 393 (1997)
Han CD, Multiphase flow in polymer processing, Academic Press, New York (1981)
Khan AA, Han CD, Trans. Soc. Rheol., 20, 595 (1976)
Khomami B, J. Non-Newton. Fluid Mech., 37, 19 (1990)
Luo XL, Mitsoulis E, Adv. Polym. Technol., 10, 47 (1990)
Marchal JM, Crochet MJ, J. Non-Newton. Fluid Mech., 26, 77 (1987)
Matsunaga K, Kajiwara T, Funatsu K, Polym. Eng. Sci., 38(7), 1099 (1998)
Mavridis H, Hrymak AN, Vlachopoulos J, AIChE J., 33, 410 (1987)
Mitsoulis E, J. Rheol., 30(S), S23 (1986)
Musarra S, Keunings R, J. Non-Newton. Fluid Mech., 32, 253 (1989)
Nickell RE, Tanner I, Caswell B, J. Fluid Mech., 65, 189 (1974)
Papanastasiou TC, Malamateris N, Ellwood K, Int. J. Numer. Methods Fluids, 14, 587 (1992)
Park SJ, Lee SJ, J. Non-Newton. Fluid Mech., 87(2), 197 (1999)
Rajagopalan D, Brown RA, Amstrong RC, J. Non-Newton. Fluid Mech., 36, 159 (1990)
Renardy M, Int. J. Numer. Methods Fluids, 24, 413 (1997)
Sani RL, Gresho PM, Int. J. Numer. Methods Fluids, 18, 983 (1994)
Southern JH, Ballman RL, J. Polym. Sci., 13, 863 (1975)
Takase M, Kihara S, Funatsu K, Rheol. Acta, 37(6), 624 (1998)
White JL, Ufford RC, Dharod KR, Price RL, J. Appl. Polym. Sci., 16, 1313 (1972)

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[1] Debae F, Legat V, Crochet MJ, J. Rheol., 38(2), 421 (1994)

[2] Dheur J, Crochet MJ, Rheol. Acta, 26, 401 (1987)

[3] Dheur J, Crochet MJ, J. Non-Newton. Fluid Mech., 32, 1 (1989)

[4] Griffiths DF, Int. J. Numer. Methods Fluids, 24, 393 (1997)

[5] Han CD, Multiphase flow in polymer processing, Academic Press, New York (1981)

[6] Khan AA, Han CD, Trans. Soc. Rheol., 20, 595 (1976)

[7] Khomami B, J. Non-Newton. Fluid Mech., 37, 19 (1990)

[8] Luo XL, Mitsoulis E, Adv. Polym. Technol., 10, 47 (1990)

[9] Marchal JM, Crochet MJ, J. Non-Newton. Fluid Mech., 26, 77 (1987)

[10] Matsunaga K, Kajiwara T, Funatsu K, Polym. Eng. Sci., 38(7), 1099 (1998)

[11] Mavridis H, Hrymak AN, Vlachopoulos J, AIChE J., 33, 410 (1987)

[12] Mitsoulis E, J. Rheol., 30(S), S23 (1986)

[13] Musarra S, Keunings R, J. Non-Newton. Fluid Mech., 32, 253 (1989)

[14] Nickell RE, Tanner I, Caswell B, J. Fluid Mech., 65, 189 (1974)

[15] Papanastasiou TC, Malamateris N, Ellwood K, Int. J. Numer. Methods Fluids, 14, 587 (1992)

[16] Park SJ, Lee SJ, J. Non-Newton. Fluid Mech., 87(2), 197 (1999)

[17] Rajagopalan D, Brown RA, Amstrong RC, J. Non-Newton. Fluid Mech., 36, 159 (1990)

[18] Renardy M, Int. J. Numer. Methods Fluids, 24, 413 (1997)

[19] Sani RL, Gresho PM, Int. J. Numer. Methods Fluids, 18, 983 (1994)

[20] Southern JH, Ballman RL, J. Polym. Sci., 13, 863 (1975)

[21] Takase M, Kihara S, Funatsu K, Rheol. Acta, 37(6), 624 (1998)

[22] White JL, Ufford RC, Dharod KR, Price RL, J. Appl. Polym. Sci., 16, 1313 (1972)