싱글-스크류 압출공정에서의 비등온 유동의 유한요소 해석

권태헌

Korean Journal of Rheology, Vol.3, No.1, 56-67, April, 1991

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싱글-스크류 압출공정에서의 비등온 유동의 유한요소 해석

Finite Element Analysis of Nonisothermal Flows in Single-Screw Extruders

권태헌

초록

압출공정에서 발생하는 전달현상을 이해하기 위하여, 싱글-스크류 압출기에서의 비뉴톤성 유체의 비등온유동에 대한 수치해석을 위한 유한요소법(FEM)을 개발하였다. FEM은 준-3차원 물리적 모델(quasi-three-dimensional physical model)을 기본으로 하였고 온도분포 해석을 위하여 전진방법(marching scheme)을 도입하였다. 본 연구에서 도입한 수치해석적 모델과 더 간단한 준-2차원 모델을 온도분포의 예측에 관하여 초점을 맞추어서 비교하였다. 압출기의 내부채널에서 순환유동(circulating flow)이 온도분포에 미치는 영향의 중요성이 강조되었다. 순환유동의 효과를 파악하기 위하여 유한요소식에서 순환과 관련된 대류항을 빼도록 유한요소 프로그램을 개조하였고, 개발된 원래의 프로그램과 개조된 프로그램의 해석을 수행한 후 해석결과 중에서 특히 온도분포에 있어서의 차이점을 비교하였다. 이로부터 간단한 준-2차원 모델은 순환효과를 무시했기 때문에 속도분포의 예측에서는 별 문제가 없으나 온도분포의 예측에 있어서는 크게 잘못될 수 있음을 알 수 있었다.

In order to understand the transport phenomena underlying the extrusion process, a finite element method (FEM) has been developed for numerical analyses of nonisothermal flows of non-Newtonian viscous fluids in single screw extruders. The FEM was based on a quasi-three dimensional physical modeling with a marching scheme employed for analyzing temperature distribution. The present numerical modeling for the extruder channel flows is compared with a simpler two-dimensional modeling especially in terms of predictability of the temperature distribution. Emphasis is made on the effect of a circulating flow on the temperature distribution in an extruder channel. In order to find the effect of the circulating flow, a modification in the FEM was made by dropping convective terms associated with the circulation in the finite element formulation and subsequently comparison was made between results from the original FEM and those from the modified FEM with respect to the temperature distribution. It is found that the temperature predicted by the simpler quasi-2D model can be quite errorneous due to the negligence of the circulating effect even though velocity field can be predicted without a significant error.

Keywords:Single-Screw Extruder;Nonisothermal Flow;Non-Newtonian Fluids;Finite Element Method;Circulating Flow;Quasi-3D Model;Quasi-2D Model

[References]

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Tadmor Z, Gogos C, "Principles of Polymer Processing," John Wiley & Sons, New York (1979)
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Denson CD, Hwang BK, Polym. Eng. Sci., 20, 965 (1980)
Bigio D, Zerafati S, SPE ANTEC Tech. Paper, 34, 85 (1988)
Kwon TH, Jaluria Y, Karwe MV, "Progress in Polymer Processing," ed. by A.I. Isayev, Hanser Publisher, p. 77 (1991)
Sastrohartono T, Esseghir M, Kwon TH, Sernas V, Polym. Eng. Sci., 30, 1392 (1990)
Gupta M, Kwon TH, Polym. Eng. Sci., 30, 1420 (1990)
Zienkiewicz OC, "The Finite Element Method," 3rd ed., McGraw-Hill, New York (1977)

[1] Eise K, Hermann H, Werner H, Burkhardt U, Adv. Plast. Technol., 1, 1 (1981)

[2] Tadmor Z, Gogos C, "Principles of Polymer Processing," John Wiley & Sons, New York (1979)

[3] Fenner RT, "Principles of Polymer Processing," Chemical Publishing, New York (1979)

[4] Tadmor Z, Klein I, "Engineering Principles of Plasticating Extrusion," Krieger Publishing Co., Florida (1978)

[5] Karwe MV, Jaluria Y, Kwon TH, "Computational Methods in Flow Analysis," ed. by H. Niki and M. Kawahara, Vol. II, Okayama University of Science, p. 1085 (1988)

[6] Gopalakrishna S, Karwe MV, Jaluria Y, "Numerical Methods in Industrial Forming Processes," ed. by E.G. Thompson et al., Balkema, Rotterdam, p. 265 (1989)

[7] Griffith RM, Ind. Eng. Chem. Fundam., 1, 1 (1962)

[8] Zamodits HJ, Pearson JRA, Trans. Soc. Rheol., 13, 3 (1969)

[9] Fenner RT, Polymer, 18 (1977)

[10] Sastrohartono T, Kwon TH, Int. J. Numer. Methods Eng., 30, 1369 (1990)

[11] Janssen LPBM, "Twin Screw Extrusion," Elsevier Scientific Publishing, Amsterdam (1978)

[12] Secor RM, Polym. Eng. Sci., 26, 647 (1986)

[13] Denson CD, Hwang BK, SPE ANTEC Tech. Paper, 26, 107 (1980)

[14] Denson CD, Hwang BK, Polym. Eng. Sci., 20, 965 (1980)

[15] Bigio D, Zerafati S, SPE ANTEC Tech. Paper, 34, 85 (1988)

[16] Kwon TH, Jaluria Y, Karwe MV, "Progress in Polymer Processing," ed. by A.I. Isayev, Hanser Publisher, p. 77 (1991)

[17] Sastrohartono T, Esseghir M, Kwon TH, Sernas V, Polym. Eng. Sci., 30, 1392 (1990)

[18] Gupta M, Kwon TH, Polym. Eng. Sci., 30, 1420 (1990)

[19] Zienkiewicz OC, "The Finite Element Method," 3rd ed., McGraw-Hill, New York (1977)