3차원 압출팽창에 대한 수치모사 연구

이성재; 이승종

Korean Journal of Rheology, Vol.2, No.2, 35-44, December, 1990

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3차원 압출팽창에 대한 수치모사 연구

Numerical Prediction of Three-Dimensional Extrudate Swell

이성재, 이승종

초록

자유표면 유동을 수반하며 복잡한 구조를 지나는 유동문제를 수치모사할 수 있는 삼차윈 유한요소법 코드를 개발하였다. 정사각관을 대상으로 하는 삼차원 압출팽창 문제를 등온 뉴톤 유동 뿐만 아니라 비뉴톤 유동 및 비등온 유동문제의 경우까지 다룰 수 있도록 확장하여 수치모사하였다. 삼차원 유한요소법 알고리듬에 pathline approach 방법과 사상방법을 적용시켜 등온 뉴톤 유체의 미동흐름에 대하여 압출팽창 문제를 푼 결과 팽창비가 대칭면에서 최대 21.0%, 관의 모서리 부분에서 최소 4.1%로 나타났다. 전단박화 현상이 있는 비뉴톤 유동의 경우 뉴톤 유동에 비해 팽창이 작게 일어났고, 비등온 유동의 경우 관벽 온도가 낮은 쪽이 높은 쪽에 비해 팽창이 크게 일어남을 알 수 있었다.

A full three-dimensional finite element code has been developed to solve the flow problems through arbitrary geometries, which may include free surfaces. This code together with the parthline approach method and the mapping method has been used to simulate three-dimensional extrudate swell from a square die in the cases of isothermal Newtonian and non-Newtonian flows and nonisothermal Newtonian flow. Extrudate swell of isothermal Newtonian creeping case exhibits a maximum swell of 21.O% at the plane of symmetry and a minimum swell of 4.1% at the corner. In the case of non-Newtonian flow, shear thinning effects produce lower swell compared to Newtonian one and in the case of nonisothermal flow, lower temperature side of the die wall exhibits higher swell compared to higher temperature side of the die wall.

Keywords:Three-dimensional flows;Extrudate swell;Finite element method;Free surface;non-Newtonian;nonisothermal

[References]

Nickell RE, Tanner RI, Caswell B, J. Fluid Mech., 65, 189 (1974)
Reddy KR, Tanner RI, Comp. Fluids, 6, 83 (1978)
Tanner RI, Nickell RE, Bilger RW, Comp. Mech. Appl. Mech. Eng., 6, 155 (1975)
Crochet MJ, Keunings R, J. Non-Newton. Fluid Mech., 7, 199 (1980)
Crochet MJ, Keunings R, J. Non-Newton. Fluid Mech., 10, 85 (1982)
Caswell B, Viriyayuthakorn M, J. Non-Newton. Fluid Mech., 12, 13 (1983)
Bush MB, Millthorpe JF, Tanner RI, J. Non-Newton. Fluid Mech., 16, 37 (1984)
Bush MB, Tanner RI, Phan-Tien N, J. Non-Newton. Fluid Mech., 18, 143 (1985)
Phuoc HB, Tanner RI, J. Fluid Mech., 98, 253 (1980)
Tanner RI, J. Non-Newton. Fluid Mech., 6, 289 (1980)
Ben-Sabar E, Caswell B, J. Rheol., 25, 537 (1981)
Huynh BP, J. Non-Newton. Fluid Mech., 13, 1 (1983)
Sugeng F, Phan-Thien N, Tanner RI, J. Rheol., 31, 37 (1987)
McClelland MA, Finlayson BA, J. Non-Newton. Fluid Mech., 27, 363 (1988)
Bush MB, Phan-Thien N, J. Non-Newton. Fluid Mech., 18, 211 (1985)
Tran-Cong T, Phan-Thien N, Rheol. Acta, 27, 21 (1988)
Tran-Cong T, Phan-Thien N, Rheol. Acta, 27, 639 (1988)
Tran-Cong T, Phan-Thien N, J. Non-Newton. Fluid Mech., 30, 37 (1988)
Karagiannis A, Hrymak AN, Vlachopoulos J, AIChE J., 34, 2088 (1988)
Karagiannis A, Hrymak AN, Vlachopoulos J, Rheol. Acta, 28, 121 (1989)
Shiojima T, Shimazaki Y, J. Non-Newton. Fluid Mech., 34, 269 (1990)
Crochet MJ, Davies AR, Walters K, "Numerical Simulation of Non-Newtonian Flow," Elsevier (1984)
Lee SJ, Suh DG, Lee SJ, HWAHAK KONGHAK, 27(4), 496 (1989)

[Referenced By]

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

[2] Reddy KR, Tanner RI, Comp. Fluids, 6, 83 (1978)

[3] Tanner RI, Nickell RE, Bilger RW, Comp. Mech. Appl. Mech. Eng., 6, 155 (1975)

[4] Crochet MJ, Keunings R, J. Non-Newton. Fluid Mech., 7, 199 (1980)

[5] Crochet MJ, Keunings R, J. Non-Newton. Fluid Mech., 10, 85 (1982)

[6] Caswell B, Viriyayuthakorn M, J. Non-Newton. Fluid Mech., 12, 13 (1983)

[7] Bush MB, Millthorpe JF, Tanner RI, J. Non-Newton. Fluid Mech., 16, 37 (1984)

[8] Bush MB, Tanner RI, Phan-Tien N, J. Non-Newton. Fluid Mech., 18, 143 (1985)

[9] Phuoc HB, Tanner RI, J. Fluid Mech., 98, 253 (1980)

[10] Tanner RI, J. Non-Newton. Fluid Mech., 6, 289 (1980)

[11] Ben-Sabar E, Caswell B, J. Rheol., 25, 537 (1981)

[12] Huynh BP, J. Non-Newton. Fluid Mech., 13, 1 (1983)

[13] Sugeng F, Phan-Thien N, Tanner RI, J. Rheol., 31, 37 (1987)

[14] McClelland MA, Finlayson BA, J. Non-Newton. Fluid Mech., 27, 363 (1988)

[15] Bush MB, Phan-Thien N, J. Non-Newton. Fluid Mech., 18, 211 (1985)

[16] Tran-Cong T, Phan-Thien N, Rheol. Acta, 27, 21 (1988)

[17] Tran-Cong T, Phan-Thien N, Rheol. Acta, 27, 639 (1988)

[18] Tran-Cong T, Phan-Thien N, J. Non-Newton. Fluid Mech., 30, 37 (1988)

[19] Karagiannis A, Hrymak AN, Vlachopoulos J, AIChE J., 34, 2088 (1988)

[20] Karagiannis A, Hrymak AN, Vlachopoulos J, Rheol. Acta, 28, 121 (1989)

[21] Shiojima T, Shimazaki Y, J. Non-Newton. Fluid Mech., 34, 269 (1990)

[22] Crochet MJ, Davies AR, Walters K, "Numerical Simulation of Non-Newtonian Flow," Elsevier (1984)

[23] Lee SJ, Suh DG, Lee SJ, HWAHAK KONGHAK, 27(4), 496 (1989)