형식에 따른 차분법을 이용한 축대칭 4:1 수축을 지나는 점탄성유동의 수치모사

송진호; 유정열

Korean Journal of Rheology, Vol.7, No.2, 110-119, August, 1995

Numerical Simulation of Viscoelastic Fluid Flow Through 4 : 1 Axi-symmetric Contraction Using Type-dependent Difference Method

송진호, 유정열

초록

본 연구에서는 Upper Convected Maxwell유체 및 Leonov-like-Giesekus 유체모형을 이용하여 축대칭 4 : 1수축을 지나는 점탄성유체의 유동을 수치해석하였다. 이러한 점탄성유체의 유동에 대한 지배방정식이 타원형-쌍곡선형으로 형식변화되므로 이를 적절히 고려할 수 있는 형태의 와도방정식을 이용하여 수치해석을 수행하였다. 와도방정식의 수치해석에서는 형식에 따른 차분법을 도입하였다. 두 유체모형에 대해서 Weissenberg수를 증가시키면서 탄성의 효과가 모서리와류의 크기, 응력의 분포, 지배방정식의 형식변화에 미치는 영향을 살펴보았다. 수치해석 결과 탄성의 효과가 증가할수록 모서리와류가 커지며, 평면유동의 경우보다 훨씬 큰 모서리와류가 관찰되어 기존의 실험결과와 잘 일치하는 것을 볼 수 있었다. 또한 수치해석 결과로부터 와도방정식의 형식변화를 확인할 수 있었다.

In this paper numerical simulation of viscoelastic fluid flow through 4:1 axi-symmetric contraction is performed by using Upper Convected Maxwell fluid and Leonov-like-Giesekus fluid model. By considering the fact that the governing equations describing above viscoelastic fluid flow change type, a proper form of vorticity equation is approximation of vorticity equation. Investigated is the effect of elasticity on the strength of corner vortex, distribution of stresses, and change of type by increasing Weissenberg number. The results show that the corner vortex gets bigger as the elasticity effect increases, and the strength and size of corner vortex is much bigger than those of planar flow, which are in the same trend with the results of existing experimental works. Also change of type of vorticity equation is clearly identified in the results of numerical simulation.

Keywords:Change of type;vorticity equation;leonov-like-Giesekus fluid;upper convected Maxwell fluid;corner vortex;type dependent difference scheme

[References]

Davis AR, Lee SJ, Webster MF, J. Non-Newton. Fluid Mech., 16, 117 (1984)
Joseph DD, Renardy M, Arch. Rat. Mech. Anal., 87(3), 213 (1984)
Yoo JY, Ahrens M, Joseph DD, J. Fluid Mech., 153, 203 (1985)
Yoo JY, Joseph DD, J. Non-Newton. Fluid Mech., 19, 15 (1985)
Song JH, Yoo JY, J. Non-Newton. Fluid Mech., 24, 221 (1987)
Murman EM, Cole JD, AIAA J., 9, 114 (1971)
Choi HC, Song JH, Yoo JY, J. Non-Newton. Fluid Mech., 29, 347 (1988)
Giesekus H, J. Non-Newton. Fluid Mech., 11, 69 (1982)
Crochet MJ, Davies AR, Walters K, Numerical Simulation of Non-Newtonian Flow, Elsevier, Amsterdam (1984)
Kawaguti M, Phys. Fluids, 2, 101 (1964)
Walters K, Webster MF, Phil. Trans. R. Soc. London A, 308, 199 (1982)
Walters K, Rawlinson DM, Rheol. Acta, 21, 547 (1982)

[1] Davis AR, Lee SJ, Webster MF, J. Non-Newton. Fluid Mech., 16, 117 (1984)

[2] Joseph DD, Renardy M, Arch. Rat. Mech. Anal., 87(3), 213 (1984)

[3] Yoo JY, Ahrens M, Joseph DD, J. Fluid Mech., 153, 203 (1985)

[4] Yoo JY, Joseph DD, J. Non-Newton. Fluid Mech., 19, 15 (1985)

[5] Song JH, Yoo JY, J. Non-Newton. Fluid Mech., 24, 221 (1987)

[6] Murman EM, Cole JD, AIAA J., 9, 114 (1971)

[7] Choi HC, Song JH, Yoo JY, J. Non-Newton. Fluid Mech., 29, 347 (1988)

[8] Giesekus H, J. Non-Newton. Fluid Mech., 11, 69 (1982)

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

[10] Kawaguti M, Phys. Fluids, 2, 101 (1964)

[11] Walters K, Webster MF, Phil. Trans. R. Soc. London A, 308, 199 (1982)

[12] Walters K, Rawlinson DM, Rheol. Acta, 21, 547 (1982)