臺灣博碩士論文加值系統

本文將進行射出成型之填充過程的水平流場計算，研究其自由液面的形狀變化。為了滿足動態接觸角，我們使用自然三次樣條法對自由液面進行修正，解決接觸線上奇異點的問題。在自由液面的壓力分佈計算上，本文參酌前人所得的自由液面壓力分佈的特性來假設一個壓力分佈方程式，透過四階龍格庫達法來找到壓力分佈對應的自由液面，並利用試誤法修正壓力分佈的係數使其對應的自由液面與流場的自由液面吻合，以此方法來找到正確的壓力分佈之值。同時，我們也可以觀察到不同壓力分佈下自由液面的形狀變化。

To study the change of free surface profile in mold-filling process, we simulating a Horizontal flow field. To ensure the required dynamic contact angle, the liquid meniscus near the wall region is corrected by natural cubic spline and thus successfully removes the stress singularity. We refer to the characteristic of the pressure distribution on free surface postulated by Lee and Liao and suppose a pressure distribution equation on free surface. Using the Runge-Kutta method of order four, the free surface profile corresponding to pressure distribution equation is found. We can correct the parameters of pressure distribution equation to make the corresponding free surface profile fitting the flow field’s free surface profile and if the free surface profile coincided, the pressure distribution is the correct value. Simultaneously, we can observe the change of free surface profile with different parameters of pressure distribution equation.

符號表.................................I
圖目錄.................................II
目錄...................................IV
第一章序論..............................1
1.1 前言...............................1
1.2 文獻回顧............................1
1.3 研究動機與方法......................3
第二章二維流場模型與統御方程式............5
2.1問題描述.........................5
2.2無因次化統御方程式，初始與邊界條件.....5
第三章數值方法..........................10
3.1 網格系統............................10
3.2 動量方程式之差分....................10
3.3 壓力聯結方程式之差分.................14
3.4自由液面變遷的演算...................15
3.4.1自由液面的動態接觸角............15
3.4.2鬼點的計算.....................17
3.5自由液面的壓力分佈...................17
3.5.1由曲率計算對應的自由液面...18
3.5.2自由液面壓力分佈給定.......19
3.6 收斂標準...........................21
3.7 計算流程...........................22
第四章結果討論..........................23
第五章結論.............................25
參考文獻...............................26
附圖...................................27

[1] W. Rose, Fluid-fluid interfaces in steady motion, Nature 191 (1961), 242-243.
[2] W. Rose, R. W. Heins, Moving interfaces and contact angle rate-dependency, Journal of Colloid Science, 17 (1962), 39-48
[3] D. J. Coyle, J. W. Blake, and C. W. Macosko, The kinematics of fountain flow in mold filling, AIChE Journal, 33 (1987), 1168-1177
[4] H. Mavridis, A. Hrymak, J. Vlachopoulos, Finite element simulation of fountain flow in injection molding, Polym. Eng. Sci. 26 (1986), 449-454.
[5] C.G. Gogos, C.F. Huang, The process of cavity filling including the fountain flow in injection molding, Polym. Eng. Sci. 26 (1986), 1457-1466.
[6] M.R. Kamal, E. Chu, P.G. Lafleur, Computer simulation of injection mold filling for viscoelastic melts with fountain flow, Polym. AIChE Journal, 34 (1988), 190-196.
[7] R.A. Behrens, M.J. Crochet, C.D. Denson, A.B. Metzner, Transient free-surface flows: motion of a fluid advancing in a tube, AIChE Journal, 33 (1987), 1178-1186.
[8]Ngan, C. G. and Dussan V., E. B., “The moving contact line with 180o advancing contact angle,” Phys. Fluids, 27 (1984), 2785-2787.
[9] H. Mavridis, A.N. Hrymak, J. Vlachopoulos, Transient free-surface flows in injection model filling, AIChE Journal, 34 (1988), 403-410.
[10] M.R. Kamal, S.K. Goyal, E. Chu, Simulation of injection mold filling of viscoelastic polymer with fountain flow, AIChE Journal, 34 (1988), 94-106.
[11] S.L. Lee, S.R. Sheu, Filling process in an open tank, ASME J. Fluids Eng. 125 (2003), 1016-1021.
[12] S.L. Lee, R.Y. Tzong, An enthalpy formulation for phase change problems with a large thermal diffusivity jump across the interface, Int. J. Heat Mass Transfer, 34 (1991), 1491-1502.
[13] S.L. Lee, W.C. Liao, Numerical simulation of a fountain flow on nonstaggered Cartesian grid system, Int. J. Heat Mass Transfer, 51 (2008), 2433-2443.
[14] S.L. Lee, R. Y. Tzong , “Artificial Pressure for Pressure-Linked Equation,” Int. J. Heat Mass Transfer, 35 (1992), 2705-2716.