澆注過程是屬於含有自由液面之流場的暫態問題。澆注與過程的數值模擬有助於瞭解模穴充填時金屬液流動的情形，對於鑄件品質的控制及鑄模的設計都有很大的幫助。
本文以數學模式來模擬金屬液於模穴之澆注過程。在澆注方面，同時考慮金屬液與空氣。流場部分,使用POWER-law法對統御方程式進行離散，並利用SIMPLE法及雙區計算模式來求解速度場。求解守衡標量方程式，以決定自由液面區的位置與型態。
探討澆注過程中，流體在模穴中流動的情形及自由液面的變化情形，本文以底澆和側澆，來比對不同的澆注位置流場的流動情形。於流場之分析中，對SIMPLE法與SIMPLER法作比較，發現後者比前者較易得到收斂速度場。計算所得之自由液面型態大致與文獻上吻合。在側澆中速度低的充填過程中，重力效應大於慣性力，容易產生潰流而影響上游流場；速度比較快的充填過程中，慣性力大於重力效應，金屬液沿著邊牆充填不會影響上游流場。但在底澆中就比較不會有這類情形，但如果速度過快，就會產生金屬液體的不穩定，而造成捲氣等缺陷，待凝固後就會產生氣孔。
本文除了在數值模式的探討及分析比對外，也希望能將此模式應用在實際澆注過程中，所以以一工字型鑄模為例。在工字型鑄模中，金屬液受到下縮孔和上擴口的影響，比矩型鑄模，流動較為平順，不過當速度增加時，金屬液流動與液氣界面就會較不穩定。

ABSTRACT
A filling process is a transient flow problem with time-varying free surface. The numerical simulation can help us to understand the flow field of a filling process, which can assist the mold design and the quality control of a casting process.
In this paper, a mathematical model, in which both liquid metal and air were considered, was built to simulate the filling processes in a mold cavity. The POWER-law was used to derive the finite difference equations of the flow field, and the SIMPLE algorithm was applied to solve the velocity field. By utilizing the Van Leer second-order scheme, the conserved scalar equation was solved to determine the position and profile of liquid/air interface.
In the beginning of this study, the computing results of the SIMPLE algorithm for a channel flow were compared with those of the SIMPLER one. The latter is easier to obtain convergent solutions than the former. In the analysis of filling process, the flow fields of both side- and bottom-fillings of a rectangle mold cavity were analyzed by the proposed model. The profiles of free surface of side filling are similar to those in the literature. For side-filling, when the gravity force is larger than the inertia force, the flow front is easier to break up and affect the upstream. On the contrary, the flow front will go up along the mold wall and will not affect the upstream. The flow front of bottom-filling is more stable than in side-filling. However, the higher inlet velocity would make the front of bottom-filling less stable. Finally, a more practical case, the flow field of filling an I-shaped mold cavity, was investigated.

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