摘要 固化製程在工業材料上的應用相當廣泛，其中由單向固化製程所生產的鑄造物，其晶體晶格排列較規則，因此有較好的機械性質，常被用於渦輪葉片的製造。然而在某些情況下，單向固化製程所生產的鑄造物會有材質不均勻的缺陷產生，使得鑄造物的機械性質降低，品質無法滿足需求。 一般推測材質不均勻的缺陷，是由於單向固化過程中會發生過冷的現象，導致固液介面的形態不穩定所造成的。許多學者從事這方面的研究，他們藉由改變固化流場中的一些相關物理參數，來觀察固化流場的變化，希望能找出抑制形態不穩定發生的方法，進而改善材質的缺陷，提高鑄造物的品質。 本文主要的目的，是探討一個週期性調變溫度場對固液介面形態穩定的影響，希望藉由溫度的調變能有效抑制形態不穩定的發生，並經過理論的分析與數值的模擬，找出這個調變系統所存在的穩定區域範圍。分析的方法如下：首先利用解析解的方法，探討溫度調變下的基態流場，並分析其特性；接著針對基態流場做線性穩定分析，來探討這個基態流場的穩定性；最後引入同步與次調和模態的觀念，並藉由電腦計算模擬這兩種模態所存在的不穩定區域。 Abstract Solidification process is generally applied to the industrial material manufacturing. In particular, the material is produced by directional solidification process with better mechanical properties. So it is usually adopted in the manufacture of turbine blades. However, in some situations, casting alloys may have the non-uniform defects, which are induced in the process of directional solidification. Casting alloy with defects cannot fulfill the demand of industry because these defects decrease casting alloy’s mechanical properties. It is believed the appearance of non-uniform defects comes from the supercooling area adjacent to the solid/liquid interface. The liquid near the interface encounters the supercooling effects and thus makes the morphological instability of solid/liquid interface. Many scholars are engaged in correlative investigations. They observed the variation of the solidification flow field by changing some correlative physical parameter, and hope to find a method that the morphological instability can be successfully inhabited; hence, the casting alloys will have better quality. The main goal of this thesis is to probe into the influences of temperature modulation on the morphological stability of solid/liquid interface. We hope that the morphological instability can be successfully inhabited by means of the temperature modulation. Using theoretical analysis and numerical simulation to find stable region of the system, my analysis approach is as follows: First, we drive the basic solution. Based on the analytical solution, we are able to identify the characteristics of basic state with temperature modulation. Then, we apply linear stability analysis to investigate the stability of the basic state. We found that the morphological instability can occur with the synchronous and subharmonic modes. The stability regions for specific modulation frequencies and amplitude were also studied.
