近年來空氣污染的問題越來越嚴重，造成許多人產生呼吸系統上的疾病(如氣喘)。為有效使用藥物噴劑，探討氣管內流場現象是一重要且有意義之工作。此一方面之研究可分為實驗、數值模擬及理論分析，在此將利用計算流體力學之方法探討空氣流經氣喘患者分歧管之行為。首先利用Ansys FLUENT商用軟體進行三維不可壓縮流之計算，然後以自行開發之可壓縮程式探討此問題。由於氣體為可壓縮流且在大部分呼吸狀態下屬於低馬赫數範圍，因此本文建立一可求解低馬赫數可壓縮流之數值法及程式。為探討氣管流，首先利用CATIA設計軟體建立氣管模型(分歧管)。然後利用介面程式，將CATIA設計軟體及自行發展之網格程式結合，以便在流場區域建立非結構四面體。在上述網格上，本研究建立一數值法以求解三維非穩態拿維-史脫克方程式。此數值方法包含四步Runge-Kutta時間積分法、 Roe通量差分分離法及求解Rossow壓力更正方程式之改良式Gauss-Seidel疊代法。為提昇計算效率，本研究在單機多核心之個人電腦上進行平行運算。為評估上述求解法及相關程式，首先探討典型之分歧管穩態層流，且將本計算解與Ansys FLUENT商業軟體所得之解與相關實驗值比較。接著進行氣喘患者分歧管之穩態層流計算，並將計算解與相關文獻之結果比較。由計算結果可觀察入口端、分歧部分及出口端之速度分佈。除了探討二次流、渦流等物理現象外，可分析氣喘患者與正常人分歧管流之差異。

In recent years, the air pollution problem is getting more and more serious, and it causes many people to have on respiratory system disease (such as asthma). For effectively inhaling the medicinal preparations, the study of flow phenomena in bifurcating airway is important and meaningful. About this topic, the research approaches may divide into experiment, numerical simulation and theoretical analysis. By using the method of computational fluid dynamics, the behavior of air flow passing through the bifurcating airway in asthmatics is investigate in this thesis. First, the FLUENT software is utilized to compute the three-dimensional incompressible flow, then a self developed compressible flow code is used to steady the problem. Because the air flow is compressible and it is within the low Mach number flow regime in the majority of breathing conditions, a numerical approach and related program are developed in this thesis to solve the low-speed compressible flows. To investigate the flow in bifurcating airway, the CATIA software is adopted to construct the trachea model (bifurcating tube). Then an interface program is adopted, so that the CATIA software and homemade mesh-generation program are combined together to construct the unstructured tetrahedral meshes in the flow domain. On the above-mentioned meshes, a numerical approach is developed to solve the unsteady three-dimensional Navier-Stokes equations. This approach includes four-step Runge-Kutta time-integration scheme, Roe’s flux-difference splitting method and Modified Gauss-Seidel iterative method for solving the Rossow’s pressure correction equation. To promote the computational efficiency, it is operated on a personal computer with multiple cores. To evaluate the above-mentioned numerical approach and related program, the steady laminar flow passing through a typical bifurcating airway is studied first, and the computed results by using the present method and FLUENT code are compared with the related experimental data. Then, the steady laminar flow passing through an asthmatic bifurcating airway is studied, and the present solutions are compared with the results in the related paper. From the computed results, the velocity distributions on the inlet, outlet and branch part of airway are observed. Besides the secondary flow and vortex phenomena are investigated, the difference between normal and asthmatic airway flows are analyzed.

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