二維分歧管流場之數值分析

Abstract

本研究將採用非結構性網格，以數值方法來計算二維、穩態且不可壓縮之分歧管流場，流場假設為層流，且工作流體為牛頓流體。而研究的對象則為對稱造型之45度夾角Y型分歧管和直角T型分歧管。在計算過程中，我們將加大兩者之下游流道寬度，使其擴張比大於二，並觀察其流場之變化。而在分岔端點處之造型，本研究採用銳角(sharp corner)造型之分岔端點，來進行分析。此外，在分歧管的出口條件上，我們採用壓力邊界條件，來觀察在出口處無壓力差和有微量壓力差時，分歧管流場中的變化。其結果發現，當出口處無壓差時，流場大部分呈現對稱的狀態；而當有壓力差時，則會造成上下方流道內的流場，出現不對稱的現象。下游流道寬度的增大，會增加流場的複雜性，同時也會在下游流道中產生許多迴流。另外，壓力差的增加和下游流道寬度的增大都會造成上下方流道出口處之流量比的差距增大。

In this thesis, we will use the numerical method to solve the Navier -Stokes equations of a two-dimensional, steady, incompressible flow in bifurcations. Laminar flow and Newtonian fluids are assumpted. A symmetrical Y branch with forty degree angle and a right angled Tee branch will be studied. In our research, we enlarge the channel width in the downstream of the both branches to make the extension ratio more than two and we observe its variation of the flows. The shape of the branching point is sharp corner. Furthermore, there are pressure conditions at the outlet boundaries of both branches and the variation of the flow with tiny and zero pressure difference is what we want to know. The results show that most flows with zero pressure difference are symmetric, but tiny pressure difference will make the flows between upper and lower channel asymmetric. The enlargement of the channel width in the downstream of the both Y and Tee branch will make the flow more complicated and produce more recirculations in the downstream channel of the both branches. Besides, regardless of the Y or the Tee branch, the enlargement of the channel width in the downstream and the pressure difference at the outlets both enlarge the difference of the mass flow between upper and lower channel.