三維頂部驅動矩形槽中流場之初始發展與演化

Abstract

本研究探討三維矩形槽中初始為靜止，受突然平移之頂部水平驅動而發展之黏性流流場。利用數值解析三維之無因次化，守恆型式Navier-Stokes方程式，並且滿足槽壁之邊界條件，以求得三維矩形槽中流場之速度與壓力。進一步探討此流場初始近似二維，受槽壁之影響進而發展為複雜之三維運動過程。而在兩側末端牆面出現之漩渦，以及規則出現於展延方向之TGL(Taylor-Gortler-Like)漩渦，此二類漩渦之生成與演化亦在我們討論的範圍之內。研究結果顯示：三維矩形槽中流場初期，有一展向噴流形成使得流場由近似二維發展為三維運動，而展向噴流之生成與末端牆面漩渦的出現有密切關係；隨著無因次時間之增加，上游區域之展向運動複雜度較下游為高，而近對稱面區域之螺旋往復運動較靠近末端牆面區域為多，在展延規則出現的TGL漩渦，隨著主漩渦流線延伸之現象亦被證實出現在我們的計算結果中。

Lid-driven flow in a rectangular cavity of span to width aspect ratio of 3：1 and depth to width aspect ratio of 1：1 is simulated numerically at Reynolds number 1500 to gain physical insight into the initial development of the three-dimensional perturbation and its subsequent evolution. The emphases are on the end-wall effect which causes the initial almost-two-dimensional flow to develop into a three-dimensional flow structure, and the evolution of such a flow structure into Taylor-Gortler-like（TGL） vortices distributing along the cavity span in planes perpendicular to the lid. It is found that spanwise jet flows and corner vortices form near the end walls immediately after the start of the motion of the lid. As time proceeds, the disturbed spanwise motions in the upstream area become more complex than those in the downstream area, and the circulating motions of fluid particles in the region near the symmetric plane are more active than those near the end walls. The axes of the TGL vortices are found to stretch along the streamlines of the primary recirculating flow.