雷諾數對三維頂部驅動矩形槽中渦漩結構的影響

Abstract

摘 要 本研究探討一初始為靜止之三維矩形槽，受突起之頂部驅動速度而形成之不可壓縮流場，其雷諾數對此流場渦漩結構之影響。利用數值解析連續方程式與Navier-Stokes方程組，滿足速度無滑移邊界條件與壓力Neumann型邊界條件，以求得三維頂部驅動矩形槽流場之速度項與壓力項。再由所推求出之速度項與壓力項，計算流場之渦度場，而藉由上述所得之數值計算結果，繪出流場之速度向量圖、渦度等值線圖與渦度等值面圖。並進一步由所繪出之圖，探討流場運動中雷諾數對於渦漩結構變化之影響；以及觀察渦漩結構產生變化後，對於流場運動所產生之擾動現象。研究結果顯示：此流場之渦漩結構會隨著流場雷諾數的不同，而明顯的由二維渦漩結構演化成三維特有之渦漩結構。且於Re=1300後，此三維渦漩結構始有明顯存在於流場中，並演變為持續發展之流場特徵，而非穩態之流場運動。此三維渦漩結構的產生，也同時為流場帶來不穩定的影響，而使得流場發生具有波浪形擾動之特徵，並隨著雷諾數的增大，此不穩定現象更加劇烈地出現於流場中。

Abstract The purpose of the present research is to investigate the effect of Reynolds number on the vortical structure in a three-dimensional cavity. This cavity flow is incompressible and it is stationary in the beginning. The primitive velocities and pressure in a set of incompressible continuity and Navier-Stokes equations are solved using the finite difference method. The velocity boundary conditions are no-slip and the pressure satisfies the Neumann boundary condition. By numerical computations, the plots of velocity vector, vorticity iso-line and vorticity iso-surface are illustrated. Then the effect of Reynolds number on the vortical structure variations and wavy disturbances in the spanwise direction are shown through these plots. The results of this study reveal that raising of the Reynolds number makes two-dimensional vortical structure will evolve into three-dimensional structure. As the Reynolds number reaches 1300, the three-dimensional vortical structure starts to exist obviously in the flow field. This flow is not a steady motion, and it will continue to become a turbulence flow with the increase of Reynolds numbers.