二維紊剪流層中大型渦流結構之研究

Abstract

The large-scale vortical structures in the evolutions of a two-dimensional turbulentshear layer is studied numerically. The motion of 192 vortices is followed on a 41 X 41grid using a numerical scheme that similar to the vortex-in-cell algorithm. The numericalscheme uses the direct summation of streamfunction contributed by all vortices on the grid.which is then differentiated to obtain the velocity field. The velocity of vortex is obtainedby bilinear interpolation from the grids that enclosing the vortex. The voriticity field of theflow field is obtained by area weighting scheme. The formation, pairing, and coalescence of large-scale vortex structures predicted bythe current scheme are in good agreement with previous numerical simulation by discretevortex methods and vortex-in-cell methods. As to the turbulence characteristics, the quantities such as mean velocities, vorticities, turbulence intensities, and Reynolds stress, are alsocalculated and compared with previous studies. It is found the self-preseveration characteristics are fairly maintained. The temporal variations of momentum flux during pairing process are also presented to visualize the characteristics of turbulent momentum transportbetween the mean flow and turbulence.

本文以數值方法探討二維紊剪流中大型渦流之演變過程。192個渦元在格點為41x41之流域內，以一類似室內渦元法之計算方式來預測其運動。此計算法中，格點上之流函數由流域中所有渦元之流函數累積而得，並由此微分求得速度場。渦元之速度，則由圍繞渦元之格點速度由雙向線性內插法求得。 本文發展之計算方法，應用於紊剪流中大型渦流結構之形成、配對、及結合等過程之模擬，並將所得之結果與過去以使用離散渦元法及室內渦元法之結果相比較，發現相當吻合。至於紊流特性，本文計算流場平均速度及渦度，紊流強度及紊應力等，並與過去之研究相比較，此物理量之縱剖面輪廓均維持自持性。 本文另亦探討，在渦流配對過程中，平均流場與紊流間動量之輸送特性。