Elucidation and control of turbulence-driven secondary flow in a rectangular duct using nonlinear traveling-wave solutions

点击翻译按钮获取中文摘要

In this study, numerical computation of nonlinear traveling-wave solutions has been performed using a Newton method in a square duct. We have succeeded in obtaining the steady traveling-wave solutionexhibiting an eight-vortex pattern similar to the turbulence-driven mean secondary flow. The streamwise-averaged velocity field of this traveling wave has a comparable intensity of the time- and streamwise-averaged turbulent velocity field, and in low-Reynolds-number range, Re=1400-2500, the traveling wave reproduces not only qualitative but also quantitative properties of turbulence-driven mean secondary flow. We have also worked on numerical computation of nonlinear-traveling waves in a rectangular duct. The eight-vortex traveling wave found in a square duct has been tracked with changing anaspect ratio of a duct cross-section. It has been found that at Re=1200, the eight-vortex traveling wave exists only for the aspect ratio smaller than 2.4. It has also been observed that when the aspect ratio is increased from unity, vertical structures in the traveling wave are localized around the bisector of the duct wall of wider span. Direct numerical simulations of turbulent square-duct flow have been performed at higher Reynolds numbers, Re=3500, 5480, to identify large-scale streamwise rolls by using the Clebsch potential for cross-stream turbulence motion. It has been suggested that the large-scale rolls of a variety of cross-stream length scales play a significant role in the generation of the mean secondary flow in high-Reynolds-number turbulence.