关键词:错列双圆柱;错列角度;CIP 方法;涡激振动;Navier-Stokes 方程;浸入边界法 Abstract The vortex-induced vibration of two cylinders with the effect of the stagger angle is studied numerically. A finite difference model based on an in-house code named CIP (constraint interpolation profile) is utilized. The model is built on a Cartesian coordinate system, with the Navier-Stokes equation solved by a third-order accuracy CIP method. The fluid-structure interaction is modelled by an immersed boundary method. Based on the CIP model, two-dimensional flow past two equal-sized circular cylinders placed at Reynolds number ( ) with different stagger angle ( with a 15 #x00B0; interval) is investigated. Main attention has been paid to the lift coefficient, drag coefficient, displacement response, vortex-shedding frequency and wake pattern of both cylinders. The results show that the drag coefficient and lift coefficient of both cylinders increase monotonically as the stagger angle increases when reduced velocity . For reduced velocity , with the increase of stagger angle, the drag coefficient of both cylinders changes slightly and the lift coefficient of both cylinders presents a “convex-like” trend and reaches maximum value at . In the case of reduced velocity , with the increase of stagger angle, the drag coefficient of both cylinders also displays little change and the lift coefficients of both cylinders show a “concave-like” trend and reach minimum value at . However, there is no obvious correspondence between the transverse oscillation amplitude and lift coefficient of cylinder as . Finally, the wake pattern of both cylinders is analyzed to explain above phenomenon. Above all, the present result could be helpful to the structure design of ocean engineering.
Keywords:staggered cylinders;stagger angle;CIP method;vortex-induced vibration;Navier-Stokes equation;immersed boundary method -->0 PDF (12108KB)元数据多维度评价相关文章收藏文章 本文引用格式导出EndNoteRisBibtex收藏本文--> 段松长, 赵西增, 叶洲腾, 王凯鹏. 错列角度对双圆柱涡激振动影响的数值模拟研究[J]. 力学学报, 2018, 50(2): 244-253 https://doi.org/10.6052/0459-1879-17-345 DuanSongchang, Zhao Xizeng, YeZhouteng, WangKaipeng. NUMERICAL STUDY OF STAGGERED ANGLE ON THE VORTEX-INDUCED VIBRATION OF TWO CYLINDERS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 244-253 https://doi.org/10.6052/0459-1879-17-345
引言
涡激振动问题发生在很多实际工程中,比如海洋立管、海底管线、高耸建筑等在受到风或海流的作用时,会因涡旋脱落而导致结构振动. 和静止圆柱绕流不同,当涡旋脱落频率接近柱体自振频率时,柱体会发生“锁定” 现象[1]. “锁定”现象的发生会使结构物发生疲劳破坏,进而缩短结构物的寿命. 双圆柱涡激振动作为多柱体涡激振动的基础,除柱体和流体本身的特性外,柱体布置方式也会影响柱体的振动响应和流场状态. 如图1所示,仅在双圆柱涡激振动中就存在3种布置方式:串列( )、并列 ( )和错列 ( ). 其中, 是两柱体中心连线和来流方向之间的夹角(锐角),下文中将其简称为“错列角度”. 显示原图|下载原图ZIP|生成PPT 图1双柱体布置示意图 -->Fig. 1Sketch of layout for two circular cylinders -->
图4和图5分别是折合速度 不同错列角度上下游圆柱的阻力系数均值和升力系数均方根随错列角度的变化情况. 其中,(a)、(b)、(c)分别对应上文中的3个区域,“UC”代表上游圆柱,“DC”代表下游圆柱. 从图4和图5可看出,除了过渡区的折合速度 ( 和9.0)外,其他折合速度下柱体升阻力随错列角度的变化规律在同一区域内具有相似性. 对于 ,如图4(a)所示, 时下游圆柱阻力几乎为零,说明上游圆柱尾流对下游圆柱的“屏蔽”作用[25]较强,即下游圆柱处在上游圆柱的尾流中,来流速度较小导致下游圆柱阻力较小. 显示原图|下载原图ZIP|生成PPT 图4折合速度上下游圆柱的阻力系数均值随错列角度的变化情况 -->Fig. 4Mean value of drag coefficient versus stagger angle for different reduced velocities -->
显示原图|下载原图ZIP|生成PPT 图5折合速度上下游圆柱的升力系数均方根随错列角度的变化情况 -->Fig. 5Root mean square lift coefficients versus stagger angle for different reduced velocities -->
为便于阐述上文中3种情况下上下游柱体的振动响应、位移响应随错列角度变化的情况,本节选取 , 5.0和13.0的工况分别作为上述3种情况的特征工况进行分析. 图6给出了3个特征工况下两柱体横流向位移均方根(图6(a))、顺流向位移均值(图6(b))以及顺流向位移均方根(图6(c))随错列角度的变化情况. 其中,横、顺流向位移均方根大小分别反映了柱体在横流向和顺流向振动的剧烈程度,顺流向位移均值大小反映了柱体在顺流向上的平均偏移程度. 如图6(a) 和图6(b)所示, 时,上下游圆柱的横流向位移均方根在 时最小,随错列角度的增大两柱体在横流向的振动程度都在增大,在 附近取得最大值,和柱体升力大小变化规律一致. 由于上游圆柱“屏蔽”作用的影响,下游圆柱的顺流向位移均值在 时几乎为零. 随错列角度的增大,下游圆柱的顺流向偏移程度逐渐变大,并逐渐接近上游圆柱,总体上和柱体阻力大小变化规律一致. 显示原图|下载原图ZIP|生成PPT 图6不同折合速度上下游柱体位移响应随错列角度的变化情况 -->Fig. 6Displacement response of both cylinders with stagger angle under different reduced velocity -->
显示原图|下载原图ZIP|生成PPT 图7不同折合速度上下游圆柱涡旋脱落主导频率随错列角度的变化情况 -->Fig. 7The main vortex shedding frequency of both cylinders versus stagger angle under different reduced velocities -->
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