力学学报  2018 , 50 (2): 233-243 https://doi.org/10.6052/0459-1879-17-346

流体力学

高雷诺数下多柱绕流特性研究1)

李聪洲, 张新曙2), 胡晓峰, 李巍, 尤云祥

上海交通大学海洋工程国家重点实验室, 上海 200240)

THE STUDY OF FLOW PAST MULTIPLE CYLINDERS AT HIGH REYNOLDS NUMBERS1)

Li Congzhou, Zhang Xinshu2), Hu Xiaofeng, Li Wei, You Yunxiang

(State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China)

中图分类号:  O35

文献标识码:  A

收稿日期: 2017-10-21

接受日期:  2017-10-21

网络出版日期:  2018-03-20

版权声明:  2018 《力学学报》编辑部 《力学学报》编辑部 所有

作者简介:

作者简介:2) 张新曙,教授,主要研究方向:船舶海洋流体力学. E-mail:xinshuz@sjtu.edu.cn

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摘要

采用改进的延迟分离涡方法数值模拟了高雷诺数下的柱体绕流,包括单圆柱绕流、单方柱绕流、串列双圆柱绕流和串列双方柱绕流,研究了不同雷诺数下圆柱绕流与方柱绕流的水动力特性. 计算结果与实验数据及其他文献的数值计算结果吻合良好,研究表明,单方柱绕流在2.0×103<Re<1.0×107范围内未出现类似于单圆柱绕流的阻力危机现象,其平均阻力系数Cd¯、升力系数均方根C'l及斯特劳哈尔数St维持在一定范围内波动. 串列双圆柱绕流与串列双方柱绕流中,均选取L/D=2.0, 2.5, 3.0, 3.5和4.0这五中间距比进行计算. 串列双圆柱绕流中,当Re=2.2×104时,在3.0<L/D<3.5内存在一临界间距比(Lc/D)使得Lc/D前后上下游圆柱的升阻力系数发生跳跃性变化,且当L/D<Lc/D时,下游圆柱的阻力系数为负数. 而当Re=3.0×106时,则不存在临界间距比,且下游圆柱的阻力系数始终为正数. 串列双方柱绕流在Re=1.6×104Re=1.0×106两种工况下的临界间距比分别处于3.0<L/D<3.53.5<L/D<4.0区间内,且当L/D<Lc/D时,两个雷诺数下的下游方柱阻力系数均为负数.

关键词: 圆柱绕流 ; 方柱绕流 ; 改进的延迟分离涡模拟方法 ; 高雷诺数

Abstract

Flow past circular cylinders and square cylinders at high Reynolds numbers are simulated by improved delayed detached-eddy simulation (IDDES), including a circular cylinder, a square cylinder, two tandem circular cylinders and two tandem square cylinders. The mean drag coefficient, the RMS values of lift coefficient and the Strouhal number are computed for various Reynolds numbers, which show a good agreement with previous experimental and numerical simulation data. It is found that the effect of Reynolds number on the global quantities for square cylinders is not much in this range of Reynolds numbers, which is different for circular cylinders. There is no drag crisis phenomenon for flow past a square cylinder at 2.0×103<Re<1.0×107. The Strouhal number is Reynolds-independent for Re>2.0×103, and the Reynolds-independent is also observed for the mean drag coefficient and the RMS lift coefficient. Simulation for two tandem circular cylinders is performed at Reynolds numbers of 2.2×104 and 3.0×106 for five different spacing L to diameter D ratios: L/D=2.0, 2.5, 3.0, 3.5 and 4.0. At the critical spacing (Lc/D) there is found a distinct step-like jump of mean drag coefficient and RMS lift coefficient of the subcritical Reynolds number of 2.2×104, and the mean drag coefficient of the downstream circular cylinder is negative for L/D<Lc/D. However, the mean drag coefficient and the RMS lift coefficient are seen to be slightly affected by spacing for Re=3.0×106, and the mean drag coefficient of the downstream circular cylinder is always positive. Flow past two tandem square cylinders is considered at Reynolds numbers of 1.6×104 and Re=1.0×106. The abrupt change in mean drag coefficient and RMS lift coefficient at the critical spacing is clearly seen on both upstream and downstream square cylinders for both Reynolds numbers. When L/D<Lc/D, the mean drag coefficient of the downstream cylinder is negative for both Reynolds numbers.

Keywords: circular cylinders ; square cylinders ; IDDES ; high Reynolds number

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李聪洲, 张新曙, 胡晓峰, 李巍, 尤云祥. 高雷诺数下多柱绕流特性研究1)[J]. 力学学报, 2018, 50(2): 233-243 https://doi.org/10.6052/0459-1879-17-346

Li Congzhou, Zhang Xinshu, Hu Xiaofeng, Li Wei, You Yunxiang. THE STUDY OF FLOW PAST MULTIPLE CYLINDERS AT HIGH REYNOLDS NUMBERS1)[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 233-243 https://doi.org/10.6052/0459-1879-17-346

引言

柱体结构(包括圆柱、方柱等)广泛应用于海洋工程领域,比如Spar平台、张力腿平台和半潜式平台等[1]. 当一定速度的流体流经柱体结构物时,由于黏性的存在,会发生边界层分离,形成漩涡,周期性的漩涡脱落导致脉动压力,进而诱发结构物大幅度振动,这可能会破坏海洋平台系泊和立管系统[2]. 柱体间的耦合干扰导致多柱式平台表现出与单柱式平台不同的涡激运动特性[3]. 因此,柱体绕流的研究具有重要的应用价值.

目前,柱体绕流研究方法主要包括实验和计算流体力学(computational fluid dynamics, CFD)数值模拟. 国内外学者已对柱体绕流做了大量实验研究[4,5,6,7]. 相比于实验研究,CFD数值模拟方法成本低、速度快. 近年来,随着计算机技术的不断发展,CFD数值模拟方法更加受到重视. Travin等[8]运用分离涡(detached-eddy simulation, DES)方法数值模拟了不同雷诺数下单圆柱绕流的情况,验证了DES方法数值模拟圆柱绕流的可行性. 及春宁等[9]采用浸入边界法研究了细长柔性圆柱在线性剪切流下的涡激振动特性. 吴应湘等[10]通过模型实验和数值模拟方法,研究了带有涡激振动抑制罩的圆柱体的水动力特性. Sohankar [11]采用大涡模拟(large eddy simulation,LES)方法研究了 1.0×103<Re<5.0×106时单方柱绕流,发现当 Re>2.0×104时,水动力系数和流态随雷诺数变化不大,方柱的分离点始终在方柱前方的直角处,不随雷诺数的变化而变化. 与单柱绕流不同,双柱绕流由于柱体间的相互干扰,双柱绕流的水动力特性要更加复杂. Kitagawa等[12]运用LES方法对 Re=2.2×104情况下的串列双圆柱绕流进行数值模拟,结果表明当两圆柱中心间距( L)与直径( D)的比值小于3.25时,只有下游圆柱有涡脱落现象,而当 L/D>3.25时,上下游圆柱均有涡脱落现象,即临界间距比 Lc/D=3.25,当 L/D>Lc/D时,上下游圆柱的平均阻力系数和升力系数均会发生跳跃性变化. 吕启兵等[13]利用RNG k-- ε模型对 Re=2.2×104下串列双方柱进行二维数值模拟,研究了不同方柱间距比时上下游方柱的水动力特性,发现串列双方柱下游方柱阻力均小于上游方柱阻力,屏蔽效应明显.

然而,在上述研究中,针对高雷诺数下的串列双圆柱绕流和串列双方柱绕流的研究均较少, 而在实际海洋工程应用中,雷诺数往往在105以上. 基于此,本文采用改进的延迟分离涡(improve delayed detached-eddy simulation, IDDES)方法数值模拟 2.0×103<Re<3.0×106下的单圆柱绕流、单方柱绕流、串列双圆柱绕流及串列双方柱绕流,研究了不同雷诺数下圆柱绕流与方柱绕流的水动力特性.

1 数值模型

1.1 改进的延迟分离涡(IDDES)方法

分离涡[14]方法(也称为DES97方法)是一种结合了雷诺平均方法(Reynolds-averaged Navier-Stokes, RANS)与LES方法的混合方法,已被证实是一种有效的数值方法. DES方法在近壁面使用RANS方法进行模拟,而在远离壁面的分离区使用LES方法模拟来捕捉大尺度分离流动.

DES97方法对长度尺度 lDES的定义如下 lDES=mind,CdesΔ(1) 其中, d为离壁面的最短距离, Δ=maxΔx,Δy,Δz, Δx, ΔyΔz分别是3个方向上的局部网格尺寸, Cdes为0.65.

从式(1)可以看出DES97方法中,RANS到LES的转换完全取决于网格尺度大小. 在某些情况下会导致RANS提前转换到LES,出现模型应力耗散(modeled stress depletion, MSD)现象,从而导致“网格诱导分离(grid-induced separation, GID)”问题. 同时DES97方法还存在“对数层不匹配(log-layer mismatch, LLM)”问题.

Spalart等[15]提出延迟分离涡(delayed detached-eddy simulation, DDES)方法来解决GID问题. DDES方法对长度尺度 lDDES的定义做了修改,具体如下 lDDES=d-fdmax0,d-CdesΔ(2) 式中, fd为延迟过渡函数, fd能避免LES在边界层内进行求解,从而解决了GID问题.

IDDES方法则是将DDES方法与WMLES (wall-modelling LES)方法相结合,从而解决了LLM问题,同时提高了近壁面湍流的求解质量[16].

1.2 计算域及网格划分

单圆柱计算域及边界条件的设定如图1所示,入口距离圆柱中心为 10D( D为圆柱直径),出口距离圆柱中心为 20D,左右两边均距离圆柱中心 10D,圆柱的展向长度为 2D,将入口边界设为速度入口,出口边界为压力出口,左右两边也设为速度入口,上下面为对称面边界条件,圆柱表面为无滑移壁面边界条件. 单方柱计算域及边界条件与单圆柱类似,计算域也为 30D×20D×2D,此时 D为方柱边长.

图1   单圆柱计算域及边界条件

Fig. 1   Computational domain and boundary conditions for a circular cylinder

串列双圆柱计算域及边界条件的设定如图2所示,入口距离上游圆柱中心为10 D,两圆柱相距 L,出口距离下游圆柱中心为20 D,左右两边均距离圆柱中心10 D,圆柱的展向长度为2 D. 间距比 L/D表示两圆柱中心距离 L与圆柱直径 D的比值,本文计算的 L/D包括2.0, 2.5, 3.0, 3.5和4.0五种工况. 同理,串列双方柱计算域和边界条件与双圆柱类似,计算域也为 30D×20D+L×2D,此时 D为方柱边长, L为两方柱中心距离.

图2   双圆柱计算域及边界条件

Fig. 2   Computational domain and boundary conditions for two tandem circular cylinders

双圆柱及双方柱网格划分如图3图4所示(以 L=3D为例),为了保证计算精度, y+值取小于1.0,边界层网格增长率为1.15,单圆柱网格以及单方柱网格同理.

图3   双圆柱网格划分示意图

Fig. 3   Grid distribution of two tandem circular cylinders

图4   双方柱网格划分示意图

Fig. 4   Grid distribution of two tandem square cylinders

2 计算结果与分析

2.1 网格收敛性分析及数值模型验证

网格的疏密程度不仅会影响计算精度,还会影响计算效率. 网格收敛性分析以 Re=3.0×106的圆柱绕流工况为例,选取3套由疏到密的网格进行计算,无量纲时间步长( Δt=tU/D, t为时间步长, U为来流速度, D为圆柱直径)取0.02,计算结果如表1所示.

表1给出了3套网格下计算的平均阻力系数 Cd¯、升力系数均方根 C'l和斯特劳哈尔数 St与实验结果和其他文献CFD计算结果的对比情况. 3套网格计算的 Cd¯C'l与实验结果吻合较好, St要比实验值大,但与其他文献的CFD计算结果较吻合. 对比3套网格的结果可以看出,标准网格G2与精细网格G3的结果很接近,而粗糙网格G1的结果则与其他两套网格有较大差距,综合计算成本和效率,本文选取标准网格来进行数值模拟.

表1   网格收敛性分析

Table 1   Sensitivity of the results to different grids

CaseGridsCd¯C'lSt
G1543 5000.4720.0670.262
G2797 3000.4840.0990.307
G31 160 7000.4860.1020.309
CFD [8,17-18]0.457~0.5350.077~0.1000.305~0.330
EXP [4,19]0.460~0.5400.060~0.1000.210~0.214

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针对圆柱绕流工况,本文所模拟的雷诺数区域包括亚临界雷诺数区域和超临界雷诺数区域,前面网格收敛性分析已经对 Re=3.0×106(超临界雷诺数区域)进行验证,因此针对圆柱绕流再选取 Re=2.2×104(亚临界雷诺数区域)进行验证,其中 Re=2.2×104时,边界层为层流分离,而 Re=3.0×106时,边界层为湍流分离. 数值模拟结果与实验以及其他文献的CFD结果比较如表2所示.

表2   Re=2.2×104时单圆柱绕流计算结果比较

Table 2   Comparison of results of a circular cylinder (Re=2.2×104)

Cd¯C'lSt
Present1.1890.4960.201
EXP<sup> [4,20-22]</sup>1.162~1.1990.314~0.4680.195~0.205

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表2中可以看出本文计算的平均阻力系数 Cd¯和斯特劳哈尔数 St与实验结果吻合较好,升力系数均方根 C'l比实验结果略大.

对于单方柱绕流选取 Re=2.2×104典型工况,计算结果与实验结果及其他文献CFD结果的比较如表3所示.

3 Re=2.2×104时单方柱绕流计算结果比较

   

Table 3   Comparison of results of a square cylinder (Re=2.2×104)

Cd¯C'lSt
Present2.2801.4590.131
CFD [17,23-24]2.180~2.3201.540~1.7100.132
EXP [6,25-26]2.100~2.2101.2100.130

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表3可以看出,本文计算的 Cd¯C'l比实验结果略大,但与其他文献的CFD结果比较接近,本文计算的 St则与实验结果以及其他文献的CFD结果吻合良好.

总体上讲,上述结果很好地验证了本文所采用的IDDES方法在模拟圆柱绕流及方柱绕流的有效性和准确性.

2.2 单圆柱绕流及单方柱绕流

单圆柱绕流的平均阻力系数 Cd¯、升力系数均方根 C'l及斯特劳哈尔数 St随雷诺数变化的情况如图5所示. 从图5(a)中可以看出本文的计算结果与实验结果吻合良好,随着雷诺数的增大,单圆柱绕流的 Cd¯先维持平稳而后出现迅速减小(即阻力危机现象),最后又缓慢增大. 从图5(b)可以看出本文计算的 C'l有的点与实验值吻合良好,部分计算值则相对

图5   不同雷诺数下单圆柱绕流的平均阻力系数、升力系数均方根和斯特劳哈尔数

Fig. 5   Mean drag coefficient, RMS lift coefficient and Strouhal number of a circular cylinder versus Re

图5(续)   不同雷诺数下单圆柱绕流的平均阻力系数、升力系数均方根和斯特劳哈尔数(续)

Fig. 5(continued)    Mean drag coefficient, RMS lift coefficient and Strouhal number of a circular cylinder versus Re

实验值偏大,但与文献[28]的计算结果接近, C'l随雷诺数的增大呈现先增大后减小最后维持平稳的变化趋势. 从图5(c)中可以看出,本文计算的 St3.0×105<Re<1.0×106区间内与实验值相差较大. 其原因是,在此雷诺数区域内,圆柱绕流的边界层从层流分离转化为湍流分离,流动较为复杂,涡脱表现为不规则,因此在此区域内计算结果不太理想,但与其他CFD结果较为吻合.

图6为单方柱绕流的平均阻力系数 Cd¯、升力系数均方根 C'l及斯特劳哈尔数 St随雷诺数的变化情况. 从图6(a)可以看出,本文计算的 C'l¯与Sohankar用LES计算的结果相符,但都比实验值略大,误差在10%左右. 从图6(b)看出本文计算的 C'l均略小于文献[11]的计算结果,更接近于实验数据,随雷诺数的增大, C'l呈现出先保持平稳而后下降最后再增大的变化趋势,但总体变化幅度不大. 从图6(c)可以看出本文计算的 St与实验数据吻合良好,随雷诺数的增大, St数无明显变化,保持在0.12 ~0.13范围内.

图6   不同雷诺数下单放柱绕流的平均阻力系数、升力系数均方根和斯特劳哈尔数

Fig. 6   Mean drag coefficient, RMS lift coefficient and Strouhal number of a square cylinder versus Re

2.0×103<Re<1.0×107区间内,单方柱绕流的系数 Cd¯, C'lSt不随雷诺数变化而发生大幅度变化,这与单圆柱绕流情况区别明显,未出现类似于单圆柱绕流的阻力危机现象,Sohankar [11]用LES方法数值模拟了较高雷诺数(最高达106量级)下的方柱绕流,其研究同样表明方柱绕流未出现阻力危机现象. 图7Re=2.2×104Re=4.0×105时,单圆柱绕流的涡量图. 从图7可以看出, Re=4.0×105时圆柱绕流的分离点后移,尾涡区变窄,即压差阻力减小,从而导致总阻力减小. 图8Re=2.2×104Re=5.0×105时,单方柱绕流的涡量图. 从图8可以看出,方柱绕流的分离点固定,压差阻力无明显变化,因此单方柱绕流未出现阻力危机现象.

图7   不同雷诺数下,单圆柱绕流的瞬时涡量图

Fig. 7   Instantaneous vorticity distributions for flow past a circular cylinder at different Reynolds numbers

图8   不同雷诺数下,单方柱绕流的瞬时涡量图

Fig. 8   Instantaneous vorticity distributions for flow past a square circular cylinder at different Reynolds numbers

2.3 串列双圆柱绕流及串列双方柱绕流

图9为雷诺数 Re=2.2×104时,不同间距比( L/D)下串列双圆柱绕流的平均阻力系数 Cd¯和升力系数均方根 C'l,其中 Cyl1表示上游圆柱, Cyl2表示下游圆柱. 本文计算的上游圆柱的 Cd¯和实验结果及其他文献的CFD计算结果吻合较好,下游圆柱在间距比小时本文的计算结果比实验值要大,但与Kitagawa的计算结果接近,在较大间距比下本文的计算结果则与实验值及Kitagawa的计算结果吻合良好. 从图9(b)中可以看出,本文计算的 C'l除下游圆柱在间距比较大时比实验值偏大,其他工况均与实验值较为吻合. Re=2.2×104时,串列双圆柱绕流在 3.0<L/D<3.5区间内存在一临界间距比( Lc/D)使得串列双圆柱绕流的 Cd¯C'l在临界间距比前后均发生跳跃性变化. 如图10所示,当 L=2.5D(L/D<Lc/D)时,前柱后方还没有单独涡脱落,而当 L=4.0D(L/D>Lc/D)时,前柱后方已经有单独的涡脱落现象,正是由于这种流态的变化才使得 Cd¯C'l发生跳跃性变化. 且当 L/D<Lc/D时,下游圆柱的阻力系数为负数,当 L/D>Lc/D时,下游圆柱的阻力系数才为正数.

图9   Re=2.2×104时,不同间距比下串列双圆绕流的${\rm{\bar C}}$d和C'l

Fig. 9   Mean drag coefficient and RMS lift coefficient of upstream and downstream circular cylinders for different spacing to diameter ratios (L/D) at Re=2.2×104

图9(续)   Re=2.2×104时,不同间距比下串列双圆绕流的${\rm{\bar C}}$d和C'l(续)

Fig. 9(continued)    Mean drag coefficient and RMS lift coefficient of upstream and downstream circular cylinders for different spacing to diameter ratios (L/D) at Re=2.2×104(continued)

图10   Re=2.2×104时,圆柱中心高度处不同间距比下的瞬时涡量图

Fig. 10   Instantaneous vorticity distributions of circular cylinders at middle of cylinder span in the case of different spacing to diameter ratios at Re=2.2×104

图11Re=2.2×104Re=3.0×106时,串列双圆柱绕流的 Cd¯C'l随间距比的变化情况,其中 Re=3.0×106为湍流分离工况, Re=2.2×104为层流分离工况. 从图中可以看出,当雷诺数处于超临界雷诺数区域时( Re=3.0×106),串列双圆柱绕流不再存在临界间距比,随着间距比的增大,下游圆柱的阻力系数和升力系数均缓慢增大,而上游圆柱的阻力系数和升力系数则趋于稳定,均无出现明显的跳跃性变化,而且下游圆柱的阻力系数始终为正数. 对比图10(b)与图12(b)可以看出,对于 Re=3.0×106的工况,当 L/D=4.0时,虽然上游圆柱后方有单独涡脱落现象,但是漩涡形成的位置离上游圆柱较远,对上游圆柱的影响较小,因此其水动力系数没有出现明显跳跃性变化现象.

图11   不同雷诺数时,不同间距比下串列双圆柱绕流的${\rm{\bar C}}$d和C'l

Fig.11   Mean drag coefficient and RMS lift coefficient of upstream and downstream circular cylinders for different spacing to diameter ratios (L/D) at different Re

图12   Re=3.0×106时,圆柱中心高度处不同间距比下的瞬时涡量图

Fig. 12   Instantaneous vorticity distributions of circular cylinders at middle of cylinder span in the case of different spacing to diameter ratios at Re=3.0×106

图13为雷诺数 Re=1.6×104时,不同间距比(L/D)下串列双方柱绕流的 Cd¯C'l,同理 Cyl1表示上游方柱, Cyl2表示下游方柱. 间距比较小时,本文计算的平均阻力系数 Cd¯与实验结果及他人计算结果吻合良好,在间距比较大时,本文计算的 Cd¯比实验值略大. 从图13(b)中可以看出,本文计算的上游方柱 C'l与实验值很接近,下游方柱的 C'l要比实验值偏大,但总体误差不大. Re=1.6×104时,串列双方柱绕流在 3.0<L/D<3.5区间内与层流分离下的串列双圆柱绕流类似,存在一临界间距比( Lc/D)使得串列双方柱绕流的 Cd¯C'l均发生跳跃性变化. 同理,如图14所示,上下游方柱水动力系数发生跳跃性变化也是由于流态发生变化而导致的. 只有在 L/D>Lc/D时,上游方柱后方才有单独的涡脱落. 且当 L/D<Lc/D时,下游方柱的阻力系数为负数,而当 L/D>Lc/D时,下游方柱的阻力系数变为正数.

图13   Re=1.6×104时,不同间距比下串列双方柱绕流的${\rm{\bar C}}$d和C'l

Fig. 13   Mean drag coefficient and RMS lift coefficient of upstream and downstream square cylinders for different spacing to diameter ratios at Re=1.6×104

图14   Re=1.6×104时,方柱中心高度处不同间距比下的瞬时涡量图

Fig. 14   Instantaneous vorticity distributions of square cylinders at middle of cylinder span in the case of different spacing to diameter ratios at Re=1.6×104

图14(续)   Re=1.6×104时,方柱中心高度处不同间距比下的瞬时涡量图(续)

Fig. 14(continued)    Instantaneous vorticity distributions of square cylinders at middle of cylinder span in the case of different spacing to diameter ratios at Re=1.6×104(continued)

图15Re=1.6×104Re=1.0×106时,串列双方柱绕流的${\rm{\bar C}}$d和C'l随间距比的变化情况. 从图中可以看出,与串列双圆柱绕流情况不同,串列双方柱绕流在两种雷诺数下均存在一临界间距比Lc/D,当 L/D>Lc/D时,上下游方柱的阻力系数和升力系数都有跳跃性变大的现象, Re=1.6×104Lc/D处于 3.0<L/D<3.5区间内,而 Re=1.0×106时, Lc/D则处于 3.5<L/D<4.0区间内. 如图16(b)所示,上游方柱后方形成的漩涡的位置与图14(b)类似,均很靠近上游方柱,因此 Re=1.0×106时也有临界间距比存在. 且当 L/D<Lc/D时,两种雷诺数下的下游方柱阻力系数均为负数.

图15   不同雷诺数时,不同间距比下串列双方柱绕流的${\rm{\bar C}}$d和C'l

Fig. 15   Mean drag coefficient and RMS lift coefficient of upstream and downstream square cylinders for different spacing to diameter ratios at different Re

图16   Re=1.0×106时,方柱中心高度处不同间距比下的瞬时涡量图

Fig. 16   Instantaneous vorticity distributions of square cylinders at middle of cylinder span in the case of different spacing to diameter ratios at Re=1.0×106

3 结论

本文采用改进的延迟分离涡方法数值模拟了较高下的圆柱绕流及方柱绕流,研究了不同雷诺数下圆柱绕流与方柱绕流的水动力特性,本文的计算结果与已有的实验数据以及其他文献的CFD计算结果吻合良好,验证了本文所采用的IDDES方法在数值模拟柱体绕流时的准确性和有效性. 通过结果的对比分析,可以得到以下结论:

(1)在 2.0×103<Re<1.0×107区间内,单方柱绕流未出现类似于单圆柱绕流的阻力危机现象,单方柱绕流的 Cd¯, C'lSt均趋于稳定,维持在一定范围内波动,这与分离点的位置有关,方柱绕流分离点固定,而圆柱绕流的分离点会随雷诺数的变化而变化.

(2)串列双圆柱绕流中,当 Re=2.2×104时,存在一临界间距比( 3.0<Lc/D<3.5)使得 Lc/D前后上下游圆柱的升阻力系数发生跳跃性变化. 而当 Re=3.0×106时,串列双圆柱绕流不再存在临界间距比,随着间距比的增大,下游圆柱的阻力系数和升力系数均缓慢增大,且下游圆柱的阻力系数始终为正数,上游圆柱的阻力系数和升力系数则趋于稳定,均无明显的跳跃性变化.

(3)串列双方柱绕流中,在 Re=1.6×104Re=1.0×106下均存在一临界间距比,当 L/D>Lc/D时,上下游方柱的升阻力系数都有跳跃性变大的现象,但是两种雷诺数下的 Lc/D值不同.

The authors have declared that no competing interests exist.


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