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摘要: 热湍流 (浮力驱动湍流) 作为一种典型的湍流现象, 广泛存在于自然界和工程应用中. Rayleigh-Bénard (RB) 湍流是从众多自然现象中抽象出来研究热湍流的经典模型, RB湍流的典型特征是系统中存在大尺度环流和羽流等不同尺度的湍流结构, 这些结构通过作用于边界层, 影响RB湍流的输运效率. 因此, 明确不同尺度湍流结构的生成、演化和作用机理, 对理解RB湍流的输运特性至关重要, 也是通过控制湍流结构调控输运效率的科学基础. 本文重点从湍流结构的时空演化规律、输运特性、湍流调控和热湍流在其他领域的拓展四个方面评述近十年来RB湍流研究所取得的新进展, 并对今后的研究方向做出展望.Abstract: Turbulent convection is ubiquitous in nature and industry. Turbulent Rayleigh-Bénard convection (RBC) is a model system for studying various turbulent convection phenomena. One of the characteristics of turbulent RBC is the formation of coherent structures of different scales, i.e., large-scale circulation and thermal plumes. These structures interact with the thermal and viscous boundary layers. As a result, they inevitably affect the transport properties of the system. Thus, understanding the formation, evolution, and interaction of coherent structures plays a vital role in understanding the transport properties in turbulent convection. This review summarizes progress in the spatial and temporal evolution of coherent structures and their effects on heat transport in the past decade. Special attention was paid to the progress in controlling turbulent convection and its extension to nontraditional cases, such as turbulent convection with rotation, viscoelastic turbulent convection, multiphase turbulent convection, inclined convection, and horizontal convection. A short outlook into future research directions will be given.
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图 1 Rayleigh-Bénard (RB) 湍流系统示意图 (周全和夏克青 2012)
图 2 大尺环流反转过程. (a)~(c) 和 (e)~(g) 分别为直接数值模拟 (Ra = 108, Pr = 4.3) 和通过PIV实验测量 (Ra = 3.8 × 108, Pr = 4.3) 得到的大尺度环流反转过程, (d) 和 (h)分别为直接数值模拟和通过PIV实验测量得到的大尺度环流角动量随时间的变化曲线 (Sugiyama et al. 2010)
图 3 阴影法拍摄的圆盘对流腔体流场图像 (Ra = 6.2 × 109, Pr = 4.4). (a)大尺度环流长时间处于的稳定状态, (b)大尺度环流短暂出现的爆发状态 (Wang, Lai et al. 2018)
图 4 (a)实验测得的准二维矩形对流腔体中大尺度环流反转频率f随Ra数的变化关系 (为了清晰显示, Pr = 5.7和Pr = 4.3的数据分别上移了10倍和100倍), (b)正常单环结构 (Ra = 7.94 × 108, Pr = 7.0), (c)反常单环结构(Ra = 1.16 × 108, Pr = 7.0) (Chen et al., 2019)
图 5 PIV测量得到的准二维矩形对流腔体中有角涡和无角涡的流场.(a)有角涡的流场 (Ra = 7.94 × 108, Pr = 7.0), (b)无角涡的流场 (Ra = 7.56 ×108, Pr = 7.0) (Chen et al. 2020)
图 6 (a)直接数值模拟所得的平均温度剖面 (空心圆) 与理论值 (实线) 的比较图, 虚线为PB边界层理论的预测值, (b)大尺度环流方向的平均速度剖面比较图, 图例与(a)一致 (Ching et al. 2019)
图 7 剪切区和羽流发射区的温度涨落剖面. (a)阴影法观测得到的大尺度流动结构示意图, 其中A为大尺度环流主导的强剪切区, B 为羽流主导的发射区, (b)双对数坐标下的羽流区与剪切区温度涨落剖面, (c)半对数坐标下的羽流区与剪切区温度涨落剖面 (He & Xia 2019)
图 8 单环与双环大尺度环流结构及输运效率与大尺度环流结构的关系. PIV测得的 (a)单环大尺度环流, (b)双环大尺度环流, (c) 双环大尺度环流消失后的单环大尺度环流, (d) Nu随着大尺度湍流结构流态的变化规律, 其中|δφ|top,bot的绝对值代表不同高度大尺度环流的角向方位, 当|δφ|top,bot=0时对应于单环大尺度环流, 当|δφ|top,bot=180时对应于双环大尺度环流 (Xi & Xia 2008)
图 9 空间约束对热湍流输运特性和湍流结构的影响. (a)不同Ra时归一化的Nu随着方腔对流腔体厚度方向宽高比Γ的变化规律, 这里Nu (Γ = 0.6)对应宽高比为Γ = 0.6时RB系统的Nu, (b) Γ = 1/2对流腔体中的瞬时温度场(颜色)和速度场(箭头), (c)Γ = 1/8对流腔体中的瞬时温度场(颜色)和速度场(箭头) (Huang et al. 2013)
图 10 实验测量得到的圆环对流腔体中大尺度湍流结构. (a)时间平均后的四极矩湍流态空间结构, 红色代表顺时针流动, 蓝色代表逆时针流动 (b) 时间平均后的偶极矩湍流态空间结构, (c) Nu随着Ra数的变化关系, 插入图为Nu的涨落σNu随着Ra数的变化关系 (Xie et al. 2018)
图 11 实验获得的粗糙壁面热湍流不同区间热输运特性, 此处粗糙元宽高比λ = 4.0. (a) Nu和Ra的标度律关系, 图中实线为拟合获得的标度律. (b) Nu Ra标度律指数α (Nu ~ Raα) 和Re与Ra标度律指数β (Re ~ Raβ) 随着粗糙元宽高比λ的变化关系 (Xie & Xia 2017)
图 12 引入振动调制的热湍流不同振动频率ω时的瞬时流动结构. (a) ω = 0, (b) ω = 1400, (c)归一化的Nu随着振动频率ω的变化关系, 这里Nu(0)对应于ω = 0时RB系统的Nu (Wang, Zhou et al. 2020)
图 13 地转区间不同
$ Ra/R{a}_{c} $ 条件下的温度脉动等值面. (a) 涡胞区间($ Ra/R{a}_{c}=1.2,Pr=7 $ ), (b)泰勒涡区间($ Ra/R{a}_{c}=3.5,Pr=7 $ ), (c)羽流区间 ($ Ra/R{a}_{c}=8.0,Pr=7 $ ), (d) 地转湍流区间 ($ Ra/R{a}_{c}= $ $ 10.3,Pr=1 $ ), 图中的直接数值模拟上下边界均为无滑移条件, 旋转控制参数为$ Ek={10}^{-7} $ (Plumley et al. 2016)
图 14 归一化的泰勒涡均方位移随着归一化的时间的变化曲线 (Chong et al. 2020)
图 15 旋转热湍流不同宽高比Γ 的圆柱对流腔体的Nu随Ra/Rac的变化关系, 插图为标度律指数γ 随着Γ 的变化关系. 图中Ek = 1.85 × 10−6, Pr = 4.38 (Lu et. al 2021)
图 16 离心力效应对热湍流输运特性和湍流结构的影响. (a) 归一化的努赛尔数Nur = Nu/Nu(1/Ro = 1) 随着1/Ro的变化曲线, 三角形和五角星分别为为无偏心和偏心率d/R = 5.15时的Nur, 插图为实验装置示意图, (b)和(c)分别为PIV测量得到的无偏心及偏心率为
$ d/R=3.5 $ 时,$ 1/Ro\approx 7.6 $ 对应的时均速度场垂直剖面图, 其颜色代表以cm/s为单位的垂直速度大小 (Hu et al. 2021)
图 17 混合边界RB湍流的Nu. (a)长方体对流腔体, 图例表示导热板和绝热板的分布形式, 其中C表示导热板, A表示绝热板, (b)圆柱对流腔体, 图例的
$ \xi $ 及分数表示绝热板占据的面积比, 中央绝热和边缘绝热分别表示绝热板置于冷板中心和边缘 (Wang et al 2017)
图 18 混合率 (mixing rate) κρ随无量纲边界层厚度δ/D的变化规律; 插图为混合效率Rf随无量纲边界层厚度的变化规律 (Wang, Huang & Xia 2018)
图 19 对流腔体中心区域时间平均的局域热流密度Jz随高聚物浓度c的变化曲线. (a)聚丙烯酰胺 (PAM) , (b) 聚氧化乙烯 (PEO) (Xie et al. 2015)
图 20 水汽输运努塞尔数Nue和热输运努塞尔数NuT随格拉晓夫数Gr变化曲线 (Zhang et al. 2019)
图 21 (a)含水平浮力热对流系统中垂直方向努塞尔数Nuv随Ra以及浮力比例Λ的变化规律, (b)该系统中垂向努塞尔数Nuv随Pr以及浮力比例Λ的变化规律, 图中的曲面表示新理论模型的预测值 (Zhang et al. 2021)
图 22 热湍流中央区域局部能量耗散率εu,c与局部努塞尔数Nuc的平衡关系实验验证.倒三角为直接测量得到的中央区域的局部努塞尔数Nuc, 其他图标为通过式9计算得到的Nuc. 两种方法得到的Nuc互相重叠在一起, 验证了εu,c与Nuc的平衡关系 (Ni et al. 2011)
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