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摘要: 理解和预测绕椭球的流动对指导飞行器和潜艇等交通工具的设计具有很强的工程意义. 近年来, 针对椭球绕流开展了大量的实验和数值模拟研究. 对有攻角下椭球绕流分离的定性描述和定量研究, 促进了对三维分离的辨识和拓扑研究. 文章对流场特性进行了分析, 介绍了分离对气动力、噪声、尾迹的影响, 以及实验条件对流动的影响. 上述定常流动与非定常机动过程之间存在明显差异, 非定常机动过程不能作为定常或准定常问题处理, 在机动过程中, 分离出现明显延迟, 气动力出现明显变化. 随后介绍了数值模拟在求解绕椭球流动中的进展, 当前求解雷诺平均的N-S方程湍流模式仍然是解决绕椭球大范围分离流动的主要工程方法, 大涡模拟和分离涡模拟等也逐渐得到了广泛应用. 受限于计算能力, 直接数据模拟只能用于较低雷诺数, 在高雷诺数流动中还不适用. 非定常机动过程的数值模拟较定常状态, 与实验结果的差距要大一些. 最后, 介绍了对椭球绕流场转捩的研究进展, 对T-S转捩与横流转捩的机理和辨识已经较为准确, 数值模拟结果与实验结果基本相符, 但对再附转捩的认识还不够清晰, 尤其是迎风面, 因此椭球绕流转捩的研究还需要依靠实验.Abstract: Understanding and predicting the flow around the prolate spheroid is of great engineering significance to guide the design of vehicles such as aircraft and submarines. In recent years, a lot of experimental and numerical studies have been carried out on the flow around the prolate spheroid. The qualitative description and quantitative research of flow separation around prolate spheroid at attack angle are presented, promoting the identification and topology research of three-dimensional separation. The experimental results of oil flow, smoke, dye, hydrogen bubble, and LDV are given. The flow field characteristics are analyzed, and the existing problems are pointed out. Based on the introduction of the above phenomena, the effects of separation on aerodynamic force, noise, and wake are introduced. The effects of test conditions such as transition zone, protrusion, depression, and tail support on flow are also discussed. There are obvious differences between the above steady flow and the unsteady maneuvering process. The unsteady maneuvering process can not be treated as a steady or quasi-steady problem. During the maneuvering process, the separation will be delayed obviously, and the aerodynamic force will also change obviously. The greater the angle of attack, the higher the maneuvering rate, the more noticeable this effect will be. At present, RANS turbulence model is still the primary engineering method to solve the large-scale separated flow around the prolate spheroid. However, LES, DES, and other methods have gradually been widely used. Due to the limitation of computer capability, DNS can only be used in the case of lower Reynolds number but not in high Reynolds number flow. The difference between the numerical simulation and the unsteady simulation is more significant. Finally, the research progress of prolate spheroid transition is introduced. The mechanism and identification of TS transition and cross-flow transition are more accurate. The numerical simulation results are basically consistent with the experimental results, but the understanding of reattachment transition is not clear enough, especially on the windward side. Therefore, the research of prolate spheroid transition still needs to rely on experiments.
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Key words:
- prolate spheroid /
- separation /
- vortex /
- wake /
- aerodynamic /
- sysnoise /
- unsteady maneuver /
- transition
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图 1 α = 20°, Re = 4.2 × 106时的横流分离拓扑(P表示一次分离, S表示二次分离) (Wetzel和Simpson 1998b)
图 3 长细比对轴对称物体体积阻力系数的影响(曲线是Hoerner公式的计算值, 散点是实验值) (Dorrington 2006)
图 4 椭球外形与坐标系定义(卞于中和张孝棣 1989)
图 9 α = 10°时椭球表面的摩阻和无黏流线. (a)背风面视角, (b) φ = 120°视角(Costis和Polen 1987)
图 10 α = 10°时椭球表面的流线模式. (a)背风面视角, (b) φ = 120°视角(Costis和Hoang 1989)
图 11 根据流动可视化所绘制摩阻线和涡层示意图(Costis和Hoang 1989)
图 12 α = 10°时通过染料获得的摩阻线和涡层示意图(Costis和Polen 1987)
图 13 磁悬浮列车尾部的分离流. (a)计算值(Siclari和Ende 1995), (b)实验值(Tyll和Liu 1996)
图 15 Re = 1.4 × 106, α = 30°, 层流状态油流显示谱. (a)头部侧视图, (b)尾部侧视图, (c)俯视图, (d)尾部数值计算结果(俯视图) (图中罗马数字I, II, III表示一次分离、二次分离、三次分离) (祝成民和忻鼎定 2002)
图 16 Re = 1.4 × 106, α = 20°, 层流状态油流显示谱. (a)侧视图, (b)俯视图(图中罗马数字I, II, III表示一次分离、二次分离、三次分离) (祝成民和忻鼎定 2002)
图 17 Re = 1.4 × 106, α = 30°, 湍流状态油流显示谱. (a)侧视图, (b)俯视图(图中罗马数字I, II, III表示一次分离、二次分离、三次分离) (祝成民和忻鼎定 2002)
图 18 Re = 1.4 × 106, α = 20°, 湍流状态油流显示谱. (a)侧视图, (b)俯视图(图中罗马数字I, II, III表示一次分离、二次分离、三次分离) (祝成民和忻鼎定 2002)
图 19 油流显示结果. (a)图气流从左至右, (b)图气流从右至左(Wetzel和Simpson 1998a)
图 20 α = 10°, Re = 7.7 × 106时一次分离位置沿流向分布(Kreplin和Vollmers 1985)
图 21 α = 10°, Re = 4.2 × 106/7.7 × 106时x/L = 0.7725站位平均和脉动压力沿周向分布(Kreplin和Vollmers 1985)
图 22 α = 10°, Re = 7.7 × 106时x/L = 0.73站位位移厚度、横流角、无量纲壁面剪切应力、β参数沿周向分布(Cebeci和Meier 1987)
图 23 α = 10°, Re = 7.7 × 106时不同站位的局部摩阻系数计算值(实线)和实验值(虚线)沿周向分布(Cebeci和Meier 1987)
图 24 α = 10°, Re = 7.7 × 106时不同站位的边界层位移厚度和动量厚度实验值(虚线与符号)和计算值(实线)沿周向分布(Cebeci和Meier 1987)
图 25 x/L = 0.7与x/L = 0.8两个站位的非主流方向的速度矢量图(体轴坐标系) (Barber和Simpson 1991)
图 26 x/L = 0.7与x/L = 0.8两个站位的位移边界层厚度沿周向的变化(图中φ需加90°) (Barber和Simpson 1991)
图 27 x/L = 0.7与x/L = 0.8两个站位的Townsend参数A1沿周向不同位置的分布(自由流坐标系, 图中φ需加90°) (Barber和Simpson 1991)
图 28 x/L = 0.7站位沿两个方向的涡黏性系数(自由流坐标系, 图中φ需加90°) (Barber和Simpson 1991)
图 29 x/L = 0.7站位沿的混合长与按二维理论计算的比值(自由流坐标系, 图中φ需加90°) (Barber和Simpson 1991)
图 30 x/L = 0.8站位沿周向的流动梯度角与剪切应力角(自由流坐标系, 图中φ需加90°) (Barber和Simpson 1991)
图 31 α = 20°时不同雷诺数下的一次分离线(实心符号)和二次分离线(空心符号) (Ahn和Simpson 1992)
图 32 α = 20°, Re = 5.6 × 106时沿流向不同站位的剪切应力角和流动梯度角(Barberis和Molton 1995)
图 33 椭球内部的三维光导纤维边界层LDV探针示意图(Chesnakas和Simpson 1996)
图 34 x/L = 0.762站位不同周向位置的雷诺正应力沿径向分布(Chesnakas和Simpson 1996)
图 35 x/L = 0.762站位、周向角φ = 123°位置的速度三重积分布(Chesnakas和Simpson 1996)
图 36 不同站位沿周向的摩阻系数分布(Chesnakas和Simpson 1996)
图 37 x/L = 0.762站位、周向角φ = 123°的流动角和湍动能分布(Chesnakas和Simpson 1996)
图 38 x/L = 0.772站位的壁面压力系数与速度分布. (a) α = 10°, (b) α = 20° (Chesnakas和Simpson 1997)
图 39 不同攻角下不同站位摩阻沿周向分布(Chesnakas和Simpson 1997)
图 40 α = 20°时x/L = 0.772站位的螺旋密度云图(Chesnakas和Simpson 1997)
图 41 α = 10°时x/L = 0.600站位湍流各向异性云图(Chesnakas和Simpson 1997)
图 42 α = 30°, Re = 6.5 × 106时x/L = 0.738站位的摩阻幅值和分量沿周向分布, 图中垂直线表示根据摩阻方向场所判断的分离位置(Goody和Simpson 2000a)
图 43 (a) α = 10° 和(b) α = 20° 时采用热膜传感器和LDV测量数据拟合后摩阻的差异(Tsai和Whitney 1999)
图 44 α = 10°时x/L = 0.600站位湍动能的二次流线云图(径向为对数坐标) (Goody和Simpson 2000a)
图 45 α = 14°时x/L = 0.652站位边界层内的速度剖面(卞于中和张孝棣 1989)
图 46 α = 30°时x/L = 0.75站位边界层内的湍动能和雷诺应力分布(严崇禄和曹露洁 2002)
图 47 α = 30°时x/L = 0.75站位的涡量分布(严崇禄和曹露洁 2002)
图 48 α = 30°时自功率谱最大幅值所在位置曲线与流动显示结果的比较(严崇禄和曹露洁 2002)
图 49 二维分离和三维分离的简化概念. (a)二维流, (b)三维流 (Delery 1992)
图 50 α = 10°, f = 6, Re = 7.7 × 106时沿流向不同站位三维位移边界层沿周向的发展(Wetzel和Simpson 1998)
图 51 α = 10°, f = 6, Re = 4.2 × 106时, x/L = 0.77站位, 距离物面不同距离时横流速度的周向分布(体轴坐标系) (Wetzel和Simpson 1998)
图 52 α = 10°, f = 6, Re = 4.2 × 106时, x/L = 0.77站位, 距离物面不同距离时横向速度沿周向的分布(垂直于局部分离线的坐标系) (Wetzel和Simpson 1998)
图 53 f = 6, Re = 4.2 × 106时, x/L = 0.77站位, 不同攻角时周向压力分布(Wetzel和Simpson 1998)
图 54 Re = 4.2 × 106时, 不同攻角, 不同站位的压力脉动沿周向分布(Wetzel和Simpson 1998)
图 55 α = 10°, f = 6, Re = 4.2 × 106时不同测量装置和识别条件下一次分离线(Wetzel和Simpson 1998)
图 56 α = 10°, f = 6时, x/L = 0.6站位(垂直于椭球长轴平面)的二次流流线以及摩阻系数的变化(图中圆点) (Wetzel和Simpson 1998)
图 57 临界点的分类(Wang 1976, Delery 1992)
图 58 三维钝头体绕流分离的临界点(Chapman 1986)
图 64 α = 10°, f = 6, Re = 1.6 × 106开式分离情况下的壁面摩阻线(Simpson 1996)
图 65 极限流线模式与三种类型的三维物面分离形式. (a)为马蹄形分离, (b)为Werle分离, (c)为横流分离(Yates和Chapman 1992)
图 66 开式分离的出现(图中数字表示攻角) (Su和Tao 1996)
图 67 开式分离及涡流随攻角的演化(图中数字表示攻角) (Su和Tao 1996)
图 68 α = 30°时开式分离及涡流的形成过程(Su和Tao 1996)
图 69 阻力系数随Re的变化(Dress 1990)
图 70 在不同攻角下地面效应对升力系数的影响(Holt和Garry 2016)
图 72 模型侧向力系数随攻角的变化(Kim和Rhee 2003)
图 73 模型侧向力系数随攻角的变化(卞于中和张孝棣 1989)
图 74 椭球头旋成体时均侧向力系数随攻角的变化曲线(刘沛清和邓学蓥 2002)
图 75 不同攻角下侧向力脉动过程及其功率谱分布(低频分量). (a)时间历程, (b)能谱 (刘沛清和邓学蓥 2002)
图 76 脉动侧向力均方根值随攻角的变化曲线(刘沛清和邓学蓥 2002)
图 77 大迎角下细长体绕流的功率谱密度分布(刘沛清和邓学蓥 2002)
图 78 α = 10°时x/L = 0.6站位内剪切层的壁面压力脉动能量谱(Goody和Simpson 2000a)
图 79 α = 10°时x/L = 0.6站位外剪切层的壁面压力脉动能量谱(Goody和Simpson 2000a)
图 80 α = 20°时x/L = 0.6站位壁面压力脉动能量谱(Goody和Simpson 2000a)
图 81 α = 10°时x/L = 0.772站二次流流线与壁面压力/脉动速度分量v的相关系数云图(Goody和Simpson 2000a)
图 82 瞬时流态与流向速度云图(以来流速度进行了无量纲化) (Cianferra和Armenio 2018)
图 83 固定转捩和自由转捩对阻力系数的影响(Dress 1990)
图 84 Re = 4.2 × 106时不同攻角下的一次分离位置(实心符号)和二次分离位置(空心符号) (Ahn和Simpson 1992)
图 85 α = 30°, Re = 4.2 × 106与7.2 × 106时x/L = 0.565站位的平均和脉动压力分布(P, S, R表示一次、二次分离线和再附线) (Ahn和Simpson 1992)
图 86 椭球绕流场分离区流线的二维投影(Ahn和Simpson 1992)
图 87 椭球头部的层流流动拓扑, 左图为油流照片, 右图为根据油流绘制的流动图谱(Wetzel和Simpson 1996)
图 88 转捩带直径(上图为0 mm, 中图为0.8 mm, 下图为1.6 mm)对椭球尾迹流动的影响(左列的偏航角为8°, 右列的偏航角为−8°) (Ashok和Buren 2015)
图 89 尾部分离区的烟线测试(Chevray 1968)
图 90 平均轴向速度差的相似剖面(Chevray 1968)
图 91 尾迹中湍流剪切应力的分布(Chevray 1968)
图 92 侧滑角20°, Re = 4.0 × 104时类椭球体模型在水槽中的染色显示, 视角为背风面, 流动从左至右(Ashok和Buren 2015)
图 93 绕椭球支撑杆的流动显示, 左图Re = 3.5 × 103为对称模式, 右图Re = 6.5 × 103为非对称模式(Tezuka和Suzuki 2006)
图 94 上仰机动过程中x/L = 0.77站位不同攻角时的集总平均压力沿周向分布(Hoang和Wetzel 1994a)
图 95 上仰机动过程中x/L = 0.56站位, 不同周向位置压力系数随时间变化(Hoang和Wetzel 1994a)
图 96 α = 30°时上仰机动过程中和定常状态下, x/L = 0.56站位的脉动压力分布(Hoang和Wetzel 1994a)
图 97 回转机动过程中x/L = 0.77站位不同攻角时的集总平均压力分布(Hoang和Wetzel 1994b)
图 98 α = 10°时, 回转机动、上仰机动、定常流动过程中x/L = 0.77站位的压力分布(Hoang和Wetzel 1994b)
图 99 俯冲机动过程中x/L = 0.83站位和三个不同z站位的集总平均压力分布(Hoang和Wetzel 1994b)
图 100 定常和上仰机动非定常分离时(α = 20.2°)的分离线(虚线和空心符号是定常分离线, 实线和实心符号是集总平均的瞬时分离线, P表示一次分离, S表示二次分离)(Wetzel和Simpson 1996)
图 101 定常和上仰机动非定常分离中三个轴向站位的分离位置随攻角的变化(Wetzel和Simpson 1996)
图 102 定常、上仰机动、回转机动时, α = 12.2°, x/L = 0.729站位的壁面剪切应力分布(Wetzel和Simpson 1996)
图 103 非定常分离数据的一阶拟合(实心符号为定常状态分离点, 空心符号表示非定常分离点, 实线为拟合值) (Wetzel和Simpson 1996)
图 104 攻角从0°变化到15°过程中准定常和非定常状态下俯仰力矩的变化(虚线是非定常状态, 实线是准定常状态) (Granlund和Simpson 2009)
图 105 不同雷诺数时, 有无尾部支杆时阻力系数的对比(Dress 1990)
图 106 风洞中的磁悬架平衡系统示意图(Ambo和Otsuki 2016)
图 107 多余物的轴向和周向位置示意图. (a) Position of x direction x/L, (b) Position of rol direction φ (°) (Amob和Otsuki 2016)
图 108 无尾部支杆时的流动显示图. (a) α = 0°, (b) α = 5° (Amob和Otsuki 2016)
图 109 无尾部支杆的流动模态. (a) α = 0°, (b) α = 5° (Amob和Otsuki 2016)
图 110 α = 10°, Re = 4.2 × 106时有无传感器对一次分离位置的影响(Wetzel和Simpson 1996)
图 111 α = 15°, Re = 4.2 × 106时有无传感器对一次分离和二次分离位置的影响(Wetzel和Simpson 1996)
图 112 α = 30°时孤立颗粒状突起对油流显示谱的影响. (a) Re = 1.4 × 106, (b) Re = 9 × 105 (祝成民和忻鼎定 2002)
图 113 椭球从静止突然起动时的瞬时分离线(Costis和Telionis 1984)
图 114 α = 6°时不同时刻下尾部区域位移速度分布(上图时间为0.17, 下图为0.19) (van Dommelen和Cowley 1990)
图 115 α = 50°时不同时刻下尾部区域位移速度分布. (a) t = 0.09, (b) t = 0.11 (van Dommelen和Cowley 1990)
图 116 α = 6°时不同时刻下尾部区域的极限流线. (a) t = 0.05, (b) t = 0.19 (van Dommelen和Cowley 1990)
图 117 α = 30°, U∞ = 45 m/s时采用流线法计算所得的分离线(严家祥和席德科 1991)
图 118 黏性流线和无黏流线的比较(严家祥和席德科 1991)
图 119 流过椭球三个不同站位沿流线的速度型(严家祥和席德科 1991)
图 121 α = 10°, 不同雷诺数时表面摩擦力线展开图. (a) Re = 100, (b) Re = 500, (c) Re = 1000, (d) Re = 2000, (e) Re = 3000, (f) Re = 5000 (祝成民和忻鼎定 2003b)
图 122 α = 30°, 不同雷诺数时椭球表面摩擦力线展开图. (a) Re = 100, (b) Re = 500, (c) Re = 1000, (d) Re = 2000, (e) Re = 3000, (f) Re = 5000 (祝成民和忻鼎定 2003b)
图 123 α = 10°, 不同雷诺数时对称面流线图. (a) Re = 100, (b) Re = 500, (c) Re = 1000, (d) Re = 2000, (e) Re = 3000, (f) Re = 5000 (祝成民和忻鼎定 2003b)
图 124 α = 30°, 不同雷诺数时对称面流线. (a) Re = 100, (b) Re = 500, (c) Re = 1000, (d) Re = 2000, (e) Re = 3000, (f) Re = 5000 (祝成民和忻鼎定 2003b)
图 125 α = 10°和α = 30°时空间涡结构. (a) 迎角10°, Re = 2000, (b) 迎角30°, Re = 5000 (祝成民和忻鼎定 2003b)
图 126 α = 0°, Re=1.2 × 107时, (a) x/L = 0.904 和(b) x/L = 0.978 两个站位的壁面剪切应力(Sung和Griffin 1993)
图 127 α = 10°, Re = 8.0 × 105时, (a) x/L = 0.481和(b) x/L = 0.567两个站位的壁面摩阻系数(温功碧和陈作斌 2004)
图 128 α = 10°, Re = 4.2 × 106时, (a) x/L = 0.77和(b) x/L = 0.83两个站位压力系数沿周向分布(温功碧和陈作斌 2004)
图 129 椭球表面极限流线(丛成华和邓小刚 2011)
图 130 α = 10°, Re = 1.6 × 106时, (a) x/L = 0.48和(b) x/L = 0.738两个站位对称面摩阻分布(向大平和邓小刚 2005)
图 131 α = 10°, Re = 1.6 × 106时对称面压力分布(丛成华和邓小刚 2011)
图 132 α = 10°, Re = 1.6 × 106时, (a) x/L = 0.395, (b) x/L = 0.565, (c) x/L = 0.738站位摩阻系数沿周向分布(丛成华和邓小刚 2011)
图 133 α = 5°, Re = 5.0×104时的极限流线和低攻角时的流场拓扑(Kim和Patel 1991)
图 134 α = 10°, Re = 5.0 × 104时的极限流线和和中等攻角时的流场拓扑(Kim和Patel 1991)
图 135 α = 25°, Re = 5.0 × 104时的极限流线和高攻角时的流场拓扑(Kim和Patel 1991)
图 136 α = 30°, Re = 5.0 × 104时两个不同站位横断面的极限流线(Kim和Patel 1991)
图 137 α = 20°, Re = 4.2 × 106时, (a) x/L = 0.600, (b) x/L = 0.772站位压力系数沿周向分布(Kim和Rhee 2003)
图 138 α = 20°, Re = 4.2 × 106时, x/L = 0.60, x/L = 0.77站位物面流动转向角沿周向分布(Constantinescu和Pasinato 2002)
图 139 α = 20°, Re = 4.2 × 106时, x/L = 0.77站位压力系数沿周向分布(Constantinescu和Pasinato 2002)
图 140 α = 20°, Re = 4.2 × 106时, x/L = 0.729站位摩阻系数(图中放大了1000倍)沿周向分布(Scott和Duque 2004)
图 141 α = 20°, Re = 4.2 × 106时, x/L = 0.772站位壁面压力系数沿周向分布(肖昌润和刘巨斌 2007)
图 142 α = 30°, Re = 4.2 × 106时, x/L = 0.5站位壁面摩阻系数沿周向分布(肖昌润和刘巨斌 2007)
图 145 α = 30°, Re = 6.5 × 106时不同湍流模型计算的x/L = 0.5站位的流线. (a) S-A模型, (b) SST模型 (陈亮中 2010)
图 147 α = 30°时x/L = 0.524, φ = 53.75°位置采用k-ω和EASM模型计算得到的湍动能分布(Morrison和Panaras 2003)
图 148 α = 30°时x/L = 0.524站位采用k-ω和EASM模型计算得到的最大湍动能沿周向分布(Morrison和Panaras 2003)
图 149 α = 30°, Ma = 0.1322, Re = 6.5 × 106时对称面压力系数沿流向分布(Alpman和Long 2005)
图 150 α = 30°, Ma = 0.1322, Re = 6.5 × 106时沿流向不同站位的涡量云图, 物面为摩阻线(Alpman和Long 2005)
图 151 α = 30°, Ma = 0.1322, Re = 6.5 × 106时, x/L = 0.738站位的纵向速度云图(Alpman和Long 2005)
图 152 α = 30°, Ma = 0.1322, Re = 6.5 × 106时, x/L = 0.738站位摩阻系数沿周向分布(Alpman和Long 2005)
图 153 (a)与(b) α = 10°、(c)与(d) α = 20° 时x/L = 0.772站位, (a)与(c)速度大小和(b)与(d)湍动能分布, 其中(a)与(c)中流线与云图重叠(Hedin和Berglund 2001)
图 154 α = 20°时x/L = 0.73站位流线和速度矢量. (a)静态LES, (b)VMS-LES (Farhat和Rajasekharan 2006)
图 155 α = 20°时x/L = 0.772站位压力系数和周向角φ = 60°位置的速度分布(Alin和Fureby 2005)
图 156 α = 20°时x/L = 0.600, x/L = 0.772站位的轴向速度云图, 物面为极限流线. (a) LES, (b) DES (Karlsson和Fureby 2009)
图 157 α = 10°时对称面压力系数与x/L = 0.772站位沿周向的压力系数(实线为TLS-LES结果, 符号为试验结果, 红色表示迎风面, 蓝色为背风面) (Ranjan和Menon 2015)
图 158 α = 10°/20°时对称面压力系数沿轴向分布(Constantinescu和Pasinato 2002)
图 159 α = 20°时x/L = 0.60站位和周向角φ = 90°时的平均速度型(Constantinescu和Pasinato 2002)
图 160 α = 20°时x/L = 0.77站位沿周向的摩阻分布(Constantinescu和Pasinato 2002)
图 161 α = 20°时x/L = 0.77站位沿周向的压力系数分布(Constantinescu和Pasinato 2002)
图 162 α = 20°时一次分离和二次分离的位置(Constantinescu和Pasinato 2002)
图 163 α = 20°时x/L = 0.77站位和周向角φ=150°时无量纲速度型(Scott和Duque 2005)
图 164 α = 30°时不同站位沿周向的压力系数. (a) x/(2a) = 0.48, (b) x/(2a) = 0.48, (c) x/(2a) = 0.48, (d) x/(2a) = 0.48, (e) x/(2a) = 0.48 (肖志祥和陈海昕 2006)
图 165 α = 20°时x/L = 0.27站位沿周向压力系数和x/L = 0.229站位沿周向切应力系数(于向阳和刘巨斌 2011)
图 166 α = 20°时背风面极限流线与分离点、再附点(胡偶和赵宁 2017)
图 167 α = 20°时x/L = 0.77站位沿周向压力系数(胡偶和赵宁 2017)
图 168 α = 20°时x/L = 0.77站位不同周向方位角的速度分布. (a) ϕ = 90°, (b) ϕ = 12°, (c) ϕ = 150°, (d) ϕ = 180° (胡偶和赵宁 2017)
图 169 α = 90°时涡结构图. (a)为子午面, (b)为三维视图, (c)为赤道平面, (d)为(a)图的局部视图 (Khoury和Andersson 2010)
图 170 (a) x/D = 3.5站位, 与椭球主轴平行的某条线上的局部Std, (b) 局部Red与局部Std的关系, 空心符号为5 < y/D < 8, 实心符号8 < y/D < 11 (Khoury和Andersson 2010)
图 171 α = 90°时(a)与(c)子午面和(b)与(d)赤道平面的流线, (a)与(b): Re = 50, (c)与(d): Re = 75 (Khoury和Andersson 2012)
图 172 α = 90°时不同雷诺数时以u = 0等值面显示的环状旋涡拓扑. (a) Re = 100, (b) Re = 150, (c) Re = 200, (d) Re = 300 (Khoury和Andersson 2012)
图 173 α = 90°, 不同Re时沿流向不同站位的无量纲瞬时流向速度云图. (a) Re = 100, (b) Re = 150, (c) Re = 200, (d) Re = 300 (深蓝为0.7, 深红为1) (Khoury和Andersson 2012)
图 174 α = 45°, Re = 1000时某个时刻的三维瞬时涡结构等值面, 三个站位沿流线的涡量等值线图(Jiang和Gallardo 2014)
图 175 α = 45°时某个时刻的三维瞬时涡结构等值面, 两个站位沿流线的涡量等值线图(Jiang和Gallardo 2015)
图 176 时均涡量分布及流线、平均压力系数(Jiang和Gallardo 2015)
图 177 无量纲轴向速度、无量纲轴向涡量、速度与涡量的协方差、平均压力系数沿涡轴的变化(Jiang和Gallardo 2015)
图 178 α = 45°时三个速度分量的能量谱: (a)中部尾迹, x/D = 4, y/D = 2, z/D = 1, (b)近椭球尾迹x/D = 0, y/D = −1, z/D = 0.31 (Jiang和Gallardo 2015)
图 179 α = 45°, Re = 4000时在yz平面三个不同截面的轴向速度(蓝色表示速度负值, 红色表示速度正值) (Strandenes和Jiang 2019)
图 180 α = 45°, Re = 4000时某个时刻Kelvin−Helmholtz失稳的三维再现(Strandenes和Jiang 2019)
图 181 机动过程中α = 20°时x/L = 0.772站位的速度大小云图 (Kotapati-Apparao和Squires 2003)
图 182 定常状态下和机动过程中α = 20°时x/L = 0.772站位周向角φ = 90°时的三个方向的平均速度型(Kotapati-Apparao和Squires 2003)
图 183 机动过程中α = 20°和α = 30°时, x/L = 0.729和x/L = 0.882站位沿周向的摩阻系数(Kotapati-Apparao和Squires 2003)
图 184 机动过程中α = 10°时x/L = 0.44和x/L = 0.77站位沿周向的压力系数(Kotapati-Apparao和Squires 2003)
图 185 f = 6、Re = 4.2 × 106时下沉运动过程中在不同下沉高度时x/L = 0.83站位不同高度沿周向的压力系数(温功碧和陈作斌 2004)
图 186 f = 6, Re = 4.2 × 106时俯仰运动过程(最大俯仰角25°)中不同攻角情况下x/L = 0.56站位沿周向的压力系数(温功碧和陈作斌 2004)
图 187 自由衰减俯仰振荡过程中不同时刻的涡量等值面和速度云图. (a) t = 0 s, (b) t = 0.5 s, (c) t = 1 s, (d) t = 1.5 s, (e) t = 2 s, (f) t = 2.5 s (熊英 2019)
图 188 自由衰减俯仰振荡过程中不同时刻y = 0切面上的压力云图和密度等值线的时间演化. (a) t = 32T, (b) t = 48T, (c) t = 64T, (d) t = 80T (熊英 2019)
图 189 密度均匀流中Re = 1.0 × 104时椭球自由运动时不同时刻的压力等值线云图. (a) t = 0.425 s, (b) t = 0.45 s, (c) t = 0.475 s, (d) t = 0.5 s (熊英 2019)
图 190 α = 50°时瞬时压力差(Zeiger和Telionis 2004)
图 191 f = 6, α = 29.7°, Re = 1.53 × 106时测量和计算得到的不同站位的压力系数分布(Stock 2006)
图 192 f = 6, α = 0°/2.5°, Re = 7.2 × 106以及f = 6, α = 5° ~ 29.7°, Re = 6.40 × 106 ~ 6.54 × 106时计算得到的转捩位置(Stock 2006)
图 193 f = 6, α = 10°, Re = 6.5 × 106, Ma = 0.13时计算和实验得到的转捩位置(Krimmdlbein和Radespiel 2005)
图 194 f = 6计算和实验得到的壁面摩阻分布和转捩位置(Krimmelbein和Krumbein 2011)
图 195 f = 6, α = 15°, Re = 6.5 × 106, Ma = 0.13时垂直壁面方向网格数目(图中64/96/128/256)和对流项格式精度对壁面摩阻计算结果的影响. (a)一阶Roe格式, (b)二阶Roe格式 (Nie和Krimmelbein 2018b)
图 196 (a) α = 5°和(b) α = 10°, f = 6, Re = 6.5 × 106, Ma = 0.13时不同计算方法得到的壁面摩阻(Nie和Krimmelbein 2018b)
图 197 f = 6, α = 15°, Re = 6.5 × 106, Ma = 0.13时不同计算方法得到的壁面摩阻(Nie和Krimmelbein 2018b)
图 198 (a) α = 20°和(b) α = 24°, f = 6, Re = 6.5 × 106, Ma = 0.13时不同计算方法得到的壁面摩阻(Nie和Krimmelbein 2018)
图 199 f = 6, α = 15°, Re = 6.5 × 106, Ma = 0.13时不同计算方法得到的壁面摩阻系数. (a) 原始 γ-Rea 模型, (b) γ-Rea-CF-SA 模型 (鞠胜军和阎超 2017)
图 200 f = 6, α = 15°, Re = 6.5 × 106, Ma = 0.13时实验和不同计算方法得到的壁面摩阻系数. (a) 实验数据, (b) 原始 γ-Rea 模型, (c) γ-Rea-CF-SST (鞠胜军和阎超 2017)
图 201 f = 6, Ma = 0.136时实验和计算得到的壁面摩阻图. (a)α = 15°, Re = 6.5 × 106, (b) α = 30°, Re = 7.2 × 106 (徐家宽 2019)
图 203 f = 6, Ma = 0.136, α = 29.5°时实验和计算得到的壁面摩阻图. (a)Re = 4.48 × 106, (b)Re = 8.52 × 106 (徐家宽 2019)
图 204 f = 6, α = 15°, Re = 6.5 × 106, Ma = 0.136时(a)计算和(b)实验得到的壁面摩阻(徐晶磊和周禹 2019)
表 1 实验条件
研究者 实验条件 Chevray 1968 风洞, 烟雾/热线, 湍流, f = 6, L = 1.524 m, α = 0°, Re = 2.75 × 106 Wilson 1971 风洞, 烟雾, 层流, f = 4, L = 0.3 m, α = 0°/3°/6°/12°/25°/31.7°,
Re = 7.5 × 104Wang 1972, 1974b, 1976 水洞, 墨水, 层流, f = 2/3/4, α = 0° ~ 90°, Re = 3.5 × 104 Han和Patel 1979 水槽, 染料/贴线, 层流, f = 4.3, α = 0° ~ 40°, Re = 8 × 104 Tobak和Peake 1982 层流, 油流, f = 6, α = 0° ~ 4° Kreplin和Vollmers 1980, 1982, 1985 风洞, 油流, 层流/湍流, f = 6, L = 2.4 m, α = 0° ~ 27°/10°/30°,
Re = 4.2 × 106/7.7 × 106Cebeci和Meier 1987 风洞, 油流, 层流/湍流, f = 6, L = 2.4 m, α = 10°, Re = 7.7 × 106 Costis和Polen 1987, Costis和Hoang 1989 水洞, 染料和粒子, 激光片光, 层流, f = 4, α = 0° ~ 30°, Re = 104 卞于中和张孝棣 1989 风洞, 油流/彩色氦气泡, 湍流, f = 6, L = 1.5 m, α = 14°/30°,
Re = 2 × 106/3 × 106Su 和Tao 1996 水槽, 染料, 层流, f = 4, α = 0° ~ 70°, Re = 1 × 104 祝成民和忻鼎定 2002 风洞, 油流, 层流/湍流, f = 4, L = 0.58 m, α = 20°, 30°,
Re = 9 × 105/1.4 × 106
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表 2 实验条件
研究者 实验条件 Kreplin和Vollmers 1980, 1982, 1985 风洞, 油流, 热线, 层流/湍流, f = 6, L = 2.4 m, α = 0° ~ 27°/10°/30°,
Re = 4.2 × 106/7.7 × 106Cebeci和Meier 1987 风洞, 油流, 热膜/探针, 层流/湍流, f = 6, L = 2.4 m, α = 10°, Re = 7.7 × 106 Barber和Simpson 1991 风洞, 油流, 热线/探针, 湍流, f = 6, L = 1.372 m, α = 10°, Re = 4 × 106 Ahn和Simpson 1992 风洞, 油流, 热线, 层流/湍流, f = 6, L = 1.372 m, α = 0° ~ 20°,
Re = 1.4 × 106 ~ 4.2 × 106Barberis和Molton 1995 风洞, LDV/探针, 湍流, f = 6, L = 1.372 m, α = 20°, Re = 5.6 × 106 Chesnakas和Simpson 1996 风洞, LDV, 湍流, f = 6, L = 1.372 m, α = 10°, Re = 4.2 × 106 Chesnakas和Simpson 1997 风洞, LDV, 湍流, f = 6, L = 1.372 m, α=10°/20°, Re = 4.2 × 106 Wetzel和Simpson 1998a 风洞, 油流, LDV/热膜, 湍流, f = 6, L=1.372 m, α = 10°, Re = 4.2 × 106 Goody和Simpson 2000a 风洞, LDV/热膜/热线, 湍流, f = 6, L = 1.372 m, α = 10°/20°, Re = 4.2 × 106 严崇禄和曹露洁 2002 风洞, 涡量探头, f = 4, L = 0.24 m, α = 30°, Re = 8 × 104 ~ 1.75 × 105
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表 3 分离类型与对应关系
研究者 分离类型 Wang 1972, 1974a, 1976 闭式分离(α < 6°, 与鞍点相伴), 开式分离(6° < α < 30°),
闭式分离(α > 30°, 与鞍点相伴)Costis和Polen 1987, Costis和Hoang 1989 闭式分离(α < 3°), 开式分离占优, 也存在闭式分离(3° < α < 30°),
闭式分离(α > 30°)Han和Patel 1979 自由涡层分离(小攻角和大攻角时), 分离泡分离(中等攻角时) Tobak和Peake 1982 全局分离(小攻角和大攻角时, 与鞍点相伴), 局部分离(中等攻角时) Chapman 1986 横流分离(中等攻角时) Ahn和Simpson 1992 前体为开式分离(α < 42°) Su和Tao 1996 闭式分离占优, 也存在开式分离(3° < α < 15°), 开式分离占优(15° < α < 65°),
闭式分离(α > 65°)
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表 4 非机动过程下的实验条件
研究者 实验条件 Hoang和Wetzel (1994) 风洞, LDV/热线, 湍流, 俯仰, f = 6, L = 1.372 m, α = 0° ~ 30°, Re = 4.2 × 106 Wetzel和Simpson (1998b) 风洞, LDV/热线, 湍流, 俯仰加滚转, f = 6, L = 1.372 m, α = 0° ~ 30°, Re = 4.2 × 106 Hosder和Simpson (2001) 风洞, 油流/热膜, 湍流, 俯仰, 类潜艇外形, L = 2.24 m, α = 1° ~ 27°, Re = 5.5 × 106 Granlund和Simpson (2009) 风洞, 油流/热膜, 湍流, 俯仰/偏转, 类潜艇外形,
L = 2.24 m, α = −15° ~ 15°/β = −15° ~ 15°
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表 5 求解边界层方程的计算条件描述
研究者 计算条件 Wang 1972, 1975 边界层方程, 层流, 涡格法, f = 4, α = 6°/30°/45° Wang 1974b 边界层方程, 层流, 隐式有限差分, f = 4, α = 0° ~ 90° Wang 1974a 边界层方程, 层流, 隐式有限差分, f = 4, α = 45° Geissler 1974 边界层方程, 层流, 流线法, 隐式有限差分, f = 4, α = 5°/10°/15° Hirsh和Cebeci 1977 边界层方程, 层流, 盒子方法/ADI格式(alternating direction implicit, ADI),
有限差分, f = 4, α = 0°/2°/6°Ramaprian和Patel 1981 边界层方程, 层流, ADI格式, f = 4, α = 0° ~ 30°, Re = 8.0 × 104 Cebeci和Khattab 1980 边界层方程, 层流, 盒子方法, 有限差分, f = 4, α = 0° ~ 90° Cebeci和Khattab 1981 边界层方程, 层流, 涡格法/盒子法, 有限差分, f = 4, α = 3°/6°/15°/30° Cebeci和Stewartson 1984 非定常边界层方程, 层流, 盒子法, 有限差分, f = 4, α = 30°/40°/45°/50° Tai 1984 不可压缩边界层方程, 湍流, 流线法, Runge−Kutta格式, f = 5.91, α = 10°/20° Patel和Baek 1985 薄层边界层方程, 层流/湍流, 涡格法, ADI格式, f = 6, L = 2.4 m, α = 10°,
Re = 1.6 × 106/7.2 × 106Ragab 1985, 1986 非定常边界层方程, 层流/湍流, 隐式有限差分, f=6, α=30° Radwan和Lekoudis 1986 不可压缩边界层方程, 层流/湍流, 反演模式法, 有限差分, f = 4, α = 3°/6°,
Re = 3.6 × 106VanDalsem和Steger 1987 非定常边界层方程, 层流/过渡流/湍流, 反演模式法, 有限差分, f = 6, α = 30°,
Re = 7.2 × 106Cebeci和Meier 1987 非定常边界层方程, 湍流, 盒子方法, 有限差分, f = 6, α = 10°,
Re = 7.2 × 106Radwan 1988 可压缩边界层方程, 层流, 四阶隐式有限差分, f=4, α=3° Telionis和Costis 1983 边界层方程, 层流/湍流, 流线方法, f = 4, α = 3°/6°/10°/15°/20°/30° Costis和Telionis 1984 非定常边界层方程, 湍流, 涡格方法, f = 4, α = 30° Costis和Telionis 1988 非定常边界层方程, 湍流, 涡格方法, f = 6, α = 15° Cebeci和Su 边界层方程, 层流, 盒子方法, 有限差分, f = 4, α = 1°/2°/3°/30° Wu和Shen 1991, 1992 非定常边界层方程, 层流, 有限差分, f = 4, α = 0°/6°/50° 严家祥和席德科 1989 边界层方程, 层流, 流线法, Runge−Kutta格式, f = 5.91, α = 30° 严家祥和席德科 1991 边界层方程, 湍流, 流线法, Runge−Kutta格式, f = 5.91, α = 15° Xin 2000 边界层方程, 湍流, 代数湍流模型, f = 6, α = 10°, Re = 3.6 × 106
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表 6 简化的N-S方程及层流计算条件描述
研究者 计算条件 Rosenfeld和Israeli 1985 不可压缩二维抛物型(即薄层)N-S方程, f = 4/6, α = 0°, Re = 1.0 × 106 Shirayama和Kuwahara 1987 非定常不可压缩N-S方程, 层流, 有限差分, α = 5°/15°/30°/45°,
Re = 1000Yates和Chapman 1988, 1992
(尖拱圆柱体)抛物型N-S方程, 层流, α = 10°/15°, Re = 3.0 × 105/1.2 × 104 Rosenfeld和Israeli 1988,
Rosenfeld和Wolfshtein 1992抛物型N-S方程, 层流, 有限差分, f = 4/6, α = 6°/10°,
Re = 1.6 × 106/2.0 × 106Vatsa和Thomas 1987 薄层N-S方程, 层流/湍流, f = 6, α = 10°/30°,
Re = (1.6/7.2/7.7) × 106Wong和Kandil 1989 (不可压缩)薄层N-S方程, 湍流, f = 6, α = 10°/30°,
Re = (1.6/7.2/7.7) × 106Zilliac 1989 (尖拱圆柱体) 不可压缩N-S方程, 层流, 有限差分, α = 30°/45°, Re = 1.0 × 103 Kim和Patel 1991 不可压缩N-S方程, 层流, ADI格式, f = 6, α = 0° ~ 30°, Re = 5.0 × 104 Zamyshlyaev和Shrager 2004 N-S方程, 层流, 有限差分, f = 1.67, α = 0°, Re = 1 ~ 100 袁礼 2002 不可压缩N-S方程, 层流, f = 4, α = 10°/30°, Re = 3 × 103/1.1 × 104 祝成民和忻鼎定 2003b 不可压缩N-S方程, 层流, f = 4, α = 10°/30°,
Re = 100/500/1000/2000/3000
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表 7 不同雷诺数下回流点的位置(°)(祝成民和忻鼎定 2003b)
Re α = 10°时上回流点 α = 10°时下回流点 α = 30°时上回流点 α = 30°时下回流点 100 180 180 174.7 174.7 500 172.1 172.1 146.1 180 1000 153.3 166.9 153.9 180 2000 152.9 162.7 158.5 177.2 3000 163.1 158.1 158.1 171.6 5000 180 155.9 146.5 162.1
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表 8 RANS方法叠加代数湍流模型的计算条件描述
研究者 计算条件 Vatsa和Thomas 1987 定常流动, 层流/湍流, f = 6, α = 10°/30°, Re = (1.6/7.2/7.7) × 106,
有限体积, 结构网格(73 × 49 × 49), B-L模型Wong和Kandil 1989 定常流动/非定常流动, 层流/湍流, f = 6, α = 10°/30°,
Re = (1.6/7.2/7.7) × 106, 有限体积, 结构网格, B-L模型Hartwich和Hall 1990 定常流动/非定常流动, 湍流, f = 6, α = 10°/30°,
Re = (1.6/7.2/7.7) × 106, 有限体积, 结构网格, B-L模型Gee和Cummings 1992 定常流动, 湍流, f = 6, Re = × 106, 有限体积,
结构网格, B-L模型/J-K模型Ramamurti和Sandberg 1994 定常流动, 层流/湍流, f = 6, α = 10°
有限元, 非结构网格, B-L模型温功碧和陈作斌 2004 定常流动/非定常流动, 湍流, f = 6, α = 10°, Re = (0.8/4.2) × 106,
有限体积, 结构网格, B-L模型Deng和Zhuang 2002, 向大平和邓小刚 2005, 丛成华和邓小刚 2011 定常流动, 湍流, f = 6, α = 10°, Re = 1.6 × 106, Ma = 0.1,
有限体积, 结构网格(91 × 65 × 73), B-L模型
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表 9 RANS方法叠加一方程和两方程湍流模型的计算条件描述
研究者 计算条件 Kim和Patel 1991 定常流动, 湍流, f = 6, Re = 5.0 × 104, α = 0°/5°/10°/15°/20°/25°/30°,
结构网格, 有限体积, k-ε模型Liu和Zheng 1998 定常流动/非定常流动, 湍流, 结构多重网格, 有限体积, k-ω模型 Tsai和Whitney 1999 定常流动, 湍流, α = 0°, 结构网格, 有限体积,
SIMPLE算法, k-ε模型(壁面函数)Kim和Rhee 2003 定常流动, 湍流, f = 6, Re = 4.2 × 106, α = α = 10°/20°/30°, 结构网格, 有限体积,
S-A/k-ω/RSM模型, 升力/力矩/压力/切应力Rhee和Hino 2002 定常流动(α = 5°/10°/15°/20°/25°/30°)/非定常流动(α = 0° ~ 30°), 湍流
非结构网格, 有限体积, S-A模型, 升力/力矩/压力/切应力Constantinescu和Pasinato 2002 定常流动, 湍流, f = 6, L = 1.372 m, α = 10°/20°, Re = 4.2 × 106, 结构网格, 有限体积,
S-A模型/S-A DES, 速度/压力/切应力Scott和Duque 2004 定常流动, 湍流, 结构网格, 有限体积,
代数湍流模型, 速度/压力/切应力Huang和Lin 2009 定常流动, 湍流, f = 6, Re = 1.6 × 106, Ma = 0.01, 结构网格, 有限体积, S-A模型, 压力 Holt和Garry 2016 定常流动, 湍流, f = 6, 结构网格, 有限体积, k-ω SST模型, 邱磊和邹早建 2004, 2005 定常流动, 层流(Re = 1.0 × 104, α = 5°/10°/15°/20°)/湍流(Re = 4.2 × 106,
α = 10°/20°/30°), f = 6, 结构网格, 有限体积, k-ε模型肖昌润和刘巨斌 2007 定常流动, 层流(Re = 1.0 × 104, α = 5°/10°/15°/20°)/湍流(Re = 4.2 × 106,
α = 10°/20°/30°), f = 6, 结构网格, 有限体积, SIMPLE算法, k-ω SST模型祝成民和忻鼎定 2003a 定常流动, 湍流, f = 4, Re = 7.2 × 106, α = 30°, 结构网格, 有限体积, k-ε模型 陈亮中 2010 定常流动, 湍流, f = 6, L = 2.4 m, Re = 6.5 × 106, α = 30°, Ma = 0.25,
结构网格, 有限体积, S-A/k-ω SST模型
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表 10 RSM计算条件描述
研究者 计算条件 Morrison和Panaras 2003 定常流动, 湍流, f = 6, α = 30°, 结构网格, 有限体积, k-ω模型/EASM模型 Liu和Zheng 1998 定常流动/非定常流动, 湍流, 结构多重网格, 有限体积, k-ω模型 Kim和Rhee 2003 定常流动, 湍流, f = 6, Re = 4.2 × 106, α = 10°/20°/30°, 结构网格, 有限体积,
S-A/k-ω/RSM模型, 升力/力矩/压力/切应力Alpman和Long 2005 定常流动, 湍流, f = 6, Re = 6.5 × 106, α = 30°, Ma = 0.1322,
非结构网格, 有限体积, RSM模型, 压力
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表 11 α = 30°, Re = 6.5 × 106, Ma = 0.1322时x/L = 0.738站位的一次分离和二次分离位置对比
RSM求解(Alpman和Long 2005) 实验测量(Kreplin和Vollmers 1985) 一次分离周向位置 105° 108° 二次分离周向位置 159° 156°
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表 12 LES计算条件描述
研究者 计算条件 Hedin和Berglund 2001 定常流动, 湍流, f = 6, Re = 4.2 × 106, α = 10°/20°, 结构网格, 有限体积,
PISO (速度和压力解耦), LESWikstrom和Svennberg 2004 非定常流动, 湍流, α = 20°, 结构网格, 有限体积, LES Alin和Fureby 2005 非定常流动, 湍流, α = 0°, 结构网格(160万), 有限体积, LES, 升力/力矩/压力 Alin和Fureby 2007 非定常流动, 湍流, α = 0°, 结构网格(160万), 有限体积, LES/URANS, 升力/力矩/压力 Farhat和Rajasekharan 2006 定常可压缩流动, 湍流, f = 6, α = 20°, 非结构重网格, 有限体积, 静态LES/动态LES Karlsson和Fureby 2009 定常流动, 湍流, f = 6, α = 20°, 结构网格, 有限体积, RANS/DES/LES, 压力 Ranjan和Menon 2015 定常流动, 湍流, f = 6, α = 10°, 结构网格, 有限体积, 混合双层LES, 压力
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表 13 LES/RANS计算条件描述
研究者 计算条件 Constantinescu和Pasinato 2002 定常流动/非定常流动, 湍流, α = 10°/20°,
非结构网格, 有限体积, S-A DESScott和Duque 2005 非定常流动, 湍流, α = 20°, 结构网格, 有限体积, DES,
升力/力矩/压力/切应力Xiao和Zhang 2007 定常流动, 湍流, f = 6, Re = 6.5 × 106, α = 30°, Ma = 0.25, 结构网格, 有限体积,
S-A DES/B-L DES, 压力/切应力于向阳和刘巨斌 2011 定常流动, 湍流, f = 6, α = 20°, 非结构网格, 有限体积, SIMPLE算法,
S-A DES/k-ω SST DES胡偶和赵宁 2017 定常流动, 湍流, f = 6, Re = 4.2 × 106, α = 20°,
Ma = 0.135, 结构网格, 有限体积, k-ω SST DES, 压力/速度/切应力
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表 14 分离点、再附点位置的计算结果比较
位置 S1/(°) R2/(°) S2/(°) 实验值(Wetzel和Simpson 1998a) 114.9 — 147.2 计算值(Xiao和Zhang 2007) 110.6 134.5 140.0 计算值(胡偶和赵宁 2017) 112.7 133.4 148.6
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表 15 非定常机动计算条件描述
研究者 计算条件 Taylor和Arabshahi 1995 非定常流动, 湍流, f = 6, 结构网格, 有限体积, 人工压缩, B-L Rhee和Hino 2002 非定常流动, 湍流, 结构网格, 有限体积, 人工黏性, 时间后差, S-A Kotapati-Apparao和Squires 2003 定常流动/非定常流动, 湍流, 非结构网格, 有限体积, DES, 压力/切应力 温功碧和陈作斌 2004 定常流动, 湍流, f = 6, α = 0° ~ 20°, 结构网格, 有限体积 熊英 2019 定常流动/非定常流动, 湍流, f = 6, L = 0.15 m, Re = 1.0 × 104/4.2 × 106, α = 45°,
结构网格, 有限体积
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表 16 超临界转捩时不同站位的二次分离的周向角(Panzer和Simpson 1995)
Re/106 转捩带 增湍网 来流湍流度 x/L = 0.389 x/L = 0.50 x/L = 0.611 2.8 无 29.5目 2.55% 142° 130° 118° 2.8 无 65.5目 1.84% 144° 138° 128° 4.2 无 无 0.03% 144° 135° 130° 2.8 有 无 0.03% 141° 130° 118°
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