柔性附属结构对5꞉1矩形柱体气动特性的影响

柔性附属结构对 5꞉1 矩形柱体气动特性的影响 Effects of flexible accessory structure on aerodynamic characteristics of a 5꞉1 rectangular cylinder 1 first-author 1 2 1 corresp 李欢，博士，讲师，从事桥梁风工程及风致振动控制研究；E-mail：lihuan2016@csu.edu.cn 李欢，博士，讲师，从事桥梁风工程及风致振动控制研究；E-mail：lihuan2016@csu.edu.cn lihuan2016@csu.edu.cn 1 1 3 中南大学 土木工程学院，湖南 长沙，410075 中南大学 土木工程学院，湖南 长沙，410075 School of Civil Engineering, Central South University, Changsha 410075, China School of Civil Engineering, Central South University, Changsha 410075, China 中南大学 高速铁路建造技术国家工程实验室，湖南 长沙，410075 中南大学 高速铁路建造技术国家工程实验室，湖南 长沙，410075 National Engineering Laboratory for High Speed Railway Construction, Central South University,Changsha 410075, China National Engineering Laboratory for High Speed Railway Construction, Central South University,Changsha 410075, China 中铁大桥勘测设计院集团有限公司，湖北 武汉，430056 中铁大桥勘测设计院集团有限公司，湖北 武汉，430056 China Railway Major Bridge Reconnaissance & Design Institution Co. Ltd., Wuhan 430056, China China Railway Major Bridge Reconnaissance & Design Institution Co. Ltd., Wuhan 430056, China 陈灿华 为了研究柔性附属结构对5꞉1矩形柱体气动特性的影响，采用烟线法对矩形柱体的分离再附流动进行可视化研究。通过改变雷诺数 Re 、风攻角 α 等参数，对矩形柱体进行测压试验。研究结果表明：柔性附属结构对矩形柱体绕流产生气动干扰作用，且随着 Re 增加，干扰作用更加明显；随着 Re 增加和 α 发生改变，柔性附属结构拍动形态主要包括稳定变形、尖部轻微摆动、中上部大幅度摆动、整体剧烈拍动、拍动并撞壁共5种；柔性附属结构可降低阻力系数，最大降幅为13.6%；柔性附属结构可降低升力系数，降低幅度与 Re 有关；矩形柱体受到的扭矩绝对值与单柱体时相比显著减小，最大降幅为98.5%。 In order to study the effect of flexible accessory structure on aerodynamic characteristics of a 5꞉1 rectangular cylinder, the smoke-wire method was used to visualize the separation and reattachment flow of rectangular cylinder. The pressure test of rectangular cylinder was carried out by changing the Reynolds number Re and the angle of attack α . The results show that the flexible structure has aerodynamic interference effect on the flow around the rectangular cylinder, and the interference effect becomes more obvious with the increase of Re . With the increase of Re and the change of α , the flapping patterns of flexible accessory structures mainly include stable deformation, slight swing of tip, large swing of middle and upper part, strong flapping of the whole, flapping and wall collision. The flexible structure can reduce the drag coefficient by 13.6%. The flexible structure can reduce the lift coefficient, which is related to Re . The absolute torque of rectangular cylinder is significantly reduced compared with that of single cylinder, and the maximum reduction is 98.5%. 柔性附属结构 矩形柱体 气动特性 flexible accessory structure rectangular cylinder aerodynamic characteristics 对矩形柱体的分离再附流动和气动特性的研究是流体力学的研究热点 [ 1 1 ] 。宽高比为5꞉1的BARC模型(Benchmark on the aerodynamics of a rectangular 5꞉1 cylinder)是研究矩形柱体绕流的基本模型。研究者采用BARC模型开展了一系列风洞试验 [ 2 2 ] 和数值模拟研究 [ 3 3 - 5 5 3-5 ] ，这些结果为研究大跨扁平箱梁气动特性提供了重要参考。BRUNO等 [ 6 6 ] 系统总结了攻角 α =0°时BARC模型的气动特性，发现其近尾流、风压系数 C P 以及阻力系数 C D 对来流条件不敏感，而其侧面流动特征、脉动升力 <math id="M1"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">L</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678518&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678516&type= 4.06400013 4.06400013 等对来流条件或数值模拟参数设置非常敏感。WU等 [ 7 7 ] 通过大涡模拟和测压试验发现BARC模型两侧剪切流对 α 非常敏感，当 α 为0°~15°时，下表面分离流会发生再附，且再附长度随 α 增加而减小，而上表面分离泡随 α 增加而增大。RICCIARDELLI [ 2 2 ] 通过风洞试验研究了振动自由度和折减风速对BARC模型气动压力和力在展向相关性上的影响，发现相关性不仅受振动幅度的影响，而且受振动形式、自由度等影响。为改变钝体绕流和旋涡脱落，常用的控制方法包括主动控制法(需要外部能量输入)和被动控制法(无外部能量输入)两大类 [ 8 8 ] 。主动控制法主要包括：采用电磁激励等离子体法控制边界层分离以影响回流再附区域 [ 9 9 ] ；通过产生二次流控制尾流涡脱以抑制涡激振动 [ 10 10 ] ；通过热效应改变流体动力黏度和密度来影响边界层分离 [ 11 11 ] 等。被动控制法主要包括：改变表面粗糙度以影响边界层速度剖面分布从而控制边界层分离点 [ 12 12 - 13 13 12-13 ] ；改变局部外形(添加整流罩 [ 14 14 ] 、壁面开槽 [ 15 15 ] 、布置风屏障 [ 16 16 ] 、边角处理 [ 17 17 ] 等)以影响流动分离再附等。主动控制法需要外部能量输入，常给工程带来不便。被动控制法仅在某一风速或攻角范围内有效，在其他工况下可能会劣化抗风性能 [ 18 18 ] 。 而自然界中，鱼类 [ 19 19 ] 、树木 [ 20 20 ] 等在应对急流、强风时，会通过改变形状以获得更强的驱动力或减少所受风阻力。自然界柔性生物体为人们有效控制钝体绕流和旋涡脱落提供了新思路。柔性结构由于具有柔软、灵活、阻力小、可自适应变形 [ 21 21 - 22 22 21-22 ] 等优点，在翼型失速控制 [ 23 23 ] 、管道内强化散热 [ 24 24 ] 、强化射流混合 [ 25 25 ] 、能量收集 [ 26 26 ] 等方面已得到成功应用。WANG等 [ 27 27 ] 通过实验研究了仿生羽毛襟翼对翼型升力的控制效果，在一定迎角下羽毛襟翼可显著提高升力，最高提升186%。虽然已有不少工程领域应用了柔性结构，但目前很少有学者研究柔性附属结构对矩形柱体的气动特性的影响。为此，本文作者首先采用烟线法对5꞉1矩形柱体的分离再附流动进行流动可视化研究，通过测压试验，改变雷诺数 Re 、攻角 α 等参数系统研究柔性附属结构对矩形柱体气动特性的影响。 1 试验测试 1 1.1 　试验装置 2 进行烟线流动可视化和测压2种试验，分别在2个试验段进行，各自使用单独的试验模型。烟线流动可视化试验在中南大学小风洞实验室进行，试验段宽×高为0.45 m×0.45 m。试验模型为矩形柱体，其宽×高×长为0.15 m×0.03 m×0.45 m(高与宽之比为5꞉1)，模型位于流场中心线位置。流动可视化试验通过人工转动的方式改变攻角，采用角度测量仪校验，精度为0.1°。采用航华烟线仪，人工释放烟线，并使用佳能相机连拍模式拍照，挑选带有清晰完整流场结构的试验照片。 测压试验在中南大学风洞实验室高速试验段 [ 28 28 ] 进行，试验段宽×高为3 m×3 m，湍流度≤0.5%，风速可调节范围为4~92 m/s。测压试验模型为矩形柱体，其宽×高×长为0.5 m×0.1 m×1.8 m(宽与高之比为5꞉1)，模型位于流场中心线位置，固定在刚性抱杆上。试验装置如 图1 图1 所示。 图1 图1 中， F L 为升力， F D 为阻力， M 为扭矩， B 为模型宽度， D 为模型高度。测压试验通过电机调整 图1 图1 (b)中转盘来改变攻角，精度为0.01°。采用PSI公司的DTCnet ESP-64HD压力扫描阀系统进行测压试验，采样频率约为333.5 Hz，采样点为20 000个。试验风速变化范围为10~20 m/s，对应 Re 范围为6.99×10 4 ~1.40×10 5 。试验 α 在0°~20°范围内变化，对应的阻塞度变化范围为2.0%~5.3%，符合BARC基准 [ 6 6 ] 的试验要求。 (a) 试验测试示意图；(b) 试验模型 矩形柱体模型采用铝合金芯梁作为支撑，外包ABS板，在中间截面布置70个测压孔。测压孔外径为2 mm，通过测压管与扫描阀连接，测压管内径为0.8 mm，管长为350 mm。测压孔布置如 图2 图2 所示。在模型两端安装端板，以保证绕流为二维流动。将柔性附属结构放置在矩形柱体模型顶部表面，在前缘和后缘处各放置1列，高度为0.2 D ( D 为模型高度， D =0.1 m)，长度等于试验模型的长度，材质为聚乙烯塑料薄膜，厚度为0.06 mm，密度为0.92 g/cm 3 。 1.2 　数据处理 2 根据公式 <math id="M2"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">2</mn><mo stretchy="false">(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>P</mi></mrow><mrow><mi mathvariant="normal">∞</mi></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mo stretchy="false">(</mo><mi>ρ</mi><msubsup><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">∞</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678577&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678576&type= 32.93532944 4.82600021 计算每个测点 i 的风压系数 <math id="M3"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678592&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678580&type= 4.48733330 3.72533321 (其中， <math id="M4"><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678604&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678594&type= 3.21733332 3.72533321 表示压力扫描阀测量的第 i 个测点的风压； i 为测点序号， i =1~70； <math id="M5"><msub><mrow><mi>P</mi></mrow><mrow><mi mathvariant="normal">∞</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678618&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678609&type= 4.14866638 3.72533321 和0.5 <math id="M6"><mi>ρ</mi><msubsup><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">∞</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678616&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678622&type= 6.60400009 4.82600021 分别表示风洞实验室试验段的静止风压和来流动风压，由放置在试验段内的皮托管测得； <math id="M7"><mi>ρ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678636&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678626&type= 2.03200006 3.38666677 为空气密度，1.225 g/cm 3 ； <math id="M8"><msubsup><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">∞</mi></mrow><mrow/></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678632&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678630&type= 4.48733330 4.06400013 为来流风速)。 <math id="M9"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678644&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678651&type= 3.89466691 3.72533321 的平均值即为平均风压系数 <math id="M10"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678660&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678647&type= 3.89466691 4.06400013 ， <math id="M11"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678673&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678669&type= 3.89466691 3.72533321 的标准偏差即为脉动风压系数 <math id="M12"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678683&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678675&type= 3.89466691 4.06400013 。皮托管位于模型上游，并连接在扫描阀上。根据风压系数 <math id="M13"><msub><mrow><mi>C</mi></mrow><mrow><mi 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mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></munderover></mstyle><mrow><mfenced separators="|"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi>i</mi></mrow></msub><mo>×</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>×</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>×</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mrow></mfenced><mo>/</mo><msup><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678757&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678751&type= 43.01066971 9.65200043 式中： <math id="M20"><mi mathvariant="normal">Δ</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678762&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678771&type= 5.16466665 3.72533321 为第 i 个测点的积分长度，即离测点最近上游中点与下游中点之间的距离； N 为测点的总数，即70； <math id="M21"><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678784&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678766&type= 2.87866688 4.48733330 为第 i 个测点的压力方向与模型 x 方向的夹角，压力方向指的是来流风作用于试验模型表面时，产生的垂直于模型表面压力的方向； <math id="M22"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678790&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678786&type= 1.94733346 2.62466669 为模型与来流方向夹角； D 为模型的高度，本文取0.1 m； B 为模型的宽度，本文取0.5 m； <math id="M23"><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678782&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678793&type= 2.62466669 3.72533321 和 <math id="M24"><msub><mrow><mi>y</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678816&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678799&type= 2.79399991 4.48733330 分别为测点 i 的几何横坐标和纵坐标。 2 结果分析 1 2.1 　流动可视化结果 2 图3 图3 所示为无柔性附属结构时矩形柱体的绕流，包括模型表面绕流烟线图和尾迹烟线图。对不同 α 下烟线流动可视化结果进行分析可以发现：模型顶部表面的分离泡随着 α 增加而变厚增大，迎风面上的前驻点由中间位置逐渐向底部表面方向移动，顶部表面的后驻点逐渐向下游移动，而下游的尾流宽度逐渐变大；模型底部表面的分离泡随着 α 增加而变薄缩小，底部表面的后驻点逐渐向上游移动直至消失，且当 α ≥18°时，流线几乎平行于模型底部表面，分离泡几乎消失。 攻角 α /(°)：(a) 0；(b) 2；(c) 4；(d) 6；(e) 8；(f) 10；(g) 12；(h) 14；(i) 16；(j) 18；(k) 20 图4 图4 所示为有柔性附属结构的矩形柱体的绕流情况，包括4种典型的 α (0°、6°、12°和20°)和4种典型的 Re (5 465、8 766、11 951和15 313)，共计16张烟线图。从烟线图可以看出：柔性附属结构对矩形柱体绕流产生气动干扰作用，且随着 Re 增大，干扰作用更加明显，会明显加剧矩形柱体上方气流同顶部表面分离再附流动的动量交换，从而改变模型表面的气动特性；相反地，柔性附属结构的干扰作用随着 α 增加而减弱，在0°攻角时，随着 Re 增加，柔性附属结构拍动形态主要包括稳定变形、尖部轻微摆动、中上部大幅摆动、整体剧烈拍动、拍动并撞壁共5种，与文献[ 22 22 ]中的形态类似；随着 α 增加，柔性附属结构变得更加“稳定”，在同样的 Re 下，小攻角会整体剧烈拍动，但大攻角可能仅会在中上部大幅度摆动，如在 图4 图4 中攻角为6°和20°、 Re =11 951时，矩形柱体上方分别有剧烈拍动的内卷涡和中上部大幅摆动的摆动涡。相应地，拍动形态也发生了改变。大攻角时，柔性附属结构的整体剧烈拍动更容易发生内卷现象，在攻角为16°和20°、 Re =15 313时，矩形柱体上方存在一系列内卷涡。 (a) α =0°， Re =5 465；(b) α =6°， Re =5 465；(c) α =12°， Re =5 465；(d) α =20°， Re =5 465；(e) α =0°， Re =8 766； (f) α =6°， Re =8 766；(g) α =12°， Re =8 766；(h) α =20°， Re =8 766；(i) α =0°， Re =11 951；(j) α =6°， Re =11 951； (k) α =12°， Re =11 951；(l) α =20°， Re =11 951；(m) α =0°， Re =15 313；(n) α =6°， Re =15 313； (o) α =12°， Re =15 313；(p) α =20°， Re =15 313 2.2 　测试结果验证 2 在无柔性附属结构情况下，在攻角为0°时，平均风压系数和脉动风压系数与文献[ 28 28 ]的试验结果对比见 图5 图5 。从 图5 图5 可见：本文结果与文献[ 28 28 ]的试验结果较吻合，且测压管长度较短，脉动风压衰减较小，因此，本文的脉动风压测量精度较高，能够较好地反映风压脉动情况。 (a) 平均风压系数 <math id="M25"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678840&type= 3.64066648 3.72533321 ；(b) 脉动风压系数 <math id="M26"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678862&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678860&type= 3.64066648 3.64066648 2.3 　柔性附属结构对风压系数 <math id="M27"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678891&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678889&type= 3.89466691 3.72533321 的影响 2 图6 图6 所示为无柔性附属结构在20 m/s(对应 Re =140 000)时，风压系数随 α (0°、2°、4°、6°、8°、10°、12°、16°和20°)的变化关系。从 图6 图6 可以看出： (a) 顶部表面平均风压系数 <math id="M28"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678918&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678901&type= 3.64066648 3.72533321 ；(b) 顶部表面脉动风压系数 <math id="M29"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678917&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678919&type= 3.64066648 3.64066648 ； (c) 底部表面平均风压系数 <math id="M30"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678918&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678901&type= 3.64066648 3.72533321 ；(d) 底部表面脉动风压系数 <math id="M31"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678917&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678919&type= 3.64066648 3.64066648 1) 随着 α 增大，顶部表面 <math id="M32"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679080&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679056&type= 3.89466691 4.06400013 的最大值向下游移动， <math id="M33"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678932&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678951&type= 3.89466691 4.06400013 最大值先增大后减小；在攻角为6°时，下于尾缘上游最近点处( x / D =4.9)， <math id="M34"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678966&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678957&type= 3.89466691 4.06400013 取得最大值0.49；在4°和8°攻角下，于尾缘上游最近点处( x / D =4.9)， <math id="M35"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub><mi mathvariant="normal">'</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678970&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678968&type= 4.82600021 3.72533321 分别为0.39和0.40，于 x / D =4.8处分别为0.30和0.30，近似相等。该现象对应于主涡核心从顶部表面上游往下游移动到尾流，结合 图3 图3 定性分析和风压系数的定量判断，可知在攻角为6°时，主涡核心位于尾缘上方附近。 2) 底部表面 <math id="M36"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679080&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679056&type= 3.89466691 4.06400013 的最大值向上游移动，对应于底部表面分离泡再附点逐渐向上游移动，分离泡缩小，且在攻角为10°时，于底部表面 x / D =2.3处取得最大值 <math id="M37"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678993&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678976&type= 3.89466691 4.06400013 =-0.04；在攻角为12°时，于底部表面 x / D =2.05处取得最大值 <math id="M38"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678995&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678982&type= 3.89466691 4.06400013 =0.02，表明在此攻角时，底部表面受到的正风压作用大于分离泡造成的负压作用。 <math id="M39"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679054&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679036&type= 3.89466691 4.06400013 最大值向上游移动，在攻角为20°时， <math id="M40"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678999&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43678990&type= 3.89466691 4.06400013 沿流线方向波动很小，表示分离泡已很萎缩。 3) 随着 α 增大，迎风面上 <math id="M41"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679052&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679050&type= 3.89466691 4.06400013 的最大值从中心点( x / D =-0.5)向底面方向移动，在攻角为6°时，于底部表面 x / D =-0.4处取得最大值0.99；在攻角为10°时，于底部表面 x / D =-0.3处取得最大值0.99，据风压系数进一步验证烟线图中迎风面上的前驻点由中间位置逐渐向底部表面方向移动；背风面 <math id="M42"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679024&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679004&type= 3.89466691 4.06400013 最大值在6°攻角下取得，可以判断此时主涡核心正处于背风面上方附近。 图7 图7 所示为0.2 D 柔性附属结构在20 m/s(对应 Re =140 000)时，风压系数随 α (0°、2°、4°、6°、8°、10°、12°、16°和20°)的变化曲线。从 图7 图7 可以看出：随着 α 增大，柔性附属结构的气动干扰作用逐渐减弱。从 图7 图7 (a)和 图7 图7 (b)可以看出：随着 α 增大，顶部表面 <math id="M43"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679034&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679039&type= 3.89466691 4.06400013 的最大值向下游移动；在小攻角(0°~6°)下， <math id="M44"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679034&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679039&type= 3.89466691 4.06400013 的最小值位于柔性附属结构( x / D =0)下游的 x / D =0.2处，而柔性附属结构的高度即为0.2 D ，由此可见柔性附属结构的干扰最强点正是其尖部； <math id="M45"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679031&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679021&type= 3.89466691 4.06400013 最大值随攻角增大逐渐减小，在0°攻角下脉动值最大。结合烟线结果分析，其原因是随着 α 逐渐增大，柔性附属结构尖部拍动到柱体顶部表面的撞壁迹线越来越长，因而，在拍向顶部表面时更容易发生内卷，致使拍动带来的风压脉动逐渐降低；除0°攻角外， <math id="M46"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679054&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679036&type= 3.89466691 4.06400013 沿着顶部表面逐渐向下游衰减。这是由于拍动涡在向下游移动时，渐渐远离矩形柱体顶部表面，并逐渐耗散。 图7 图7 (c)和 图7 图7 (d)中底部表面 <math id="M47"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679034&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679039&type= 3.89466691 4.06400013 的最大值向上游移动， <math id="M48"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679054&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679036&type= 3.89466691 4.06400013 最大值向上游移动。 (a) 顶部表面平均风压系数；(b) 顶部表面脉动风压系数；(c) 底部表面平均风压系数；(d) 底部表面脉动风压系数 图8 图8 所示为有、无柔性附属结构在20 m/s(对应 Re =140 000)时，风压系数随 α (0°、4°、8°和16°)变化的对比图(其中，0 D 为无柔性附属结构，0.2 D 为有柔性附属结构)。从 图8 图8 可见：柔性附属结构的拍动导致顶部表面上游区域的 <math id="M49"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679052&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679050&type= 3.89466691 4.06400013 更低，也使得 <math id="M50"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679054&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679036&type= 3.89466691 4.06400013 更高，同时，干扰了顶部表面的分离再附流动；底部表面 <math id="M51"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679080&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679056&type= 3.89466691 4.06400013 的最大值由于受柔性附属结构的影响，整体向上游偏移，但攻角越大，偏移效果越不明显；同样地，底部表面 <math id="M52"><msubsup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679076&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679073&type= 3.89466691 4.06400013 最大值由于受柔性附属结构的影响，整体向上游偏移，但攻角越大，偏移效果越不明显。由于柔性附属结构也安装在背风面与顶部表面交叉的边缘，因此，当攻角较小(0°~8°)时，其在一定程度上阻止了漩涡向尾流移动并耗散部分能量，导致背风面 <math id="M53"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679080&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679056&type= 3.89466691 4.06400013 的绝对值整体减小，而迎风面 <math id="M54"><mover><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679085&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43679083&type= 3.89466691 4.06400013 的绝对值几乎不变，从而减小了柱体的压差阻力 F D 。 (a) 顶部表面平均风压系数；(b) 顶部表面脉动风压系数；(c) 底部表面平均风压系数；(d) 底部表面脉动风压系数 2.4 　柔性附属结构对气动力特性的影响 2 气动力系数随 α 的变化情况见 图9 图9 。从 图9 图9 可见： (a) 平均阻力系数；(b) 平均升力系数；(c) 平均扭矩系数 1) 在0°~10°攻角范围内，柔性附属结构可降低阻力系数，最大降幅为13.6%；当攻角超过10°时，柔性附属结构会略微增加阻力系数。 2) 在0°~8°攻角范围内，柔性附属结构可产生与升力方向相反的下沉力，并降低升力系数，降低幅度与 Re 有关；柔性附属结构有效地干扰了矩形柱体模型顶部表面的分离流动，使得气流分离不再明显。随 α 增大，单独矩形柱体模型升力系数降低不再明显，柔性附属结构使得矩形柱体的升力系数曲线变化更加平稳。 3) 在0°~12°攻角范围内，柔性附属结构明显改变了矩形柱体的扭矩系数，在 Re 足够大时，扭矩系数绝对值趋近于0。特别地，在攻角为6°时， C M =0.001 1，矩形柱体受到的扭矩绝对值比单柱体时的扭矩绝对值显著减小，最大降幅为98.5%。 3 结论 1 1) 柔性附属结构对矩形柱体绕流产生气动干扰作用，且随着 Re 增加，干扰作用更加明显，加剧矩形柱体上方气流同顶部表面分离再附流动的质量交换，从而改变模型表面的气动特性。相反地，柔性附属结构的气动干扰作用随着 α 增加而减弱。 2) 随着 Re 增加和 α 改变，柔性附属结构拍动形态主要包括稳定变形、尖部轻微摆动、中上部大幅摆动、整体剧烈拍动、拍动并撞壁共5种。 3) 在0°~10°攻角范围内，柔性附属结构可降低阻力系数，最大降幅为13.6%。在0°~8°攻角范围内，柔性附属结构可降低升力系数，降低幅度与 Re 有关。柔性附属结构使得矩形柱体的升力系数曲线在“失速”攻角附近的变化更加平稳。 4) 在0°~12°攻角范围内，柔性附属结构明显改变了矩形柱体的扭矩系数，矩形柱体受到的扭矩绝对值比单柱体时的扭矩绝对值显著减小，最大降幅为98.5%。 参考文献 HE Xuhui , LI Huan , WANG Hanfeng , et al . 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Journal of Central South University(Science and Technology), 2023, 54(4): 1603-1612. YIN Yapeng, WANG Hanfeng, LI Huan, et al. Effects of flexible accessory structure on aerodynamic characteristics of a 5꞉1 rectangular cylinder[J]. Journal of Central South University(Science and Technology), 2023, 54(4): 1603-1612. 国家自然科学基金资助项目(52078505) Project(52078505) supported by the National Natural Science Foundation of China 2022-05-10 2022-06-25 2023-04-26 2023-05-22 37690950 中南大学学报(自然科学版) 4 54