RESEARCH ON AERODYNAMIC INTERFERENCE BETWEEN TWO ARCH RIBS WITH RECTANGLE CROSS SECTIONS
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摘要: 以某拱桥为例,通过数值模拟研究了串列双矩形拱肋的气动干扰效应,及其对两截面气动力系数的影响。在对计算模型进行验证的基础上,进一步研究了截面宽高比、间距比和来流风攻角对拱肋周围流场的影响,并结合压力云图和湍动能云图解释了气动力系数的变化规律,讨论了不同宽高比截面的漩涡脱落频率与结构自振频率之间的关系,分析了两拱肋升力时程的差异对整体扭矩可能产生的增大效应。结果表明:串列拱肋间的气动干扰效应显著。受上游截面尾流的影响,下游截面的阻力系数明显减小,其值与漩涡的形态、能量大小、移动轨迹等因素密切相关。上、下游截面的升力时程在幅值和相位上存在明显差异,导致拱肋整体的力矩增大,其效应随宽高比或间距比的增大而明显加强,随风攻角的增大而有所降低。漩涡脱落频率随宽高比的增大呈先增大后减小的趋势,而受间距比、风攻角的影响有限。对漩涡脱落频率与宽高比的变化进行多项式拟合,结合结构的模态频率可为拱肋的气动外形设计提供参考。Abstract: Taking an arch bridge as the example, the aerodynamic interference between two rectangular arch ribs in tandem arrangement and the effect on the aerodynamic coefficients of the cross sections are studied by numerical simulations. After checking the reliability of the numerical models, the flow fields are simulated around the arch ribs with different aspect ratios, spacing ratios, and angles of attack. The variations of the aerodynamic coefficients are explained based on pressure contours and turbulent kinetic energy contours. The relationships are discussed between the vortex shedding frequencies with different aspect ratios and the structural modal frequencies. The differences of the lift time series are also analyzed between the two arch ribs, which may increase the whole torsional moment. The results show that the aerodynamic interference is significant between the two arch ribs in tandem arrangement. In the wake of the upstream one, the drag coefficient of the downstream one largely decreases, which is closely related to the form, to the vorticity, and to the motion trail of the vortices. The contrast of the lift time series of the two cross sections shows the differences in amplitude and phase. As a result, the whole torsional moment increases, which is significantly enhanced with the increase of aspect ratio or of spacing ratio, while slightly weakened with the increase of attack angle. The vortex shedding frequency increases first and then decreases with the increase of aspect ratio, while it is less affected by the spacing ratio and by the attack angle. The variation of the vortex shedding frequency versus the aspect ratio is fitted by a polynomial and the structural modal frequencies are compared, which provides a reference for the aerodynamic configuration design of the arch.
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表 1 计算断面参数取值
Table 1. Parameters of section for calculation
计算区域参数 变高度模型 变间距模型 C=b/h C=d/b b/m 3 3 3 3 3 h/m 3.0~4.0 5.0~7.5 8.6~10 20 3.3 C 1~0.75 0.6~0.4 0.35~0.3 0.15 1~15 L1/m 25b 30b 40b 50b 25b L2/m 60b 100b 120b 150b 60b−(23.5−d) d/m 23.5 23.5 23.5 23.5 3~45 H/m 50h 50h 50h 50h 50h 表 2 单个矩形阻力系数CH验证结果
Table 2. CH verification of single rectangle
宽高比b/h=0.9矩形 宽高比b/h=1方形 网格数量 时间步长t/s CH 相对本文采用误差/(%) CH CH参考值, 雷诺数Re/(×104) 51 400 0.01 2.23 8.3 1.99(Re=3×106) 2.00[15]2.21, 2.2[2]2.00, 8[5]2.10, 69[16]2.04~2.05,30~350[17]2.2, 2.2[18]1.97, 0.3[19]2.1, 2.14[20] 139 800 2.06 − 196 000 2.08 1.0 285 000 2.10 1.9 139 800 0.005 2.11 2.4 0.01 2.06 − 0.05 1.98 3.9 0.1 1.81 12.1 规范取值[15] 2.06 0.0 注:带下划线的网格数量和时间步长为本文采用计算参数。 表 3 串列矩形阻力系数CH验证结果
Table 3. CH verification of tandem rectangle
宽高比b/h=0.9 网格数量 上游CH 下游CH 上游CH误差/(%) 下游CH误差/(%) 时间步长0.01 s 224 300 2.01 0.77 0.5 15.4 275 368 2.02 0.91 − − 315 975 2.00 0.94 1.0 3.3 338 300 1.99 0.89 1.5 2.2 b/h=0.9 时间步长/s 上游CH 下游CH 上游CH误差/(%) 下游CH误差/(%) 网格数量275 368 0.005 2.04 0.89 1.0 2.2 0.01 2.02 0.91 − − 0.05 1.64 0.83 18.8 8.8 0.1 1.69 0.73 16.3 19.8 注:带下划线的网格数量和时间步长为本文采用计算参数。 表 4 力矩系数均方根值RMS和K值随宽高比b/h的变化
Table 4. RMS moment coefficient and K versus b/h
高度h /m 宽高比b/h 串列矩形RMS K值 上游 下游 整体 20.00 0.15 15.2 8.4 34.3 1.5 10.00 0.30 2.2 1.0 9.2 2.9 8.57 0.35 1.5 0.9 13.1 5.6 7.50 0.40 0.9 0.4 16.8 12.2 6.60 0.45 0.7 0.4 19.0 18.2 6.00 0.50 0.7 0.4 19.4 18.3 5.45 0.55 0.6 0.4 18.7 20.7 5.00 0.60 0.4 0.2 17.8 30.4 4.00 0.75 0.2 0.1 14.3 46.4 3.33 0.90 0.1 0.1 9.9 50.1 3.00 1.00 0.1 0.1 11.4 50.5 表 5 串列矩形力矩系数均方根值RMS和K值随间距比d/b的变化
Table 5. RMS moment coefficient and K versus d/b
间距d/m 间距比d/b 串列矩形RMS K值 上游 下游 整体 3.0 1.00 0.0 0.1 0.9 7.7 6.3 2.10 0.0 0.1 1.0 8.0 6.6 2.20 0.1 0.3 3.7 9.7 6.9 2.30 0.1 0.3 3.9 9.9 7.2 2.40 0.1 0.2 3.5 9.8 9.0 3.00 0.1 0.2 3.1 11.1 18.0 6.00 0.1 0.1 5.1 24.0 23.5 7.83 0.1 0.1 9.9 50.1 27.0 9.00 0.1 0.1 11.2 65.3 36.0 12.00 0.1 0.1 10.6 54.4 45.0 15.00 0.1 0.1 14.0 75.2 表 6 串列矩形力矩系数均方根值RMS和K值随风攻角的变化
Table 6. RMS moment coefficient and K versus wind attack angle
风攻角/(°) b/h=0.75 b/h=0.60 b/h=0.45 RMS K值 RMS K值 RMS K值 上游 下游 整体 上游 下游 整体 上游 下游 整体 0 0.23 0.07 14.23 46.35 0.43 0.15 17.79 30.38 0.68 0.37 19.05 18.18 3 0.19 0.05 10.01 41.42 0.42 0.17 17.46 29.34 0.67 0.27 18.24 19.42 5 0.20 0.15 14.12 40.14 0.40 0.21 17.59 28.67 0.67 0.30 16.91 17.36 7 0.23 0.09 13.44 42.77 0.42 0.18 18.03 30.43 0.68 0.26 18.25 19.43 10 0.19 0.05 10.06 41.37 0.42 0.18 17.02 28.49 0.74 0.40 18.57 16.40 12 0.19 0.06 10.35 41.28 0.40 0.21 17.09 27.94 0.84 0.35 18.21 15.21 -
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