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Pressure Distribution and Global Forces on a Bridge Deck Section:Experimental and CFD Analysis of Static Aerodynamic Forces 桥面板上的压力分布和整体力:静动力分析 Two different experimental approaches for the e

valuation of a bridge deck’s stationary aerodynamic forces are studied in this paper :both wind tunnel measurement of global force and pressure distribution are evaluated on deck sectional models. Advantages and drawbacks of these different approaches are discussed using the results obtained on a simple deck section ,specifically chosen to compare the differences of methods.Two-dimensional computation fluid dynamics(CFD)simulations have been performed to provide an insight into the differences of the aerodynamic forces measured with the two methods. Specifically, the effect of shear stresses , measurement discretization , and axial correlation of pressures are addressed. In CFD analysis, several turbulence models are tested and discussed using Reynolds-averaged Navier-Stokes(RANS) equations. DOI:10.1061/(ASCE)BE.1943-5592.0000695. 对于桥面静止空气动力研究了本文的评价两种不同的实验方法: 全球性力量和压力分布的两 个风洞测试都在桥面的断面模型上进行评估。 这些不同的方法使用一个简单的桥面部分获得 的结果进行讨论优点和缺点,特别是选择比较的方法的差异。二维计算流体动力学( CFD) 模拟已经执行,以提供深入了解与两种方法测得的空气动力的差异。具体而言,剪切应力, 测量离散化和轴向压力的相关性的效果得到解决。在 CFD 分析,一些湍流模型进行了测试 和使用雷诺平均纳维 - 斯托克斯(RANS)方程的讨论。 Author Keywords : Pressure distribution; Dynamometric balance; Reynolds-averaged Navier-Stokes(RANS)models; Computation fluid dynamics(CFD); Static aerodynamic forces; Bridge deck section; Wind tunnel testing. 关键词: 压力分布;测力天平;雷诺平均纳维 - 斯托克斯 (RANS) 模型;计算流体动力学 (CFD) ; 静态空气动力;桥面部分;风洞测试。 Introduction 介绍 Three different approaches can be adopted for the evaluation of the aerodynamic forces of bridge decks: measurement of global forces, measurement of pressure distribution, and computational fluid dynamics (CFD) analysis. Each of these approaches has its benefits and drawbacks. On the one hand, if experimental methods are considered, the knowledge of pressure distributions is important to understand the underlying physics of the fluid-structure interaction, but it is not applicable to estimate global force coefficients if traffic barriers, railings, or wind shields are present. In this case, the only practicable way is to measure global forces with dynamometric models. On the other hand, CFD simulations are not reliable unless they are validated against experimental data and are therefore used as a complementary tool to assess the experimental results and eventually to perform some numerical aerodynamic tailoring before a final check in the wind tunnel. 三种不同的方法可用于桥梁断面的气动力的评价: 全球力量测量、 压力分布测量和计算流体 动力学 MIC(CFD)分析。每一种方法都有它的好处和缺点。另一方面,如果考虑到实验方 法、压力分布的知识是重要的理解三维基础物理的流体-结构相互作用,但它是不适用于估 计全球力系数,如果交通障碍,栏杆,或风盾是本。在这种情况下,第唯一可行的方法是用 测力模型测量的全球力量。另一方面,计算流体力学模拟是不可靠的,除非他们是对实验数 据进行验证,因此,美国 SED 作为辅助性的工具来评估实验结果和最终执行一些气动数值 裁剪在风洞中的最后一个检查。

In light of these considerations, the present research aims to compare the first two approaches for the evaluation of the static (stationary) aerodynamic forces on a simple deck section without barriers. Experimental aerodynamic forces are measured in wind tunnels both by using a dynamometric balance and by integrating the pressure distribution along the contour of the deck section; the results are then compared. A CFD analysis is then used as a complementary tool to analyze the differences between the two experimental measurement systems. 鉴于这些考虑,本研究的目的是为静态(固定)空气动力的评价前两种方法在一个简单的甲 板部分无壁垒比较。 试验气动力是在风洞中都使用一个测力计平衡并通过整合沿甲板部分的 轮廓的压力分布测量;结果进行比较。然后,CFD 分析被用作补充工具来分析两个实验测量 系统之间的差异。 Concerning CFD, several authors reported that, for bridge decks, three-dimensional (3D) models considering detached eddy simulations (DES) or large eddy simulations (LES) provide more accurate results than two-dimensional (2D) Reynolds-averaged Navier-Stokes (RANS) simulations (Watanabe and Fumoto 2008; Watanabe et al. 2004; Bai et al. 2010; Sarwar et al. 2008; Mannini et al. 2010). In this study, however, a 2D RANS approach is adopted for its low computational cost, with the objective of using the numerical results as a tool for the evaluation of the measurement errors induced by both tap discretization and the lack of shear-stress effects. In the numerical analysis, several turbulence models for the RANS equations are analyzed. The deck section aerodynamics are investigated comparing the modification of the pressure distribution and the corresponding global forces at different angles of attack. Different considerations can be done for different angles of attack because of the different flow field structure around the section and in particular because of the presence of flow separation and the effects of shear stresses. 关于 CFD,几位作者报告说,对于桥面,考虑分离涡模拟(DES)或大涡模拟三维(3D)模 型(LES)提供更准确的结果比二维(2D)雷诺平均纳维 - 斯托克斯(RANS)模拟(渡边和 2008 年麓; Watanabe 等人 2004;白重恩等人,2010 年;萨瓦尔等人 2008;曼尼尼等 2010) 。在 这项研究中,然而,一个二维 RANS 方法被采用是因为它的低计算成本,在使用数值计算结 果, 作为由两个抽头离散和缺乏剪切应力作用引起的测量误差的评估的工具的目标。 在数值 分析, 为雷诺平均方程的几个湍流模型进行了分析。 断面部分的空气动力学进行了研究比较 的压力分布的变形,并在攻击的不同角度相应的全局的力。不同的考虑可以做到,因为周围 的部分不同的流场结构的攻击的不同角度和特别是因为流动分离的情况下和剪切应力的作 用。 Ricciardelli and Hangan (2001) compared experimental pressure distributions and aerodynamic forces on a different simplified deck section and found some discrepancies between the results of the two measurement methods. The larger differences concern the drag coefficient, but these discrepancies are not deeply investigated because the aim of their paper was not the comparison of the two different measurement approaches. In this study, using a different simplified deck section specifically chosen for this purpose, similar discrepancies are obtained and discussed, with the support of experimental and numerical results. Ricciardelli 和 Hanggan(2001 年)相比,在不同的简化的甲板部分实验压力分布和空气动力 和发现的两种测量方法的结果之间存在一些差异。 较大的分歧涉及风阻系数, 但这些差异没 有深入的研究,因为他们的文章的目的是不是两种不同的测量方法的比较。在这项研究中, 采用专门选择用于此目的的不同简化甲板部分, 得到了讨论类似的差异, 与之相配套的实验 和数值结果。

The results presented in this paper, focused on the evaluation of stationary aerodynamic forces, are part of a larger research project aimed at validating the postprocess of the dynamometric measurements during forced and free-motion tests (Diana et al. 2004). In particular, it is important to assess the dynamic performances of the dynamometric measurement systems to correctly measure self-excited nonstationary forces during aeroelastic tests on suspended section models. Such tests are necessary to validate 2D aerodynamic force models, especially when aerodynamic nonlinearities are investigated (Diana et al. 2013, 2008, 2010). In fact, direct dynamometric force measurements give the sum of the aerodynamic and inertial contribution as a result, whereas a pressure system only allows the measurement of aerodynamic effects. In stationary conditions the inertial effects are not present, and the direct dynamometric measurement is taken as a reference to investigate the critical aspects of distributed pressure measurements. The analysis of experimental aerodynamic forces in nonstationary aeroelastic conditions has been presented in Argentini et al. (2012), and a CFD investigation will be presented in a future paper. 在本文中,专注于固定空气动力的评价呈现的结果,是一个更大的研究项目,目的是在强迫 和自由运动试验验证测力测量的后处理(戴安娜等,2004)的一部分。特别是,它以评估测 力测量系统的动态性能期间暂停部分型号的气动弹性测试来正确地测量自激非平稳力是重 要的。这样的检查是必要的,以验证气动 2D 力模型,尤其是在空气动力学非线性进行了研 究(戴安娜等人。2013 年,2008 年,2010 年) 。事实上,直接测力力测量得到的结果的气 动和惯性的贡献的总和, 而压力的系统只允许的空气动力效应的测定。 在静止的条件下的惯 性效应不存在,并直接测力测量时作为参考,以调查分布式压力测量的关键方面。在非平稳 气动弹性条件下试验气动力的分析是 argentini 等人提出的。 (2012) ,和 CFD 的调查将在后 面的文章呈现。 This paper is structured as follows. The characteristics of the experimental setup are summarized, with a specific focus on the force measurement devices, pointing out the assumptions and the hypothesis adopted. Then, a critical analysis of the experimental results is presented, highlighting the differences that emerged from the two different measurement systems. Discrepancies between the results are then investigated by means of a 2D CFD RANS analysis using a commercial code. The CFD results and model settings are described: geometry, mesh, boundary conditions, and turbulence models. Numerical results are used to assess experimental results. Finally, conclusions and final remarks are presented. 本文的结构如下。实验装置的特点进行了总结,并特别注重力测量装置,指出假设和假设采 用。 然后, 对实验结果的一个关键的分析提出, 强调来自两个不同的测量系统中出现的差异。 结果之间的差异,然后通过使用商业码二维 RANS CFD 分析方法研究。 CFD 的结果和模式设 置描述:几何,网格,边界条件和湍流模型。数值结果用于评估实验结果。最后,结论和最 后发言介绍。

Wind tunnel tests 风洞试验 Wind tunnel tests were performed at the Wind Tunnel of Politecnico di Milano. A single-box deck section with a simple shape was chosen to perform the desired tests. The deck shape is taken from an actual highway bridge, neglecting the traffic barriers on the upper surface (Fig. 1). This simplification allows the measurement of the aerodynamic forces directly through the integration of the pressure distribution (Ricciardelli and Hangan 2001), considering the contribution of shear stresses as negligible. The deck section model is 2.91 m long and 1 m wide. The geometry and main dimensions are reported in Fig.?1. The wind tunnel blockage is less than 1%, whereas the residual turbulence intensities in the vertical and horizontal directions are, respectively, 风洞试验是在米兰理工大学的风洞中进行。 一个简单形状的一个单一的方块截面部分, 以执 行所需的测试。截面形状从实际的公路桥梁采取,忽略在上表面的交通障碍(图 1) 。这种 简化允许气动力的测量直接通过压力分布(Ricciardelli 和 2001 Hanggan)的整合,考虑可忽 略的剪切应力的贡献。 截面部分模型长 2.91 米, 宽 1 米。 几何形状和主要尺寸示于 (图 1) 。 风洞堵塞小于 1%,而在垂直和水平方向的残留湍流强度分别是-----The dynamometric measurement system is mounted in the central part of the sectional model (0.91 m long) and consists of a set of seven load cells that are able to measure the force and moment components (Diana et al. 2004). The pressure measurement system consists of a ring of 78 pressure taps placed around the middle section of the model (Fig. 2), which are connected to high-frequency pressure scanners, allowing for a sampling frequency of 100 Hz. Sixteen additional pressure taps are distributed along four lines (correlation lines) aligned with the deck axis (see open diamonds in Fig. 2). To measure the pressure correlation in the axial direction, two are in the upper part and two are in the lower part. The distribution of the pressure taps was studied to refine the measurement where a strong pressure gradient was expected. Pressure measurements are performed simultaneously with the global force measurements obtained by internal balance. 该测力测量系统被安装在截面模型的中心部分 (0.91 米长) 和由一组能够测量的力和力矩部 件 7 负载细胞(黛安娜等,2004)的。压力测量系统由周围放置模型(图 2) ,它们被连接 到高频压力扫描器的中间部分 78 压抽头的一环,允许 100Hz 的采样频率。另外 16 个测压 口连同甲板轴(请参阅 open 钻石图 2)排列的四线(对比线)分布。为了测量在轴向方向 上的压力的相关性,二是在上部和两个都在下部。测压孔的分布进行了研究,以改进,其中 一个强大的压力梯度预计测量。压力测量与内部均衡所获得的全球性力量的测量同时进行。 The incoming wind is measured one chord upwind from the leading edge by means of a four-hole probe that resolves the instantaneous vertical and horizontal wind components. A photograph of the experimental setup is given in Fig. 3. 来风通过解析瞬时垂直和水平风分量的四孔探针的装置测量的一个和弦逆风从前缘。 实验装 置的照片示于图 3。 Experimental Aerodynamic Coefficients and Pressure Distributions 实验气动系数和压力分布 Static aerodynamic drag, lift, and pitching moment coefficients are expressed as 静态空气阻力,升力和俯仰力矩系数表示为

where ρ = air density; U= mean wind horizontal velocity; B = deck chord; D, L, and M = mean lift force, drag force, and pitching moment per unit length, respectively; and θ = angle of attack. Sign conventions for forces and pitch rotation are shown in Fig. 4. 在ρ =空气密度;U =平均水平风速;B 截面和弦;D,L,M =平均升力、阻力和俯仰力矩的 单位长度,和θ =迎角。符号转换力和俯仰旋转符号如图 4 所示。 Aerodynamic forces D, L, and M are obtained either from the measurement of the load cells or from the integration of the pressure distribution, assigning a tributary area to each pressure tap. In general, Reynolds number dependence should be considered (Hui et al. 2008). In the following, the Reynolds number is kept constant at 7×1057×105 (R=UB/ν ,R=UB/ν , U=10 m/s,U=10 m/s). 气动力 D,L,和 M 或者从负载小区的测量,或从压力分布的积分获得,分配的支流区域到 每个压力抽头。在一般情况下,雷诺数依赖性,应考虑(惠等人,2008) 。在下文中,雷诺 数为 7×1057×105 保持恒定(R = UB /ν ,R = UB /ν ,U= 10 米/秒,U =10 米/秒) 。 Fig. 5 shows the aerodynamic coefficients as a function of the angle of attack. The following considerations can be done: the drag coefficient is underestimated by the pressure integration for negative angles of attack; or the lift and moment coefficients show a good agreement, but a slightly different slope of the coefficients is noticed. The lift coefficient from the pressure integration has a smaller slope, whereas the moment coefficient has a larger slope. These results are coherent with those found by Ricciardelli and Hangan (2001) for the Sunshine Skyway Bridge deck section. 图 5 展示出了气动力系数作为迎角的功能。 可以做以下考虑: 阻力系数由压力集成负迎角低 估;或升力和力矩系数显示出良好的协议,但略有不同的系数的斜率注意。来自压力积分升 力系数具有较小的斜率,而力矩系数具有较大的斜率。这些结果是一致的与那些 Ricciardelli 和 Hanggan(2001)发现的阳光高架桥桥面部分。 Comments about these results need a more accurate understanding of the flow-structure interaction mechanism. The knowledge of pressure distributions as a function of the angle of attack, shown in Figs. 6 and 7, provides a basis for this analysis. Pressure coefficients, Cp , defined as p/(1/2ρ U2)p/(1/2ρ U2), are shown as arrows normal to the deck surface that are pointing outward if pressure p is negative (suction); however, they point inward if p is positive. 对这些结果的意见所需要的流结构相互作用机制的一个更准确的了解。 压力分布作为迎角的 函数的知识, 如图 6 和 7, 提供了用于此分析的基础。 压力系数, CP, 定义为 P / (1 /2ρ U2) P /(1 /2ρ U2) ,如果压力 p 为负(抽吸);那截面箭头显示指向外,然而,他如果 p 是正的 则指向内。 For an angle of attack of -9°, the values of the pressure coefficients on the upper surface are low and positive toward the leading edge, which is an indication of no-flow separation around the upwind upper corner. In the lower surface, there is a complete separation, with negative pressure coefficients with high gradients, especially in the leading edge portion. 在俯角为-9°时,上表面上的压力系数的值变低,正朝向前缘,是表示绕逆风上角不流动的 分离现象。在较低的表面,有一个完全分离的,具有高梯度负压系数,特别是在前缘部分。

Increasing the angle of attack at -6 and -3°, there is an increasing small separation in the upper surface of the leading edge with negative pressures, followed by a smooth reattachment with very low pressure values. The lower surface is still in suction, with pressure coefficients that are smaller in the leading edge portion and nearly unchanged elsewhere. 俯角从-6 增加到-3°,则与负压力的前缘的上表面越来越小分离,然后以非常低的压力值来 平滑复位。下表面仍处于吸力,与处于前缘部更小,别处的压力系数几乎没有变化。 For positive angles of attack, from 0 and 6°, there is an increasing portion of the upper surface, which is in suction, with a flow reattachment that increasingly moves toward the trailing edge. The lower part of the leading edge experiences an initial positive pressure region followed by a separation that anticipates the surface edge. At 9° there is a full separation, with negative constant pressure coefficients in the upper surface, whereas the separation in the lower part of the leading edge occurs near to the lower surface edge. 攻击的正角度,从 0 和 6°,存在的上表面,这是在吸入,与流再附着了日益朝向后缘移动 的增加部分。前缘的下部经历随后是预期的表面边缘的分离的初始正压力区。在 9°有一个 完整的分离,与在上表面负恒压系数,而在前缘的下部分离时靠近到下表面边缘。 In comparing the pressure distributions around the deck section for different angles of attack, the following considerations about the global coefficients may be drawn. The lift force is caused by the balance between the pressure on the upper and lower surfaces of the deck. The coefficient CL is negative up to 3 ° where the separation bubble on the upwind upper region counterbalances the negative pressure produced on the lower surfaces by the flow acceleration. 在比较周围不同迎角截面部分中的压力分布, 对全球系数以下考虑可得出。 升力由截面的上 和下表面上的压力之间的平衡造成的。系数 CL 为最多-3°,其中在迎风的上部区域的分离 泡抵消由流加速度的下表面上产生的负压。 The moment coefficient is negative up to -3°. At -9°there are two negative contributions to the pitching moment caused by the positive pressure on the upwind upper region and the negative pressure on the lower surfaces, which are mainly present in the upwind part. Moving toward the positive angles of attack, a negative pressure zone appears and expands in the upwind upper surface and a positive pressure field appears in the lower upwind region. The stagnation zone moves along the tilted surface for increasing angles of attack giving a positive contribution to the aerodynamic moment. 此刻系数最多为-3°。在-9°有引起的在迎风上部区域和正压力的下表面,其是主要存在于 迎风部上的负压俯仰力矩两个负贡献。朝向攻击的正角度移动,一个负压区出现,并在逆风 上表面膨胀和正压字段出现在下迎风区域。 停滞区沿倾斜表面移动为增加攻击给人以气动力 矩积极贡献的角度。 The discrepancies between the results of the two different measurement systems might be ascribed to the effect of 不同测量系统的结果之间的差异可能归因于 Axial correlation (bidimensionality); 轴向相关(性) Shear stresses; or 剪切应力;或 Measurement grid discretization. 测量网格离散化

The bidimensionality of the flow field can be assessed by comparing the experimental mean pressure values along the correlation lines. Fig. 8 shows the spanwise mean pressure along the four axial lines (A, B, C, and D in Fig. 2), with respect to the central taps that are used for the integration of the pressure field. The diagrams also show the accuracy band of the pressure scanners (±2 Pa±2 Pa). In general, the pressure values are consistent, with some higher differences at specific locations/angles of attack. 流场的维数可以通过沿着相关行对比实验的平均压力值进行评估。 图 8 显示了在四轴线的展 向平均压力(A,B,C 和 D 在图 2) ,相对于所使用的压力场的积分的中心抽头。该图也显 示了压力扫描器(±2 帕±2 帕)的准确性带。在一般情况下,压力值是一样的,与在攻击 的特定位置/角度一些更高差异。 These experimental comparisons can be used to estimate a correction of the pressure field nearby the correlation taps. For shear-stress and measurement grid discretization effects, a numerical analysis has been conducted to evaluate their influence through the definition of a discretization error and a shear-stress error. 这些实验的比较可以被用来估计压力场附近的相关抽头的校正。 对于剪应力和测量网格的影 响,数值分析已经进行了通过离散误差的定义,剪切应力误差,以评估他们的影响力。 CFD Analysis CFD 分析 The numerical analysis is focused on an investigation of experimental results to evaluate the discrepancies in the experimental mean aerodynamic coefficients between force and pressure systems. In particular, CFD are used to define the discretization error and shear-stress error. 数值分析的重点是实验结果的调查, 以评估力和压力系统之间的实验平均空气动力学系数的 差异。特别是,CFD 被用来定义离散化误差和剪切应力的误差。 The 2D steady-state flow simulations have been performed to compute the mean pressure distribution and mean aerodynamic forces because no significant unsteady phenomena and small separated flow regions are present in the experimental data. Steady-state RANS simulations are considered a good compromise between the achievable quality of the results and the computational effort for the analyzed problem; however, their shortcomings are well known. 二维稳态流动模拟计算的平均压力分布和平均空气动力, 因为没有显著的不稳定现象和小分 离流动区域中存在的实验数据。稳态 RANS 模拟考虑的结果实现的质量和用于所分析的问题 的计算工作量之间很好的妥协;然而,它们的缺点是众所周知的。 Different turbulence models have been tested and compared in terms of accuracy and effectiveness in reproducing the experimental results, especially with regard to their capability of reproducing the separated flow regions. The solution of the fluid dynamic equations allows the separation of the effect of pressure and the shear contribution acting on the bridge surfaces. The resulting forces on the bridge deck are then computed by integrating the pressure and friction components along the boundary on the deck surfaces. Numerical results are compared with experimental measurements in terms of the pressure distribution around the deck profile and global force coefficients. The numerical solutions are carried out using FLUENT 6.3 CFD code. 不同的湍流模型进行了测试和比较的准确性和有效性再现的实验结果, 特别是关于他们的能 力的再现分离流动区。 的流体动力学方程的解决方案允许的压力和作用于桥表面的剪切贡献 的分离。由此产生的力量然后,通过将压力和摩擦元件沿截面表面的边界积分计算出桥面。 数值结果与在围绕截面轮廓和整体力系数的压力分布方面实验测量比较。使用 FLUENT 软件 6.3 CFD 代码进行的数值解。

Fluid Domain, Geometry, and Boundary Conditions 流体区域,几何和边界条件 The computational domain considered for CFD simulation reproduces the geometry of the bridge deck section in model scale and the wind tunnel test room. The dimensions of the fluid domain are shown in Fig. 9. The domain has been generated considering six deck chords before and 12 deck chords after the bridge deck section, respectively, to ensure independence from the boundary inlet condition and to allow for the development of the turbulent wake. 考虑 CFD 模拟计算域再现模型规模桥面部分和风洞试验室的几何形状。流体域的尺寸如图 9.域已经生成考虑前 6 甲板和弦和桥面部分 12 后甲板和弦,分别以确保独立性从边界条件 入口,并允许湍流尾迹的发展。 To perform a significant comparison between the numerical and experimental results, boundary conditions are set to reproduce the wind tunnel setup. The boundary conditions for the fluid domain are shown in Fig. 9. The fluid domain is surrounded by boundaries Γ up, Γ down, Γ in, and Γ out. The boundary conditions are applied on the domain boundaries as specified. 执行数值模拟和实验结果之间的显著比较, 边界条件设定重现风洞设置。 用于流体域的边界 条件如图 9 所示.流体域由边界Γ up,Γ down,Γ in 和Γ out 包围。边界条件作为指定的域 边界。 Γ up and Γ down: the symmetry condition is used instead of the wall no-slip condition because no significant differences on the aerodynamic forces are shown between these two conditions. On the other hand, the symmetry condition allows for the reduction of the number of cells in the entire domain. Γ up 和Γ down:对称性条件来代替壁无滑移条件,因为有这两个条件之间显示出的空气动 力无显著差异。另一方面的对称条件允许在整个域中的细胞的数目的减少。 Γ in: the uniform inlet-velocity profile, normal to the boundary, has a magnitude of 10 m/s and 2% turbulence intensity as measured in wind tunnel tests. Γ in:均匀入口速度分布,垂直于边界时,具有 10 米/秒和 2%湍流强度的幅度在风洞试验 测定。 Γ out: the zero-pressure outlet condition is used. (Note that this condition is legitimate only if the outlet boundary is far enough from the bridge trailing edge.) Γ out: 使用零压力出口条件。 (请注意, 此条件是合法只有在出口边界是从桥后缘足够远) 。 In numerical simulations an ideal geometry for the deck section is used, neglecting superficial roughness and corner shape imperfections. 在数值模拟中的一个理想的几何形状的截面部分的使用,忽略了表面粗糙度和角形缺陷。

Mesh and Settings 网格和设置 The computational grid was defined through refining tests to obtain a mesh-independent solution. To lower the computational effort, a wall function is used to model flow in the near-wall region, reducing the number of elements required in the boundary layer with respect to the wall-treatment approach. A structured grid is used in the boundary layer to both achieve the fine resolution of the flow structure in this region and obtain a regular mesh around the corners of the deck profile, as shown in Fig. 10. 通过细化试验,得到的计算网格,以获得一个网格独立的解决方案。为了降低计算工作量, 墙的功能是用来在近壁区流动模型,降低在边界层中所需的元素的数目相对于壁处理方法。 在边界层中使用一个结构化的网格, 以实现精细的分辨率的流量在这个区域, 得到结构在截 面的拐角处一个规则的网格,如图 10 所示。 Triangular elements with nonstructured mesh are used for the remaining region of the fluid domain. A total of 58,936 elements are used to construct the overall computational grid. A circular region around the deck section is set to manage the different angles of attack without modifying the refined mesh near the surfaces. Besides, a dense mesh region downwind the trailing edge is provided to correctly simulate the turbulent wake effects (Fig. 11). Because the global aerodynamics of the deck are influenced by the flow separation occurring on the upwind surfaces, the mesh and choice of the turbulence model are critical for the numerical solution. 非结构化网格三角形的元素被用于流体域的其余区域。 总共有 58936 个元素被用来构建整体 的计算网格。 圆形区域在断面设置管理的不同角度, 而无需修改表面附近的细化网格。 此外, 顺风后缘的致密网格区域被提供给正确模拟湍流尾流效应(图 11) 。因为截面的全球空气动 力是受发生的逆风表面上的流动分离所影响, 湍流模型的网格和选择都为数值解是至关重要 的。 Turbulence Modeling 湍流模型 Turbulence modeling is a critical matter in bluff body aerodynamics, when separated flow fields are present. Different turbulence models were tested: k- ε standard (STD), k- ε Murakami-Mochida-Kondo (MMK), k-ω shear stress transport (SST), and Reynolds stress model (RSM). 湍流模型是钝体空气动力学中的一个关键问题, 当分离流场时。 不同的湍流模型进行了测试: Kε 标准(STD) ,Kω 剪切应力运输(SST) ,和雷诺兹应力模型(RSM) 。 A standard k-ε model is used just for comparison reasons to better assess the improvement of more sophisticated approaches. Its limitations in the description of complex flows with separation and a strong stream line curvature and its tendency to overestimate the turbulence production in the impingement region, whose convection around the body results in a reduction of the extent of the flow separation, are known. 一个标准的 K -ε 模型仅用于比较的原因来更好的评估更复杂的方法的改进。其在复合物的 描述的限制与分离和强烈的流线曲率及其高估湍流的生产在冲击区域, 其围绕本体的结果而 减少其流动分离的程度的对流,是已知的倾向流动。

A k-ε MMK model, widely adopted in building aerodynamics, is used to overcome the k-ε STD limitation in predicting flow separation around sharp edges. This model is not implemented in FLUENT 6.3, but it has been added by customized user-defined functions (UDFs), introducing a new expression for the turbulence kinetic energy production term (Tsuchiya et al. 1997). 一个 Kε MMK 模型,在构建空气动力学广泛采用,用于克服在预测围绕尖锐边缘流动分离 第 k-ε 性病限制。 这种模式是不是在 FLUENT6.3 实现, 但它已被定制的用户定义函数 (UDF) 增加,引入对湍流动能产生项新的表达式(土屋等,1997) 。 Results obtained with these simple k-ε models are compared with those obtained with the k-ω SST and RSM. The first is suitable for complex boundary layer flows under an adverse pressure gradient, even if separations are early and overpredicted, whereas the second one takes into account the anisotropies arising because of the flow separation around the edges. Every model is used in conjunction with standard wall functions for the near-wall flow field. 这些简单的 K-ε 模型得到的结果与用 K-ω SST 和 RSM 获得的进行比较。第一个是适合于不 利的压力梯度下复杂边界层流动, 即使分离是早期和 overpredicted,而第二个考虑是因为周 围的边缘流动分离所引起的各向异性。每一个模型是与近壁流场标准壁面功能一起使用。 CFD Results CFD 结果 Two parameters, δ and ε , are defined on the basis of the analysis of the experimental pressure results previously presented (Fig. 12). The parameter δ is the distance between the leading edge and the point along the upwind lower surface where the pressure value changes its sign, whereas ε represents the reattachment length on the upper surface, measured from the leading edge. These points are defined only if they are existent. 两个参数,δ 和ε ,在压力实验结果先前提出的分析的基础上定义(图 12) 。参数δ 为前缘 和沿迎风下表面,其中所述压力值改变符号,而ε 表示在上表面上的附着长度,与前缘测量 点之间的距离。这些点被定义仅当它们是存在的。 Figs. 13 and 14 show the trend of these parameters as a function of the angle of attack, estimated both experimentally and numerically. An offset of approximately 2° between the experimental and numerical curves could be estimated, relying on δ , which is more reliable than ε for high positive angles. Extensive investigations about this offset were performed varying the simulation parameters (domain extension, boundary conditions, sharp-rounded edges). Because this effect cannot be explained from a numerical point of view, it could be related to an experimental issue. 图 13 和 14 显示这些参数作为迎角的函数的趋势, 预计实验和数值。 一个的实验和数值曲线 之间大约 2°偏移可估计,依靠δ ,这比ε 为高正角度更可靠。进行不同的仿真参数(域扩 展,边界条件,尖圆边)这个偏移广泛调查。因为这种效果不能从一个数值点进行说明,它 可能与一个实验问题有关。 In the following, the numerical results will be compared taking into account this offset. As an example, Fig. 15 shows how this offset leads to a good agreement between the numerical and experimental results in terms of pressure distributions for different angles of attack. 在下文中,计算结果将被比较考虑到这一偏移。作为一个例子,图 15 显示了如何抵消导致 一个很好的协议之间的数值和实验不同攻角下的压力分布结果。

Considering the experimental results at 0° compared with the numerical one at 2° (Fig. 16), a similar pressure distribution is predicted on the lower surface by all the turbulence models, whereas higher discrepancies appear on the upwind upper surface. The k-ω SST underestimates the regions with negative pressures in the lower surface compared with the other models, whereas, in the upper upwind part close to the separation corner, it shows the best result. 考虑在 0℃的实验结果与在 2℃(图 16)的数值技术相比,类似的压力分布的下表面上通过 所有的湍流模型预测的,而较高的差异出现在迎风上表面上。第 kω SST 低估与其他模型相 比在较低的表面负压力的区域,而在接近分离角上部上风部,它显示了最好的结果。 Fig. 17 shows how the different models simulate the separation around the leading edge. This region is very important for the lift and moment coefficients. Looking at the slopes of the pressure distribution just around the corner and close to the reattachment point, it is possible to appreciate the different results. 图 17 显示了不同的模型如何模拟出领先优势的分离。这个地区是升力和力矩系数非常重要 的。纵观压力分布指日可待,靠近再附着点的山坡上,可以欣赏到不同的结果。 The k-ε STD predicts a strong negative initial slope, with an overestimation of the very first pressure values, producing a completely wrong separation bubble with a small ε . 第 k-ε STD 预测存在较强的负初始斜率,与第一个压力值高估,产生一个小ε 一个完全错误 的分离泡。 The RSM has a slightly negative initial slope that leads to an underestimation of the negative pressure values, but it accurately predicts the pressure distribution in the reattachment region. 该 RSM 具有导致负压力值的低估稍负的初始斜率,但它准确地预测在复位区的压力分布。 The k-ε MMK underestimates the separation bubble, even if it presents a small initial slope, close to the experimental one, and a comparable value for ε . Kε MMK 低估了气泡分离,即使它提出了一个小的初始斜率,接近实验,并ε 可比价值。 The k-ω SST produces the best results in the initial part, showing pressure values and a slope close to the experimental ones, but it overestimates the ε value. Kω SST 在初始部分产生最好的结果,显示压力值和斜率接近实验值,但它高估了ε 值。 Similar considerations hold for the other angles of attack (Fig. 15). At negative angles of attack, the numerical pressure field fits the experimental measurement both in the lower and upper surfaces. In particular, the k-ω SST model is closer to the experimental results in the lower region than the RSM model, whereas in the upper region (positive pressure), both models reproduce the same behavior in a satisfactory way. 类似的考虑保持攻击的其它角度(图 15) 。在负迎角,数值压力场适合无论在上下表面的实 验测量。特别是 kω SST 模型比 RSM 模型在下部区域更接近实验结果,而在上部区域(正压 力) ,这两种模式再现以令人满意的方式相同的方式。 At positive angles of attack, only the upper region is critical for numerical simulation. Similar pressure distribution is obtained by both turbulence models, but the RSM model seems to better fit the reattachment length. 在正攻角下,只有上部区域是数值模拟的关键。采用湍流模型得到的是类似的压力分布,但 RSM 模式似乎更适合的再附着长度。

At strongly positive angles of attack, k-ω SST correctly reproduces the shape of the pressure distribution only in the upwind region, introducing error in the upper downwind part. A possible explanation of this behavior could be the wall-function approach. In fact, a low magnitude reverse flow is present in this section and a wall function could amplify the flow to enforce the boundary layer function. The RSM model gives a uniform underestimated pressure field in all the upper surfaces. 在攻击强阳性的角度,Kω SST 正确地再现只有在逆风区的压力分布的形状,在上下部分引 入的误差。一种可能的解释关于这种行为,可以是壁函数方法。事实上,小幅度的反向流在 这段和壁面函数可以放大流量执行边界层的功能离子。RSM 模型对所有的上表面均匀的被 低估的压力场。 Comparison between Pressure Integration and Dynamometric Balance 压力集成和测力天平的比较 Numerical results are used to assess the effects of shear stresses and the integration error caused by the discretized pressure measurement grid on the aerodynamic force coefficients. This analysis, in conjunction with the analysis of the experimental axial correlation of the pressure field, gives a useful tool to identify the causes of the differences between the two measurement systems. 数值结果用于评估剪切应力并在空气动力系数所引起的离散压力测量栅格积分误差的影响。 这一分析, 在与压力场的实验轴向相关的分析相结合, 给出了一个有用的工具来识别的两个 测量系统之间的差异的原因。 Focusing on the drag coefficient, which has more relevant differences, it is therefore possible to identify a correction of the experimental pressure integration, consisting of three distinct terms: correlation error, discretization error, and τ error. 聚焦的阻力系数,其中有更多的相关的差异,因此,因此可以识别实验压力积分的修正,由 三个不同的方面:相关误差,离散误差,和τ 错误。 The correlation error for each line (A, B, C, and D) is computed from the experimental data as the ratio between the mean of the pressure values along the correlation line and the one of the correspondent central tap. The pressure magnitude measured by the taps nearby (±0.1 m±0.1 m) each correlation line is scaled with these correction factors 对于每一行的相关误差(A,B,C 和 D)从实验数据沿相关线中的压力值的平均值和对应的 中央抽头的所述一个之间的比率来计算。测量的压力幅值附近(0.1 米)附近的每一个相关 线与这些校正因子缩放。 The discretization error is computed integrating the CFD results, sampling the pressure field with a different spatial resolution. In particular, the error is defined comparing a grid equivalent to the experimental one (78 equivalent taps) and the finer CFD grid (522 equivalent taps). 离散误差计算积分的 CFD 的结果,与不同的空间分辨率采样压力场。特别是,被定义的误 差进行比较的网格相当于实验酮(78 当量抽头)和较细的 CFD 网格(522 当量抽头) 。

To estimate the contribution of the shear stresses in the definition of the global force, a percentage error is computed in the numerical analysis comparing the aerodynamic coefficients obtained integrating both normal and shear stresses with those obtained integrating only normal stresses. These errors have been evaluated for the k-ε MMK, k-ω SST, and RSM turbulence models, and similar results are obtained. Fig. 18 shows the estimated error on the drag coefficient measured with pressure integration for different angles of attack using the k-ω SST CFD results. The solid line represents the total error that is the sum of the correlation error (black bar), discretization error (gray bar), and shear-stress error (white bar). 估计剪应力在全球力定义的贡献百分比误差在数值分析比较得到完整的气动系数的计算额 定值正常和剪切应力与那些得到的整合只有正常的应力。这些错误已被评估为第 k-ε MMK, K-ω SST,和 RSM 湍流模型,并得到类似的结果。 图 18 显示了估计误差对测得的阻力系数 与压力集成不同攻角对 Kω SST CFD 计算结果。实线表示总误差是这样的相关误差(黑条) , 离散误差(灰色条) ,和剪切应力误差(白条)的总和。 Looking at the trends of the three errors, the following points can be observed. 三个错误的趋势,可以观察到以下几点。 1. The effect of the axial correlation of the pressure field is relevant for negative angles of attack. This effect is mainly caused by the A and B correlation lines. As shown in Fig. 6, the lower downwind surface (A correlation line) gives a positive contribution to the drag global force, whereas the lower upwind surface (B correlation line) gives a negative one. Therefore, referring to Fig. 8, the underestimation of the A pressure modulus together with the overestimation of the B one lead to an underestimation of the global drag force. 1.压力场的轴向相关的效果是相关的负迎角。这种效应主要是由 A 和 B 的相关性的行。如图 6 所示,下顺风表面(A 相关线)给出迎风面(B 相关线) ,以拖全球力量作出了积极贡献, 而较低的给出了否定的。因此,指的是图 8,压力模数与低估的 B 一路领先高估了全球阻力 低估在一起。 2.The discretization of the pressure field leads to an overestimation of the global drag coefficient caused by the rough description of pressure gradients, particularly on the leading edge frontal surface. For this reason the maximum error is done at θ =0° where the contribution of this surface to the global drag force is maximum. 2.压力场的离散导致引起压力梯度的粗略描述全球阻力系数的过高估计, 特别是在前缘前表 面。由于这个原因,最大误差是在θ =0°,其中该表面的到全球拖曳力的贡献是最大完成。 3.The shear-stress effect is not negligible for an accurate estimate of the global drag coefficient. Neglecting this effect leads to an underestimation of the drag coefficient with a parabolic trend with a maximum of -15% around θ =0°. 3.剪切应力的作用是不可忽略的,为全球阻力系数的精确估计。忽视这种影响导致抛物线趋 势的阻力系数达到最大的θ = 0°到 15%左右。 Negligible effects of τ , discretization, and the correlation of CLCL and CMCM are encountered (<1%). 对τ ,离散的影响可以忽略不计,而 CLCL 和 CMCM 相关时(<1%) 。

Fig. 19 shows the comparison between the drag coefficient curve measured by the dynamometric balance and the one obtained by the integration of the measured pressure field. The pressure-integrated curve is plotted, applying the correction for the estimated error (Fig. 18), and the result shows a good match with the dynamometric measurements. 图 19 显示了比较的阻力系数曲线之间由测力平衡和一个由所测得的压力场的积分得到测量。 综合目前的压力我的策划,运用修正的估计误差(图 18) ,结果显示与测力的测量。 有着良好的匹配。 Concluding Remarks 结束语 In this paper the authors presented an extended comparison between two different measurement systems for the global aerodynamic forces on a bridge deck: a dynamometric balance and a pressure field integration. The pressure measurement has the advantage of showing the distribution of the aerodynamic force field; however, it has some intrinsic critical issues that have been pointed out and deeply studied. 在本文中, 作者提出了两种不同的测量系统之间对桥面全球空气动力扩展的比较: 一个压力 场一体化测力平衡。压力测量具有表示空气动力场的分布的优点;然而,它具有已指出并深 入研究了一些固有的关键问题。 The following three main effects should be accounted for: axial correlation, discretization of the pressure measurement grid, and shear-stress contribution. A 2D CFD analysis together with the experimental results allowed for evaluation of the absolute and relative weight of these three effects on the global force coefficients, pointing out that the drag force coefficient is the most sensitive. By correcting the pressure integrated coefficients a good matching of the two measurement system’s results is achieved. 以下是三个主要影响:轴向相关性,压力测量网格的离散化,和剪切应力的贡献。与实验结 果的二维 CFD 分析一起允许对全球动力系数这三个效果绝对和相对权重的评价,指出了阻 力系数是最敏感的。通过压力综合系数的校正,实现了双测量系统的良好匹配。 The correlation error could be reduced using multiple integration path lines along the deck axis to take into account the 3D flow field and achieve a more robust global averaging. The discretization error shows that a fine measurement grid must be adopted for such deck shapes to better describe the pressure gradients on the frontal surfaces that are the main responsible for the drag force generated by normal stresses. The CFD results may help in minimizing the discretization error in the design stage of the wind tunnel tests. The viscous stress effect could be estimated with CFD simulations; nevertheless, in a real bridge deck shape with barriers and railings, its contribution is less important. 可以减少使用多个集成路径线沿甲板轴的相关错误, 考虑到三维流场, 并实现更强大的全球 平均。 离散误差表明, 精细测量电网必须采用这种形状的甲板更好地描述额面是主要负责对 正应力产生的阻力的压力梯度。 CFD 的结果可能有助于在风洞试验的设计阶段尽量减少离 散误差。该粘性应力作用可能与 CFD 模拟进行估计;尽管如此,在一个由障碍和栏杆形成的 真正的桥面,其贡献不是那么重要的。


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