桥梁风效应的数值方法及应用
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摘要
近年来，随着计算速度的迅猛发展，基于计算流体动力学的数值方法正在迅速成熟，虽然这些方法还不能代替风洞试验，但已成为研究桥梁风效应问题的另一种有效手段。本文借助数值方法所作的研究概括为二个方面，一是桥梁气动弹性；二是横风中车辆、桥梁的气动特性。完成了下述工作，并得到了一些有益的结论：
1)在计算域内采用描述流体和结构的任意拉格朗日—欧拉坐标系，推导了二维流变区域的控制方程。通过使用动网格技术，可实现对桥梁断面等刚体截面绕流场的模拟。
2)首次将一种新的二阶Projection算法应用于描述刚体气动弹性问题的非定常不可压N-S方程的求解。通过对控制方程中对流项的时间、空间不同处理，将此算法分别引入到有限差分法和有限体积法中，并借助多层网格法对压力Possion方程迭代收敛速度的提高，达到有效、快捷地模拟不可压流动问题的目的。
3)采用强迫振动数值法计算了平板的气动导数，包括理想平板和薄平板二部分。其中理想平板气动导数计算采用有限差分法，计算结果与Theodorsen理论解的偏差很小。薄平板气动导数计算采用有限体积法，气动导数计算结果和理想平板Theodorsen理论解、薄平板强迫振动法风洞试验结果一致性都很好，流线型截面的几个重要的气动导数，与理论解和风洞试验很吻合。
4)采用有限体积法和强迫振动数值法计算了虎门大桥的气动导数和颤振临界风速。虎门大桥气动导数计算结果与节段模型强迫振动法、自由振动法风洞试验值一致性较好，流线型箱梁截面的几个重要的气动导数，与风洞试验的偏差很小。由数值计算得到的颤振临界风速很靠近全桥气动弹性模型风洞试验值。为评估初始攻角对桥梁断面颤振特性的影响，计算了虎门大桥在+3°、-3°初始攻角下的气动导数，研究表明正的初始攻角对虎门大桥颤振稳定性有不利影响，也证实了强迫振动法风洞试验获得的+3°初始攻角下A_2曲线趋势的正确性。
5)采用有限体积法和强迫振动数值法计算了丹麦大海带东桥的气动导数和颤振临界风速，并将计算结果与风洞试验值、离散涡方法计算结果作了比较。本文气动导数结果与风洞试验值一致性好、偏差小，也优于离散涡方法得到的计算结果。数值模拟的颤振临界风速稍微高于风洞试验值，由于风洞试验模型包含了栏杆等附属物，因此本文的计算结果是合理的。
中南大学博士学位论文
6）用数值方法探讨了提高桥梁颤振稳定性的气动措施，采用有限差分法计
算了具有不同中央开槽率的理想平板的气动导数，计算证实中央开槽能有效地提
高理想平板的颤振稳定性，且颤振临界风速的提高幅度随开槽率的增大而增大。
采用有限体积法计算了同一宽高比桥梁截面加不同形状风嘴后的气动导数。研究
也显示，不同形状风嘴对同一宽高比截面的颤振稳定性影响不同，风嘴上、下面
能改善桥梁截面前缘绕流特性的形状就能有效地提高截面的部振临界风速。
刀与采用强迫振动法、自由振动法风洞试验测定气动导数技术相比，本文
数值模拟能较准确地得到了气动导数中包含的常数，从而具备更精确的计算颤振
临界风速的可能性，这也是本文数值模拟优于风洞试验的地方。
8）借助数值方法研究了在横向风中，YZ力型车辆、双层客车车辆、YZ。2型
车辆在 16m铁路简支梁桥上、双层客车车辆在 24m铁路简支梁桥或高路堤上的
气动特性。研究发现，当YZ22型车辆、双层客车车辆运行在铁路桥梁上时，它
们受到的气动力明显大于他们单独存在的情况。并评估了桥梁对车辆气动特性的
影响。比较了这二种车辆气动特性的差异。研究还发现，铁路桥梁也因为车辆运
行在其上面而受到比无车辆运行时增大的风荷载。因此，与《铁路桥涵设计基本
规范》所给出的设计风荷载相比，建议铁路简支梁桥采用更大的设计风荷载值。
与风洞试验相比，用本文数值方法研究桥梁风效应问题，无需昂贵的风洞试
验设备和测量仪器，也不涉及到试验模型的设计和制作，可重复性很好，摆脱了
风洞试验周期长、费用高的问题。数值方法完全可实现气动选型和对模型的参数
识别。同时，由于风洞试验不能得到气动导数中包含的常数，而数值模拟可比较
准确地计算出其中的常数，因此，如将数值模拟和风洞试验相结合，可更为准确
的评估桥梁主梁截面的颤振稳定性。
With the immense leap in computational speeds in the recent past, numerical experiments via Computational Fluid Dynamics are fast maturing as a viable complement, if not an alternative, to wind tunnel investigations to study the various wind effects on bridges. Based on numerical approaches, the present study focuses mainly on two sections, one is aeroelasticity of bridge, the other is aerodynamic characteristics of bridges and vehicles in crosswind. It should be generalized as follows:
1) The two-dimensional governing equations in deforming domain are derived by using an Arbitrary Lagrangian-Eulerian(ALE) coordinate system for the description of both the structure and the fluid in computational domain. The moving grid technique is adopted to simulate the fluid fields around the rigid body such as bridge girder cross-sections.
2) A novel second-order Projection method is employed, for the first time, to efficiently solve problems governed by unsteady, incompressible Navier-Stokes equations for the description of aeroelasticity of rigid body. With different temporal and spatial treatments to the convective terms, this method has entered into both the Finite Different Method(FDM) and the Finite Volume Method(FVM), then, multigrid algorithm is employed to speedup the convergence of the Possion's equation for pressure, all this make it possible to simulate incompressible flow efficiently and quickly.
3) The forced oscillating procedure is used to compute flutter derivatives of both the ideal flat plate and the thin plate, with the discretization methods FDM and FVM, respectively. Results of the ideal flat plate are closed to the Theodorsen's theoretic solutions. Results of the thin plate match both the Theodorsen's theoretic solutions and results from wind tunnel tests by using the Forced Vibration Technique(FVT).
4) The FVM code is employed to compute flutter derivatives and onset wind speeds for flutter of the Humen Bridge in China. Numerical results of the Humen Bridge are compared to data obtained from section model tests in wind tunnel by using the FVT and the Free Vibration Method, better agreements are found. The comparison of onset wind speed for flutter between present study and full aeroelastic
bridge model wind tunnel test is satisfactory. In order to evaluate the effect of original angle of attack on flutter characteristics, numerical simulations are also carried out to compute the flutter derivatives of the Humen Bridge girder cross-section in original angle of attack +3° and -3°, it is noted that positive original angle of attack take negative effect on flutter stability of Humen Bridge, also, the correctness of the trend line of A'2 in original angle of attack +3? which was obtained from section model tests by using the FVT, is validated.
5) The FVM code is used to compute the flutter derivatives and critical wind speeds of the Great Belt East Bridge in Denmark. It is shown that the flutter derivatives of the Great Belt East Bridge are closed to results from section model wind tunnel tests, and the computed onset wind speed for flutter obtained from simulations is little higher than that from wind tunnel tests, and reasonable explanations are presented.
6) The aerodynamic devices used to improve bridge flutter stability under smooth flow are discussed by means of numerical methods. The flutter derivatives, including those of the ideal flat plate with different slot ratio in center and different shape of fairing attached to box girder section, are computed. It is shown that a slot in center is effective to increase the onset wind speeds for flutter, and the onset wind speeds for flutter increase with the width of slot. It also indicates that different shape of fairing has different effect on flutter stability of bridge girder cross-section, the effective shapes for individual girder cross-sections can be determined by the flow properties around the cross-section, that is, the both side angle of the fairing should be almost the same as t
1)在计算域内采用描述流体和结构的任意拉格朗日—欧拉坐标系，推导了二维流变区域的控制方程。通过使用动网格技术，可实现对桥梁断面等刚体截面绕流场的模拟。
2)首次将一种新的二阶Projection算法应用于描述刚体气动弹性问题的非定常不可压N-S方程的求解。通过对控制方程中对流项的时间、空间不同处理，将此算法分别引入到有限差分法和有限体积法中，并借助多层网格法对压力Possion方程迭代收敛速度的提高，达到有效、快捷地模拟不可压流动问题的目的。
3)采用强迫振动数值法计算了平板的气动导数，包括理想平板和薄平板二部分。其中理想平板气动导数计算采用有限差分法，计算结果与Theodorsen理论解的偏差很小。薄平板气动导数计算采用有限体积法，气动导数计算结果和理想平板Theodorsen理论解、薄平板强迫振动法风洞试验结果一致性都很好，流线型截面的几个重要的气动导数，与理论解和风洞试验很吻合。
4)采用有限体积法和强迫振动数值法计算了虎门大桥的气动导数和颤振临界风速。虎门大桥气动导数计算结果与节段模型强迫振动法、自由振动法风洞试验值一致性较好，流线型箱梁截面的几个重要的气动导数，与风洞试验的偏差很小。由数值计算得到的颤振临界风速很靠近全桥气动弹性模型风洞试验值。为评估初始攻角对桥梁断面颤振特性的影响，计算了虎门大桥在+3°、-3°初始攻角下的气动导数，研究表明正的初始攻角对虎门大桥颤振稳定性有不利影响，也证实了强迫振动法风洞试验获得的+3°初始攻角下A_2曲线趋势的正确性。
5)采用有限体积法和强迫振动数值法计算了丹麦大海带东桥的气动导数和颤振临界风速，并将计算结果与风洞试验值、离散涡方法计算结果作了比较。本文气动导数结果与风洞试验值一致性好、偏差小，也优于离散涡方法得到的计算结果。数值模拟的颤振临界风速稍微高于风洞试验值，由于风洞试验模型包含了栏杆等附属物，因此本文的计算结果是合理的。
中南大学博士学位论文
6）用数值方法探讨了提高桥梁颤振稳定性的气动措施，采用有限差分法计
算了具有不同中央开槽率的理想平板的气动导数，计算证实中央开槽能有效地提
高理想平板的颤振稳定性，且颤振临界风速的提高幅度随开槽率的增大而增大。
采用有限体积法计算了同一宽高比桥梁截面加不同形状风嘴后的气动导数。研究
也显示，不同形状风嘴对同一宽高比截面的颤振稳定性影响不同，风嘴上、下面
能改善桥梁截面前缘绕流特性的形状就能有效地提高截面的部振临界风速。
刀与采用强迫振动法、自由振动法风洞试验测定气动导数技术相比，本文
数值模拟能较准确地得到了气动导数中包含的常数，从而具备更精确的计算颤振
临界风速的可能性，这也是本文数值模拟优于风洞试验的地方。
8）借助数值方法研究了在横向风中，YZ力型车辆、双层客车车辆、YZ。2型
车辆在 16m铁路简支梁桥上、双层客车车辆在 24m铁路简支梁桥或高路堤上的
气动特性。研究发现，当YZ22型车辆、双层客车车辆运行在铁路桥梁上时，它
们受到的气动力明显大于他们单独存在的情况。并评估了桥梁对车辆气动特性的
影响。比较了这二种车辆气动特性的差异。研究还发现，铁路桥梁也因为车辆运
行在其上面而受到比无车辆运行时增大的风荷载。因此，与《铁路桥涵设计基本
规范》所给出的设计风荷载相比，建议铁路简支梁桥采用更大的设计风荷载值。
与风洞试验相比，用本文数值方法研究桥梁风效应问题，无需昂贵的风洞试
验设备和测量仪器，也不涉及到试验模型的设计和制作，可重复性很好，摆脱了
风洞试验周期长、费用高的问题。数值方法完全可实现气动选型和对模型的参数
识别。同时，由于风洞试验不能得到气动导数中包含的常数，而数值模拟可比较
准确地计算出其中的常数，因此，如将数值模拟和风洞试验相结合，可更为准确
的评估桥梁主梁截面的颤振稳定性。
With the immense leap in computational speeds in the recent past, numerical experiments via Computational Fluid Dynamics are fast maturing as a viable complement, if not an alternative, to wind tunnel investigations to study the various wind effects on bridges. Based on numerical approaches, the present study focuses mainly on two sections, one is aeroelasticity of bridge, the other is aerodynamic characteristics of bridges and vehicles in crosswind. It should be generalized as follows:
1) The two-dimensional governing equations in deforming domain are derived by using an Arbitrary Lagrangian-Eulerian(ALE) coordinate system for the description of both the structure and the fluid in computational domain. The moving grid technique is adopted to simulate the fluid fields around the rigid body such as bridge girder cross-sections.
2) A novel second-order Projection method is employed, for the first time, to efficiently solve problems governed by unsteady, incompressible Navier-Stokes equations for the description of aeroelasticity of rigid body. With different temporal and spatial treatments to the convective terms, this method has entered into both the Finite Different Method(FDM) and the Finite Volume Method(FVM), then, multigrid algorithm is employed to speedup the convergence of the Possion's equation for pressure, all this make it possible to simulate incompressible flow efficiently and quickly.
3) The forced oscillating procedure is used to compute flutter derivatives of both the ideal flat plate and the thin plate, with the discretization methods FDM and FVM, respectively. Results of the ideal flat plate are closed to the Theodorsen's theoretic solutions. Results of the thin plate match both the Theodorsen's theoretic solutions and results from wind tunnel tests by using the Forced Vibration Technique(FVT).
4) The FVM code is employed to compute flutter derivatives and onset wind speeds for flutter of the Humen Bridge in China. Numerical results of the Humen Bridge are compared to data obtained from section model tests in wind tunnel by using the FVT and the Free Vibration Method, better agreements are found. The comparison of onset wind speed for flutter between present study and full aeroelastic
bridge model wind tunnel test is satisfactory. In order to evaluate the effect of original angle of attack on flutter characteristics, numerical simulations are also carried out to compute the flutter derivatives of the Humen Bridge girder cross-section in original angle of attack +3° and -3°, it is noted that positive original angle of attack take negative effect on flutter stability of Humen Bridge, also, the correctness of the trend line of A'2 in original angle of attack +3? which was obtained from section model tests by using the FVT, is validated.
5) The FVM code is used to compute the flutter derivatives and critical wind speeds of the Great Belt East Bridge in Denmark. It is shown that the flutter derivatives of the Great Belt East Bridge are closed to results from section model wind tunnel tests, and the computed onset wind speed for flutter obtained from simulations is little higher than that from wind tunnel tests, and reasonable explanations are presented.
6) The aerodynamic devices used to improve bridge flutter stability under smooth flow are discussed by means of numerical methods. The flutter derivatives, including those of the ideal flat plate with different slot ratio in center and different shape of fairing attached to box girder section, are computed. It is shown that a slot in center is effective to increase the onset wind speeds for flutter, and the onset wind speeds for flutter increase with the width of slot. It also indicates that different shape of fairing has different effect on flutter stability of bridge girder cross-section, the effective shapes for individual girder cross-sections can be determined by the flow properties around the cross-section, that is, the both side angle of the fairing should be almost the same as t
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