预条件可压流算法在桥梁风工程中的应用研究
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摘要
论文简要回顾了桥梁风工程的发展,总结了桥梁计算风工程中的研究现状。基于预条件处理技术下可压流N-S方程的求解算法,建立了低速非定常流场求解的有限体积方法。采用Delaunay三角形背景网格算法,实现了流场中运动网格的数值模拟。开发了可用于桥梁断面气动参数计算和气动现象模拟的专用软件,分别进行了典型桥梁断面的静力三分力计算、涡激振动现象模拟和参数计算、颤振导数计算。本文的主要研究内容有：
1.在桥梁断面绕流数值计算中引入预条件处理技术求解可压流非定常N-S方程,克服了传统可压缩流N-S方程求解算法在计算低速流场时面临的收敛慢、精度低的“刚性”问题。
2.采用Delaunay三角形背景网格算法定位网格点关系,实现了对运动网格的模拟,并与传统的弹簧网格算法进行了对比。计算结果表明,基于Delaunay背景图映射的动态网格变形方法无需迭代计算,效率高,稳定性好。
3.开发了能有效模拟运动边界、实现动网格功能的非定常流场的计算软件。众多典型算例的结果表明,预条件处理技术将可压缩流N-S方程的应用范围拓展到了低马赫数的桥梁风工程流场环境,有效地提高了收敛速度。同时,还将固体振动方程融入所开发的流体计算软件中,实现了对流固耦合问题的求解。
4.采用自研软件分别对两种典型桥梁断面的三分力进行了数值求解,其结果均与试验值吻合较好；基于钝体桥梁断面研究了不同湍流模型下静力三分力的计算精度问题。
5.采用自研软件对桥梁断面涡激振动现象进行了数值模拟,结合对数值绕流场的分析,明确了桥梁断面涡激振动发生发展的气动机理：桥梁断面受涡激力作用发生振动,从而导致其上气动载荷的增大,进而引起桥梁断面振动加剧,并逐渐达到“锁定”状态。
6.采用自研软件,基于强迫振动法对薄平板和某大跨度桥梁断面的颤振导数开展了数值求解。利用竖弯和扭转条件下的自激气动力计算数据和最小二乘算法获得了8个颤振导数,并与理论值和风洞试验结果进行了对比,验证了该软件用于颤振导数计算的可行性。
This dissertation reviewed the researches of wind effects on the long span bridge, and summarized the current researches on the numeric simulation in bridge wind engineering. Based on the solving algorithm of unsteady compressible N-S equations considering a preconditioning processing technic, the finite volume method for solving the unsteady low velocity flow field had been established. Using Delaunay triangulation mesh algorithm, the generation of dynamic mesh during unsteady flow field had been achieved. Developed professional software can be used for effective numerical calculation of aerodynamic parameters and numerical simulating of aerodynamic phenomena of bridge girders. The static aerodynamic force coefficients and flutter derivatives can be obtained, and the phenomenon of vortex-induced vibration can be simulated using the software.
The dissertation mainly contains following contents:
1. By using a preconditioning processing technic expanded into the unsteady compressible N-S equations, the problems of the algorithm tending to fare poorly for low speed flow fields can be solved.
2. Using Delaunay triangulation mesh to locate the relationship between grid points, the generation of dynamic mesh during unsteady flow field calculation had been achieved. Comparing with the traditional spring mesh method, Delaunay triangulation mesh method need any iterative computation and can provide high efficiency and good stability.
3. Developed professional software for effective numerical calculation and simulation of unsteady low velocity flow fields with moving boundaries. The results of several examples indicated that the preconditioning processing technic can extend the effective calculating range of the compressible algorithm to the low Mach number, especially to the low flow velocity condition of wind engineering for bridges. By combining with the structural dynamic equations, the software can provide the simulation of fluid-bridge coupling interaction.
4. The static aerodynamic forces of bridge girders were treated with unsteady numerical simulation using the software. The results had a good agreement with the ones in wind tunnel tests. Based on the bluff body bridge girder section and different turbulence models, the solving precision of the static aerodynamic forces had been studied.
5. Based on the numerical simulation for the vortex-induced vibration phenomenon in bridges and the analysis of the numerical flow field, a mechanism of vortex-induced vibration is eventually formed:when the vortex-induced vibration occurs, the bridge girder motion induced by initial vortex-induced aerodynamic loads can magnify the following aerodynamic loads, and the amplitude of bridge girder is increasing until the "lock in" status.
6. Based on the least squares fitting and the aerodynamic force in vertical and torsion motion, the flutter derivatives of thin plate and bridge girder had been obtained using forced vibration method of numerical simulation. The comparison between calculated results and theoretical results and wind tunnel test results can validate the feasibility of the software in the calculation of flutter derivatives.
1.在桥梁断面绕流数值计算中引入预条件处理技术求解可压流非定常N-S方程,克服了传统可压缩流N-S方程求解算法在计算低速流场时面临的收敛慢、精度低的“刚性”问题。
2.采用Delaunay三角形背景网格算法定位网格点关系,实现了对运动网格的模拟,并与传统的弹簧网格算法进行了对比。计算结果表明,基于Delaunay背景图映射的动态网格变形方法无需迭代计算,效率高,稳定性好。
3.开发了能有效模拟运动边界、实现动网格功能的非定常流场的计算软件。众多典型算例的结果表明,预条件处理技术将可压缩流N-S方程的应用范围拓展到了低马赫数的桥梁风工程流场环境,有效地提高了收敛速度。同时,还将固体振动方程融入所开发的流体计算软件中,实现了对流固耦合问题的求解。
4.采用自研软件分别对两种典型桥梁断面的三分力进行了数值求解,其结果均与试验值吻合较好；基于钝体桥梁断面研究了不同湍流模型下静力三分力的计算精度问题。
5.采用自研软件对桥梁断面涡激振动现象进行了数值模拟,结合对数值绕流场的分析,明确了桥梁断面涡激振动发生发展的气动机理：桥梁断面受涡激力作用发生振动,从而导致其上气动载荷的增大,进而引起桥梁断面振动加剧,并逐渐达到“锁定”状态。
6.采用自研软件,基于强迫振动法对薄平板和某大跨度桥梁断面的颤振导数开展了数值求解。利用竖弯和扭转条件下的自激气动力计算数据和最小二乘算法获得了8个颤振导数,并与理论值和风洞试验结果进行了对比,验证了该软件用于颤振导数计算的可行性。
This dissertation reviewed the researches of wind effects on the long span bridge, and summarized the current researches on the numeric simulation in bridge wind engineering. Based on the solving algorithm of unsteady compressible N-S equations considering a preconditioning processing technic, the finite volume method for solving the unsteady low velocity flow field had been established. Using Delaunay triangulation mesh algorithm, the generation of dynamic mesh during unsteady flow field had been achieved. Developed professional software can be used for effective numerical calculation of aerodynamic parameters and numerical simulating of aerodynamic phenomena of bridge girders. The static aerodynamic force coefficients and flutter derivatives can be obtained, and the phenomenon of vortex-induced vibration can be simulated using the software.
The dissertation mainly contains following contents:
1. By using a preconditioning processing technic expanded into the unsteady compressible N-S equations, the problems of the algorithm tending to fare poorly for low speed flow fields can be solved.
2. Using Delaunay triangulation mesh to locate the relationship between grid points, the generation of dynamic mesh during unsteady flow field calculation had been achieved. Comparing with the traditional spring mesh method, Delaunay triangulation mesh method need any iterative computation and can provide high efficiency and good stability.
3. Developed professional software for effective numerical calculation and simulation of unsteady low velocity flow fields with moving boundaries. The results of several examples indicated that the preconditioning processing technic can extend the effective calculating range of the compressible algorithm to the low Mach number, especially to the low flow velocity condition of wind engineering for bridges. By combining with the structural dynamic equations, the software can provide the simulation of fluid-bridge coupling interaction.
4. The static aerodynamic forces of bridge girders were treated with unsteady numerical simulation using the software. The results had a good agreement with the ones in wind tunnel tests. Based on the bluff body bridge girder section and different turbulence models, the solving precision of the static aerodynamic forces had been studied.
5. Based on the numerical simulation for the vortex-induced vibration phenomenon in bridges and the analysis of the numerical flow field, a mechanism of vortex-induced vibration is eventually formed:when the vortex-induced vibration occurs, the bridge girder motion induced by initial vortex-induced aerodynamic loads can magnify the following aerodynamic loads, and the amplitude of bridge girder is increasing until the "lock in" status.
6. Based on the least squares fitting and the aerodynamic force in vertical and torsion motion, the flutter derivatives of thin plate and bridge girder had been obtained using forced vibration method of numerical simulation. The comparison between calculated results and theoretical results and wind tunnel test results can validate the feasibility of the software in the calculation of flutter derivatives.
引文
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