基于CV Newmark-β法的桥梁风致振动FSI数值模拟

FSI Numerical Simulation of Bridge Wind-induced Vibration Based on CV Newmark-β Method

为求解桥梁断面风致振动问题,首先介绍了两类数值微分方程解法,然后以Ansys Fluent为计算平台,通过嵌入自定义函数的方法实现了流线型桥梁断面的流固耦合数值模拟。通过理论推导发现,通过以常规的Newmark-β法嵌入UDF来驱动桥梁断面附近网格做刚体运动建立起的流固耦合计算模型计算得到的位移,与Fluent程序中网格更新的实际位移不一致,因而提出了一种修正速度的Newmark-β法以消除这种误差效应,并且建立了相应的桥梁断面流固耦合计算模型。针对某具体桥梁断面分别采用以常规Newmark-β法和修正速度的Newmark-β法建立的流固耦合计算模型,进行了低风速下和高风速下的桥梁断面风致振动数值模拟。研究表明:断面小振幅运动下不同计算模型获得的位移时程曲线基本吻合,以常规的Newmark-β法计算获得的位移与网格运动的真实位移之间的误差较小,低风速下这种算法与网格真实运动之间的位移不匹配效应产生的误差可以忽略;高风速桥梁断面大振幅颤振下不同计算模型获得的位移时程曲线差距较大,以常规的Newmark-β法建立起的流固耦合计算模型计算获得的位移与网格真实运动之间的位移不一致效应造成的误差不可忽略;低风速和高风速下以修正速度的Newmark-β法建立起的流固耦合计算模型获得的位移均与程序中网格真实运动位移一致。进行桥梁断面风致振动CFD数值模拟颤振问题时,应尤其注意处理这种位移误差效应,以建立合理的流固耦合计算模型。

In order to solve the problem of wind-induced vibration of bridge section, 2 kinds of solution of numerical differential equation are introduced at first. Then, taking Ansys Fluent as the computing platform and embedding user defined function （UDF） , the FSI numerical simulation for streamlined bridge section is realized. After theoretical analysis, it is found that the displacement obtained by the FSI calculation model, where the grids near the bridge section are driven by conventional Newmark-beta program embedded in UDF, differs from that of grid updated in Fluent program, so a corrected velocity Newmark-β （ CV Newmark-β） method is proposed to eliminate such error effect, and the corresponding bridge section FSI computation model is set up. For a concrete bridge section, the numerical simulations of wind-induced vibration of bridge section under low and high wind speeds are conducted using the FSI models established by conventional Newmark-β method and CV Newmark-β method respectively. The research shows that （ 1 ） while the bridge section taking small amplitude motion, the displacement time history curves obtained by different calculation models are basically consistent, the error of displacement from conventional Newmark-β method and actual gird motion is smaller, and the error of the displacement mismatch effect between this algorithm and the real motion of the grid can be ignored under low wind speed; （2） while the bridge section taking lager amplitude flutter motion under high wind speed, the disparities of the displacement time history curves obtained by different calculation models are large, so that the error of the displacement mismatch effect between the value calculated by the FSI model established by conventional Newmark-β algorithm and the value of the real motion of the grid cannot be ignored; （3） whether under low wind speed or high wind speed, the displacement obtained by the FSI calculation model set by CV Newmark-β method is in consistent with the real displacement of the grid motion updated in Fluent program. Therefore, while performing the CFD numerical simulation of the wind-induced bridge section flutter, such mismatch effect should be cared respectably to establish a reasonable FSI calculation model.