摘要
随着计算机科学和数值求解技术的飞速发展,基于计算流体动力学(Computational Fluid Dynamic, CFD)的湍流风场数值模拟以及风和结构的流固耦合(Fluid-Structure Interaction,FSI)分析已经成为结构工程中的研究热点。
首先,提出了一种计算不可压缩粘性流问题的新型稳定化流体有限元方法。将半隐式三步方法(Three-step Method)和流线迎风Petrov-Galerkin (SUPG)稳定化方法相结合,运用SUPG迎风格式进行空间离散,对速度场和压力场则采用同阶的线性插值函数,从而有效提高了流体速度和压力的计算稳定性与计算效率。方腔拖拽流、平行四边形腔拖拽流以及三角形腔拖拽流的数值计算结果与已有文献结果吻合较好,验证了本文方法的精确性和有效性。
其次,在本文的新型稳定化流体有限元方法的基础上,发展了一种新型稳定化流体有限元大涡模拟方法。将经典Smagorinsky亚格子模型(Sub-grid Scale model)与SUPG稳定化方法相结合,并成功应用于瞬态、非定常高雷诺数湍流流场的数值模拟。对空间离散,采用速度和压力同阶的插值函数;对时间离散,采用二阶精度且高稳定化的三步方法。数值计算显示,本方法可有效消除高雷诺数下的速度场和压力场的数值振荡现象,在较粗糙网格条件下得到较准确的速度场、压力场和气动力特性参数等计算结果。
第三,针对动态亚格子模型(Dynamic Sub-grid Scale model)的滤波过程,将节点滤波函数和广义盒式滤波函数相结合,发展了一种简单、快速的非结构化网格滤波方法。在本文的新型稳定化流体有限元方法和动态亚格子模型的基础上,发展了一种适用于模拟结构周围风场湍流流动特性的新型动态大涡模拟方法。数值计算结果表明,本方法可模拟复杂结构形体周围的湍流流动问题,刻画建筑结构周围风场的特征旋涡结构。
第四,针对流体域网格更新问题,本文改进了弹簧近似法(Spring Analogy Method),在弹簧刚度定义中考虑了网格形状和尺度的影响。改进弹簧近似法具备线性弹簧和扭转弹簧的优点,适用于二维和三维边界移动问题。另一方面,基于本文新型稳定化流体有限元大涡模拟方法,推导了任意拉格朗日-欧拉(Arbitrary Lagrangian-Eulerian,ALE)描述下的风场控制方程有限元列式,并用于数值模拟结构在大振幅强迫振动下的湍流风场。
最后,针对大跨空间结构的风致振动问题,运用流固耦合(FSI)力学理论,建立了结构风振分析方法,即采用包含流体域、结构域和网格域三个计算模块的分区算法。在流固耦合计算中,运用新型稳定化有限元大涡模拟方法计算流体域,采用有限元列式的Newmark逐步积分方法计算结构域,采用改进弹簧近似方法更新计算网格域。另一方面,运用上述方法,数值模拟了单层网壳球面屋盖结构的风振问题,揭示了球面屋盖结构的绕流特性和结构周围的特征旋涡结构,对比分析了刚性模型和考虑流固耦合模型的结构屋面平均风压、脉动风压分布情况以及结构自身的动力响应。
With the great progresses in computer technique and numerical methods, the turbulent wind simulations and the FSI (Fluid-Structure Interactions) between wind and structures, based on CFD (Computational Fluid Dynamic), have already been hot issues in structural engineering.
First, a novel stabilized fluid finite element method is proposed for the predictions of incompressible viscous fluid problems. With the combination of semi-implicit three step method and streamline upwind Petrov-Galerkin (SUPG) method, the SUPG stabilized scheme is used for the spatial discretization, the same order interpolations are performed for both velocity and pressure fields. Thus, the computational stabilization on both velocity and pressure, and the computational efficiency are effectively improved. The numerical predictions on lid driven flows in square, triangular and skewed cavities are close to reference results which testify the accuracy and efficiency of present method.
Secondly, based on present novel stabilized fluid finite element method, a novel large eddy simulation of stabilized fluid finite element is developed. With the combination of classical Smagorinsky sub-grid scale model and the SUPG stabilized method, the present method can be successfully applied for numerical simulation of both transient and unsteady turbulent flows with high Reynolds number. The same order interpolation is employed for spatial discretization of both velocity and pressure. The temporal discretization is applied by three-step technique which is second order accurate and high stabilized. Numerical examples show that present method can effectively suppress the computational oscillation of velocities and pressure fields, as well as yield compared accurate velocity and pressure fields as well as aerodynamic parameters.
Thirdly, for the second filtering progress of dynamic sub-grid scale model, a simple and fast spatial filtering method on unstructured finite element grids is developed by the combination of both node-based filter and generalized box filter. Then, based on present novel stabilized fluid finite element method and dynamic sub-grid scale model, dynamic large eddy simulation is developed to predict turbulent flow characteristics around structures. Numerical simulation shows that present numerical method can model the turbulent flow problems with complex structural geometry and describe typical vortex structures of wind around structures.
Fourthly, for the grids update of the fluid domain, spring analogy method is improved by introducing scale and shape parameters to the definition of the spring stiffness. The improved spring analogy method has the strongpoints of both lineal spring method and torsional spring method, and adapts both two and three dimensional boundary movement problems. On the other hand, based on present large eddy simulation technique of stabilized fluid finite element method, the finite element formulation of wind field described by arbitrary Lagrangian-Eulerian (ALE) formulation is deduced to numerically simulate turbulent wind field under the circumstance of large amplitude structural forced vibration.
Finally, by applying the FSI theory, a numerical method is constituted for wind induced vibration analysis of long span spatial structures. Partitioned procedure is adopted, including fluid domain, structure domain and grid domain. Present large eddy simulation technique of finite element method is applied for the prediction of fluid domain. Newmark integral method based on finite element formulation is applied for the computation of structure domain. And improved spring analogy method is applied for the gird update of grid domain. The wind induced vibration of spherical single layer lattice shell structure is predicted, and the bluff flow characteristics and typical vortex structures around structures are indicated. Further more, the mean wind pressure, fluctuating wind pressure and dynamical responses of structures based on the rigid structural model and structural model considering FSI are analysed, respectively.
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