含运动边界钝体绕流风场的大涡模拟数值算法
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摘要
薄膜屋盖结构与风场之间的流固耦合作用是影响结构风振响应的重要因素。数值模拟是流固耦合研究的重要手段,准确模拟流体域的时变特性是掌握流固耦合效应产生机理和发展规律的前提。风与薄膜结构流固耦合运动中的流体域是含动边界的钝体绕流近地风场,在采用计算流体动力学(Computational Fluid Dynamics,CFD)技术对其进行大涡模拟(Large-eddy Simulation, LES)数值近似计算时,仍存在一些亟待解决的问题。
建立适于大型工程应用的亚格子模型是大涡模拟方法理论研究中的热点问题之一。在求解近地风场大涡模拟控制方程时,投影法是一种高效的压力速度解耦算法。目前大多数投影格式对压力的计算在时间方向上比速度的计算至少低一阶精度,而压力场的时间精度将直接影响流固耦合效应的计算精度。因此,投影法的压力时问精度还有待提高。此外,动边界绕流模拟适宜在任意拉格朗日欧拉(Arbitrary Lagrangian Eulerian, ALE)动态网格框架下进行。模拟过程中网格更新频繁,其几何品质和更新前后的一致性是影响模拟精度的重要因素。目前大部分动网格更新算法仅关注更新后网格的几何品质,对更新前后网格一致性的测试不够；而动网格更新算法的计算耗时也是需要考虑的一个课题。
针对上述问题,本文对亚格子模型、投影法及其在ALE动态网格下的应用以及动网格更新技术等内容进行了理论和数值研究,开展的研究工作和提出的解决方案主要包括：
1、亚格子模型的测试和对比。在阐述近地风场的大涡模拟无量纲控制方程以及多种亚格子模型的构造过程后,在笛卡尔静态网格下编制了方程求解程序。以该程序为计算平台,对多种亚格子模型的适用性、准确性和计算效率进行了测试。结果表明,钝体绕流风场的大涡模拟工程应用中可以采用阻尼修正的标准S模型。
2、动态网格下数值求解方法的建立。以ALE描述为基础,在动态网格下建立了大涡模拟控制方程(下文简称ALE-LES方程),并对方程中的网格运动参数和流动参数进行解耦,建立了交错求解方程的数值计算方法。期间,为提高数值方法的时间计算精度,构造了压力和速度能达到同一高阶时间精度的全精度连续投影方法,并将其与求解网格运动的二阶预测校正格式相结合,得到了ALE-LES方程的全二阶精度投影格式。将建立的数值求解方法进行坐标转换,在贴体坐标系下编制了ALE-LES方程求解程序的核心模块。
3、动网格更新算法的对比研究。归纳整理出网格质量评价模型,并据此在两种畸变网格算例中,为适用于结构网格的多种动网格更新算法对网格几何品质的改善力度进行了对比；同时,对不同算法在更新前后网格的一致性和计算效率方面进行了测试,指出九点网格重构法综合性能最为优异。将九点网格重构法扩展到三维研究领域并更名为距离加权法,据此编制了网格动态更新子程序模块。
4、数值模拟程序的开发和验证。将亚格子模型子程序模块和网格动态更新子程序模块与求解ALE-LES方程的核心程序相结合,开发了适用于模拟含运动边界钝体绕流风场的CFD计算程序。分别以二维方腔驱动流和Taylor涡列问题验证了程序的稳定性和时间计算精度。
5、振动屋盖绕流特性的数值分析。以下部封闭式大跨度平屋盖结构为研究对象,应用本文开发程序,对屋盖以二阶谐波模态振动时的结构绕流场进行了数值模拟,通过与相同尺寸刚性屋盖结构绕流模拟结果的对比分析,研究了屋盖的振动对模型表面风压系数分布和绕流场流动结构的影响。结果表明,屋盖振动是影响建筑结构表面平均、脉动风压系数的重要因素；屋盖振动导致绕流场旋涡结构复杂化,特征湍流度增加；屋盖的振动对绕流场瞬时风压分布的影响明显,二阶谐波模态的振动形式容易引发脉动风与屋盖的共振,不利于屋盖的抗风稳定。自主开发程序的成功应用表明了该程序可作为薄膜结构流固耦合效应数值模拟计算平台的流体域求解器。
The fluid-structure interaction (FSI) between membrane structures and atmospheric wind is a very important factor for the wind-induced response of membrane. Numerical simulation is an effective research tool for the FSI. Accurately simulating the time-dependent feature of flow field is one precondition to figure out the formation mechanism and development pattern of the FSI. The flow field in the FSI between wind and membrane is a near ground wind field around a bluff body involving moving boundaries. There are some problems to be solved in the Large-eddy Simulation (LES) of the wind field using the Computational Fluid Dynamics (CFD) technique.
Firstly, Sub-grid Scale (SGS) model that suit for large project is one of the hotspot problems in the theoretical research of LES. Secondly, the projection method is an effective algorithm for decoupling the velocities and pressure in governing equations of the near-ground wind which is treated as incompressible flow. The time accuracy of pressure is lower than that of velocity in most existing projection algorithms. The time accuracy of pressure is a direct influence factor in FSI simulation. Therefore, pressure accuracy of projection method should be improved. Furthermore, an appropriate grid system for simulating the flow field involving moving boundaries is the Arbitrary Lagrangian Eulerian (ALE) dynamic grid. Mesh updating is quite frequent in the simulation. Geometric quality of grid and the grid conformance during update are two key factors for the accuracy of the simulation. Grid quality is the only concern in most existing mesh updating strategies, and their grid conformance is not tested. Likewise, the computational time of mesh updating strategies needs to be considered.
To respond to the above problems, theoretical investigations and numerical researches about the SGS model, a projection method and its implement in ALE dynamic grid system, dynamic mesh updating strategy are conducted. The corresponding solution and main works of this thesis could be summarized as follows:
1. Test and comparison of SGS models. Non-dimensional LES governing equations that describe near ground wind field and the construction processes of some SGS models were elaborated. A CFD code that solves the equations above was compiled on Cartesian static grid system using finite differencing method. The applicability, accuracy and efficiency of various SGS models were tested. An efficient and relatively accurate SGS model was selected for the LES of the wind field around a bluff body and was compiled as a subprogram module.
2. Establishment of numerical method in dynamic grid framework. LES governing equations in ALE dynamic grid system (ALE-LES equations) were expounded. By decoupling the grid motion and the physical parameters of the wind field, a staggered ALE (SALE) strategy was established. Meanwhile, a Fully high-order accurate continuous Projection algorithm (FP) by which the time-accuracy of pressure could reach the same order of velocity was constructed. By combination with a second-order accurate predictor-corrector scheme for grid velocity, a fully second-order accurate projection method for solving ALE-LES equations was proposed. Then, a coordinates transformation from Cartesian grid system to Body-Fitted curvilinear Structured (BFS) grid system was performed on the proposed numerical method, and the main program module based on the transformed method was compiled.
3. Comparison of analyses for mesh updating strategies. A grid quality evaluation model was concluded and used for testing the grid quality improvement of various mesh updating strategies in two skewed meshes. The grid conformance during updating and the efficiency are also tested and compared. The comparison of results showed that Nine-point rezone strategy was an optimum from comprehensive performance. Then, Nine-point rezone strategy was extended from two-dimension into three-dimension, and was renamed to be a distance weighting strategy according to the basic idea. A dynamic mesh updating subprogram module was compiled.
4. Development and validation of the numerical simulation program. A CFD program called (BFS\SALE-D\FP)LES for simulating the near-ground wind field around a bluff body involving moving boundaries was developed by combining the chosen SGS model and the chosen mesh updating strategy with the main program module described above. The two dimensional lid-driven flow and the Taylor vortex streets were used to validate the stability and accuracy of this CFD program respectively.
5. Application of the numerical simulation program. The near-ground wind field around an enclosed building of which the flat roof vibrating in second-order harmonic mode was simulated by (BFS\SALE-D\FP)LES program. By comparison with the wind field around the same building with a rigid roof, the effect of roof vibration on the pressure coefficient at the building surface and on the flow phenomenon nearby building was investigated. The comparison shows that the roof vibration is a key factor that influences the mean and rms pressure coefficient on the building. The roof vibration complicates the vortex structure, and increases the characteristic turbulence intensity of the wind field around the building. The roof vibration has notable influence on the instantaneous pressure distribution and value. The second-order harmonic vibration mode may induce resonance of fluctuating wind and roof, and is not conducive for the wind-resistant of building.
The successful application of the (BFS\SALE-D\FP)LES program indicated that this program could used as an effective fluid solver for the FSI numerical simulation platform of membrane structures.
建立适于大型工程应用的亚格子模型是大涡模拟方法理论研究中的热点问题之一。在求解近地风场大涡模拟控制方程时,投影法是一种高效的压力速度解耦算法。目前大多数投影格式对压力的计算在时间方向上比速度的计算至少低一阶精度,而压力场的时间精度将直接影响流固耦合效应的计算精度。因此,投影法的压力时问精度还有待提高。此外,动边界绕流模拟适宜在任意拉格朗日欧拉(Arbitrary Lagrangian Eulerian, ALE)动态网格框架下进行。模拟过程中网格更新频繁,其几何品质和更新前后的一致性是影响模拟精度的重要因素。目前大部分动网格更新算法仅关注更新后网格的几何品质,对更新前后网格一致性的测试不够；而动网格更新算法的计算耗时也是需要考虑的一个课题。
针对上述问题,本文对亚格子模型、投影法及其在ALE动态网格下的应用以及动网格更新技术等内容进行了理论和数值研究,开展的研究工作和提出的解决方案主要包括：
1、亚格子模型的测试和对比。在阐述近地风场的大涡模拟无量纲控制方程以及多种亚格子模型的构造过程后,在笛卡尔静态网格下编制了方程求解程序。以该程序为计算平台,对多种亚格子模型的适用性、准确性和计算效率进行了测试。结果表明,钝体绕流风场的大涡模拟工程应用中可以采用阻尼修正的标准S模型。
2、动态网格下数值求解方法的建立。以ALE描述为基础,在动态网格下建立了大涡模拟控制方程(下文简称ALE-LES方程),并对方程中的网格运动参数和流动参数进行解耦,建立了交错求解方程的数值计算方法。期间,为提高数值方法的时间计算精度,构造了压力和速度能达到同一高阶时间精度的全精度连续投影方法,并将其与求解网格运动的二阶预测校正格式相结合,得到了ALE-LES方程的全二阶精度投影格式。将建立的数值求解方法进行坐标转换,在贴体坐标系下编制了ALE-LES方程求解程序的核心模块。
3、动网格更新算法的对比研究。归纳整理出网格质量评价模型,并据此在两种畸变网格算例中,为适用于结构网格的多种动网格更新算法对网格几何品质的改善力度进行了对比；同时,对不同算法在更新前后网格的一致性和计算效率方面进行了测试,指出九点网格重构法综合性能最为优异。将九点网格重构法扩展到三维研究领域并更名为距离加权法,据此编制了网格动态更新子程序模块。
4、数值模拟程序的开发和验证。将亚格子模型子程序模块和网格动态更新子程序模块与求解ALE-LES方程的核心程序相结合,开发了适用于模拟含运动边界钝体绕流风场的CFD计算程序。分别以二维方腔驱动流和Taylor涡列问题验证了程序的稳定性和时间计算精度。
5、振动屋盖绕流特性的数值分析。以下部封闭式大跨度平屋盖结构为研究对象,应用本文开发程序,对屋盖以二阶谐波模态振动时的结构绕流场进行了数值模拟,通过与相同尺寸刚性屋盖结构绕流模拟结果的对比分析,研究了屋盖的振动对模型表面风压系数分布和绕流场流动结构的影响。结果表明,屋盖振动是影响建筑结构表面平均、脉动风压系数的重要因素；屋盖振动导致绕流场旋涡结构复杂化,特征湍流度增加；屋盖的振动对绕流场瞬时风压分布的影响明显,二阶谐波模态的振动形式容易引发脉动风与屋盖的共振,不利于屋盖的抗风稳定。自主开发程序的成功应用表明了该程序可作为薄膜结构流固耦合效应数值模拟计算平台的流体域求解器。
The fluid-structure interaction (FSI) between membrane structures and atmospheric wind is a very important factor for the wind-induced response of membrane. Numerical simulation is an effective research tool for the FSI. Accurately simulating the time-dependent feature of flow field is one precondition to figure out the formation mechanism and development pattern of the FSI. The flow field in the FSI between wind and membrane is a near ground wind field around a bluff body involving moving boundaries. There are some problems to be solved in the Large-eddy Simulation (LES) of the wind field using the Computational Fluid Dynamics (CFD) technique.
Firstly, Sub-grid Scale (SGS) model that suit for large project is one of the hotspot problems in the theoretical research of LES. Secondly, the projection method is an effective algorithm for decoupling the velocities and pressure in governing equations of the near-ground wind which is treated as incompressible flow. The time accuracy of pressure is lower than that of velocity in most existing projection algorithms. The time accuracy of pressure is a direct influence factor in FSI simulation. Therefore, pressure accuracy of projection method should be improved. Furthermore, an appropriate grid system for simulating the flow field involving moving boundaries is the Arbitrary Lagrangian Eulerian (ALE) dynamic grid. Mesh updating is quite frequent in the simulation. Geometric quality of grid and the grid conformance during update are two key factors for the accuracy of the simulation. Grid quality is the only concern in most existing mesh updating strategies, and their grid conformance is not tested. Likewise, the computational time of mesh updating strategies needs to be considered.
To respond to the above problems, theoretical investigations and numerical researches about the SGS model, a projection method and its implement in ALE dynamic grid system, dynamic mesh updating strategy are conducted. The corresponding solution and main works of this thesis could be summarized as follows:
1. Test and comparison of SGS models. Non-dimensional LES governing equations that describe near ground wind field and the construction processes of some SGS models were elaborated. A CFD code that solves the equations above was compiled on Cartesian static grid system using finite differencing method. The applicability, accuracy and efficiency of various SGS models were tested. An efficient and relatively accurate SGS model was selected for the LES of the wind field around a bluff body and was compiled as a subprogram module.
2. Establishment of numerical method in dynamic grid framework. LES governing equations in ALE dynamic grid system (ALE-LES equations) were expounded. By decoupling the grid motion and the physical parameters of the wind field, a staggered ALE (SALE) strategy was established. Meanwhile, a Fully high-order accurate continuous Projection algorithm (FP) by which the time-accuracy of pressure could reach the same order of velocity was constructed. By combination with a second-order accurate predictor-corrector scheme for grid velocity, a fully second-order accurate projection method for solving ALE-LES equations was proposed. Then, a coordinates transformation from Cartesian grid system to Body-Fitted curvilinear Structured (BFS) grid system was performed on the proposed numerical method, and the main program module based on the transformed method was compiled.
3. Comparison of analyses for mesh updating strategies. A grid quality evaluation model was concluded and used for testing the grid quality improvement of various mesh updating strategies in two skewed meshes. The grid conformance during updating and the efficiency are also tested and compared. The comparison of results showed that Nine-point rezone strategy was an optimum from comprehensive performance. Then, Nine-point rezone strategy was extended from two-dimension into three-dimension, and was renamed to be a distance weighting strategy according to the basic idea. A dynamic mesh updating subprogram module was compiled.
4. Development and validation of the numerical simulation program. A CFD program called (BFS\SALE-D\FP)LES for simulating the near-ground wind field around a bluff body involving moving boundaries was developed by combining the chosen SGS model and the chosen mesh updating strategy with the main program module described above. The two dimensional lid-driven flow and the Taylor vortex streets were used to validate the stability and accuracy of this CFD program respectively.
5. Application of the numerical simulation program. The near-ground wind field around an enclosed building of which the flat roof vibrating in second-order harmonic mode was simulated by (BFS\SALE-D\FP)LES program. By comparison with the wind field around the same building with a rigid roof, the effect of roof vibration on the pressure coefficient at the building surface and on the flow phenomenon nearby building was investigated. The comparison shows that the roof vibration is a key factor that influences the mean and rms pressure coefficient on the building. The roof vibration complicates the vortex structure, and increases the characteristic turbulence intensity of the wind field around the building. The roof vibration has notable influence on the instantaneous pressure distribution and value. The second-order harmonic vibration mode may induce resonance of fluctuating wind and roof, and is not conducive for the wind-resistant of building.
The successful application of the (BFS\SALE-D\FP)LES program indicated that this program could used as an effective fluid solver for the FSI numerical simulation platform of membrane structures.
引文
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