【作者】 张建；

【导师】 杨庆山；

【作者基本信息】 北京交通大学 ， 结构工程， 2011， 博士

【摘要】 采用计算流体力学技术(Computational Fluid Dynamics, CFD)模拟土木工程建构筑物的风荷载分布就是求解复杂边界条件下Navier-Stokes (N-S)方程的特征解。高雷诺流动是实际工程的最重要的风场特性,包括大涡模拟(Large Eddy Simulation, LES)和直接模拟(Direct Numerical Simulation, DNS)方法均无法很好的解决这个问题。雷诺时均方法(Reynolds Averaged Navier-Stokes, RANS)是基于时均化理论将非稳态的湍流运动处理为平均流场和雷诺应力场,这种方法的最大优点在于在保证流场大尺度流动特性的基础上,采用模型化方法计算雷诺应力场从而极大地节约计算资源。RANS方法中,包括大气边界层模型化、粗糙壁面处理方法以及涡粘模型(eddy-viscosity modelling)等仍存在一些问题亟待解决。若无法合理解决上述问题,会造成建构筑物风荷载计算的误差,以致在某些风敏感结构的设计与使用中产生隐患和危害。CFD技术在土木工程中应用首要解决的问题是准确模拟大气边界层的湍流流动。基于RANS理论求解湍流问题,是对模型化雷诺应力输运方程的求解。涡粘模型(eddy viscosity models)将雷诺应力表示为湍流特征尺度和平均风特征尺度的函数,是现阶段应用最广泛的雷诺应力模型化方法。随着计算精度要求的逐渐提高,非线性涡粘(nonlinear eddy viscosity models)逐步取代线性涡粘模型成为风工程研究中主要涡粘描述方法。同时,基于模型化大气边界层提取的来流条件和粗糙壁面处理方法也对湍流模拟产生重要影响。对于平均风和湍流特征量来流需满足平衡边界层假定和边界层内应力分布假定,由此得到的剖面形式才能更好的描述边界层上游流的特点。尽管对近壁流动处理的方法较多,但是模拟粗糙壁面流动的方法还不够成熟,其主要原因在于由地表粗糙产生小特征尺度无法用已有特征尺度表示,所以推导适用于不同湍流的粗糙壁面流动处理方法是亟待解决的重要问题之一。针对上述问题,本文围绕非线性涡粘模型、来流条件以及粗糙壁面处理方法,开展了理论和数值研究,主要工作和取得的成果如下：1.引入非线性涡粘模型。非线性涡粘模型能够考虑雷诺应力的各向异性特性,且需确保湍流模型的计算稳定性和准确性。由此,本文基于二次Boussinesq假定并将这类涡粘假定扩展到三维流动中,用于6m立方体绕流分析来模拟流场的脉动特性和变化。2.新型平均风和湍流特征量来流条件。引入经典气动粗糙高度y0来描述地表粗糙特性和湍流特征量的交换与输运,并将该模型与相关实测结果进行对比,证明本文选取模型的可行性与正确性。再将y0引入到平均风和湍流特征量剖面表达式中来描述上游粗糙效应的影响。3.近壁粗糙流处理。常用的壁面条件无法描述地表粗糙对流动的影响,由此本文基于平衡边界层假定,针对不同湍流模型推导适合近壁流动处理表达式；这些表达式与对应湍流模型结合来模拟平衡边界层流动,并与相关理论解对比,证明粗糙近壁流动模型的正确性。4.来流条件与近壁流动模型的渐进分析。本文采用渐进分析方法来验证来流条件与近壁流动模型的正确性和适用性,该方法采用两种特征尺度,对N-S方程进行处理,得到粘性子层和完全湍流区的雷诺应力表达式；将二者在缓冲层匹配后得到整个边界层内雷诺应力分布的渐进解。将来流条件和近壁流动模型与渐进解进行对比,证明来流条件和近壁流动模型的正确性。5.6m立方体绕流分析。基于Fluent平台,将上述非线性涡粘假定、来流条件与近壁流动模型结合,进行6m立方体的绕流分析。在两类风向角条件下,通过数值结果与实测结果对比发现,新型来流条件与粗糙壁面模型具有较好的普适性和较高的精确性。对相关结果进行分析,并对湍流模型的适用性进行总结。更多还原

【Abstract】 Practical engineering applications of the Computational Fluid Dynamics (CFD) are largely based on the numerical solution of the Reynolds averaged Navier-Stokes (RANS) equations. Turbulent flow problems of engineering interest often feature high Reynolds numbers and are thus difficult to solve by means of large eddy simulation, not to mention the direct numerical simulation. The biggest advantage of using the RANS in simulating turbulence flows is that they allow to treat the turbulence as a steady phenomena, i.e. if a flow is unsteady only because of turbulence the RANS simulation will be a steady simulation, with great saving of computational means. With appliation of RANS turbulence models, there are still several problems encountered like modelling of Atmosphere Boundary Layer (ABL), rough wall treatments, eddy-viscosity modelling etc.. These deficiencies hamper the development of wind loading simulation of the building structures aerodynamics accurately. This may cause deviations in research and un-safeties in design, especially for wind-sensitive engineering structures.The most imperative and basic requirement of CFD in civil engineering is accurate modeling turbulent flow in the simulated ABL. Of the first importance, it is required to model Reynolds stress transport. Eddy viscosity modelling is still by far the most popular method of RANS turbulence modelling. The constitutive model provides the Reynolds stress tensor as a function of the turbulent scales and the mean-velocity gradient. The constitutive models range from the simple linear Boussinesq-relation up to high-order tensor-polynomial expressions which can be derived from some underlying stress-transport closure by invoking an ad-hoc basis (nonlinear eddy viscosity models). Currently, a move from standard linear eddy-viscosity modelling towards nonlinear viscosity assumptions, seems to be going on in some areas of wind-related engineering. It should also be noticed that the proper choice of inlet flows represent the influence of the upstream surroundings. However, these boundary conditions are not fully known. For steady RANS simulations, the mean velocity and turbulence quantities profiles are required. The general derivation of these profiles and the resulting formulae should be obtained from the assumption of an equilibrium boundary layer. Despite many occurrences of near wall treatments in practical engineering applications, a robust model has yet to be fully developed. Fundamentally this is due to the small scale of the roughness relative to the largest scales of the boundary layer. The predictability roughness expressions of near wall flow will provide great supplement for turbulence modeling.To response to the above circumstances, this thesis adopted theoretical and numrical methods to carry out simulation of flow around6m cube, combined with appropriate inlet condition, rough wall treatments and turbulence models. The main works are as follows:I. To implant non-linear eddy viscosity in turbulence models. These investigations suggest that a turbulence model, suitable for wind engineering applications, should be able to model the anisotropy of turbulent flow while maintaining the ease of use and computational stability of the κ-ε models. Therefore, the quadratic non-linear expansions of the Boussinesq hypotheses, have been tested in an attempt to account for anisotropic turbulence and curvature related strain effects.II. New inlet profiles of mean wind and turbulence quantities based on ABL characteristics. Aerodynamic roughness height (?) is adopted to describe rough surface characteristics and turbulence exchange of underlying earth. And the comparison of (?) functions and experiment data are made to verify the numerical models. And then (?) is imported back into mean wind and turbulence quantities profiles to represent the upstream roughness influences.III. Rough wall treatment used for near wall flow. It was known that the standard near wall treatments are insufficient to estimate the effects of roughness on the flow quantities. So several new approaches of roughness effects corresponding to the turbulence models are taken into consideration based on the near wall flow characteristics. The new models are then applied to equilibrium boundary flow tested to analyze the effects on the rough wall effects. Overall agreement between the computational predictions and analytical findings is acceptable.IV. Asymptotic analysis of new inlet profiles and near wall treatments. Asymptotic analysis method here is used to verify the boundary conditions of ABL models propoed in the thesis. Two separate length scales of ABL flows are import into N-S functions to get two individual Reynolds stress functions corresponding to the viscosity sublayer and fully developed turbulent region. The uniform expression is derived based on the matching condition. This model provides good predictions on the Reynolds stress distribution along the ABL and well agreement on the near wall flow condition.V. Flow around6m cube. Three RANS turbulence models based on the anisotropic eddy viscosity assumptions combined with inlet profiles and new near wall treatmens are tested for the flow around6m cube model using Fluent as the solver. The numerical results are compared with the experimental findings in full scale measurements available in the literature of two incident flow directions. The results are analyzed and the effects of different turbulence parameters used in the modeling are discussed. Each turbulence model is individually reviewed for the correctness of its predictions and the best model in this set is chosen.更多还原