圆柱绕流的非线性动力学

本文利用非线性动力学的概念和方法来研究粘性不可压缩流体的二维圆柱绕流问题．计算了定常流失稳以及出现混沌的临界雷诺数，并估计了混沌解的一些统计特征．     

串列双圆柱绕流问题的数值模拟

本文运用有限体积方法,对绕串列放置的双圆柱的二维不可压缩流动进行了数值计算。为研究两圆柱不同间距对圆柱相互作用和尾流特征的影响,选取间距比Ｌ／Ｄ（Ｌ为两圆柱中心间的距离,Ｄ为圆柱直径）在１．５～５．０之间每隔０．５共八个有代表性的间距进行了计算模拟。计算均在Ｒｅ＝２００条件下进行。计算结果表明：对该绕流问题,流动特征在很大程度上取决于间距的大小。且间距存在一临界值,间距比从小于临界值变化到大于临界     

均匀来流中旋转圆柱黏性绕流的数值研究

从不可压非定常Ｎ－Ｓ方程出发，首次数值求解了均匀来流中圆柱作周向旋转振荡的黏性绕流问题。探讨了旋转角速度振幅、振荡频率及Ｒｅ数等因素对流场结构及其非定常演化过程的影响，并根据计算结果，给出了在旋转振动频率。速度振幅平面内流场涡结构的分区图。     

分块法研究圆柱绕流升阻力

使用新的分块耦合方法，分别对单圆柱和串列双圆柱绕流进行了数值模拟．对于单圆柱绕流，低Re下计算所得到的定常涡尺寸与实验非常接近．对于串列双圆柱绕流，研究分析了改变双圆柱中心间距对上下游圆柱的升阻力系数和脉动频率所产生的影响，计算结果与实验非常吻合，为进一步研究涡致振动提供了依据．     

非定常圆柱绕流的实验研究

本文采用流场显示方法研究单圆柱在非定常流动中的涡旋脱落规律。实验结果表明：在不同的ＫＣ数（ＫＣ＝Ｕ∞Ｔ／Ｄ）下，非常圆柱绕流的涡旋脱落特性是不相同的，一般随ＫＣ数值的增加，其涡旋脱落对数也增加，但有明显的阶梯性，同时圆柱分离点的周期变化后于流场的变化。     

基于动态混合网格的不可压非定常流计算方法

鱼类、昆虫等运动速度较低,对它们的数值模拟需要解决不可压问题.虚拟压缩方法通过在连续性方程中加入压强对虚拟时间的偏导数,从而把压力场和速度场耦合起来,解决了不可压缩流的计算问题.基于动态混合网格技术,利用双时间步方法耦合虚拟压缩方法来解决非定常不可压缩流的计算问题.为了加快每一虚拟时间步内的收敛速度,子迭代采用了高效的块LU-SGS方法,并且耦合了基于混合网格的多重网格方法.利用该方法数值模拟了不同雷诺数下的静止圆柱、振荡圆柱的绕流,得到了与实验和他人计算一致的结果.     

亚临界雷诺数下圆柱绕流的大涡模拟

本文应用Smagorinsky涡粘性模式和二阶精度的有限体积法对圆柱绕流的流场进行大涡模拟．求解了非正交曲线坐标系下的N-S方程,对雷诺数为100和20000的工况进行了计算．计算结果与实验及动力涡粘性模式的结果进行了比较,表明计算对于层流及高亚临界雷诺数的湍流流动是合理的     

不可压缩机翼绕流的有限谱法计算

结合有限谱QUICK格式求解不可压缩粘性流问题。这一格式用于模拟不同攻角下的NACA1200机翼绕流问题。利用体积力,提出了将流场速度从0加速到来流速度的方法。区别于传统的压力梯度为零的边界条件,推导出一个更精确的压力边界条件。为使速度散度保持为零,在泊松方程中给速度散度一个特殊的处理。这一成果说明了有限谱法不但具有很高的精度,而且能灵活地和其他格式一起构造出新的格式,从而成功地应用到复杂流场不可压缩流动的数值计算中。     

钝锥三维粘性绕流背风面分离的数值模拟

本文将作者在文献[1]中提出的方法推广应用于求解三维可压缩 N-S 方程和简化 N-S 方程,并对近似因式分解法应用于三维问题的稳定性进行了分析。指出,对二维问题原无条件稳定的格式,经近似因式分解后仍是无条件稳定的;对于三维问题,原无条件稳定的格式经普通近似因式分解后所得到的格式可能是不稳定的或条件稳定的。利用系数矩阵分裂法所得到的近似因式分解格式可仍是无条件稳定的,只要适当加大分裂后的系数反差即可。 文中给出了钝锥超音速三维粘性绕流结果。得到了背风面分离的流动图像,物面压力值与实验值吻合。     

分块法研究圆柱绕流升阻力

 使用新的分块耦合方法，分别对单圆柱和串列双圆柱绕流进行了数值 模拟. 对于单圆柱绕流，低$Re$下计算所得到的定常涡尺寸与实验非常接近. 对于 串列双圆柱绕流，研究分析了改变双圆柱中心间距对上下游圆柱的升阻力系数和脉动频率所 产生的影响，计算结果与实验非常吻合，为进一步研究涡致振动提供了依据.     

非定常不可压N-S方程的最小二乘算子分裂有限元法数值求解

采用最小二乘算子分裂有限元法求解非定常不可压N-S(Navier-Stokes)方程,即在每个时间层上采用算子分裂法将N-S方程分裂成扩散项和对流项,这样既能考虑对流占优特点又能顾及方程的扩散性质。扩散项是一个抛物型方程,时间离散采用向后差分格式,空间离散采用标准Galerkin有限元法。对流项的时间项采用后向差分格式,非线性部分用牛顿法进行线性化处理,再用最小二乘有限元法进行空间离散,得到对称正定的代数方程组系数矩阵。采用Re=1000的方腔流对该算法的有效性进行检验,表明其具有较高的精度,能够很好地捕捉流场中的涡结构。同时,对圆柱层流绕流进行了数值研究,通过流线图、压力场、阻力系数、升力系数及斯特劳哈数等结果的分析与对比,表明本文算法对于模拟圆柱层流绕流是准确和可靠的。     

粘性流基于特征线的四阶Runge-Kutta有限元法

对于二维不可压缩粘性流，通过沿流线方向的坐标变换，推导了无对流项的二维N-S（Navier-Stokes）方程。采用四阶Runge-Kutta法对N-S方程进行时间离散，并沿流线进行Taylor展开，得到显式的时间离散格式，然后利用Galerkin法对其进行空间离散，得到了高精度的有限元算法。利用本文算法对方腔驱动流和圆柱绕流进行了数值计算，通过对时间步长、网格尺寸和流场区域的计算分析，进一步验证了本文算法相比经典CBS法在时间步长、收敛性、耗散性和计算精度方面更具有优势。     

Numerical simulation on an interaction of a vortex street with an elliptical leading edge using an unstructured grid

An algorithm for a time accurate incompressible Navier–Stokes solver on an unstructured grid is presented. The algorithm uses a second order, three‐point, backward difference formula for the physical time marching. For each time step, a divergence free flow field is obtained based on an artificial compressibility method. An implicit method with a local time step is used to accelerate the convergence for the pseudotime iteration. To validate the code, an unsteady laminar flow over a circular cylinder at a Reynolds number of 200 is calculated. The results are compared with available experimental and numerical data and good agreements are achieved. Using the developed unsteady code, an interaction of a Karman vortex street with an elliptical leading edge is simulated. The incident Karman vortex street is generated by a circular cylinder located upstream. A clustering to the path of the vortices is achieved easily due to flexibility of an unstructured grid. Details of the interaction mechanism are analysed by investigating evolutions of vortices. Characteristics of the interactions are compared for large‐ and small‐scale vortex streets. Different patterns of the interaction are observed for those two vortex streets and the observation is in agreement with experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

A high-order compact scheme for solving the 2D steady incompressible Navier-Stokes equations in general curvilinear coordinates

In this paper, a high-order compact finite difference algorithm is established for the stream function-velocity formulation of the two-dimensional steady incompressible Navier-Stokes equations in general curvilinear coordinates. Different from the previous work, not only the stream function and its first-order partial derivatives but also the second-order mixed partial derivative is treated as unknown variable in this work. Numerical examples, including a test problem with an analytical solution, three types of lid-driven cavity flow problems with unusual shapes and steady flow past a circular cylinder as well as an elliptic cylinder with angle of attack, are solved numerically by the newly proposed scheme. For two types of the lid-driven trapezoidal cavity flow, we provide the detailed data using the fine grid sizes, which can be considered the benchmark solutions. The results obtained prove that the present numerical method has the ability to solve the incompressible flow for complex geometry in engineering applications, especially by using a nonorthogonal coordinate transformation, with high accuracy.     

A vorticity formulation for computational fluid dynamic and aeroelastic analyses of viscous flows

The paper deals with a novel computational formulation for the analysis of viscous flows past a solid body. The formulation is based upon a convenient decomposition of the flow field into potential and rotational velocity contributions, which has the distinguishing feature that the rotational velocity vanishes in much of, if not all, the region in which the vorticity is negligible. Contrary to related formulations implemented by the authors in the past, in the proposed approach, discontinuities of the potential and rotational velocity fields across a prescribed surface emanating from the trailing edge (such as the wake mid-surface) are eliminated, thereby facilitating numerical implementations. However, the main novelty is related to the application of the boundary condition: first, the expression for the velocity used for the condition on the body boundary is consistent with that for the velocity in the field; also—contrary to related formulations used by the authors in the past—in the proposed approach, the condition on the body boundary does not require the evaluation of the total vorticity (inside and outside the computational domain). The proposed algorithm, valid for three-dimensional compressible flows, is validated—as a first step—for the case of two-dimensional incompressible flows. Specifically, numerical results are presented for the aerodynamic analysis of two-dimensional incompressible viscous flows past a circular cylinder and past a Joukowski airfoil. In order to verify the desirable absence of artificial damping, we present also results pertaining to the flutter (i.e., dynamic aeroelastic) analysis of a spring-mounted circular cylinder in a viscous flow, free to move in a direction orthogonal to the unperturbed flow. In both cases (aerodynamics and aeroelasticity), the results are in good agreement with existing literature data.     

Computation of viscous incompressible flow using pressure correction method on unstructured Chimera grid

In this paper, a pressure correction algorithm for computing incompressible flows is modified and implemented on unstructured Chimera grid. Schwarz method is used to couple the solutions of different sub-domains. A new interpolation to ensure consistency between primary variables and auxiliary variables is proposed. Other important issues such as global mass conservation and order of accuracy in the interpolations are also discussed. Two numerical simulations are successfully performed. They include one steady case, the lid-driven cavity and one unsteady case, the flow around a circular cylinder. The results demonstrate a very good performance of the proposed scheme on unstructured Chimera grids. It prevents the decoupling of pressure field in the overlapping region and requires only little modification to the existing unstructured Navier–Stokes (NS) solver. The numerical experiments show the reliability and potential of this method in applying to practical problems.     

Diffusion toward a cylinder in the case of an arbitrary viscous flow. Diffusive boundary layer approximation

Steady convective diffusion of a dissolved substance toward the surface of a cylinder (optionally circular) in a viscous flow is examined. An analytical solution is obtained in [1, 2] for the case of laminar flow around a curved cylinder when the freestream flow is straight and uniform. More complex hydrodynamical problems are examined in [3, 4]. In the present work an approximate analytical expression is obtained for diffusive flow of a substance toward the surface of a solid cylinder in the case of an arbitrary two-dimensional flow. Formulas are given for calculating the mass transfer at a circular cylinder in some shear flows of a viscous, incompressible fluid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 163–166, September–October, 1976.The authors thank Yu. P. Gupalo and Yu. S. Ryazantseva for formulating the problem and their attention to the work.     

Numerical modeling of flow past a volumeless and thin rigid body using direct forcing immersed boundary method

The new capability has been added as the numerical method for modeling volumeless and thin rigid bodies to the direct forcing immersed boundary (DFIB) method. The DFIB approach is based on adding a virtual force to the Navier–Stokes equations of incompressible flow to account for the interaction between the fluid and structures. The volume of a solid function (VOS) identifies the stationary or moving solid structures in a given fluid domain. A new VOS-based algorithm was developed to identify thin, rigid structure boundary points in fluid flow and ensure that the fluid cannot cross through the boundary of a thin rigid structure while moving or stationary. The DFIB method was first validated in a three-dimensional (3D) turbulent flow over a circular cylinder. The large-eddy simulation simulated the turbulent flow scales. The proposed algorithm was tested using a 3D turbulent flow past a stationary and rotating Savonius wind turbine that functions as a thin, rigid body. The validation results showed that the selected DFIB approach, combined with the novel algorithm, could simulate a thin, volumeless, rigid structure that is stationary and rotating in incompressible turbulent flows. The current method is also applicable for two-way fluid-structure interaction problems.     

多维SUPG格式不可压流动高精度算法研究

在传统流线迎风Petrov-Galerkin (SUPG)有限元法基础上，通过对稳定因子关键参数进行分析，提出了基于流向投影的最优特征高度参数确定方法，同时针对不可压流动引入变量分裂算法，发展了一种可用于高雷诺数不可压流动计算的高精度稳定化SUPG方法．详细地给出了三角形单元基于流向的最优特征高度确定方法的分析过程，并给出了基于分裂算法的有限元计算步骤和公式．采用该方法对典型的方腔拖曳、圆柱绕流流动问题进行了分析，在网格较稀疏，且雷诺数较大的情况下，依然可以得到稳定的计算结果，从而验证了该方法的稳定性、有效性，对实际工程应用具有积极的意义．