Two‐dimensional prediction of time dependent,turbulent flow around a square cylinder confined in a channel

This paper presents two‐dimensional and unsteady RANS computations of time dependent, periodic, turbulent flow around a square block. Two turbulence models are used: the Launder–Sharma low‐Reynolds number k–ε model and a non‐linear extension sensitive to the anisotropy of turbulence. The Reynolds number based on the free stream velocity and obstacle side is Re=2.2×10⁴. The present numerical results have been obtained using a finite volume code that solves the governing equations in a vertical plane, located at the lateral mid‐point of the channel. The pressure field is obtained with the SIMPLE algorithm. A bounded version of the third‐order QUICK scheme is used for the convective terms. Comparisons of the numerical results with the experimental data indicate that a preliminary steady solution of the governing equations using the linear k–ε does not lead to correct flow field predictions in the wake region downstream of the square cylinder. Consequently, the time derivatives of dependent variables are included in the transport equations and are discretized using the second‐order Crank–Nicolson scheme. The unsteady computations using the linear and non‐linear k–ε models significantly improve the velocity field predictions. However, the linear k–ε shows a number of predictive deficiencies, even in unsteady flow computations, especially in the prediction of the turbulence field. The introduction of a non‐linear k–ε model brings the two‐dimensional unsteady predictions of the time‐averaged velocity and turbulence fields and also the predicted values of the global parameters such as the Strouhal number and the drag coefficient to close agreement with the data. Copyright © 2009 John Wiley & Sons, Ltd.     

A local domain‐free discretization method for simulation of incompressible flows over moving bodies

This paper presents a local domain‐free discretization (DFD) method for the simulation of unsteady flows over moving bodies governed by the incompressible Navier–Stokes equations. The discretization strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. All the mesh points are classified as interior points, exterior dependent points and exterior independent points. The functional values at the exterior dependent points are updated at each time step by the approximate form of solution near the boundary. When the body is moving, only the status of points is changed and the mesh can stay fixed. The issue of ‘freshly cleared nodes/cells’ encountered in usual sharp interface methods does not pose any particular difficulty in the presented method. The Galerkin finite‐element approximation is used for spatial discretization, and the discrete equations are integrated in time via a dual‐time‐stepping scheme based on artificial compressibility. In order to validate the present method for moving‐boundary flow problems, two groups of flow phenomena have been simulated: (1) flows over a fixed circular cylinder, a harmonic in‐line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a pure pitching airfoil, a heaving–pitching airfoil and a deforming airfoil. The predictions show good agreement with the published numerical results or experimental data. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐dimensional computation for flow‐induced vibrations in in‐line and cross‐flow directions of a circular cylinder

We present numerical results for in‐line and cross‐flow vibrations of a circular cylinder, which is immersed in a uniform flow and is elastically supported by damper‐spring systems to compute vibrations of a rigid cylinder. In the case of a circular cylinder with a low Scruton number, it is well‐known that two types of self‐excited vibrations appear in the in‐line direction in the range of low reduced velocities. On the other hand, a cross‐flow vibration of the circular cylinder can be excited in the range of high reduced velocities. Therefore, we compute the flow‐induced vibrations of the circular cylinder in the wide range of the reduced velocities at low and high Scruton numbers and discuss about excitation mechanisms in the in‐line and cross‐flow directions. Copyright © 2011 John Wiley & Sons, Ltd.     

基于VLES模型的振动圆柱数值模拟

本文将一种VLES(Very Large Eddy Simulation)模型引入到动网格数值计算中,并验证了VLES模型用于模拟类似振动圆柱绕流的动边界问题的有效性。数值求解了不同振幅和频率下非稳态振动圆柱绕流问题。研究表明:随着振幅和激励频率的增加,绕圆柱流动涡脱离形式从2S模式转换到2P0模式,再到P+S模式。在高振幅和激励频率比fe/fs=0.95时,涡脱离形式却表现为2P0模式到P+S模式的过渡状态,振动圆柱在上升或下降过程中涡的脱离造成在每个周期升力曲线的左右侧发生不规则的"跳动"现象,尽管脱落涡可能为涡对或者单涡.     

转筒黏度计测量液体黏度方法研究

用黏性流体力学理论求得测量装置中旋转液体径向速度梯度的理论公式,进而得到转筒法测量黏度的较精确公式.指出了国内的一些教材和文献在推导中使用近似公式的错误,用参数估计的方法求得测量装置的摩擦阻力力矩,使测量结果得到进一步校正.实验研究表明:按照近似公式与精确公式计算求得的径向速度梯度之差可达到13.1%,求得的液体黏度之差可达到28.6%;在蓖麻油的温度为25.5℃时测得测量装置的摩擦阻力力矩为9.482×10-5 N·m,相当于0.540克重物产生的力矩.     

Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder

Analytical study for electromagnetothermoelastic behaviors of a hollow cylinder composed of functionally graded piezoelectric material (FGPM), placed in a uniform magnetic field, subjected to electric, thermal and mechanical loads are presented. For the case that the electric, magnetic, thermal and mechanical properties of the material obey an identical power law in the radial direction, exact solutions for electric displacement, stresses, electric potential and perturbation of magnetic field vector in the FGPM hollow cylinder are determined by using the infinitesimal theory of electromagnetothermoelasticity. Some useful discussions and numerical examples are presented to show the significant influence of material inhomogeneity, and adopting a certain value of the inhomogeneity parameter β and applying suitable electric, thermal and mechanical loads can optimize the FGPM hollow cylindrical structures. This will be of particular importance in modern engineering design.     

椭圆柱电缆单位长度的自感计算

利用复数坐标系z上的儒可夫斯基变换,计算长直椭圆柱电缆单位长度的自感,并对结果进行讨论.     

Numerical simulation of laminar flow past a circular cylinder

The present paper focuses on the analysis of two- and three-dimensional flow past a circular cylinder in different laminar flow regimes. In this simulation, an implicit pressure-based finite volume method is used for time-accurate computation of incompressible flow using second order accurate convective flux discretisation schemes. The computation results are validated against measurement data for mean surface pressure, skin friction coefficients, the size and strength of the recirculating wake for the steady flow regime and also for the Strouhal frequency of vortex shedding and the mean and RMS amplitude of the fluctuating aerodynamic coefficients for the unsteady periodic flow regime. The complex three dimensional flow structure of the cylinder wake is also reasonably captured by the present prediction procedure.     

Fluid forces on a square cylinder in oscillating flows with non‐zero‐mean velocities

The unsteady forces on a square cylinder in sinusoidally oscillating flows with non‐zero‐mean velocities are investigated numerically by using a weakly compressible‐flow method with three‐dimensional large eddy simulations. The major parameters in the analysis are Keulegan–Carpenter number (KC) and the ratio between the amplitude and the mean velocities of the approaching flow (A_R). By varying the values of KC and A_R the resulting drag and lift of the cylinders are analyzed systematically at two selected approaching‐flow attack angles (0 and 22.5^°). In the case of the non‐zero attack angle, results show that both the drag and lift histories can be adequately described by Morison equations. However, Morison equations fail to correctly describing the lift history as the attack angle is zero. In addition, when the ratio of A_R/KC is near the Strouhal number of the bluff‐body flow, the resulting drag is promoted due to the occurrence of resonance. Based on the results of systematic analyses, finally, the mean and inertia force coefficients at the two selected attack angles are presented as functions of KC and A_R based on the Morison relationships. Copyright © 2008 John Wiley & Sons, Ltd.     

Efficient computation of mean drag for the subcritical flow past a circular cylinder using general Galerkin G2

General Galerkin (G2) is a new computational method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier–Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation, such as large eddy simulation, and thus no Reynolds stresses are introduced, which need modelling. In this paper, G2 is used to compute the drag coefficient c_D for the flow past a circular cylinder at Reynolds number Re=3900, for which the flow is turbulent. It is found that it is possible to approximate c_D to an accuracy of a few percent, corresponding to the accuracy in experimental results for this problem, using less than 10⁵ mesh points, which makes the simulations possible using a standard PC. The mesh is adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, which in this paper is c_D. Both the stopping criterion and the mesh‐refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals times derivatives of the solution of a dual problem, linearized at the approximate solution, and with data coupling to the output of interest. Copyright © 2008 John Wiley & Sons, Ltd.