当地DFD方法在扑翼流动数值模拟中的应用

应用当地DFD（Domain-Free Discretization）方法对包含复杂运动边界的扑翼流场进行了数值模拟。该方法通过壁面法线方向的外插确定外部相关点上的流动变量值,同时强加相应的边界条件。应用这种方法,动边界流动的模拟可以在固定网格上实现,无需为了跟随物体的运动而在每个时间步上对网格进行实时更新。对三种拍动模式的双翅流场进行了数值模拟,升、阻力系数时间历程的计算结果与参考文献的实验数据吻合很好,验证了当地DFD方法处理复杂动边界问题的可靠性。最后,数值模拟了完整昆虫模型的扑翼流场,并详细分析了涡系结构和飞行机理。     

Adaptive mesh refinement‐enhanced local DFD method and its application to solve Navier–Stokes equations

Recently, the domain‐free discretization (DFD) method was presented to efficiently solve problems with complex geometries without introducing the coordinate transformation. In order to exploit the high performance of the DFD method, in this paper, the local DFD method with the use of Cartesian mesh is presented, where the physical domain is covered by a Cartesian mesh and the local DFD method is applied for numerical discretization. In order to further improve the efficiency of the solver, the newly developed solution‐based adaptive mesh refinement (AMR) technique is also introduced. The proposed methods are then applied to the simulation of natural convection in concentric annuli between a square outer cylinder and a circular inner cylinder. Numerical experiments show that the present numerical results agree very well with available data in the literature, and AMR‐enhanced local DFD method is an effective tool for the computation of flow problems. Copyright © 2005 John Wiley & Sons, Ltd.     

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Reslts show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds numberRe and rotation parameter α, is built by a kinematic analysis of the steady flow fields. The project supported by the National Natural Science Foundation of China     

Development of circular function‐based gas‐kinetic scheme (CGKS) on moving grids for unsteady flows through oscillating cascades

In this paper, the circular function‐based gas‐kinetic scheme (CGKS), which was originally developed for simulation of flows on stationary grids, is extended to solve moving boundary problems on moving grids. Particularly, the unsteady flows through oscillating cascades are our major interests. The main idea of the CGKS is to discretize the macroscopic equations by the finite volume method while the fluxes at the cell interface are evaluated by locally reconstructing the solution of the continuous Boltzmann Bhatnagar–Gross–Krook equation. The present solver is based on the fact that the modified Boltzmann equation, which is expressed in a moving frame of reference, can recover the corresponding macroscopic equations with Chapman–Enskog expansion analysis. Different from the original Maxwellian function‐based gas‐kinetic scheme, in improving the computational efficiency, a simple circular function is used to describe the equilibrium state of distribution function. Considering that the concerned cascade oscillating problems belong to cases that the motion of surface boundary is known a priori, the dynamic mesh method is suitable and is adopted in the present work. In achieving the mesh deformation with high quality and efficiency, a hybrid dynamic mesh method named radial basic functions‐transfinite interpolation is presented and applied for cascade geometries. For validation, several numerical test cases involving a wide range are investigated. Numerical results show that the developed CGKS on moving grids is well applied for cascade oscillating flows. And for some cases where nonlinear effects are strong, the solution accuracy could be effectively improved by using the present method. Copyright © 2017 John Wiley & Sons, Ltd.     

Regimes of vortex shedding from an in-line oscillating circular cylinder in the uniform flow

A finite volume method for the time dependent viscous incompressible flow around an in-line oscillating circular cylinder at Reynolds number of 200, 855 is presented in this paper. The Navier-Stokes equations in a finite volume form are solved with a moving grid system, based on a time dependent coordinate transformation. To investigate the vortex-shedding characteristics behind the circular cylinder and the effects of Reynolds number and other non-dimensional parameters such as reduced amplitude and reduced frequency， several numerical schemes have been tested with different amplitude and frequency close to Sto and a harmonic at each Reynolds number. Present numerical results indicate several types of vortex shedding mode which is known mainly depending on the reduced frequency and also the reduced amplitude, which is called synchronization or lock-on.     

Transient flow around an impulsively started cylinder using a dynamic mesh method

The finite volume method (FVM) with a dynamic mesh method (DMM) to deal with the moving boundary was applied to the simulation of two-dimensional incompressible viscous flow past a circular cylinder that is impulsively started into rotation and translation. The non-dimensional rotating to translating speed ratio α is varied from 0.28 to 2.07, with the Reynolds number being 200 for the range of α. The computation covers a period, during which the cylinder translates seven times its diameter. The current scheme handles the impulsively moving boundary directly by DMM, which is implemented using both mesh deforming and local remeshing. The instantaneous asymmetrical flow configurations for various α are presented and compared with the experimental visualizations. Quantitatively, the velocity distributions with drag and lift coefficients are also compared with the experimental and numerical results. Results show that the flow is strongly influenced by the rotation. Comparisons are found to be satisfactory.     

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.     

Numerical study of the effects of particles on the near wake around a circular cylinder

In this work, we investigate the dynamics of the near wake in a turbulent flow going past a circular cylinder with/without particles at a moderate Reynolds number using a direct numerical simulation method. High-order finite-deference schemes are applied to solve for the bulk fluid properties, and a Lagrangian approach is adopted to track the individual particles. The single-phase flow is analysed and validated using previous experimental data. Two converged states, U- and V-shaped, are observed in the near wake, which are consistent with the experimental results. For the two-phase flow, the addition of smaller particles shortens the length of the recirculation region and causes a V-shaped profile to form behind the circular cylinder. Furthermore, the particles increase the drag force from the circular cylinder and suppress the vortex shedding frequency. An increase in the turbulent statistics in the very near wake and a decrease in the turbulent statistics further downstream are also observed.     

Computation of incompressible flows with immersed bodies by a simple ghost cell method

The incompressible Navier–Stokes equations are solved by an implicit pressure correction method on Cartesian meshes with local refinement. A simple and stable ghost cell method is developed to treat the boundary condition for the immersed bodies in the flow field. Multigrid methods are developed for both velocity and pressure correction to enhance the stability and convergence of the solution process. It is shown that the spatial accuracy of the method is second order in L₂ norm for both velocity and pressure. Various steady and unsteady flows over a 2D circular cylinder and a 3D sphere are computed to validate the present method. The capability of the present method to treat a moving body is also demonstrated. Copyright © 2008 John Wiley & Sons, Ltd.     

A numerical study of the vortex motion in oscillating flow around a circular cylinder at low and middlieKc numbers

A new hybrid model, which is based on domain decomposition and proposed by the authors, is used for calculating the flow around a circular cylinder at low and middle Keulegan-Carpenter numbers (Kc=2−18) respectively. The vortex motion patterns in asymmetric regime, single pair (or transverse) regime and double pair (or diagonal) regime are successfully simulated. The calculated drag and inertial force coefficients are in better agreement with experimental data than other recent computational results. The project supported by the National Natural Science Foundations of China and the LNM, Institute of Mechanics, Academia Sinica     

近床面水平圆柱局部冲刷二维数值模拟

为研究近床面水平圆柱的局部冲刷问题,基于N-S方程和有限体积法,在FLUENT中通过二次开发建立了局部冲刷二维数值模型。模型采用标准κ-ε紊流模型来计算水平圆柱周围的流场,同时借助FLUENT软件中的自定义函数功能提取床面剪应力参数来计算该时刻的推移质输沙率及床面节点位移变化值,然后运用动网格技术来模拟床面地形的变化,通过物理模型试验来进行模型验证。结果表明,计算结果与试验结果基本一致,从而证实了冲刷模型的准确性。     

Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.     

Unsteady characteristics of the cavity flow around a rough circular cylinder

Effects of surface roughness on the unsteady cavitating flow around a two-dimensional circular cylinder were experimentally investigated at Reynolds numbers from 1.36 × 10⁵ to 1.78 × 10⁵. Two patterns of surface roughness were investigated, a double-cut pattern and a single-cut pattern. The cavity elongates with an increase of the surface roughness, especially in supercavitating flow. However, for some roughness parameters tested, the cavity length exhibits an extreme decrease. In a particular case of the double-cut pattern, there exists the minimum cavity behind the cylinder.     

基于浸入边界算法的振动钝体绕流模拟研究

传统CFD方法在振动钝体绕流计算中常借助动网格技术,网格再生任务繁重。针对于此,本文利用可在静止网格中计算动边界绕流问题的浸入边界算法(IBM),编写数值模拟程序,分别对竖向强迫正弦振动方柱(Re=UD/v=103、振幅恒定、振动频率变化)以及桥梁断面(Re=UB/v=7.5×103、振幅、振动频率均变化)展开气动特性和流场特征结构分析。初步研究结果表明,振幅恒定为方柱高度的14%时,其涡脱锁定区长度为0.06~0.2,锁定区后端(Stc0.2)振动方柱涡脱频率回归静止涡脱频率;不同振幅下的桥梁断面阻力系数均在静止涡脱频率处产生峰值,桥梁断面升力系数则在此处均出现归零效应,且振幅越大,归零效应愈明显。     

Milu-CG method and the numerical study on the flow around a rotating circular cylinder

I.IntroductionTilenowaroundarotatitlgcircularcylinderisacomplexunsteadyone.ItincludesmanycomplicatedtlowphenomenaSuchastheunsteadyboundarylayerseparation,thegenerationandsheddingofvorticesandtheinteractionwitllwakesetc..Therotationofacircularcylillderarounditsaxiswilldecreaseandsuppresstheflowseparationandvortexsheddingononesideofthecylinder,whileincreasinganddevelopingonanothel,side.Atransverseliftforcewillactonthecylinder,andthisphenomenoniscalledtheMagnuseffect.Themost.importantparameterf…     

Investigation of scale effect for the computation of turbulent flow around a circular cylinder

In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers （criteria） based on turbulent kinetic and dissipation rates associ- ated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged NavierStokes equations （RANS）. The RNG k-s models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102 to l07 is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ≥ 3 × 10^6. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.     

Hydrodynamics of flow over a transversely oscillating circular cylinder beneath a free surface

In this paper, hydrodynamic force coefficients and wake vortex structures of uniform flow over a transversely oscillating circular cylinder beneath a free surface were numerically investigated by an adaptive Cartesian cut-cell/level-set method. At a fixed Reynolds number, 100, a series of simulations covering three Froude numbers, two submergence depths, and three oscillation amplitudes were performed over a wide range of oscillation frequency. Results show that, for a deeply submerged cylinder with sufficiently large oscillation amplitudes, both the lift amplitude jump and the lift phase sharp drop exist, not accompanied by significant changes of vortex shedding timing. The near-cylinder vortex structure changes when the lift amplitude jump occurs. For a cylinder oscillating beneath a free surface, larger oscillation amplitude or submergence depth causes higher time-averaged drag for frequency ratio (=oscillation frequency/natural vortex shedding frequency) greater than 1.25. All near-free-surface cases exhibit negative time-averaged lift the magnitude of which increases with decreasing submergence depth. In contrast to a deeply submerged cylinder, occurrences of beating in the temporal variation of lift are fewer for a cylinder oscillating beneath a free surface, especially for small submergence depth. For the highest Froude number investigated, the lift frequency is locked to the cylinder oscillation frequency for frequency ratios higher than one. The vortex shedding mode tends to be double-row for deep and single-row for shallow submergence. Proximity to the free surface would change or destroy the near-cylinder vortex structure characteristic of deep-submergence cases. The lift amplitude jump is smoother for smaller submergence depth. Similar to deep-submergence cases, the vortex shedding frequency is not necessarily the same as the primary-mode frequency of the lift coefficient. The frequency of the induced free surface wave is exactly the cylinder oscillation frequency. The trends of wave length variation with the Froude number and frequency ratio agree with those predicted by the linear theory of small-amplitude free surface waves.     

NUMERICAL STUDY ON THE FLOW AROUND A CIRCULAR CYLINDER WITH SURFACE SUCTION OR BLOWING USING VORTICITY-VELOCITY METHOD

A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme (MILU-CG). The effects of surface suction or blowing ' s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re = 100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen , can reduce the drag force significantly , too.     

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．