中等Reynolds数下并列方柱统流的数值模拟──MAC－AF1方法及其应用

本文通过采用ＭＡＣ－ＡＦ１方法求解原始变量二维不可压非定常Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，对中等Ｒａｙｎｏｌｄｓ数绕流下的并列方柱绕流进行了数值模拟。通过对Ｒｅ＝３００、５００、１０００、２０００及间隙度为ｓ／ｈ＝２．３时并列方柱的数值计算表明：Ｒｅ数对横向力的变化频率毫无影响，恰好是单方柱绕流横向力变化频率的两倍。阻力的频率与横向力的频率相同，阻力的时间平均值基本上与Ｒｅ数无关，但随着Ｒｅ数的增大，阻力和横向力随时间变化的波动幅度稍微有所增加。本文计算的方柱阻力时间平均值和横向力的频率与实验值符合得很好。     

基于FD/MLSFD的混合算法计算 二维浅水方程

将基于最小二乘法的无网格有限差分方法(MLSFD方法)和传统有限差分方法(FDM)相结 合,生成了一种混合算法。研究并解决了差分网格/无网格混合算法的藕合问题,将混合算法运用于 求解二维浅水方程,通过计算高雷诺数(Re =105)条件下的圆柱绕流模型揭示了该混合算法在进行二 维浅水模型的数值模拟方面具有较高的精确度。     

圆柱非定常绕流及涡致振动的数值计算

用基于一般曲线坐标系和交错网格的差分法求解原始变量二维不可压粘性流体的N-S方程，计算了雷诺数从100到1×10     

基于LES方法圆柱绕流三维数值模拟

该文采用计算流体软件CFX5中Large-eddy simulation(LES)模型计算了均匀流场中三维圆柱绕流的水动力特性。使用有限体积法对三维N-S方程进行求解。数值模拟着重研究了高雷诺数时展向各截面的压力、阻力、升力及涡管特性。数值计算结果表明:展向各截面柱体受力关于中截面对称且小于二维情况,柱体周围流场呈现明显的三维特性。     

FORCE REDUCTION OF FLOW AROUND A SINUSOIDAL WAVY CYLINDER

A large eddy simulation of cross-flow around a sinusoidal wavy cylinder at Re=3000 was performed and the load cell measurement was introduced for the validation test. The mean flow field and the near wake flow structures were presented and compared with those for a circular cylinder at the same Reynolds number. The mean drag coefficient for the wavy cylinder is smaller than that for a corresponding circular cylinder due to the formation of a longer wake vortex generated by the wavy cylinder. The fluctuating lift coefficient of the wavy cylinder is also greatly reduced. This kind of wavy surface leads to the formation of 3-D free shear layers which are more stable than purely 2-D free shear layers. Such free shear layers only roll up into mature vortices at further downstream position and significantly modify the near wake structures and the pressure distributions around the wavy cylinder. Moreover, the simulations in laminar flow condition were also performed to investigate the effect of Reynolds number on force reduction control.     

NUMERICAL SIMULATION OF THREE-DIMENSIONAL VORTEX DYNAMICS IN WAKE OF A CIRCULAR CYLINDER

The studies concerning the wake transition regime of the flow around a circular cylinder have drawn much attention in these years. Many experiments have been conducted for this problem but no accurate three-dimensional numerical simulations have hitherto been made. In this paper, a parallel procedure was developed to solve the three-dimensional Navier-Stokes equations on an SGI Origin3900 machine. Two different parallel strategies on this application were analyzed about their efficiency. It is found that the critical Reynolds number is 195, and the wake flow below this Reynolds number is purely two dimensional one, while the Reynolds number goes beyond this critical point, the wake flow becomes unstable under three-dimensional small disturbances. The transition regime involves two modes of small-scale three-dimensional instability (modes A and B), depending on the regime of Reynolds number ( Re ). It is also found that the two different modes A and B exhibit different physical features of the flow. And many other important questions were addressed in this paper.     

近底水平圆柱振荡绕流的三维数值模拟

在Honji和Sarpkaya等人的实验研究中发现，绕圆柱的振荡流并不是简单的二维流动，而是存在复杂的三维流态。本文用有限元方法求解原始变量的Navier-Stokes方程，模拟了Re数为392、Kc数为2时正弦振荡流绕平面附近圆柱的流动。分析了三维流场结构的特点，并分析了平面边界对尾流结构的影响。     

NUMERICAL INVESTIGATION ON OSCILLATING FLOWSPAST A HALF CIRCULAR CYLINDER ON A PLANE

l.INTRoDUCTIoNTheunsteadyflowpastabluffbodyhasreceivedagreatdealofattentionowingmainlytoitstheoreticalandpracticalsignificance.Foranoscillatingflowpastacircularcylinder,thetwoparametersgoverningthedevelopmentoftheflowaretheReynoldsnumber,de-finedbyRe=2U,R/v,WhereU,isthemaximumvelocityoftheambientflow,visthekine-maticviscosityandRistheradiusofthecircularcylinder;andtheKeulegan-Carpenternum-ber,definedasKC=U,T/2R,whereTistheoscillationperiod.Todescirbethisproblem,earlierstudiesofviscou…     

2-D eddy resolving simulations of flow past a circular array of cylindrical plant stems

In the present study, 2-D large eddy simulations(LES) are conducted for flow past a porous circular array with a solid volume fraction(SVF) of 8.8%, 15.4% and 21.5%. Such simulations are relevant to understanding flow in natural streams and channels containing patches of emerged vegetation. In the simulations discussed in the paper, the porous cylinder of diameter D contains a variable number of identical solid circular cylinders(rigid plant stems) of diameter d= 0.048 D. Most of the simulations are conducted at a Reynolds number of 2 100 based on the diameter D and the velocity of the steady uniform incoming flow. Though in all cases wake billows are shed in the regions where the separated shear layers(SSLs) forming on the sides of the porous cylinder interact, the effect of these wake billows on the mean drag is different. While in the high SVF case(21.5%), the total drag force oscillates quasi-regularly in time, similar to the canonical case of a large solid cylinder, in the cases with a lower SVF the shedding of the wake billows takes place sufficiently far from the cylinder such that the unsteady component of the total drag force is negligible. The mean amplitude of the oscillations of the drag force on the individual cylinders is the largest in a streamwise band centered around the center of the porous cylinder, where the wake to wake interactions are the strongest. In all cases the maximum drag force on the individual cylinders is the largest for the cylinders directly exposed to the flow, but this force is always smaller than the one induced on a small isolated cylinder and the average magnitude of the force on the cylinders directly exposed to the flow decreases monotonically with the increase in the SVF. Predictions of the global drag coefficients, Strouhal numbers associated with the wake vortex shedding and individual forces on the cylinders in the array from the present LES are in very good agreement with those of 2-D direct numerical simulations conducted on finer meshes, which suggests LES is a better option to numerically investigate flow in channels containing canopy patches, given that LES is computationally much less expensive than DNS at high Reynolds number. To prove this point, the paper also discusses results of 2-D LES conducted at a much higher Reynolds number, where the near-wake flow is strongly turbulent. For the higher Reynolds number cases, where the influence of the turbulence model is important, the effect of the sub-grid scale model and the predictive capabilities of the unsteady Reynolds averaged Navier-Stokes(RANS) approach to predict flow past porous cylinders are discussed.     

两层黏性流体中直立圆柱体绕流的三维数值模拟

研究了两层流体中直立贯底圆柱体的三维黏性绕流问题.以不可压缩Navier-Stokes方程为控制方程,应用VOF方法追踪两层流体的内界面,建立了该问题的数值模拟方法.成功地数值模拟了两层流体中圆柱体黏性绕流产生的三维尾涡特征,表明了流体的密度分层效应对直立贯底圆柱体的尾涡特性和阻力系数都是有影响的.在海洋立管涡激振动的研究中,考虑流体的密度分层效应是重要的.     

绕圆柱非定常周期性涡旋脱落的数值模拟

利用非定常流函数涡量方程数值模拟圆柱突然起动尾流涡旋的形成及周期性脱落过程。对求解的流函数的一阶导数即速度项采用四阶精度的Hermitian公式，而方程的对流项则采用四阶精度的差分格式，并利用ADI方法迭代求解差分方程组。当雷诺数Re不大于40时，圆柱尾流为附体的两个对称涡，为定常解。当Re大于40后流动为非定常及非对称的，圆柱尾流呈现周期性涡旋交替脱落而形成著名的Karman涡街。选择Re=100为例，在初始条件未加任何扰动情况下，成功地模拟了圆柱非定常涡旋形成与脱落的完整过程（无量纲时间算到t=250及以上）。所计算的阻力系数与实验结果及其它数值方法的计算结果一致。约在t=200形成严格的Karman涡街。对涡量方程ADI求解方法的稳定性进行了分析。对流项采用四阶精度差分格式，若应用于定常问题，将极大提高数值求解的精度，若应用于非定常问题的求解，将对求解精度有所改善，其中时间空间两阶混合偏导数的处理是关键，有待进一步的数值实验。     

Vortex Induced Vibrations of Finned Cylinders

This article presents the results of a numerical simulation on the vortex induced vibration of various fumed cylinders at low Reynolds number. The non-dimensional, incompressible Navier-Stokes equations and continuity equation were adopted to simulate the fluid around the cylinder. The cylinder （with or without fins） in fluid flow was approximated as a mass-spring system. The fluid-body interaction of the cylinder with fins and uniform flow was numerically simulated by applying the displacement and stress iterative computation on the fluid-body interfaces. Both vortex structures and response amplitudes of cylinders with various arrangements of fins were analyzed and discussed. The remarkable decrease of response amplitude for the additions of Triangle60 fins and Quadrangle45 fins was found to be comparable with that of bare cylinder. However, the additions of Triangle00 fins and Quadrangle00 fins enhance the response amplitude greatly. Despite the assumption of two-dimensional laminar flow, the present study can give a good insight into the phenomena of cylinders with various arrangements of fins.     

NUMERICAL SIMULATION FOR EARLY DEVELOPMENT OF WAKE VORTICES BEHIND A SEMICIRCULAR-SECTION CYLINDER

o.INThoDUCTIONThenumericlmodellingoffluidflowproblemswithwakesisveryimportantinhydrthdynamicsandaeredynamics.Thefiniteelementmethod,withtheflexibilityofavariablemesh,issuperiortothefinitedifferencemethodinsolvingtheseproblems.However,thefi-nitedifferencemethedismuchlesscomplicatedthanthefiniteelementmethodatleastinre-spectofcomputerprogramming.Theboundary-fittedcoordinatesystem,whichhasboththeadvantagesofthegeometricflexibilityofthefiniteelementmethedandthesimplicityofthefinitedifferenceme…     

高雷诺数下带自由表面的重力波的有限元数值模型

本文基于扩展的虚拟浓度和Sommerfeld线性辐射边界条件建立了数值波浪水槽。用有限元方法结合大涡模拟（LES）湍流模型在Euler坐标系统中求解了二维不可压粘性流体的N－S方程，而自由表面函数方程是在沿流体质点迹线定义的Lagrange系统中求解的。为了检验该数值波浪模型的有效性，本文中用该数值波浪水槽进行了海底管线在波浪场中受力的数值实验，并与物模实验的结果做了对比，其雷诺数Re为10700。     

Vortex shedding in the flow around two side-by-side circular cylinders of different diameters

In this paper,the 3-D turbulent flow around two side-by-side circular cylinders of different diameters,at sub-critical Reynolds number(Re=3 900),is numerically simulated by the large eddy simulation(LES).The spacing ratios(T/D)between the two cylinders are considered in four cases(T/D=1.2,1.5,1.8 and 2.7)to study the vortex shedding and turbulent properties in the flow field.The main results are focused on the drag and lift coefficients,the vortex shedding frequency,the coherent structure,and the scale properties.It is shown that when T/D is equal to 1.2,the vortex shedding of the main cylinder is strongly suppressed by the small cylinder,the drag and lift coefficients of the main cylinder are smaller than those in other three cases.While T/D is equal to 1.5,the vortex shedding of the main cylinder can be improved,the drag and lift coefficients of the main cylinder are larger than those in other three cases.The empirical mode decomposition(EMD)method is applied to decompose the velocity signals traced by the LES.It is shown that there is a linear relationship between the mean period and the mode in the semi-log coordinates.The vortex shedding period of the main cylinder is consistent with the period of the restructured coherent structures quantitatively.     

基于FLUENT的小雷诺数下方柱绕流的数值模拟

采用FLUENT对小雷诺数（Re〈52）下方柱绕流进行数值模拟,分析方柱后对称反向漩涡的图谱与漩涡尺寸的特点,分析研究表明：在小雷诺数下,方柱绕流的图谱与圆柱绕流图谱相似,并存在两个特征雷诺数,但两个特征雷诺数较圆柱绕流的小些;方柱绕流对称反向漩涡尺寸与雷诺数呈线性关系变化,并且漩涡发生得比圆柱绕流更为剧烈;方柱绕流柱体后的漩涡能够较容易达到稳定状态。研究结论进一步丰富方柱绕流问题。     

A TVD Scheme for Incompressible Flow Coupled With Different Turbulence Modles on A Ground-Mounted Square-RIB Flow

A finite-difference Total Variation Diminishing (TVD) numerical simulation model for coupling the Reynolds Averaged Navier-Stokes (RANS) equations, pressure-relative continuity equation and various k-ε turbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group (RNG) and Chen-Kim k-ε turbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-ε model.     

Numerical investigation of drag force on flow through circular array of cylinders

A 2-D model for flow through a circular patch with an array of vertical circular cylinders in a channel is established using the Navier-Stokes equations with a hybrid RANS/LES turbulence model–the Scale Adaptive Simulation (SAS) model. The applicability of the model is first validated by test cases where experimental data are available for comparison with the computed results. It is verified that the present model can predict well the average velocity and turbulence structure. The drag force and drag coefficient are then calculated using the present model for a number of cases with different solid volume fractions, cylinder Reynolds numbers and patch diameters. It is shown that the drag coefficient increases with increasing solid volume fraction, but decreases with increasing Reynolds number. However, the drag coefficient is independent of the diameter of circular batch when the solid volume fraction and Reynolds number are kept constant.     

低Reynolds数横向排列双圆柱绕流的POD-Galerkin谱方法数值模拟

该文将恰当正交分解(POD)方法应用到低Reynolds数(Re)二维横向排列双圆柱绕流问题.采用Fluent数值模拟得到Re=90时的流场数据库,在此基础上采用snapshot的方法构造了POD基.基于此POD基,构造了求解二维不可压缩Navier-Stokes方程组的低维Galerkin谱方法.采用该低维数值模拟方法,再现了低Reynolds数横向排列双圆柱绕流的多种复杂流动模式,其结果与已有的高精度直接数值模拟的结果符合较好,而计算量却非常小,显示了POD方法的有效性和优越性.     

不等直径串列圆柱绕流大涡模拟

为研究背负式海底管线中增设的小直径附属管线对主管线的水动力影响,将大涡模拟中经典Smagorinsky亚格子模型与特征线算子分裂有限元法结合,并引入出口对流边界条件,完善了基于特征线算子分裂有限元的大涡模拟方法。通过自编程序数值模拟Re=1 000的单圆柱绕流,计算结果与相关文献吻合较好,验证了该算法计算圆柱绕流的有效性,并分析了Re=1 000时不同直径比、间距比情况下的串列双圆柱绕流,根据流场的不同涡脱落形态及两圆柱平均阻力系数、升力系数随直径比、间距比变化的规律得到了不同直径比条件下的临界间距范围。达到临界间距后,流场由单一涡脱落状态转变为双涡旋脱落状态。最后分析了两圆柱平均阻力系数及升力系数在临界间距后急剧增加的原因,为背负式海底管线的布局优化提供了理论依据。