分区Lagrangian涡方法及瞬时起动圆柱初期流动的模拟

本文提出一种分区Lagrangian涡方法:将附着流动和分离流动分开处理,在附着区解边界层方层,只在分离区用涡方法解N-S方程。由于将尺度不同的区域分开了,求解分离区流动的涡方法中,每一时间步上物面引出的涡数在较小程度上依赖于Re数。这样,求解高Re数流动时,流场内的涡数,因而计算机内存和时间得以大大减小。用该方法计算了瞬时起动圆柱的初期流动,与实验结果比较相符很好。     

双圆柱绕流特性的模拟研究

采用格子Boltzmann方法对低雷诺数下气体绕流圆柱的规律进行了研究. 对比计算了双圆柱在不同圆心距、不同Re数、不同来流速度与双圆柱圆心连线角度的情况下,各个圆柱的受力大小和曳力系数. 结果表明,若Re数为20, 改变圆柱间距,圆柱间距在1.2d和1.4d之间时,下游圆柱所受曳力有极小值;双圆柱间距为1.6d时,双圆柱受到总曳力最小;圆柱间距大于2d时,上游颗粒受到的曳力不再受到下游颗粒的影响. 若圆柱间距为1.2d, 改变雷诺数,Re数在30和40之间,下游圆柱所受曳力有极小值. 另外,来流速度角度对圆柱的受力影响很大. 上述规律为低Re数下圆柱绕流的深入研究与应用打下基础.      

高雷诺数下多柱绕流特性研究

采用改进的延迟分离涡方法数值模拟了高雷诺数下的柱体绕流,包括单圆柱绕流、单方柱绕流、串列双圆柱绕流和串列双方柱绕流,研究了不同雷诺数下圆柱绕流与方柱绕流的水动力特性.计算结果与实验数据及其他文献的数值计算结果吻合良好,研究表明,单方柱绕流在2.0×10~3Re1.0×10~7范围内未出现类似于单圆柱绕流的阻力危机现象,其平均阻力系数C_d、升力系数均方根C'_1及斯特劳哈尔数S t维持在一定范围内波动.串列双圆柱绕流与串列双方柱绕流中,均选取L/D=2.0,2.5,3.0,3.5和4.0这五中间距比进行计算.串列双圆柱绕流中,当Re=2.2×10~4时,在3.0L/D3.5内存在一临界间距比(L_c/D)使得L_c/D前后上下游圆柱的升阻力系数发生跳跃性变化,且当L/DL_c/D时,下游圆柱的阻力系数为负数.而当Re=3.0×10~6时,则不存在临界间距比,且下游圆柱的阻力系数始终为正数.串列双方柱绕流在Re=1.6×10~4和Re=1.0×10~6两种工况下的临界间距比分别处于3.0L/D3.5和3.5L/D4.0区间内,且当L/DL_c/D时,两个雷诺数下的下游方柱阻力系数均为负数.     

虚拟边界法研究正交双圆柱及串列双圆球绕流

把Goldstein等人提出的虚拟边界法推广到三维情况，研究了 Re=150时不同间距下正交双圆柱绕流，和Re=250时不同间距下串列双 圆球绕流流场. 对于正交双圆柱绕流，当间距比大于3，下游圆柱对上游圆柱尾流的影响只 限定在下游圆柱的尾流所扫过的范围之内；当间距比小于等于3，下游圆柱对上游圆柱尾流 的影响扩大，下游圆柱尾流扫过区上下出现两排三维流向二次涡结构. 对于串列圆球绕流， 研究发现，在小间距比(L/D≈ 1.5)的情况下，由于上下游圆球尾流区的相互抑 制消除了压力不稳定性，整个流场呈现稳 态轴对称特征；间距比为2.0时，周向压力梯度诱发出流体的周向输运，流场呈现稳态非对 称性，但流场中存在特定的对称面；间距比增大到2.5后，绕流场开始周期振荡，原有的对 称面依旧存在；在间距比3.5时下游圆球下表面的涡结构强度有所减弱，导致占优频率发生 交替；间距比增至7.0时，整个流场恢复稳态特征，两圆球尾部同时出现双线涡，这时流场 对称面的位置发生了变动.     

流向强迫振荡圆柱绕流的涡脱落模态分析

通过求解采用ALE方法描述的运动坐标系Navier-Stokes方程组，分析均匀来流下雷诺 数为150的静止和流向振荡的圆柱绕流. 主要研究了强迫振荡频率和较大振幅比 (A/D=0.3-1.2)对圆柱升力、阻力变化特性以及涡脱落模态的影响. 研究表 明，流向振荡圆柱绕流存在多种涡脱落模态，如对称S以及反对称A-I, A-III, A-IV等多种形式；比较研究结果，拓展了各模态下对应的锁定区域，并将其分为5个 子区；A-I模态中圆柱受力较以前所知更复杂；通过分析计算结果，发现最大加速度 比Af_{c}^{2}/Df_{s0}^{2}可能是涡脱落模态(尤其是对称S模态)最有效的控制参数.     

基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

流向磁场作用下圆柱绕流的直接数值模拟

绕流是托卡马克装置中液态包层内常见的流动形态,对流场与热量分布有着重要的影响.本文通过直接数值模拟(DNS),研究了不同磁场强度下$Re=3900$的圆柱绕流,分析了磁场强度对于湍流尾迹的影响.无磁场情况下,直接数值模拟的结果与前人的实验及模拟结果吻合很好.圆柱下游的尾迹中,随着流向距离的增大, 流向速度剖面逐渐从U型进化呈V型, 并慢慢趋于平缓,这表明尾迹中的流动结构受圆柱影响逐渐减小.圆柱后方两侧的剪切层中,由于Kelvin-Helmholtz不稳定性的影响,可以清晰地看到小尺度剪切层涡的脱落.通过对无磁场的计算结果施加流向磁场,本文计算了哈特曼数($Ha$)分别为20, 40和80的工况,以研究磁场效应对于湍流的影响.结果表明磁场较弱时,流动依然呈三维湍流状态.随着磁场增强, 近圆柱尾流区受磁场抑制明显,回流区被拉长,剪切层失稳位置向下游转移.圆柱后方的涡结构由于受到竖直方向洛伦兹力的挤压作用,随着哈特曼数的增加尾迹区域逐渐变窄.相比于无磁场情况的涡结构,由于磁场的耗散作用,相应的涡结构尺度变小.该研究不仅扩展了现有磁场下湍流运动的参数范围,对于液态包层的设计及安全运行同样具有重要的理论指导意义和工程应用价值.      

DIRECT NUMERICAL SIMULATIONS ON THE TURBULENT FLOW PAST A CONFINED CIRCULAR CYLINDER WITH THE INFLUENCE OF THE STREAMWISE MAGNETIC FIELDS1)

绕流是托卡马克装置中液态包层内常见的流动形态,对流场与热量分布有着重要的影响.本文通过直接数值模拟(DNS),研究了不同磁场强度下$Re=3900$的圆柱绕流,分析了磁场强度对于湍流尾迹的影响.无磁场情况下,直接数值模拟的结果与前人的实验及模拟结果吻合很好.圆柱下游的尾迹中,随着流向距离的增大, 流向速度剖面逐渐从U型进化呈V型, 并慢慢趋于平缓,这表明尾迹中的流动结构受圆柱影响逐渐减小.圆柱后方两侧的剪切层中,由于Kelvin-Helmholtz不稳定性的影响,可以清晰地看到小尺度剪切层涡的脱落.通过对无磁场的计算结果施加流向磁场,本文计算了哈特曼数($Ha$)分别为20, 40和80的工况,以研究磁场效应对于湍流的影响.结果表明磁场较弱时,流动依然呈三维湍流状态.随着磁场增强, 近圆柱尾流区受磁场抑制明显,回流区被拉长,剪切层失稳位置向下游转移.圆柱后方的涡结构由于受到竖直方向洛伦兹力的挤压作用,随着哈特曼数的增加尾迹区域逐渐变窄.相比于无磁场情况的涡结构,由于磁场的耗散作用,相应的涡结构尺度变小.该研究不仅扩展了现有磁场下湍流运动的参数范围,对于液态包层的设计及安全运行同样具有重要的理论指导意义和工程应用价值.     

均匀旋转对圆柱水动力及流动结构的影响

基于格子Boltzmann方法 (LBM)对均匀旋转控制下的低雷诺数(Re=100)圆柱绕流问题进行了数值模拟,得到了转速比从0～10变化下,旋转控制对圆柱水动力及流动结构的影响规律.使用动态模态分解(DMD)对流场特征进行提取,并分析了施加旋转控制之后转速比对流场不同模态和增长率的影响.结果表明,随着转速比增大,圆柱下游流动结构依次呈现出卡门涡街、剪切层、反向剪切层、单侧涡和附着涡5种结构;阻力系数时均值先减小,随后在转速进入单侧涡区间后增大,升力系数与力矩系数的时均值均单调增加,同时,在出现涡脱落的两个转速区间内,水动力出现了明显的波动,且二次失稳时波动幅度更大. DMD的结果表明,圆柱下游的流动结构主要受圆柱壁面的旋转影响而发生改变并产生全新流动模态;旋转会对流动稳定性产生影响:在未充分发展阶段,旋转对流动稳定性的影响不显著,而在充分发展后,各转速下的流场不稳定模态数均远少于未充分发展阶段,随着转速比的增大,流动稳定性会产生不同程度的增强或减弱,且无涡脱落时的稳定性高于有涡脱落时,因此,通过旋转控制抑制尾涡脱落可以有效增强流动的稳定性.     

NUMERICAL STUDY OF PARTICLE DISTRIBUTION IN WAKE OF LIQUID-PARTICLE FLOWS PAST A CIRCULAR CYLINDER USING DISCRETE VORTEX METHOD

Particle-laden water flows past a circular cylinder were numerically investigated. The discrete vortex method (DVM) was employed to evaluate the unsteady water flow fields and a Lagrangian approach was applied for tracking individual solid particles. A dispersion function was defined to represent the dispersion scale of the particle. The wake vortex patterns, the distributions and the time series of dispersion functions of particles with different Stokes numbers were obtained. Numerical results show that the particle distribution in the wake of the circular cylinder is closely related to the particle's Stokes number and the structure of wake vortices: (1) the intermediate sized particles with Stokes numbers, St, of 0.25, 1.0 and 4.0 can not enter the vortex cores and concentrate near the peripheries of the vortex structures, (2) in the circular cylinder wake, the dispersion intensity of particles decreases as St is increased from 0.25 to 4.0.     

The turbulent flow field around a circular cylinder

The flow field around a circular cylinder mounted vertically on a flat bottom has been investigated experimentally. This type of flow occurs in several technical applications, e.g. local scouring around bridge piers. Hydrogen bubble flow visualization was carried out for Reynolds numbers ranging from 6,600 to 65,000. The main flow characteristic upstream of the cylinder is a system of horse-shoe vortices which are shed quasi-periodically. The number of vortices depends on Reynolds number. The vortex system was found to be independent of the vortices that are shed in the wake of the cylinder. The topology of the separated flow contains several separation and attachment lines which are Reynolds number dependent. In the wake region different flow patterns exist for each constant Reynolds number.     

圆柱绕流流场结构的大涡模拟研究

为进一步揭示绕流现象的形成机理,本文分别对处于层流稳态区、尾流过渡区、剪切层转换区Re分别为26、200、1.4×105的三种典型流态下的单圆柱绕流进行了二维数值模拟研究。Re为26时应用层流模型直接求解N-S方程,而Re分别为200、1.4×105时使用大涡模拟的方法进行计算。数值模拟很好地再现了稳定的涡旋结构、周期性交替脱落的卡门涡街结构、不规则的涡旋结构,在此基础上分析了尾流结构的基本特征及其压强分布规律、平均的流场特性、积分参数(如升力系数、阻力系数、斯特劳哈尔等),并与有关研究成果进行了对比。研究发现,采用不同流动介质时流场特性有所差异,空气为介质时的计算结果更符合实验的成果,而水为介质时计算结果偏差较大,这主要是由尾流涡旋产生的不合理负压造成的。     

Numerical simulation of flow around a square cylinder in uniform-shear flow

This paper presents results obtained from a numerical simulation of a two-dimensional (2-D) incompressible linear shear flow over a square cylinder. Numerical simulations are performed, using the lattice Boltzmann method, in the ranges of 50⩽Re⩽200 and 0⩽K⩽0.5, where Re and K are the Reynolds number and the shear rate, respectively. The effect of the shear rate on the frequency of vortex shedding from the cylinder, and the lift and drag forces exerted on the cylinder are quantified together with the flow patterns around the cylinder. The present results show that vortex structure behind the cylinder is strongly dependant on both the shear rate and Reynolds number. When Re=50, a small K can disturb the steady state and cause an alternative vortex shedding with uneven intensity. In contrast, a large value of K will suppress the vortex shedding from the cylinder. When Re>50, the differences in the strength and size of vortices shed from the upper and lower sides of the cylinder become more pronounced as K increases. Vortex shedding disappears when K is larger than a critical value, which depends on Re. The flow patterns around the cylinder for different Re tend towards self-similarity with increasing K. The lift and drag forces exerted on the cylinder, in general, decrease with increasing K. Unlike a shear flow past a circular cylinder, the vortex shedding frequency past a square cylinder decreases with increasing the shear rate. A significant reduction of the drag force occurs in the range 0.15<K<0.3.     

Calculation of oseen flows past a circular cylinder at low reynolds numbers

The velocity, pressure, vorticity and streamfunction are computed in the Oseen hydrodynamic field of an unbounded fluid past a circular cylinder in the Reynolds Number range going from 0.4 to 12. The boundary condition is satisfied by means of the method of least squares that determines suitable coefficients for Faxén series. Particular investigation is made of the wake region in which calculations are made of flow patterns, velocity and vorticity distributions. It is shown that, attached vortices arise at the rear of the cylinder at Reynolds Number Re=3.025. Calculated drag coefficients are in good agreement with known results of the works of several authors up to a Reynolds Number of 20.     

Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

Formation of vortex street and vortex pair from a circular cylinder oscillating in water

The flow around a circular cylinder undergoing sinusoidal oscillating movement in still water is investigated by phase-locked PIV measurements. The pattern and development of large-scale vortex structures in the flow are studied from the velocity vectors and vorticity contours obtained at eight successive phases of an oscillating cycle. Experiments are performed at three Keulegan–Carpenter numbers; KC=12, 6.28 and 4.25. Results at KC=12 reveal the mechanism of vortex formation and the development of the shed vortices into a vortex street at a lateral direction to the line of cylinder movement. The role of a biased flow stream and the length of the cylinder stroke in the formation of the vortex street are discussed. At the lower KC numbers, a symmetric pair of vortices is found attached to the leeward face of the cylinder. The vortex pair exhibits an increasing degree of asymmetry when KC increases from 4.25 to 6.28. An explanation in terms of the length of the cylinder strokes and the degree of flow asymmetry is offered for the transition of flow regimes from a vortex pair to a vortex street. The present results are compared with the observations made in previous experimental and numerical studies in the literature.     

Vortex shedding and three-dimensional behaviour of flow past a cylinder confined in a channel

A numerical investigation of the flow past a circular cylinder centred in a two-dimensional channel of varying width is presented. For low Reynolds numbers, the flow is steady. For higher Reynolds numbers, vortices begin to shed periodically from the cylinder. In general, the Strouhal frequency of the shedding vortices increases with blockage ratio. In addition, a two-dimensional instability of the periodic vortex shedding is found, both empirically and by means of a Floquet stability analysis. The instability leads to a beating behaviour in the lift and drag coefficients of the cylinder, which occurs at a Reynolds number higher than the critical Reynolds number for the three-dimensional mode A-type instability, but lower than a Reynolds number for any mode B-type instability.