绕Apollo飞船的高超声速化学非平衡流动的数值模拟

利用混合通量分裂方法，建立了很方便求解的隐式ＮＮＤ格式，求解了完全气体和化学非平衡空气绕Ａｐｏｌｌｏ飞船的流动，计算结果和实验值作了比较，应用拓扑分析方法，研究了背风区和尾迹内的流动结构。     

方柱绕流的数值模拟

采用有限差分法,对雷诺数为2.2×10~4的方柱绕流进行了大涡模拟(简称LES)。运用时间分裂控制(Split-Operator)法,将N-S方程分为对流步、扩散步和传播步。对Smagorinsky假设在近壁区的发散问题用两层模型进行处理。对流项用迎风—中心差分格式模拟,压力方程用SOR法迭代求解。计算得到的沿对称线的时均顺流向速度与文献上的实验结果进行了比较,结果吻合较好,同时还对绕方柱流的流场结构进行了分析研究。     

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。     

三维大钝头体简谐振动绕流的数值模拟

用数值模拟方法研究了大钝头体外形（双子星座飞船）在超声速下俯仰振动的绕流特性，数值模拟的出发方程为三维全Ｎ－Ｓ方程，格式为二阶迎风ＴＶＤ格式，研究结果给出了物体在俯仰振动过程中激波、分离结构和物面压力分布等非定常特征。     

并列圆柱绕流的格子Boltzmann数值模拟

采用非均匀不可压格子Boltzmann模型对低雷诺数下并列圆柱绕流进行了数值模拟,给出了数值计算结果,分析了间距g对圆柱尾流及升力、阻力的影响,并在此基础上得到了4种尾迹模式.此外,研究了流场的初始扰动对流动分岔现象的影响,发现在适当的扰动下可以很快得到同步同相的尾流.对Re=160和200下圆柱的升、阻力进行了对比,结果表明升力和阻力受间距g的影响大于雷诺数.     

钝头体高超声速绕流底部失稳特征数值模拟

利用数值模拟方法对高超声速钝锥及Apollo返回舱底部尾迹流场进行了研究, 分析尾迹流动的失稳过程. 对钝锥模型, 在M_∞=6, Re=1.71× 10⁶(Re以球头半径为参考长度)条件下观察到了底部流动的不稳定性. 不添加任何扰动, 数值模拟首先得到的流动是稳定解, 在底部发展出一个主分离区和一个二次分离区, 流动是轴对称状态. 继续进行计算, 发现二次分离线率先变形, 底部流场发展出非定常周期流动. 对Apollo返回舱模型, 在相同条件下 (Re以前面圆弧半径为参考长度), 数值模拟首先得到的流动同样是稳定解, 出现以二次分离线率先变形为起始的结构失稳, 演化出周期性过程, 但持续时间较短, 很快出现了非周期非对称状态. 研究表明, 高超声速钝锥及Apollo返回舱底部流场均存在不稳定性问题, Apollo返回舱的底部流场更加不稳定.     

绕流直接数值模拟误差分析

对于无边界绕流问题的计算流体力学模拟通常是将物体置于“足够大”的槽道中,而通过不断改变槽道尺寸以及离散网格密度,后验对比方式来检查模拟误差。本文结合多种经典流场理论,提出一种简单的先验误差估计方法来确定槽道尺寸以及相应的网格分布。在此方法中,对于槽道尺寸的确定基于线性叠加原理（即在极小雷诺数下采用Stokes理论解叠加,而在其他雷诺数条件下采用势流理论解叠加）,来估计槽道尺寸对绕流结果的影响。而对网格尺寸与分布,则是使用多项式逼近中的基本误差分析工具,应用到速度边界层,远场势流,以及Rankine涡等简单流动,从而确定整个绕流问题中的离散误差。为了验证前面的理论分析结果,本文模拟了相当大雷诺数范围内的二维翼型以及三维圆球绕流,所得数值结果非常好地验证了理论分析。结果表明,对于Stokes流动问题,槽道尺寸需要大约100倍于物体特征尺寸来保证其结果与无边界绕流相差不超过1%;而在雷诺数超过大约100时,槽道尺寸只需10倍（二维绕流）或者5倍（三维绕流）于物体特征尺寸来达到同等精度。在此先验误差估计方法可应用于一般化的绕流问题。

     

环形通道内湍流旋流流动的数值模拟

本文应用一种考虑湍流－旋流相互作用及湍流脉动各向异性的新的代数Ｒｅｙｎｏｌｄｓ应力模型,对环形通道内的湍流旋流流动进行了数值模拟,研究了改主为旋流流数,进口轴向速度及半径比等参数对环形通道内湍流流动的影响,以及对强化环形通道内传热的作用。     

二维溃坝绕流的WENO格式数值模拟

WENO(Weighted essentially non-oscillatory scheme)格式是一类新的高精度无振荡差分格式.本文将WENO格式和Runge-Kutta时间离散的思想应用于二维浅水方程组的求解,数值模拟矩形河道中大坝瞬间局部溃倒,下游有障碍物的洪水演进过程,并对模拟结果进行了分析,表明采用WENO格式所建立的高分辨率模型能够有效地模拟溃坝波的演进过程.     

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     

Numerical simulation of the unsteady flow over an elliptic cylinder at different orientations

A numerical method is developed for investigating the two‐dimensional unsteady viscous flow over an inclined elliptic cylinder placed in a uniform stream of infinite extent. The direction of the free stream is normal to the cylinder axis and the flow field unsteadiness arises from two effects, the first is due to the flow field development following the start of the motion and the second is due to vortex shedding in the wake region. The time‐dependent flow is governed by the full conservation equations of mass and momentum with no boundary layer approximations. The parameters involved are the cylinder axis ratio, Reynolds number and the angle of attack. The investigation covers a Reynolds number range up to 5000. The minor–major axis ratio of the elliptic cylinder ranges between 0.5 and 0.6, and the angle of attack ranges between 0° and 90°. A series truncation method based on Fourier series is used to reduce the governing Navier–Stokes equations to two coupled infinite sets of second‐order differential equations. These equations are approximated by retaining only a finite number of terms and are then solved by approximating the derivatives using central differences. The results reveal an unusual phenomenon of negative lift occurring shortly after the start of motion. Various comparisons are made with previous theoretical and experimental results, including flow visualizations, to validate the solution methodology. Copyright © 2001 John Wiley & Sons, Ltd.     

并列双椭圆柱绕流的格子Boltzmann-虚拟区域方法的模拟研究

采用格子Boltzmann-虚拟区域方法对并列双椭圆柱绕流进行了模拟研究。首先,通过与并列双圆柱的结果进行对比,验证了数值方法的有效性。其次对雷诺数为200时两种间距(g=0.5a和2.0a,g为柱体表面间距,a为椭圆长轴)的情况进行了研究,考察了椭圆长轴与短轴之比,即α值对柱体升阻力系数及涡结构的影响。研究发现,与圆柱相比,对于g=0.5a椭圆柱的升阻力系数可能出现两种变化,一是升阻力随时间演化较规则,接近周期性;二是流场可能长时间偏向于其中一个椭圆柱,这些变化与α的值有关。对于g=2.0a,两个椭圆柱后的某一区域内会出现四列涡街,经过一段时间,四列涡街又会演化成两列向两侧扩张的涡街。     

翼型空泡周期性流动的数值模拟及机理分析

采用基于正压关系的均质平衡流空化模型和低雷诺数修正的k-ε湍流模式,自行开发了空泡流数值模拟方法和计算软件,对绕翼型空泡的周期性流动现象进行了数值模拟.计算结果与实验数据的对比表明,空泡的宏观特征、流动特性、周期性脱落的斯坦顿数St等与试验结果接近,验证了计算结果的可靠性.空泡在大约一个周期的2/3时间段内成长,并在大约1/3周期时刻发生断裂脱落.这两个特征时间与高速摄像实验结果一致.所取工况对应的组合参数σ/2α=2.865,以翼弦长计算可得St=0.217,与文献的最新试验结果吻合.空泡周期性运动过程中升阻系数也周期性振荡,时均值C<,1>=0.41,C<,d>=0.097,振荡频率与空泡脱落频率一致.对空泡运动过程中流场结构的变化进行了分析,结果表明在大攻角条件下,空泡闭合区后的逆压梯度导致涡的形成及回射流的发展,沿壁面逆向流动的混合介质射流是引起空泡断裂的原因,回射流发展、涡结构变化与空泡非稳态演化过程存在密切的联系,探讨了翼型空泡发生周期性脱落的一些机理.     

Numerical predictions of low Reynolds number flows over two tandem circular cylinders

Flows over two tandem cylinders were analysed using the newly developed collocated unstructured computational fluid dynamics (CUCFD) code, which is capable of handling complex geometries. A Reynolds number of 100, based on cylinder diameter, was used to ensure that the flow remained laminar. The validity of the code was tested through comparisons with benchmark solutions for flow in a lid‐friven cavity and flow around a single cylinder. For the tandem cylinder flow, also mesh convergence was demonstrated, to within a couple of percent for the RMS lift coefficient. The mean and fluctuating lift and drag coefficients were recorded for centre‐to‐centre cylinder spacings between 2 and 10 diameters. A critical cylinder spacing was found between 3.75 and 4 diameters. The fluctuating forces jumped appreciably at the critical spacing. It was found that there exists only one reattachment and one separation point on the downstream cylinder for spacings greater than the critical spacing. The mean and the fluctuating surface pressure distributions were compared as a function of the cylinder spacing. The mean and the fluctuating pressures were significantly different between the upstream and the downstream cylinders. These pressures also differed with the cylinder spacing. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Unsteady flow of a second-order fluid between concentric cylinders

The unsteady motion of an incompressible second-order fluid contained between two finite coaxial cylinders is examined when the outer cylinder is held fixed while the inner cylinder is constrained to execute an arbitrary angular velocity. A solution is obtained in closed form with the aid of transforms and an expression is obtained for the couple experienced. The particular case of a periodic angular velocity is then examined and some numerical work done. There is a marked difference between the results obtained and their classical counterparts.     

Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid

The interaction between two circular cylinders was studied in the slow flow of a Bingham viscoplastic fluid in an infinite medium without any inertia effects. The configuration studied is that in which the flow direction is parallel to the centre line of the cylinders. Finite-element numerical simulations were used with an approximation by Papanastasiou's regularisation method. The case of high yield stress effect was particularly examined. The convergence of the solutions was examined in detail. Changes in the rigid zones, kinematics and stresses were determined in relation to the degree of interaction, which is a function of the distance between the cylinders and the effect of yield stress. The results compared with the case of a single cylinder show that yield stress reduces interaction effects. The transition between configurations with interacting cylinders and configuration with isolated cylinders was examined as a function of the effect of yield stress. Correlations were proposed for the drag coefficient and the stability criterion when the cylinders are interacting.     

Numerical simulation of viscous flow around unrestrained cylinders

A 2-D analysis is made for the dynamic interactions between viscous flow and one or more circular cylinders. The cylinder is free to respond to the fluid excitation and its motions are part of the solution. The numerical procedure is based on the finite volume discretization of the Navier–Stokes equations on adaptive tri-tree grids which are unstructured and nonorthogonal. Both a fully implicit scheme and a semi-implicit scheme in the time domain have been used for the momentum equations, while the pressure correction method based on the SIMPLE technique is adopted to satisfy the continuity equation. A new upwind method is developed for the triangular and unstructured mesh, which requires information only from two neighbouring cells but is of order of accuracy higher than linear. A new procedure is also introduced to deal with the nonorthogonal term. The pressure on the body surface required in solving the momentum equation is obtained through the Poisson equation in the local cell. Results including flow field, pressure distribution and force are provided for fixed single and multiple cylinders and for an unrestrained cylinder in steady incoming flow with Reynolds numbers at 200 and 500 and in unsteady flow with Keulegan–Carpenter numbers at 5 and 10.     

Very slow flow of Bingham viscoplastic fluid around a circular cylinder

Numerical simulations have been used to study the flow of a Bingham viscoplastic fluid around a circular cylinder in an infinite medium with negligible inertia effects. Papanastasiou's regularisation technique has been adopted to approximate the model. The case corresponding to preponderant plasticity effects has been particularly studied and convergence of the solutions examined in detail. The flow kinematics and stresses have been determined. The rigid zones have been identified and characterised. At large Oldroyd numbers, when plasticity effects become preponderant, a viscoplastic boundary layer appears around the cylinder. The characteristics of this viscoplastic boundary layer are quantified. The results are compared with existing theoretical results, concerning particularly the predictions of the viscoplastic boundary layer theory and the plasticity theory.     

大气绕山体的运动及其输移特性的研究

对分层大气山体绕流的流动模式及扩散输移特性进行了数值模拟。采用隐式时间离散方法在贴体网格系统下求解雷诺平均的N-S方程,计算结果描述出大气流动的特征,证实了分层(以Froude数为特征参数,定义为F=U/NH,U为来流风速,N为Brunt-Vaisala频率,H为山体高度)变化对山体绕流流态的影响。数值结果表明:当Froude数大于4.0时,山体绕流的流动不再依赖于大气分层的变化。当Froude数介于4.0和1.0之间时,流场中出现了Lee波,并随着Froude数的进一步减小,流动分离发生及Lee波破碎现象。同时模型也预测了在各种流动模式下大气中夹杂着的污染物绕山体的传输特性,表明大气的分层现象对污染物的分布有着非常重要的影响。