旋翼尾流与地面干扰时地面涡现象的研究

用Ｎ－Ｓ方程对近地飞行时旋翼尾流与地面干扰时产生的地面涡现象进行了数值计算旋翼对流场的作用由分布在特定区域内的动量源项模拟结果表明，旋翼尾流撞到地面后的卷起和轴向流动的拉伸作用是形成地面涡的原因；地面边界层形成的二次分离涡向地面涡内输入（与尾流所携带的涡量）相反的涡量，而使地面涡保持平衡；地面涡的存在和运动使旋翼附近流场大大改变     

平板湍流边界层内的锥形涡

用拟三维流动显示技术观察与分析了平板边界层内的流动结构，讨论了雷诺数Ｒｅ在３００－６５０范围内大尺度结构间的联系，并指出锥形涡的形成是边界层中一系列复杂运动现象产生的关键。     

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。     

混合层中的流向涡与Rayleigh离心不稳定

用有限差分方法求解三维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和连续性方程，对时间发展的平面混合层中流向涡的产生原因进行了分析．将Ｒａｙｌｅｉｇｈ的轴对称无粘离心不稳定理论推广应用于分析混合层的二维基本流，并导出一无量纲量Ｒａｙ＝－（ｒ／νθ）νθ／ｒ，其中νθ为一流体质点相对于平均速度的速度，ｒ为该质点迹线的曲率半径．当Ｒａｙ＞１．０时就会发生离心不稳定．采用这一判别式后发现混合层中展向涡的周围，尤其是在辫带区，的确存在离心不稳定区域，而过去的实验结果也表明三维不稳定产生于展向涡之间的辫带区．因此有理由认为，除非雷诺数特别小，离心不稳定是流向涡产生和发展的主要原因     

分离涡方法对梢涡中脉动量的数值模拟

分别用RANS-SA方法和DES方法对NACA0012翼端梢涡进行模拟计算,分析了梢涡区域网格局部加密对梢涡计算结果的影响,并与实验结果进行了对比.相比于RANS-SA方法,DES方法在梢涡流场计算中具有更好的适用性,能够得到更准确的流动信息和更精细的涡结构;另外,网格局部加密对脉动量的计算影响很大.通过对脉动量的分析发现,在近尾缘处,几股涡的融合产生了比较强烈的脉动,随着梢涡的逐渐稳定,脉动量也逐渐减小;现有的实验结果显示在偏下游处会产生梢涡的振荡现象,使统计脉动量增大,而本文计算中未发现该现象.     

均匀来流中旋转圆柱黏性绕流的数值研究

从不可压非定常Ｎ－Ｓ方程出发，首次数值求解了均匀来流中圆柱作周向旋转振荡的黏性绕流问题。探讨了旋转角速度振幅、振荡频率及Ｒｅ数等因素对流场结构及其非定常演化过程的影响，并根据计算结果，给出了在旋转振动频率。速度振幅平面内流场涡结构的分区图。     

绕旋转圆柱流动涡尾流结构和临界状态特性

采用作者提出的基于区域分解，有限差分法与涡法杂交的数值方法，结合高阶隐式差分格式，和以修正的不完全ＬＵ分解为预处理器的共轭梯度法作求解器，系统地研究了雷诺数Ｒｅ＝１０００，旋转速度比α∈（０．５，３．２５）范围内，绕旋转圆柱从突然起到充分发展，长时间内尾流旋涡结构和阻力，升力系数的变化规律，计算所得流动图案与实验流场显示符合很好。数值试验证帝了临界状态的存在，并首次给出了临界状态时的旋涡结构特性。     

剪切湍流的涡黏张量模式

对剪切湍流提出了涡黏系数为四阶张量的涡黏张量模式。引入近代数学中Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ广义逆矩阵的研究结果，给出了构造涡黏张量各分量的计算公式。用平面后台阶流动验算了剪切湍流的涡黏张量模式，比ＲＳＭ和ｋ－ε模式更接近实验结果。提出了剪切湍流涡黏张量模式的应用设想。     

叶轮机内部流场的修正Taylor—Galerkin（MDTGFE）有限元法

首先改进了ＴＧＦＥ的基本假设考虑前后时间步之间的非线性效应，对流函数－涡量方程进行有限元离散，得到了修正Ｔａｙｌｏｒ－Ｇａｌｅｒｋｉｎ算法的有限元离散公式。采用这种方法，我们计算了后台阶绕流流动。另外，还用本方法的思想计算了叶轮机内部准三元流动。     

均匀来流中横向振动圆柱近迹涡结构的数值模拟

从涡量流函数形式的N-S方程出发,在不同的振动频率、振幅及Re数下数值研究了均匀来流中横向振动圆柱粘性统流的涡脱泻现象。着重探讨了近迹复杂的涡结构及其非定常演化过程,以及它们对物体受力特性的影响,并首次成功地模拟了近年来实验研究中所发现的一些重要的流动现象,如相位“开关”现象(phase switch phenomena)及复杂涡结构(complex vortex structure),等等。通过数值模拟,不仅能够再现实验研究中所发现的一些重要的流动现象,还可进一步预示某些新的流动现象,使数值计算起到与实验研究相辅相成的作用。     

NUMERICAL STUDY OF HIGH-REYNOLDS-NUMBER FLOW PAST A BLUFF OBJECT

A semi-explicit finite difference scheme is proposed to study unsteady two-dimensional, incompressible flow past a bluff object at high Reynolds number. The bluff object comes from a class of elliptical cylinders in which the aspect ratio and the angle of attack are two controlled parameters. Associated with the streamfunction–vorticity formulation, the interior vorticity, streamfunction and wall vorticity are updated in turn for each time step. The streamfunction and wall vorticity are solved by means of a multigrid method and a projection method respectively. In regard to the vorticity transport equation, implicitness is merely associated with the diffusion operator, which can be made semi-explicit via approximate factorization. Low-diffusive upwinding is devised to handle the convection part. Numerical results are reported for Reynolds numbers up to 40,000. Comparisons with other numerical or physical experiments are included.     

A comparison of primitive variables and streamfunction–vorticity for fem depth-averaged modelling of steady flow

The governing equations for depth-averaged turbulent flow are presented in both the primitive variable and streamfunction–vorticity forms. Finite element formulations are presented, with special emphasis on the handling of bottom stress terms and spatially varying eddy viscosity. The primitive variable formulation is found to be preferable because of its flexibility in handling spatial variation in viscosity, variability in water surface elevations, and inflow and outflow boundaries. The substantial reduction in computational effort afforded by the streamfunction–vorticity formulation is found not to be sufficient to recommend its use for general depth-averaged flows. For those flows in which the surface can be approximated as a fixed level surface, the streamfunction–vorticity form can produce results equivalent to the primitive variable form as long as turbulent viscosity can be estimated as a constant.     

Finite volume solution of the Navier–Stokes equations in velocity–vorticity formulation

For the incompressible Navier–Stokes equations, vorticity‐based formulations have many attractive features over primitive‐variable velocity–pressure formulations. However, some features interfere with the use of the numerical methods based on the vorticity formulations, one of them being the lack of a boundary conditions on vorticity. In this paper, a novel approach is presented to solve the velocity–vorticity integro‐differential formulations. The general numerical method is based on standard finite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a so‐called generalized Biot–Savart formula combined with a fast summation algorithm, which makes the velocity boundary conditions implicitly satisfied by maintaining the kinematic compatibility of the velocity and vorticity fields. The well‐known fractional step approaches are used to solve the vorticity transport equation. The paper describes in detail how we accurately impose no normal‐flow and no tangential‐flow boundary conditions. We impose a no‐flux boundary condition on solid objects by the introduction of a proper amount of vorticity at wall. The diffusion term in the transport equation is treated implicitly using a conservative finite update. The diffusive fluxes of vorticity into flow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential‐flow boundary condition. As application examples, the impulsively started flows through a flat plate and a circular cylinder are computed using the method. The present results are compared with the analytical solution and other numerical results and show good agreement. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical simulations of inviscid and viscous free‐surface flows with application to nonlinear water waves

The purpose of the present study is to establish a numerical model appropriate for solving inviscid/viscous free‐surface flows related to nonlinear water wave propagation. The viscous model presented herein is based on the Navier–Stokes equations, and the free‐surface is calculated through an arbitrary Lagrangian–Eulerian streamfunction‐vorticity formulation. The streamfunction field is governed by the Poisson equation, and the vorticity is obtained on the basis of the vorticity transport equation. For computing the inviscid flow the Laplace streamfunction equation is used. These equations together with the respective (appropriate) fully nonlinear free‐surface boundary conditions are solved using a finite difference method. To demonstrate the model feasibility, in the present study we first simulate collision processes of two solitary waves of different amplitudes, and compute the phenomenon of overtaking of such solitary waves. The developed model is subsequently applied to calculate (both inviscid and the viscous) flow field, as induced by passing of a solitary wave over submerged rectangular structures and rigid ripple beds. Our study provides a reasonably good understanding of the behavior of (inviscid/viscous) free‐surface flows, within the framework of streamfunction‐vorticity formulation. The successful simulation of the above‐mentioned test cases seems to suggest that the arbitrary Lagrangian–Eulerian/streamfunction‐vorticity formulation is a potentially powerful approach, capable of effectively solving the fully nonlinear inviscid/viscous free‐surface flow interactions. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite difference and finite element methods for mhd channel flows

A Galerkin finite element method and two finite difference techniques of the control volume variety have been used to study magnetohydrodynamic channel flows as a function of the Reynolds number, interaction parameter, electrode length and wall conductivity. The finite element and finite difference formulations use unequally spaced grids to accurately resolve the flow field near the channel wall and electrode edges where steep flow gradients are expected. It is shown that the axial velocity profiles are distorted into M-shapes by the applied electromagnetic field and that the distortion increases as the Reynolds number, interaction parameter and electrode length are increased. It is also shown that the finite element method predicts larger electromagnetic pinch effects at the electrode entrance and exit and larger pressure rises along the electrodes than the primitive-variable and streamfunction–vorticity finite difference formulations. However, the primitive-variable formulation predicts steeper axial velocity gradients at the channel walls and lower axial velocities at the channel centreline than the streamfunction–vorticity finite difference and the finite element methods. The differences between the results of the finite difference and finite element methods are attributed to the different grids used in the calculations and to the methods used to evaluate the pressure field. In particular, the computation of the velocity field from the streamfunction–vorticity formulation introduces computational noise, which is somewhat smoothed out when the pressure field is calculated by integrating the Navier–Stokes equations. It is also shown that the wall electric potential increases as the wall conductivity increases and that, at sufficiently high interaction parameters, recirculation zones may be created at the channel centreline, whereas the flow near the wall may show jet-like characteristics.     

Interactive vortex shedding from a pair of circular cylinders in a transverse arrangement

Interactive vortex shedding in the multiply connected domain formed by a pair of circular cylinders is analysed by the FEM–FDM blending technique. The vorticity–streamfunction formulation is used to solve the incompressible Navier–Stokes equations at Re = 100, with the time-dependent wall streamfunctions determined from the pressure constraint condition and the far-field streamfunctions from the integral series formula developed earlier by the authors. The standard Galerkin finite element method is used in the relatively small FEM subdomain and the finite difference method based on the general co-ordinate system in the rest of the flow domain. Symmetric, antisymmetric and asymmetric wake patterns are obtained confirming the earlier experimental findings. The bistable nature of the asymmetric vortex shedding as well as the intermittent drifting from one status to the other between symmetric and antisymmetric wake patterns are reported.     

Numerical study of vortex shedding from a rotating cylinder immersed in a uniform flow field

A numerical study is made of the unsteady two‐dimensional, incompressible flow past an impulsively started translating and rotating circular cylinder. The Reynolds number (Re) and the rotating‐to‐translating speed ratio (α) are two controlled parameters, and the influence of their different combinations on vortex shedding from the cylinder is investigated by the numerical scheme sketched below. Associated with the streamfunction (ψ)–vorticity (ω) formulation of the Navier–Stokes equations, the Poisson equation for ψ is solved by a Fourier/finite‐analytic, separation of variable approach. This approach allows one to attenuate the artificial far‐field boundary, and also yields a global conditioning on the wall vorticity in response to the no‐slip condition. As for the vorticity transport equation, spatial discretization is done by means of finite difference in which the convection terms are handled with the aid of an ENO (essentially non‐oscillatory)‐like data reconstruction process. Finally, the interior vorticity is updated by an explicit, second‐order Runge–Kutta method. Present computations fall into two categories. One with Re=10³ and α≤3; the other with Re=10⁴ and α≤2. Comparisons with other numerical or physical experiments are included. Copyright © 2000 John Wiley & Sons, Ltd.     

Finite element solution of the streamfunction-vorticity equations for incompressible two-dimensional flows

The streamfunction-vorticity equations for incompressible two-dimensional flows are uncoupled and solved in sequence by the finite element method. The vorticity at no-slip boundaries is evaluated in the framework of the streamfunction equation. The resulting scheme achieves convergence, even for very high values of the Reynolds number, without the traditional need for upwinding. The stability and accuracy of the approach are demonstrated by the solution of two well-known benchmark problems: flow in a lid-driven cavity at Re ? 10,000 and flow over a backward-facing step at Re = 800.     

A boundary integral equation method for Navier-Stokes equations—application to flow in annulus of eccentric cylinders

A novel Navier-Stokes solver based on the boundary integral equation method is presented. The solver can be used to obtain flow solutions in arbitrary 2D geometries with modest computational effort. The vorticity transport equation is modelled as a modified Helmholtz equation with the wave number dependent on the flow Reynolds number. The non-linear inertial terms partly manifest themselves as volume vorticity sources which are computed iteratively by tracking flow trajectories. The integral equation representations of the Helmholtz equation for vorticity and Poisson equation for streamfunction are solved directly for the unknown vorticity boundary conditions. Rapid computation of the flow and vorticity field in the volume at each iteration level is achieved by precomputing the influence coefficient matrices. The pressure field can be extracted from the converged streamfunction and vorticity fields. The solver is validated by considering flow in a converging channel (Hamel flow). The solver is then applied to flow in the annulus of eccentric cylinders. Results are presented for various Reynolds numbers and compared with the literature.     

A numerical study of heat and momentum transfer for tube bundles in crossflow

A numerical scheme is developed to predict the heat transfer and pressure drop coefficients in flow through rigid tube bundles. The scheme uses the Galerkin finite element technique. The conservation equations for laminar steady-state flow are cast in the form of streamfunction and vorticity equations. A Picard iteration method is used for the solution of the resulting system of non-linear algebraic equations. Results for the heat transfer and pressure drop coefficients are obtained for tube arrays of pitch ratios of 1·5 and 2·0. Very good agreement of the present results and experimental data obtained in the past is observed up to Reynolds numbers of 1000. It is also observed that the results of the present method show better agreement with the experimental data and that they are applicable for higher Reynolds numbers than results of other studies.