A high-order compact scheme for solving the 2D steady incompressible Navier-Stokes equations in general curvilinear coordinates

In this paper, a high-order compact finite difference algorithm is established for the stream function-velocity formulation of the two-dimensional steady incompressible Navier-Stokes equations in general curvilinear coordinates. Different from the previous work, not only the stream function and its first-order partial derivatives but also the second-order mixed partial derivative is treated as unknown variable in this work. Numerical examples, including a test problem with an analytical solution, three types of lid-driven cavity flow problems with unusual shapes and steady flow past a circular cylinder as well as an elliptic cylinder with angle of attack, are solved numerically by the newly proposed scheme. For two types of the lid-driven trapezoidal cavity flow, we provide the detailed data using the fine grid sizes, which can be considered the benchmark solutions. The results obtained prove that the present numerical method has the ability to solve the incompressible flow for complex geometry in engineering applications, especially by using a nonorthogonal coordinate transformation, with high accuracy.     

System identification of the kinematics of an oscillating cylinder using wake velocities

A classical problem in vortex-induced vibration is to know the flow field past an oscillating cylinder. In this paper we use system theory to identify the oscillatory behaviour of a circular cylinder from flow variables in the wake. We use numerical simulations (CFD) of the flow past a cylinder oscillating in the cross-flow direction at different oscillation frequencies and amplitudes to construct a transfer function that relates the displacement of the cylinder and the resulting flow field. This transfer function can then be inverted to ‘predict’ the displacement of the cylinder given the flow field (as determined by simulations or measurements). We investigate this technique in the so-called lock-in region, where the vortex shedding frequency is synchronised with the oscillation frequency of the cylinder.     

On the use of adaptive hierarchical meshes for numerical simulation of separated flows

This paper describes the use of adaptive hierarchical grids to predict incompressible separated flow at low Reynolds number. The grids consist of a quadtree system of hierarchical Cartesian meshes which are generated by recursive subdivision about seeding points. The governing equations are discretized in collocated primitive variable form using finite volumes and solved using a pressure correction scheme. The mesh is locally adapted at each time step, with panel division or removal dependent on the vorticity magnitude. The resulting grids have fine local resolution and are economical in array size. Results are presented for unidirectional, impulsively started flow past a circular and a square cylinder at various Reynolds numbers up to 5000 and 250 respectively. It is clear that hierarchical meshes may offer gains in efficiency when applied to complex flow domains or strongly sheared flows. However, as expected, the stepped approximation to curved boundaries resulting from the Cartesian quadtree representation adversely affects the accuracy of the results for flow past a circular cylinder. © 1998 John Wiley & Sons, Ltd.     

The critical separation reynolds number for streaming flow past a circular cylinder

Employing a complex variable approach to the equations of motion for an incompressible viscous fluid and a more general approximation to the convecting stream function it is possible to calculate an approximation to the vorticity on the boundary for streaming flow past a circular cylinder without solving first for the complete flow field. In particular it is found that separation at the rear stagnation point first occurs when $\text{R1 = 2.78}$, where $\text{R1}$ is the critical Reynolds number. This result is in good agreement with the value of $\text{R1}$ obtained by experiment and the value obtained numerically. The convecting stream function satisfies the conditions of no slip and vorticity is not convected through the cylinder as it is in small Reynolds number Oseen theory.     

纳米尺度圆柱绕流尾迹区流动形式模拟研究

采用非平衡分子动力学模拟方法,对微尺度低{Re}数下的圆柱绕流问题进行了研究,模拟结果表明:当{Re}<12时,圆柱下游形成对称、无分离的定常流;当{Re}>20时,圆柱下游形成周期性交替出现的对称涡;当12相似文献   

NUMERICAL STUDY OF THE FLOW PAST A CYLINDER EXCITED TRANSVERSELY TO THE INCIDENT STREAM. PART 1: LOCK-IN ZONE,HYDRODYNAMIC FORCES AND WAKE GEOMETRY

The numerical study of the flow past a circular cylinder forced to oscillate transversely to the incident stream is presented herein, at a fixed Reynolds number equal to 106. The finite element technique was favoured for the solution of the Navier–Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The cylinder oscillation frequency ranged between 0·80 and 1·20 of the natural vortex-shedding frequency, and the oscillation amplitude extended up to 50% of the cylinder diameter. Since the resolution of the characteristics of synchronized wakes is the focus of the study, the first task is the determination of the boundary of the lock-in region. The computation revealed that, when the cylinder oscillation frequency exceeds the frequency of the natural shedding of vortices, the flow is not absolutely periodic at subsequent cycles but a quasiperiodic flow pattern occurs, which creates difficulty in the determination of the lock-in boundary. The time histories of the drag and lift forces for various oscillation parameters are presented, while the vorticity contours were favoured for the numerical flow visualization. The hydrodynamic forces, the phase angle between the lift force and the cylinder displacement, and the parameters of the wake geometry when steady state was reached, are presented in cumulative diagrams. These diagrams indicate the effect of the oscillation parameters on the hydrodynamic forces and on the wake geometry.     

Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method

We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large Courant–Friedrichs–Lewy number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback forcing scheme of the virtual boundary method with Peskin's regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta functions. The stability regime of the 4‐point regularized delta function was much wider than that of the 2‐point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite‐difference and fractional‐step context. The proposed method was tested on several flow problems, including the flow past a stationary cylinder, inline oscillation of a cylinder in a quiescent fluid, and transverse oscillation of a circular cylinder in a free‐stream. The findings were in excellent agreement with previous numerical and experimental results. Copyright © 2008 John Wiley & Sons, Ltd.     

Helical Outflow through a Circular Hole in the Bottom of a Semi-Infinite Cylinder (Modification of a Slezkin Problem)

The steady axisymmetric helical flow of an incompressible ideal fluid in a semi-infinite cylinder due to the presence of a circular hole in its bottom is analyzed. At an infinite distance from the bottom, in contrast to the similar problem considered by N. A. Slezkin, constant axial and angular components of the quasi-rigid rotation are maintained and the hole-induced flow is uniformly helical in the Zhukovsky sense, that is, the vorticity vector of the absolute motion is collinear to the relative velocity. In the coordinate system rotating with the fluid, this flow can be represented as the superposition of a straight-line translational flow in the direction of the bottom and a uniformly helical Gromeka-Beltrami flow. The problem is solved using the generalized stream function. The limiting cases of a helical sink in the bottom of a semi-infinite cylinder and helical flow out of a half-space through a circular hole on the boundary are considered. The results are compared with those for potential flow.     

Incompressible fluid flow past a circular cylinder with linear relation between the vorticity and the stream function

Incompressible fluid flow with a linear relationship between the vorticity and the stream function past a circular cylinder is studied.Vortical flows about profiles have been considered in several studies [1–15], but in all these studies with the exception of [15] a constant vorticity was assumed (in [15] an approximate solution is found of the problem of incompressible fluid flow about a Zhukovskii profile with parabolic distribution of the velocities in the approaching stream).A freestream velocity profile similar to that considered below occurs, for example, in a planar jet (laminar or turbulent), in the wake behind a bluff body, in the boundary layer along an infinite plane [4,13], in turbulent jet flows with reverse fluid currents [16]. A similar situation also arises in the flow past an array of cylinders with large spacing which is located in the wake of another array.The author wishes to thank V. E. Davidson for posing the problem and for guidance in its solution.     

An experimental study of the dynamic characteristics in boundary layer in the flow past a two-dimensional circular cylinder at subcritical reynolds numbers

An experimental study of the dynamic characteristics of flow past a two-dimensional circular cylinder is described. The fluctuationsoof wall shear stress, surface-pressure and velocity of the flow are measured with hot-film, hot-wire and pressure transducer. The frequency feature of fluctuations of wall shear stress is given. The cross-correlation functions of these fluctuations at any two points are calculated. The experimental results reveal that there is an overall syncronous fluctuation, at the shedding frequency, in boundary layer in the flow past a two-dimensional circular cylinder at subcritical Reynolds number.     

Topology of vortex creation in the cylinder wake

We analyze the topology of the two-dimensional flow around a circular cylinder at moderate Reynolds numbers in the regime where the vortex wake is created. A normal form for the stream function close to the cylinder is presented and used to predict the streamline pattern both in the steady and the periodic regime, where two different vortex shedding scenarios are identified. The theoretical predictions are verified numerically. For the vorticity, a very different topology occurs with infinite nested sequences of iso-curves moving downstream. General equations of motion for critical points are derived.     

Steady forces on a cylinder with oblique vortex shedding

We present a curious situation of a fluid-flow wherein the body experiences non-fluctuating fluid-flow force despite being associated with an unsteady flow comprising of sustained vortex shedding. The flow past a circular cylinder at Re=100 is investigated. It is shown that the spatio-temporal periodicity of the oblique vortex shedding results in constant-in-time force experienced by a cylinder placed in uniform flow. On the contrary, parallel vortex shedding leads to fluid force that fluctuates with time. It is found that, both, the parallel and oblique shedding are linearly unstable eigenmodes of the Re=100 steady flow past a cylinder.     

Numerical investigation of fluid flow past circular cylinder with multiple control rods at low Reynolds number

Laminar flow past a circular cylinder with multiple small-diameter control rods is numerically investigated in this study. The effects of rod-to-cylinder spacing ratio, rod and cylinder diameter ratio, cylinder Reynolds number, number of control rods and angle of attack on the hydrodynamics of the main circular cylinder are investigated. Four different flow regimes are identified based on the mechanism of lift and drag reduction. The range of rod-to-cylinder spacing ratio where significant force suppression can be achieved is found to become narrower as the Reynolds number increases in the laminar regime, but is insensitive to the diameter ratio. The numerical results for the case with six identical small control rods at Re=200 show that the lift fluctuation on the main cylinder can be suppressed significantly for a large range of spacing ratio and various diameter ratios, while the drag reduction on the main cylinder is also achieved simultaneously. The six-control-rod arrangement has shown better performance in flow control than the arrangements with less control rods, especially in terms of force reduction at various angles of attack.     

Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder

In this work, the natural convection in a concentric annulus between a cold outer square cylinder and a heated inner circular cylinder is simulated using the differential quadrature (DQ) method. The vorticity‐stream function formulation is used as the governing equation, and the coordinate transformation technique is introduced in the DQ computation. It is shown in this paper that the outer square boundary can be approximated by a super elliptic function. As a result, the coordinate transformation from the physical domain to the computational domain is set up by an analytical expression, and all the geometrical parameters can be computed exactly. Numerical results for Rayleigh numbers range from 104 to 106 and aspect ratios between 1.67 and 5.0 are presented, which are in a good agreement with available data in the literature. It is found that both the aspect ratio and the Rayleigh number are critical to the patterns of flow and thermal fields. The present study suggests that a critical aspect ratio may exist at high Rayleigh number to distinguish the flow and thermal patterns. Copyright © 2002 John Wiley & Sons, Ltd.     

Effects of an axial flow component on the Honji instability

This paper is concerned with a numerical study of the three-dimensional Honji instability that can arise in an oscillatory flow impinging on a circular cylinder. It is well known that when the fluid motion far from the cylinder is perpendicular to its axis then the flow is liable to a three-dimensional breakdown via this instability which initially appears as an axially periodic mushroom-like structure attached to the surface of the cylinder. Here the focus is on examining the Honji instability under an oblique inflow. The obliqueness of the free stream is represented by an angle of attack through introducing an axial flow component. It is found that the Honji mode is suppressed by increasing the axial flow component, and when this component is sufficiently large the instability mechanism is no longer operative so that all that remains is a featureless two-dimensional columnar flow. At smaller values of angle of attack, though the Honji structure remains, it is deformed by the axial flow component. The developed two-layer near-cylinder vortical structures can be related to the energy and momentum transfer between the two layers.     

ONSET OF ASYMMETRY: FLOW PAST CIRCULAR AND ELLIPTIC CYLINDERS

A computational study of the development of two- dimensional unsteady viscous incompressible flow around a circular cylinder and elliptic cylinders is undertaken at a Reynolds number of 10,000. A higher- order upwind scheme is used to solve the Navier–Stokes equations by the finite difference method in order to study the onset of computed asymmetry around bluff bodies. For the computed cases the ellipses develop asymmetry much earlier than the circular cylinder. The receptivity of the computed flows in the presence of discrete roughness and surface vibration is studied. Finally, the role of discrete roughness in triggering asymmetry for flow past a circular cylinder is studied and compared with flow visualization experiments at Re=10,000     

横向振荡圆柱绕流的格子Boltzmann方法模拟

基于格子Boltzmann方法(LBM)对不可压横向振荡圆柱绕流问题进行了数值研究. 与传统的求解宏观的N-S方程的数值方法不同, LBM求解此类问题不需要采用动网格, 而且不需要对网格进行特殊处理, 从而节约了计算成本. 结果显示, 当振荡频率增加到相应的静止圆柱绕流的自然涡脱落频率附近时, 圆柱后最新形成的集中涡距离柱体越来越近, 直到达到一个极限位置. 随后, 集中涡突然转向圆柱体另一侧脱落. 当振荡频率接近于静止圆柱的自然涡脱落频率时, 发生频率同步的现象. 随着振荡频率远离自然涡脱落频率, 同步现象消失. 在几种次谐振荡和超谐振荡下, 尾流区的涡脱落频率仍为相应的静止圆柱绕流的自然涡脱落频率.      

不可压缩粘性流动的CBS有限元解法

对于二维不可压缩粘性流动,首先通过坐标变换的方式得到了的不含对流项的NS方程,并给出了CBS有限元方法求解的一般过程。结合一类同时含有压力和速度的出口边界条件,对方腔顶盖驱动流、后向台阶绕流和圆柱绕流进行了计算。所得结果与基准解符合良好,验证了CBS算法对于定常、非定常粘性不可压缩流动问题的可行性和所用出口边界条件的无反射特性。特别的,对于圆柱绕流,Re=100时非定常升、阻力系数及漩涡脱落等非定常都得到了较好地模拟,为一进步研究自激振动等更加复杂的非定常流动问题奠定了基础。     

A mesh-free radial basis function–based semi-Lagrangian lattice Boltzmann method for incompressible flows

In this paper, a local radial basis function–based semi-Lagrangian lattice Boltzmann method (RBF-SL-LBM) is proposed. This is a mesh-free method that can be used for the simulation of incompressible flows. In this method, the collision step is performed locally, which is the same as in the standard LBM. In the meanwhile, the steaming step is solved in a semi-Lagrangian framework. The distribution functions at the departure points, which may be not the grid points in general, are computed by the local radial basis function interpolation. Several numerical tests are conducted to validate the present method, including the lid-driven cavity flow, the steady and unsteady flow past a circular cylinder, and the flow past an NACA0012 airfoil. The present results are in good agreement with those published in the previous literature, which demonstrates the capability of RBF-SL-LBM for the simulation of incompressible flows.     

Local moving least square‐one‐dimensional integrated radial basis function networks technique for incompressible viscous flows

This paper presents a local moving least square‐one‐dimensional integrated radial basis function networks method for solving incompressible viscous flow problems using stream function‐vorticity formulation. In this method, the partition of unity method is employed as a framework to incorporate the moving least square and one‐dimensional integrated radial basis function networks techniques. The major advantages of the proposed method include the following: (i) a banded sparse system matrix which helps reduce the computational cost; (ii) the Kronecker‐ δ property of the constructed shape function which helps impose the essential boundary condition in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of integration instead of conventional differentiation to construct the local radial basis function approximations. Several examples including two‐dimensional (2D) Poisson problems, lid‐driven cavity flow and flow past a circular cylinder are considered, and the present results are compared with the exact solutions and numerical results from other methods in the literature to demonstrate the attractiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.