二维振荡叶栅非定常粘性流动数值模拟

采用显式四步Runge-Kutta格式，结合Baldwon-Lomax紊流模型求解Navier-Stokes方程，借助运动网格技术，完成了对二维振荡叶栅非定常粘性流动的数值模拟。为了加速求解过程，引入了变系数隐式残差光顺方法，取得了较好效果。数值结果与已公布的数据有很好的一致性。     

Flow past a transversely oscillating square cylinder in free stream at low Reynolds numbers

This paper reports simulation results for free‐stream flow past an oscillating square cylinder at Re=100 and 150, for oscillating‐to‐natural‐shedding frequency ratios of 0.5?f_r?3.0 at a fixed oscillation amplitude of 0.2 of the cylinder width. The transformed governing equations are solved in a non‐inertial frame of reference using the finite volume technique. The ‘lock‐in’ phenomena, where the vortex shedding becomes one with the oscillation frequency, is observed near the natural shedding frequency (f_r≈1). Beyond the synchronization band, downstream recovery of the wake to its stationary (natural) state (frequency) is observed in cross‐stream velocity spectra. At higher forcing frequencies, a phase lag between the immediate and the far wake results in a shear layer having multi‐polar vortices. A ‘Vortex‐switch’ accompanied by a change in the direction of energy transfer is identified at the ‘lock‐in’ boundaries. The variation of aerodynamic forces is noticed to be different in the lock‐in regime. The velocity phase portrait in the far wake revealed a chaotic state of flow at higher excitation though a single (natural) frequency appears in the spectra. Copyright © 2008 John Wiley & Sons, Ltd.     

Application of Differing Forcing Function Models on Simulated Flow Past an Oscillating Cylinder in a Uniform Low Reynolds Number Flow

A Computational Fluid Dynamics (CFD) model is presented for the uniform viscous two dimensional flow past an oscillating cylinder at low Reynolds number. Numerical simulations are made to study the effect of differing forced induced oscillation mechanisms with a large range of cylinder forcing frequencies. In the first case sinusoidal velocity slip boundary conditions are adopted for the cylinder surface to simulate cylinder oscillation. The implication suggests that no modification or additional term need to be added to the Navier-Stokes equations. In the second case this time extra body force terms which are assumed to account for velocity effects due to cylinder movement are included in the Navier-Stokes equations with the imposition of same boundary conditions. Drag and lift coefficients are extracted from present numerical results and other detailed computations of these coefficients are made at a Reynolds number of 80 and an amplitude-to diameter ratio 0.14. The results are found to be in agreement with each other at low force driving frequencies below and near lock-in. However, differences are found at higher frequencies above lock-in. Agreement are also found with experimental results at some frequency ranges.     

流向振荡柱体尾流控制研究进展

详细介绍了近几年采用尾部喷射、隔离板和小窄条控制件等3 种方法对流向振荡柱体绕流旋涡脱落的抑制情况. 在研究范围内存在非锁频和3种锁频旋涡脱落模式. 风洞实验表明, 尾部喷射对这4 种模式都有抑制效果,窄条控制件对非锁频和2种锁频模式具有抑制效果, 而隔离板仅对非锁频和1 种锁频模式有效. 在不同流动和振荡条件下找出了每种方法的有效控制区, 研究了减阻和减少脉动力的效果, 并探讨了控制机理.      

Effects of Periodic Excitation on the Flow Around a D-Shaped Cylinder at Low Reynolds Numbers

The baseline and forced flow around a bluff body with semi-elliptical D-shape was investigated by solving the 2D Navier–Stokes equations at low Reynolds numbers. A D-shape rather than the canonic circular-cylinder was selected due to the fixed separation points in the latter, enabling to study a pure wake rather than boundary-layer control. The correlation between Strouhal and Reynolds numbers, the mean drag, the lift and drag oscillations vs. the Reynolds number and wake structure were investigated and compared to experimental and numerical data. Effects of open-loop forcing, resulting from the influence of zero-mass-flux actuators located at the fixed separation points, were studied at a Reynolds number of 150. Fluidic rather than body motion or volume forcing was selected due to applicability considerations. The motivation for the study was to quantify the changes in the flow field features, as captured by Proper Orthogonal Decomposition (POD) analysis, due to open-loop forcing, inside and outside the “lock-in” regime. This is done in order to evaluate the suitability of low-order-models based on POD modes of this changing flow field, for future feed-back flow control studies. The evolution of the natural and the excited vortices in the Kármán wake were also investigated. The formation and convection regions of the vortex evolution were documented. It was found that the forcing causes an earlier detachment of the vortices from the boundary-layers, but does not affect their circulation or convection speeds. The results of the POD analysis of the near-wake flow show that the influence of the bluff body shape (“D”-shaped versus circular cylinder) on the baseline POD wake modes is small. It was found that the eigenfunctions (mode-shapes) of the POD velocity modes are less sensitive to slot excitation than the vorticity modes. As a result of the open-loop excitation, two types of mode-shape-change were observed: a mode can be exchanged with a lower-energy mode or shifted to a low energy level. In the latter case, the most energetic mode becomes the “actuator” mode. The evolution of one-slot excitation on still fluid (“Synthetic jet”) was studied and compared to published data and to “actuator” modes with external flow present. Based on the current findings, it is hypothesized that the cross-flow velocity POD modes are suitable for feedback control of wake flow using periodic excitation, due to their low sensitivity to the excitation as compared to the streamwise velocity or vorticity modes.     

Regimes of vortex shedding from an in-line oscillating circular cylinder in the uniform flow

A finite volume method for the time dependent viscous incompressible flow around an in-line oscillating circular cylinder at Reynolds number of 200, 855 is presented in this paper. The Navier-Stokes equations in a finite volume form are solved with a moving grid system, based on a time dependent coordinate transformation. To investigate the vortex-shedding characteristics behind the circular cylinder and the effects of Reynolds number and other non-dimensional parameters such as reduced amplitude and reduced frequency， several numerical schemes have been tested with different amplitude and frequency close to Sto and a harmonic at each Reynolds number. Present numerical results indicate several types of vortex shedding mode which is known mainly depending on the reduced frequency and also the reduced amplitude, which is called synchronization or lock-on.     

侧柱与串列双柱绕流之间的干扰

本文给出了关于串列双柱与创柱间流动干扰的实验研究结果。当三个圆柱排成等边三角形并靠得很近时，由于三圆柱间强烈的缝隙流动，大大地改变了绕流其中的串列双圆柱的流态。特别，当三圆柱中心距等于二倍圆柱直径时，在串列双柱的前、后柱之间形成了强烈的偏斜的缝隙流，出现了独特的压力分布以及要比单柱高出三倍以上的旋涡脱落频率。     

Oscillations of a Cylinder Induced by Free Surface Flow

The results of experiments in which a cylinder freely located on a fixed shaft performs small harmonic oscillations driven by a subcritical free stream in an open channel are given. Examples of the strong feedback effect of the cylinder oscillations on the hydrodynamic wake and surface gravity waves are obtained.     

The Relaminarization Mechanisms of Turbulent Channel Flow at Low Reynolds Numbers

The mechanisms of laminarization in wall-bounded flows have been investigated by performing direct numerical simulations (DNS) of turbulent channel flows. By decreasing Reynolds numbers systematically, the effects of the low Reynolds number are studied in connection with the near-wall turbulent structure and turbulent statistics. At approximately the critical Reynolds number, the turbulent skin friction is reduced, and the turbulent structure changes qualitatively in the very near-wall region. Instantaneous turbulent structures reveal that streamwise vortices, the cores of which are at y+ 10, disappear, although low speed streaks and Reynolds shear stress are still produced by larger streamwise vortices located in the buffer region y+ > 10. Sweep motions induced by these vortical structures are shifted toward the center of a channel and also significantly deterred, which may heighten the effects of the viscous sublayer over most of the channel section and suppress the regeneration mechanisms of new streamwise vortices in the very near-wall region. To investigate the details of how large-scale coherent vortices affect the viscous sublayer and the relevant small-scale streamwise vortices, a body force is virtually imposed in the wall-normal direction to enhance the large streamwise vortices. As a result, it is found that when they are sufficiently enhanced, the small-scale vortices reappear, and the sweep events are again dominant in the viscous sublayer.     

各种间隙比下水平圆柱绕流特性的实验研究

采用粒子图像测速仪(PIV)和超声测速仪(ADV)系统,对间隙比G为0.0~7.0(即为圆柱与底壁相接触时至圆柱与水面相接触时)浅水横流水平圆柱绕流流动进行了系统实验研究。根据所测结果,讨论了在各种间隙比情况下圆柱上、下游的紊动强度、雷诺应力沿水深的分布规律;分析了在各种间隙比情况下旋涡的生成、发展和演化的现象和规律;分析了瞬时数据时均化后的时均流场结构特性;比较了瞬时流场和时均流场的特点及差别。本文成果对具有类似流动特点的工程问题具有指导意义。     

Suppression of vortex shedding from a rectangular cylinder at low Reynolds numbers

Small elements of circular, square, triangular and thin-strip cross-sections are used to suppress vortex shedding from a rectangular cylinder of stream-wise to transverse scale ratio L/B=3.0 at Reynolds numbers in the range of Re=V_∞B/ν=75–130, where V_∞ is the on-coming velocity of the stream, and ν is the kinematic viscosity. The relative transverse dimension of the small element b/B is fixed at 0.2. The results of numerical simulation and visualization experiment show that, vortex shedding from both sides of the cylinder can be suppressed and the fluctuating drag and lift of the cylinder can be greatly reduced, if the element is placed in a certain region referred to as the effective zone. Comparisons at a specific Reynolds number indicate that the square element produces the largest size of the effective zone, whereas the triangular element yields the smallest. Results also show that the effective zone for the square element shrinks with increasing Re and disappears at Re>130. Independent of element cross-section shape and Reynolds number, the center of the effective zone is always at X/B=2.5–3.0 and Y/B≈1.0. The mechanism of the suppression is discussed from the view points of velocity profile stability and stress distribution.     

Active Control of a Circular Cylinder Flow at Transitional Reynolds Numbers

Active and passive control of flow around a circular cylinder, at transitional Reynolds numbers was investigated experimentally by measuring cylinder surface pressures and wake velocity profiles. Two- and three-dimensional passive boundary layer tripping was considered and periodic active control using piezo-fluidic actuators was introduced from a two-dimensional slot that was nearly tangential to the cylinder surface. The slot location was varied circumferentially by rotating the cylinder and this facilitated either upstream- or downstream-directed actuation using sinusoidal or modulated wave-forms. Separation was controlled by two distinct methods, namely: by forcing laminar-turbulent transition when applied at relatively small angles (30–60°) from the forward stagnation point; and by directly forcing the separated shear-layer at larger angles. In the latter case, actuation produced the largest load changes when it was introduced at approximately 90° from the forward stagnation point. When the forcing frequency was close to the natural vortex-shedding frequency, the two frequencies “locked-in” creating clear and persistent structures. These were examined and categorized. The “lock-in” effect lowered the base pressure and increased the form-drag whereas delaying separation from the cylinder did the opposite.     

Effect of a Dispersed Admixture on the Flow Pattern and Heat Transfer in a Supersonic Dusty-Gas Flow Around a Cylinder

A mathematical model of two-phase (gas-solid particle) flow which takes into account particle-particle collisions and the feedback effect of the admixture on the gas parameters is proposed. The dispersed phase is described by a kinetic equation of the Boltzmann type and the carrier gas by modified Navier-Stokes equations. Using this model, a supersonic uniform dusty-gas flow past a cylinder is calculated. The fields of the macroparameters of the admixture and the carrier medium are obtained. The dependence of the heat transfer at the stagnation point on the relative particle size and the free-stream admixture concentration is studied in detail. The ranges of these parameters on which particle collisions and the feedback effect of the admixture on the carrier-gas flow are important are found.     

Effect of Large Scale 3-D Structures on the Flow Around a Heated Cylinder at Low Reynolds Number

This work presents results of flow around a heated circular cylinder in mixed convection regime and demonstrates that Prandtl number and angle of attack of the incoming flow have a large influence on the characterisation of the flow transition from 2-D to 3-D. Previous studies show that heat transfer can enhance the formation of large 3-D structures in the wake of the cylinder for Reynolds numbers between 75 and 127 and a Richardson number larger than 0.35. This transitional mode is generally identified as “mode E”. In this work, we compare the results for water-based flow (large Prandtl number) with the ones for air-based flows (low Prandtl number). The comparison is carried out at two Reynolds numbers (100 and 150) and at a fixed Richardson number of 1. It shows that at the low Reynolds number of 100 the low Prandtl number flow does not enter into transition. This is caused by the impairment of the baroclinic vorticity production provoked by the spanwise temperature gradient. At low Prandtl number temperature gradients are less steep. For an air-based flow at Reynolds number 150, several Richardson numbers have been simulated. In this situation, the flow enters into transition and exhibits the characteristics of “mode E”, with the development of Λ-shaped structures in the near wake and mushroom-like structures in the far wake. It is also observed that the transition is delayed at Richardson number of 0.5. Simulations are also carried to investigate the effect of the angle of attack on the incoming flow on the development of large coherent structures. When the angle of attack is positive, the development of the wake tends to return to a more bi-dimensional configuration, where large scale coherent structures are impaired. In contrast, when the angle of attack is negative, large scale tri-dimensional structures dominate the flow in the wake, but with a very chaotic behaviour and the regular pattern of zero angle of attack is destroyed. The different behaviour of the flow with the variation of the angle of attack is also related to the baroclinic vorticity production, where new terms appear in the equations, leading to a positive effect of the vorticity production in case of a negative angle of attack and the opposite for a positive angle of attack.     

Numerical Study of the Effect of Periodic Velocity Excitation on Aerodynamic Characteristics of an Oscillating Circular Cylinder

A finite element method based on ALE formulation has been adopted in order to examine the effect of periodic velocity excitation on the aerodynamic characteristics of an oscillating circular cylinder. Periodic excitation, which was placed on the cylinder surface, stimulated the separated shear layers around the cylinder, and numerical results showed that some excitation can reduce negative damping, which is caused by unsteady lift force, and thereby stabilize the aerodynamics of the cylinder. Furthermore, the change of lift phase caused by periodic excitation seems to be important in stabilizing the aerodynamics of the cylinder. The simulation also confirmed that periodic excitation can suppress the vortex-induced vibration of the cylinder.     

Characterization of long time fluctuations of forces exerted on an oscillating circular cylinder at KC=10

Flow dynamics, in-line and transverse forces exerted on an oscillating circular cylinder in a fluid initially at rest are studied by numerical resolution of the two-dimensional Navier-Stokes equations. The Keulegan-Carpenter number is held constant at KC=10 and Re is increased from 40 to 500. For the different flow regimes, links between flow spatio-temporal symmetries and force histories are established. Besides simulations of long duration show that in two ranges of Re, forces exhibit low frequency fluctuations compared to the cylinder oscillation frequency. Such observations have been only mentioned in the literature and are more deeply examined here. In both ranges, force fluctuations correspond to oscillations of the front and rear stagnation points on the cylinder surface. However, they occur in flow regimes whose basic patterns (V-shaped mode or diagonal mode) have different symmetry features, inducing two distinct behaviors. For 80≤Re≤100, fluctuations are related to a spectral broadening of the harmonics and to a permutation between three vortex patterns (V-shaped, transverse and oblique modes). In the second range 150≤Re≤280, amplitude fluctuations are correlated to the appearance of low frequency peaks interacting with harmonics of the cylinder frequency. Fluctuations are then a combination of a wavy fluctuation and an amplitude modulation. The carrier frequency corresponding to the wavy fluctuation depends on Re and is related to a fluid characteristic time; the modulation frequency is independent of Re and equal to 1/4 of the cylinder oscillation frequency.     

Simulation of vortex shedding past a square cylinder with different turbulence models

This paper presents the results of numerical simulations of vortex shedding past a free-standing square cylinder at Re_D=22 000, obtained with different turbulence models. Using wall functions, the standard k–ε model is compared with a modification suggested by Kato and Launder (Proc. 9th Symp. Turbulent Shear Flows, Kyoto, 10-4-1 (1993)). In addition, both versions are used in a two-layer approach, in which the flow close to the cylinder is computed with a locally more suitable one-equation turbulence model and only outside the viscous near-wall layer with the two mentioned high-Re model versions. To allow a comparison, the simulations are performed first using the same computational domain and boundary conditions as in previous investigations. Then results are presented that were obtained on a computational domain and with boundary conditions more suitable for a comparison with the experiments. © 1998 John Wiley & Sons, Ltd.     

Large Eddy Simulation of Flow around a Rectangular Cylinder Using the Finite Element Method

In previous papers, we proposed finite element schemes based on the Petrov-Galerkin weak formulation using exponential weighting functions for solving accurately, and in a stable manner, the flow field of an incompressible viscous fluid. In this paper, we present the Petrov-Galerkin finite element scheme for turbulent flow fields based on large eddy simulation using the standard Smagorinsky model with the Van Driest damping function. The filtered incompressible Navier-Stokes equations are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth explicit differencing for both convection an diffusion terms. In order to evaluate more accurately a mass matrix, the well-known multi-pass algorithm was also adopted in this study. Numerical results obtained are compared through flow around a rectangular cylinder at Re = 22,000 with the experimental data and other existing numerical data.