Numerical simulation of a flow around an impulsively started radially deforming circular cylinder

The development of a two‐dimensional viscous incompressible flow generated by a deformable circular cylinder impulsively started into rectilinear motion is studied numerically for the Reynolds numbers equal to 550 and 3000. The vorticity transport equation is solved by a second‐order finite difference method in both directions of the domains. The Poisson equation for the streamfunction is solved by a Fourier–Galerkin method in the direction of the flow that is assumed to remain symmetrical and a second‐order finite difference for the radial direction. The advance in time is achieved by a second‐order Adams–Bashforth scheme. The computed results are compared qualitatively with experimental and numerical results done before in the particular non‐deformable case. The comparison is found to be satisfactory. The influence of the deformation of the cylinder on the flow structure and the drag coefficient is then analyzed. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical solutions for impulsively started and decelerated viscous flow past a circular cylinder

A finite difference study of the unsteady two-dimensional flow past a circular cylinder has been conducted using vorticity and streamfunction as the dependent variables. The two cases considered were impulsively started and decelerated flows. The impulsively started problem was considered to validate the method and has yielded results which agree quite closely with existing results from both calculations and experiments. The decelerated flow analysis produced results which can be explained in terms of induced velocity effects from existing wake vortices for both suddenly stopped and uniformly decelerated flows.     

Numerical study of the effects of particles on the near wake around a circular cylinder

In this work, we investigate the dynamics of the near wake in a turbulent flow going past a circular cylinder with/without particles at a moderate Reynolds number using a direct numerical simulation method. High-order finite-deference schemes are applied to solve for the bulk fluid properties, and a Lagrangian approach is adopted to track the individual particles. The single-phase flow is analysed and validated using previous experimental data. Two converged states, U- and V-shaped, are observed in the near wake, which are consistent with the experimental results. For the two-phase flow, the addition of smaller particles shortens the length of the recirculation region and causes a V-shaped profile to form behind the circular cylinder. Furthermore, the particles increase the drag force from the circular cylinder and suppress the vortex shedding frequency. An increase in the turbulent statistics in the very near wake and a decrease in the turbulent statistics further downstream are also observed.     

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder atRe=200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number. The project supported by the State Key Fundamental Research Project of “Large Scale Scientific Computation Research” (G199903281)     

Experimental investigation of a circular radially deforming cylinder near wake using an infrared technique

The present experimental study aims at developing a method to control the circular cylinder near wake by radial deformation and understand the underlying physics. Using an infra-red camera, we examine the temperature distribution of the near wake center line of a sinusoidal law radially deforming circular cylinder. From these measurements, the near wake is characterized by the length of the recirculation zone, the vortex formation zone length, the temperature fluctuation maximum intensity and the vortex street shedding frequency. For several deformations frequencies, we study the radial deformation influence on the near wake characteristics. It is noted that the wake structure is strongly affected by the deformation frequency. Among other things, we note the recirculation zone length reduction and the vortex formation zone length reduction when the radial vibrations are close to the “Lock-in” fundamental range. It is also noted that the variations of the vortex shedding frequency depend on the deformation frequency.     

利用O型环抑制圆柱绕法流涡脱落的数值研究

圆柱绕流涡脱落诱发较大的振动和声,如何有效地抑制值得关注.利用大涡模拟技术求解了Navier-Stokes方程,得到了涡脱落频率,升力脉动幅值及平均阻力系数.计算表明二维模拟不能体现流动基本特征,三维计算与实验吻合较好.为了抑制涡脱落,在直径为D的圆柱表面装入间距为1D,直径为0.0167D的O型环.通过升力、速度谱分析以及柱向横截面流场分析可知,在光滑圆柱外表面加入O型环能诱发流体边界层分离,有效地抑制涡脱落现象,升力脉动和观测点速度脉动幅值几乎完全消失,阻力系数也略微降低,适合在实际工程中采用.     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical simulation of two-degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary

Two-degree-of-freedom vortex-induced vibrations (VIV) of a circular cylinder close to a plane boundary are investigated numerically. The Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the Arbitrary Lagrangian Eulerian (ALE) scheme with a k-ω turbulence model closure. The numerical model is validated against experimental data of VIV of a cylinder in uniform flow and VIV of a cylinder close to a plane boundary at low mass ratios. The numerical results of the vibration mode, vibration amplitude and frequency agree well with the experimental data. VIV of a circular cylinder close to a plane boundary is simulated with a mass ratio of 2.6 and gap ratios of e/D=0.002 and 0.3 (gap ratio is defined as the ratio of gap between the cylinder and the bed (e) to cylinder diameter (D)). Simulations are carried out for reduced velocities ranging from 1 to 15 and Reynolds numbers ranging from 1000 to 15 000. It is found that vortex-induced vibrations occur even if the initial gap ratio is as small as e/D=0.002, although reported research indicated that vortex shedding behind a fixed circular cylinder is suppressed at small gap ratios (e/D<0.3 or 0.2). It was also found that vibration amplitudes are dependant on the bouncing back coefficient when the cylinder hits the plane boundary. Three vortex shedding modes are identified according to the numerical results: (i) single-vortex mode where the vortices are only shed from the top of the cylinder; (ii) vortex-shedding-after-bounce-back mode; (iii) vortex-shedding-before-bounce-back mode. It was found that the vortex shedding mode depends on the reduced velocity.     

Influence of rounding corners on the wake of a finite-length cylinder: An experimental study

This study aims to investigate experimentally the influence of rounding corners (r) as well as aspect ratio (AR) on the flow structures of a surface-mounted finite cylinder. The cylinders with sharp (r* = r/D = 0) and rounded corners (r*=0.167, 0.25 and 0.5) and aspect ratio or height-to-width/diameter ratio (AR = H/D) between 2 and 7 are utilized. The experiments are based on the five-hole probe and hot-wire measurements as well as the oil flow visualization. Wake measurements are made in an open return wind tunnel at the Reynolds number, Re = 1.6 × 10⁴, where Re is defined based on the side width/diameter (D) of the cylinder cross-section and the freestream velocity. It is found that r* and AR have significant effects on the flow structure from the perspective of wake topology, strength of streamwise vortices, and vortex shedding frequency. For all r* considered, the wake is characterized by a quadrupole type (both the tip and base vortices are present) at AR = 7, while a dipole type occurs for AR = 2 and 4 (the base vortices are absent). The strength (circulation) of the streamwise vortex structures is affected by r*. For all AR examined in the present study, the strengths of tip and base vortex structures decrease with increasing r*. The oil flow visualization demonstrates that the features of the horseshoe vortex are sensitive to r* and AR. With increasing r*, the location of the separation line moves downstream and the distance between horseshoe vortex legs decreases. Velocity measurements reveal that the downwash flow enhances with increasing r*. It is also found that the Strouhal number increases progressively by 60% as r* increases from 0 to 0.5, regardless of AR.     

Numerical solution to the initial-boundary-value problem of electroelasticity for a radially polarized hollow piezoceramic cylinder

The paper proposes and analyzes different approaches to constructing numerical schemes to solve the nonstationary vibration problem for a radially polarized piezoelectric hollow cylinder with different electric boundary conditions under mechanical loading. It is established that when the cylinder is subjected to internal pressure, the radial displacements are similar and the longitudinal displacements substantially different in cylinders with electroded and nonelectroded surfaces __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 67–75, December, 2006.     

Large-eddy simulation of circular cylinder flow at subcritical Reynolds number: Turbulent wake and sound radiation

The flows past a circular cylinder at Reynolds number 3900 are simulated using large-eddy simulation(LES) and the far-field sound is calculated from the LES results. A low dissipation energy-conserving finite volume scheme is used to discretize the incompressible Navier–Stokes equations. The dynamic global coefficient version of the Vreman's subgrid scale(SGS) model is used to compute the sub-grid stresses. Curle's integral of Lighthill's acoustic analogy is used to extract the sound radiated from the cylinder. The profiles of mean velocity and turbulent fluctuations obtained are consistent with the previous experimental and computational results. The sound radiation at far field exhibits the characteristic of a dipole and directivity. The sound spectra display the-5/3 power law. It is shown that Vreman's SGS model in company with dynamic procedure is suitable for LES of turbulence generated noise.     

Experimental investigation of the flow around a radially vibrating circular cylinder

This work aims to develop a process for controlling a cylinder wake, especially the von Karman vortex street, in such way so as to drastically reduce the drag coefficient. A new technique for influencing the cylinder wake is proposed in the present experimental study. The flow around a circular cylinder is perturbed by temporarily changing the cylinder diameter. Experiments have been performed for Reynolds numbers in the range Re=9,500 to Re=31,500. Three values of the controlling frequencies are considered: fs₁=0.41, fs₂=0.54 and fs₃=0.73, in addition to the stationary case corresponding to a non-deformable cylinder, fs₀=0. The visualisation flow shows that the pulsing motion of the cylinder walls greatly influences both the near and far wake dynamics. A decrease of the drag is expected.

Effect of blockage on free vibration of a circular cylinder at low Re

The effect of the blockage on vortex‐induced vibrations of a circular cylinder of low non‐dimensional mass (m^*=10) in the laminar flow regime is investigated in detail. A stabilized space–time finite element formulation is utilized to solve the incompressible flow equations in primitive variables form in two dimensions. The transverse response of the cylinder is found to be hysteretic at both ends of synchronization/lock‐in region for 5% blockage. However, for the 1% blockage hysteresis occurs only at the higher Re end of synchronization/lock‐in region. Computations are carried out at other blockages to understand its effect on the hysteretic behavior. The hysteresis loop at the lower Re end of the synchronization decreases with decrease in blockage and is completely eliminated for blockage of 2.5% and less. On the other hand, hysteresis persists for all values of blockage at the higher Re end of synchronization/lock‐in. Although the peak transverse oscillation amplitude is found to be same for all blockage (～0.6D), the peak value of the aerodynamic coefficients vary significantly with blockage. The r.m.s. values show lesser variation with blockage. The effect of streamwise extent of computational domain on hysteretic behavior is also studied. The phase between the lift force and transverse displacement shows a jump of almost 180° at, approximately, the middle of the synchronization region. This jump is not hysteretic and is independent of blockage. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

A large eddy simulation of the near wake of a circular cylinder

Viscous flow around a circular cylinder at a subcritical Reynolds number is investigated using a large eddy simulation (LES) coupled with the Smagorinsky subgrid-scale (SGS) model. A fractional-step method with a second-order in time and a combined finite-difference/spectral approximations are used to solve the filtered three-dimensional incompressible Navier-Stokes equations. Calculations have been performed with and without the SGS model. Turbulence statistical behaviors and flow structures in the near wake of the cylinder are studied. Some calculated results, including the lift and drag coefficients, shedding frequency, peak Reynolds stresses, and time-average velocity profile, are in good agreement with the experimental and computational data, which shows that the Smagorinsky model can reasonably predict the global features of the flow and some turbulent statistical behaviors. The project supported by the National Science Fund for Distinguished Scholars (10125210), the Special Funds for Major State Basic Research Project (G1999032801) and the National Natural Science Foundation of China (19772062)     

Spanwise correlations in the wake of a circular cylinder and a trapezoid placed inside a circular pipe

The spanwise correlation of a circular cylinder and a trapezoidal bluff body placed inside a circular pipe in fully developed turbulent regime is studied using hotwire anemometer. The present configuration possesses complex fluid structure interaction owing to the following features: high blockage effect; low aspect ratio of the body; upstream turbulence and interaction of axisymmetric flow with a two dimensional bluff body. The spatial correlation of such configuration is seldom reported in the literature. Results are presented for Reynolds number of Re_D=1×10⁵. Three different blockage ratios (0.14, 0.19 and 0.28) are considered in the present study. Correlation coefficient is observed to improve with increase in blockage ratio. Compared to a circular cylinder, a trapezoidal bluff body possesses high correlation length. The near wall effects tend to increase the phase drift, which is reflected in low correlation coefficients close to the pipe wall. The results show that the simultaneous effect of curvature, low aspect ratio and upstream turbulence reduces the correlation coefficients significantly as compared to unconfined and confined (parallel channel) flows. The low frequency modulations with a circular cylinder are higher for lower blockage ratios. The three-dimensionality of vortex shedding for trapezoid with a blockage ratio of 0.28 was observed to be lower compared to circular cylinder and all other blockage ratios. Low frequency modulations were found to be responsible for weak vortex shedding from a circular cylinder compared to a trapezoidal bluff body. The vortex shedding is observed to be nearly two dimensional in case of a trapezoidal bluff body of blockage ratio 0.28.     

Direct numerical simulation of turbulent wake behind a surface-mounted square cylinder

In this research, direct numerical simulation has been performed to study the turbulent wake behind a wall-mounted square cylinder with aspect ratio 4 and Reynolds number 12 000 (based on the free-stream velocity and obstacle side length) in a developing boundary layer. Owing to the relatively high Reynolds number and high aspect ratio of the cylinder tested, the wake is wide spread behind the cylinder and exhibits complex and energetic vortex motions. The lateral and tip vortex shedding patterns at different frequencies, coherent structures downstream of the obstacle, the production rate and distribution of turbulent kinetic energy, and the instantaneous pressure distribution in the wake region have been thoroughly investigated. In order to validate the numerical results, the first- and second-order flow statistics obtained from the simulations have been carefully compared against available wind-tunnel measurement data.     

Large eddy simulation of a vortex ring impinging on a three-dimensional circular cylinder

A vortex ring impacting a three-dimensional circular cylinder is studied using large eddy simulation (LES) for a Reynolds number Re = 4 × 10⁴ based on the initial translation speed and diameter of the vortex ring. We have investigated the evolution of vortical structures and identified three typical evolution phases. When the primary vortex closely approaches to the cylinder, a secondary vortex is generated and its segment parts move inward to the primary vortex ring. then two large-scale loop-like vortices are formed to evolve in opposite directions. Thirdly, the two loop-like vortices collide with each other to form complicated small-scale vortical structures. Moreover, a series of hair-pin vortices are generated due to the stretching and deformation of the tertiary vortex. The trajectories of vortical structures and the relevant evolution speeds are analyzed. The total kinetic energy and enstrophy are investigated to reveal their properties relevant to the three evolution phases.     

Numerical simulation of an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder

This article presents a numerical investigation of turbulent flow in an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder. The governing equations were discretized by the finite-volume method and SIMPLER method was applied to solve the equations on a staggered grid. The turbulent flow was numerically simulated using the standard k–ε, Abe–Kondoh–Nagano (AKN) and Shear Stress Transport (SST) turbulence models. The comparisons made between numerical results and experimental measurements showed that the SST model is superior to other models in the present calculation.Computations were performed for three different Reynolds numbers of 6000, 10 000 and 20 000 based on the cylinder diameter. To our knowledge, this study represents the first numerical investigation of the present flow configuration. The computational results were validated with the available experimental data of reattachment length, mean velocity distribution and wall static pressure coefficient in the turbulent blunt circular cylinder flows. Further, other characteristics of the flow, such as turbulent kinetic energy, pressure, streamlines, and the velocity vectors are discussed.The results show that the main characteristics of the turbulence flow in the separation region, such as reattachment length or velocity profiles, are nearly independent of the Reynolds number. The obtained results showed that a secondary separation bubble may appear in the main separation bubble near the leading edge. Furthermore, it was found that the turbulent kinetic energy has a large effect on the formation of the secondary bubble.     

Numerical simulation of the flow around a porous covering square cylinder in a channel via lattice Boltzmann method

In this paper, a detailed investigation on the flow past a porous covering cylinder is presented through the lattice Boltzmann method. The Brinkman‐Forchheimer‐extended Darcy model is adopted for the entire flow field with the solid, fluid, and porous medium. The effects of several parameters, such as porous layer thickness, Darcy number, porosity, and Reynolds number on flow field are discussed. Compared with the case of a solid cylinder, the present work shows that the porous layer may play an important role on the flow, the lift and drag force exerted on the cylinder. The numerical results indicate that the maximal drag coefficient C_d and maximal amplitude of lift coefficient C_l exist at certain Darcy number which is in the range of 10^?6–10^?2. Copyright © 2010 John Wiley & Sons, Ltd.