Three-dimensional computation for flow-induced vibrations of an upstream circular cylinder in two tandem circular cylinders

It is well known from a lot of experimental data that fluid forces acting on two tandem circular cylinders are quite different from those acting on a single circular cylinder. Therefore, we first present numerical results for fluid forces acting on two tandem circular cylinders, which are mounted at various spacings in a smooth flow, and second we present numerical results for flow-induced vibrations of the upstream circular cylinder in the tandem arrangement. The two circular cylinders are arranged at close spacing in a flow field. The upstream circular cylinder is elastically placed by damper-spring systems and moves in both the in-line and cross-flow directions. In such models, each circular cylinder is assumed as a rigid body. On the other hand, we do not introduce a turbulent model such as the Large Eddy Simulation (LES) or Reynolds Averaged Navier-Stokes (RANS) models into the numerical scheme to compute the fluid flow. Our numerical procedure to capture the flow-induced vibration phenomena of the upstream circular cylinder is treated as a fluid-structure interaction problem in which the ideas of weak coupling is taken into consideration.     

Measurements of velocity fields in finite cylinder arrays with and without tip clearance

The velocity field in a finite cylinder array was investigated experimentally in a water towing tank and an acoustic Doppler velocimeter (ADV). The experimental system consisted of a staggered cylinder array having 14 rows to permit streamwise evolution of the flow. The boundaries were manipulated to create several global flow configurations. Three basic configurations were studied: a globally unidirectional flow, a flow with partial lateral blockage at the inlet and outlet planes, and a flow with the top boundary separated from the cylinders creating a tip clearance. The three components of the velocity vector were measured at various points within the model. Time-averaged results are presented for the different flow configurations. The results provide insight into the development of the flow field in cases of a finite array with complex geometry and boundary effects.     

Flow patterns and turbulence effects in large cylinder arrays

Studies on flow-induced vibrations in large tube bundles are usually focused solely on frequency analysis, without considering the flow patterns which are responsible for the fluid forces. Furthermore, investigations which involve variations in the spacing ratios do not separate transversal and longitudinal proximity effects. The purpose of this article is to separately analyze the influence of the transversal (T/D) and longitudinal (L/D) spacing ratios of a confined in-line cylinder array with five rows on the flow characteristics and to identify flow patterns. The laser Doppler anemometry technique was employed to acquire the mean velocity and its fluctuations in the transversal and longitudinal directions between the cylinder rows. Strouhal numbers and regimes reported in the literature were identified in the experiments. The same regime did not always persist along all cylinder rows for a given spacing ratio, as a result of the combined longitudinal and transversal proximity effects and also of the generation of turbulence by the array. For the smallest T/D ratio, a quasi-steady behavior associated with the biased flow pattern was noted in the experimental set-up and flip-flopping was observed in one case. Additionally, the flow characteristics in these arrays diverged from tube bundle classifications described in the literature. The behavior of the fluid forces and susceptibility to vibrations in the array were predicted based on the turbulence intensity of the incident flow of the cylinders. The results reinforced the need to extend flow pattern investigations to arrays with more cylinder rows and to consider both transversal and longitudinal proximity effects, when studying flow-induced vibrations.     

Oscillations of elastically mounted cylinders in regular waves

Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrody-namic forces on an array of three bottom-mounted, surface-piercing circular cylinders. The responses of the cylinders induced by wave excitation are determined by the equa-tions of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves.     

Identification of a laminar-turbulent interface in partially turbulent flow

Viscous incompressible fluid flow along the clearance between two parallel eccentric circular cylinders is studied numerically. The geometric parameters and the Reynolds number are taken so that the turbulent flow regime takes place in a part of flow, namely, in the zone where the clearance is wide, while the low is laminar in the narrow clearance zone. Criteria using which these zones can be distinguished are discussed.     

Large eddy simulation of cross-flow through a staggered tube bundle at subcritical Reynolds number

The Large Eddy Simulation (LES) technique is used to study the vortex shedding characteristics inside a staggered tube array consisting of six rows with intermediate spacings (S_L/D×S_T/D=1.6×3.6) at the subcritical Reynolds number of 8600 (based on the gap velocity). The filtered equations are discretised using the finite volume method in an unstructured, collocated grid arrangement with second-order accurate methods in space and time. The predictions of mean velocities and Reynolds stresses are in very good agreement with detailed LDA measurements performed in 17 stations along the depth of the array. The sizes of the recirculation zones behind the cylinders in the first and third row also compare favourably with available correlations. Two distinct and independent shedding frequencies are detected behind the first two rows, but the high-frequency component vanishes in the downstream rows. The corresponding Strouhal numbers agree well with measurements available in the literature for similar tube spacings. The lift coefficient as well as instantaneous flow patterns of the whole array are also examined.     

正方形排列四圆柱体绕流特性及互扰效应研究

基于计算流体动力学理论,运用大涡模拟方法对雷诺数Re=3900三维正方形排列四圆柱体结构群的绕流问题进行数值计算,主要分析来流攻角与间距比两个参数对四圆柱体结构群流体参数及流场模态的影响。结果表明:来流攻角与间距比均对四圆柱体结构群绕流特性有较强的影响;来流攻角θ=0°、22.5°、45°下,临界间距比分别为3.5、4.0、3.0;间距比的变化会导致下游圆柱表面压力系数分布发生改变;另一方面,间距比较小时,四圆柱体结构之间的互扰作用均以临近效应为主;随间距比增大,上游圆柱尾流对下游圆柱有显著影响,其互扰作用会转变尾激效应。     

Nonlinear free surface action with an array of vertical cylinders

Nonlinear diffraction of regular waves by an array of bottom-seated circular cylinders is investigated in frequency domain, based on a Stokes expansion approach. A complete semi-analytical solution is developed which allows an efficient evaluation of the second-order potentials in the entire fluid domain, and the wave forces on the structure. Expressions are derived for the second-order potential in the vicinity of individual cylinders. These expressions have a simple form, thus providing an effective means for investigating the wave enhancement due to nonlinear interactions with multiple cylinders. Based on the present method, the wave run-up and free-surface elevations around an array of two, three and four cylinders are investigated numerically.     

The flow field near the edge of a model porous medium

The flow field near the edge of a model porous medium was investigated using particle-image velocimetry (PIV). The medium was an annular array of regularly spaced rods, and the adjacent flow field was circular Couette flow. Since the radius of curvature was large, the flow was approximately linear, with the result that the medium was effectively a square array of rods and the external flow was effectively a simple shear flow. The velocity field was found under creeping flow conditions for three arrays with small solid volume fractions. Streamlines computed from the velocity vectors revealed flow circulation between the first and second rows of rods for volume fractions of 5.2% and 10%; circulation was not observed inside a 2.5% array. These observations confirmed earlier numerical predictions.     

Experimental investigation of flow through a bank of cylinders of varying geometry

An experimental investigation of a model forming fabric was conducted. The forming fabric was simplified and represented by a bank of two rows of cylinders. Particle image velocimetry (PIV), pressure drop, and hydrogen bubble visualization were used to evaluate the upstream and gross flow patterns for various diameter ratios and cylinder spacings at a Reynolds number of 65. It was found that for a row separation of 0.75 times the upstream cylinder diameter, the upstream flow matched that for a single row of cylinders. Further, it was found that when the pressure drop through the bank of cylinders was equal to the sum of the individual rows’ pressure drops, the upstream flow converged to that of a single row.     

Flow of wormlike micelle solutions past a confined circular cylinder

In this paper, we present the results of an investigation into the flow of a series of viscoelastic wormlike micelle solutions past a confined circular cylinder. Although this benchmark flow has been studied in great detail for polymer solutions, this paper reports the first experiments to use a viscoelastic wormlike micelle solution as the test fluid. The flow kinematics, stability and pressure drop were examined for two different wormlike micelle solutions over a wide range of Deborah numbers and cylinder to channel aspect ratios. A combination of particle image velocimetry and pressure drop measurements were used to characterize the flow kinematics, while flow-induced birefringence measurements were used to measure the micelle deformation and alignment in the flow. The pressure drop was found to decrease initially due to the shear thinning of the test fluid before increasing at higher flow rates as elastic effects begin to dominate the flow. Above a critical Deborah number, an elastic instability was observed for just one of the test fluids studied, the other remained stable for all Deborah number tested. Flow-induced birefringence and velocimetry measurements showed that observed instability originates in the extensional flow in the wake of the cylinder and appears not as periodic counter-rotating vortices as has been observed in the flow of polymer solutions past circular cylinders, but as a chaotic rupture event in the wake of the cylinder that propagates axially along the cylinder. Reducing the cylinder to channel aspect ratio and the degree of shearing introduced by the channel walls had a weak impact on the stability of the flow. These measurements, when taken in conjunction with previous work on flow of wormlike micelle solutions through a periodic array of cylinders, definitively show that the instability can be attributed to a breakdown of the wormlike micelle solutions in the extensional flow in the wake of the cylinder.     

Diffraction of regular waves by an arbitrarily oriented system of vertical circular cylinders

The linear theory of small-amplitude waves is used to construct a solution to the problem of the diffraction of surface gravity waves by a system of arbitrarily oriented vertical circular cylinders. Analytic expressions are obtained for the wave forces and overturning moments acting on each cylinder of the system. A system of two rows of cylinders with three cylinders in each row is considered as an example. It is shown that for certain relationships between the diameter of the cylinders, the distance between them, the angle of approach of the wave, and its wavelength, the maximal values of the hydrodynamic forces acting on the cylinders of the system with allowance for the interaction of the diffracted fields may be appreciably greater than when no allowance is made for it.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 177–181, January–February, 1984.     

Circular cylinder wakes and vortex-induced vibrations

This paper presents a selective review of recent research on vortex-induced vibrations of isolated circular cylinders and the flow and vibration of circular cylinders in a tandem arrangement; a common thread being that the topics raised are of particular interest to the author. The influence of Reynolds number on the response of isolated cylinders is presented and recent developments using forced vibration are discussed. The response of a cylinder free to respond in the in-line and transverse directions is contrasted with that of a cylinder responding in only one direction. The interference between two circular cylinders is discussed and prominence given to the case of cylinders in a tandem arrangement. The origin of the time–mean lift force on the downstream cylinder is considered together with the cause of the large amplitude transverse vibration experienced by the cylinder above vortex resonance. This wake-induced vibration is shown to be a form of vortex-induced vibration.     

An improved hybrid Cartesian/immersed boundary method for fluid–solid flows

An improved hybrid Cartesian/immersed boundary method is proposed based on ghost point treatment. A second‐order Taylor series expansion is used to evaluate the values at the ghost points, and an inverse distance weighting method to interpolate the values due to its properties of preserving local extrema and smooth reconstruction. The present method effectively eliminates numerical instabilities caused by matrix inversion and flexibly adopts the interpolation in the vicinity of the boundary. Some typical fluid–solid flows, including viscous flow past a circular cylinder, a sphere, two cylinders in a side‐by‐side arrangement, and an array of 18 staggered cylinders, are examined. These benchmark simulations reasonably indicate the reliability and capability of the present method. Copyright © 2007 John Wiley & Sons, Ltd.     

AN EVALUATION OF THE BOUNCE-BACK BOUNDARY CONDITION FOR LATTICE BOLTZMANN SIMULATIONS

The bounce-back boundary condition for lattice Boltzmann simulations is evaluated for flow about an infinite periodic array of cylinders. The solution is compared with results from a more accurate boundary condition formulation for the lattice Boltemann method and with finite difference solutions. The bounce-back boundary condition is used to simulate boundaries of cylinders with both circular and octagonal cross-sections. The convergences of the velocity and total drag associated with this method are slightly sublinear with grid spacing. Error is also a function of relaxation time, increasing exponentially for large relaxation times. However, the accuracy does not exhibit a trend with Reynolds number between 0·1 and 100. The square lattice Boltzmann grid conforms to the octagonal cylinder but only approximates the circular cylinder, and the resulting error associated with the octagonal cylinder is half the error of the circular cylinder. The bounce-back boundary condition is shown to yield accurate lattice Boltzmann simulations with reduced computational requirements for computational grids of 170×170 or finer, a relaxation time less than 1·5 and any Reynolds number from 0·1 to 100. For this range of parameters the root mean square error in velocity and the relative error in drag coefficient are less than 1 per cent for the octagonal cylinder and 2 per cent for the circular cylinder. © 1997 John Wiley & Sons, Ltd.     

Investigation of turbulent flow past a yawed wavy cylinder

A large eddy simulation (LES) study was conducted to investigate the three-dimensional characteristics of the turbulent flow past wavy cylinders with yaw angles from 0° to 60° at a subcritical Reynolds number of 3900. The relationships between force coefficients and vortex shedding frequency with yaw angles for both wavy cylinders and circular cylinders were investigated. Experimental measurements were also performed for the validation of the present LES results. Comparing with corresponding yawed circular cylinders at similar Reynolds number, significant differences in wake vortex patterns between wavy cylinder and circular cylinder were observed at small yaw angles. The difference in wake pattern becomes insignificant at large yaw angles. The mean drag coefficient and the Strouhal number obey the independence principle for circular cylinders at yaw angle less than 45°, while the independence principle was found to be unsuitable for yawed wavy cylinders. In general, the mean drag coefficients and the fluctuating lift coefficients of a yawed wavy cylinder are less than those of a corresponding yawed circular cylinder at the same flow condition. However, with the increase of the yaw angle, the advantageous effect of wavy cylinder on force and vibration control becomes insignificant.     

Two circular cylinders in cross-flow: A review

Pairs of circular cylinders immersed in a steady cross-flow are encountered in many engineering applications. The cylinders may be arranged in tandem, side-by-side, or staggered configurations. Wake and proximity interference effects, which are determined primarily by the longitudinal and transverse spacing between the cylinders, and also by the Reynolds number, have a strong influence on the flow patterns, aerodynamic forces, vortex shedding, and other parameters. This paper reviews the current understanding of the flow around two “infinite” circular cylinders of equal diameter immersed in a steady cross-flow, with a focus on the near-wake flow patterns, Reynolds number effects, intermediate wake structure and behaviour, and the general trends in the measurements of the aerodynamic force coefficients and Strouhal numbers. A primary focus is on the key experimental and numerical studies that have appeared since the last major review of this subject more than 20 years ago.     

The effect of arrangement of two circular cylinders on the maximum efficiency of Vortex-Induced Vibration power using a Scale-Adaptive Simulation model

The complex behaviour of an unsteady flow around two circular cylinders in tandem is of interest for many civil engineering applications across a wide range of aerospace, mechanical and marine applications. The present paper analyses Vortex-Induced Vibration (VIV) for the flow around two circular cylinders. It has been shown that the amount of kinetic energy which can be captured by VIV is a function of the arrangement of the two cylinders. The upstream cylinder is fixed while the downstream is mounted elastically with one degree of freedom normal to the mean flow direction. The efficiency of the VIV power obtained from downstream cylinder is compared for different arrangement of the cylinders. For this purpose, the longitudinal and lateral distances between the cylinders were varied and the Reynolds number was kept constant. Scale-Adaptive Simulation (SAS) and Shear Stress Transport (SST) CFD models are utilized to analyse the validity of the SAS turbulence model. The results indicate that both turbulence models predict the flow characteristics around the cylinders with reasonable precision; however, the predictions from SAS were more accurate compared to the SST. Based on this comparison, SAS model was chosen as a tool to analyse the VIV response of the downstream cylinder. The location of the downstream cylinder has been altered in the wake of upstream one in order to obtain the optimum efficiency of the VIV power. The results reveal that the arrangement of the cylinders can significantly change the efficiency. It is also observed that cylinders offset from one another show a higher efficiency compared to cylinders with their centres aligned.     

Hysteresis phenomenon at interaction of shock waves generated by a cylinder array

This paper describes investigations of the interaction between bow shock waves generated by cylindrical bodies in a supersonic flow. Numerical simulations are performed using the inviscid Euler equations for cylinders whose axes are parallel to each other and normal to the flow direction. Mostly an infinite periodical cylinder array is considered, but the case of two cylinders is also briefly discussed. Three different regimes of the shock wave interaction, a regular interaction, a Mach interaction, and a choked flow, have been observed for the flow through the periodical cylinder array. In the case of the flow around two bodies, the choked flow is replaced by a regime with a collective bow shock. The transition between different flow regimes is studied by varying the inflow Mach number or the distance between the cylinders. A hysteretic behavior at the transition between the regular and Mach interactions has been observed. The transition is governed by the theoretical detachment and von Neumann criteria based on the local shock wave inclination at the interaction point.