Experimental investigation of the interaction between a pulsating bubble and a rigid cylinder

In this paper, the behavior of a bubble near a rigid cylinder is studied experimentally as the positions of bubble induction change, and several cylinders with different diameters are used in the experiment. The main results are as follows. The behavior of a bubble near a rigid cylinder is distinct from that near a rigid plate. When the cylinders are laid in deep water, there will occur three kinds of typical bubble shapes as the distance between bubble and cylinder increases. And the bubble shapes are different as the diameter of cylinder varies. When the cylinders are laid near a free surface, the behaviors of bubble near cylinders with different diameters are similar. For a certain distance between bubble and free surface, as the distance between bubble and cylinder increases, "double jet", "inclined jet" and "downward jet" will take place successively.     

Acoustic radiation force on an elastic cylinder in a Gaussian beam near an impedance boundary

Acoustic radiation force (ARF) is studied by considering an infinite elastic cylinder near an impedance boundary when the cylinder is illuminated by a Gaussian beam. The surrounding fluid is an ideal fluid. Using the method of images and the translation-addition theorem for the cylindrical Bessel function, the resulting sound field including the incident wave, its reflection from the boundary, the scattered wave from the elastic cylinder, and its image are expressed in terms of the cylindrical wave function. Then, we deduce the exact equations of the axial and transverse ARFs. The solutions depend on the cylinder position, cylinder material, beam waist, reflection coefficient, distance from the impedance boundary, and absorption in the cylinder. To analyze the effects of the various factors intuitively, we simulate the radiation force for non-absorbing elastic cylinders made of stainless steel, gold, and beryllium as well as for an absorbing elastic cylinder made of polyethylene, which is a well-known biomedical polymer. The results show that the impedance boundary, cylinder material, absorption in the cylinder, and cylinder position in the Gaussian beam significantly affect the magnitude and direction of the force. Both stable and unstable equilibrium regions are found. Moreover, a larger beam waist broadens the beam domain, corresponding to non-zero axial and transverse ARFs. More importantly, negative ARFs are produced depending on the choice of the various factors. These results are particularly important for designing acoustic manipulation devices operating with Gaussian beams.     

Interference effect of two equal‐sized square cylinders in tandem arrangement: With planar shear flow

Numerical simulations have been performed for flow past two equal‐sized square cylinders in tandem arrangement subjected to incoming planar shear flow. Effect of L/d ratio and the shear parameter has been studied. The range of L/d ratio (ratio of center‐to‐center distance (L) to cylinder width (d)) is varied from 2 to 7 and the non‐dimensional shear parameter (K) is varied from 0.0 to 0.4 in steps of 0.1. For all the cases the Reynolds number (Re) based on centerline velocity and cylinder width is fixed at 100. The results are compared with that of isolated square cylinder with uniform flow. Strouhal number decreases with increasing shear parameter. There are more than one shedding frequency at high shear parameters and L/d ratios. The mean drag coefficient is decreased with shear parameter and lesser than that of the single cylinder. The root mean square (RMS) value of both lift and drag coefficients is higher for the downstream cylinder for all values of shear parameter. With increasing L/d ratio, for both lift and drag, the RMS value increases and then decreases for upstream cylinder, whereas it continuously increases for the downstream cylinder. The stagnation point is moved towards the top leading edge with increasing shear. The critical L/d ratio, which is defined as the distance between two cylinders, beyond which the vortex shedding from the upstream cylinder occurs, decreases with increasing shear parameter. Copyright © 2007 John Wiley & Sons, Ltd.     

A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder

Forced convection heat transfer from an unconfined circular cylinder in the steady cross-flow regime has been studied using a finite volume method (FVM) implemented on a Cartesian grid system in the range as 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. The numerical results are used to develop simple correlations for Nusselt number as a function of the pertinent dimensionless variables. In addition to average Nusselt number, the effects of Re, Pr and thermal boundary conditions on the temperature field near the cylinder and on the local Nusselt number distributions have also been presented to provide further physical insights into the nature of the flow. The rate of heat transfer increases with an increase in the Reynolds and/or Prandtl numbers. The uniform heat flux condition always shows higher value of heat transfer coefficient than the constant wall temperature at the surface of the cylinder for the same Reynolds and Prandtl numbers. The maximum difference between the two values is around 15–20%.     

两端铰接的细长柔性圆柱体涡激振动响应特性数值研究

目前细长柔性圆柱体涡激振动响应的研究方法主要包括实验方法、计算流体动力学方法以及半经验模型方法. 鉴于实验方法研究成本较高、计算流体动力学方法计算时间较长,本文基于尾流振子模型对线性剪切来流下两端铰接的细长柔性圆柱体涡激振动响应特性进行了半经验模型方法研究. 先建立了柔性圆柱体结构振子以及尾流振子之间的耦合模型,紧接着基于二阶精度中心差分格式对耦合模型先离散后迭代进行求解. 对不同剪切参数下柔性圆柱体涡激振动响应的振动波长、振动频率、振动位移以及响应频率随时间的变化特性等参数进行了分析. 分析结果表明:圆柱体的涡激振动响应由驻波和行波混合组成. 当无量纲弯曲刚度较小时,在圆柱体两端附近,驻波占主导;而在圆柱体中间段附近,行波占主导. 当无量纲弯曲刚度较大时,在圆柱体整个长度区间上均为驻波占主导. 随着剪切参数的增大,振动位移以及振动波长均逐渐减小,而振动频率和频率带宽均逐渐增大.      

On characteristics of two-degree-of-freedom vortex induced vibration of two low-mass circular cylinders in proximity at low Reynolds number

Two-degree-of-freedom vortex induced vibrations (VIVs) of two identical spring-supported circular cylinders in proximity with the mass ratio of 2 and zero damping at Re of 100 are numerically studied. Totally 20 arrangements of cylinders are investigated combining four stagger angles and five normalized center-to-center spacings. Results show that the in-line vibration amplitude is comparable to the transverse one for most arrangements and usually accompanies irregular cylinder trajectories. Extremely slender figure-8 cylinder trajectories usually seen in single-cylinder VIVs exist only for the tandem arrangements. Arranging the trailing cylinder to vibrate near the wake boundary of the leading cylinder enhances the possibility of irregular trajectories and impacts of both cylinders. Impact between cylinders must occur in cases with irregular cylinder trajectories; however, irregular cylinder trajectories could be found in impact-free cases. The stagger angle significantly changes the attribute of the transverse vibration frequency, toward either the single-cylinder VIV frequency or natural structure frequency in still fluid. The major transverse vibration frequency and the natural structure frequency in still fluid are decoupled for all the side-by-side arrangements and some far spaced tandem arrangements and highly correlated for non-tandem and non-side-by-side arrangements. The time-averaged impact frequency increases with decreasing normalized center-to-center spacing for most combinations of stagger angle and reduced velocity. Apart from the side-by-side arrangements, high-frequency impacts occur when the trailing cylinder is initially located in or near the wake zone of the leading cylinder. The mechanism of trailing cylinder chopping the gap-flow vortices plays an important role in determining the near-wake vortex structures for all non-side-by-side arrangements.     

Stationäre Temperatur oder Konzentrationsfelder in endlichen Zylindern für verschiedene Randbedingungen erster Art

Steady state temperature fields within a finite circular cylinder are calculated for the boundary conditions of constant temperature at the bottom and the wall of the cylinder whereas its top temperature is described by some temperature distributions which can be expressed by polynomial functions. These temperature distributions are evaluated for the cases, that the temperature drops from the center point value T₁ linearly or parabolically to a specified value T₂ at a certain distance r₁. The results are given in terms of dimensionless numbers. The “disturbing” temperatures at the cylinder top influence the temperatures within the cylinders less if the distance r₁ is small, over which the temperature changes from T₁ to T₂, if this change occurs linearly, if T₂ approaches the value of the wall and bottom temperature and if the cylinders are slender, e. g. if their length are greater than their radius. The slenderness of the cylinders has an important influence. By analogy the results are valid also for concentration fields.     

Spiral and Wavy Vortex Flows in Short Counter-Rotating Taylor–Couette Cells

Differentially rotating cylinders result in a rich variety of vortical flows for cylindrical Couette flow. In this study we investigate the case of a short, finite-length cavity with counter-rotating cylinders via direct numerical simulation using a three-dimensional spectral method. We consider aspect ratios ranging from 5 to 6. Two complex flow regimes, wavy vortices and interpenetrating spirals, occur with similar appearance to those found experimentally for much larger aspect ratios. For wavy vortices the wave speed is similar to that found for counter-rotating systems and systems in which the outer cylinder is stationary. For the interpenetrating spiral structure, the vortices are largely confined to the unstable region near the inner cylinder. The endwalls appear to damp and stabilize the flow as the aspect ratio is reduced to the point that in some cases the vortical flow is suppressed. At higher inner cylinder speeds, the interpenetrating spirals acquire a waviness and the vortices, while generally near the inner cylinder, can extend all of the way to the outer cylinder. Received 5 November 2001 and accepted 29 March 2002 Published online 2 October 2002 Communicated by H.J.S. Fernando     

Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.     

Bending of a circular cylinder containing a crack

The study of bending of cracked circular cylinders is of more significance. The bending of cylinders containing radical crack or cracks was discussed by refs. [1]–[4] and that of concentrically craked circular cylinders was studied by [5]. Continuing [6] and using complex variable methods in elasticity, this paper deals with the bending problems of a circular cylinder, containing an internal linear crack at any position under an acting force perpendicular to the crack. The general forms of displacements, stresses, and stressintensity factors, expressed in terms of series, are obtained and to this bending problems with small Ah are presented good approximate formulas for the stress-intensity factors whose variations with the center of the crack are analysed. Finally, the twist angle per unit length and the center of bending for the radically cracked circular cylinder, one of whose crack-tips is located at the origin, have been computed and the results are almost the same as that calculated in [1].     

Flow structure around two finite circular cylinders located in an atmospheric boundary layer: side-by-side arrangement

The flow structure around the free-end region of two adjacent finite circular cylinders embedded in an atmospheric boundary layer (ABL) was investigated experimentally. The experiments were carried out in a closed-return-type subsonic wind tunnel, in which two finite cylinders with an aspect ratio of 6 were mounted vertically on a flat plate in a side-by-side arrangement. The Reynolds number based on the cylinder diameter was about Re=2×10⁴. Systems with gap ratios (i.e., center-to-center distance/cylinder diameter) in the range 1.0–2.0 were investigated. A hot-wire anemometer was employed to measure the wake velocity, and the mean pressure distribution on the cylinder surface was also measured. The flow past two finite cylinders was found to have a complicated three-dimensional wake structure in the region near the free ends. As the gap ratio increases, regular vortex-shedding becomes dominant, but the length of the vortex formation region decreases. The pressure distribution and flow structure around two cylinders were found to differ substantially from the behavior of a two-dimensional circular cylinder due to mutual interference. The three-dimensional flow structure seems to originate from the strong entrainment of irrotational fluids caused by the downwash counter-rotating vortices separated from the finite cylinder (FC) free ends.     

Force coefficients and Strouhal numbers of three circular cylinders subjected to a cross-flow

In this paper, wind tunnel experiments were conducted to measure the mean force coefficients and Strouhal numbers for three circular cylinders of equal diameters in an equilateral-triangular arrangement when subjected to a cross-flow. These experiments were carried out at five subcritical Reynolds numbers ranging from 1.26 × 10⁴ to 6.08 × 10⁴. The pressure distributions on the surface of the cylinders were measured using pressure transducers. Furthermore, the hot-wire anemometer was employed to measure the vortex shedding frequencies behind each cylinder. Six spacing ratios (l/d) varying from 1.5 to 4 were investigated. It is observed that for l/d > 2, the upstream cylinder experiences a lower mean drag coefficient compared with the downstream cylinders. The minimum values of the drag coefficient for the downstream cylinders occur at l/d = 1.5 and l/d = 2, because there is no vortex shedding from the foregoing cylinders. Also, the value of the pressure coefficient behind the upstream cylinder reduces by increasing l/d. Moreover, by decreasing the value of l/d, the Strouhal number for the upstream cylinder increases. It can be concluded that the flow pattern and aerodynamic coefficients are basically dependent on l/d; in other words, decreasing l/d results in an increase in the effects of the flow interference between the cylinders.     

串列双圆柱流致振动的数值模拟及其耦合机制

对雷诺数Re= 100 条件下串列双圆柱的流致振动进行了数值模拟. 圆柱的质量比m*均为2.0,间距比L/D 为2.0 5.0. 考虑两种工况:(a) 上游圆柱固定,下游圆柱可沿横流向自由振动;(b) 上、下游圆柱均可沿横流向自由振动. 结果表明:无论上游圆柱静止或者振动,下游圆柱横向振幅明显大于单圆柱的. 工况(b) 的下游圆柱最大振幅要大于工况(a) 的,这是由于两圆柱均振动时,两圆柱之间耦合作用增强,上游圆柱的尾流和下游圆柱的振动之间“相互调节” 作用显著. 对工况(b) 的下游圆柱振动和间隙流之间的作用机制进行了详细的研究,发现当上游圆柱脱落的自由剪切层重新附着于下游圆柱上并且完全从间隙之间通过时,下游圆柱的振幅最大.      

Vortex-shedding from single and tandem cylinders in the presence of applied sound

A single cylinder and two tandem cylinder configurations with longitudinal pitch ratios L/D=1.75 and 2.5 were rigidly mounted in an open circuit wind tunnel and a standing acoustic pressure wave was imposed so that the acoustic particle velocity was normal to both the cylinder axis and the mean flow velocity. The effect of sound on the vortex-shedding was investigated for various amplitudes by means of pressure taps on the cylinders and wake hot-wire probes. These tests show that applied sound can entrain and shift the natural vortex-shedding frequency to the frequency of excitation and produce nonlinearities in the wake. The lock-in envelope for the tandem cylinders is considerably larger than for the single cylinder. The lock-in range for the smaller tandem cylinder spacing was broader still than either the single cylinder, or the L/D=2.5 tandem cylinder case. The pressure and hot-wire measurements show for the single cylinder, and tandem cylinder configuration with pitch ratio L/D=2.5, that there was a phase jump near the coincidence of the vortex-shedding frequency and the excitation frequency, while there was no jump for the pitch ratio of 1.75. As well, the applied sound field was also noted to induce vortex-shedding in the gap for the L/D=2.5 case, while no vortex-shedding was noted for the smaller pitch ratio.     

NUMERICAL INVESTIGATION ON FLOW-INDUCED VIBRATION OF TWO CYLINDERS IN TANDEM ARRANGEMENTS AND ITS COUPLING MECHANISMS

对雷诺数Re= 100 条件下串列双圆柱的流致振动进行了数值模拟. 圆柱的质量比m^*均为2.0,间距比L/D 为2.0 5.0. 考虑两种工况:(a) 上游圆柱固定,下游圆柱可沿横流向自由振动;(b) 上、下游圆柱均可沿横流向自由振动. 结果表明:无论上游圆柱静止或者振动,下游圆柱横向振幅明显大于单圆柱的. 工况(b) 的下游圆柱最大振幅要大于工况(a) 的,这是由于两圆柱均振动时,两圆柱之间耦合作用增强,上游圆柱的尾流和下游圆柱的振动之间“相互调节” 作用显著. 对工况(b) 的下游圆柱振动和间隙流之间的作用机制进行了详细的研究,发现当上游圆柱脱落的自由剪切层重新附着于下游圆柱上并且完全从间隙之间通过时,下游圆柱的振幅最大.     

Flow-induced oscillation of two circular cylinders in tandem arrangement at low Re

Results are presented for flow-induced vibrations of a pair of equal-sized circular cylinders of low nondimensional mass (m^*=10) in a tandem arrangement. The cylinders are free to oscillate both in streamwise and transverse directions. The Reynolds number, based on the free-stream speed and the diameter of the cylinders, D is 100 and the centre-to-centre distance between the cylinders is 5.5D. The computations are carried out for reduced velocities in the range 2≤U^*≤15. The structural damping is set to zero for enabling maximum amplitudes of oscillation. A stabilized finite element method is utilized to carry out the computations in two dimensions. Even though the response of the upstream cylinder is found to be qualitatively similar to that of an isolated cylinder, the presence of a downstream cylinder is found to have significant effect on the behaviour of the upstream cylinder. The downstream cylinder undergoes very large amplitude of oscillations in both transverse and streamwise directions. The maximum amplitude of transverse response of the downstream cylinder is quite similar to that of a single cylinder at higher Re beyond the laminar regime. Lock-in and hysteresis are observed for both upstream and downstream cylinders. The downstream cylinder undergoes large amplitude oscillations even beyond the lock-in state. The phase between transverse oscillations and lift force suffers a 180 jump for both the cylinders almost in the middle of the synchronization regime. The phase between the transverse response of the two cylinders is also studied. Complex flow patterns are observed in the wake of the freely vibrating cylinders. Based on the phase difference and the flow patterns, the entire flow range is divided into five sub-regions.     

Drag force on a free surface-piercing yawed circular cylinder in steady flow

The force distribution on a surface-piercing yawed cylinder surface differs significantly from that on a surface-piercing vertical cylinder. The established numerical model for flow past the surface-piercing yawed cylinder with yaw angles from −45° to 45° was solved by the standard large-eddy simulation (LES) methodology. Six cases at intervals of ±15° relative to the vertical were studied at the Reynolds number of 27 000 and the Froude number of 0.8 based on the cylinder diameter and free-stream velocity, among which the drag forces on four cylinders with yaw angles from −15° to 30° were tested for the validation of the LES approach. The results revealed that the time-averaged total drag coefficient for all cases increases with the increase of yaw angle compared to that of the surface-piercing vertical cylinder, even over 2.5 for the ±45°-yawed cylinders. The sectional drag coefficients for the negatively yawed cylinders are much greater than that for the vertical cylinder, and much less for the positively yawed cylinders. The unbalanced hydrostatic pressures on the inclined section are mainly responsible for those increment and decrement. Once the hydrostatic pressure was removed, the sectional drag coefficient on the mid-span of the positively yawed cylinder increases from the top section to the bottom, and decreases for the negatively yawed cylinder. The corresponding integrated total drag coefficient decreases with the increase of the yaw angle to ±15°, then increases with the further increase of the magnitude of yaw angle.     

Natural convection due to solar radiation over a non-absorbing plate with and without heat losses

Natural convection over a non-reflecting, non-absorbing, ideally transparent semi-infinite vertical flat plate due to absorption of incident radiation (solar radiation) is considered. The absorbed radiation acts as a distributed source which initiates buoyancy-driven flow and convection in the absorbing layer. The plate when heated by the absorbing fluid loses heat to the surroundings from its external side. Solution of the governing equations of the flow under these circumstances is non-similar because of both the heat source term in the energy equation and the temperature boundary condition at the plate. A local non-similar technique is used to obtain solutions for a wide range of the dimensionless distance along the plate and of the dimensionless loss coefficient to the surroundings. The results show that the temperature distribution has a maximum temperature in the depth of the fluid rather than on the plate. A new definition for a local heat transfer coefficient between the plate and the absorbing fluid is introduced which is based on the local maximum temperature rise in the fluid. A formula to calculate this heat transfer coefficient is given for the anticipated range of the loss coefficient.     

Wake flow pattern modified by small control cylinders at low Reynolds number

Passive wake control behind a circular cylinder in uniform flow is studied by numerical simulation for Re_D ranging from 80 to 300. Two small control cylinders, with diameter d/D=1/8, are placed at x/D=0.5 and y/D=±0.6. Unlike the 1990 results of Strykowski and Sreenivasan, in the present study, the vortex street behind the main cylinder still exists but the fluctuating lift and the form drag on the main cylinder reduces significantly and monotonously as the Reynolds number increases from 80 to 300. Obstruction of the control cylinders to the incoming flow deflects part of the fluid to pass through the gap between the main and control cylinders, forming two symmetric streams. These streams not only eliminate the flow separation along the rear surface of the main cylinder, they also merge toward the wake centerline to create an advancing momentum in the immediate near-wake region. These two effects significantly reduce the wake width behind the main cylinder and lead to monotonous decrease of the form drag as the Reynolds number increases. As the Reynolds number gets higher, a large amount of the downstream advancing momentum significantly delays the vortex formation farther downstream, leading to a more symmetric flow structure in the near-wake region of the main cylinder. As the Reynolds number increases from 80 to 300, both increasing symmetry of the flow structure in the near-wake and significant delay of the vortex formation are the main reasons for the fluctuating lift to decrease monotonously.     

Slot/slots air jet impinging cooling of a cylinder for different jets–cylinder configurations

Heat transfer characteristics of a slot/slots jet air impinging on a cylinder have been experimentally investigated for two different orientations of slot/slots jet plan with respect to cylinder axis. The experiments were carried out to study the effects of orientation of slot/slots jet plan with respect to cylinder axis on the rate of heat transfer from the cylinder. Two different jet–cylinder configurations were studied: (1) single slot jet aligned with cylinder axis (slot length = cylinder length), and (2) multiple slot jets equally spaces distributed orthogonal to cylinder axis (each slot length = cylinder diameter and sum of slots lengths = cylinder length). For each configuration, parametric effects of Reynolds numbers (Re) ranging from 1,000 to 10,000, dimensionless slot widths (W/d) ranging from 0.125 to 0.5, and dimensionless slot orifice-to-cylinder spacing (Z/W) ranging from 1 to 12 on local and average Nusselt numbers around cylinder surface have been investigated. The results showed that: (1) cooling the cylinder by multiple slots jets situated orthogonal to cylinder axis gave more uniform surface temperature distributions and higher heat transfer rate than the case of cooling the cylinder by single slot jet aligned with cylinder axis, (2) for both configurations the Nusselt number around the cylinder increased with increasing Re and W/d, and (3) for both configurations there was a certain Z/W in the range 4<Z/W<6 at which the stagnation and mean Nusselt number were maximum. Correlations for the mean Nusselt numbers around cylinder surface have been presented for both configurations. Comparisons between the correlations predictions and the present and other previous experimental data have been conducted.