Critical Gap Ratio Research Articles

A modified phase-field model for cohesive interface failure in quasi-brittle solids

We formulate a modified phase-field model for cohesive interface failure in quasi-brittle solids. Our model has two novel features: (i) a traction–separation-damage law for damage process; (ii) an energetic degradation function controlled by critical gap ratio. This modification offers an attractive approach to simulate the cohesive interface failure process. We also provide a robust numerical solution strategy to treat the spatio-temporal evolution of cohesive interface failure. Our model is validated by two benchmark problems including the constant strain patch test and mode-I delamination test. The numerical simulations are compared with some published data. We proceed to apply this model to study the complex failure mechanism of a peeling test on bi-material plates and crack impinging on interfaces in different scenarios, where the effects of critical gap ratios and interface inclination angles are discussed.

Three-dimensional flow past a circular cylinder in proximity to a stationary wall

In this paper, we present direct numerical simulations (DNS) of the three-dimensional flow around a circular cylinder near a stationary wall at the Reynolds number of 500. The gap (G) between the cylinder surface and the stationary wall varies in the range of 0–3.0D where D is the cylinder diameter. We observe that the proximity wall significantly affects the flow topology around the cylinder, which is characterized by the asymmetric wake, upward gap flow, and strong interactions of the cylinder vortices with the wall-generated boundary layer. Three flow regimes are identified with variations of the fluid forces and vortex dynamics. (i) Steady regime: at G/D < 0.3, vortex shedding is suppressed in the near wake, and scattered streamwise vortices form in the far wake where the upper side shear layer meets the stationary wall. No fluctuating forces act on the cylinder. (ii) Biased unsteady regime: at 0.3 ≤ G/D < 1.5, the gap flow deflects upward and the vortices shed from the gap side are significantly suppressed. The cylinder has enlarged fluctuating drag and lift forces with identical dominant frequencies. (iii) Parallel unsteady regime: at G/D ≥ 1.5, vortices shed from both sides of the cylinder are of almost identical intensities while the gap flow is approximately parallel to the wall. The vortex dynamics approaches that of an isolated circular cylinder in unconfined flows. Flow features of each regime are illuminated through the flow fields, vorticity contours, statistics of the enstrophies and gap flow, and pressure distribution on the cylinder surface. Finally, we investigate the critical gap ratio for the onset of the vortex-shedding of the upper shear layer and discuss the underlying physics. Moreover, we observe that the occurrence of the second harmonic lift and fundamental drag frequencies are resulted from the asymmetric wake because of the proximity of the stationary wall.

The Wake Dynamics Behind a Near-Wall Square Cylinder

Abstract Particle image velocimetry is used to experimentally study the wake dynamics behind a near-wall square cylinder subjected to a thick oncoming turbulent boundary layer. The turbulent boundary layer thickness was 3.6 times the cylinder height (h) while the Reynolds number based on the freestream velocity and the cylinder height was 12,750. The gap distance (G) between the bottom face of the cylinder and the wall was varied, resulting in gap ratios (G/h) of 0, 0.3, 0.5, 1.0, 2.0, 4.0, and 8.0. The effects of varying the gap ratio on the mean flow, Reynolds stresses, triple velocity correlation, two-point autocorrelation, and the unsteady wake characteristics were examined. The results indicate that as gap ratio decreases, asymmetry in the wake flow becomes more pronounced, and the size of the mean separation bubbles increases. The magnitudes of the Reynolds stresses and triple velocity correlations generally decrease with the decreasing gap ratio. Moreover, the size of the large-scale structures increases with decreasing gap ratio, and the critical gap ratio, below which Kármán vortex shedding is suppressed, is found to be 0.3. The dominant Strouhal number in the wake flow expressed in terms of the streamwise mean velocity at the cylinder vertical midpoint increases as gap ratio decreases while that based on the freestream velocity is less sensitive to gap ratio for the offset cases (G/h &amp;gt; 0).

Stratified Shear-Thinning Fluid Flow Past Tandem Cylinders in the Presence of Mixed Convection Heat Transfer With a Channel-Confined Configuration

Abstract The article examines the consequence of thermal buoyancy-driven cross-flow and heat transfer for shear-thinning power-law fluids on the tandem orientation of two cylinders. Finite volume methodology is used to investigate the effect of the gap ratio (2.5 ≤ S/D ≤ 5.5), power-law index (0.2 ≤ n ≤ 1), and Richardson number (0 ≤ Ri ≤ 1) on flow and thermal output parameters at Reynolds number Re = 100 and Prandtl number Pr = 50 in a confined channel. An unprecedented jump has been witnessed in the flow/thermal parameters at the critical gap ratio (critical spacing). At forced convection (Ri = 0), this critical spacing keeps on increasing with shear-thinning character, from S/D = 3.9 (at n = 1) to 4.9 (at n = 0.2). On the contrary, an increase in shear-thinning characteristic leads to a decrease in critical spacing from S/D = 3.9 (at n = 1) to 2.8 (at n = 0.4) for Ri = 1 (mixed convection). The heat transfer rate increases with shear-thinning behavior, with a maximum heat transfer, noted at n = 0.2. A higher unprecedented increment for flow/thermal parameters is seen at critical spacing for the downstream cylinder than the upstream cylinder. At the highest gap ratio, the output parameters for the upstream cylinder approximate that of an isolated cylinder. The time-variant fluctuations in lift coefficients for a shear-thinning flow in a tandem arrangement provide a new understanding of coshedding and extended body flow regimes.

The Effect of the Gap Ratio on the Flow and Heat Transfer over a Bluff Body in Near-Wall Conditions

In order to study the effect of different gap ratios on the thermofluid-dynamic field around a bluff body located in proximity to a heated wall, a series of experiments and numerical simulations have been conducted. The former were carried out using an open circulating water tank experimental platform and a single cylinder and square column as geometrical models (their characteristic length being D). The latter were based on the well-known SIMPLE algorithm for incompressible flow. The results show that the gap ratio is an important factor affecting the wake characteristics of near-wall bluff bodies. When the gap ratio is small, the influence of the wall on the bluff body wake is large. With an increase in the gap extension, periodic vortex shedding is enabled and heat transfer is strengthened accordingly; in addition, the vortex shedding period is larger for the square column. The square column displays hysteresis compared with the cylinder at the same gap ratio (the critical gap ratio of cylinder is 0.2∼0.4, while that of square column is 0.4∼0.6).

Local scour around tandem square porous piles in steady current

Experimental study on the local scour around tandem square porous piles in steady current has been carried out in the live-bed flow condition. The influence of the porosity (P) of both front and rear piles in the tandem configuration (P = 0–38.5 %) and the gap ratios (G/D = 2–12) are quantified based on the measurement of the development of the local scour, time scale, three-dimensional scour profiles and the scour characteristics were analysed. Three regimes are identified regarding on the porosity distributions of the front and rear pile. The distinct features were found at the porosity of the front was small than its counterpart of the rear. The global scour can be recognized at G/D < 4. The dimensions of the scour hole for the rear pile decrease first as a trade-off is observed between the sediment deposit landed around the rear pile and its weak erosion. A critical gap ratio, at which the minimum scour dimensions were observed is strongly depend on the difference of the porosity between the front and rear piles.

Steady flow around a square cylinder near a plane boundary

Steady flow around a square cylinder placed near a plane wall boundary is investigated experimentally in the present work covering the range of Reynolds number of Re = 7.34 × 104–4.12 × 105, gap ratios of G/D = 0–3 with two different freestream turbulent intensity Iu = 1% and 9%. The influence of Reynolds number, gap ratios and turbulent intensity on the hydrodynamic characteristics have been studied systematically. Two-dimensional Large-eddy simulation (LES) were employed for flow visualizations. It is found that the hydrodynamic forces on a square cylinder are independent of Re even for the very small gap ratio cases. For the influence of the low turbulent intensity (Iu = 1%), the hydrodynamic features and vortex shedding are insensitive to the gap effect as G/D > 1. With the decrease of G/D, the increase of the base pressure Cpb results in the decrease of the drag coefficient CD. The amplitude of the periodic fluctuations of the vortex shedding process decreases with the vortex shedding process continuing. As G/D ≤ 0.3, the vortex shedding is observed to be completely suppressed. The blockage effect leads to an entrainment of the flow passing through the gap and a low-speed recirculation is formed at the plane boundary in the region of x/D < 7.75. High turbulence tends to increase the base pressure and reduce the drag coefficient of the square cylinder for large gap ratio. For G/D ≤ 0.8, the high turbulence triggers the growth of separated shear layer and inherent instabilities for the near-wall cylinder, which results in the higher fluctuating drag and lift coefficient. The critical gap ratio for the vortex shedding suppression is reduced to G/D = 0.2.

Mobility edge of the two-dimensional Bose-Hubbard model

We analyze the disorder driven localization of the two dimensional Bose-Hubbard model by evaluating the full low energy quasiparticle spectrum via a recently developed fluctuation operator expansion method. For any strength of the local interaction we find a mobility edge that displays an approximately exponential decay with increasing disorder strength. We determine the finite-size scaling collapse and exponents at this critical line finding that the localization of excitations is characterized by weak multi-fractality and a thermal-like critical gap ratio. A direct comparison to a recent experiment yields an excellent match of the predicted finite-size transition point and scaling of single particle correlations.

Numerical experiments of the flow around a bluff body with and without roughness model near a moving wall

Numerical tests at high Reynolds number flows were taken on circular cylinder placed near and parallel to a moving ground. A moving ground running at the same speed as the free stream eliminates the confusing effects of the boundary layer formed on the ground being, therefore, more effective to establish a better understanding of the relationship between complete vortex shedding suppression and surface roughness. A detailed quantitative measurement of the flow field around the cylinder using Lagrangian vortex method with roughness model was carried out. The effect of higher surface roughness heights is studied because it introduces greater instabilities in the boundary layer of bluff bodies. The purpose is to investigate supercritical flow patterns from subcritical Reynolds number flow simulations. The present results are compared against those measured for smooth cylinder under the same flow conditions. It is found that certain critical gap ratio between the rougher cylinder bottom and the moving wall significantly reduces the drag force. The lift force points away from the wall plane. The full vortex shedding suppression is successfully anticipated. In addition, the Strouhal number vanishes. The contribution of this research is to report that von Kaman-type vortex shedding totally ceases and instead two nearly parallel shear layers are formed behind the cylinder in moving ground when employing two-dimensional modeling of roughness. Previous numerical results for flow around smooth cylinder placed closer to the moving ground did not capture the behavior of Strouhal number equal to zero. Unfortunately, there is a lack of experimental results for rough cylinder near a moving wall, which motives the present study.

Flow and heat transfer analysis around tandem cylinders: critical gap ratio and thermal cross-buoyancy

The focus of the current numerical investigation is to study the fluid flow and mixed convective (thermal cross-buoyancy) heat transfer of incompressible fluid across identical cylinders organized in a confined tandem configuration because of their enormous engineering and industrial applications such as heat exchange tubes, electronic cooling, twin chimney stacks, cooling tower, etc. The involved flow and energy equations are solved for different gap ratios (S/D = 2.5, 3, 3.5, 4, 5, and 5.5) with varying Richardson number (Ri = 0, 0.5, and 1) at Reynolds number Re = 100, Prandtl number Pr = 0.7 and wall confinement β = 25% by using a finite volume method-based commercial solver ANSYS Fluent. It is found that after a certain gap ratio there is a drastic change in the physical parameters and after that gap ratio the change is gradual; this gap ratio is termed as a critical gap ratio. The introduction of thermal cross-buoyancy (Ri > 0) plays a deep impact on the physical parameters, and it is to be noted that the critical spacing shifts towards a lower value with increasing Ri. The analysis of lift coefficients shows that the fluctuations in lift signal shift from zero average value at Ri = 0 towards the nonzero negative average value for the tandem cylinders at Ri > 0. The local Nusselt number shows the shift in the front stagnation point on both cylinders with increasing thermal cross-buoyancy. The drag coefficient and Nusselt number of the downstream cylinder are always less than the upstream cylinder, but the percentage increment in the physical parameters of the downstream cylinder after critical spacing is much more than its upstream counterpart.

Forced convection for flow across two tandem cylinders with rounded corners in a channel

This work presents the first numerical investigation on the forced convection of flow across two tandem cylinders with rounded corners in a channel at Re = 100. Both cylinders have the geometry of a square rounded at all corners with a radius of curvature R, which is non-dimensionalized as R+ = R/D where D is the cylinder diameter, thus the cylinder geometry can be square (R+ = 0.0), partially rounded (R+ = 0.1–0.4) or circular (R+ = 0.5). The two cylinders are separated at a distance in the streamwise direction as characterized by the parameter of gap ratio (GR) chosen at GR = 1(1)8. The objective of this work is to explore the effects of two significant parameters, i.e., gap ratio and corner radius, on the flow unsteadiness and heat transfer characteristics of the tandem arrangement that has not been studied before. The effects of the two parameters are exhibited and analyzed by the instantaneous temperature and vorticity fields, variation of representative aerodynamic and heat transfer quantities, spatial distributions of local heat transfer rate, flow behaviors in the gap and the near-wake regions, and temperature distribution and variation on the channel wall. The results are presented by time-averaged and fluctuating quantities to reflect both mean and pulsating behaviors. We observed that the cylinder geometry determines the unsteadiness of the near-wake flow after the downstream cylinder; the flow is always unsteady for square-like cylinders where the corner radius is small, while the flow can be stabilized by the circular-like cylinders with larger corner radii that the flow fluctuation is greatly weakened or even fully suppressed at small GRs. Numerical results also reveal that the gap flow is steady at small GRs and unsteady at large GRs, as categorized as steady gap flow regime and unsteady gap flow regime. There are drastic variations for the representative characteristic quantities at the critical GR where the gap flow transits from steady to unsteady. The different flow regimes categorized by GR and R+ also substantially determine the flow patterns in the gap and near-wake regions, the mean and fluctuating of heat transfer rate on the cylinder surface and the temperature variation on the channel wall.

Flow past a near-wall retrograde rotating cylinder at varying rotation and gap ratios

The flow past a circular cylinder that is rotating retrograde near a turbulent wall boundary layer at Re = 10 000 has been investigated experimentally using particle image velocimetry (PIV). The cylinder rotates in retrograde direction with different rotation ratios from α = 0 to 2, where α is defined as the ratio of the peripheral speed on the cylinder surface divided by the free-stream velocity. The gap ratio, G* = G/D, is varied between 0 and 1.6, where G is the gap between the cylinder and the plane wall, and D is the cylinder diameter. The flow structure is greatly modified due to the influence of wall proximity and cylinder rotation, notably the onset/suppression, frequency and strength of vortex shedding. Similar to a near-wall stationary cylinder, there exists a critical gap ratio (about 0.4) below which periodic vortex shedding from the cylinder is suppressed. On the other hand, the cylinder rotation causes vortex shedding to cease at α ≥ 1.6, which is slightly lower than the reported value of α ≈ 2 in the literature on rotating cylinder in uniform flow. However, reducing G* and increasing α do not always favor the suppression of vortex shedding. In fact, cylinder rotation promotes vortex shedding over a certain range (α < 1). As α increases, the length of recirculation region behind the cylinder, which is indicated by the movement of the mean saddle point, decreases almost linearly. The effects of wall proximity and cylinder rotation are also evident on the ensemble-averaged flow field, such as the turbulent kinetic energy and Reynolds shear stress.

Vortex dynamics for flow over a circular cylinder in proximity to a wall

The dynamics of vortical structures in flow over a circular cylinder in the vicinity of a flat plate is investigated using particle image velocimetry (PIV). The cylinder is placed above the flat plate with its axis parallel to the wall and normal to the flow direction. The Reynolds number $Re_{D}$ based on the cylinder diameter $D$ is 1072 and the gap $G$ between the cylinder and the flat plate is varied from gap-to-diameter ratio $G/D=0$ to $G/D=3.0$. The flow statistics and vortex dynamics are strongly dependent on the gap ratio $G/D$. Statistics show that as the cylinder comes close to the wall ($G/D\leqslant 2.0$), the cylinder wake becomes more and more asymmetric and a boundary layer separation is induced on the flat plate downstream of the cylinder. The wake vortex shedding frequency increases with decreasing $G/D$ until a critical gap ratio (about $G/D=0.25$) below which the vortex shedding is irregular. The deflection of the gap flow away from the wall and its following interaction with the upper shear layer may be the cause of the higher shedding frequency. The vortex dynamics is investigated based on the phase-averaged flow field and virtual dye visualization in the instantaneous PIV velocity field. It is revealed that when the cylinder is close to the wall ($G/D=2.0$), the cylinder wake vortices can periodically induce secondary spanwise vortices near the wall. As the cylinder approaches the wall ($G/D=1.0$) the secondary vortex can directly interact with the lower wake vortex, and a further approaching of the cylinder ($G/D=0.5$) can result in more complex interactions among the secondary vortex, the lower wake vortex and the upper wake vortex. The breakdown of vortices into filamentary debris during vortex interactions is clearly revealed by the coloured virtual dye visualizations. For $G/D&lt;0.25$, the lower shear layer is strongly inhibited and only the upper shear layer can shed vortices. Investigation of the vortex formation, evolution and interaction in the flow promotes the understanding of the flow physics for different gap ratios.

An immersed interface method for flow past circular cylinder in the vicinity of a plane moving wall

SummaryTwo‐dimensional flows past a stationary circular cylinder near a plane boundary are numerically simulated using an immersed interface method with second‐order accuracy. Instead of a fixed wall, a moving wall with no‐slip boundary is considered to avoid the complex involvement of the boundary layer and to focus only on the shear‐free wall proximity effects for investigating the force dynamics and flow fields. To analyze the convergence and accuracy of our implementation, numerical studies have been first performed on a simple test problem of rotational flow, where the second order of convergence is confirmed through numerical experiments and an optimal range of relative grid‐match ratio of Lagrangian to Eulerian grid sizes has been recommended. By comparing the force quantities and the Strouhal number, the accuracy of this method has been demonstrated on the flow past a stationary isolated cylinder. The cylinder is then put in proximity to the wall to investigate the shear‐free wall proximity effects in the low Reynolds number regime (20≤Re≤200). The gap ratio,e/D, whereedenotes the gap between the cylinder and the moving wall andDdenotes the diameter of the cylinder, is taken from 0.10 to 2.00 to determine the critical gap ratio, (e/D)critical, for the alternate vortex shedding, where the fluid forces, flow fields and the streamwise velocity profiles are studied. One of the key findings is that the (e/D)criticalfor the alternate vortex shedding decreases as the Reynolds number increases. We also find that, in this low Reynolds number regime, the mean drag coefficient increases and peaks ate/D= 0.5 with the increase ofe/Dand keeps decreasing gently frome/D= 0.5 toe/D= 2.0, while the mean lift coefficient decreases monotonically with the increase ofe/D. New correlations are then proposed for computing force coefficients as a function ofReande/Dfor a cylinder in the vicinity of a moving plane wall. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Gap ratio effect on flow characteristics behind side-by-side cylinders of diameter ratio two

This study investigates the vortex interaction, the spatial distributions in the flow and the streamwise evolution of the spectral amplitude along the shear layer behind side-by-side cylinders of diameter ratio two at different gap ratios via dye flow visualization and particle image velocimetry (PIV). The frequency responses are measured at Re=1000, 2000, 5000 as the gap ratio changes. Velocity measurements are made and analyzed at Re=1000 for gap ratios of 1.25, 0.75 and 0.25. It is found that, as the gap ratio increases, the Strouhal number of the narrow wake decreases monotonously but that of the wide wake increases also in the monotonous way. The gap flow is always stably deflected toward the small cylinder. For side-by-side cylinders of diameter ratio two and Re=1000, two different vortex interaction scenarios are found leading to two different flow categories. The critical gap ratio for diameter ratio two is slightly smaller than that for equal diameter. The frequency ratio of the narrow and wide wakes depends strongly upon the gap ratio and the diameter ratio; but is independent of the Reynolds number studied. This frequency ratio is related to the ratio of the averaged streamwise distance of the local maxima of each spectral component. For side-by-side cylinders of diameter ratio two, two flow characteristics are modified relative to that of a single cylinder. First, the onset locations of the shear layer instability. Second, the spatial growing rates of the shear layers. For the side-by-side cylinders of diameter two (D/d=2), the influence on the wide wake is more significant but is less pronounced on the narrow wake. Besides, the influences on both the narrow and the wide wakes are even pronounced for D/d=1 than those for D/d=2.

Effects of gap width on flow motions around twin-box girders and vortex-induced vibrations

Twin-box girders are employed in long-span suspension bridges for flutter stability. However, the flow around a twin-box girder is notably complicated. The effects of gap width on the flow characteristics at Re=5.58×104 and the vortex-induced vibration (VIV) of a twin-box girder at about Re=1.17×104 were experimentally investigated using a sectional model. In the experiments, the gap ratio (defined as the ratio of the width L between two box girders to the central height of the girder D) varied from 0.855 to 10.260. The flow velocities around the model and the surface pressures of the model were measured during static tests, and the acceleration of sectional model also measured during dynamic tests. In addition, corresponding smoke-wire flow visualization tests were conducted under low wind speeds for the same sectional model. The test results show that all of the pressure characteristics, the aerodynamic force, the Strouhal number, the flow pattern and the VIV are dramatically influenced by the gap width. At a gap ratio of L/D=2.138 (defined as the critical gap ratio), the flow motion around the gap between the upstream and downstream box girders suddenly changes, and an alternate shedding vortex appears. According to vortex shedding pattern of the twin-box girder, the flow can be categorized into three basic patterns: pattern A, vortices alternately shedding behind the downstream box girder when the gap ratio is smaller than the critical gap ratio (L/D<2.138); pattern B, vortices alternately shedding behind the upstream box girder (in the gap) when the gap ratio is in the moderate range (2.138≤L/D≤10.26); and pattern C, vortices freely shedding behind the upstream and downstream box girders when the gap ratio approaches infinity. For the VIVs, the twin-box girder experiences four types of VIV as the gap ratio increases: when L/D<1.710, no VIV occurs; when 1.710≤L/D≤2.138, only vertical VIV occurs; when 2.566≤L/D≤2.933, both vertical and torsional VIVs occur; and when L/D≥3.421, only torsional VIV forms.

Local scour around two pipelines in tandem in steady current

In this study, local scour around two identical pipelines in a tandem arrangement are investigated numerically. The two-dimensional Reynolds-averaged Navier–Stokes (RANS) equations, together with the conservation equation of the sediment mass are solved to simulate the flow around two pipelines and the evolution of the local scour profile below the pipelines. The gap ratios between the two pipelines (G/D) range from 0.5 to 5 with an interval of 0.5, where G is the gap between the two pipelines and D is the diameter of the pipelines. The focus of the study is to investigate the effects of the gap ratio on the scour depth and scour time scale. It is found that the scour depth below the downstream pipeline is greater than that below the upstream pipeline under both clear water and live bed conditions because of the effect of the vortex shedding from the upstream pipeline. The maximum scour depth below the downstream pipeline occurs at G/D=2.5 under both clear water and live bed conditions, which is about the critical gap ratio beyond which vortex shedding from the upstream pipeline occurs. As the gap ratio exceeds 2.5, the scour depth below the downstream pipeline decreases with increasing gap ratio due to the weakening effect of the vortex shedding from the upstream pipeline on the scour. The scour under the clear water condition is simulated at a velocity 25% lower than the critical velocity for live bed scour. The variations of the scour depths below the two pipelines in the clear water and live bed conditions are found to be similar to each other. Strong positive mean lift coefficient on the downstream pipeline was observed during the scour process, which is believed to have a negative effect on the stability of downstream pipeline. The RMS lift coefficient on the downstream pipeline increases significantly when the vortex shedding from the upstream pipeline occurs.

Vortex-induced vibrations of a neutrally buoyant circular cylinder near a plane wall

This paper presents an experimental study of the motions, drag force and vortex shedding patterns of an elastically mounted circular cylinder, which is held at various heights above a plane wall and is subject to vortex-induced vibration (VIV) in the transverse direction. The cylinder is neutrally buoyant with a mass ratio m⁎=1.0 and has a low damping ratio ζ=0.0173. Effects of the gap ratio (S/D) ranged from 0.05 to 2.5 and the free-stream velocity (U) ranged from 0.15 to 0.65m/s (corresponding to 3000≤Re≤13 000, and 1.53≤U⁎≤6.62) are examined. The flow around the cylinder has been measured using particle image velocimetry (PIV), in conjunction with direct measurements of the dynamic drag force on the cylinder using a piezoelectric load cell. Results of the vibrating cylinder under unbounded (or free-standing) condition, as well as those of a near-wall stationary cylinder at the same gap ratios, are also provided. For the free-standing cylinder, the transition from the initial branch to the upper branch is characterized by a switch of vortex pattern from the classical 2S mode to the newly-discovered 2PO mode by Morse and Williamson (2009). The nearby wall not only affects the amplitude and frequency of vibration, but also leads to non-linearities in the cylinder response as evidenced by the presence of super-harmonics in the drag force spectrum. In contrast to the case of a stationary cylinder that vortex shedding is suppressed below a critical gap ratio (S/D≈0.3), the elastically mounted cylinder always vibrates even at the smallest gap ratio S/D=0.05. Due to the proximity of the plane wall, the vortices shed from the vibrating cylinder that would otherwise be in a double-sided vortex street pattern (either 2S or 2PO mode) under free-standing condition are arranged into a single-sided pattern.

Influence of the Position Angle of the Small Pipeline on Vortex Shedding Flow Around a Sub-Sea Piggyback Pipeline

The vortex shedding flow past a piggyback pipeline close to a plane boundary is investigated numerically. The piggyback pipeline is comprised of a large pipeline and a small pipeline. The aim of the study is focused on the effects of the position angle of the small pipeline on the vortex shedding and the hydrodynamic forces of the pipeline bundle. The two-dimensional Reynolds-averaged Navier-Stokes equations are solved using the finite element method. The equations are enclosed by the κ–ω turbulent model. The ratio of the small pipeline diameter (d) to the large one (D) is 0.2. The Reynolds number based on the free stream velocity (U 0) and the large pipeline diameter (D) is Re = 2 × 104. Simulations are carried out for the positional angles (α) of the smaller pipeline relative to the larger one ranging from 0 to 180° with an interval of 15°, and the gaps (G) between the large pipeline and the plane boundary ranging from 0.2 to 0.6D. It is found that the critical gap ratio, below which the vortex shedding is suppressed, is a function of the positional angle of the small pipeline. The effects of the position angle of the small pipeline on the hydrodynamic forces on the pipeline system are investigated numerically.

低間隔における直列２円柱の流れ方向および流れ直交方向の流力振動に関する３次元数値解析

We present numerical results for hydrodynamic vibrations of two circular cylinders in tandem arrangement, which are mounted in a uniform flow. Two circular cylinders are assumed as each rigid body, and the circular cylinders are supported by damper-spring systems in in-line and cross-flow directions. In our computations, the gap ratio between the centers of two circular cylinders is set as 3 which is smaller than the critical gap ratio of two stationary circular cylinders. In addition, the Scruton number is given by 0.99. Vibration amplitudes in the in-line and cross-flow directions of the circular cylinders are computed by a third-order upwind finite element scheme and the numerical results are discussed in detail.