Gap Ratio Increases Research Articles

Scour around twin-piles under combined wave–current flows

The paper presents three dimensional simulations of scour around a pair of piles arranged side-by-side configurations under combined wave–current flow conditions using a computational fluid dynamics model. The Reynolds-averaged Navier–Stokes (RANS) equation is solved using the k-ω turbulence model in the present work. The Exner equation is used to measure the variations in bed elevation. The level-Set approach is used to capture the free surface realistically. The numerical model couples the hydrodynamic module with the morphological module to simulate the scour process. For accurate erosion and deposition calculations in the sediment bed, the morphological model employs a modified bed shear stress formula on a sloping bed in combination with a sand slide algorithm. In the present study, the simulations have been done in a truncated numerical wave tank with the Dirichlet boundary condition and active wave absorption method. The numerical model is validated with the experimental results of combined wave–current hydrodynamics and scour around a pair of piles. The validated numerical model is utilized to study the effect of the gap ratio and the effect of KC number in the various combined wave–current environment. In low KC conditions, normalized scour depth increments owing to waves alone, weak currents, and moderate currents are less, whereas the scour depth increases dramatically for waves with high currents. It is also found that the gap flow between the piles increases the depth of scour in a significant manner. For a given pile gap ratio, the scour depth is dependent on the KC number, which implies the larger the KC number, the larger scour depth. For a given KC number, the scour hole stretch in the flow direction reduces as the gap ratio increases, whereas the perpendicular stretch increases. It is also observed that the normalized scour depth decreases as the gap ratio increases for a fixed KC number and fixed Ucw. It is evident from the present research that the normalized scour depth increases with increase in KC number for a fixed wave–current parameter (Ucw).

Effects of a detached splitter on the vortex-induced vibration of a 5:1 rectangular cylinder

The present paper examines the vortex-induced vibration (VIV) of a 5:1 rectangular cylinder with a detached splitter in its near wake. The tested gap ratio between the cylinder and the splitter (g/D, where g is the gap between the cylinder rear and the splitter and D is the depth of the rectangular cylinder) ranges from 0.5 to 2.0, with an increment of 0.5. To serve as a reference case, the rectangular cylinder without the splitter is also tested under the same conditions. The test Reynolds number ranges from 32 320 to 56 507. This study delves into the vibration response, pressure distributions, and power spectral densities (PSD) of the cylinder under varying gap ratios. Based on qualitative and quantitative analyses between the cylinder and the splitter using phase average techniques, smoke-wire visualization, and numerical simulation, the different vortex shedding modes according to different gap ratios were identified. Experimental and numerical results show that the detached splitter and its gap ratio play important roles in determining the cylinder VIV properties. For g/D = 0.5, the detached splitter has a sensible mitigation on the cylinder VIV. However, as the gap ratio increases, the VIV response initially recovers to the reference case at g/D = 1.0 and subsequently enlarges at g/D = 1.5 and 2.0. The pressure distribution results showed that the detached splitter demonstrates its effects primarily through fluctuations in the pressure field rather than the mean field. In addition, at g/D = 0.5, a sensibly decayed PSD is observed, while at g/D = 1.0–2.0, an intensified PSD is detected. The underlying mechanism of the detached splitter on the VIV of the 5:1 rectangular cylinder should be attributed to the von Kármán vortex street compared to the reference case.

Numerical Investigation of Vortex-Induced Vibrations of a Rotating Cylinder near a Plane Wall

Numerical simulations are carried out to investigate the vortex-induced vibrations of a two-degree-of-freedom (2DOF) near-wall rotating cylinder. Considering the effects of gap ratio, reduced velocity and rotational rate, the amplitude response, wake variations and fluid forces are analyzed, with the Reynolds number of 200 and the mass ratio set to 1.6. The correlative mechanism in the wake–hydrodynamics–vibration is revealed. The results show that the influence of the wall dominates the vortex-induced vibration of the cylinder. The effect of the wall on the vibration weakens as the gap ratio increases, and the effect of the wall on the vibration is negligible when H/D > 1.1. The forward rotation of the cylinder enhances the wall effect, while the backward rotation presents the reverse effect. The vortex-induced vibration of the cylinder is suppressed when 0 < α < 1, and the amplitude range is concentrated at Vr ∈ (3, 5). The wake mode can be divided into five modes, and the wake modes are clarified under different rotation rates and reduced velocities.

The gap ratio effects on vortex evolution behind a circular cylinder placed near a wall

The vortex evolution behind a circular cylinder placed near a wall is investigated experimentally with particle image velocimetry. The Reynolds number based on the cylinder diameter D is Re=1500, and the gap ratio G/D varies from 0 to 2.5 (where G is the net gap between the lower surface of the cylinder and the wall). The proper orthogonal decomposition and the vortex identification method λci are applied to capture vortex structures, and the effects of the gap ratio on vortex evolution behind the cylinder are revealed. (i) For G/D≤0.25, the regular and alternate wake vortex shedding are suppressed, and the wake vortex shedding is associated with the upper shear layer of the cylinder. The wake vortex is shed from the curling of the upper shear layer and finally breaks down into some smaller vortices at G/D = 0. (ii) For G/D=0.5, there is a vortex merging process among the upper wake vortex and the secondary vortex; meanwhile, some smaller vortices broken from the secondary vortex are entrained into the recirculation region. (iii) For 0.5<G/D≤1, the lower wake vortex can directly interact with the secondary vortex while the direct interaction is reduced at 1<G/D≤2. (iv) For G/D>2, the flow of the region is similar to that of an isolated cylinder. The variation of the Strouhal number (St) is dependent on the gap ratio, and the St increases as the gap ratio decreases down to G/D = 0.25, and there is nearly a 92% increase from St = 0.192 at G/D = 2.5 to St = 0.369 at G/D = 0.25, which is caused by the deflection of the gap flow. Moreover, the regular and alternate vortex structure can be formed as the gap ratio increases, and the flow characteristics and the vortex evolution are strongly affected by the gap ratio.

Near-wall effect on flow around an elliptic cylinder translating above a plane wall

In this work, the flow over an elliptic cylinder near a moving wall is investigated for Reynolds numbers less than 150. Here, the ratio between the gap (i.e., the distance between the cylinder and the wall) and the length of the semi-major axis of the elliptic cylinder varies from 0.1 to 5. This ratio is hereafter denoted as the gap ratio. The resulting Kármán vortex street, the two-layered wake, and the secondary vortex street have been investigated and visualized. Numerical simulations show that for the steady flow, the wake is composed of two asymmetric recirculation vortices, while a decrease in the gap ratio suppresses the vortex shed from the lower part of the cylinder. For the unsteady flow, the wake can be classified into four different patterns based on the wake structures (the Kármán vortex street, the two-layered wake, and the secondary vortex street). The regions of these wake patterns are given in the gap ratio and Reynolds number space, showing that the critical Reynolds number for the transition between different patterns increases as the gap ratio decreases. An overall increase in the mean drag coefficient with increasing gap ratios is observed, except for a sudden drop that occurs within a small gap ratio range. Moreover, as the gap ratio increases, the onset location of the two-layered wake first decreases due to a decrease in flow velocity in the gap and then increases due to the weakening of the wall suppression effect.

Numerical simulation of local scour around two pipelines in tandem using CFD–DEM method

In the field of offshore oil and gas engineering, the arrangement of multiple pipelines are becoming more common, the spacing between the pipelines and the incoming stream velocity will significantly affect the scouring process around the pipelines. In this study, the effect of space ratio (G/D) and the stream velocity on the scouring process around two pipelines in tandem are investigated using the coupled approach of computational fluid dynamics (CFD) and discrete element method (DEM). Here G is the spacing between the pipelines and D is the diameter of the pipeline. Specifically, the effect of space ratio and the stream velocity are discussed by simulating the gap ratio (G/D) between two pipelines ranging from 1 to 3 with an interval of 1, under the stream velocity U = 0.5,1 and 2 m/s, The results indicate that when G/D ≤ 2, the equilibrium scour depth below the upstream pipeline (S1) is slightly larger than that under the downstream pipeline (S2), S1 and S2 slightly increase as the gap ratio increases. Whereas for G/D > 2, the equilibrium scour depth beneath the upstream pipeline is slightly smaller than that under the downstream pipeline, S1 and S2 slightly decrease as the gap ratio increases. Furthermore, the scour depths are highly dependent on and positively related to the incoming stream velocity, the equilibrium bed profiles are similar under the same incident stream velocity with different gap ratios.

Wake analysis and regimes for flow around three side-by-side cylinders

In this study, an analysis of flow field around three circular cylinders in side-by-side configuration at various gap ratios and Reynolds number has been carried out. This work is among the first experimental efforts in the low Reynolds number regime. The instantaneous and time averaged flow structures were obtained using the particle image velocimetry technique. The gap ratio utilized for the experiment is from 1.5 ≤ s/D ≤ 4.0 (where s is the distance between the cylinders and D is the diameter of the cylinder). The Reynolds number is in the range of 90 ≤ Re ≤ 560. Five different types of flow regimes were observed: three biased flow regimes namely, asymmetric biased flow, bi-stable biased flow and equal biased flow at lower gap ratios (s/D < 3); two unbiased flow regimes namely, equal unbiased flow and synchronous equal flow as the gap ratio increases. The biased flow regimes are produced because of the shear layer interaction. The flow regime characteristics are shown in the downstream distance of 1.5D–6D. When the gap ratios are small, the interaction of the inner shear layers formed between the cylinders are more compared to the interaction between the shear layers formed around a cylinder. The drag coefficient variation shows that the value of drag coefficient is comparatively higher for asymmetric biased flows. It is found that the variation in both Reynolds number and gap ratio affects the formation of flow regimes as well as variation in drag coefficient in the Reynolds number regime 90 < Re < 600.

Wake-boundary layer interaction behind an elliptic cylinder at different Reynolds numbers

ABSTRACT In this paper, hot-wire anemometry (HWA) is used to experimentally investigate interactions between a fully developed turbulent boundary layer and wake of an elliptic cylinder where axis ratio (AR) of the cylinder is 2. The elliptic cylinder was located inside and outside a turbulent boundary layer with a thickness (δ) of 0.38B. Furthermore, experiments were conducted at different Reynolds numbers (13,250 and 26,500) based upon the smallest cylinder diameter (B). Mean velocity, turbulence intensity and higher-order central moments of velocity signals (i.e. skewness and flatness) measurements were performed using HWA upon wake-boundary layer interactions on a flat plate. Results showed that profiles of stream-wise mean velocity and turbulence intensity were greatly dependent on gap ratio (G/B) and Reynolds number (Re) in near-wake region. It was also observed that, except for G/B = 0.1, the wake-boundary layer interactions were faster at Reynolds number of 26,500 rather than 13,250. The interactions occurred earlier upon fluctuating the velocity rather than the case where a fixed mean velocity was considered. The results further show that an increase in the gap ratio increases Strouhal number almost independent of δ/B. Behind the cylinder, relatively smaller wake region was obtained at Re = 26,500 rather than Re = 13,250, where the velocity profiles quickly converged to the flat plate boundary layer velocity profiles.

Numerical simulation of VIV for a circular cylinder with a downstream control rod at low Reynolds number

A numerical simulation of the vortex-induced vibration (VIV) at Reynolds number of 500 is carried out for a circular cylinder with a downstream rigidly connected control rod. The mass ratio (m*) and damping ratio (ξ) are fixed as 10 and 5×10−4. The fluid dynamics is obtained by solving arbitrary Lagrangian–Eulerian (ALE) Navier–Stokes equations, and the structure dynamics is solved using Newmark-β method. The grid convergence is tested using five different grids to select the proper mesh. The model and computational method are validated by comparing with the previous research, and a good agreement is reached. The VIV of the cylinder system at eight different gap ratios (G∕D=0.01∼2) are simulated. The responses of the cylinder system are discussed following the classification of the flow patterns at different gap ratios. The same VIV characteristic can be observed in the same flow pattern. The sub-harmonic resonance is observed in the VIV of the cylinder system for large reduced velocity as G∕D<0.7. A simple formula is used to explain the sub-harmonic resonance. The vortex shedding mode and the frequency of the lift force on the cylinders in the lock-in regime are used to validate the formula. The smaller the gap ratio is, the more lock-in regimes can be excited, and the higher-order sub-harmonic resonance can be observed. The control rod has a great influence or even is decisive on the VIV of the cylinder system at small gap ratio. As the gap ratio increases, the effect of the control rod is becoming weak. Besides the natural frequency of the cylinder system, the frequency corresponding to the vortex shedding mode is observed in the lift coefficient of the cylinders.

Effect of bed vicinity on vortex shedding and force coefficients of fluid flow on an offshore pipeline

The effect of rigid bed proximity on flow parameters and hydrodynamic loads in offshore pipelines exposed to turbulent flow is investigated numerically. The Galerkin finite volume method is employed to solve the unsteady incompressible 2D Navier–Stokes equations. The large eddy simulation turbulence model is solved using the artificial compressibility method and dual time-stepping approach. The proposed algorithm is developed for a wide range of turbulent flows with Reynolds numbers of 9500 to 1.5×104. Evaluation of the developed numerical model shows that the proposed technique is capable of properly predicting hydrodynamic forces and simulating the flow pattern. The obtained results show that the lift and drag coefficients are strongly affected by the gap ratio. The mean drag coefficient slightly increases as the gap ratio increases, although the mean lift coefficient rapidly decreases. The vortex shedding suppression happen at the gap ratio of less than 0.2.

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.

An experimental study on the unsteady vortices and turbulent flow structures around twin-box-girder bridge deck models with different gap ratios

In the present study, an experimental investigation was conducted to characterize the unsteady vortices and turbulent flow structures around twin-box-girder (TBG) bridge deck models with and without cross beams. While the oncoming wind speed was fixed at U∞=8.0m/s (i.e., the corresponding Reynolds number, Re=1.01×104, based on the height of the box girder) during the experiments, the gap width between the TBG was varied to have four different gap ratios (i.e., the ratio of the gap width between the TBG to the deck height). The corresponding test cases were classified into two categories: the cases with relatively small gap ratios (i.e., gap ratio=0.85 and 1.70) and the cases with relatively large gap ratios (i.e., gap ratio=2.55 and 3.40). In addition to measuring the surface pressure distributions around the TBG bridge deck models using an array of digital pressure transducers, a high-resolution particle image velocimetry (PIV) system was utilized to perform detailed flow field measurements to quantify the evolution of the unsteady vortex structures around the TBG bridge deck models. The measurements reveal that as the gap ratio increases, the vortex shedding moves from the trailing edge of the leeward box to the rear edge of the windward box, which simultaneously increases the turbulent kinetic energy in the gap region and the fluctuating pressures on the leeward box. The vortex dimensions and the core-to-core distances between two neighboring vortices are also affected by the gap ratio. Combining with the estimation of the pressure field and the measured fluctuating pressure coefficient distributions on the TBG models, it is found that the TBG bridges with larger gap ratios will dramatically strengthen the fluctuating pressure coefficients on the leeward box which are greatly higher than those for the small gap ratio cases. Moreover, for large gap ratio cases, the test model with cross beams also has higher fluctuating pressure coefficients on the leeward box which just decrease a little comparing with the test model without cross beams.

Effect of trunk length on the flow around a fir tree

Flow around a small white fir tree was investigated with varying the length of the bottom trunk (hereafter referred to as bottom gap). The velocity fields around the tree, which was placed in a closed-type wind tunnel test section, were quantitatively measured using particle image velocimetry (PIV) technique. Three different flow regions are observed behind the tree due to the bottom gap effect. Each flow region exhibits a different flow structure as a function of the bottom gap ratio. Depending on the gap ratio, the aerodynamic porosity of the tree changes and the different turbulence structure is induced. As the gap ratio increases, the maximum turbulence intensity is increased as well. However, the location of the local maximum turbulence intensity is nearly invariant. These changes in the flow and turbulence structures around a tree due to the bottom gap variation significantly affect the shelter effect of the tree. The wind-speed reduction is increased and the height of the maximum wind-speed reduction is decreased, as the gap ratio decreases.

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=2×10 4. 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.

THE STRUCTURE OF TURBULENT SHEAR FLOW AROUND A TWO-DIMENSIONAL POROUS FENCE HAVING A BOTTOM GAP

The flow field behind porous fences of geometric porosity ε=38·5% with various bottom gaps (G) has been investigated using a hybrid PTV velocity field measurement technique. Four gap ratiosG /H=0·0, 0·1, 0·2 and 0·3 were tested in this study. One thousand instantaneous velocity vector fields in the x–y plane were consecutively measured for each gap ratio. The free-stream velocity was fixed at 10cm/s and the corresponding Reynolds number based on the fence height (H) was Re=2985. The results show that the gap ratio G/H=0·1 gives the best shelter effect among the four gap ratios tested in this study, having a small shelter parameter ψ in a large area behind the fence. As the gap ratio increases, the region of mean velocity reduction decreases and the lower shear layer developed from the bottom gap expands upward. From the spatial distributions of turbulence statistics including turbulence intensities, Reynolds shear stress and turbulent kinetic energy, the wake characteristics can be divided into two categories depending on the gap ratio. When the gap ratio is aboveG /H=0·2, the turbulence statistics have large values in the lower shear layer. For the gap ratio G/H≤0·1, however, the lower shear layer displays small turbulence-statistics values and approach those of the no-gap case (G/H=0) with increasing distance downstream. In the upper shear layer separated from the fence top, the turbulence statistics are nearly independent of the gap ratio.

GROUND EFFECT OF FLOW AROUND AN ELLIPTIC CYLINDER IN A TURBULENT BOUNDARY LAYER

The flow characteristics around an elliptic cylinder with an axis ratio of AR=2 located near a flat plate were investigated experimentally. The elliptic cylinder was embedded in a turbulent boundary layer whose thickness is larger than the cylinder height. For comparison, the same experiment was carried out for a circular cylinder having the same vertical height. The Reynolds number based on the height of the cylinder cross-section was 14000. The pressure distributions on the cylinder surface and on the flat plate were measured for various gap distances between the cylinder and the plate. The wake velocity profiles behind the cylinder were measured using hot-wire anemometry. In the near-wake region, the vortices are shed regularly only when the gap ratio is greater than the critical value of G/B=0·4. The critical gap ratio is larger than that of a circular cylinder. The variation of surface pressure distributions on the elliptic cylinder with respect to the gap ratio is much smaller than that on the circular cylinder. This trend is more evident on the upper surface than the lower one. The surface pressures on the flat plate recover faster than those for the case of the circular cylinder at downstream locations. As the gap ratio increases, the drag coefficient of the cylinder itself increases, but the lift coefficient decreases. For all gap ratios tested in this study, the drag coefficient of the elliptic cylinder is about half that of the circular cylinder. The ground effect of the cylinder at small gap ratio constrains the flow passing through the gap, and restricts the vortex shedding from the cylinder, especially in the lower side of the cylinder wake. This constraint effect is more severe for the elliptic cylinder, compared to the circular cylinder. The wake region behind the elliptic cylinder is relatively small and the velocity profiles tend to approach rapidly to those of a flat plate boundary layer

Anisotropic electron coupling as a phenomenological model for high-Tc superconductors.

A three-dimensional weak coupling BCS model with an {\it anisotropic} pairing interaction in momentum space is reported. It exhibits an anisotropic gap in accord with recent experimental observations for high-$T_c$ oxides. The gap ratio ${2 \Delta / k_B T_c }$ is calculated as function of the anisotropy ratio of the electron pairing. It is found that the mean gap ratio decreases with increasing anisotropy of the electron pairing, whereas the maximum gap ratio increases. Assuming a unique strength of the effective electron interaction the transition temperature turns out to be always larger than in the isotropic case. The temperature dependence of the gap in the Cu-O plane and along the c-axis of YBaCuO is presented.

The effects of gap width and dilute solution properties on the viscoelastic Taylor-Couette instability

The effects of finite gap and various dilute solution properties on the previously studied purely elastic Taylor-Couette instability reported by Muller et al. (1989) and Larson et al. (1990) are investigated. The dilute solution properties which we consider are the ratio of the second to the first normal stress coefficient, ψ2/ψ1, and the ratio of the solvent to the polymer contribution to the shear viscosity, S. Linear stability predictions for the flow of an Oldroyd-B fluid are presented over a wide range of Deborah number, De, gap ratio, ε, and S. In addition, the Oldroyd-B model is modified to include second normal stress differences, and new stability predictions are presented for small negative and small positive ψ2/ψ1. Both the critical conditions and changes in the flow structure are presented. It is demonstrated that finite-gap effects are stabilizing even for relatively small gap ratios (0 &lt; ε &lt; 0.35). Furthermore, it is shown that there are two possible flow structures which can be chosen near the onset of instability: a standing wave structure (i.e. radially propagating vortices) or a travelling wave (i.e. vortices propagating up or down the coaxial cylinders). However, the strength and both the axial and radial dimensions of these vortices depend markedly on the gap, with both dimensions decreasing as the gap ratio increases. Thus, the number of vortices filling the gap increases with the gap ratio.In a second study, we show that the instability is sensitive to the presence of second normal stress differences. Positive second normal stress differences are shown to be destabilizing, while negative differences are strongly stabilizing. Furthermore, when both finite-gap effects and small negative second normal stress differences are included, the predicted gap dependence of the critical De is in good agreement with previous measurements on the flow of a dilute polyisobutylene solution. Finally, we present new measurements of the critical values of the De for a series of dilute, viscous polystyrene solutions, for which ψ2 was found to be near zero. We find that as the polymer concentration increases (and therefore S decreases) the critical Deborah number decreases, in qualitative agreement with the theoretical predictions.