Computational study on near wake interaction between undulation body and a D-section cylinder

We present a numerical study on the hydrodynamic performance of undulation NACA0012 foil in the near wake of D-section cylinder. Computations are conducted using unsteady incompressible Navier-Stokes equations with a moving adaptive mesh based on laminar flow. Investigations are focused on the effect of distance ratio between foil tip and centre of cylinder (L/D≤2.0) on the thrust/drag performance of foil and cylinder at various foil undulation frequency (St). We found that, foil thrust coefficient (C_t) increases considerably with the appearance of cylinder and an optimal distance exists at which C_t reaches maxima. The maximum increment is about eleven times that of its counterpart of single foil, which is obtained at St=0.23 and L/D=0.5. Our results for the cylinder drag coefficient (C_d) observed the existence of optimal parametric map, combined with various gap ratios and foil frequencies. With these parameters, insertion of an undulation foil can significantly lead to the drag reduction indicating that undulating foil could work efficiently as a passive vortex control device for cylinder drag reduction.     

Physical modeling and swirling strength analysis of vortex shedding from near-bed piggyback pipelines

The vortex shedding from near-bed piggyback pipelines in a steady flow has been investigated experimentally in a large water flume. A specially arranged PIV system with upward-illumination of pulsed laser arrays from the flume bottom was employed for the flow visualization and quantitative measurement of the lee-wake flow in a sub-critical regime around the piggyback pipelines in the proximity of a plane boundary. Based on dimensional analyses, a dimensionless maximum swirling strength (W_m) is used for analyzing the vortex shedding intensity and its frequency. Time-averaged swirling strength analyses indicate that the lee-wake patterns for the near-bed piggyback pipelines are dependent on the configuration factors, including the gap-to-diameter ratio (e/D), the spacing-to-diameter ratio (G/D), and the diameter ratio of two pipes (d/D), etc. The swirling strength in the lee-wake is obviously asymmetric for piggyback pipelines with bed proximity. For the fixed values of G/D and d/D, the maximum swirling strength decreases with the decrease of e/D. Moreover, for the examined G/D range (0 ≤ G/D ≤ 0.5), minimum values of W_m and corresponding VIV amplitude for the piggyback pipelines are evidently within the same range of spacing-to-diameter ratio G/D ≈ 0.05–0.20.     

Comparison of flow patterns in the near wake of a circular cylinder and a square cylinder placed near a plane wall

The flow patterns in the near wake of a cylinder (either circular or square in shape, D=25 mm) placed in the proximity of a fully developed turbulent boundary layer (thickness δ=0.4D) are investigated experimentally using particle image velocimetry (PIV). The effects of changing the gap height (S) between the cylinder bottom and the wall surface, over the gap ratio range S/D=0.1–1.0, have been investigated. The results show that both the ensemble-averaged and instantaneous flow fields are strongly dependent on S/D. The flow patterns for the two types of cylinders share many similarities with respect to the change in S/D, such as the reduced recirculation length and increased velocity fluctuation in the near wake with increasing S/D, as well as the trend of suppression of vortex shedding at small S/D and onset of vortex shedding at large S/D. However, developments of the shear layers, in terms of wake width, flow curvature, etc., are considerably different for these two types of cylinders. In general, the wake development and momentum exchange for the square cylinder are slower those for the circular cylinder at the same gap ratio. Correspondingly, it is shown that the periodic vortex shedding is delayed and weakened in the case of square cylinder, as compared to that of the circular cylinder at the same S/D.     

Numerical modeling of flow and scour below a pipeline in currents: Part I. Flow simulation

The performance of the standard k–ε, Wilcox high-Reynolds-number k–ω, Wilcox low-Reynolds-number k–ω and Smagorinsky's subgrid scale (SGS) turbulence models is examined against the flow around a circular cylinder 0.37 diameter above a rigid wall. The governing equations are solved using finite difference method in a non-orthogonal boundary-fitted curvilinear coordinate system. A mesh dependence study for the four turbulence models is carried out on computational meshes with different densities. In addition, the performance of the k–ω models with either wall function or no-slip boundary condition on the cylinder surface is examined on the finest mesh. It is found that the SGS model over-predicts the shedding of vortices from the cylinder and is sensitive to the computational mesh and the model constant C_s used. The standard k–ε and the Wilcox k–ω models predict the mean velocity field quite well but generally under-predict the velocity and hydrodynamic force oscillations using wall functions on the cylinder surface. It is also found that the Wilcox k–ω models with the no-slip boundary condition on the cylinder surface give better predictions on the shedding of vortices than their counterparts using the wall function boundary condition.     

Numerical simulation of flow around a circular cylinder close to a flat seabed at high Reynolds numbers using a k–ε model

High Reynolds number flows around a circular cylinder close to a flat seabed have been computed using a two-dimensional standard high Reynolds number k–ε turbulence model. The effects of gap to diameter ratio, Reynolds number and flat seabed roughness for a given boundary layer thickness of the inlet flow upstream of the cylinder have been investigated. Hydrodynamic quantities and the resulting bedload transport have been predicted, and the vortex shedding mechanisms have been investigated. Predictions of hydrodynamic quantities around a cylinder located far away from the bed (so that the effect of the bed is negligible) are in satisfactory agreement with published experimental data and numerical results obtained for the flow around an isolated cylinder. Results for lower Reynolds number flows have also been computed for comparison with the high Reynolds number flow results. Overall it appears that the present approach is suitable for design purposes at high Reynolds numbers which are present near the seabed in the real ocean.     

Otec cold water pipe design for problems caused by vortex-excited oscillations

Vortex-excited oscillations of marine structures result in reduced fatigue life, large hydrodynamic forces and induced stresses, and sometimes lead to structural damage and to destructive failures. The cold water pipe of an Ocean Thermal Energy Conversion (OTEC) plant is nominally a bluff, flexible cylinder with a large aspect ratio (L/D = length/diameter), and is likely to be susceptible to resonant vortex-excited oscillations. The objective of this paper is to survey recent results pertaining to the vortex-excited oscillations of structures in general and to consider the application of these findings to the design of the OTEC cold water pipe. Practical design calculations are given as examples throughout the various sections of the report.This paper is limited in scope to the problems of vortex shedding from bluff, flexible structures in steady currents and the resulting vortex-excited oscillations. The effects of flow non-uniformities, surface roughness of the cylinder, and inclination to the incident flow are considered in addition to the case of a smooth cylinder in a uniform stream. Emphasis is placed upon design procedures, hydrodynamic coefficients applicable in practice, and the specification of structural response parameters relevant to the OTEC cold water pipe. There are important problems associated with the shedding of vortices from cylinders in waves and from the combined action of waves and currents, but these complex fluid/structure interactions are not considered in this paper.     

波流共同作用下海底子母管线水动力的物理模型试验研究

通过物理模型试验研究海底子母管线分别在规则波加流和不规则波加流作用下的水动力特性。基于Morison方程,采用"等效直径法"分析得到子母管线拖曳力系数C_D,惯性力系数C_M和升力系数C_L(C_D+,C_L-)。试验分别考察了流速比U_c/U_w,母管与海床间隙比e/D及子母管间的相对缝隙G/D对海底子母管线水动力系数的影响。结果表明水动力系数随U_c/U_w的增大而减小;当e/D<0.5时,海床对子母管线受力的影响比较明显,C_D,C_M及C_L+均随e/D增大而减小,|C_L-|随e/D增大而增大;对子母管间的相互影响也不可忽略,C_D,C_M和|C_L-|均随G/D增大而减小,C_L+值随G/D增大而增大。     

波流共同作用下海底子母管线水动力的物理模型试验研究

通过物理模型试验研究海底子母管线分别在规则波加流和不规则波加流作用下的水动力特性。基于Morison方程,采用"等效直径法"分析得到子母管线拖曳力系数C_D,惯性力系数C_M和升力系数C_L(C_D⁺,C_L^-)。试验分别考察了流速比U_c/U_w,母管与海床间隙比e/D及子母管间的相对缝隙G/D对海底子母管线水动力系数的影响。结果表明水动力系数随U_c/U_w的增大而减小;当e/D<0.5时,海床对子母管线受力的影响比较明显,C_D,C_M及C_L⁺均随e/D增大而减小,|C_L^-|随e/D增大而增大;对子母管间的相互影响也不可忽略,C_D,C_M和|C_L^-|均随G/D增大而减小,C_L⁺值随G/D增大而增大。     

The effect of shroud on vortex shedding mechanism of cylinder

In the present study, flow characteristics were investigated experimentally using particle image velocimetry technique (PIV) in a gap between a solid cylinder and a shroud to reveal the effect of shroud diameter (D_s) and porosity (β) on the vortex shedding mechanism of the cylinder. Porosity (varied from β = 0.3 to 0.7) and diameter ratio (D/D_s = 0.4, 0.5 and 0.6) were main parameters examined at a Reynolds number of Re = 5000. For the porosity values of β ≤ 0.5, it is observed that vortex formation of the cylinder occurs only in the gap and shroud produces its own wake flow patterns. Penetrating flow through the shroud extends the shear layers on the both sides of the shroud through the downstream direction and prevents the interaction of shear layers in the near wake region. The diameter ratio and the porosity are impactful on the wake flow patterns in outer region of the shroud since they are determinant of the penetrating flow rate. Force measurements were also performed in the air tunnel in order to reveal the effect of shroud on the drag coefficient of cylinder. It is found that the drag coefficient of the cylinders are reduced significantly by shrouds when compared with that obtained from the bare cylinder case. However, the drag coefficient of the cylinder together with the shroud is higher than the bare cylinder for all cases since the shrouds enlarge the area exposed to the flow.     

Flow around a partly buried cylinder in a steady current

The flow around a cylinder, surface mounted or partly buried has been examined at Reynolds number of 1.3×10⁴ and 2.6×10⁴ by using the flow visualization method in the case of steady current. The lengths of the upstream and downstream separation regions were determined and the characteristics of the flow area were discussed for the cylinder having different burial depth to the diameter ratio (G/D). For comparsion, some numerical results obtained from the application of the FLUENT, computational fluid dynamics (CFD) software package have also been presented. Both experimental and numerical results indicated that the lengths of the separation regions near the upstream and downstream of the cylinder decreased with the increasing burial ratio (G/D=0, 0.20, 0.50). The results have significant implications both for the illustration of the potential for using CFD software and highlighting the need for data of two dimensional flow around the buried cylinder.     

Force and flow characteristics of a circular cylinder with uniform surface roughness at subcritical Reynolds numbers

The main purpose of this study is to establish a better understanding of the relationship between drag reduction and surface roughness. Experiments were conducted to measure the force and flow characteristics of a circular cylinder with different types of artificial surface roughness over the range 6 × 10³ < Re < 8 × 10⁴ (Re is based on the cylinder diameter D). The roughness cylinder was formed by covering the exterior surface of the cylinder with uniformly distributed (1) sandpaper, (2) netting, and (3) dimples. The roughness coefficient ranged from k/D = 0.0028 to 0.025 (k is the roughness height). A detailed quantitative measurement of the flow field around the cylinder using Particle Imaging Velocimetry (PIV) was carried out. The hydrodynamic force coefficients (drag and lift) of the rough cylinders are compared against those of a smooth cylinder measured under the same flow conditions. It is found that certain configuration of surface roughness significantly reduces the mean drag coefficient of the cylinder, particularly at large Reynolds numbers. In addition, the root-mean-square (r.m.s.) lift coefficient of the rough cylinders is considerably lower than that of a smooth cylinder.     

Minimization of drift force on a floating cylinder by optimizing the flexural rigidity of a concentric annular plate

The deployment of suitable configurations of mutually interacting floating bodies for efficiently controlling their hydrodynamic interactions towards the reduction of the wave drift forces and, thus, of the mooring lines’ loads, has, nowadays, gained a great scientific interest. In this paper, the hydrodynamic behaviour of a floating cylinder and a concentric annular flexible plate is analysed in the frequency domain aiming at the minimization of the drift forces acting on the cylinder by optimizing the flexural rigidity of the plate. The diffraction/radiation problem is solved using a higher-order boundary element method. The analysis is implemented assuming that both floating bodies oscillate freely in heave, while for the plate, flexible modes are, additionally, considered for describing its structural deformations. The required modes shapes are determined in vacuum (“dry” mode superposition approach) through analytical expressions. The flexural rigidity of the plate, D, is optimized at a specific wave number using a real-coded genetic algorithm. Initially, results are compared with numerical results of other investigators for the case of two rigid concentric floating cylinders. Next, extended results are presented, focusing on the effect of D, including its optimum value, on various physical quantities describing the behaviour of both the cylinder and the plate. Contrary to the isolated cylinder, the presence of the plate introduces sharp peaks in the variation pattern of the drift force of the cylinder, bounded at specific wave numbers, where resonance of the seiche mode of water motion in the annular cavity or of specific flexible modes of the plate occurs. However, by reducing D to its optimum value, the cylinder’s drift force obtains practically zero values at the target wave number, due to an efficient improvement of the wave field in the annular cavity around the cylinder. Moreover, a great reduction of the drift force compared to the isolated cylinder is achieved in the subsequent high frequency range.     

Nonlinear hydrodynamic pressures generated by a moving high-rise offshore cylinder

Both analytical (small time expansion) and numerical (finite-difference) approaches have been used to solve the earthquake-induced nonlinear hydrodynamic pressure acting on a rigid high rise offshore cylinder. For the high rise offshore cylinder, the most part of the flow field is independent of z and a three dimensional hydrodynamic analysis can be reduced to a two dimensional analysis. At onset, the dimensionless ground displacement ?² = 0 for the two dimensional analysis, the normalized hydrodynamic pressures across cylinder face is a constant and is independent of the radius of the cylinder. The normalized horizontal force coefficient C_fx is independent of intensity of ground acceleration and is approximately linear and proportional to ?² and its onset value is equal to π. For a linear analysis i.e. neglecting nonlinear convective acceleration, the normalized hydrodynamic pressure coefficient is also independent of the radius of cylinder. The analytical method was good for ground motion in a single direction, the results of simultaneous action of two components of ground acceleration can be obtained by the superposition of the results due to separate excitation. But the superposition method is only valid in the linear analysis. For highly nonlinear problem, the present finite difference approach is recommended.     

Three-dimensional flow around a square cylinder near a wall

In this study, two- and three-dimensional numerical simulations were performed to investigate the effect of the flow structure in the wake of a square cylinder placed near a plane wall by applying a fully implicit finite-difference method to the Navier-Stokes equations. The gap ratio between the cylinder and the wall, G/D, was varied from 0.2 to 4 for the Reynolds numbers of 175, 185 and 250. The role of the 3D structure on the lift and drag coefficients and Strouhal number was investigated. The results were compared with those of the 2D numerical simulations. The deviations of the 3D flow structure of the cylinder-wall pair from that of a single cylinder were also reported. At Re=250, B type secondary vortices were determined in the wake region. At Re=175 and 185, transition from A type vortex to fully periodic B type vortices was observed when the cylinder was brought closer to the wall.     

Numerical investigation on the suppression of VIV for a circular cylinder by three small control rods

Laminar flow past a circular cylinder with 3 small control rods is investigated by numerical simulation. This study is concerned with the suppression efficacy of vortex induced vibration by small control rods located around a main cylinder. The effects of the attack angle and rod-to-cylinder gap ratio on the hydrodynamics and vibration responses of the main cylinder are investigated. The attack angle of α = 45° is performed as the critical angle for VIV suppression of 3 control rods. The 3 control rods have no effect on VIV suppression when the attack angle is less than the critical angle. The 3 control rods have an excellent VIV suppression efficacy when the attack angle is larger than the critical angle. The transverse vibration frequency of the cylinder with 3 control rods is less than that for an isolated cylinder for all the configurations. The numerical results for the configurations of α = 45° & 60°, G/D = 0.6–1.2 show excellent suppression efficient among the cases investigated in this study. The best suppression efficient is found at α = 45°, G/D = 0.9 for 3 control rods. 2 rods in behind of the main cylinder perform more efficient than that of 1 rod in front for VIV suppression as the gap ratio of G/D less than 1.0.     

The influence of corner radius on the forces experienced by cylindrical bluff bodies in oscillatory flow

Measurements are presented of the effects of corner radius on the hydrodynamic forces experienced by cylindrical bluff bodies in oscillatory flow over the Keulegan Carpenter number range from 1 to 100. The range of Reynolds number covered is from 200 to 2 × 10⁴ and two basic cross-sectional shapes, namely a square and a diamond, were used in the investigation. Drag coefficients in oscillatory flow are found to be more sensitive to corner radius than in steady flow. At a fixed Keulegan Carpenter number the drag coefficient of a diamond section decreases with increasing corner radius and the reduction is more marked at low Keulegan Carpenter numbers. The drag of a square section does not follow a consistent trend with corner radius and for high Keulegan Carpenter numbers the rounded square with a corner radius of 0.265D (where D is the width of the model normal to the flow) can have a drag coefficient equal to half the value for a circular cylinder.     

Flow induced vibrations of a sharp edge square cylinder in the wake of a circular cylinder

The response of an oscillating circular cylinder at the wake of an upstream fixed circular cylinder was classified by different researchers as galloping, wake induced galloping or wake induced vibration. Furthermore it is already known that a sharp edge square cylinder would undergo galloping if it is subjected to uniform flow. In this study the influence of the wake of a fixed circular cylinder on the response of a downstream square cylinder at different spacing ratios (S/D = 4, 8, 11) is experimentally investigated. The subject appears not to have received previous attention. The lateral displacements, lift forces and the pressure data from gauges mounted in the wake of the oscillating cylinder are recorded and analyzed. The single degree of freedom vibrating system has a low mass-damping parameter and the Reynolds number ranges from 7.7 × 10² to 3.7 × 10⁴.In contrast to that for two circular cylinders in tandem arrangement, the freely mounted downstream square cylinder displays a VIV type of response at all spacing ratios tested. There is no sign of galloping or wake induced galloping with the square cylinder. With increase at the spacing ratio the cross-flow oscillations decrease. It is shown that the vortices arriving from the upstream fixed circular cylinder play a major role on the shedding mechanism behind the downstream square cylinder and cause the square cylinder to shed vortices with frequencies above Strouhal frequency of the fixed square cylinder (St = 0.13). The VIV type of oscillations in the downstream square cylinder is most probably caused by the vortices newly generated behind the square cylinder.     

On a translating and transversely oscillating cylinder: Part 2: Effect of the velocity ratio on the hydrodynamic forces and the near-wake structure

The unsteady flow past a circular cylinder which starts translating and transversely oscillating from rest in a viscous fluid is investigated at a Reynolds numbers of R=10³ and at a Strouhal number of π/4 and for the maximum oscillatory to translational velocity ratios between 0.1 and 1.0. This study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations. The object of the study is to examine the effect of increase of velocity ratio on the near-wake structure as well as the hydrodynamic forces acting on the cylinder. For all velocity rates a periodic structure of vortex evaluation and shedding develops which is repeated exactly as time advances. Vortex dynamics close behind the body are affected by changing acceleration of the cylinder and a changeover from one mode to a different mode of vortex formation is observed with increase in velocity ratio. A comparison of the present results with the impulsively started translating case has been included to illustrate the effect of velocity ratio on drag at small values of velocity ratio.     

Wave forces on, and water-surface fluctuations around a vertical cylinder encircled by a perforated square caisson

The wave forces and moments on and the water surface fluctuations around a vertical circular cylinder encircled by a perforated square caisson were experimentally investigated. The porosity of the outer square caisson was varied from 4.24 to 14.58%. The in-line wave forces on the inner vertical cylinder are influenced by changing the porosity of the outer caisson, whereas the variations in the water surface fluctuations are less influenced in this porosity range. The in-line moment on the vertical cylinder is relatively less sensitive when the porosity is increased from 4.24 to 8.75%, but varies substantially when it is increased from 8.75 to 14.58%. The force and moment ratio (i.e. the ratio of the force or moment on the vertical cylinder, when it is encircled by the perforated caisson to the force or moment on the cylinder without any protection around it) reduces with increased wave height, H, and wave length, L, whereas the wave height ratio (ratio of the wave height at a point in the vicinity of the structure to the incident wave height) is less sensitive for the varying H and L. A new non-dimensional parameter, p^1.5 (D/L)/(H/d), is introduced to predict the in-line force and moment on the inner vertical cylinder, where d is local water depth, D is the diameter of the inner cylinder and p is the porosity of the outer caisson in percentage. Simple predictive equations for forces, moments and water surface fluctuations are provided.