Hydrodynamic Force Coefficients Research Articles

Freely vibrating circular cylinder in the vicinity of fully developed scour holes at low Reynolds numbers

In this work, a numerical study is conducted on the flow past an elastically mounted circular cylinder with two degrees of freedom (2-DoF) placed in the vicinity of a fully developed scour hole in both two-dimension (2D) and three-dimension (3D). This paper focuses to study how different fully developed scour profiles affect the hydrodynamic quantities of vortex-induced vibrations (VIV) of an elastically mounted circular cylinder in proximity and the flow fields. To begin with, we systematically conduct the 2D simulations at Reynolds number of Re=200 in the laminar flow regime and characterize the cylinder amplitudes, the hydrodynamic force coefficients and phase differences. For the 2D study, two representative fully developed scour hole profiles with Shields parameters of θ*=0.098 and 0.048 are considered and the case of a plane wall (i.e. θ*=∞) is taken into account as a reference for comparison. In the 3D simulations at Re=300, which is at the beginning of the subcritical flow regime, with θ*=0.098, the cylinder response characteristics and the 3D flow fields are investigated. It is shown that the upper boundary of the lock-in regime at θ*=0.048 is much smaller than those of θ*=0.098 and ∞, and the vortex shedding is ceased for Ur ≥ 5.3 at θ*=0.048. It is also found that the equilibrium scour profile affects the mean force coefficients to a large extent: the mean lift coefficient CL¯ for θ*=∞ is larger than those of θ*=0.098 and 0.048 in the pre-lock-in and post-lock-in regimes; and the mean drag coefficient CD¯ for θ*=∞ is larger than those of θ*=0.098 and 0.048 in all regimes.

Water entry of deformable spheres

When a rigid body collides with a liquid surface with sufficient velocity, it creates a splash curtain above the surface and entrains air behind the sphere, creating a cavity below the surface. While cavity dynamics has been studied for over a century, this work focuses on the water entry characteristics of deformable elastomeric spheres, which has not been studied. Upon free surface impact, an elastomeric sphere deforms significantly, giving rise to large-scale material oscillations within the sphere resulting in unique nested cavities. We study these phenomena experimentally with high-speed imaging and image processing techniques. The water entry behaviour of deformable spheres differs from rigid spheres because of the pronounced deformation caused at impact as well as the subsequent material vibration. Our results show that this deformation and vibration can be predicted from material properties and impact conditions. Additionally, by accounting for the sphere deformation in an effective diameter term, we recover previously reported characteristics for time to cavity pinch off and hydrodynamic force coefficients for rigid spheres. Our results also show that velocity change over the first oscillation period scales with the dimensionless ratio of material shear modulus to impact hydrodynamic pressure. Therefore, we are able to describe the water entry characteristics of deformable spheres in terms of material properties and impact conditions.

Structure Design and Force Analysis for a Novel Spherical Robot

At present, exploring the vast unknown fields (including space and ocean) has become a hot topic in various agencies. As a moving carrier, the mobile intelligent robot plays an important role, such as communication base stations and observation platform. In order to adapt to a variety of working conditions, a new type of robot was proposed, which can move freely on land or in water with a circular shell, a single propeller and a pair of heavy pendulum. The pendulum inside the robot is used to adjust the attitude, which makes the robot move flexibly, and the circular shell has the excellent compression capability. In order to analyze the kinematics and dynamics characteristics in water, the hydrodynamic forces are studied before the manufacture by CFD simulation. The new type of spherical robot is simplified into spherical finite element model with the pipe. The hydrodynamic force coefficients of robot are calculated by straight shipping, oblique shipping and cantilevered pool simulation. The testing data of robot are obtained in pool for straight shipping by the experiment. Through the above calculation and contrast, the hydrodynamic results can be proved effectively, which can save time for the improved design of robot in the future.

Towards an understanding of marine fouling effects on the vortex-induced vibrations of circular cylinders: partial coverage issue

The results of in-water vortex-induced vibration (VIV) experiments on circular cylinders artificially covered with barnacles are reported. The paper focusses on the effects of the partial coverage and the shape of the fouling elements. An artificial barnacle typical of marine fouling was synthesised using 3-D printing. Coverage ratios of 80, 50 and 30% were examined and the results compared with those from a smooth cylinder. The Reynolds number ranged from 5.8 × 103 to 6.6 × 104. The experimental results show that the fouling reduced the peak VIV amplitude, narrowed the synchronisation region and lowered the hydrodynamic force coefficients such as the coefficients of lift force RMS, the mean drag force and the fluctuating drag force RMS. The shape of the artificial barnacles had little effect on the maximum oscillation amplitude. The coverage ratio appeared to have a lower impact on the lift force than those on the amplitude and the frequency responses.

Hydrodynamics of pedestrians' instability in floodwaters

Abstract. People's safety is the first objective to be fulfilled by flood risk mitigation measures, and according to existing reports on the causes of casualties, most of the fatalities are due to inappropriate behaviour such as walking or driving in floodwaters. Currently available experimental data on people instability in floodwaters suffer from a large dispersion primarily depending on the large variability of the physical characteristics of the subjects. This paper introduces a dimensionless mobility parameter θP for people partly immersed in flood flows, which accounts for both flood and subject characteristics. The parameter θP is capable of identifying a unique threshold of instability depending on a Froude number, thus reducing the scatter of existing experimental data. Moreover, a three-dimensional (3-D) numerical model describing the detailed geometry of a human body and reproducing a selection of critical pairs of water depth and velocity is presented. The numerical results in terms of hydrodynamic forces and force coefficients are analysed and discussed. Both the mobility parameter θP and the numerical results hint at the crucial role of the Froude number and relative submergence as the most relevant dimensionless numbers to interpret the loss of stability. Finally, the mobility parameter θP is compared with an analogous dimensionless parameter for vehicles' instability in floodwaters, providing a new contribution to support flood risk management and educating people.

Calculations of the flow resistance and heat emission of a sphere in the laminar and high-turbulent gas flows

An early drag crisis can occur at high turbulence of incoming gas flow to a sphere. To study the influence of a crisis on heat transfer from a sphere to gas, a numerical experiment was carried out in which the free gas flow around a sphere with a temperature lower than the sphere temperature was simulated for two cases. The flow was laminar in the first case and highly turbulent in the second case. To take into account turbulence, the kinematic coefficient of turbulent viscosity with a value, which is much higher (up to 2000 times) than that for physical viscosity, was introduced. The results of calculations show that the early drag crisis occurs at Reynolds numbers of about 100 and results in considerable (by four to seven times) decrease in the hydrodynamic force and sphere drag coefficient C d . The early drag crisis is also accompanied by the crisis of heat transfer from a sphere to gas with a decrease in Nusselt numbers Nu by three to six times.

Nonlinear Hydrodynamics of a Floating Cylinder in Oscillatory Flow Alone and Combined with a Current

AbstractThis paper experimentally investigates the nonlinear hydrodynamic forces on a semisubmerged floating collar under full-scale Reynolds number (R) and Keulegan-Carpenter number (KC) oscillatory flow alone and combined with a current. The collar was forced to oscillate harmonically in the direction of the current within a wide range of oscillation amplitudes and frequencies. The first five orders of the horizontal hydrodynamic forces are obtained using Fourier transformation techniques. The influence of the KC, the frequency parameter (β), and the reduced velocity (Vr) on the high-order components of the hydrodynamic force were investigated. The results show that, under oscillatory flows, the first five harmonics of the hydrodynamic force coefficients increase with an increase of KC and β. As the reduced velocity (Vr) increases, the first- and second-order components are greatly affected. These first two order components contribute greatly to the overall hydrodynamic force in the combined flow condit...

Vortex-induced vibration of a flexible cylinder: Interaction of the in-line and cross-flow responses

It has been known that in-line (IL) response will influence cross-flow (CF) vortex shedding forces and vice versa. However, empirical codes for prediction of vortex induced vibrations (VIV) of slender marine structures have so far been limited to handle CF or IL response separately without taking into account the interaction between the two response modes. The present study uses the data from two flexible cylinder VIV experiments. The IL and CF interaction is studied by investigating the response trajectories and the corresponding hydrodynamic force coefficients under different flow conditions. It is found that the hydrodynamic force coefficients estimated from flexible cylinder tests are clearly associated with the trajectories or the motion phase angles between IL and CF displacement. The energy transfer from the fluid to the pipe is related to counter-clockwise trajectories inside the excitation region; while clockwise trajectories are associated with hydrodynamic damping forces. It is also found that the spatial variation of the motion phase angle of a flexible cylinder is influenced by the presence of traveling waves in the response. The motion phase angle is one of the key parameters to be included in the empirical VIV prediction codes in order to model the IL and CF interaction of a flexible cylinder.

Numerical Investigation of Water Entry of Half Hydrophilic and Half Hydrophobic Spheres

A numerical simulation to investigate the water entry of half-half sphere which is hydrophobic on one hemisphere and hydrophilic on the other is performed. Particular attention is given to the simulation method based on solving the Navier-Stokes equations coupled with VOF (volume of fluid) method and CSF (continuum surface force) method. Numerical results predicted experimental results, validating the suitability of the numerical approach to simulate the water entry problem of sphere under different wetting conditions. Numerical results show that the water entry of the half-half sphere creates an asymmetric cavity and “cardioid” splash, causing the sphere to travel laterally from the hydrophobic side to the hydrophilic side. Further investigations show that the density ratio and mismatch of asymmetric in wetting condition affect the trajectory, velocity, and acceleration of the half-half sphere during water entry. In addition, the total hydrodynamic force coefficient is investigated as a result of the forces acting on the sphere during water entry dictated by the cavity formation.

U-shaped fairings suppress vortex-induced vibrations for cylinders in cross-flow

We employ three-dimensional direct and large-eddy numerical simulations of the vibrations and flow past cylinders fitted with free-to-rotate U-shaped fairings placed in a cross-flow at Reynolds number $100\leqslant \mathit{Re}\leqslant 10\,000$. Such fairings are nearly neutrally buoyant devices fitted along the axis of long circular risers to suppress vortex-induced vibrations (VIVs). We consider three different geometric configurations: a homogeneous fairing, and two configurations (denoted A and AB) involving a gap between adjacent segments. For the latter two cases, we investigate the effect of the gap on the hydrodynamic force coefficients and the translational and rotational motions of the system. For all configurations, as the Reynolds number increases beyond 500, both the lift and drag coefficients decrease. Compared to a plain cylinder, a homogeneous fairing system (no gaps) can help reduce the drag force coefficient by 15 % for reduced velocity $U^{\ast }=4.65$, while a type A gap system can reduce the drag force coefficient by almost 50 % for reduced velocity $U^{\ast }=3.5,4.65,6$, and, correspondingly, the vibration response of the combined system, as well as the fairing rotation amplitude, are substantially reduced. For a homogeneous fairing, the cross-flow amplitude is reduced by about 80 %, whereas for fairings with a gap longer than half a cylinder diameter, VIVs are completely eliminated, resulting in additional reduction in the drag coefficient. We have related such VIV suppression or elimination to the features of the wake flow structure. We find that a gap causes the generation of strong streamwise vorticity in the gap region that interferes destructively with the vorticity generated by the fairings, hence disorganizing the formation of coherent spanwise cortical patterns. We provide visualization of the incoherent wake flow that leads to total elimination of the vibration and rotation of the fairing–cylinder system. Finally, we investigate the effect of the friction coefficient between cylinder and fairing. The effect overall is small, even when the friction coefficients of adjacent segments are different. In some cases the equilibrium positions of the fairings are rotated by a small angle on either side of the centreline, in a symmetry-breaking bifurcation, which depends strongly on Reynolds number.

Numerical simulation of flow past twin near-wall circular cylinders in tandem arrangement at low Reynolds number

Fluid flow past twin circular cylinders in a tandem arrangement placed near a plane wall was investigated by means of numerical simulations. The two-dimensional Navier-Stokes equations were solved with a three-step finite element method at a relatively low Reynolds number of Re = 200 for various dimensionless ratios of 0.25 ≤ G/D ≤ 2.0 and 1.0 ≤ L/D ≤ 4.0, where D is the cylinder diameter, L is the center-to-center distance between the two cylinders, and G is the gap between the lowest surface of the twin cylinders and the plane wall. The influences of G/D and L/D on the hydrodynamic force coefficients, Strouhal numbers, and vortex shedding modes were examined. Three different vortex shedding modes of the near wake were identified according to the numerical results. It was found that the hydrodynamic force coefficients and vortex shedding modes are quite different with respect to various combinations of G/D and L/D. For very small values of G/D, the vortex shedding is completely suppressed, resulting in the root mean square (RMS) values of drag and lift coefficients of both cylinders and the Strouhal number for the downstream cylinder being almost zero. The mean drag coefficient of the upstream cylinder is larger than that of the downstream cylinder for the same combination of G/D and L/D. It is also observed that change in the vortex shedding modes leads to a significant increase in the RMS values of drag and lift coefficients.

Hydrodynamics of flow over a transversely oscillating circular cylinder beneath a free surface

In this paper, hydrodynamic force coefficients and wake vortex structures of uniform flow over a transversely oscillating circular cylinder beneath a free surface were numerically investigated by an adaptive Cartesian cut-cell/level-set method. At a fixed Reynolds number, 100, a series of simulations covering three Froude numbers, two submergence depths, and three oscillation amplitudes were performed over a wide range of oscillation frequency. Results show that, for a deeply submerged cylinder with sufficiently large oscillation amplitudes, both the lift amplitude jump and the lift phase sharp drop exist, not accompanied by significant changes of vortex shedding timing. The near-cylinder vortex structure changes when the lift amplitude jump occurs. For a cylinder oscillating beneath a free surface, larger oscillation amplitude or submergence depth causes higher time-averaged drag for frequency ratio (=oscillation frequency/natural vortex shedding frequency) greater than 1.25. All near-free-surface cases exhibit negative time-averaged lift the magnitude of which increases with decreasing submergence depth. In contrast to a deeply submerged cylinder, occurrences of beating in the temporal variation of lift are fewer for a cylinder oscillating beneath a free surface, especially for small submergence depth. For the highest Froude number investigated, the lift frequency is locked to the cylinder oscillation frequency for frequency ratios higher than one. The vortex shedding mode tends to be double-row for deep and single-row for shallow submergence. Proximity to the free surface would change or destroy the near-cylinder vortex structure characteristic of deep-submergence cases. The lift amplitude jump is smoother for smaller submergence depth. Similar to deep-submergence cases, the vortex shedding frequency is not necessarily the same as the primary-mode frequency of the lift coefficient. The frequency of the induced free surface wave is exactly the cylinder oscillation frequency. The trends of wave length variation with the Froude number and frequency ratio agree with those predicted by the linear theory of small-amplitude free surface waves.

Numerical Simulation of Transient Flows around a 3D Pitching Hydrofoil

The objective of this paper is to investigate the hydrodynamic characteristics of the transient flows around a 3D pitching hydrofoil via numerical studies, where the effects of tunnel wall boundary layer and gap flows are considered. Simulations are performed using an unsteady Reynolds Average Navier-Stokes solver and the k-ω SST turbulence model, coupled with a two-equation γ-Reθ transition model. Hydrodynamic forces and flow structures are compared to the results with the equivalent 2D computations. During the upward pitching stage, the transition phenomenon is accurately captured by both the 2D and 3D simulations. The slightly lower lift and suction side loading coefficients predicted by the 3D simulation are due to the pressure effects caused by the tip gap flow. During the dynamic stall stage, the 2D case exhibits a clear overshoot on the hydrodynamic force coefficients and the 3D simulation results better agree with the experimental results. During the downward pitching stage, the flow transitions back to laminar. As for the effect of gap flow and the wall boundary condition, the gap flow causes disturbances to the formation and development of the vortex structures, resulting in the complex distribution of the three-dimensional streamlines and the particle path.

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.

Introduction of MMG standard method for ship maneuvering predictions

Abstract A lot of simulation methods based on Maneuvering Modeling Group (MMG) model for ship maneuvering have been presented. Many simulation methods sometimes harm the adaptability of hydrodynamic force data for the maneuvering simulations since one method may be not applicable to other method in general. To avoid this, basic part of the method should be common. Under such a background, research committee on “standardization of mathematical model for ship maneuvering predictions” was organized by the Japan Society of Naval Architects and Ocean Engineers and proposed a prototype of maneuvering prediction method for ships, called “MMG standard method”. In this article, the MMG standard method is introduced. The MMG standard method is composed of 4 elements; maneuvering simulation model, procedure of the required captive model tests to capture the hydrodynamic force characteristics, analysis method for determining the hydrodynamic force coefficients for maneuvering simulations, and prediction method for maneuvering motions of a ship in fullscale. KVLCC2 tanker is selected as a sample ship and the captive mode test results are presented with a process of the data analysis. Using the hydrodynamic force coefficients presented, maneuvering simulations are carried out for KVLCC2 model and the fullscale ship for validation of the method. The present method can roughly capture the maneuvering motions and is useful for the maneuvering predictions in fullscale.

Shape Effects on Viscous Damping and Motion of Heaving Cylinders1

Fluid viscosity is known to influence hydrodynamic forces on a floating body in motion, particularly when the motion amplitude is large and the body is of bluff shape. While traditionally these hydrodynamic force or force coefficients have been predicted by inviscid-fluid theory, much recent advances had taken place in the inclusion of viscous effects. Sophisticated Reynolds-Averaged Navier–Stokes (RANS) software are increasingly popular. However, they are often too elaborate for a systematic study of various parameters, geometry or frequency, where many runs with extensive data grid generation are needed. The Free-Surface Random-Vortex Method (FSRVM) developed at UC Berkeley in the early 2000 offers a middle-ground alternative, by which the viscous-fluid motion can be modeled by allowing vorticity generation be either turned on or turned off. The heavily validated FSRVM methodology is applied in this paper to examine how the draft-to-beam ratio and the shaping details of two-dimensional cylinders can alter the added inertia and viscous damping properties. A collection of four shapes is studied, varying from rectangles with sharp bilge corners to a reversed-curvature wedge shape. For these shapes, basic hydrodynamic properties are examined, with the effects of viscosity considered. With the use of these hydrodynamic coefficients, the motion response of the cylinders in waves is also investigated. The sources of viscous damping are clarified.

Wave Forces on Linear Arrays of Rigid Vertical Circular Cylinders in Regular Waves

The present investigation aims to experimentally determine the variation of forces and force coefficients acting on circular cylinders, which are arranged in a linear array along the direction of the waves. Most commonly used structural and non-structural elements in the construction of offshore platforms are circular cylindrical members. In many cases, these members are found in very close neighbourhood of each other, thus modifying the surrounding flow and wave forces acting on them. Model tests were conducted in the wave tank on a maximum of four cylinders of the same diameter. A reasonable scale factor was chosen considering the pertinent factors such as water depth, wave generating capability and accuracy of measurements. The cylinders were installed inside the wave tank as vertical cantilevers fixed at the top. Wave forces acting on the cylinders were measured using special wave force sensors exclusively designed and fabricated for the present project, while the wave profiles were recorded using wave probes installed in the wave basin. The results confirmed the presence of a force shielding effect on the trailing cylinders by the leading cylinders with few exceptions. The findings also substantiated the significant modification of the forces on cylinders when they are present in a linear array. A common practice adopted for the design of offshore platforms was identified with a possibility of underestimating the wave forces acting on the cylindrical elements. In many cases, the experimentally computed hydrodynamic force coefficients were found to be lower than the standard values adopted by various design codes. These findings portray the significance of the present work in achieving economy in the design of jacket platforms and risers.

A numerical investigation of flow around octopus-like arms: near-wake vortex patterns and force development

The fluid dynamics of cephalopods has so far received little attention in the literature, due to their complexity in structure and locomotion. The flow around octopuses, in particular, can be complicated due to their agile and dexterous arms, which frequently display some of the most diverse mechanisms of motion. The study of this flow amounts to a specific instance of the hydrodynamics problem for rough tapered cylinder geometries. The outstanding manipulative and locomotor skills of octopuses could inspire the development of advanced robotic arms, able to operate in fluid environments. Our primary aim was to study the hydrodynamic characteristics of such bio-inspired robotic models and to derive the hydrodynamic force coefficients as a concise description of the vortical flow effects. Utilizing computational fluid dynamic methods, the coefficients were computed on realistic morphologies of octopus-like arm models undergoing prescribed solid-body movements; such motions occur in nature for short durations in time, e.g. during reaching movements and exploratory behaviors. Numerical simulations were performed on translating, impulsively rotating, and maneuvering arms, around which the flow field structures were investigated. The results reveal in detail the generation of complex vortical flow structures around the moving arms. Hydrodynamic forces acting on a translating arm depend on the angle of incidence; forces generated during impulsive rotations of the arms are independent of their exact morphology and the angle of rotation; periodic motions based on a slow recovery and a fast power stroke are able to produce considerable propulsive thrust while harmonic motions are not. Parts of these results have been employed in bio-inspired models of underwater robotic mechanisms. This investigation may further assist elucidating the hydrodynamics underlying aspects of octopus locomotion and exploratory behaviors.

Experimental study of the hydrodynamic force on a pipeline subjected to vertical seabed movement

Using an underwater shaking table, model tests of a free-spanning flexible submarine pipe subjected to vertical seabed movement were carried out. The fluid field adjacent to the pipe and the hydrodynamic force exerted on the pipe were measured. Based on Morison's equation, the hydrodynamic force coefficients related to earthquake, such as the drag coefficient CD and the added mass coefficient CA, were obtained by the least squares method. The effects of the Reynolds number Re, the Keulegan–Carpenter number Kc, the water depth d, and the span height e on the hydrodynamic coefficients were analyzed. The experimental results illustrate that Re and Kc have a strong effect on the hydrodynamic forces imposed on the pipeline under vertical earthquakes. The variation of the hydrodynamic coefficients with Re and Kc is fitted by a regression analysis. The calculated results from the hydrodynamic force model suitable for vertical earthquakes are in good agreement with the measured data.

Hydroelasticity of Four Flexible Cylinders in Square Arrangement Subjected to Uniform Cross-Flow

Groups of cylinders can be found in many engineering fields such as marine and civil applications. The behavior of the group cylinders can be very complex because it undergoes the mutual effects of adjacent cylinders arranged in different positions. In this paper, the results of a study on the dynamics of a group of flexible cylinders in square arrangements along with a single (isolated) cylinder subjected to uniform cross-flow (CF) are presented. Four flexible cylinders of the same size, properties, and pretensions were tested in two configurations with different center-to-center separations. Reynolds number ranged from 1400 to 20,000 (subcritical regime).The parameter of reduced velocity reached up to 19. The aspect ratio of all the cylinders was 162 (length/diameter). Mass ratio (cylinders mass/displaced water) was 1.17. The amplitude ratio of the CF vibration of the downstream cylinders, hydrodynamic force coefficients including mean and fluctuating components of the drag and lift forces, tension variation of the downstream cylinder, and frequency responses in both CF and inline (IL) directions were analyzed. All the cylinders excited up to the second and fourth mode of vibrations for CF and IL directions, respectively. Mean drag coefficient of the upstream cylinders are almost twice those of the downstream cylinders. The mean lift coefficient is much higher for the upstream cylinders than the downstream cylinders with different positive and negative signs. The IL and CF frequencies of the downstream cylinders are lower than those of the upstream ones and the single cylinder.