Vertical Hydrodynamic Forces Research Articles

A comparative study on water entry and water walking events of elastic spheres

This paper presents a comparative study on water entry and water walking events of elastic spheres using a fluid–structure interaction method. The sphere displacements, cavity formations, and hydrodynamic characteristics during the water entry and water walking events are investigated. When the impact angle decreases, an obliquely impacting elastic sphere on the water surface can undergo a transition from water entry events to water walking events. Based on the morphological classification of the cavity opening, the shapes of cavity openings formed by elastic spheres can be roughly predicted from material properties and impact conditions. Furthermore, the water walking event is characterized by three typical stages: impact below the surface, walking across the surface, and skipping from the surface. Each stage is analyzed in terms of sphere displacements and hydrodynamic characteristics. The results also show that the vertical hydrodynamic forces acting on elastic spheres are not always smaller than those acting on rigid spheres at all impact angles. The critical impact angle that results in an equivalent vertical hydrodynamic force acting on both elastic and rigid spheres can be predicted from the material properties and impact conditions of the elastic sphere.

Water impact of deformable spheres with vertical and oblique entries

At low Froude numbers, vertical and oblique impacts of deformable spheres into water are performed. The dependence levels of the hydrodynamics, cavity formations, and stress responses on the oblique angle are investigated. Based on theoretical and numerical analyses, the differences between the vertical and oblique impacts in sphere deformations and cavity formations are clarified. Elastic forces inside the sphere induce different models of the deformation behaviors during oblique water entry, and the sphere with a smaller oblique angle extends the formation time of the oblate deformation and nested cavity. Over a single deformation period, the vertical hydrodynamic forces do not continuously increase with the oblique angle, and they depend on the deformation behavior. Additionally, the evolution in the high-stress area at the bottom of the sphere caused by the oblique motion is similar to a solar eclipse. Over the first deformation period, the energy change in the sphere with different oblique angles can be predicted from the dimensionless ratio of the material shear modulus to the impact hydrodynamic pressure.

Numerical simulation of free-surface waves past semi-submerged two-dimensional rectangular prisms with different aspect ratios and rounding chamfer radii

Free-surface waves past two-dimensional, semi-submerged horizontal rectangular prisms are simulated using OpenFOAM. The effects of prism aspect ratios, rounding chamfer radii, incident wave amplitudes and wavelengths on the hydrodynamic forces on the prism are investigated. The simulations are performed by solving the Navier-Stokes equations without turbulence modelling, and the volume of fluid (VOF) method is employed to capture the interface between water and air. Validation studies are carried out by simulating free-surface waves past a semi-submerged horizontal circular cylinder and a semi-submerged rectangular prism. A good agreement between the present numerical results and the published experimental data in terms of the vertical hydrodynamic force is observed. The present numerical results for the rectangular prisms show that the horizontal hydrodynamic force decreases with increasing rounding chamfer radius, whereas the vertical hydrodynamic force dose not vary significantly with the corner radius over the range from 0.1D to 0.5D (D is the height of the rectangular prism). In addition, both the vertical and horizontal hydrodynamic forces increase with the increase in incident wave amplitude and prism aspect ratio respectively. Finally, the flow mechanism of water particles around the prism is revealed by investigating the velocity magnitude contours with streamlines.

On the stability of submerged rigid breakwaters against solitary waves

The stability of submerged rigid breakwaters subject to the action of solitary waves is here investigated by an experimental and numerical approach. Attention is paid to the features of the horizontal and vertical hydrodynamic forces which could make these marine structures unstable. The current work considers submerged barriers with square and rectangular sections and three different relative heights. Experimental tests were undertaken in a wave flume, adopting twelve pressure sensors along the external contour of the barriers in order to calculate the hydrodynamic loads. Numerical simulations were performed using the weakly-compressible δ-LES-SPH model. The aim of these simulations was to enlarge the laboratory cases in order to achieve potential critical conditions against sliding, overturning and bearing capacity of foundation. It was found that, by increasing the relative height of the breakwaters, the wave loads tended to grow, particularly for the horizontal ones. This aspect implied that the barrier with the highest relative height represents the most disadvantageous configuration for its stability. For the square barrier, the critical conditions against sliding and overturning appeared in correspondence of the highest wave amplitudes, while an effective area at the foundation/soil interface occurred starting from moderate wave amplitudes. Practical semi-empirical equations to determine the minimum safety factors as a function of wave amplitude, water depth, barrier geometry and materials were deduced.

Performance of submerged semi-circular breakwater under solitary wave in consideration of porous media

Submerged breakwater as the main structure of coastal engineering to protect coast is widely laid on the seabed because of its significant wave-dissipation performance. To reveal the interaction mechanism between waves and submerged breakwater, the hydrodynamic characteristics of a wave passing over different solid breakwaters were numerically and experimentally studied. Compared with the previous research, considering breakwater made up of porous media and the effects of extreme waves generated by hurricanes or tsunamis, this paper systematically investigates the effects of the semi-circular porous medium breakwater on the breaking solitary wave run-up based on a numerical model with the immersed boundary (IB) method. The computational capability of this model is verified firstly. Then, depending on the model, a series of cases are carried out to research the effects of different breakwaters on the run-up of solitary waves. The results show that the influence of porous breakwater on wave propagation is more significant than that of the solid breakwater. With the increase of the gravel particle median diameter, the maximum run-up height and the horizontal hydrodynamic force on the breakwater decrease, while the vertical hydrodynamic force on the breakwater increases. Increasing the size of the breakwater is beneficial to reducing the wave run-up height and the forces on the sloping beach. Compared with the single breakwater, the impact of the tandem breakwater on the wave propagation is more significant.

Determination of Force Coefficients for a Submerged Rigid Breakwater under the Action of Solitary Waves

We present an analysis related to the evaluation of Morison and transverse force coefficients in the case of a submerged square barrier subject to the action of solitary waves. To this purpose, two-dimensional experimental research was undertaken in the wave flume of the University of Calabria, in which a rigid square barrier was provided by a discrete battery of pressure sensors to determine the horizontal and vertical hydrodynamic forces. A total set of 18 laboratory tests was carried out by varying the motion law of a piston-type paddle. Owing to the low Keulegan–Carpenter numbers of the tests, the force regime of the physical tests was defined by the dominance of the inertia loads in the horizontal direction and of the lift loads in the vertical one. Through the use of the time series of wave forces and the undisturbed kinematics, drag, horizontal inertia, lift, and vertical inertia coefficients in the Morison and transverse semi-empirical schemes were calculated using time-domain approaches, adopting the WLS1 method for the minimization of the difference between the maximum forces and the linked phase shifts by comparing laboratory and calculated wave loads. Practical equations to calculate these coefficients as a function of the wave non-linearity were introduced. The obtained results highlighted the prevalence of the horizontal forces in comparison with the vertical ones which, however, prove to be fundamental for stability purposes of the barrier. An overall good agreement between the experimental forces and those calculated by the calibrated semi-empirical schemes was found, particularly for the positive horizontal and vertical loads. The analysis of the hydrodynamic coefficients showed a decreasing trend for the drag, horizontal inertia, and lift coefficients as a function of the wave non-linearity, while the vertical inertia coefficient underlined an initial increasing trend and a successive slight decreasing trend.

Effect of convergent duct geometry on the energy extraction performance of tandem oscillating hydrofoils system

In the present study, a new hydrokinetic energy harvester concept based on the tandem oscillating hydrofoils configuration is numerically investigated. Unsteady turbulent two dimensional flow simulations were performed, by using the commercial finite volume computational fluid dynamics code FLUENT, to study the power extraction from tandem hydrofoils oscillating inside a convergent duct. A sinusoidal function was used to interpret the plunging/pitching motion of NACA 0015 hydrofoil. Computations were carried out for the different configurations of area ratios (AR) that is defined as the ratio of the upstream hydrofoil’s inlet cross section (A1) to the downstream hydrofoil’s inlet cross section (A2) ranging from 1.0 (without the convergent section) to AR = 2.6. The study revealed that the power extraction was enhanced by the increased incoming flow velocity enabled by the geometry of the convergent duct, which positively affected the total pressure as well as the hydrofoil-vortex interaction time and resulted the generation of larger vertical hydrodynamic force. Upon analysis of the obtained results, it is found that the energy extraction efficiency is improved, compared to that of the conventional tandem configuration where the hydrofoils move in an open flow space, and, as the area ratio (AR) increased, the amount of extracted power becomes higher in a proportion ranging from 4% to 80%. The concept was numerically tested for tandem and single configurations and for non-dimensional frequencies in the range of f∗=0.04 - 0.20. One interesting finding is that, due to some positive effect of hydrofoil-vortex interaction, and at a specified area ratio and frequency, the downstream hydrofoil efficiency exceeds the efficiency of a single hydrofoil located at exactly same position as the downstream hydrofoil in the tandem configuration. The frequency and the area ratio are found to be critical factors that determine whether the downstream hydrofoil-vortex interaction is favorable or unfavorable. An optimal area ratio/frequency combination results in a positive hydrofoil-vortex interaction effect and allows the downstream hydrofoil to contribute positively to the total power extraction as a single hydrofoil. Based on the present results, and for an optimal efficient energy harvester design, a new correlation is suggested in order to properly control the area ratio in accordance with the variation of the oscillating frequency leading to more power production and high performance of the oscillating tandem hydrofoils. It is anticipated that this new innovative technique will be applied to improve the existing energy harvester devices.

Lifting off a solid sphere from a flat bottom by laminar fluid flow

AbstractWe perform quantitative visualization experiments on the vertical (z‐direction) motion of a spherical solid particle being lifted off a horizontal flat bottom due to laminar fluid flow generated by a revolving impeller. Describing the observed motion of the particle in terms of a constant vertical hydrodynamic force overcoming gravity and the lubrication force has limited success. For this reason, we hypothesize that the hydrodynamic force on the particle quickly increases with its distance from the bottom. This hypothesis is supported by detailed numerical simulations of the flow around the particle. Integrating the equation of motion of the sphere with the vertical hydrodynamic force as a linear function ofzderived from simulations provides an adequate description of the experimentally observed vertical motion of the particle.

Comparison of CFD determined squat on sailing ship MIRCEA with empirical methods

The paper presents a study of hydrodynamic parameters related to ship squat acting on sailing ship MIRCEA hull in shallow waters, using CFD methods. The vertical hydrodynamic forces obtained in ANSYS CFX were analysed in respect with various domain depths and ship’s speeds, but also used for squat calculations. In order to evaluate the reliability of previously determined squat, a comparison study was made with nine of the most common empirical formulae for calculating squat in open shallow waters, ranging from Barrass to Huuska or Eryuzlu and Hausser. Some of these methods offer good results and were often experimentally validated with scale models.

An experimental and numerical study on solitary wave loads at cylinders near the bed

The present study describes an experimental and numerical investigation on the horizontal and vertical hydrodynamic forces given by solitary waves on horizontal circular cylinders placed near a rigid horizontal bed. The experimental campaign was conducted in the wave channel of the University of Calabria in which twelve pressure sensors were installed along the external surface of a cylinder located at gap-to-diameter ratios equal to 0.25 and 0.1. The numerical modeling was carried out using the open source OlaFlow model, based on the OpenFOAM solver, in order to simulate the wave forces, also extending the range of experiments. The resulting force field was defined by the dominance of the horizontal inertia force along the flow direction and by the lift force along the transversal one. The values of the hydrodynamic forces and the free stream kinematics were adopted to calibrate the hydrodynamic coefficients (drag, lift and horizontal and vertical inertia) involved in the Morison formula and in a proposed version of the transverse equation through the use of the weighted least square approach. For practical aims, semi-analytical relationships to determine the hydrodynamic coefficients as a function of wave amplitude and water depth are presented.

Numerical simulations of free-surface waves past two vertically aligned horizontal circular cylinders

A two-dimensional numerical model based on Navier-Stokes equations is employed to simulate free surface waves past two vertically aligned horizontal circular cylinders. The volume of fluid method is used to capture the characteristics of the free surface. The numerical simulations of free surface waves past a partially-submerged horizontal circular cylinder with different submerged depths and wave heights are carried out as validation studies of the present numerical model. The numerical results agree well with the published experimental results obtained by Dixon et al. (1979) in terms of vertical hydrodynamic forces. Free surface waves past two vertically aligned horizontal circular cylinders are computed using the validated numerical model. The influences of the spacing between the two cylinders on the vertical hydrodynamic forces on and the free surface elevations around the cylinders are investigated in the present study. The results indicate that the vertical spacing between the two cylinders has a significant effect on the vertical hydrodynamic forces of the cylinder at the lower location, while the vertical hydrodynamic forces of the cylinder at the upper location can be only affected when the vertical spacing is small.

Numerical Study of the Influence of Tidal Current on Submarine Pipeline Based on the SIFOM–FVCOM Coupling Model

The interaction between coastal ocean flows and the submarine pipeline involved with distinct physical phenomena occurring at a vast range of spatial and temporal scales has always been an important research subject. In this article, the hydrodynamic forces on the submarine pipeline and the characteristics of tidal flows around the pipeline are studied depending on a high-fidelity multi-physics modeling system (SIFOM–FVCOM), which is an integration of the Solver for Incompressible Flow on the Overset Meshes (SIFOM) and the Finite Volume Coastal Ocean Model (FVCOM). The interactions between coastal ocean flows and the submarine pipeline are numerically simulated in a channel flume, the results of which show that the hydrodynamic forces on the pipeline increase with the increase of tidal amplitude and the decrease of water depth. Additionally, when scour happens under the pipeline, the numerical simulation of the suspended pipeline is also carried out, showing that the maximum horizontal hydrodynamic forces on the pipeline reduce and the vertical hydrodynamic forces grow with the increase of the scour depth. According to the results of the simulations in this study, an empirical formula for estimating the hydrodynamic forces on the submarine pipeline caused by coastal ocean flows is given, which might be useful in engineering problems. The results of the study also reveal the basic features of flow structures around the submarine pipeline and its hydrodynamic forces caused by tidal flows, which contributes to the design of submarine pipelines.

Experimental Measurement of Dolphin Thrust Generated during a Tail Stand Using DPIV

Estimation of force generated by dolphins has long been debated. The problem was that indirect estimates of force production for dolphins resulted in low values that could not be validated. Bubble digital particle image velocimetry (DPIV) measured hydrodynamic force production for swimming dolphins and demonstrated high force production. To validate the bubble DPIV and reconcile force production measurements, two bottlenose dolphins (Tursiops truncatus) performing tail stands were measured with bubble DPIV. Microbubbles were generated from a finely porous hose and compressed air source. Displacement of the bubbles by the propulsive motions of the dolphin was tracked with a high-speed video camera. Oscillations of the dolphin flukes generated strong vortices and a downward directed jet flow into the wake. Application of the Kutta–Joukowski theorem measuring vortex circulations yielded forces up to 997.3 N. Another video camera recorded body height above the water surface to determine the mass-force of the dolphin above the water surface. For the dolphin to hold its position above the water surface, the mass-force approximately balanced the vertical hydrodynamic force from the flukes. The results demonstrated the fluke motions generate high sustained forces roughly equal to the dolphin’s weight out of the water. Bubble DPIV validated high forces measured previously for thrust generated in swimming by animals and demonstrated a more accurate technique compared to standard aerodynamic analysis.

On-Bottom Stability Analysis of Cylinders under Tsunami-Like Solitary Waves

A two-dimensional (2D) laboratory investigation on the horizontal and vertical hydrodynamic forces induced by tsunami-like solitary waves on horizontal circular cylinders placed on a rigid sea bed is presented. A series of 30 physical model tests was conducted in the wave channel of the University of Calabria in which a rigid circular cylinder was equipped with 12 pressure transducers placed along its external surface to determine the wave loads, with three wave gauges to record the surface elevation. The observed experimental range was characterized by the prevalence of the inertia component for the horizontal forces and of the lift component for the vertical ones. On the basis of the performance of several time-domain methods, the wave loads and the undisturbed velocity and acceleration derived from the surface elevation of the cylinder section were used to calculate the drag, lift, and horizontal and vertical inertia coefficients in the practical Morison and transverse semi-empirical equations.

Solitary wave-induced forces on horizontal circular cylinders: Laboratory experiments and SPH simulations

This work deals with an experimental and numerical study on the horizontal and vertical hydrodynamic forces induced by solitary waves on submerged horizontal circular cylinders. Laboratory tests were performed in the wave flume of the University of Calabria. A battery of pressure transducers was mounted along the external contour of a cylinder placed at half water depth, while four wave gauges were located close to the cylinder and an ultrasonic sensor behind the paddle to measure its displacement. From the numerical viewpoint, a diffusive weakly-compressible SPH model was adopted. To prevent spurious flows near the cylindrical contour, a packing algorithm has been applied to initialize the SPH fluid particles. The acoustic components occurring in the numerical pressure field were filtered through the application of Wavelet Transform. Experimental and numerical analyses were performed in the inertia-dominated regime where these force components are more relevant than the drag and lift ones. The deviation from the fully inertia regime was highlighted in the simulations by the occurrence of a couple of asymmetric vortices behind the cylinder. The good agreement between experimental and SPH forces and kinematics at the cylinder has allowed the numerical calibration of the hydrodynamic coefficients in the Morison and transverse semi-empirical equations by different time-domain methods. For engineering purposes, we propose simple empirical formulas based on the knowledge of wave amplitude to calculate the hydrodynamic coefficients.

The time asymmetric pitching effects on the energy extraction performance of a semi-active flapping wing power generator

Inspired from the bird and insect’s flight in nature, the time asymmetric pitching motion is proposed for the semi-active flapping wing power generator instead of conventional time symmetric pitching motion to seek better energy extraction performance. The NACA0012 wing, with prescribed pitching motion, is employed to represent as a power generator, where the vertical hydrodynamic force activates its heaving motion. A novel numerical coupling model is developed to simulate the interaction between the fluid and the semi-active power generator, and the effects of time asymmetric pitching on the energy extraction performance of the generator is analyzed. It is found that the time asymmetric pitching motion has a noticeable effect on the energy extraction performance of the generator, as it affects the instantaneous energy coefficient, energy efficiency and the flow structures. It is also concluded that with an optimal time asymmetric pitching motion, the maximal efficiency increases as high as 17% over the time symmetric pitching power generator.

Numerical simulation of free-surface waves past two semi-submerged horizontal circular cylinders in tandem

Two-dimensional (2D) numerical simulations are performed to investigate free surface waves past two semi-submerged horizontal circular cylinders in tandem. The 2D simulations are carried out by solving the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations with the k-ω turbulence model. The level set method is employed to model the free-surface waves. Validation studies of a numerical wave tank have been performed by comparing the numerical simulations with free-surface waves past a partially-submerged horizontal cylinder with the published experimental data under regular-wave and deep water conditions. Cases with different submerged depths of the cylinder and incident wave properties have been studied. The numerical results are in good agreement with the experimental measurement in terms of hydrodynamic forces. Subsequently, free surface waves past two semi-submerged horizontal cylinders in tandem are computed numerically. The effect of spacing between the two cylinders is investigated by examining the changes in the vertical hydrodynamic forces on and the free surface elevations around the cylinders.

Effects of non-sinusoidal pitching motion on energy extraction performance of a semi-active flapping foil

Numerical simulations are used to study the energy harvester based on a semi-active flapping foil, in which the profile of the pitching motion is prescribed and the heaving motion is activated by the vertical hydrodynamic force. We consider a two-dimensional NACA0015 airfoil with the Reynolds number Re = 1000. First, for the sinusoidal pitching, an optimal combination of the parameters of pitching amplitude θ0 = 75° and reduced frequency f∗ = 0.16 is identified, with the highest energy harvesting efficiency of 32% being recorded. Then we study non-sinusoidal pitching, with a gradual change from a sinusoid to a square wave as β is increased from one. We find that its effect of efficiency enhancement is limited for the parameters approaching their optimal values, and the upper boundary of the efficiency appears not to be increased. In detail, we report that when the pitching amplitude is small, non-sinusoidal pitching motions can indeed improve the performance of the system. However, when both the pitching amplitude and the flapping frequency are close to their optimal values, non-sinusoidal pitching motions contribute negatively to the harvesting efficiency. We suggest that a non-sinusoidal profile, at least a simple trapezoidal-like one is ineffective in the semi-active system reported by the current study.

Direct Numerical Simulation of Multiple Particles Sedimentation at an Intermediate Reynolds Number

AbstractIn this work the previously developed Lattice Boltzmann-Direct Forcing/ Fictitious Domain (LB-DF/FD) method is adopted to simulate the sedimentation of eight circular particles under gravity at an intermediate Reynolds number of about 248. The particle clustering and the resulting Drafting-Kissing-Tumbling (DKT) motion which takes place for the first time are explored. The effects of initial particle-particle gap on the DKT motion are found significant. In addition, the trajectories of particles are presented under different initial particle-particle gaps, which display totally three kinds of falling patterns provided that no DKT motion takes place, i.e. the concave-down shape, the shape of letter “M” and “in-line” shape. Furthermore, the lateral and vertical hydrodynamic forces on the particles are investigated. It has been found that the value of Strouhal number for all particles is the same which is about 0.157 when initial particle-particle gap is relatively large. The wall effects on falling patterns and particle expansions are examined in the final.

COMPUTATIONAL FLUID DYNAMIC ANALYSIS OF HIGHWAY BRIDGES EXPOSED TO HURRICANE WAVES

In present paper, numerical code STAR CCM+ by CD-adapco which works based on compressible two-phase Navier Stokes equations is used to evaluate hydrodynamic forces exerted on prototype of I10 Bridge over Escambia Bay which was extensively damaged during Hurricane Ivan. Volume of Fluid (VOF) is used to capture dynamic free surface which is well suited for simulating complex discontinuous free surface associated with wave-deck interactions. 2D and 3D models were setup and properly configured. Simulations were conducted on High performance Computing and Communication Center (HPCC) at University of Southern California. Simulation results are compared to experimental data available from Hinsdale Wave Laboratory at Oregon State University. Comparison of experimental data to simulation results show the importance of proper mesh size and time step choice on accuracy of horizontal and vertical hydrodynamic force predictions applied to bridge superstructure.