Numerical Simulation of Hydrodynamics of a Circular Disk Oscillating Near a Seabed

2013 ◽  
Author(s):  
Carlos A. Garrido-Mendoza ◽  
Antonio Souto-Iglesias ◽  
K. P. Thiagarajan
Keyword(s):  
Circular Disk ◽  
Critical Value ◽  
Added Mass ◽  
Post Processing ◽  
Hydrodynamic Problem ◽  
Sandy Bottom ◽  
Disk Radius ◽  
Vortex Lines ◽  
Solid Disk ◽  
Hydrodynamics Coefficients

This paper studies how the hydrodynamics coefficients of added mass and damping varies when an oscillating disk approaches a seabed. Analysis was performed by OpenFOAM code using the ‘PIMPLE’ algorithm. The simulations considered the flow as laminar and hence no turbulence model was used. Simulations were conducted for a solid disk of 200 mm diameter, 2 mm thick, oscillating at amplitudes varying from 1–48 mm and elevation ‘h’ of the disk from the seabed varying from 0.2–2 times the disk radius. The geometry and parameters used here were the same as that of Wadhwa et al. (2010) [1] and Vu et al. (2008) [2]. The forces on the disk were calculated using a Tool for post-processing force/lift/drag data with function tool available in OpenFOAM. The motions of the disk were restricted to axial (heave) direction. The calculated forces and displacement were analyzed using a Fourier projection to separate the added mass and damping effects. Numerical results were compared with the experiments conducted by Wadhwa et al. (2010) [1] with a sandy bottom. Results show that the added mass and damping increase monotonically with the Keulegan-Carpenter number (KC) up to a critical value, beyond which the behavior becomes random. The critical KC increases linearly with increasing distance from the seabed. The hydrodynamic problem has important applications in structures such as foundation templates and subsea structures oscillating in proximity to the seabed. The computations show vortex lines of the flow, and the influence of the seabed on the flow around the structure.

Variation of Heave Added Mass and Damping Near Seabed

2010 ◽  
Author(s):  
Hemlata Wadhwa ◽  
Balaji Krishnamoorthy ◽  
Krish P. Thiagarajan
Keyword(s):  
High Sensitivity ◽  
Circular Disk ◽  
Added Mass ◽  
Displacement Transducer ◽  
Hydrodynamic Behavior ◽  
Disk Radius ◽  
Damping Coefficients ◽  
Solid Disk ◽  
Exploration And Production ◽  
The Mean

During installation of subsea structures such as mud mats, the tension in crane wires can experience spikes when the structure is near the seabed. It is hypothesized that such spikes may be caused by the structure undergoing resonant oscillations, which in turn may be due to changes in added mass and damping near the seabed. Such motions can cause hardship for operators as they interfere with precise positioning during installation. With increasing exploration and production in deep and remote fields, the size and weight of subsea equipments are continuously increasing. Installation operations such as lifting and lowering, positioning of the object require good knowledge of the hydrodynamic coefficients. Following on ideas used in Norwegian offshore, the mud mat is modeled as a circular disk. Experiments are conducted on an oscillating solid disk of diameter and thickness 200 mm and 2 mm respectively. The heave oscillations are forced by a programmable actuator, at amplitudes varying from 1–56 mm and frequencies from 1.0–1.8 Hz. The elevation ‘h’ of the disk from the mean seabed is varied from 0.2–2 times the disk radius. The forces on the disk are measured using a submersible high-sensitivity load cell. The motions of the disk are restricted to axial (heave) direction, and are measured with a displacement transducer. The measured forces and displacement are analyzed using a Fourier Transform algorithm to separate the added mass and damping effects. The authors have found similar trends in the hydrodynamic behavior of a disk approaching the seabed to what was found when the disk approached the free surface in Wadhwa & Thiagarajan [1]. The added mass and damping coefficients were found to increase with increasing KC, as well as with increasing proximity to the seabed. Another noticeable feature of the experiments was the cavity formation underneath the oscillating structure. The width of the cavity was about 3–4 times the radius of the disk and depth was about one third/fourth of the radius of the disk. The size of the cavity and the increase in hydrodynamic forces near the seabed suggest the importance of knowledge of hydrodynamic behavior near the seabed.

Ricochet Off Water of Spherical Projectiles

1991 ◽  
Vol 35 (02) ◽  
pp. 91-100
Author(s):  
T. Miloh ◽  
Y. Shukron
Keyword(s):  
Free Surface ◽  
Incident Angle ◽  
Equations Of Motion ◽  
Critical Value ◽  
Added Mass ◽  
Water Entry ◽  
Lagrange Equations ◽  
Specific Density ◽  
Empirical Expression ◽  
Actual Trajectory

The oblique water-entry problem of a spherical projectile is analytically analyzed with special reference to the ricocheting phenomena of the object off a free surface. Under the assumption of large impact velocity, the Kelvin-Kirchoff-Lagrange equations of motion are formulated in terms of the various time-dependent added-mass coefficients and their time derivatives. The actual trajectory of the sphere below the free surface is obtained by integration of these equations, and a critical value for the projectile incident angle (ricochet) is obtained in terms of the initial Froude number and the specific density of the solid. It is demonstrated that for infintely large Froude numbers this solution reduces to the well-known empirical expression for the critical angle of a sphere in oblique water-entry.

Experimental Assessment of Hydrodynamic Coefficients of Disks Oscillating Near a Free Surface

2009 ◽  
Author(s):  
Hemlata Wadhwa ◽  
Krish P. Thiagarajan
Keyword(s):  
Free Surface ◽  
Circular Disk ◽  
Added Mass ◽  
Rate Of Change ◽  
Forced Oscillations ◽  
Base Case ◽  
Published Data ◽  
Hydrodynamic Coefficients ◽  
Widespread Application ◽  
Field Development

The use of different types of subsea equipment is continuously increasing in offshore field development. Installation operations such as lifting and lowering of these equipments require knowledge of the hydrodynamic coefficients of the object. An accurate prediction of these coefficients on typical subsea structures is a challenging task. The main coefficients in this context relate to added mass, damping and slamming effects. Formulations have been presented by various authors in literature for evaluating these coefficients for simple shapes. Some of them have found widespread application in the industry. The authors have considered a solid circular disk as a base case for initiating study on subsea module hydrodynamics. Experiments were conducted on an oscillating solid disk of diameter 200 mm and thickness 2 mm near the free surface. Forced oscillations were conducted at amplitudes varying from 3mm–36mm and frequencies 0.9–1.5 Hz respectively. The forces on the disk were measured using a submersible high-sensitivity load cell. The motions of the disk were restricted to axial (heave) direction, and were measured with a displacement transducer. The measured forces and displacement were analyzed using a Fast Fourier Transform algorithm to separate the added mass and damping effects. From the rate of change of added mass with depth of submergence, slamming forces were identified. The measured coefficients were compared with similar published data by Vu et al [1] and Tao & Dray [2]. The paper presents various formulations for added mass, damping and slamming obtained from literature and currently in use in the industry. These formulations are compared with measured values of the coefficients and suggestions are made on the importance of these formulations for flat subsea structures.

scholarly journals Dynamics of Cosmic Neutrinos in Galaxies

2014 ◽  
Vol 23 (2) ◽  
Author(s):  
A. Sapar
Keyword(s):  
Differential Equations ◽  
Linear Part ◽  
Neutrino Flux ◽  
Circular Disk ◽  
Fermi Velocity ◽  
Disk Galaxies ◽  
Rest Energy ◽  
Disk Radius ◽  
Stellar Orbits ◽  
Cosmic Background

AbstractThe cosmic background of massive (about 1 eV rest-energy) neutrinos can be cooled to extremely low temperatures, reaching almost completely degenerated state. The Fermi velocity of the neutrinos becomes less than 100 km/s. The equations of dynamics for the cosmic background neutrinos are derived for the spherical and axisymmetrical thin circular disk galaxies. The equations comprise the gravitational potential and gravity of the uniform baryonic disk galaxies. Then the equations are integrated analytically over the disk radius. The constant radial neutrino flux in spherical galaxies favors formation of the wide unipotential wells in them. The neutrino flux in the axisymmetrical galaxies suggests to favor the evolution in the direction of a spherically symmetrical potential. The generated unipotential wells are observed as plateaux in the velocity curves of circular stellar orbits. The constant neutrino density at galactic centers gives the linear part of the curves. The derived system of quasilinear differential equations for neutrinos in the axisymmetrical galaxies have been reduced to the system of the Lagrange-Charpit equations: the coupled differential equations, specifying the local neutrino velocities and dynamics of motion along trajectories, and an additional interconnected equation of the neutrino mass conservation, which can be applied for the determination of density of the neutrino component in galaxies.

Mutual friction in a heat current in liquid heliumn. II. IV. Critical heat currents in wide channels

1958 ◽  
Vol 243 (1234) ◽  
pp. 400-413 ◽  
Keyword(s):  
Vortex Line ◽  
Unit Volume ◽  
Critical Value ◽  
Channel Width ◽  
Heat Current ◽  
Mutual Friction ◽  
Superfluid Turbulence ◽  
Wide Channel ◽  
Vortex Lines ◽  
Single Term

Experiments are described in which a heat current in a wide channel is suddenly increased from a small value W 1 to a large value W 2 ; the time characterizing the build-up of the Gorter-Mellink mutual friction to its equilibrium value in the heat current W 2 is studied as a function of W 1 . Interpretation of the results on the basis of the idea that the mutual friction is associated with turbulence (in the form of vortex lines) in the superfluid shows that some mutual friction exists in the heat current W 1 even when the latter is less than the critical value described in parts I and II, and that, as the channel width is increased or the temperature raised, the magnitude of the subcritical mutual friction increases until the critical heat current ceases to exist. It is shown that these observations on mutual friction in small heat currents can be described semi-quantitatively if a single term is added to the expression obtained in part III for the length of vortex line per unit volume in a heat current in a channel of infinite width, and that this term can probably arise either from an annihilation of vortex lines at the walls of the channel or from interference by the walls with the mechanisms of growth and decay of superfluid turbulence discussed in part III. Finally, an explanation is suggested of some of the results described in part II on the decay of mutual friction in the presence of a subcritical heat current.

Hydrodynamic Interactions for Small Arrays of Wave Energy Devices

2002 ◽  
Author(s):  
P. A. P. Justino ◽  
A. F. de O. Falca˜o
Keyword(s):  
Efficient Method ◽  
Wave Energy ◽  
Finite Depth ◽  
Added Mass ◽  
Boundary Element Methods ◽  
Hydrodynamic Interactions ◽  
Rigid Sphere ◽  
Energy Devices ◽  
Simple Geometry ◽  
Hydrodynamics Coefficients

The main object of this work is to develop accurate solutions for hydrodynamics coefficients of arrays of simple-geometry wave-energy devices. Use is made of a computationally very efficient method, to model the wave energy absorption by a rigid sphere moving in heave and sway in water of constant (finite) depth, that employs a series of pulsating multipoles located at the centre of the sphere; a monopole or source can be added to simulate the effect of pulsating volume. In the present work, this is extended to model the interaction between spheres in a finite array, by locating series of multipoles at the centre of each sphere and computing the multipoles intensities from the boundary conditions at the spheres’ surfaces in order to find the matrices of damping and added-mass coefficients in several oscillating modes. Numerical results are obtained for small arrays. This may be used to validate results from boundary-element methods.

Numerical Investigation of the Flow Features Around Heave Plates Oscillating Close to a Free Surface or Seabed

2014 ◽  
Author(s):  
Carlos A. Garrido-Mendoza ◽  
K. P. Thiagarajan ◽  
Antonio Souto-Iglesias ◽  
Benjamin Bouscasse ◽  
Andrea Colagrossi
Keyword(s):  
Free Surface ◽  
Vortex Shedding ◽  
Flow Characteristics ◽  
Added Mass ◽  
Offshore Structures ◽  
Vortical Structures ◽  
Damping Coefficients ◽  
Solid Disk ◽  
Flow Features ◽  
Heave Plate

Performance of heave plates used in offshore structures is strongly influenced by their added mass and damping, which are affected by proximity to a boundary. A previous paper by the authors presented numerical simulations of the flow around a circular solid disk oscillating at varying elevations from seabed [1]. The force calculated was used to evaluate the added mass and damping coefficients for the disk. The simulations suggest that as the structure moves closer to the seabed the added mass and damping coefficients (Ca and Cb) increases continuously. In order to understand the physics behind the added mass and damping trends, when a heave plate is moving near a seabed or closer to the free surface, the flow characteristics around the heave plate are examined numerically in this paper. Flow around oscillating disks is dominated by generation and development of phase-dependent vortical structures, characterized by the KC number and the distance from the seabed or free surface to the heave plate. Numerical calculations presented in this paper have comprised the qualitative analysis of the vortex shedding and the investigation of the links between such vortex shedding and, on one hand the damping coefficient, and on the other hand, pairing mechanisms such as the shedding angle.

A Practical Method for the Prediction of Planing Craft Motions in Regular and Irregular Waves

2008 ◽  
Author(s):  
Luca Sebastiani ◽  
Dario Bruzzone ◽  
Paola Gualeni ◽  
Guido Rambaldi ◽  
Danilo Ruscelli ◽  
...  
Keyword(s):  
Performance Prediction ◽  
Practical Method ◽  
Added Mass ◽  
Hydrodynamic Performance ◽  
Irregular Waves ◽  
Design Tools ◽  
High Complexity ◽  
Hydrodynamic Problem ◽  
Planing Craft ◽  
Momentum Theory

Leisure boats market has constantly grown during the recent years, entailing an increasing need of design tools. This seems particularly urgent for seakeeping and hydrodynamic performance prediction in the field of planing boats. Numerical methodologies are almost consolidated instruments for conventional displacement ships, while some shortcomings are still to be faced and overcome concerning planing craft, due to the high complexity of the hydrodynamic problem. The present paper describes a simplified methodology for the prediction of pitch, heave and roll motions of a planing boat, in regular and irregular waves. In the formulation, a 2D approach is adopted, based on ‘momentum theory’; various aspects of the wedge-theory are used in order to model the sectional characteristics, with particular attention to the added mass. A validation of the proposed methodology concerning vertical motions is presented against data available in literature.

APPLYING THE ISF TECHNOLOGY TO PRODUCE THE CAR PART MODELS

2010 ◽  
Vol 13 (4) ◽  
pp. 91-98
Author(s):  
Tuan Dinh Phan ◽  
Binh Thien Nguyen ◽  
Dien Khanh Le ◽  
Phuong Hoang Pham
Keyword(s):  
Rapid Prototyping ◽  
Incremental Sheet Forming ◽  
Cad Model ◽  
Post Processing ◽  
Technological Parameters ◽  
Batch Production ◽  
Complex Products ◽  
3D Cad ◽  
Real Size ◽  
Single Batch

The paper presents an application the research results previously done by group on the influence of technological parameters to the deformation angle and finish surface quality in order to choose technology parameters for the incremental sheet forming (ISF) process to produce products for the purpose of rapid prototyping or single-batch production, including all steps from design and process 3D CAD model, calculate and select the technological parameters, setting up manufacturing and the stage of post-processing. The samples formed successfully showed high applicability of this technology to practical work, the complex products with the real size can be produced in industries: automotive, motorcycle, civil...

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