Impact Motion of a Buoyant Cylinder Released Underwater on a Surface Body

1979 ◽  
Vol 101 (3) ◽  
pp. 167-170
Author(s):  
J. S. Chung ◽  
R. G. Butler
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Present Method ◽  
Body Shape ◽  
Equations Of Motion ◽  
Terminal Velocity ◽  
Cavitation Inception ◽  
Operational Safety ◽  
Deepwater Riser ◽  
Impact Motion

Surface impact velocities and accelerations of a buoyant module released underwater have been analyzed. The associated equations of motion are presented. The analyses include the effects of cavitation inception possibility, free surface and surface wave action. Velocities and accelerations of rising trajectories are computed as a function of buoyancy, body shape and release depth, with a special application to buoyant modules encasing a deepwater riser. The released module reaches terminal velocity shortly after release. The results and analyses can serve as a practical guide for the operational safety of handling buoyant modules in deep water. The present method of analyses can be applied to other similar bodies.

BEM Modeling of Viscous Motion of Surface Water Waves

2004 ◽  
Author(s):  
Mirmosadegh Jamali
Keyword(s):  
Numerical Modeling ◽  
Free Surface ◽  
Surface Wave ◽  
Water Waves ◽  
Wave Motion ◽  
Equations Of Motion ◽  
Solid Surfaces ◽  
Finite Difference Technique ◽  
Surface Water Waves ◽  
Motion Characteristics

This study is concerned with numerical modeling of viscous surface wave motion using boundary element method (BEM). The equations of motion for thin boundary layers at the solid surfaces are coupled with the potential flow in the bulk of the fluid, and a mixed BEM-finite difference technique is used to obtain the surface wave motion characteristics including the decay rate. The technique is presented for a standing surface wave motion. The extension to other free surface problems is discussed.

scholarly journals Surface Wave Speed of Functionally Graded Magneto-Electro-Elastic Materials with Initial Stresses

2014 ◽  
Vol 44 (3) ◽  
pp. 49-64 ◽  
Author(s):  
Li Li ◽  
P. J. Wei
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Elastic Material ◽  
Short Circuit ◽  
Equations Of Motion ◽  
Open Circuit ◽  
Functionally Graded ◽  
Initial Stresses ◽  
Shear Surface ◽  
Traction Boundary Conditions

Abstract The shear surface wave at the free traction surface of half- infinite functionally graded magneto-electro-elastic material with initial stress is investigated. The material parameters are assumed to vary ex- ponentially along the thickness direction, only. The velocity equations of shear surface wave are derived on the electrically or magnetically open circuit and short circuit boundary conditions, based on the equations of motion of the graded magneto-electro-elastic material with the initial stresses and the free traction boundary conditions. The dispersive curves are obtained numerically and the influences of the initial stresses and the material gradient index on the dispersive curves are discussed. The investigation provides a basis for the development of new functionally graded magneto-electro-elastic surface wave devices.

Large amplitude progressive interfacial waves

1979 ◽  
Vol 93 (3) ◽  
pp. 433-448 ◽  
Author(s):  
Judith Y. Holyer
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Surface Waves ◽  
Large Amplitude ◽  
Phase Speed ◽  
Maximum Height ◽  
Interfacial Waves ◽  
Free Surface Waves ◽  
Lower Fluid ◽  
Over The Top

This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Padé approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.

Fourth‐order finite‐difference P-SV seismograms

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1425-1436 ◽  
Author(s):  
Alan R. Levander
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Fourth Order ◽  
Equations Of Motion ◽  
Dispersion Analysis ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Order System ◽  
Surface Boundary ◽  
Lamb’S Problem

I describe the properties of a fourth‐order accurate space, second‐order accurate time, two‐dimensional P-SV finite‐difference scheme based on the Madariaga‐Virieux staggered‐grid formulation. The numerical scheme is developed from the first‐order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses. The Madariaga‐Virieux staggered‐grid scheme has the desirable quality that it can correctly model any variation in material properties, including both large and small Poisson’s ratio materials, with minimal numerical dispersion and numerical anisotropy. Dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints/wavelength. The scheme can be used to accurately simulate wave propagation in mixed acoustic‐elastic media, making it ideal for modeling marine problems. Explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free‐surface or within a layer and to satisfy free‐surface boundary conditions. Benchmark comparisons of finite‐difference and analytical solutions to Lamb’s problem are almost identical, as are comparisons of finite‐difference and reflectivity solutions for elastic‐elastic and acoustic‐elastic layered models.

Numerical Solution of Thermal and Fluid Flow With Phase Change by VOF Method

2000 ◽  
Author(s):  
Hidemi Shirakawa ◽  
Yasuyuki Takata ◽  
Takehiro Ito ◽  
Shinobu Satonaka
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Phase Change ◽  
Calculation Result ◽  
Bubble Growth ◽  
Present Method ◽  
Spherical Shape ◽  
Superheated Liquid ◽  
One Dimensional ◽  
Solidification Problem

Abstract Numerical method for thermal and fluid flow with free surface and phase change has been developed. The calculation result of one-dimensional solidification problem agrees with Neumann’s theoretical value. We applied it to a bubble growth in superheated liquid and obtained the result that a bubble grows with spherical shape. The present method can be applicable to various phase change problems.

Analysis of dynamic characteristics of bubble rise under a free surface

2020 ◽  
Vol 98 (11) ◽  
pp. 981-992
Author(s):  
Ying Zhang ◽  
Qiang Liu ◽  
Wenbin Li ◽  
Xiaolong Lian ◽  
Jinglun Li ◽  
...  
Keyword(s):  
Free Surface ◽  
Immersed Boundary Method ◽  
Weber Number ◽  
Front Tracking ◽  
Terminal Velocity ◽  
Immersed Boundary ◽  
Tracking Method ◽  
Free Interface ◽  
Front Tracking Method ◽  
Moving Interface

The rising process of a bubble occurs in several natural and industrial apparatuses. This process is computationally studied using the front tracking method for a moving interface whose surface properties are solved in terms of an immersed-boundary method. The results show that the free interface does not influence the bubble before the centroid velocity of the bubble reaches the terminal velocity, which reaches a stable value or fluctuates at it, with the distance h (between the centroid of the bubble and the free surface) reaching a certain value. When the Reynolds number increases, the time to reach terminal velocity will decrease, and the influence of the viscous factor on the terminal velocity is also weakened. The dramatic interaction between a bubble and free surface is beneficial to accelerate film draining out. It is also shown that the shape of the bubble gradually becomes an ellipse as the Weber number (We) decreases, and it is beneficial to reduce the resistance of the bubble. The free surface could accelerate the bubble breaking at high We values.

scholarly journals Study on liquid sloshing characteristics of a swaying rectangular tank with a rolling baffle

2019 ◽  
Vol 119 (1) ◽  
pp. 23-41 ◽  
Author(s):  
Jing-Han Wang ◽  
Shi-Li Sun
Keyword(s):  
Free Surface ◽  
Present Method ◽  
Velocity Potential ◽  
Solution Procedure ◽  
Liquid Sloshing ◽  
Published Data ◽  
Free Surface Elevation ◽  
Separate Variable ◽  
Rectangular Tank ◽  
Vertical Baffle

Abstract This study addresses the sloshing characteristics of a liquid contained in a tank with a vertical baffle mounted at the bottom of the tank. Liquid sloshing characteristics are studied through an analytical solution procedure based on the linear velocity potential theory. The tank is forced to sway horizontally and periodically, while the baffle is fixed to the tank or rolling around a hinged point. The rectangular tank flow field is divided into a few sub-domains. The potentials are solved by a separate variable method, and the boundary conditions and matching requirements between adjacent sub-domains are used to determine the sole solution. The free surface elevations with no baffle or a low fixed baffle are compared with those in published data, and the correctness and reliability of the present method are verified. Then the baffle is forced to rotate around the bottom-mounted point. It is found that the baffle’s motion, including the magnitude and the phase together, can be adjusted to suppress the free surface elevation, and even the sloshing wave can be almost eliminated.

Towed Underwater SPIV Measurement of Flow Fields Around a Surface-Piercing Cylinder With Free Surface Effects

2015 ◽  
Author(s):  
Jeonghwa Seo ◽  
Bumwoo Han ◽  
Shin Hyung Rhee
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Surface Wave ◽  
Flow Field ◽  
Cross Section ◽  
Surface Effects ◽  
Flow Fields ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Wave Induced

Effects of free surface on development of turbulent boundary layer and wake fields were investigated. By measuring flow field around a surface piercing cylinder in various advance speed conditions in a towing tank, free surface effects were identified. A towed underwater Stereoscopic Particle Image Velocimetry (SPIV) system was used to measure the flow field under free surface. The cross section of the test model was water plane shape of the Wigley hull, of which longitudinal length and width were 1.0 m and 100 mm, respectively. With sharp bow shape and slender cross section, flow separation was not expected in two-dimensional flow. Flow fields near the free-surface and in deep location that two-dimensional flow field was expected were measured and compared to identify free-surface effects. Some planes perpendicular to longitudinal direction near the model surface and behind the model were selected to track development of turbulent boundary layer. Froude numbers of the test conditions were from 0.126 to 0.40 and corresponding Reynolds numbers were from 395,000 to 1,250,000. In the lowest Froude number condition, free-surface wave was hardly observed and only free surface effects without surface wave could be identified while violent free-surface behavior due to wave-induced separation dominated the flow fields in the highest Froude number condition. From the instantaneous velocity fields, Time-mean velocity, turbulence kinetic energy, and flow structure derived by proper orthogonal decomposition (POD) were analyzed. As the free-surface effect, development of retarded wake, free-surface waves, and wave-induced separation were mainly observed.

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