scholarly journals Asymmetric impact between liquid and solid wedges

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120203 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Mapping Function ◽  
Solution Procedure ◽  
Contact Angles ◽  
The Body ◽  
Surface Shape ◽  
Parameter Plane ◽  
Complex Velocity Potential ◽  
The Impact

The hydrodynamic problem of impact between a solid wedge and a liquid wedge is analysed. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is assumed to be irrotational and therefore can be described by the velocity potential theory. The solution procedure is based on the analytical derivation of the complex-velocity potential in a parameter plane and the function mapping conformally the parameter plane onto the similarity plane. The mapping function is found as a combination of the derivatives of the complex potential in the similarity and parameter planes, through the integral equations for mixed and homogeneous boundary-value problems in terms of the velocity modulus and the velocity angle with the fluid boundary, together with the dynamic and kinematic boundary conditions. These equations are solved through a numerical method. The procedure is first verified through comparisons with some known results. Simulations are then made for a variety of cases, and detailed results are presented in terms of the free surface shape, streamlines, pressure distribution on the wetted solid surface, and contact angles between the free surface and the body surface.

The nonlinear problem of a gliding body with gravity

2013 ◽  
Vol 727 ◽  
pp. 132-160 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Body Surface ◽  
Breaking Waves ◽  
The Body ◽  
Surface Shape ◽  
Parameter Plane ◽  
Hodograph Method ◽  
Wide Range ◽  
Free Surface Shape ◽  
Analytical Expressions

AbstractAnalysis based on the velocity potential free flow theory with the fully nonlinear boundary condition is made for the steady flow generated by a body gliding along a free surface. Employing the integral hodograph method, we derive analytical expressions for the complex velocity and for the derivative of the complex potential with the coordinate of a parameter plane. The boundary value problem is transformed into a system of two integro-differential equations for the velocity modulus on the free surface and for the slope of the wetted body surface in the parameter plane. The same slope and curvature of the free surface and the body surface at the intersection are adopted to determine the separation points of the flow and from the body. Numerical results are provided for a gliding flat plate and a circular cylinder. The pressure distribution along the body and the free surface shape are presented for a wide range of Froude numbers, within the limit for which the solution corresponding to non-breaking waves downstream can be obtained.

scholarly journals Impact of liquids with different densities

2015 ◽  
Vol 766 ◽  
pp. 5-27 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu ◽  
A. A. Korobkin
Keyword(s):  
Velocity Potential ◽  
Normal Component ◽  
Mapping Function ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Complex Conjugate ◽  
Hodograph Method ◽  
Velocity Magnitude ◽  
Complex Velocity Potential ◽  
The Impact

AbstractThe collision of liquids of different densities is studied theoretically for the case of liquids having wedge-shaped configuration before the impact. Both liquids are assumed to be ideal and incompressible, and the velocity potential theory is used for the flow of each liquid. Surface tension and gravity effects are neglected. The problem is decomposed into two self-similar problems, one for each liquid. Across the interface between the liquids, continuity of the pressure and the normal component of the velocity is enforced through iteration. This determines the shape of the interface and other flow parameters. The integral hodograph method is employed to derive the solution consisting of analytical expressions for the complex-velocity potential, the complex-conjugate velocity, and the mapping function. They are all defined in the first quadrant of a parameter plane, in which the original boundary-value problem is reduced to a system of integro-differential equations in terms of the velocity magnitude and the velocity angle relative to the flow boundary. They are solved numerically using the method of successive approximations. The results are presented through streamlines, interface and free-surface shapes, the pressure and velocity distributions. Special attention is given to the structure of the splash jet rising as a result of the impact.

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.

scholarly journals Splash formation at the nose of a smoothly curved body in a stream

1999 ◽  
Vol 40 (4) ◽  
pp. 421-436 ◽  
Author(s):  
E. O. Tuck ◽  
S. T. Simakov
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Velocity Potential ◽  
Integral Form ◽  
The Body ◽  
Front Face ◽  
Separation Condition ◽  
Polygonal Approximation ◽  
Side Condition ◽  
Two Dimensional Flow

AbstractIn two-dimensional flow past a body close to a free surface, the upwardly diverted portion may separate to form a splash. We model the nose of such a body by a semi-infinite obstacle of finite draft with a smoothly curved front face. This problem leads to a nonlinear integral equation with a side condition, a separation condition and an integral constraint requiring the far-upstream free surface to be asymptotically plane. The integral equation, called Villat's equation, connects a natural parametrisation of the curved front face with the parametrisation by the velocity potential near the body. The side condition fixes the position of the separation point, whereas the separation condition, known as the Brillouin-Villat condition, imposes a continuity relation to be satisfied at separation. For the described flow we derive the Brillouin-Villat condition in integral form and give a numerical solution to the problem using a polygonal approximation to the front face.

Methodology to Evaluate Slamming Loads on Ocean Platforms

2008 ◽  
Author(s):  
Marcio Domingues Maia Junior ◽  
Antonio Carlos Fernandes ◽  
Marcela Trindade ◽  
Andre Ramiro
Keyword(s):  
Free Surface ◽  
Pressure Distribution ◽  
Pressure Sensor ◽  
Potential Flow ◽  
Experimental Methods ◽  
The Body ◽  
Platform Motion ◽  
Air Pocket ◽  
Accuracy And Precision ◽  
The Impact

The purpose of the study is suggest a methodology to be applied in ocean platforms and ships in order to appraise the maximum impact pressure due to the slamming occurrence in the hull shape near its bottom or horizontal regions. This methodology uses a theory based on potential flow. However, there are some phenomena such as creation of a compressible air pocket between the body and free surface at the impact moment that requires a more complete theory and or experimental methods. This gives rise to experimental coefficients to reduce the theoretical errors. The procedure presented here goes by the platform motion dynamics and “impact topology” to allow the potential to be used. Due to the complexity of the phenomenon studied and need for certifying accuracy and precision of the results, tank tests at the LabOceano model basin were carried out. The results showed a good fitting between numerical results and experiments. It should also be pointed out that the pressure sensor used in these experiments gives a pressure distribution over the instrumented area what brings more reliability on the results and a better visibility to the slamming phenomenon. Lastly the methodology in this work stands out as an important tool to evaluate slamming loads.

A Second-Order Theory for the Potential Flow About Thin Hydrofoils

1984 ◽  
Vol 28 (01) ◽  
pp. 55-64
Author(s):  
Colen Kennell ◽  
Allen Plotkin
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Potential Flow ◽  
Order Theory ◽  
Wave Drag ◽  
Second Order ◽  
The Body ◽  
Surface Shape ◽  
Surface Boundary ◽  
Free Surface Boundary Condition

This research addresses the potential flow about a thin two-dimensional hydrofoil moving with constant velocity at a fixed depth beneath a free surface. The thickness-to-chord ratio of the hydrofoil and disturbances to the free stream are assumed to be small. These small perturbation assumptions are used to produce first-and second-order subproblems structured to provide consistent approximations to boundary conditions on the body and the free surface. Nonlinear corrections to the free-surface boundary condition are included at second order. Each subproblem is solved by a distribution of sources and vortices on the chord line and doublets on the free surface. After analytic determination of source and doublet strengths, a singular integral equation for the vortex strength is derived. This integral equation is reduced to a Fredholm integral equation which is solved numerically. Lift, wave drag, and free-surface shape are calculated for a flat plate and a Joukowski hydrofoil. The importance of free-surface effects relative to body effects is examined by a parametric variation of Froude number and depth of submergence.

Radiation and diffraction of second-order surface waves by floating bodies

1988 ◽  
Vol 196 ◽  
pp. 65-91 ◽  
Author(s):  
P. D. Sclavounos
Keyword(s):  
Free Surface ◽  
Linear Problem ◽  
Velocity Potential ◽  
Surface Condition ◽  
Second Order ◽  
The Body ◽  
Green Functions ◽  
Floating Bodies ◽  
Free Surface Condition ◽  
Body Boundary

The paper studies the radiation and diffraction by floating bodies of deep-water bichromatic and bidirectional surface waves subject to the second-order free-surface condition. A theory is developed for the evaluation of the second-order velocity potential and wave forces valid for bodies of arbitrary geometry, which does not involve the evaluation of integrals over the free surface or require an increased accuracy in the solution of the linear problem. Explicit sum- and difference-frequency ‘Green functions’ are derived for the radiation and diffraction problems, obtained from the solution of initial-value problems that ensure they satisfy the proper radiation condition at infinity. The second-order velocity potential is expressed as the sum of a particular and a homogeneous component. The former satisfies the non-homogeneous free-surface condition and is expressed explicitly in terms of the second-order Green functions. The latter is subject to the homogeneous free-surface condition and enforces the body boundary condition by the solution of a linear problem. An analysis is carried out of the singular behaviour of the second-order potential near the intersection of the body boundary with the free surface.

Lateral Force and Moment on Ships in Oblique Waves

1962 ◽  
Vol 6 (02) ◽  
pp. 40-50
Author(s):  
Pung Nien Hu
Keyword(s):  
Differential Equation ◽  
Free Surface ◽  
Velocity Potential ◽  
Lateral Force ◽  
Exciting Force ◽  
The Body ◽  
Regular Waves ◽  
Oblique Waves ◽  
Added Masses ◽  
Slender Bodies

A method for evaluating the exciting force and moment on surface ships as well as on fully submerged bodies in oblique waves is developed, based on the assumptions of long regular waves and slender bodies. The differential equation, together with the boundary conditions, for each component of the velocity potential is studied. Momentum theorems for slender-body sections are derived and applied to the evaluation of stripwise force and moment on bodies in the presence of a free surface. The result is found to be directly related to the added masses of the body sections. Lateral added masses of body sections in the presence of a free surface are investigated in detail and numerical values are presented for Lewis sections.

Hydroelastic Analysis of a Simple Oscillator Impacting the Free Surface

2000 ◽  
Vol 44 (04) ◽  
pp. 278-289
Author(s):  
A. lafrati ◽  
A. Carcaterra ◽  
E. Ciappi ◽  
E. F. Campana
Keyword(s):  
Free Surface ◽  
Theoretical Model ◽  
Boundary Integral ◽  
The Body ◽  
Elastic Response ◽  
Closed Form Expression ◽  
Suitable Model ◽  
Spring Stiffness ◽  
Elastic Forces ◽  
The Impact

The coupling between the hydrodynamic and elastic forces arising when a simple oscillator impacts the free surface is considered. The system is a two-mass oscillator, the lower mass being wedge-shaped, free falling on the free surface. Attention is devoted to a parametric investigation of the maximum of both hydrodynamic and elastic forces induced by the impact. The study is performed by a simplified theoretical model and by a numerical simulation of the fluid-structure interaction. The theoretical model suggested here provides an efficient tool for the computation of the hydrodynamic and elastic forces and of the corresponding maxima as a function of some parameters such as deadrise angle of the wedge, entry velocity, spring stiffness, and the masses. In particular, a closed-form expression for the critical value of the spring constant leading to the maximum elastic response is achieved as a function of the other parameters. Numerically, a panel method is adopted to solve the boundary integral formulation for the velocity potential. A suitable model is introduced to deal with the flow singularity at the intersection point between the free surface and the body contour. Time histories of the hydrodynamic and elastic forces are computed for different values of the spring stiffness and are compared with the corresponding results provided by the simplified theoretical model. The comparison shows that, despite the strong assumptions, the theoretical model allows a good estimate of the system critical condition.

Influence of Trapped Air on the Slamming of a Ship

2003 ◽  
Vol 47 (03) ◽  
pp. 187-193 ◽  
Author(s):  
Ken Takagi ◽  
Junya Dobashi
Keyword(s):  
Local Structure ◽  
Surface Deformation ◽  
Three Dimensional ◽  
The Body ◽  
Surface Shape ◽  
Natural Period ◽  
Trapped Air ◽  
Calm Water ◽  
Spring System ◽  
The Impact

We describe a theoretical approach to a distorted plate penetrating calm water surface as a flow model of the water impact in rough seas. Further simplifications are employed so that the structure of ship is modeled by a tandem mass and spring system and a sequence of circular hollows is used as a bottom shape of the body instead of the surface shape of short crested waves. The results show that the model-scale ship experiences much larger stress at the local structure because of the influence of trapped air. Some results for the full-scale ship show that the three-dimensional effect, that is, the shape of sea surface deformation, is dominant for the cushioning of the impact force, and the trapped air affects some of this effect according to the magnitude of P and the natural period of the local structure.

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