scholarly journals Wave-induced response of a floating two-dimensional body with a moonpool

2015 ◽  
Vol 373 (2033) ◽  
pp. 20140109 ◽  
Author(s):  
Arnt G. Fredriksen ◽  
Trygve Kristiansen ◽  
Odd M. Faltinsen
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Resonance Frequency ◽  
Hybrid Method ◽  
Two Dimensional ◽  
Body Boundary ◽  
Flow Domain ◽  
Wave Induced ◽  
Piston Mode ◽  
Nonlinear Hybrid

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier–Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency.

A Method of Computing Nonlinear Wave Resistance of Thin Ships by Coordinate Straining

1975 ◽  
Vol 19 (03) ◽  
pp. 149-154
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Nonlinear Wave ◽  
Wave Resistance ◽  
Second Order ◽  
Forward Displacement ◽  
Nonlinear Solution ◽  
First Order ◽  
Body Boundary ◽  
Flow Domain

A systematical procedure is derived for determining the distribution of sources along the centerplane of a thin ship which generate a flow (and the associated wave resistance) satisfying the free-surface and body boundary conditions at second order. The method relies on a mapping of the flow domain onto a new domain by slightly straining the coordinates. The horizontal straining is selected such that the nonlinear solution should be easily derived from the first-order (Michell) solution in the strained domain. The results are shown to be similar to those obtained by Guilloton's method, but new features, such as the forward displacement of the bow singularities, are present.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

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.

Displacements and Stresses in a Two-Dimensional Wedge-Shaped Medium

1974 ◽  
Vol 41 (3) ◽  
pp. 719-724
Author(s):  
Y.-C. Teng ◽  
J. T. Kuo
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Elastic Constants ◽  
Numerical Results ◽  
Two Dimensional ◽  
Residue Theorem ◽  
Line Load ◽  
Body Forces ◽  
Formal Solutions

This paper deals with two-dimensional wedge problems in elastostatics—a single wedge and a welded multiwedge of arbitrary wedge angles and different elastic constants subjected to an inclined line load on the free surface of the wedge; and a single wedge subjected to an Nth multipole line load on the free surface of the wedge. The general expressions of stresses and displacements are obtained, neglecting body forces, in terms of Papkovitch functions. By satisfying the boundary conditions of the wedge problems, the formal solutions of stresses and displacements are obtained. The stresses and displacements for r < r0 and r > r0, where r0 is the position of load in r-direction, are evluated separately by means of the residue theorem. As examples, numerical results are obtained for several particular cases.

scholarly journals Two-Dimensional Supercavitating Plate Oscillating Under a Free Surface

1965 ◽  
Vol 9 (02) ◽  
pp. 40-55
Author(s):  
C. S. Song
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Region ◽  
Integral Form ◽  
Cavitation Number ◽  
Two Dimensional ◽  
First Order ◽  
Upper Half Plane ◽  
Order Quantities

The problem of a supercavitating flat plate at zero and nonzero cavitation numberoscillating under a free surface is analyzed by a linearized method using the accelerationpotential. The analysis is based on the concept of small velocity perturbations where in all second-order quantities are neglected. The flow is assumed two-dimensional, irrotational, incompressible, and gravitation-free. The potential-flow region is mapped on to an upper half-plane and the solution is expressed in an integral form using Cheng andRott's method. Special attention is given to the effect of approximate wake boundary conditions on the computed force and moment. It was estimated that the effect is of secondorder when the cavitation number is a first-order small quantity.

A multimodal method for liquid sloshing in a two-dimensional circular tank

2010 ◽  
Vol 665 ◽  
pp. 457-479 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Analytical Form ◽  
The Body ◽  
Liquid Sloshing ◽  
Two Dimensional ◽  
Surface Conditions ◽  
Natural Modes ◽  
Body Boundary ◽  
Multimodal Method

Two-dimensional forced liquid sloshing in a circular tank is studied by the multimodal method which uses an expansion in terms of the natural modes of free oscillations in the unforced tank. Incompressible inviscid liquid, irrotational flow and linear free-surface conditions are assumed. Accurate natural sloshing modes are constructed in an analytical form. Based on these modes, the ‘multimodal’ velocity potential of both steady-state and transient forced liquid motions exactly satisfies the body-boundary condition, captures the corner-point behaviour between the mean free surface and the tank wall and accurately approximates the free-surface conditions. The constructed multimodal solution provides an accurate description of the linear forced liquid sloshing. Surface wave elevations and hydrodynamic loads are compared with known experimental and nonlinear computational fluid dynamics results. The linear multimodal sloshing solution demonstrates good agreement in transient conditions of small duration, but fails in steady-state nearly-resonant conditions. Importance of the free-surface nonlinearity with increasing tank filling is explained.

A numerical nonlinear analysis of two-dimensional ventilating entry of surface-piercing hydrofoils with effects of gravity

2010 ◽  
Vol 658 ◽  
pp. 383-408 ◽  
Author(s):  
VIMAL VINAYAN ◽  
SPYROS A. KINNAS
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Numerical Scheme ◽  
Suction Side ◽  
Nonlinear Boundary Conditions ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Surface Boundary Conditions ◽  
Dimensional Boundary ◽  
Nonlinear Free Surface

The presence of the free surface adds an element of difficulty to the development of numerical and theoretical methods for the performance prediction of surface-piercing hydrofoils. Existing methods of analysis for two-dimensional surface-piercing hydrofoils or blade sections of a surface-piercing propeller solve either a linear problem, assuming a thin section and ventilated surface along with linear free-surface boundary conditions, or a nonlinear problem in a self-similar setting. Both these approaches cannot be used when the effects of gravity are important, which is the case when a craft is operating at low speeds. A two-dimensional boundary-element-method-based numerical scheme is presented here that overcomes these drawbacks by solving the fully ventilated flow past a surface-piercing hydrofoil of finite dimensions and includes the whole gamut of nonlinear free-surface interactions. The unique aspect of the numerical scheme is that fully nonlinear boundary conditions are applied on the free surface which allows for the accurate modelling of the jet generated on the wetted boundary and the ventilated surface formed on the suction side as a result of the passage of the hydrofoil through the free surface. Moreover, the effects of gravity can be considered to take into account the influence of the Froude number. Ventilated-surface shapes predicted by the present scheme are compared with existing experimental results and are shown to be in good agreement.

A Localized Finite-Element Method for Two-Dimensional Steady Potential Flows with a Free Surface

1978 ◽  
Vol 22 (04) ◽  
pp. 216-230
Author(s):  
Kwang June Bai
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Boundary Conditions ◽  
Complex Geometry ◽  
The Body ◽  
Finite Domain ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Test Functions ◽  
Infinite Domain

A numerical method is presented for solving two-dimensional uniform flow problems with a linearized free-surface boundary condition. The boundary-value problem governed by Laplace's equation is replaced by a weak formulation (also known as Galerkin's method) with certain essential boundary conditions. The infinite domain of the fluid is reduced to a finite domain by utilizing known solution spaces in certain subdomains. The bases for the trial and test functions are chosen from the same subspace of the polynomial function space in the reduced subdomain. The essential boundary conditions are properly taken into account by an unconventional choice of the basis for the trial functions, which is different from that for the test functions in other subdomains. This method is applied to two-dimensional steady flow past a submerged elliptic section, a hydrofoil at an arbitrary angle of attack, and a bump on the bottom. In each example the body boundary condition is satisfied exactly. Both subcritical and supercritical flows are treated. We present the numerical results of wave resistance, lift force, moment, circulation strength, and flow blockage parameter. The computed pressure distributions on the hydrofoil and wave profiles are shown. The test results obtained by the present method agree very well with existing results. The main advantage of this method is that any complex geometry of the boundary can be easily accommodated.

Wakes of Developed Cavities

1977 ◽  
Vol 21 (04) ◽  
pp. 225-238
Author(s):  
Jean-Marie Michel
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Drag Coefficient ◽  
Cavity Length ◽  
Lift Coefficient ◽  
Cavity Flow ◽  
Numerical Results ◽  
Two Dimensional ◽  
Flow Configuration ◽  
Wake Model

A linearized wake model with a momentum defect is presented for the two-dimensional cavity flow around a base-vented foil which is placed in a free-surface channel. The numerical results show that, for a given cavity underpressureσ, the boundary conditions on the wake of the cavity have repercussions on the cavity length and the lift coefficient, whereas the drag coefficient is not modified. Similar features can be expected whenever the flow configuration is made strongly asymmetric by the external boundaries, especially by a free surface.

On Wave Diffraction of a Two-Dimensional Moonpool in a Two-Layer Fluid in Finite Water Depth

2018 ◽  
Author(s):  
Xingyu Song ◽  
Xin Xu ◽  
Xinshu Zhang ◽  
Yunxiang You
Keyword(s):  
Free Surface ◽  
Resonance Frequency ◽  
Internal Wave ◽  
Wave Mode ◽  
Resonance Frequencies ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Free Surface Wave ◽  
Piston Mode ◽  
Wave Elevations

This paper studies the wave diffraction of a two-dimensional moonpool in a two-layer fluid in finite water depth by using a domain decomposition scheme and an eigenfunction matching method. The formulae of the wave exciting forces, the free surface and internal wave elevations at zero-frequency are derived. Numerical convergence has been assessed by repeating the computations for increasing values of the truncation orders. The present model has been validated by comparing a limiting case with a single-layer fluid case and the comparisons are in general satisfactory. Although the wave exciting forces and free surface wave elevations around resonance frequency are overestimated, the piston mode resonance frequency is well predicted. Two typical configurations with different moonpool widths are selected for computations in both free surface and internal wave modes. It is found that, the wave exciting forces, free surface and internal wave elevations in internal wave mode are much smaller than those in free surface wave mode. In addition, the wave exciting forces in internal wave mode attenuate to zero quickly as incident wave frequency increases. For moonpool with small width, only piston mode resonance can be observed. The piston mode resonance frequencies identified in free surface and internal wave modes are the same. The characteristics of piston mode resonance can also be observed in the horizontal and vertical wave exciting forces. Around the piston mode resonance frequency, the wave exciting forces reach their local maximums. It is revealed that, as moonpool width increases, the piston mode resonance frequency decreases. Meanwhile, it shows that more asymmetric and symmetric sloshing mode resonances appear alternately and occur at higher frequencies than the piston mode resonance. Moreover, the predicted sloshing mode resonance frequencies are compared with those estimated by a simple approximate formula.

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