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 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.

Irregular Frequency Removal and Convergence in Higher-Order BEM for Wave Diffraction/Radiation Analysis

2019 ◽  
Author(s):  
Tomoaki Utsunomiya
Keyword(s):  
Free Surface ◽  
Wave Diffraction ◽  
Higher Order ◽  
The Body ◽  
Diffraction Radiation ◽  
First Order ◽  
Irregular Frequency ◽  
Intersection Line ◽  
Order Quantities ◽  
Drift Forces

Abstract Higher-order boundary element method (HOBEM) for wave diffraction/radiation analysis is a powerful tool for its applicability to a general (curved) geometry. Inspired by the paper which examined the convergence of BIE code with constant panels (Martic, et al., 2018; OMAE2018-77999), the convergence characteristics of HOBEM with quadrilateral panels have been examined. Here, the effect of removal of irregular frequencies is particularly focused as discussed by Martic, et al. (2018). The irregular frequency removal has been made by the rigid-lid method which is applicable to HOBEM, where the intersection line between the body-surface and the free-surface should be carefully handled. The results show that for first order quantities the convergence is quite good for both cases with/without irregular frequency removal (except where the irregular frequencies affect for the case without irregular frequency removal). For mean drift forces, the convergence becomes poor particularly for the case without irregular frequency removal. The convergence characteristics are examined and some discussions are made.

REEF3D::FNPF: A Flexible Fully Nonlinear Potential Flow Solver

2019 ◽  
Author(s):  
Hans Bihs ◽  
Weizhi Wang ◽  
Tobias Martin ◽  
Arun Kamath
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Surface Boundary ◽  
Flow Solver ◽  
Surface Boundary Conditions ◽  
Nonlinear Potential ◽  
Numerical Wave ◽  
Computational Resources

Abstract In situations where the calculation of ocean wave propagation and impact on offshore structures is required, fast numerical solvers are desired in order to find relevant wave events in a first step. After the identification of the relevant events, Computational Fluid Dynamics (CFD) based Numerical Wave Tanks (NWT) with an interface capturing two-phase flow approach can be used to resolve the complex wave structure interaction, including breaking wave kinematics. CFD models emphasize detail of the hydrodynamic physics, which makes them not the ideal candidate for the event identification due to the large computational resources involved. In the current paper a new numerical wave model is represented that solves the Laplace equation for the flow potential and the nonlinear kinematic and dynamics free surface boundary conditions. This approach requires reduced computational resources compared to CFD based NWTs. In contrast to existing approaches, the resulting fully nonlinear potential flow solver REEF3D::FNPF uses a σ-coordinate grid for the computations. Solid boundaries are incorporated through a ghost cell immersed boundary method. The free surface boundary conditions are discretized using fifth-order WENO finite difference methods and the third-order TVD Runge-Kutta scheme for time stepping. The Laplace equation for the potential is solved with Hypres stabilized bi-conjugated gradient solver preconditioned with geometric multi-grid. REEF3D::FNPF is fully parallelized following the domain decomposition strategy and the MPI communication protocol. The model is successfully tested for wave propagation benchmark cases for shallow water conditions with variable bottom as well as deep water.

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.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

Explicit Approximations for Calculating Potential Flow About a Body

1983 ◽  
Vol 27 (01) ◽  
pp. 1-12
Author(s):  
F. Noblesse ◽  
G. Triantafyllou
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wave Resistance ◽  
Two Dimensional ◽  
Regular Waves ◽  
Practical Applications ◽  
Flow Problems ◽  
Unbounded Fluid

Several explicit approximations for calculating nonlifting potential flow about a body in an unbounded fluid are studied. These approximations are shown to be exact in the particular cases of flows due to translations of ellipsoids, and they are compared with the exact potential for two-dimensional flows about ogives in translatory motions. Two approximations, given by formulas (31) and (32) in the conclusion, appear to be of particular interest for practical applications, and they can be extended to free-surface flow problems, for example, ship wave resistance, and radiation and diffraction of regular waves by a body.

Steep Wave Loads From Irregular Waves on an Offshore Wind Turbine Foundation: Computation and Experiment

2013 ◽  
Author(s):  
Bo Terp Paulsen ◽  
Henrik Bredmose ◽  
Harry B. Bingham ◽  
Signe Schløer
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Surface Elevation ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Free Surface Elevation ◽  
Fully Nonlinear ◽  
Flow Solver ◽  
Nonlinear Potential

Two-dimensional irregular waves on a sloping bed and their impact on a bottom mounted circular cylinder is modeled by three different numerical methods and the results are validated against laboratory experiments. We here consider the performance of a linear-, a fully nonlinear potential flow solver and a fully nonlinear Navier-Stokes/VOF solver. The validation is carried out in terms of both the free surface elevation and the inline force. Special attention is paid to the ultimate load in case of a single wave event and the general ability of the numerical models to capture the higher harmonic forcing. The test case is representative for monopile foundations at intermediate water depths. The potential flow computations are carried out in a two-dimensional vertical plane and the inline force on the cylinder is evaluated by the Morison equation. The Navier-Stokes/VOF computations are carried out in three-dimensions and the force is obtained by spatial pressure integration over the wettet area of the cylinder. In terms of both the free surface elevation and the inline force, the linear potential flow model is shown to be of limited accuracy and large deviations are generally seen when compared to the experimental measurements. The fully nonlinear Navier-Stokes/VOF computations are accurately predicting both the free surface elevation and the inline force. However, the computational cost is high relative to the potential flow solvers. Despite the fact that the nonlinear potential flow model is carried out in two-dimensions it is shown to perform just as good as the three-dimensional Navier-Stokes/VOF solver. This is observed for both the free surface elevation and the inline force, where both the ultimate load and the higher harmonic forces are accurately predicted. This shows that for moderately steep irregular waves a Morison equation combined with a fully nonlinear two-dimensional potential flow solver can be a good approximation.

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.

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