Second-Order Diffraction Forces on an Array of Vertical Cylinders in Bichromatic Bidirectional Waves

1995 ◽  
Vol 117 (1) ◽  
pp. 12-18 ◽  
Author(s):  
J. H. Vazquez ◽  
A. N. Williams
Keyword(s):  
Cross Section ◽  
Finite Depth ◽  
Hydrodynamic Forces ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Order Problem ◽  
First Order ◽  
Wave Directionality ◽  
Vertical Cylinders ◽  
Green Function Approach

A complete second-order solution is presented for the hydrodynamic forces due to the action of bichromatic, bidirectional waves on an array of bottom-mounted, surface-piercing cylinders of arbitrary cross section in water of uniform finite depth. Based on the constant structural cross section, the first-order problem is solved utilizing a two-dimensional Green function approach, while an assisting radiation potential approach is used to obtain the hydrodynamic loads due to the second-order potential. Results are presented which illustrate the influence of wave directionality on the second-order sum and difference frequency hydrodynamic forces on a two-cylinder array. It is found that wave directionality may have a significant influence on the second-order hydrodynamic forces on these arrays and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.

Sum-Frequency Diffraction Loads on Tension-Leg Platforms in Bidirectional Waves

1997 ◽  
Vol 119 (1) ◽  
pp. 14-19
Author(s):  
J. H. Vazquez ◽  
A. N. Williams
Keyword(s):  
Numerical Technique ◽  
Diffraction Theory ◽  
Potential Method ◽  
Second Order ◽  
Surface Integral ◽  
Hydrodynamic Loads ◽  
Infinite Depth ◽  
Sum Frequency ◽  
Wave Directionality ◽  
Green Function Approach

Second-order diffraction theory is utilized to compute the sum-frequency diffraction loads on a deepwater tension-leg platform (TLP) in bidirectional waves. The linear diffraction solution is obtained utilizing a Green function approach using higher-order boundary elements. The second-order hydrodynamic loads explicitly due to the second-order potential are computed using the indirect, assisting radiation potential method. An efficient numerical technique is presented to treat the free-surface integral which appears in the second-order load formulation. Numerical results are presented for a stationary ISSC TLP in water of infinite depth. It is found that wave directionality may have a significant influence on the second-order hydrodynamic loads on a TLP and that the assumption of unidirectional waves does not always lead to conservative estimates of the sum-frequency loading.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

First and Second Order Wave-Current Interactions for Floating Bodies

2012 ◽  
Author(s):  
Charles Monroy ◽  
Yann Giorgiutti ◽  
Xiao-Bo Chen
Keyword(s):  
Field Method ◽  
Boundary Integral ◽  
Second Order ◽  
Boundary Integral Method ◽  
Diffraction Radiation ◽  
Floating Bodies ◽  
Order Problem ◽  
First Order ◽  
Wave Drift Damping ◽  
Order Quantities

The influence of current in sea-keeping problems is felt not only for first order quantities such as wave run-ups in front of the structure, but also mainly for second order quantities. In particular, the wave drift damping (which is expressed as the derivative of drift force with respect to the current) is of special interest for mooring systems. The interaction effects of a double-body steady flow on wave diffraction-radiation is studied through a decomposition of the time-harmonic potential into linear and interaction components. A boundary integral method is used to solve the first order problem. Ultimately, a far-field method is proposed to get access to second order drift forces.

A New Nonslender Ringing Load Approach Verified Against Experiments

1998 ◽  
Vol 120 (1) ◽  
pp. 20-29 ◽  
Author(s):  
J. R. Krokstad ◽  
C. T. Stansberg ◽  
A. Nestega˚rd ◽  
T. Marthinsen
Keyword(s):  
Wave Model ◽  
Second Order ◽  
Wave Load ◽  
Peak Wavelength ◽  
Third Order ◽  
Load Model ◽  
Order Analysis ◽  
First Order ◽  
Load Effects ◽  
Vertical Cylinders

New results from the most recent work within the Norwegian Joint Industry Project (JIP) “Higher Order Wave Load Effects on Large Volume Structures” are presented. A nonslender theoretical model is validated from experiments for two fixed, vertical cylinders with different diameter/peak wavelength ratios. A combination of complete diffraction first-order simulations, sum and difference frequency second-order simulations, and third-order FNV (Faltinsen, Newman, and Vinje, nonlinear long wave model) is implemented in order to develop a simplified and robust ringing load model for a large range of cylinder diameter/peak wavelength ratios. Results from the full diffraction second-order analysis show a significant reduction of second-order loads compared to pure FNV in the wavelength range relevant for ringing loads. The results show improved correspondence with high-frequency experimental loads compared with the unmodified FNV. Results for different cylinder peak wavelength ratios are presented, including validation against experiments. In addition, a few simplified response simulations are carried out demonstrating significant improvements with the modified FNV model.

Interaction of a Second-Order Solitary Wave With an Array of Four Vertical Cylinders

2006 ◽  
Author(s):  
A. Basmat ◽  
M. Markiewicz ◽  
S. Petersen
Keyword(s):  
Solitary Wave ◽  
Differential Equations ◽  
Order Approximation ◽  
Boussinesq Equations ◽  
Second Order ◽  
Nonlinearity Parameter ◽  
Wave Forces ◽  
Weakly Nonlinear ◽  
First Order ◽  
Vertical Cylinders

In this paper the interaction of a plane second order solitary wave with an array of four vertical cylinders is investigated. The fluid is assumed to be incompressible and inviscid. The diffraction analysis assumes irrotationality, which allows for the use of Boussinesq equations. A simultaneous expansion in a small nonlinearity parameter (wave amplitude/depth) and small dispersion parameter (depth/horizontal scale) is performed. Boussinesq models, which describe weakly nonlinear and weakly dispersive long waves, are characterized by the assumption that the nonlinearity and dispersion are both small and of the same order. An incident plane second order solitary wave is the Laitone solution of Boussinesq equations. The representation of variables as the series of small nonlinearity parameters leads to the sequence of linear boundary value problems of increasing order. The first order approximation can be determined as a solution of homogeneous differential equations and the second order approximation follows as a solution of non-homogeneous differential equations, where the right hand sides may be computed from the first order solution. For the case of a single cylinder an analytical solution exists. However, when dealing with more complex cylinder configurations, one has to employ numerical techniques. In this contribution a finite element approach combined with an appropriate time stepping scheme is used to model the wave propagation around an array of four surface piercing vertical cylinders. The velocity potential, the free surface elevation and the subsequent evolution of the scattered field are computed. Furthermore, the total second order wave forces on each individual cylinder are determined. The effect of the incident wave angle is discussed.

The Von Neumann-Mullins Theory of Grain Growth – Valid or Not?!

2004 ◽  
Vol 467-470 ◽  
pp. 1111-1116 ◽  
Author(s):  
Lasar S. Shvindlerman ◽  
Günter Gottstein ◽  
Anthony D. Rollett
Keyword(s):  
Relative Rate ◽  
Second Order ◽  
Rate Of Change ◽  
Recent Analysis ◽  
Order Problem ◽  
Von Neumann ◽  
First Order ◽  
Dimensional Network ◽  
The Stability ◽  
Grain Topology

We present a new analysis of the relative rate of growth or shrinkage of grains in a two-dimensional network, based on the classical Von Neumann-Mullins (VN-M) analysis. We find that an analysis of the stability of the grain shape during shrinkage or growth shows that any change in the regular 2D grain leads to changes in the shape. We also re-examine a recent analysis that claims to have invalidated the VN-M relationship, but find that it is still valid, and that the cited analysis, in fact, confused a second order correction with a first order problem, partly because their derivation was in error. The erroneous magnitude of the discrepancy led them to use unphysical issues to explain the discrepancy. The way in which the curvature is distributed along the perimeter of a grain only gives rise only to second order corrections to the rate of change of area as a function of grain topology (number of sides).

scholarly journals Second-order supercavitating hydrofoil theory

1962 ◽  
Vol 13 (3) ◽  
pp. 321-332 ◽  
Author(s):  
C. F. Chen
Keyword(s):  
Exact Solutions ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Lift Coefficient ◽  
Integral Form ◽  
Order Theory ◽  
Second Order ◽  
Order Problem ◽  
First Order ◽  
Lift And Drag

The second-order problem of Helmholtz flow past lifting hydrofoils and symmetric struts has been formulated and solved. The solution involves elementary operations on the known solutions of the first-order problem. The second-order lift and drag coefficients are given in integral form. Results obtained for a flat plate at incidence and a symmetric wedge agree with the exact solutions up to the second order. In terms of quantitative improvements, the present second-order theory predicts a lift coefficient for a flat plate at 45° incidence with an error of 8%, and a drag coefficient for a symmetric wedge of 50° included angle with an error of 5%; the corresponding angles at which the linear theory would predict force coefficients incurring the same errors are 5° and 15° respectively.

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