scholarly journals Numerical Analysis of Combined Wave Radiation and Diffraction on a Floating Barge

Water ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 205
Author(s):  
Yajie Li ◽  
Bin Xu ◽  
Desheng Zhang ◽  
Xi Shen ◽  
Weibin Zhang
Keyword(s):  
Incident Wave ◽  
Radiation Effects ◽  
Nonlinear Boundary Conditions ◽  
The Body ◽  
Wave Radiation ◽  
Test Cases ◽  
Horizontal Force ◽  
Dimensional Boundary ◽  
Lagrangian Scheme ◽  
Sway Motion

A two-dimensional boundary element method (BEM) based on the potential flow theory is adopted to study the combined wave radiation and diffraction by a single barge. The wave-body interaction problems are simulated using a mixed Euler-Lagrangian scheme, with fully nonlinear boundary conditions. The numerical schemes are verified through comparing with existing results, which show that both the wave runups on the barge and hydrodynamic forces can be calculated with sufficient accuracy. Cases of a single barge subjected to sway motion and regular waves are studied. The real contribution of this study is the outcomes of the spectral analysis conducted for test cases when wave radiation effects are considered in addition to pure wave diffraction. The cases of sway motion with the same frequency as incident wave are simulated first. It is found that sway motion will reduce the overall horizontal force when the frequency is lower than a critical frequency. After that, the higher the frequency, the bigger the horizontal force increasing effect. When the frequency of sway motion is lower than that of incident wave, in terms of the magnitude of the horizontal force, sway motion of the body will always make the resultant force larger than that of pure diffraction case.

Theory of Short Wave Excitation

1986 ◽  
Vol 30 (03) ◽  
pp. 147-152
Author(s):  
Yong Kwun Chung
Keyword(s):  
Incident Wave ◽  
Characteristic Length ◽  
Finite Depth ◽  
Short Wave ◽  
The Body ◽  
Wave Number ◽  
Floating Body ◽  
Wave Excitation ◽  
Exciting Forces ◽  
Wave Exciting Forces

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.

An Improved Body-Exact Method to Predict Large Amplitude Ship Roll Responses

2018 ◽  
Author(s):  
Rahul Subramanian ◽  
Naga Venkata Rakesh ◽  
Robert F. Beck
Keyword(s):  
Incident Wave ◽  
Large Amplitude ◽  
Nonlinear Models ◽  
Body Position ◽  
Computational Cost ◽  
Offshore Structures ◽  
The Body ◽  
Surface Boundary ◽  
Strip Theory ◽  
New Formulation

Accurate prediction of the roll response is of significant practical relevance not only for ships but also ship type offshore structures such as FPSOs, FLNGs and FSRUs. This paper presents a new body-exact scheme that is introduced into a nonlinear direct time-domain based strip theory formulation to study the roll response of a vessel subjected to moderately large amplitude incident waves. The free surface boundary conditions are transferred onto a representative incident wave surface at each station. The body boundary condition is satisfied on the instantaneous wetted surface of the body below this surface. This new scheme allows capturing nonlinear higher order fluid loads arising from the radiated and wave diffraction components. The Froude-Krylov and hydrostatic loads are computed on the intersection surface of the exact body position and incident wave field. The key advantage of the methodology is that it improves prediction of nonlinear hydrodynamic loads while keeping the additional computational cost small. Physical model tests have been carried out to validate the computational model. Fairly good agreement is seen. Comparisons of the force components with fully linear and body-nonlinear models help in bringing out the improvements due to the new formulation.

An analytical theory of distributed axisymmetric barotropic vortices on the β-plane

1994 ◽  
Vol 269 ◽  
pp. 301-321 ◽  
Author(s):  
G. M. Reznik ◽  
W. K. Dewar
Keyword(s):  
Radiation Effects ◽  
Planetary Wave ◽  
Complete Solution ◽  
Asymptotic Series ◽  
Vortex Motion ◽  
Present Theory ◽  
Analytical Theory ◽  
Wave Radiation ◽  
Initial Value ◽  
Numerical Predictions

An analytical theory of barotropic β-plane vortices is presented in the form of an asymptotic series based on the inverse of vortex nonlinearity. In particular, a solution of the initial value problem is given, in which the vortex is idealized as a radially symmetric function of arbitrary structure. Motion of the vortex is initiated by its interaction with the so-called ‘β-gyres’ which, in turn, are generated by the vortex circulation. Comparisons of analytical and numerical predictions for vortex motion are presented and demonstrate the utility of the present theory for times comparable to the ‘wave’ timescale. The latter exceeds the temporal limit derived from formal considerations. The properties of the far-field planetary wave radiation are also computed.This theory differs from previous calculations by considering more general initial vortex profiles and by obtaining a more complete solution for the perturbation fields. Vortex trajectory predictions accrue error systematically by integrating vortex propagation rates which are too strong. This appears to be connected to higher-order planetary wave radiation effects.

scholarly journals Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack

2018 ◽  
Vol 845 ◽  
pp. 682-712 ◽  
Author(s):  
Zhi Fu Li ◽  
Guo Xiong Wu ◽  
Chun Yan Ji
Keyword(s):  
Green Function ◽  
Circular Cylinder ◽  
Body Surface ◽  
Ice Sheet ◽  
Integral Form ◽  
Multipole Expansion ◽  
The Body ◽  
Wave Radiation ◽  
Surface Boundary ◽  
The Green Function

Wave radiation and diffraction by a circular cylinder submerged below an ice sheet with a crack are considered based on the linearized velocity potential theory together with multipole expansion. The solution starts from the potential due to a single source, or the Green function satisfying both the ice sheet condition and the crack condition, as well as all other conditions apart from that on the body surface. This is obtained in an integral form through Fourier transform, in contrast to what has been obtained previously in which the Green function is in the series form based on the method of matched eigenfunction expansion in each domain on both sides of the crack. The multipole expansion is then constructed through direct differentiation of the Green function with respect to the source position, rather than treating each multipole as a separate problem. The use of the Green function enables the problem of wave diffraction by the crack in the absence of the body to be solved directly. For the circular cylinder, wave radiation and diffraction problems are solved by applying the body surface boundary condition to the multipole expansion, through which the unknown coefficients are obtained. Extensive results are provided for the added mass and damping coefficient as well as the exciting force. When the cylinder is away from the crack, a wide spacing approximation method is used, which is found to provide accurate results apart from when the cylinder is quite close to the crack.

Subharmonic resonant interaction of a gravity–capillary progressive axially symmetric wave with a radial cross-wave

2019 ◽  
Vol 869 ◽  
pp. 439-467 ◽  
Author(s):  
Meng Shen ◽  
Yuming Liu
Keyword(s):  
Free Surface ◽  
Evolution Equation ◽  
Threshold Value ◽  
Resonant Interaction ◽  
The Body ◽  
Wave Radiation ◽  
Axially Symmetric ◽  
Damping Term ◽  
The Cross ◽  
Cross Waves

We theoretically investigate the problem of subharmonic resonant interaction of a progressive (axially symmetric) ring wave with a radial cross-wave in the context of the potential-flow formulation for gravity-capillary waves. The objective is to understand the nonlinear mechanism governing energy transfer from a progressive ring wave to its subharmonic cross-waves through triadic resonant interactions. We first show that for an arbitrary three-dimensional body floating in an unbounded free surface, there exists a set of homogeneous solutions at any frequency in the gravity-capillary wave context. The homogeneous solution depends solely on the mean free-surface slope at the waterline of the body and physically represents a progressive radial cross-wave. Unlike standing cross-waves, a progressive cross-wave loses energy during propagation by overcoming the work done by surface tension at the waterline and through wave radiation. We then consider the subharmonic interaction of a progressive ring wave, which is forced by a radial swelling–contraction deformation of a vertical circular cylinder, with subharmonic cross-waves. We derive the nonlinear spatial–temporal evolution equation governing the motion of the cross-wave by use of the average Lagrangian method. In addition to energy-input terms from the interaction with the forced ring wave, the evolution equation contains a damping term associated with energy loss in cross-wave propagation. We show that the presence of the damping term leads to a non-trivial threshold value of the ring wave steepness (or amplitude) beyond which the cross-wave becomes unstable and grows with time by taking energy from the ring wave. Finally, we extend this analysis to the experimental case of Tatsuno et al. (Rep. Res. Inst. Appl. Mech. Kyushu University, vol. 17, 1969, pp. 195–215) in which asymmetric wave patterns are observed during high-frequency vertical oscillations of a surface-piercing sphere. The theoretical prediction of the threshold value of oscillation amplitude and characteristic features of generated radial cross-waves agrees reasonably well with experimental observations.

The radiation and scattering of surface waves by vertical barriers

1974 ◽  
Vol 63 (4) ◽  
pp. 625-634 ◽  
Author(s):  
D. Porter
Keyword(s):  
Boundary Value Problem ◽  
Surface Waves ◽  
Incident Wave ◽  
Small Amplitude ◽  
Fluid Motion ◽  
Vertical Plane ◽  
Wave Radiation ◽  
Two Dimensional ◽  
Radiation Problem ◽  
Vertical Barriers

A train of small-amplitude surface waves is incident normally on an arbitrary arrangement of thin barriers lying in a vertical plane in deep water. Each barrier is allowed to make small rolling or swaying oscillations of the same frequency as that of the incident wave. The boundary-value problem for the consequent fluid motion, assumed two-dimensional, is solved exactly using a technique which enables the amplitudes of the scattered waves far from the barriers to be readily determined. Reference is made to the associated wave radiation problem and to the calculation of forces and moments on the barriers.

Effect of vortex shedding on the coupled roll response of bodies in waves

1988 ◽  
Vol 189 ◽  
pp. 243-261 ◽  
Author(s):  
M. J. Downie ◽  
P. W. Bearman ◽  
J. M. R. Graham
Keyword(s):  
Vortex Shedding ◽  
Degrees Of Freedom ◽  
Rectangular Cross Section ◽  
Vortex Method ◽  
The Body ◽  
Wave Radiation ◽  
Viscous Damping ◽  
Discrete Vortex ◽  
Hydrodynamic Damping ◽  
Main Component

Hydrodynamic damping of floating bodies is due mainly to wave radiation and viscous damping. The latter is particularly important in controlling those responses of the body for which the wave damping is small. The roll response of ship hulls near resonance in beam seas is an example of this. The present paper applies a discrete vortex method as a local solution to model vortex shedding from the bilges of a barge hull of rectangular cross-section and hence provides an analytic method for predicting its coupled motions in three degrees of freedom, including the effects of the main component of viscous damping. The method provides a frequency-domain solution satisfying the full linearized boundary conditions on the free surface.

Can polymetastatic disease be arrested using SABR? A dosimetric analysis to inform development of a phase I trial.

2020 ◽  
Vol 38 (15_suppl) ◽  
pp. e21567-e21567
Author(s):  
Mark Thomas Corkum ◽  
Hatim Fakir ◽  
David A. Palma ◽  
Timothy K. Nguyen ◽  
Glenn Bauman
Keyword(s):  
Clinical Trial ◽  
Phase I ◽  
Dose Level ◽  
Phase I Trial ◽  
The Body ◽  
Phase Iii ◽  
Whole Body ◽  
Stereotactic Ablative Radiotherapy ◽  
Test Cases ◽  
Dose Escalation Study

e21567 Background: Phase II randomized trials suggest that stereotactic ablative radiotherapy (SABR) improves progression-free and overall survival in patients with oligometastatic cancer, with phase III trials currently testing SABR in up to 10 metastases. Whether SABR could provide similar benefits in polymetastatic disease ( > 10 metastases) is unknown. A critical first step is to determine the feasibility of planning SABR for a large number of metastases throughout the body while maintaining acceptable organ at risk (OAR) doses. Therefore, we sought to evaluate the dosimetric feasibility of using SABR in polymetastatic disease ( > 10 sites) while adhering to OAR constraints to be used in a phase I trial (ARREST). Methods: Five craniospinal CT simulations were utilized to retrospectively contour 24 (n = 2), 30 (n = 2) and 50 (n = 1) tumour targets not present on the initial scan. Standard PTV margins were added based on institutional immobilization practices. OAR constraints from published clinical trial protocols were used. Radiotherapy plans for the highest dose level in our planned phase I trial (30Gy in 5 fractions) were created utilizing a minimum number of isocentres. Plans were created using Raystation (RaySearch Laboratories, Stockholm, Sweden) for delivery on linear accelerators using volumetric modulated arc therapy. Results: The gross tumour volumes (GTVs) ranged from 134.8– 184.2cm3 in our five test cases. The first two cases with 24 GTVs have been planned and were deemed to be clinically acceptable. PTV volumes were 483.0cm3 and 417.4cm3, utilizing five and six isocentres for treatment respectively. Median PTV D95 was 29.7Gy and 29.0Gy, whole body V10 was 21.2% and 17.4%, and V5 was 41.8% and 44.8%. All OAR goals were met, though low-dose conformality was less than traditional SABR treatment plans (R100 of 1.04 and 0.93; R50 of 9.90 and 6.98, respectively). The remainder of the test cases will be presented. Conclusions: In our test cases, planning SABR in polymetastatic disease appears dosimetrically feasible. Our phase I clinical trial (ARREST) is under development, which will evaluate the feasibility and toxicity of delivering SABR in polymetastatic disease in a 3+3 dose escalation study. The starting dose level will be 12Gy in 2 weekly fractions, escalating the dose by adding 6Gy weekly until our target dose of 30Gy in 5 weekly fractions. Our study population will include > 10 sites of disease, all tumour types, and patients must have exhausted standard lines of systemic therapy.

The heat balance of sheep standing in the sun

1957 ◽  
Vol 8 (3) ◽  
pp. 271 ◽  
Author(s):  
CHB Priestley
Keyword(s):  
Heat Balance ◽  
Heat Load ◽  
The Body ◽  
Wave Radiation ◽  
The Sun ◽  
Convective Heat Loss ◽  
Radiation Exchange ◽  
Long Wave ◽  
The Heat Balance ◽  
Long Wave Radiation

An extension is made of Lee's (1950) original discussion of the heat balance of sheep exposed to a tropical sun. Methods are given for calculating the two quantities, convective heat loss and long-wave radiation exchange, which automatically compensate to a large extent for the added heat load. There appear to be advantages in distinguishing between the heat balance of the fleece and that of the body of the sheep, and this provides a method of estimating the heat conducted to the body as a consequence of the insolation.

Transient Fluid Forces on a Rigid Circular Cylinder Subjected to Small Amplitude Motions

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Cédric Leblond ◽  
Vincent Melot ◽  
Jean-François Sigrist ◽  
Christian Lainé ◽  
Bruno Auvity ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Compressible Fluid ◽  
Small Amplitude ◽  
Fluid Model ◽  
The Body ◽  
Analytical Models ◽  
Fluid Forces ◽  
History Effects ◽  
Perturbation Problem ◽  
Dimensional Boundary

The present paper treats the transient fluid forces experienced by a rigid circular cylinder moving along a radial line in a fluid initially at rest. The body is subjected to a rapid displacement of relatively small amplitude in relation to its radius. Both infinite and cylindrically confined fluid domains are considered. Furthermore, non-negligible amplitude motions of the inner cylinder, and viscous and compressible fluid effects are addressed, successively. Different analytical methods and models are used to tackle each of these issues. For motions of non-negligible amplitude of the inner cylinder, a potential flow is assumed and the model, formulated as a two-dimensional boundary perturbation problem, is solved using a regular expansion up to second order. Subsequently, viscous and compressible effects are handled by assuming infinitesimal amplitude motions. The viscous fluid forces are formulated by solving a singular perturbation problem of the first order. Compressible fluid forces are then determined from the wave equation. A nonlinear formulation is obtained for the non-negligible amplitude motion. The viscous and compressible fluid forces, formulated in terms of convolution products, are linked to fluid history effects induced by wave propagation phenomena in the fluid domain. These models are expressed with dimensionless parameters and illustrated for a specific motion imposed on the inner cylinder. The different analytical models permit coverage of a broad range of motions. Hence, for a given geometry and imposed displacement, the appropriate fluid model can be identified and the resulting fluid forces rapidly estimated. The limits of these formulations are also discussed.

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