• Title/Summary/Keyword: Nonlinear wave equations

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Motion Analysis of Two Point Moored Oil Tanker (2점 계류된 선박에 대한 운동 해석)

  • Lee, Ho-Young;Lim, Choon-Gyu
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2003.10a
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    • pp.232-236
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    • 2003
  • The anchor is laid on seabed and the main engine is worked to against incident environmental loads in typoon. As the main engine is broken down in the storm, the anchor chain is cutted and the vessel is drifted. Although a ship is moored by two point mooring lines to keep the her position, a ship is crashed into a rock because of typoon and the accident of oil spilling may be occured. In this paper, we studied the position-keeping of a ship which is analyized based on the slow motion maneuvering equations considering wave, current and wind. The direct integration method is employed to estimate wave loads. The current forces are calculated by using mathematical of MMG. The two point mooring forces are quasisatatically evaluated by using the catenary equation. The coefficeints of wind forces are modeled from Isherwood’s emperical data and the variation of wind speed is estimated by wind spectrum. The nonlinear motions of a two point moored ship are simulated considering wave, current, wind load in time domain.

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Drift Motion Analysis on Horizontal Plane of a Two-Point Moored Oil Tanker (2점 계류된 선박에 대한 수평면상 표류운동 해석)

  • 이호영;임춘규
    • Journal of Ocean Engineering and Technology
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    • v.18 no.3
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    • pp.8-12
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    • 2004
  • The anchor is laid on the seabed, and the main engine is working against incident environmental loads in a typhoon. As the main engine is broken Mum in the storm, the anchor chain is cut and the vessel drifts. Although a ship is moored by two-point mooring lines to maintain her position, it has crashed into a rock because of a typhoon, resulting in a possible accidental oil spillage. In this paper, we studied maintenance of a ship's position, which is analyzed based on the slow motion maneuvering equations considering wave, current, and wind. To estimate wave loads, the direct integration method is employed. The current forces are calculated, using MMG (Mathematical Modeling Group). Th two-point mooring forces are quasi-statistically evaluated, using the catenary equation. Th coefficients of wind forces are modeled from Isherwood's empirical data, and the variation of wind speed is estimated by wind spectrum. The nonlinear motions of a two-point moored ship are simulated, considering wave, current, and wind load, in specific domain of time.

A CHARACTERISTICS-BASED IMPLICIT FINITE-DIFFERENCE SCHEME FOR THE ANALYSIS OF INSTABILITY IN WATER COOLED REACTORS

  • Dutta, Goutam;Doshi, Jagdeep B.
    • Nuclear Engineering and Technology
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    • v.40 no.6
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    • pp.477-488
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    • 2008
  • The objective of the paper is to analyze the thermally induced density wave oscillations in water cooled boiling water reactors. A transient thermal hydraulic model is developed with a characteristics-based implicit finite-difference scheme to solve the nonlinear mass, momentum and energy conservation equations in a time-domain. A two-phase flow was simulated with a one-dimensional homogeneous equilibrium model. The model treats the boundary conditions naturally and takes into account the compressibility effect of the two-phase flow. The axial variation of the heat flux profile can also be handled with the model. Unlike the method of characteristics analysis, the present numerical model is computationally inexpensive in terms of time and works in a Eulerian coordinate system without the loss of accuracy. The model was validated against available benchmarks. The model was extended for the purpose of studying the flow-induced density wave oscillations in forced circulation and natural circulation boiling water reactors. Various parametric studies were undertaken to evaluate the model's performance under different operating conditions. Marginal stability boundaries were drawn for type-I and type-II instabilities in a dimensionless parameter space. The significance of adiabatic riser sections in different boiling reactors was analyzed in detail. The effect of the axial heat flux profile was also investigated for different boiling reactors.

Hydraulic and Numerical Experiments of Stem Waves along a Vertical Wall (직립벽을 따른 연파의 수리 및 수치실험)

  • Lee, Jong In;Yoon, Sung Bum
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.4B
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    • pp.405-412
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    • 2006
  • This study investigates the characteristics of stem waves along a vertical wall generated by obliquely incident monochromatic waves through laboratory experiments conducted in a wave basin and numerical simulations using parabolic approximation equations. The investigation is focused on the nonlinear effect of incident waves on the propagation characteristics of stem waves. Numerical results are compared with laboratory measurements and good agreements are obtained. The main results of this study show that the normalized stem wave height along the wall decreases and the stem width increases as the angle of incident waves decreases or the nonlinearity of the incident waves increases.

Numerical Simulation of Two-Dimensional Shipping Water by Using a Simplified Model (단순화 모델에 의한 2차원 갑판침입수의 수치 시뮬레이션)

  • Kim, Yong J.;Kim, In C.
    • Journal of the Society of Naval Architects of Korea
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    • v.33 no.2
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    • pp.1-12
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    • 1996
  • Hydrodynamic characteristics of shipping water on deck are investigated by using a simplified two-dimensional model. Formulation of the shipping water on deck leads to a nonlinear hyperbolic system of equations based on the shallow-water wave theory. Time-domain solution of these equations are obtained numerically using a finite difference method which adopts predictor-corrector method for time-marching and 2nd upwind differencing method for convection term calculation. To confirm the validity of the present numerical method, we calculated some shallow-water wave problems accompanying a bore and compared the obtained results with the analytic solutions. We found good agreements between them. Though the calculation results of shipping water on deck, we show that the shipping water flows into the deck as a rarefying wave arid grows into a bore after colliding with a deck structure. Also we examined the effects of acceleration and slope of deck and found that they have significant influences on the flow of shipping water.

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Empirical Equation of Wave Run-up Height (도파고 경험식)

  • Yoo Dong Hoon;Kim In Ho
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.16 no.4
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    • pp.233-240
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    • 2004
  • For the development of empirical equation of run-up height, a new surf parameter called' wave action slope' $S_x$ is introduced. Approximate equation has been produced for each band of water depth for the computation of wave run-up height using the laboratory graph of Saville(1958). On the other hand using the laboratory data of Ahrens(1988) and Mase(1989), empirical equations of run-up height have been developed for the general application with considering roughness effect covering a wide range of water depth and wall slope. When Mase tried to relate the run-up height to the Iribarren number, nonlinear relation has been obtained and hence the empirical equation has a power law. But when the wave action slope is adopted as a major factor for the estimation of run-up height the empirical equation shows a linear relationship with very good correlation for the wide range of water depth and wall slope.

Numerical Analysis of Wave Impact Forces in Numerical Wave Basin (수치파 수조를 이용한 파랑 충격력 수치해석)

  • Shin, Young-Seop;Hong, Key-Yong
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • v.1
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    • pp.205-210
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    • 2006
  • The impact forces of the highly nonlinear waves are one of the important factors in designing the ocean structures. The impact forces are very difficult to analyze numerically and experimentally because they are impulsive in magnitude and occur instantaneously. In this study the numerical program based on N.S. equations are used to investigate the impact forces of steep waves where the waves are gene rated by the wave maker in the numerical wave basin. The arbitrary steep waves are generated by the superposition of waves of single frequency and the impact forces on vertical cylinder are simulated on the multiblock grids. V.O.F. and the local height function methods are used to track the free surfaces. To validate the numerical analysis the numerical results are compared with the experimental ones and the acceptable agreements are found. It is thought that more studies on the simulations of the incoming breaking waves and the impact forces on the vertical cylinder should be made to obtain the useful results to be applied in the offshore design.

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Numerical Analysis of Nonlinear Shoaling Characteristics over Surf Zone Using SPH and Lagrangian Dynamic Smagronsky Model (Lagrangian Dynamic Smagronsky 난류모형과 SPH를 이용한 쇄파역에서의 비선형 천수거동에 관한 연구)

  • Cho, Yong-Jun;Lee, Heon
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.19 no.1
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    • pp.81-96
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    • 2007
  • Nonlinear shoaling characteristics over surf zone are numerically investigated based on spatially averaged NavierStokes equation. We also test the validity of gradient model for turbulent stresses due to wave breaking using the data acquainted during SUPERTANK LABORATORY DATA COLLECTION PROJECT(Krauss et al., 1992). It turns out that the characteristics length scale of breaking induced current is not negligible, which firmly stands against ever popular gradient model, ${\kappa}-{\varepsilon}$ model, but favors Large Eddy Simulation with finer grid. Based on these observations, we model the residual stress of spatially averaged NavierStokes equation after Lagrangian Dynamic Smagorinsky(Meneveau et al., 1996). We numerically integrate newly proposed wave equations using SPH with Gaussian kernel function. Severely deformed water surface profile, free falling water particle, queuing splash after landing of water particle on the free surface and wave finger due to structured vortex on rear side of wave crest(Narayanaswamy and Dalrymple, 2002) are successfully duplicated in the numerical simulation of wave propagation over uniform slope beach, which so far have been regarded very difficult features to mimic in the computational fluid mechanics.

Wave Forces Acting on Large Vertical Circular Cylinder and Consequent Wave Transformations by Full-Nonlinear Analysis Method after Wave Breaking (강비선형해석법에 의한 대형연직원주구조물에 작용하는 쇄파후의 파력 및 파랑변형)

  • Lee, Kwang-Ho;Shin, Dong-Hoon;Kim, Do-Sam
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.20 no.4
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    • pp.401-412
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    • 2008
  • Simulations of three-dimensional numerical wave tank are performed to investigate wave force acting on a large cylindrical structure and consequent wave deformation, which are induced by bore after breaking waves. The numerical model is based on the three-dimensional Navier-Stokes equations with a finite-difference method combined with a volume of fluid(VOF) method, which is capable of tracking the complex free surface, including wave breaking. In order to promote wave breaking of the incident wave, the approach slope was built seaward of the structure with a constant slope and a large cylindrical structure was installed on a flat bed. The incident waves were broken on the approach slope or flat bed by its wave height. In the present study, all waves acting on the large cylindrical structure were limited to breaking bore after wave breaking. The effects of the position of the structure and the incident wave height on the wave force and wave transformations were mainly investigated with the concern of wave breaking. Further, the relations between the variation of wave energy by wave propagation after wave breaking and wave force acting on the structure were discussed to give the understanding of the full-linear wave-structure interactions in three-dimensional wave fields.

Computation of Aeolian Tones from Twin-Cylinders Using Immersed Surface Dipole Sources

  • Cheong, Cheol-Ung;Ryu, Je-Wook;Lee, Soo-Gab
    • Journal of Mechanical Science and Technology
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    • v.20 no.12
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    • pp.2292-2314
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    • 2006
  • Efficient numerical method is developed for the prediction of aerodynamic noise generation and propagation in low Mach number flows such as aeolian tone noise. The proposed numerical method is based on acoustic/viscous splitting techniques of which acoustic solvers use simplified linearised Euler equations, full linearised Euler equations and nonlinear perturbation equations as acoustic governing equations. All of acoustic equations are forced with immersed surface dipole model which is developed for the efficient computation of aerodynamic noise generation and propagation in low Mach number flows in which dipole source, originating from unsteady pressure fluctuation on a solid surface, is known to be more efficient than quadrupole sources. Multi-scale overset grid technique is also utilized to resolve the complex geometries. Initially, aeolian tone from single cylinder is considered to examine the effects that the immersed surface dipole models combined with the different acoustic governing equations have on the overall accuracy of the method. Then, the current numerical method is applied to the simulation of the aeolian tones from twin cylinders aligned perpendicularly to the mean flow and separated 3 diameters between their centers. In this configuration, symmetric vortices are shed from twin cylinders, which leads to the anti-phase of the lift dipoles and the in-phase of the drag dipoles. Due to these phase differences, the directivity of the fluctuating pressure from the lift dipoles shows the comparable magnitude with that from the drag dipoles at 10 diameters apart from the origin. However, the directivity at 100 diameters shows that the lift-dipole originated noise has larger magnitude than, but still comparable to, that of the drag-dipole one. Comparison of the numerical results with and without mean flow effects on the acoustic wave emphasizes the effects of the sheared background flows around the cylinders on the propagating acoustic waves, which is not generally considered by the classic acoustic analogy methods. Through the comparison of the results using the immersed surface dipole models with those using point sources, it is demonstrated that the current methods can allow for the complex interactions between the acoustic wave and the solid wall and the effects of the mean flow on the acoustic waves.