• 제목/요약/키워드: Nonlinear wave equations

검색결과 168건 처리시간 0.023초

선수부 갑판침입수의 수치시뮬레이션에 대한 기초연구 (A Fundamental Study for the Numerical Simulation Method of Green Water Occurrence on Bow Deck)

  • 정광열;이영길;김남철
    • 대한조선학회논문집
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    • 제47권2호
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    • pp.188-195
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    • 2010
  • Green water load is an important parameter to be considered in designing a modern ship or offshore structures like FPSO and FSRU. In this research, a numerical simulation method for green water phenomenon is introduced. The Navier-Stokes equations and the continuity equation are used as governing equations. The equations are calculated using Finite Difference Method(FDM) in rectangular staggered grid system. To increase the numerical accuracy near the body, the Cartesian cut cell method is employed. The nonlinear free-surface during green water incident is defined by Marker-density method. The green waters on a box in regular waves are simulated. The simulation results are compared with other experimental and computational results for verification. To check the applicability to moving ship, the green water of the ship which is towed by uniform force in regular wave, is simulated. The ship is set free to heave and to surge.

최대 엔트로피 방법을 이용한 비선형 불규칙 파고의 확률분포함수 (Probability Distribution of Nonlinear Random Wave Heights Using Maximum Entropy Method)

  • 안경모
    • 한국해안해양공학회지
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    • 제10권4호
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    • pp.204-210
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    • 1998
  • 최대 엔트로피 방법을 이용하여 강한 비정규분포과정의 특성을 갖는 비선형 불규칙 파고의 확률밀도 함수를 유도하였다. 파랑의 파고가 쇄파고(또는 수심)에 의해 제한되고 파고의 1, 2차 모멘트만 주어졌을 경우, 유도된 확률밀도함수는 $H_{b}$ (쇄파고), $H_{m}$(평균파고), $H_{rms}$(파고의 제곱평균평방근)의 매개변수로 폐합형(closed form)으로 표시된다. 파고의 3차 이상의 모멘트가 주어진 경우에는 최대 엔트로피를 갖는 확률밀도함수의 매개변수를 구하기 위해서 비선형 적분 방정식 계를 Newton-Raphson 방법을 이용하여 수치적으로 구하였다. 최대 엔트로피 방법을 이용하여 유도된 파고의 확률밀도함수를 비정규분포의 특성이 강한 실측자료와 비교하였다. 실측자료는 폭풍시 중간수심과 천해에서 측정된 쇄파고에 가까운 자료로서 강한 비선형 불규칙 파랑의 특성을 지니며, 이 경우에도 유도된 확률밀도함수가 측정된 파고의 막대그래프와 잘 일치하였다. 강한 비선형 불규칙파의 특성을 갖는 파랑의 파고일 경우에도 파고의 1, 2차 모멘트만으로도 파고의 분포를 잘 나타낼 수 있었다. 최대 엔트로피 방법을 이용하여 구해진 파고의 확률분포함수는 해안구조물의 설계파를 결정하는 극치파고분포와 파고의 통계적인 특성을 추정하는데 매우 유용하게 이용될 수 있다.

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Numerical hydrodynamic analysis of an offshore stationary-floating oscillating water column-wave energy converter using CFD

  • Elhanafi, Ahmed;Fleming, Alan;Macfarlane, Gregor;Leong, Zhi
    • International Journal of Naval Architecture and Ocean Engineering
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    • 제9권1호
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    • pp.77-99
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    • 2017
  • Offshore oscillating water columns (OWC) represent one of the most promising forms of wave energy converters. The hydrodynamic performance of such converters heavily depends on their interactions with ocean waves; therefore, understanding these interactions is essential. In this paper, a fully nonlinear 2D computational fluid dynamics (CFD) model based on RANS equations and VOF surface capturing scheme is implemented to carry out wave energy balance analyses for an offshore OWC. The numerical model is well validated against published physical measurements including; chamber differential air pressure, chamber water level oscillation and vertical velocity, overall wave energy extraction efficiency, reflected and transmitted waves, velocity and vorticity fields (PIV measurements). Following the successful validation work, an extensive campaign of numerical tests is performed to quantify the relevance of three design parameters, namely incoming wavelength, wave height and turbine damping to the device hydrodynamic performance and wave energy conversion process. All of the three investigated parameters show important effects on the wave-pneumatic energy conversion chain. In addition, the flow field around the chamber's front wall indicates areas of energy losses by stronger vortices generation than the rear wall.

The structural safety assessment of a tie-down system on a tension leg platform during hurricane events

  • Yang, Chan K.;Kim, M.H.
    • Ocean Systems Engineering
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    • 제1권4호
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    • pp.263-283
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    • 2011
  • The performance of a rig tie-down system on a TLP (Tension Leg Platform) is investigated for 10-year, 100-year, and 1000-year hurricane environments. The inertia loading on the derrick is obtained from the three-hour time histories of the platform motions and accelerations, and the dynamic wind forces as well as the time-dependent heel-induced gravitational forces are also applied. Then, the connection loads between the derrick and its substructure as well as the substructure and deck are obtained to assess the safety of the tie-down system. Both linear and nonlinear inertia loads on the derrick are included. The resultant external forces are subsequently used to calculate the loads on the tie-down clamps at every time step with the assumption of rigid derrick. The exact dynamic equations including nonlinear terms are used with all the linear and second-order wave forces considering that some dynamic contributions, such as rotational inertia, centripetal forces, and the nonlinear excitations, have not been accounted for in the conventional engineering practices. From the numerical simulations, it is seen that the contributions of the second-order sum-frequency (or springing) accelerations can be appreciable in certain hurricane conditions. Finally, the maximum reaction loads on the clamps are obtained and used to check the possibility of slip, shear, and tensile failure of the tie-down system for any given environment.

잠제의 형상 변화에 따른 반사파 및 투과파의 거동특성 (Behaviors of Reflected and Transmitted Waves for Geometric Change of Submerged Breakwater)

  • 이철응;오원택
    • 산업기술연구
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    • 제20권A호
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    • pp.139-148
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    • 2000
  • A numerical model is represented to calculate the wave fields such as the reflected waves, the transmitted waves, and depth averaged velocities over submerged breakwaters for the normally incident wave trains of nonlinear monochromatic wave. The numerical model is correctly formulated by using both the finite amplitude shallow water equations with the effects of bottom friction and the explicit dissipative Lax-Wendroff finite difference scheme, also satisfactorily verified by comparison with the other results. The behaviors of reflected and transmitted waves with respect to geometric parameters of submerged breakwater such as the slope, crest depth, and crest width are numerically analyzed in this study. In particular, the reflection and transmission coefficients are quantitatively calculated as the function of geometric parameter of submerged breakwater. It is found that the crest depth among parameters related to practical design may be the most important parameter in designing the submerged breakwater. Therefore, the effective and economic performances of submerged breakwater should be depended on the determination of optimal crest depth.

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Seismic response analysis of layered soils considering effect of surcharge mass using HFTD approach. Part II: Nonlinear HFTD and numerical examples

  • Saffarian, Mohammad A.;Bagheripour, Mohammad H.
    • Geomechanics and Engineering
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    • 제6권6호
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    • pp.531-544
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    • 2014
  • Studies of earthquakes over the last 50 years and the examination of dynamic soil behavior reveal that soil behavior is highly nonlinear and hysteretic even at small strains. Nonlinear behavior of soils during a seismic event has a predominant role in current site response analysis approaches. Common approaches to ground response analysis include linear, equivalent linear and nonlinear methods. These methods of ground response analysis may also be categorized into time domain and frequency domain concepts. Simplicity in developing analytical relations and accuracy in considering soils' dynamic properties dependency to loading frequency are benefits of frequency domain analysis. On the other hand, nonlinear methods are complicated and time consuming mainly because of their step by step integrations in time intervals. In part Ι of this paper, governing equations for seismic response analysis of surcharged and layered soils were developed using fundamental of wave propagation theory based on transfer function and boundary conditions. In this part, nonlinear seismic ground response is analyzed using extended HFTD method. The extended HFTD method benefits Newton-Raphson procedure which applies regular iterations and follows soils' fundamental stress-strain curve until convergence is achieved. The nonlinear HFTD approach developed here are applied to some examples presented in this part of the paper. Case studies are carried in which effects of some influencing parameters on the response are investigated. Results show that the current approach is sufficiently accurate, efficient, and fast converging. Discussions on the results obtained are presented throughout this part of the paper.

경계요소법을 이용한 비선형파의 재현 (Simulation of Nonlinear Water Waves using Boundary Element Method)

  • 오영민;이길성;전인식
    • 한국해안해양공학회지
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    • 제5권3호
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    • pp.204-211
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    • 1993
  • Laplace 방정식을 Green 공식으로 해석한 경계요소법을 이용하여 수치수조에서 비선형파를 재현하였다. 미지수는 유체영역의 경계에 설정한 각 절점에서의 속도포텐셜과 수면변위이며 이를 구하기 위하여 지배방정식과 자유수면 경계조건을 기본식으로 하는 연립 1차방정식을 구성하였다. 동력학적 자유수면 경계조건에서 속도의 제곱항을 고려하였으며 자유수면 경계에서 속도포텐셜의 연직변화를 고려하여 이의 시간미분을 계산하였다. 본 수치모델을 이용하여 고립파와 Stokes의 2차 파낭을 재현한 결과, 이론치와 매우 잘 일치함을 확인하였다.

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Influence of Tether Length in the Response Behavior of Square Tension Leg Platform in Regular Waves

  • El-gamal, Amr R.;Essa, Ashraf
    • International Journal of Ocean System Engineering
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    • 제4권1호
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    • pp.19-28
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    • 2014
  • The tension leg platform (TLP) is a vertically moored structure with excess buoyancy. The TLP is regarded as moored structure in horizontal plan, while inherit stiffness of fixed platform in vertical plane. In this paper, a numerical study using modified Morison equation was carried out in the time domain to investigate the influence of nonlinearities due to hydrodynamic forces and the coupling effect between surge, sway, heave, roll, pitch and yaw degrees of freedom on the dynamic behavior of TLP's. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables and the nonlinear equations of motion were solved utilizing Newmark's beta integration scheme. The effect of tethers length and wave characteristics such as wave period and wave height on the response of TLP's was evaluated. Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e. 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether length, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations about that is significantly dependent on tether length.

다공벽을 전파하는 압축파에 관한 수치해석적 연구 (Numerical Study of Compression Waves Propagating Through Porous Walls)

  • 김희동
    • 대한기계학회논문집B
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    • 제21권11호
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    • pp.1403-1412
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    • 1997
  • When a high-speed railway train enters a tunnel, a compression wave is generated ahead of the train and propagates through the tunnel, compressing and accelerating the rest air in front of the wave. At the exit of the tunnel, an impulsive wave is emitted outward toward the surrounding, which causes a positive impulsive noise like a kind of sonic boom produced by a supersonic aircraft. With the advent of high-speed train, such an impulsive noise can be large enough to cause the noise problem, unless some attempts are made to alleviate its pressure levels. In the purpose of the impulsive noise reduction, the present study calculated the effect of porous walls on the compression wave propagating into a model tunnel. Two-dimensional unsteady compressible equations were differenced by using a Piecewise Linear Method. Calculation results show that the cavity/porous wall system is very effective for a compression wave with a large nonlinear effect. The porosity of 30% is most effective for the reduction of the maximum pressure gradient of the compression wave front. The present calculation results are in a good agreement with experimental ones obtained previously.

집중질량 라인모델을 이용한 Steel Lazy Wave Riser의 비선형 동적 해석 (Nonlinear Dynamic Analysis of Steel Lazy Wave Riser using Lumped Mass Line Model)

  • 오승훈;정재환;박병원;권용주;정동호
    • 한국해양공학회지
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    • 제33권5호
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    • pp.400-410
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    • 2019
  • In this study, the numerical code for the 3D nonlinear dynamic analysis of an SLWR (Steel Lazy Wave Riser) was developed using the lumped mass line model in a FORTRAN environment. Because the lumped mass line model is an explicit method, there is no matrix operation. Thus, the numerical algorithm is simple and fast. In the lumped mass line model, the equations of motion for the riser were derived by applying the various forces acting on each node of the line. The applied forces at the node of the riser consisted of the tension, shear force due to the bending moment, gravitational force, buoyancy force, riser/ground contact force, and hydrodynamic force based on the Morison equation. Time integration was carried out using a Runge-Kutta fourth-order method, which is known to be stable and accurate. To validate the accuracy of the developed numerical code, simulations using the commercial software OrcaFlex were carried out simultaneously and compared with the results of the developed numerical code. To understand the nonlinear dynamic characteristics of an SLWR, dynamic simulations of SLWRs excited at the hang-off point and of SLWRs in regular waves were carried out. From the results of these dynamic simulations, the displacements at the maximum bending moments at important points of the design, like the hang-off point, sagging point, hogging points, and touch-down point, were observed and analyzed.