Unsteady interaction of shock wave diffracting around a circular cylinder in air

The reflection and diffraction of a planar shock wave around a circular cylinder are a typical problem of the complex nonlinear shock wave phenomena in literature. It has long been studied experimentally, analytically as well as numerically. Takayama in 1987 obtained clear experimental pictures of isopycnics in shock tube under the condition that the impinging shock wave propagates as far as 3 diameters away from the cylinder. To know more completely the whole unsteady process, it is desirable to get experimental results in a region which is more than 10 diameters away from the cylinder. This is what has been done in this paper by using the pulsed laser holographic interferometry for several shock Mach numbers of the impinging shock. Results for several moments are shown, giving more knowledge about the whole unsteady flow field. This is useful for a reliable and complete understanding of the changing force acting on the cylinder, and provides interesting data to check the performance of many recently developed high resolution numerical methods for unsteady shock wave calculation. The project suported partially by National Natural Science Foundation of China     

Development of a one-way coupled diffraction/trapped air model for predicting wave loading on bridges under water wave attack

In recent years, a number of researchers have applied various computational methods to study the wave and tsunami forcing on bridge superstructure problems. Usually, these computational analyses have relied upon application of computational fluid dynamic (CFD) codes. While CFD models provide accurate results, their disadvantage is that they tend to be computationally expensive. Thus, it may be difficult to apply these techniques during risk assessment analyses. During this study, an alternative computational method was explored in which a previously-developed diffraction model was combined with a previously-developed trapped air model under worst-case wave loading conditions (i.e., when the water surface was at the same elevation as the bottom bridge chord elevation). The governing equations were solved using a finite difference algorithm for the case where the bridge was attacked by a single wave in two dimensions. Resultant water forces were computed using results from the diffraction/trapped air computations, and water force values were compared with data from three datasets. In general, excellent agreement between the diffraction/trapped air model and data was observed. The computational time associated with the model was only approximately one hour per bridge configuration, which would appear to be an improvement when compared with other computational techniques.     

An analytical soluion of wave forces on large square cylinder

Wave forces on large square cylinder are determined by using the conformal transformation method. It is found that only for square cylinder, the governing equation is still the Helmholtz equation after the conformal transformation. An analytical solution of wave forces on square cylinder is presented by using the solution of wave forces on a circular cylinder.     

On solitary wave diffraction by multiple,in-line vertical cylinders

The interaction of solitary waves with multiple, in-line vertical cylinders is investigated. The fixed cylinders are of constant circular cross section and extend from the seafloor to the free surface. In general, there are N of them lined in a row parallel to the incoming wave direction. Both the nonlinear, generalized Boussinesq and the Green–Naghdi shallow-water wave equations are used. A boundary-fitted curvilinear coordinate system is employed to facilitate the use of the finite-difference method on curved boundaries. The governing equations and boundary conditions are transformed from the physical plane onto the computational plane. These equations are then solved in time on the computational plane that contains a uniform grid and by use of the successive over-relaxation method and a second-order finite-difference method to determine the horizontal force and overturning moment on the cylinders. Resulting solitary wave forces from the nonlinear Green–Naghdi and the Boussinesq equations are presented, and the forces are compared with the experimental data when available.     

Vortex shedding around a near-wall circular cylinder induced by a solitary wave

This study developed a two-dimensional generalized vortex method to analyze the shedding of vortices and the hydrodynamic forces resulting from a solitary wave passing over a submerged circular cylinder placed near a flat seabed. Numerical results for validation are compared with other numerical and experimental results, and satisfactory agreement is found. A series of simulations were performed to study the effects of gap-to-diameter ratio and incident wave height on vorticity pattern as well as the forces exerted on the cylinder. The range of the heights of incident waves is from 0.3h to 0.7h, where h is the still water depth. The range of the gap-to-diameter ratios is from 0.1 to 0.8. The results indicate that the flow pattern and the pressure distribution change significantly because of the close proximity of the seabed where the vorticity flux on the seabed-side surface of the cylinder is suppressed. Placing the cylinder nearer the seabed increases the drag and the positive lift on the cylinder. When the gap-to-diameter ratio increases, the pattern of vortices changes because of the interaction between the main recirculation zone and the shear layers separated from the gap. The maxima of drag, lift and total force increase linearly with the height of the incident wave.     

定常流作用于波浪形边界附近的圆柱上的水动力

本文介绍在水洞中做的作用于波浪形边界附近的水动力特性的实验研究。在基于圆柱模型直径的 R_c=10~4～1.9×10~4 范围内,测量了圆柱在波谷、波峰和不同距离上的阻力、升力脉动变化的频率。流谱显示实验揭示了尾流结构随距离-直径比 G/D 的变化情况及圆柱与边界相互作用的机制。     

非定常不可压N-S方程的最小二乘算子分裂有限元法数值求解

采用最小二乘算子分裂有限元法求解非定常不可压N-S(Navier-Stokes)方程,即在每个时间层上采用算子分裂法将N-S方程分裂成扩散项和对流项,这样既能考虑对流占优特点又能顾及方程的扩散性质。扩散项是一个抛物型方程,时间离散采用向后差分格式,空间离散采用标准Galerkin有限元法。对流项的时间项采用后向差分格式,非线性部分用牛顿法进行线性化处理,再用最小二乘有限元法进行空间离散,得到对称正定的代数方程组系数矩阵。采用Re=1000的方腔流对该算法的有效性进行检验,表明其具有较高的精度,能够很好地捕捉流场中的涡结构。同时,对圆柱层流绕流进行了数值研究,通过流线图、压力场、阻力系数、升力系数及斯特劳哈数等结果的分析与对比,表明本文算法对于模拟圆柱层流绕流是准确和可靠的。     

Fully nonlinear modeling of radiated waves generated by floating flared structures

The nonlinear radiated waves generated by a structure in forced motion, are simulated numerically based on the potential theory. A fully nonlinear numerical model is developed by using a higher-order boundary element method （HOBEM）. In this model, the instantaneous body position and the transient free surface are updated at each time step. A Lagrangian technique is employed as the time marching scheme on the free surface. The mesh regridding and interpolation methods are adopted to deal with the possible numerical instability. Several auxiliary functions are proposed to calculate the wave loads indirectly, instead of directly predicting the temporal derivative of the velocity potential. Numerical experiments are carried out to simulate the heave motions of a submerged sphere in infinite water depth, the heave and pitch motions of a truncated flared cylinder in finite depth. The results are verified against the published numerical results to ensure the effectiveness of the proposed model. Moreover, a series of higher harmonic waves and force components are obtained by the Fourier transformation to investigate the nonlinear effect of oscillation frequency. The difference among fully nonlinear, body-nonlinear and linear results is analyzed. It is found that the nonlinearity due to free surface and body surface has significant influences on the numerical results of the radiated waves and forces.     

LOW-FREQUENCY RESPONSES OF NONLINEARLY MOORED VESSELS IN RANDOM WAVES: COUPLED SURGE,PITCH AND HEAVE MOTIONS

The responses of a multi-degree-of-freedom model of a moored vessel are analysed, accounting for the hydroelastic interaction between the nonlinear wave hydrodynamics and the nonlinear mooring stiffness. A two-scale perturbation method developed by Sarkar & Eatock Taylor to determine low-frequency hydrodynamic forces on a single-degree-of-freedom model of a nonlinearly moored vessel has been extended to analyse the nonlinear multi-degree-of-freedom dynamics of the system. Surge, heave and pitch motions are considered. The perturbation equations of successive orders are derived. To illustrate the approach, semi-analytical expressions for the higher-order hydrodynamic force components have been obtained for a truncated circular cylinder in finite water depth. In addition to conventional quadratic force transfer functions, a new type of higher-order force transfer function is introduced. This is used to characterize the hydrodynamic forces on the vessel which arise due to nonlinearity of the mooring stiffness. These are a type of radiation force, generated by the nonlinear interaction of the fluid–structure coupled system. Based on a Volterra series model, the power spectral densities of the new higher-order forces are then derived for the case of Gaussian random seas. It is shown that the additional response arising due to nonlinear dynamics of the mooring system can significantly contribute to low-frequency drift forces and responses of the vessel. Unlike conventional non-Gaussian second-order forces which are quadratic transformations of a Gaussian random process, the new higher-order forces arising due to the nonlinear mooring stiffness are polynomials of a Gaussian random process (up to fourth order for a Duffing oscillator model). This may significantly influence the extreme responses.     

孤立波与淹没平板相互作用的三维波面和水动力实验研究

在波浪水池中进行了孤立波作用下有限长度和有限宽度淹没平板的三维模型水池实验. 首次应用多目视觉立体重构技术测量局部三维自由表面变形, 该系统的有效测量水平范围为1.7 m$\times $1.6 m. 用4个三分力测力传感器组成水下测力系统, 在不影响波面的情况下测量孤立波对平板的作用力和力矩. 针对波浪不破碎的情况, 选择0.4 m水深和0.16 m波高的来波条件, 平板淹没深度为0.1 m. 实验结果表明, 孤立波经过淹没平板时自由面有明显的三维变形, 导致孤立波波幅的时空变化. 波幅在平板尾缘中心线处达到最大值, 并沿展向逐渐减小. 利用多目视觉立体重构系统得到的波面变化过程与浪高仪给出定点波面时间序列相互印证, 表明建立标识码波面测量方法是有效的. 孤立波对淹没平板作用的水动力载荷变化分为6个典型阶段, 并与利用波面三维重构得到的波面测量标识码并讨论. 基于多目视觉立体重构技术得到了垂向力和俯仰力矩极值点出现时的三维波面形态. 建立的多目视觉立体重构系统将为海洋工程结构物的水池物理模型实验提供新的波面测量手段.      

Numerical modeling of wave interactions with coastal structures by a constrained interpolation profile/immersed boundary method

A high‐order difference method based multiphase model is proposed to simulate nonlinear interactions between water wave and submerged coastal structures. The model is based on the Navier–Stokes equations using a constrained interpolation profile (CIP) method for the flow solver, and employs an immersed boundary method (IBM) for the treatment of wave–structure interactions. A more accurate interface capturing scheme, the volume of fluid/weighed line interface calculation (VOF/WLIC) scheme, is adopted as the interface capturing method. A series of computations are performed to verify the application of the model for simulations of fluid interaction with various structures. These problems include flow over a fixed cylinder, water entry of a circular cylinder and solitary waves passing various submerged coastal structures. Computations are compared with the available analytical, experimental and other numerical results and good agreement is obtained. The results of this study demonstrate the accuracy and applications of the proposed model to simulate the nonlinear flow phenomena and capture the complex free surface flow. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical study on the suppression of the vortex-induced vibration of an elastically mounted cylinder by a traveling wave wall

In the present paper, the commercial CFD code “Fluent” was employed to perform 2-D simulations of an entire process that included the flow around a fixed circular cylinder, the oscillating cylinder (vortex-induced vibration, VIV) and the oscillating cylinder subjected to shape control by a traveling wave wall (TWW) method. The study mainly focused on using the TWW control method to suppress the VIV of an elastically supported circular cylinder with two degrees of freedom at a low Reynolds number of 200. The cross flow (CF) and the inline flow (IL) displacements, the centroid motion trajectories and the lift and drag forces of the cylinder that changed with the frequency ratios were analyzed in detail. The results indicate that a series of small-scale vortices will be formed in the troughs of the traveling wave located on the rear part of the circular cylinder; these vortices can effectively control the flow separation from the cylinder surface, eliminate the oscillating wake and suppress the VIV of the cylinder. A TWW starting at the initial time or at some time halfway through the time interval can significantly suppress the CF and IL vibrations of the cylinder and can remarkably decrease the fluctuations of the lift coefficients and the average values of the drag coefficients; however, it will simultaneously dramatically increase the fluctuations of the drag coefficients.     

Analysis of transient wave scattering from an inclusion with an unilateral smoothly contact interface by BEM

Summary A 2D time-domain Boundary Element Method (BEM) is applied to solve the problem of transient scattering of plane waves by an inclusion with a unilateral smooth contact interface. The incident wave is assumed strong enough so that localized separations take place along the interface. The present problem is indeed a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (separation and contact regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of plane waves by the cross section of a circular cylinder embedded in an infinite solid. Numerical results for the near field solutions are presented. The distortion of the response waves and the variation of the interface states are discussed. The financial support by the China National Natural Science Foundation under Grant No. 19872001 and No. 59878004 is gratefully acknowledged. The second author is also grateful to the support of the National Science Fund for Distinguished Young Scholars under Grant No. 10025211.     

Frequency-domain analysis of non-linear wave effects on offshore platform responses

In this study, the effects of second-order non-linear random waves on the structural response of slender fixed offshore platforms are investigated based on frequency-domain Volterra-series approach and previously proposed correlation function/FFT-based cumulant spectral method. The cumulants of non-Gaussian water particle kinematics are derived and, Morison force is approximated in cubic functional transformations of Gaussian processes. Volterra series is applied to evaluate the power spectra of wave force and induced structural displacement. The more convenient and more efficient power spectral and tri-spectral analyses by cumulant spectral method are presented as well. The thereby estimated variance, skewness and kurtosis excess agree well with time-domain simulation results. It is found that non-linear wave effects result in stronger non-Gaussian behavior of wave force and structural response, especially in seas of finite water depth.     

AN ANALYTICAL SOLUTION OF SECOND－ORDER WAVE FORCE ON A VERTICAL CIRCULAR CYLINDER

ＡＮＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＯＦＳＥＣＯＮＤ－ＯＲＤＥＲＷＡＶＥＦＯＲＣＥＯＮＡＶＥＲＴＩＣＡＬＣＩＲＣＵＬＡＲＣＹＬＩＮＤＥＲＺｈｏｕＺｈｉ－ｌｉ（邹志利）（ＤａｌｉａｎＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ,Ｄａｌｉａｎ）Ｄａｉ...     

On the interactions of surface waves with immersed structures

The fluid forces resulting from wave interaction with large submerged structures may be calculated using numerical procedures based on the solution of the associated boundary-value problem. In this paper, the analysis of wave interaction with a fixed submerged object of arbitrary cross-section and infinite length using a two-dimensional boundary value formation based on linear diffraction theory is summarized. Subsequently, the application of the boundary element method to obtain a solution is presented. The numerical considerations are emphasized with particular reference to computational efficiency. Numerical results are presented in the form of dimensionless wave force plots for various structural shapes. In the case of a bottom-seated half cylinder, for which there exists a closed-form solution, comparisons are made between results generated using both boundary element and equivalent finite element approaches. In the case of a submerged cylinder, comparisons are made between boundary element derived values and experimental results. The boundary element results compare well with both the closed-form solution and the experimental values.     

Diffraction of cnoidal waves by vertical cylinders in shallow water

Diffraction of nonlinear waves by single or multiple in-line vertical cylinders in shallow water is studied by use of different nonlinear, shallow-water wave theories. The fixed, in-line, vertical circular cylinders extend from the free surface to the seafloor and are located in a row parallel to the incident wave direction. The wave–structure interaction problem is studied by use of the nonlinear generalized Boussinesq equations, the Green–Naghdi shallow-water wave equations, and the linearized version of the shallow-water wave equations. The wave-induced force and moment of the Green–Naghdi and the Boussinesq equations are presented when the incoming waves are cnoidal, and the forces are compared with the experimental data when available. Results of the linearized equations are compared with the nonlinear results. It is observed that nonlinearity is very important in the calculation of the wave loads on circular cylinders in shallow water. The variation of wave loads with wave height, wavelength and the spacing between cylinders is studied. Effect of the neighboring cylinders, and the shielding effect of upwave cylinders on the wave-induced loads on downwave cylinders are discussed.     

An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged body

An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave–body interaction problem into body and free‐surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free‐surface problem satisfies modified nonlinear free‐surface boundary conditions. It is then shown that the nonlinear free‐surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free‐surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo‐spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd.