Wave forces acting on a submerged horizontal circular cylinder in oblique waves and on a vertical cylinder in deep waves

This paper presents a method of estimating wave forces acting on a submerged horizontal circular cylinder fixed in oblique waves.The experiments show that drag and inertia coefficients in beam sea are available for calculating the wave forces in oblique waves.Wave forces exerted on a vertical circular cylinder in deep waves are also investigated.The experimental results show that wave forces acting on the vertical cylinder coincide approximately with hydrodynamic forces acting on a submerged circular cylinder in an oscillating fluid.     

Tension during parametric excitation in submerged vertical taut tethers

The construction of a suspension bridge with floating pylons or a submerged floating tunnel requires the installation of a mooring system. The option of taut vertical tethers, similar to those used in tension-leg platforms, has been suggested in preliminary designs. The environmental loading on the tether, mainly due to wind waves and swell, results in a parametrically excited system. Certain loading conditions develop instabilities that translate into large horizontal motion. However, the effects of parametric resonance on the tension values have rarely been investigated. This paper aims to clarify the relation between lateral displacement and tether tension and to quantify the extreme tension values in the event of parametric resonance. The presented analysis is based on a full numerical model of the tether that includes geometric and hydrodynamic nonlinear effects. This model is used to investigate a representative example that illustrates parametric resonance and multiple parametric studies to assess the effects of the excitation frequency, amplitude, initial pretension, tether length and inclination angle on the tether’s response. The results reported here provide the basis for a recommendation on designing a tether under parametric resonance regarding the ultimate extreme values and fatigue life.     

Hydrodynamic coefficients for vertical circular cylinders at finite depth

Hydrodynamics coefficients for vertical circular cylinders at finite water depth are obtained and presented for different depth to radius and draft to radius ratios. A summary of equations for computer application is presented. Limiting values for heave added mass for zero frequency are discussed. A matching technique is used to satisfy the continuity of pressure and normal velocities.     

Second-order vertical and horizontal wave forces on a circular dock

A second-order potential solution is presented for the diffraction of a nonlinear progressive wave in finite-depth water, incident on a fixed circular dock. The usual perturbation analysis is used to produce first- and second-order subproblems. The mathematical method is based on the assumption that inner and outer solutions exist and these are matched by the requirements of continuity for mass flux and pressure between adjacent regions. It is shown that the solutions for the second-order problem can be derived in the same manner as in the first-order theory.     

Hydrodynamic forces on a partially submerged cylinder at high Reynolds number in a steady flow

The hydrodynamic forces on the stationary partially submerged cylinder are investigated through towing test with Reynolds number ranging from 5 × 10⁴ to 9 × 10⁵. Three test groups of partially submerged cylinders with submerged depths of 0.25 D, 0.50 D, and 0.75 D and one validation group of fully submerged cylinders are conducted. During the experiments, the hydrodynamic forces on the cylinders are measured using force sensors. The test results show a considerable difference in the hydrodynamic coefficients for the partially submerged cylinders versus the fully submerged cylinders. A significant mean downward lift force is first observed for the partially submerged cylinders in a steady flow. The maximum of the mean lift coefficients can reach 1.5. Two distinct features are observed due to the effects of overtopping: random distributions in the mean drag coefficients and a clear quadratic relationship between the mean lift coefficients and the Froude number appear in the non-overtopping region. However, the novel phenomenon of a good linear relationship with the Froude number for the mean hydrodynamic coefficients is clearly shown in the overtopping region. In addition, fluctuating hydrodynamic coefficients are further proposed and investigated. These results are helpful to have a better understanding of the problem and to improve related structural designs.     

Measurements of higher harmonic wave forces on a vertical truncated circular cylinder

Wave forces on a vertical truncated circular cylinder in Stokes waves with the wave slopes ranging from 0.06 to 0.24, are measured in a wave tank. The higher harmonic wave forces are compared with the available values from theories of the FNV (Faltisen–Newman–Vinje) model and Varyani solution. The first harmonic horizontal forces measured are much larger than the theoretical values from the FNV model, while the first harmonic vertical forces are well predicted by the Varyani theory. It was also found that the FNV model significantly overpredicts the second harmonic horizontal forces in high frequency waves, but under predicts the third harmonic forces. The differences between the actual measurement and the theory, in the second and third harmonic horizontal forces, become smaller at low wave frequencies as the wave slope increases. In addition, the transverse instabilities in the incoming waves with high wave slope were observed, which is due to the nonlinear modulation. Measurements were, thus, carried out before the instability occurred.     

Hydrodynamic interactions between two vertical circular cylinders in linear oscillatory flow

Linear potential theory is used to investigate the hydrodynamic interactions between two vertical cylinders in harmonic flow. The behaviour of the added mass and damping is studied for various cylinder diameters, lengths of immersion and spacing between the cylinders. In practice, the results have relevance to the fluid loading on offshore structural members, such as risers and platform legs, and pipeline bundles. On a more theoretical level, comparisons are possible between the results of a three-dimensional diffraction program and various asymptotic expressions to establish the range of validity of the latter and the need, where appropriate, of the former.     

Wave forces acting on a vertical circular cylinder with a constant forward velocity

Wave forces acting on submerged circular cylinders moving forward with a constant velocity in regular waves are investigated experimentally. Hydrodynamic forces acting on the cylinder forced to surge in a steady are also measured and hydrodynamic coefficients were obtained. Wave force coefficients obtained from wave force measurements are compared with the hydrodynamic coefficients from surging tests, and the similarity and difference between them are discussed. Experiments show that these coefficients are quite different from those of the cylinder without a forward velocity.     

Nonlinear wave interaction with a vertical circular cylinder: wave forces

Second-order wave forces on a large diameter vertical circular cylinder, computed according to a semi-analytic nonlinear diffraction theory, are compared to results of 22 laboratory experiments with regular waves. In general, predicted forces agree quite well with measured forces. In most tests, both measured and predicted maximum forces exceeded linear theory by 5 to 15%. In a few cases, however, the measured forces were less than those predicted by linear theory, in contrast to the second-order predictions. It is shown that these results are related to the phasing of various linear and nonlinear wave force components, and are consistent with those obtained by other investigators.     

Hydrodynamic performance of vertical porous structures under regular waves

The hydrodynamic efficiency of the vertical porous structures is investigated under regular waves by use of physical models. The hydrodynamic efficiency of the breakwater is presented in terms of the wave transmission (kt ), reflection (kr) and energy dissipation (kd ) coefficients. Different wave and structural parameters affecting the breakwater efficiency are tested. It is found that, the transmission coefficient (kt ) decreases with the increase of the relative water depth (h/L), the wave steepness (Hi/L), the relative breakwater widths (B/L, B/h), the relative breakwater height (D/h), and the breakwater porosity (n). The reflection coefficient (kr) takes the opposite trend of kt when D/h=1.25 and it decreases with the increasing h/L, Hi/L and B/L when D/h 1.0. The dissipation coefficient (kd) increases with the increasing h/L, Hi/L and B/L when D/h 1.0 and it decreases when D/h=1.25. In which, it is possible to achieve values of kt smaller than 0.3, krlarger than 0.5, and kd larger than 0.6 when D/h=1.25, B/h=0.6, h/L 0.22, B/L 0.13, and Hi/L 0.04. Empirical equations are developed for the estimation of the transmission and reflection coefficients. The results of these equations are compared with other experimental and theoretical results and a reasonable agreement is obtained.     

Hydrodynamic interaction forces on multi-moduled structures

The size, complexity and critical operations of many offshore structures, including the mobile offshore bases (MOBs) of current interest, require careful determination of wave forces on the neighboring structures, including their interactions. This paper describes an analytical/numerical approach that determines the wave forces on multiple structures in the vicinity of one another. The method involves the consideration of multiple vessel interaction and scattering in waves. The analysis is an extension of the semi-analytical multiple vertical cylinder analysis published by the author. The analysis is similar to the one proposed by Kagemoto and Yue for axisymmetric bodies.The direct method of linear diffraction, while quite accurate and efficient in solving the hydrodynamic problem, demands a large amount of memory and requires considerable execution time. The present analysis is very efficient in these respects. It is accomplished by marrying the direct method with a semi-closed analytical method of multiple scattering developed for an array composed of vertical cylindrical structures. It is recognized that this analytical method has a limitation owing to the geometry of many offshore structures including MOBs. Therefore, the analysis is extended to an arbitrary geometry. In this method, the direct matrix method of diffraction problem is applied to an isolated module and then extended to structures with the multiple scattering technique to account for the interaction of multiple structures.Comparisons are made of the results from the analytical and conventional numerical diffraction theory with those of the semi-analytical tool using the above-mentioned analysis.     

两层流体中振荡水平圆柱潜体水动力特性

研究了有限深两层流体中水平圆柱潜体的振荡辐射问题。在线性势流理论框架内,建立求解辐射势的多极展开理论,提出附加质量和阻尼系数的计算方法,进行了数值计算分析,并且与均匀流中的情况进行比较。结果表明,在圆柱潜体的某个振荡频率范围内,流体的分层效应对其附加质量和阻尼系数是有重要影响的。同时,对水平圆柱潜体振荡产生的自由面和内界面波动特性进行了数值分析。     

Parametric vibration of submerged floating tunnel tether under random excitation

For the study of the parametric vibration response of submerged floating tunnel tether under random excitation,a nonlinear random parametric vibration equation of coupled tether and tube of submerged floating tunnel is set up.Subsequently,vibration response of tether in the tether-tube system is analyzed by Monte Carlo method.It may be concluded that when the tube is subjected to zero-mean Gaussian white noise random excitation,the displacement and velocity root mean square responses of tether reach the peak if the circular frequency of tube doubles that of tether;the displacement and velocity root mean square responses of tether increase as the random excitation root mean square increases;owing to the damping force of water,the displacement and velocity root mean square responses of tether decrease rapidly compared with tether in air;increasing the damping of the tether or tube reduces the displacement and velocity root mean square responses of tether;the large-amplitude vibration of tether may be avoided by locating dampers on the tether or tube.     

Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents

Local scour around a submerged vertical circular cylinder in steady currents was studied both experimentally and numerically. The physical experiments were conducted for two different cylinder diameters with a range of cylinder height-to-diameter ratios. Transient scour depth at the stagnation point (upstream edge) of the cylinder was measured using the so-called conductivity scour probes. Three-dimensional (3D) seabed topography around each model cylinder was measured using a laser profiler. The effect of the height-to-diameter ratio on the scour depth was investigated. The experimental results show that the scour depth at the stagnation point is independent on cylinder height-to-diameter ratio when the later is smaller than 2. The increase rate of equilibrium scour depth with cylinder height increases with an increase in Shields parameter.     

Wave forces on a large, horizontal submerged cylinder

A numerical boundary integral equation method combined with a non-linear time stepping procedure is used for the calculation of wave forces on a large, submerged, horizontal circular cylinder. As the method is based on potential theory, all computations are performed in the inertia dominated domain, that is, for small Keulegan-Carpenter numbers. Computations are carried out for the Eulerian mean current under wave trough level equal to zero. When the cylinder is moved towards the sea bed the computations show that the inertia coefficients increase significantly, which is associated with a blockage effect. Furthermore, the effect of the wave steepness is reduced when the submergence of the cylinder is increased. In the vicinity of the free water surface the vertical inertia coefficient is highly dependent upon the wave steepness, which tends to reduce it, whereas the horizontal inertia coefficient is only slightly dependent on the wave steepness. Computations are also carried out for cylinder diameters comparable with the wave length. Finally, inertia coefficients computed by the present method are compared with some analytical results by Ogilvie [(1963), First and second order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16, 451–472]. As long as the assumptions leading to Ogilvie's theory are fulfilled (cylinder radius small compared to the wave length), the results are quite similar.     

不规则波远破波对直墙的作用

基于物模试验、理论推理、因次分析和工程实例验证等综合分析方法,就不规则波远破波对直墙作用力的计算方法进行了研究,用推荐的方法得到的结果与工程实例符合较好.     

Higher-harmonic focused-wave forces on a vertical cylinder

This paper considers higher-harmonic forces due to wave focusing on a vertical circular cylinder. A series of experiments has been conducted in a wave flume. The first six-harmonic components of the measured wave forces are analyzed using the scale-averaged wavelet spectrum. It is noted that due to the transient nature of focused (freak) waves, Fourier analysis would not provide equivalent information to that gleaned from the analyses used herein. The results for the experiments with very steep wave crests show significant amplitudes at the fourth and fifth harmonics. These harmonics exhibit amplitudes that are the same order as the second harmonic, but much larger than those of the third harmonic. The wavelet-based bicoherence is used to detect the quadratic nonlinearity of the measured forces. And the bicoherence spectra reveal the primary mathematical reason for the existence of the striking amplitudes of the fourth and fifth harmonics: the interaction between the lower-harmonic components couple more strongly with the fourth and fifth harmonics, thus the fourth and fifth harmonics glean more energy than those of the third-harmonic components. However, the physical explanation for this remains elusive.     

Wave forces on vertical cylinders upon shoals

An experimental study has been carried out on the forces from plunging breaking regular and irregular waves on a vertical cylinder on a shoal. Total as well as local wave forces have been measured. Engineering formulae for the calculation of the horizontal forces and overturning moments have been derived. The duration of the impact forces have been measured and compares fairly well with theoretical values.