Lateral ice force acting on a vertical cylinder

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均匀流中直立圆柱体绕流三维数值模拟

研究直立贯底圆柱体的三维粘性绕流问题。以不可压缩Navier-Stokes方程为控制方程,采用有限体积法和SIMPLE算法,建立了数值模拟方法。考察在不同水平和垂直断面上,圆柱体绕流产生的尾涡和流动速度场的分布特性,成功地数值模拟了直立贯底圆柱体绕流场的三维特性。结果表明,在考虑重力影响的情况下,直立圆柱体周围的流动具有明显的三维特性,而且沿圆柱体轴向不同断面上的尾涡分布是不相同的。     

Wave-current force on horizontal cylinder

For the calculation of wave-current force on horizontal cylinder a modified Morison's equation is used. A redefined Keulegan- Carpenter number KC2 is determined for the horizontal cylinder in wave-current co-existing field. The force coefficients are well related to the redefined KC2 number. As to the comparison with the force on vertical cylinder, the characteristics of force on horizontal cylinder are quite similar to those on vertical cylinder, but the force coefficients for horizontal cylinder are larger than those for vertical cylinder. It is proved by the authors' calculation that the results of monochromatic wave can be used directly for the determination of irregular wave-current force on horizontal cylinder in time domain.     

Artificial neural network ability in evaluation of random wave-induced inline force on a vertical cylinder

An approach based on artificial neural network (ANN) is used to develop predictive relations between hydrodynamic inline force on a vertical cylinder and some effective parameters. The data used to calibrate and validate the ANN models are obtained from an experiment. Multilayer feed-forward neural networks that are trained with the back-propagation algorithm are constructed by use of three design parameters (i.e. wave surface height, horizontal and vertical velocities) as network inputs and the ultimate inline force as the only output. A sensitivity analysis is conducted on the ANN models to investigate the generalization ability (robustness) of the developed models, and predictions from the ANN models are compared to those obtained from Morison equation which is usually used to determine inline force as a computational method. With the existing data, it is found that least square method (LSM) gives less error in determining drag and inertia coefficients of Morison equation. With regard to the predicted results agreeing with calculations achieved from Morison equation that used LSM method, neural network has high efficiency considering its convenience, simplicity and promptitude. The outcome of this study can contribute to reducing the errors in predicting hydrodynamic inline force by use of ANN and to improve the reliability of that in comparison with the more practical state of Morison equation. Therefore, this method can be applied to relevant engineering projects with satisfactory results.     

Minimization of drift force on a floating cylinder by optimizing the flexural rigidity of a concentric annular plate

The deployment of suitable configurations of mutually interacting floating bodies for efficiently controlling their hydrodynamic interactions towards the reduction of the wave drift forces and, thus, of the mooring lines’ loads, has, nowadays, gained a great scientific interest. In this paper, the hydrodynamic behaviour of a floating cylinder and a concentric annular flexible plate is analysed in the frequency domain aiming at the minimization of the drift forces acting on the cylinder by optimizing the flexural rigidity of the plate. The diffraction/radiation problem is solved using a higher-order boundary element method. The analysis is implemented assuming that both floating bodies oscillate freely in heave, while for the plate, flexible modes are, additionally, considered for describing its structural deformations. The required modes shapes are determined in vacuum (“dry” mode superposition approach) through analytical expressions. The flexural rigidity of the plate, D, is optimized at a specific wave number using a real-coded genetic algorithm. Initially, results are compared with numerical results of other investigators for the case of two rigid concentric floating cylinders. Next, extended results are presented, focusing on the effect of D, including its optimum value, on various physical quantities describing the behaviour of both the cylinder and the plate. Contrary to the isolated cylinder, the presence of the plate introduces sharp peaks in the variation pattern of the drift force of the cylinder, bounded at specific wave numbers, where resonance of the seiche mode of water motion in the annular cavity or of specific flexible modes of the plate occurs. However, by reducing D to its optimum value, the cylinder’s drift force obtains practically zero values at the target wave number, due to an efficient improvement of the wave field in the annular cavity around the cylinder. Moreover, a great reduction of the drift force compared to the isolated cylinder is achieved in the subsequent high frequency range.     

Nonlinear wave loads on a vertical cylinder

Nonlinear contributions due to elevation of the free surface, the dynamic head, and the second-order velocity potential on the wave loads are presented in closed-form expressions. Such nonlinearities resulting from large-amplitude ocean waves are associated with the irrotational flow interacting with a fixed bottom-mounted vertical cylinder piercing the surface. These are expressed in the form of dynamic, waterline and quadratic forces all of which depend on the square of the wave amplitude. The appropriate modifications are made to both the classical Morison equation and the well-known linear diffraction theory of MacCamy and Fuchs for accounting the second-order effects.A limited comparative study is performed to verify the present theoretical derivations. In general, satisfactory agreements have been obtained with the test results from various laboratory studies by different researchers. However, under certain environmental conditions, some discrepancies still exist with the measured results.     

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.     

Experimental study of interactions between multi-directional focused wave and vertical circular cylinder,part II: Wave force

We describe experiments with multi-directional focused waves interacted with a vertical circular cylinder in a 3D wave basin. The focus of this study is on the run-up of multi-directional focused waves, wave forces, and wave pressures on the cylinder. Part I, the study on wave run-up, has already been presented by Li et al. (2012). In this paper, the analysis of the wave force on the vertical cylinder is presented.In this experiment, a cylinder with 0.25 m in diameter was adopted and different wave parameters, such as focused wave amplitude, peak frequency, frequency bandwidth and directional spreading index, are considered. The model scale k_pa (k_p is the wave number corresponding to peak frequency, a is the radium of the cylinder) varies from 0.32 to 0.65. The maximum forces of multi-directional focused wave on cylinder were measured and investigated. The results showed that the wave parameters have a significant influence on the wave force, and that the spatial profile of the surface of multi-directional focused wave can also affect its force on the cylinder, which is different from two-dimensional wave. In addition, the ‘secondary loading cycle’ phenomenon was also observed and discussed. In our experiments, the ‘secondary loading cycles’ occur when kA > 0.36 for all cases. While in some referred small scale experiments, the secondary load cycles are observed even for kA = 0.2, when the waves are longer enough. To larger model scale, the pronounced secondary load cycle occurs with larger wave steepness waves.     

In-line force on a cylinder translating in oscillatory flow

Experiments were conducted with smooth and sand-roughened cylinders moving with constant velocity in a sinusoidally oscillating flow to determine the drag and inertia coefficients and to examine the effect of wake biasing on the modified Morison equation. The various flow parameters such as the relative cylinder velocity. Reynolds number, and the Keulegan-Carpenter number were varied systematically and the in-line force measured simultaneously. The principal results, equally valid for both smooth and rough cylinders, are as follows: the drag coefficient decreases with increasing relative current for a given Reynolds number and Keulegan-Carpenter number; the effect of wake biasing on the drag and inertia coefficients is most pronounced in the drag-inertia dominated regime; and the two-term Morison equation with force coefficients obtained under no-current conditions is not applicable to the prediction of wave and current induced loads on circular cylinders.     

Wave runup on a surging vertical cylinder in regular waves

The wave runup caused by a vertical cylinder surging in regular waves is studied both experimentally and numerically. The so-called DualSPHysics Smoothed Particle Hydrodynamics (SPH) code is used for the 3-D numerical modelling. A wide range of cylinder sizes and wave conditions is investigated with results comparing favourably between the experimental and SPH model under both fixed and forced-surge conditions. The experimental and SPH results are further used to predict the maximum runup amplification, in particular the ratio of the runup caused by the surging cylinder to that of the fixed, over the phase difference between the incident wave and surge motion. This maximum runup ratio has been analysed for its dependence on factors such as wave steepness, wave scattering and surge amplitude. An empirical equation is proposed for predicting the maximum runup ratio from known incident wave and surge conditions. Comparison with results from linear solvers suggests that the linear solvers under-predict the full nonlinear runup by a factor of 1.3–1.5.     

Nondeterministic wave force on fixed small vertical piles

The moment generating function and the probability function for non-deterministic wave forces on a small diameter fixed vertical pile are derived for linear, Gaussian waves. The dimensionless force covariance function is obtained by taking the expectation of the dimensionless force. An indefinite integral is obtained which may be conveniently solved using Laplace transforms. These results are compared with previously published covariance expressions.     

Numerical study on cnoidal wave run-up around a vertical circular cylinder

A finite element model of Boussinesq-type equations was set up, and a direct numerical method is proposed so that the full reflection boundary condition is exactly satisfied at a curved wall surface. The accuracy of the model was verified in tests. The present model was used to further examine cnoidal wave propagation and run-up around the cylinder. The results showed that the Ursell number is a nonlinear parameter that indicates the normalized profile of cnoidal waves and has a significant effect on the wave run-up. Cnoidal waves with the same Ursell number have the same normalized profile, but a difference in the relative wave height can still cause differences in the wave run-up between these waves. The maximum dimensionless run-up was predicted under various conditions. Cnoidal waves hold entirely distinct properties from Stokes waves under the influence of the water depth, and the nonlinearity of cnoidal waves enhances rather than weakens with increasing wavelength. Thus, the variations in the maximum run-up with the wavelength for cnoidal waves are completely different from those for Stokes waves, and there are even significant differences in the variation between different cnoidal waves.     

浅水浮式生产储油系统(FPSO)二阶定常力数值仿真研究

应用三维线性势流理论和Ir J A Pinkster的近场分析方法,对超大型浮式生产储油系统(32万吨FPSO)的二阶波浪定常力进行了数值仿真分析,研究浅水情况下,不同水深对FPSO受到二阶波浪定常力的影响,对浅水油田中FPSO的设计应用有一定的实用意义。     

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.     

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.