URANS investigation of the interaction between the free surface and a shallowly submerged underwater vehicle at steady drift

An axisymmetric underwater vehicle (UV) at a steady drift angle experiences the complex three-dimensional crossflow separation. This separation arises from the unfavorable circumferential pressure gradient developed from the windward side toward the leeward side. As is well known, the separated flow in the leeward side gives rise to the formation of a pair of vortices, which affects considerably the forces and moments acting on the UV. In this regard, the main purpose of the present study is to evaluate the role of the leeward vortical flow structure in the hydrodynamic behavior of a shallowly submerged UV at a moderate drift angle traveling beneath the free surface. Accordingly, the static drift tests are performed on the SUBOFF UV model using URANS equations coupled with a Reynolds stress turbulence model. The simulations are carried out in the commercial code STARCCM+ at a constant advance velocity based on Froude number equal to F_n = 0.512 over submergence depths and drift angles ranging from h = 1.1D to h = ∞ and from β = 0 to β = 18.11°, respectively. The validation of the numerical model is partially conducted by using the existing experimental data of the forces and moment acting on the totally submerged bare hull model. Significant interaction between the low-pressure region created by the leeward vortical flow structure and the free surface is observed. As a result of this interaction, the leeward vortical flow structure appears to be largely responsible for the behavior of the forces and moments exerted on a shallowly submerged UV at steady drift.     

Some properties of tidal currents estimated from analytical and LES simulation studies

Some features of tidal current ellipses near the ocean floor are estimated from the bottom-limit solutions of the tidal equations with constant eddy viscosity. It is verified that a clockwise rotating ellipse becomes broad descending through the bottom boundary, whereas a counterclockwise ellipse becomes narrow except near the critical latitude. The major axis of an ellipse near the floor is directed 45° leftward (rightward) against that of the overlying tidal flow ellipse poleward from the critical latitude in the northern (southern) hemisphere. Equatorward from the critical latitude, the major axis near the floor lines up with that of the overlying tidal current ellipse in both hemispheres. The retrograde rotating hodograph against the overlying clockwise tidal hodograph appears near the floor around the critical latitude. These features are confirmed from the numerical studies using the large eddy simulation model. The deflection of the major axis poleward from the critical latitude is a little smaller, about 19°. Furthermore, the effects of nontraditional Coriolis force resulting from the horizontal component of the earth-rotating vector on the development of turbulence were investigated. When the diurnal tidal current is directed westward, the effective vertical eddy viscosity becomes maximum with developing turbulence. While in the case of a semidiurnal tide, a northward tidal current is preferred for turbulence development.     

扁平潜器微速操纵性研究

针对扁平潜器的特点建立了其微速操纵性运动方程,提出了忽略攻角、漂角与旋转角速度耦合影响的水动力模型,由拖曳水池模型试验确定了攻角、漂角水动力,近似估算了旋转水动力.在主辅推进器的PD控制下,数值仿真计算了水平面航向保持与改变、垂直面潜浮的微速运动控制.     

Steady drift force on vertical cylinder - viscous vs. potential

The contribution of the steady drift force on a floating structure may arise from waves, wind and current. The component of the wave drift force may be due to the second-order diffraction theory or potential effect and may be due to the velocity squared force or viscous effect. The presence of current in waves increases the effect of the viscous force. The expressions for these terms for a vertical cylinder are derived and their relative importance is investigated. Plots are presented showing the regions where the viscous or potential drift force predominates. Experiments were conducted with both small and large diameter cylinders. The mean drift forces obtained in these tests are compared with the theory.     

基于UDF的水平轴潮流能水轮机被动旋转水动力性能研究

针对水平轴潮流能水轮机被动旋转问题,基于Fluent 17.0,运用UDF(User Defined Function)控制滑移网格对网格进行动态调整,仿真研究水轮机在不同安放角下被动旋转的水动力特性。通过仿真分析,结果表明:潮流能水轮机随着叶片安放角度的增加,尖速比、输出功率、捕能系数都是先增大后减小,叶片安放角为6°时,叶轮前后速度差最大,对潮流能利用充分,且各项性能均达到最佳;通过分析叶片受力,叶尖叶素在安放角为2°时阻力最大,3°时升力最大,升阻比在6°时最大,此时叶尖叶素升阻比C_L/C_D=6.27、攻角α=3.06°。由仿真结果可知水平轴潮流能叶轮的自启动过程由5个阶段组成,即加速度增大的加速运动段—加速度减小的加速运动段—加速度反向增大的减速运动段—加速度反向减小的减速运动段—稳定运行段,这对潮流能水轮机的设计具有重要的指导意义。     

A quasi-cloaking phenomenon to reduce the wave drift force on an array of adjacent floating bodies

The mooring of offshore floating structures, such as offshore platforms, in large waves against drift forces and rotational moments is a challenging problem in offshore engineering. To accurately investigate such problems, called positioning problems, the time-averaged steady forces of the second order known as the wave drift forces must be taken into account. Fortunately, a cloaking phenomenon occurs under certain conditions and dramatically reduces the wave drift force acting on such a floating body, as previously reported by several researchers. In the diffraction problem of water waves, cloaking refers to the condition where there is no scattering in the form of radial outgoing waves. The reduction of wave drift force on a truncated cylinder with the occurrence of cloaking phenomenon has been numerically and experimentally confirmed. In this paper, the arrangement of several small circular cylinders at regular intervals in a circle concentric with a fixed floating body is considered as an effective means of reducing the wave drift force. Using a combination of a higher-order boundary element method (HOBEM) and wave interaction theory, the influences of the geometric parameters of the outer surrounding cylinders on the wave drift force and the total scattered-wave energy are systematically investigated and discussed. A quasi-cloaking phenomenon is first found and reported in the present study, which is beneficial and flexible for application in practical engineering. More than one quasi-cloaking trigger (where a trigger is an occurrence condition) can be found simply by varying the distance between the inner and outer floating bodies.     

Hydrodynamics of oil jets without and with dispersant: Experimental and numerical characterization

In this paper, we present the analysis of an underwater horizontal oil jet experimental measurement and Computational Fluid Dynamics (CFD) using the Reynolds Averaged Navier Stokes (RANS) equations. Two oil subsurface releases were conducted: one with crude oil and another with crude oil premixed with dispersant at the dispersant to oil ratio (DOR) of 1:20. The jet profile was captured by a camera at moderate resolution, and the instantaneous velocity was measured by a Vectrino Profiler. The velocity components, turbulence kinetic energy, and turbulence dissipation rate from the experiment agreed well with those from the CFD simulation using the k-epsilon turbulence model. The spread angle of the jet was found to be around 21° and 24° from the experiment measurement, for oil without dispersant and oil with dispersant, respectively. The latter is close to the angle of miscible jets at 23°. The jet profile of oil with dispersant had a smaller buoyancy than that without dispersant, which is probably due to the large water entrainment for the oil with dispersant jet. The cross sections of the jet for both cases gradually became flattened with distance, as the plume turned upward.     

Iceberg drift affected by wave action

A mathematical model to predict iceberg drift pattern has been developed, which includes the wave drift force, in addition to the other conventional force components such as forces due to wind, current, Coriolis effect, and geostrophic effect. Trajectories of two icebergs were computed first with the wave effect then without the wave effect. All were compared with the observed results from the field. The model with the wave effect shows a significant improvement in the correlation.     

Analysis of wave induced drift forces acting on a submerged sphere in finite water depth

A solution is presented for the wave induced drift forces acting on a submerged sphere in a finite water depth based on linearised velocity potential theory. In order to obtain the velocity potential, use has been made of multipole expansions in terms of an infinite series of Legendre functions with unknown coefficients. The series expression for the second order mean forces (drift forces) is provided by integrating the fluid pressure over the body surface. The horizontal drift force is also expressed by a series solution obtained using the far-field method.     

Identification of non-linear effects in predicting the motion response of an offshore platform

This paper presents the results of an extensive parametric study to investigate various non-linear aspects of the prediction of the large-amplitude motion responses of a semi-submersible. The main objectives of the parametric studies were to investigate the following aspects, which can non-linearly influence the motion responses and which cannot be studied by linear frequency-domain prediction techniques. These aspects are the effects on the motion responses of flooding time and mass; non-linear wave-exciting and rigid-body induced motion (i.e. added mass and damping) forces; non-linear restoring forces; steady wind and current; variation of GM (transverse metacentric height); and the initial position of the semi-submersible. The investigations were carried out for a particular semi-submersible geometry using a numerical simulation technique in the time domain. The simulations were performed for the model during intact, progressive and post-flooding conditions under the combined loading of regular waves, steady wind and current for two different heading angles. This paper is thus intended to provide some insight into the physical effects of the non-linear terms in the equations of motion which are associated with the wave-excitation forces, rigid-body induced motion forces and restoring forces. Since the resulting motion responses could have a steady component as well as the oscillatory one, the force and motion phenomena were also highlighted through the computation of these components.     

Extreme Case Study of Quay Wall Stability under Earthquake and Tsunami

This study was conducted to determine the stability of a quay wall under the combined action of an earthquake and tsunami. Adopting the limit equilibrium method, the stability of the quay wall was assessed for both the sliding and overturning modes under passive and active conditions. The variation in the stability of the quay wall was determined by parametric studies, including those for the tsunami wave height, seismic acceleration coefficient, internal friction angle of soil, wall friction angle, and pore water pressure ratio. The stability of the wall was also compared with the case of no earthquake and tsunami forces. When the earthquake and tsunami were considered simultaneously, the stability of the wall under the passive condition decreased significantly. The critical mode of the quay wall under the earthquake and tsunami forces was found to be that of the overturning mode. In the active condition, the safety factors for sliding and overturning increased, because the tsunami acted as a resisting force. However, it should be noted that, if a tsunami wave spills over the quay wall and then flows backward to the wall active condition, the tsunami no longer acts as a resisting force.     

Turbulence modeling in ocean circulation problems

A physical formulation of the problem is considered. A mathematical model and a numerical algorithm of the turbulence model as part of the ocean circulation model for simulations for decades are formulated. The model is based on the evolution equations for turbulent kinetic energy (TKE) and the frequency of its viscous dissipation. A numerical solution algorithm for both the circulation model and the turbulence model is based on implicit schemes of splitting with respect to physical processes and geometric coordinates. For the turbulence model, this provided analytical solutions at a splitting step related to TKE generation and dissipation. Numerical experiments have been performed with a model of the joint circulation of the North Atlantic, the Arctic Ocean, and the Bering Sea to reproduce the annual cycle and synoptic disturbances of ocean characteristics. The model has a resolution of 0.25° in latitude and longitude and 40 levels in the vertical, which are compressed toward the surface to reproduce the process of developed turbulence better. The results are compared with observations and with the results of simulations using traditional parameterizations of the upper ocean mixing. It is shown that the model reproduces ocean characteristics correctly, only slightly increasing the computation time in comparison with simple parameterizations. Spatial and temporal characteristics of turbulence are analyzed.     

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).     

Numerical prediction of MODUs drift during Hurricane Katrina

Severe hurricanes, such as Katrina, broke the mooring lines of a number of mobile offshore drilling units (MODU) deployed in the Gulf of Mexico and some of those MODUs went adrift. A drifting MODU may damage other critical elements of the offshore oil and gas infrastructure by colliding with floating or fixed production systems and transportation hubs, or by rupturing pipelines owing to their dragging anchors over the seabed. To avoid or mitigate the damage caused by a drifting MODU, it is desirable to understand the mechanics of the drift of a MODU under the impact of severe wind, wave and current and have the capability of predicting the trajectory of the drift. To explore the feasibility and accuracy of predicting the trajectory of a drifting MODU based on hindcast met-ocean conditions and limited knowledge of the condition of the drifting MODU, this study employed a simplified equation describing only the horizontal (surge, sway and yaw) motions of a MODU under the impact of steady wind, current and wave forces. The simplified hydrodynamic model neglects the first- and second-order oscillatory wave forces, unsteady wind forces (owing to wind gustiness), wave drift damping, and the effects of the body oscillation on the steady wind and current forces. It was assumed that the net effects of the oscillatory forces on the steady motion are insignificant. To verify the accuracy and feasibility of our simplified approach, the predicted drifting trajectories of two MODUs were compared with the corresponding measurements recorded by the global positioning system (GPS).     

Downwind sail aerodynamics: A CFD investigation with high grid resolution

A computational fluid dynamics (CFD) code was applied to an America's Cup Class Yacht to investigate sailing performance in a downwind configuration. Apparent wind angles at 45°, 105° and 120° are reported, sailed with mainsail and asymmetrical spinnakers. Numerical results are in good agreement with wind tunnel data. A large mesh investigation was performed, ranging from 60,000 elements up to 37 million elements, which shows a converging trend to the experimental values with differences smaller than 3% in both lift and drag. The most commonly used turbulence models in sail applications were tested and the results are presented here in two meshes with 1 million elements and 6.5 millions, respectively. All turbulence models over-estimate forces more than solving the Navier–Stokes system without any additional equations, hence turbulence models do not increase solution accuracy according to these results.     

Viscous drift forces in regular and irregular waves

A method to compute wave- and current-induced viscous drift forces and moments on floating platforms in regular and random waves is presented. The relative velocity drag term of Morison's equation is used in conjunction with frequency domain first-order motion transfer functions to compute the drift forces and moments. Mean viscous drift forces and moments in regular waves in all six degrees-of-freedom of a tension leg platform are computed. The relative importance of the free-surface force integration, steady current, wave-current interaction and platform motions on the computed drift forces and moments are discussed. The results from this method, in the frequency domain, are used to compute the drift forces and responses in irregular waves using existing methods developed for potential drift computations. Comparisons with results from time-domain computations are also presented and good agreement between the frequency-domain and time-domain results is found. Some comparisons with experimental data are also made. The frequency-domain method is found to be an efficient and useful tool for the analysis of semi-submersible and tension leg platforms during the preliminary design stage in which extensive parametric studies need to be undertaken.     

CFD, system-based and EFD study of ship dynamic instability events: Surf-riding, periodic motion, and broaching

CFD and system-based simulation are used to predict broaching, surf-riding, and periodic motion for the ONR Tumblehome model, including captive and free model test validation studies. CFD shows close agreement with EFD for calm water resistance, static heel (except for sway force and yaw moment), and static drift (except for roll moment). CFD predictions of static heel in following waves also compare well with EFD except for surge force, sway force, and pitch angle. Froude-Krylov calculations of wave-induced surge force in following waves provides good agreement for high Froude number, but significantly overestimates for Froude number less than 0.2. On the other hand, CFD successfully reproduces the reduction of the wave-induced surge force near Froude number 0.2, probably because CFD can capture the 3D wave pattern. CFD free model simulations are performed for several speeds and headings and validated for the first time for surf-riding, broaching, and periodic motions. System-based simulations are carried out based on inputs from EFD, CFD, and Froude-Krylov for a dense grid of speeds and headings to predict the instability map, which were found to produce fairly similar results.     

斜向波浪作用下双层水平板式防波堤波浪荷载试验研究

In this study, systematic physical model tests were performed to investigate the wave forces on the twin-plate breakwater under irregular waves. Based on the experimental results, the effects of the relative plate width B/L,wave height Hs/D and incident angle θ0 on the wave forces were analyzed and discussed. The results showed that:(1) The envelopes of the total wave pressure were generally symmetrical along the direction of plate width under the incident angles(θ0) being 0°, 15°, 30°, 45° and 60°. In particular, the envelopes of wave pressure atθ0=30° were larger than all other cases.(2) The synchronous pressure distribution of the breakwater under oblique wave action was more complicated comparing to the normal incident waves.(3) Based on data analysis, an empirical formula was obtained to estimate the total vertical force of the twin-plate breakwater.This empirical formula can be a good reference for the design basis of engineering applications under specified wave conditions.     

Three-dimensional velocity measurements around bridge piers in gravel bed

The experimental results of time average velocity components measured around circular pier models during transient scour stage using acoustic Doppler velocimeter are shown for flow pattern and turbulence characteristics. Totally, four experiments were performed under clear water scour conditions in a model of gravel bed stream. Four circular pier models of diameter 6.6, 8.4, 11.5, and 13.5?cm were used for this study. Detailed controlled measurements on velocity components, and turbulence intensities near the pier and in scour hole at 0° and 180° plane are shown. Flow structure around a pier model in the presence of a scoured region was compared with the flow structure similarly noticed around all pier model runs by utilizing the observations taken at 0° and 180° plane from flow axis. Size of the primary vortex at 0° plane with largest diameter pier model in place (R4 run) is found to be maximum and was approximately 61% larger than that for smallest diameter pier model in place (R1 run). The time-averaged velocity components of turbulence intensities plots at 0° and 180° planes are also presented around each pier.     

Numerical investigation of the hydrodynamic interaction between two underwater bodies in relative motion

The hydrodynamic interaction between an Autonomous Underwater Vehicle (AUV) manoeuvring in close proximity to a larger underwater vehicle can cause rapid changes in the motion of the AUV. This interaction can lead to mission failure and possible vehicle collision. Being self-piloted and comparatively small, an AUV is more susceptible to these interaction effects than the larger body. In an aim to predict the manoeuvring performance of an AUV under the effects of the interaction, the Australian Maritime College (AMC) has conducted a series of computer simulations and captive model experiments. A numerical model was developed to simulate pure sway motion of an AUV at different lateral and longitudinal positions relative to a larger underwater vehicle using Computational Fluid Dynamics (CFDs). The variables investigated include the surge force, sway force and the yaw moment coefficients acting on the AUV due to interaction effects, which were in turn validated against experimental results. A simplified method is presented to obtain the hydrodynamic coefficients of an AUV when operating close to a larger underwater body by transforming the single body hydrodynamic coefficients of the AUV using the steady-state interaction forces. This method is considerably less time consuming than traditional methods. Furthermore, the inverse of this method (i.e. to obtain the steady state interaction force) is also presented to obtain the steady-state interaction force at multiple lateral separations efficiently. Both the CFD model and the simplified methods have been validated against the experimental data and are capable of providing adequate interaction predictions. Such methods are critical for accurate prediction of vehicle performance under varying conditions present in real life.