Wake II model for hydrodynamic forces on marine pipelines including waves and currents

The Wake II model for the determination of the hydrodynamic forces on marine pipelines is extended to include currents and waves. There are two main differences between the Wake II and the traditional model. First, in the Wake II model the velocity is modified to include the pipe's encounter with the wake flow when the velocity reverses. Second, the model uses time dependent drag and lift coefficients. The flow field is assumed to be the linear superposition of regular waves and uniform current and is treated as wave only but in two different phases. The model requires eight empirical parameters that are obtained from comparisons with field data for various Keulegan–Carpenter numbers and current to wave ratios. The effective velocity and the force predictions are compared with field data from Exxon Production Research Company and with the conventional model. The model gives satisfactory results and predicts lift forces that in shape, magnitude and phase relative to the velocity are in very close agreement with measured forces. For the horizontal forces the results are very accurate. A substantial improvement is obtained over the predictions with the conventional model. This work is applicable to the design of submarine pipelines laying on the sea bottom in water depths where waves or waves and currents contribute to the hydrodynamic forces.     

Prediction of hydrodynamic forces on submarine pipelines using an improved Wake II Model

The hydrodynamic force model for prediction of forces on submarine pipelines as described includes flow history effect (wake effects) and time dependence in the force coefficients. The wake velocity correction is derived by using a closed-form solution to the linearized Navier–Stokes equations for oscillatory flow. This is achieved by assuming that the eddy viscosity in the wake is only time dependent and of a harmonic sinusoidal form. The forces predicted by the new Wake (Wake II) Model have been compared to Exxon Production Research Company Wake Model in terms of time histories (force shape) and magnitudes of peak forces. Overall, the model predictions by the Wake II Model are satisfactory and represent a substantial improvement over the predictions of the conventional models. The conventional force models representing adaptations of Morison's equation with ambient velocity and constant coefficients give predictions that are in poor agreement with the measurements especially for the lift force component. The Wake II Force Model can be used for submarine pipeline on-bottom stability design calculations for regular waves with various pipe diameters.     

Prediction of hydrodynamic forces on submarine pipelines using an improved Wake II Model

The hydrodynamic force model for prediction of forces on submarine pipelines as described includes flow history effect (wake effects) and time dependence in the force coefficients. The wake velocity correction is derived by using a closed-form solution to the linearized Navier–Stokes equations for oscillatory flow. This is achieved by assuming that the eddy viscosity in the wake is only time dependent and of a harmonic sinusoidal form. The forces predicted by the new Wake (Wake II) Model have been compared to Exxon Production Research Company Wake Model in terms of time histories (force shape) and magnitudes of peak forces. Overall, the model predictions by the Wake II Model are satisfactory and represent a substantial improvement over the predictions of the conventional models. The conventional force models representing adaptations of Morison's equation with ambient velocity and constant coefficients give predictions that are in poor agreement with the measurements especially for the lift force component. The Wake II Force Model can be used for submarine pipeline on-bottom stability design calculations for regular waves with various pipe diameters.     

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.     

Studies on wave-subsea pipeline interaction

Estimation of wave induced loadings on subsea pipelines involves the evaluation of the hydrodynamic coefficients of drag, inertia, vertical inertia and lift. These coefficients vary with the methodology adopted and the order of wave theory used to compute the water particle kinematics. This paper presents a new and simple method to determine the hydrodynamic coefficients for subsea pipelines in the drag and inertial flow regime. The results are reported for three relative clearances of a pipeline model from the simulated ocean floor.     

Wake model of hydrodynamic forces on pipelines

The hydrodynamic force model for pipelines presented includes flow history effects (wake effects) and time dependence in the force coefficients. These two features in the model were necessary to obtain satisfactory agreement between model predictions and full scale field measurements of pipeline forces. Conventional force models which represent adaptations of Morison's equation with ambient velocity and constant coefficients give predictions which for the lift component of the force in particular are in very poor agreement with the measurements. The parameters in the new model have been estimated on the basis of the full scale measurements and reflect a wide range of flow conditions. The model can be used in pipeline on-bottom stability design calculations for regular or irregular waves.     

Numerical simulation of a partially buried pipeline in a permeable seabed subject to combined oscillatory flow and steady current

Hydrodynamic forces exerting on a pipeline partially buried in a permeable seabed subjected to combined oscillatory flow and steady current are investigated numerically. Two-dimensional Reynolds-Averaged Navier-Stokes equations with a k−ω turbulent model closure are solved to simulate the flow around the pipeline. The Laplace equation is solved to calculate the pore pressure below the seabed with the simulated seabed hydrodynamic pressure as boundary conditions. The numerical model is validated against the experimental data of a fully exposed pipeline resting on a plane boundary under various flow conditions. Then the flow with different embedment depths, steady current ratios and KC numbers is simulated. The amplitude of seepage velocity is much smaller than the amplitude of free stream velocity as expected. The normalized Morison inertia, drag and lift coefficients based on the corresponding force coefficients of a fully exposed pipeline are investigated. The normalized Morison force coefficients reduce almost linearly with the increase of embedment depth and that the KC only has minor effect on the normalized Morison coefficients. It is also found that the permeable seabed condition causes a slight increase on the inline force and has a little effect on the lift force, compared with corresponding conditions in an impermeable bed.     

Experimental study of hydrodynamic forces and wave forces exerted on a truss structure

The drag and added mass coefficients of a truss leg of an ocean platform are obtained by using the forced-oscillation technique in a still water. Higher order forces and lift forces are also measured.The drag and inertia coefficients of the truss leg model are obtained by measuring the wave forces acting on it in regular deep waves. The moment lever of the wave force is compared with theoretical results.     

聚焦波作用下平面网衣结构的水动力特性研究

由于沿海区域的限制以及愈加严重的环境污染,渔业养殖正从近海走向深远海。深远海海域的海况更加恶劣,给养殖装备的设计与性能评估带来新的挑战。为解决该问题,对极端波浪与养殖装备网衣结构的相互作用开展研究。基于waves2Foam建立数值波浪水池,极端波浪模拟采用基于NewWave理论的聚焦波模型,网衣结构模拟采用多孔介质模型,并通过与Morison模型计算的网衣受力等效分析,获得多孔介质模拟网衣结构阻力系数的直接估计方法。然后将多孔介质模型嵌入waves2Foam中,开展聚焦波与网衣结构相互作用的数值模拟,同时开展水槽试验,验证数值模拟的准确性。基于数值模拟结果,系统地分析了不同网衣密实度及不同波浪参数下网衣结构的升阻力特性以及网衣结构对波浪场的扰动规律。研究表明：聚焦波波峰幅值和网衣密实度对网衣结构的升阻力影响较大,且升力峰值出现在阻力为0的时刻;网衣结构对聚焦波的时空演化特性有影响,改变了聚焦波波形。     

Wave forces on large offshore pipelines

A laboratory investigation of wave forces induced by a regular train of waves on a large pipeline resting on the bed and at various clearances from the bed is presented. From considerations of dimensional analysis horizontal and vertical components of wave forces acting on the pipeline are expressed as force coefficients which are shown to be functions mainly of H/2a, gT²/2a, d/a and e/2a. A simple unseparated flow model based on potential flow theory and Morison's equation is presented for evaluating the maximum forces on the pipeline. The experimental results are com3ared with the theoretical results and data from existing literature. Based on the experimental results, hydrodynamic coefficients C_M and C_L have been evaluated     

Regular wave pressures and forces on submerged pipelines near a sloping boundary

The hydrodynamic pressures induced by regular waves around the circumference of a pipeline normal to the wave direction and near a rigid bed of slope 1:10 have been investigated in a wave flume. The pressures were integrated to obtain the force time history, from which the peak horizontal and vertical forces are evaluated. The maximum and root mean square horizontal and transverse force coefficients are correlated with the Keulegan–Carpenter (KC) number. The effect of the distance between the sloping bed and the pipeline on the force coefficients is discussed. The force coefficients are found to decrease with an increase in KC number and with the decrease in the relative clearance of the pipeline from the boundary. In addition, the reflection characteristics of the sloping bed in the presence of the pipeline as a function of surf similarity parameter and their comparison with the results from existing literature are also reported. The details of the model setup, experimental procedure, results and discussion are presented in this paper.     

Computation of the inertia-dominated forces on horizontal circular cylinders placed in oblique waves and near to a plane bed

Wave-force coefficients of horizontal circular cylinders inclined with respect to the incoming waves, are studied numerically under conditions when the effects of flow separation are insignificant. The mathematical model is set in terms of a boundary-value problem for the velocity potential of the wave, which is formulated under the assumption of the linear diffraction theory, and solved numerically by the boundary element method. The numerical calculations are performed in the vertical plane, assuming uniform water depths in the direction along the axis of the cylinder. A first-order correction to the pressures is introduced to take account of the asymmetry of the velocity field around the cylinder when it is close to the plane bed. The correction procedure is found to be highly effective in computing the transverse forces for small gap ratios. The numerical results show that irrespective of the values of the gap ratio, the in-line forces are always sensitive to the wave directionality. The transverse forces, however, show sensitivity only for the smaller gap ratios. It is also shown that by accounting for the wave directionality effects in the wave kinematics only, the forces could be estimated to a certain extent by using the hydrodynamic force coefficients of inertia and lift corresponding to the normal waves.     

Forces on a single pile caisson in breaking waves and current

The effect of breaking and steep non-breaking waves on a vertical pile such as found in minimal caisson structures in the Gulf of Mexico shallow water environment was studied in a wave tank testing. The waves generated were both regular and irregular. The irregular waves were of Bretschneider type. In some tests current was combined in the direction of waves. Specially steep waves in the recorded wave profile were chosen for the analysis of wave forces. It was observed that the forces on the caisson at the wave frequency due to breaking waves were no higher in general than those in nonbreaking steep waves. The drag coefficients in waves alone were much higher than those in a combined wave-current field. The wave-current drag coefficients approached those found in the steady current alone.     

The Lift Forces Acting on a Submarine Composite Pipeline in a Wave-Current Coexisting Field

- A composite pipeline is defined as a main big pipe composed of one or several small pipes. The flow behaviour around a submarine composite pipeline is more complicated than that around a single submarine pipeline. A series model test of composite pipelines in a wave-current coexisting field was conducted by the authors. Both in-line and lift forces were measured, and the resultant forces were also analyzed. The results of lift forces and resultant forces are reported in this paper. It is found that the lift force coefficients for composite pipelines are well related to the KC number. The lift force coefficients for an irregular wave-current coexisting field are smaller than those for a regular wave-current coexisting field. The frequency of lift force is usually twice the wave frequency or higher. The authors test indicates that the resultant forces are about 10 to 20 percent larger than in-line forces (horizontal forces). The effect of water depth is analyzed. Finally, the relationship between lift f     

Hydrodynamic coefficients of a harmonically oscillated tower

A tower hinged at the bottom was oscillated mechanically in a sinusoidal fashion in a plane in still water. An instrumented section in the tower measured the inline and transverse forces locally on the tower due to the hydrodynamic effects. These forces are analyzed for the added mass, drag and lift coefficients which are presented as functions of Keulegan-Carpenter and Reynolds number. The lift force frequencies are also investigated. The measured overall reactions on the tower are used to verify the values of the local coefficients. The results presented here are not only applicable to articulated towers but to other moving elements of an offshore structure, e.g. risers, tension-legs, etc.     

半潜式平台内孤立波载荷计算方法及其试验验证

针对半潜式平台的立柱群和沉箱群,设计了两套独立的载荷测量系统,利用大型重力式密度分层水槽,在不同来波方向下对孤立波中半潜式平台载荷进行了系列模型试验。研究表明,对平台立柱部分,其内孤立波载荷可以用Morison公式进行计算,基于试验结果建立了Morison公式中其拖曳力系数以及惯性力系数的经验公式;对于半潜式平台的沉箱部分,当来波方向与其中纵剖面不平行时,其水平内孤立波载荷同样可以使用Morison公式进行计算,并建立了Morison公式中其拖曳力系数以及惯性力系数的经验公式;当来波方向与半潜式平台中纵剖面平行时,沉箱群的水平内孤立波载荷可以采用Froude-Krylov公式进行计算;同时,在不同来波方向下沉箱群的垂向载荷同样可以采用Froude-Krylov公式进行计算。     

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

Interaction mechanisms among waves,currents and a submerged plate

Wave-induced loads on a submerged plate, representative of submerged breakwater, coastal-bridge deck and a certain type of wave energy converter, in a uniform current are investigated in this study using fully nonlinear numerical wave tanks (NWTs) based on potential flow theory. The coupling effect of wave and current is explored, and the underlying interaction mechanisms of the hydrodynamic forces are described. The presence of a background current modifies the frequency dispersion. It produces changes of the water-surface elevation, and also has an effect on wave-induced loads. Depending on the nonlinearity, higher harmonic wave components are generated above the submerged plate. These contribute to the wave forces. It is found that the horizontal and the vertical force, hence the moment, are affected in the opposite way by the currents. The Doppler shifted effect dominates the vertical force and the moment on the plate. Whereas, the Doppler shifted effect and the generation of higher wave harmonics play opposite roles on the horizontal forces. The contribution of 2^nd order harmonics is found to be up to 30% of the linear component. The current-induced drag force, represented by the advection term ρU∂φ/∂x in the pressure equation, is found to lead to a decrease in the moment for the most range of wavelengths considered, and an increase in the moment for a small range of longer waves.     

Experimental investigation of hydrodynamic force coefficients over AUV hull form

Extensive use of autonomous underwater vehicles (AUVs) in oceanographic applications necessitates investigation into the hydrodynamic forces acting over an AUV hull form operating under deeply submerged condition. This paper presents a towing tank-based experimental study on forces and moment on AUV hull form in the vertical plane. The AUV hull form considered in the present program is a 1:2 model of the standard hull form Afterbody1. The present measurements were carried out at typical speeds of autonomous underwater vehicles (0.4-1.4 m/s) by varying pitch angles (0-15°). The hydrodynamic forces and moment are measured by an internally mounted multi-component strain gauge type balance. The measurements were used to study variation of axial, normal, drag, lift and pitching moment coefficients with Reynolds number (Re) and angle of attack. The measurements have also been used to validate results obtained from a CFD code that uses Reynolds Average Navier-Stokes equations (ANSYS™ Fluent). The axial and normal force coefficients are increased by 18% and 195%; drag, lift and pitching moment coefficients are increased by 90%, 182% and 297% on AUV hull form at α=15° and Re_v=3.65×10⁵. These results can give better idea for the efficient design of guidance and control systems for AUV.     

Wave forces on submarine pipelines near a plane boundary

Forces induced by regular waves on submarine pipelines resting on as well as near a plane boundary and aligned parallel to wave fronts of the oncoming waves are investigated experimentally. The inline hydrodynamic coefficients of drag and inertia are evaluated through the use of Morison equation and the least squares method. The transverse force is analysed in terms of maximum transverse force and transverse root mean square (r.m.s.) coefficients. The resulting inline and transverse hydrodynamic coefficients are correlated with the period parameter or Keulegan-Carpenter number and relative clearance of the pipeline from the plane boundary. The effect of depth parameter on these coefficients and the correlation between maximum transverse force and transverse r.m.s. coefficients are also reported.