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.     

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.     

New model to determine forces at on-bottom slender pipelines

The present paper proposes a numerical model to determine horizontal and vertical components of the hydrodynamic forces on a slender submarine pipeline lying at the sea bed and exposed to non-linear waves plus a current. The new model is an extension of the Wake II type model, originally proposed for sinusoidal waves (Soedigdo et al., 1999) and for combined sinusoidal waves and currents (Sabag et al., 2000), to the case of periodic or random waves, even with a superimposed current. The Wake II type model takes into account the wake effects on the kinematic field and the time variation of drag and lift hydrodynamic coefficients. The proposed extension is based on an evolutional analysis carried out for each half period of the free stream horizontal velocity at the pipeline. An analytical expression of the wake velocity is developed starting from the Navier–Stokes and the boundary layer equations. The time variation of the drag and lift hydrodynamic coefficients is obtained using a Gaussian integration of the start-up function. A reduced scale laboratory investigation in a large wave flume has been conducted in order to calibrate the empirical parameters involved in the proposed model. Different wave and current conditions have been considered and measurements of free stream horizontal velocities and dynamic pressures on a bottom-mounted pipeline have been conducted. The comparison between experimental and numerical hydrodynamic forces shows the accuracy of the new model in evaluating the time variation of peaks and phase shifts of the horizontal and vertical wave and current induced forces.     

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.     

Study on Model Tests and Hydrodynamic Force Models for Free Spanning Submarine Pipelines Subjected to Earthquakes

A test rig is built to model the dynamic response of submarine pipelines with an underwater shaking table in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. Model tests are carried out to consider the effects of exciting wave directions and types. Based on the experimental results, two hydrodynamic force models derived from Morison equation and Wake model are presented respectively. By use of hydrodynamic force models suitable for free spanning submarine pipelines under earthquakes, discretized equations of motion are obtained and finite element models are established to analyze dynamic response of free spanning submarine pipeline subjected to multi-support seismic excitations. The comparison of numerical results with experimental results shows that the improved Morison and Wake hydrodynamic force models could satisfactorily predict dynamic response on the free spanning submarine pipelines subjected to earthquakes.     

Numerical analysis of a cylinder moving through rate-dependent undrained soil

Geo-hazard assessment of the potential damage to a pipeline caused by a submarine landslide requires a quantitative model to evaluate the impact forces on the pipeline. In contrast with typical geotechnical problems, the strain rate within the fast moving, flow-like submarine landslide is typically far higher, which will lead to enhancement of the soil strength and therefore result in larger impact forces. Generally, there are two possible predictive frameworks for strain-rate dependence: a fluid dynamics framework and a geotechnical framework. By comparison of common rheological models adopted in these two different approaches, a unified additive power-law model, a normalised form of the Herschel-Bulkley model from fluid mechanics, is explored in this paper. This model has been used in conjunction with a large deformation finite element approach to investigate the undrained limiting loads on a cylinder moving steadily through inertia-less soft rate-dependent material, in order to quantify the strain-rate effects.The flow mechanism and the effects of the shear-thinning index and Oldroyd number on the shear zones are explored. The calculated resistance factors are compared with the drag coefficients obtained from computational fluid dynamics analysis. The average rate of strain experienced by the soil flowing past the cylinder is estimated for a given flow velocity and an expression in the form of a conventional bearing capacity equation, but with shear strength linked directly to the normalised flow velocity, is proposed to predict the magnitude of the viscous force exerted by the debris flow.     

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     

海底滑坡对海洋单桩冲击力试验研究

为了研究海底滑坡对海洋单桩的冲击力大小,首先通过调整高岭土、粉砂的不同含量,得到不同流变特性、不同密度的碎屑流,采用Herschel-Bulkley模型和幂率模型对流体流变性质进行描述;随后利用自制海底滑坡模型槽,模拟碎屑流在不同流速和黏度下对模型桩的冲击;并结合流体力学理论,建立阻力系数与非牛顿流体雷诺数之间关系表达式。试验数据表明:碎屑流黏度和流速是影响海底滑坡冲击力的主要因素,海底滑坡冲击力随着泥浆黏度和流速的增加而增大。同时,考虑碎屑流剪切稀释特性,得到管桩阻力系数随雷诺数变化的拟合公式,为海洋桩基础设计提供参考。     

Numerical Investigation of Submarine Hydrodynamics and Flow Field in Steady Turn

This paper presents numerical simulations of viscous flow past a submarine model in steady turn by solving the Reynolds-Averaged Navier?Stokes Equations (RANSE) for incompressible, steady flows. The rotating coordinate system was adopted to deal with the rotation problem. The Coriolis force and centrifugal force due to the computation in a body-fixed rotating frame of reference were treated explicitly and added to momentum equations as source terms. Furthermore, velocities of entrances were coded to give the correct magnitude and direction needed. Two turbulence closure models (TCMs), the RNG model with wall functions and curvature correction and the Shear Stress Transport (SST) model without the use of wall functions, but with curvature correction and low-Re correction were introduced, respectively. Take DARPA SUBOFF model as the test case, a series of drift angle varying between 0° and 16° at a Reynolds number of 6.53×106 undergoing rotating arm test simulations were conducted. The computed forces and moment as a function of drift angle during the steady turn are mostly in close agreement with available experimental data. Though the difference between the pressure coefficients around the hull form was observed, they always show the same trend. It was demonstrated that using sufficiently fine grids and advanced turbulence models will lead to accurate prediction of the flow field as well as the forces and moments on the hull.     

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.     

Numerical analysis of the impact forces exerted by submarine landslides on pipelines

Submarine pipelines that transport crude oil and natural gas are often in a complex marine geological environment and may become unstable and fail upon impact by submarine landslides. Previous research has mostly focused on the impact forces exerted by submarine landslides on suspended pipelines, but the impact of submarine landslides on pipelines laid on the seafloor at various impact angles, θ, have been relatively infrequently discussed, and the effects of suspended height, H, on the impact forces exerted by submarine landslides on pipelines have not been thoroughly investigated. In this study, based on the Herschel–Bulkley model, the impact forces exerted by a submarine landslide on laid-on or suspended pipelines at various impact angles θ were simulated using the computational fluid dynamics (CFD) approach. Equations for calculating the axial and normal drag coefficients of a submarine pipeline were proposed. The CFD numerical simulation results were rearranged based on the soil mechanics approach. By comparing the parameters, an essentially corresponding relationship was found between the soil mechanics and CFD approaches when the equations were used to calculate the impact forces exerted by a submarine landslide on a pipeline. In addition, a semi-analytical expression for the failure envelope was provided. Furthermore, the effects of H on the forces on a pipeline were discussed, and an equation for calculating the acting forces on a pipeline along the flow direction of a submarine landslide that comprehensively accounts for the effects of θ and H was proposed. The lift force was discussed preliminarily and the results provide a basis for further investigation. The achievement of this study is applicable for selecting locations of submarine pipeline routes and for designing submarine pipelines.     

Measurement and modeling of bed shear stress under solitary waves

Direct measurements of bed shear stresses (using a shear cell apparatus) generated by non-breaking solitary waves are presented. The measurements were carried out over a smooth bed in laminar and transitional flow regimes (~ 10⁴ < R_e < ~ 10⁵). Measurements were carried out where the wave height to water depth (h/d) ratio varied between 0.12 and 0.68; maximum near bed velocity varied between 0.16 m/s and 0.51 m/s and the maximum total shear stress (sum of skin shear stress and Froude–Krylov force) varied between 0.386 Pa and 2.06 Pa. The total stress is important in determining the stability of submarine sediment and in sheet flow regimes. Analytical modeling was carried out to predict total and skin shear stresses using convolution integration methods forced with the free stream velocity and incorporating a range of eddy viscosity models. Wave friction factors were estimated from skin shear stress at different instances over the wave (viz., time of maximum positive total shear stress, maximum skin shear stress and at the time of maximum velocity) using both the maximum velocity and the instantaneous velocity at that phase of the wave cycle. Similarly, force coefficients obtained from total stress were estimated at time of maximum positive and negative total stress and at maximum velocity. Maximum positive total shear stress was approximately 1.5 times larger than minimum negative total stress. Modeled and measured positive bed shear stresses are well correlated using the best convolution model, but the model underestimates the data by about 4%. Friction factors are dependent on the choice of normalizing using the maximum velocity, as is conventional, or the instantaneous velocity. These differ because the stress is not in phase with the velocity in general. Friction factors are consistent with previous data for monochromatic waves, and vary inversely with the square-root of the Reynolds number. The total shear stress leads the free stream fluid velocity by approximately 50°, whereas the skin friction shear stress leads by about 30°, which is similar to that reported by earlier researchers.     

Forces on a smooth submarine pipeline in random waves — A comparative study

Forces on a smooth submarine pipeline, fixed horizontally near a plane boundary, have been investigated under random wave conditions. The submarine pipeline was subjected to Pierson-Moskowitz spectrum (P-M spectrum) at various energy levels. The water particle kinematics were computed based on the linear random wave model and the Morison equation was chosen as the wave force predictor model. The inline hydrodynamic coefficients of drag and inertia were evaluated using two different methods, one in the frequency domain and the other in the time domain. Five mathematical formulations were considered for the analysis of transverse wave forces and these were compared in terms of the correlation coefficient. The transverse force was also analyzed in terms of the transverse root mean square (rms) coefficient. The inline hydrodynamic coefficients of drag and inertia and the transverse rms coefficient were correlated with the Keulegan-Carpenter number or period parameter, the relative clearance of the pipeline from the bed and the depth parameter. Finally, the results of the random wave tests were compared with those of regular waves under similar pipeline conditions.     

Laboratory, numerical, and theoretical modeling of the flow in a far wake in a stratified fluid

The far-wake flow past a sphere towed in a fluid with high Reynolds and Froude numbers and with a pycnocline-form salt-density stratification is studied in a laboratory experiment based on particle image velocimetry and in numerical and theoretical modeling. In the configuration under consideration, the axis of sphere towing is located under a pycnocline. Flow parameters, the profiles of density and average velocity, and the initial field of velocity fluctuation in numerical modeling are specified from the data of the laboratory experiment. The fields of fluid velocity at different times and the time dependences of integral parameters of wake flow, such as the average velocity at the axis and the transverse width of the flow, are obtained. The results of numerical modeling are in good qualitative and quantitative agreement with the data of the laboratory experiment. The results of the laboratory experiment and numerical modeling are compared to the predictions of a quasi-linear and quasi-two-dimensional theoretical model. The time evolution of both the average velocity at the axis and the transverse width of the wake is obtained with the model and is in good agreement with the experimental data. The results of numerical modeling also show that, under the effect of velocity fluctuation in the wake, internal waves whose spatial period is equal to the characteristic period of the wake’s vortex structure are excited efficiently in the pycnocline.     

Experimental analysis of the flow field around horizontal axis tidal turbines by use of scale mesh disk rotor simulators

Understanding the flow field around horizontal axis marine current turbines is important if this new energy generation technology is to advance. The aim of this work is to identify and provide an understanding of the principal parameters that govern the downstream wake structure and its recovery to the free-stream velocity profile. This will allow large farms or arrays of devices to be installed whilst maximising device and array efficiency. Wake characteristics of small-scale mesh disk rotor simulators have been measured in a 21 m tilting flume at the University of Southampton. The results indicate that wake velocities are reduced in the near wake region (close behind the rotor disk) for increasing levels of disk thrust. Further downstream all normalised wake velocity values converge, enforcing that, as for wind turbines, far wake recovery is a function of the ambient flow turbulence. Varying the disk proximity to the water surface/bed introduces differential mass flow rates above and below the rotor disk that can cause the wake to persist much further downstream. Finally, the introduction of increased sea bed roughness whilst increasing the depth-averaged ambient turbulence actually decreases downstream wake velocities. Results presented demonstrate that there are a number of interdependent variables that affect the rate of wake recovery and will have a significant impact on the spacing of marine current turbines within an array.     

Experimental study on effect of a new vortex control baffler and its influencing factor

The horseshoe vortex generated around the sail-body junction of submarine has an important influence on the non-uniformity of submarine wake at propeller disc.The flow characteristics in the horseshoe vortex generated area are analyzed,and a new method of vortex control baffler is presented.The influence of vortex control baffler on the flow field around submarine main body with sail is numerically simulated.The wind tunnel experiment on submarine model is carried out,and it is proved that the vortex control baffler can weaken the horseshoe vortex and decrease the non-uniformity of the wake at propeller disc.It is shown from the experiment results that the effect of vortex control baffler depends on its installation position;with a proper installation position,the non-uniform coefficient of submarine wake would be declined by about 50%;the Reynolds number of submarine model has an influence on the effect of vortex control baffler too,and the higher the Reynolds number is,the better the effect of the vortex control baffler is.     

The influence of scale,slope and channel geometry on the flow dynamics of submarine channels

Submarine channels are major morphological features of the sea floor and are important in the transport of sediment to the deep ocean. Although much is known concerning the large-scale distribution of sediment within and surrounding submarine channels, there is little understanding of the fluid dynamic processes that control this sedimentation. Direct measurement of flow velocities and concentrations has proved to be extremely difficult within submarine channels, with the resultant paucity of direct observations making physical laboratory modelling a critical technique for examining the processes that operate in, and control, submarine channel development.Recent experimental and numerical studies have proposed a new model of secondary circulation within submarine channel bends, characterised by a reversal in the orientation of the secondary circulation cell relative to that found in meandering rivers. This new paradigm for submarine channels thus predicts basal flow from the inside to the outside of the bend at a bend apex, with an upper return flow directed towards the inner bend. The reversal in orientation of the secondary flow cell has been linked to the vertical distribution of downstream velocity and associated changes in centrifugal and pressure gradient forces. However, previous work has additionally proposed that shearing of the within-channel flow by overbank flow may also generate secondary flow reversal.This study assesses the applicability of the proposed submarine bend flow model against a range of key channel parameters. We demonstrate that the sense of secondary circulation is the same for all experimental conditions, strongly supporting the new model of secondary flow in submarine channels. Furthermore, investigation of overbank shear induced secondary circulation confirms for the first time that this mechanism can occur, and identifies the channel styles most likely to exhibit this effect. Such shear-induced circulation is, however, shown to be a secondary mechanism, with the vertical distribution of downstream velocity the principal mechanism. In certain channel configurations, the two mechanisms may act to augment one another.     

Calculation of transverse hydrodynamic coefficients using computational fluid dynamic approach

Computational Fluid Dynamic (CFD) based on Reynolds Averaged Navier–Stokes equation is used for determining the transverse hydrodynamic damping force and moment coefficients that are needed in the maneuverability study of marine vehicles. Computations are performed for two geometrical shapes representing typical AUVs presently in use. Results are compared with available data on similar geometries and from some of the available semi-empirical relations. It is found that the CFD predictions compares reasonable well with these results. In particular, the CFD predictions of forces and moments are found to be nonlinear with respect to the transverse velocity, and therefore both linear and nonlinear coefficients can be derived. A discussion on the sources of the component forces reveal that the total force and moment variations should in fact be nonlinear.     

Modelling of multi-bodies in close proximity under water waves—Fluid forces on floating bodies

This work presents two-dimensional numerical results of the dependence of wave forces of multiple floating bodies in close proximity on the incident wave frequency, gap width, body draft, body breadth and body number based on both viscous fluid and potential flow models. The numerical models were validated by the available experimental data of fluid oscillation in narrow gaps. Numerical investigations show that the large amplitude responses of horizontal and vertical wave forces appear around the fluid resonant frequencies. The convectional potential flow model is observed to un-physically overestimate the magnitudes of wave forces as the fluid resonance takes place. By introducing artificial damping term with appropriate damping coefficients μ∈[0.4, 0.5], the potential flow model may work as well as the viscous fluid model, which agree with the damping coefficients used in our previous work for the predication of wave height under gap resonance. In addition, the numerical results of viscous fluid model suggest that the horizontal wave force is highly dependent on the water level difference between the opposite sides of an individual body and the overall horizontal wave force on the floating system is generally smaller than the summation of wave force on each body.