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.     

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.     

Aerodynamic loads on a typical tension leg platform

The wind load effects on tension leg platforms have been recognized to be a significant environmental loading. An accurate assessment of the aerodynamic loads is, therefore, a prerequisite for the design of an economic and a reliable structure. The design codes and specifications recommend the use of a projected area approach that is thought to be conservative. The code recommendations fail to quantify aerodynamically induced forces in directions different to the mean wind flow. The interference and shielding effects suggested in some specifications provide only a simplistic view. Physical modeling as reported in this paper, therefore, continues to serve as the most accurate and practical means of predicting aerodynamic loads.The mean aerodynamic force and moment coefficients of a typical tension leg platform for various approach wind directions were measured on a scale model exposed to simulated flow conditions in a boundary layer wind tunnel. Major components on the upper deck of the model were designed for easy removal so that measurements could be obtained for different platform configurations. A parametric study was conducted to determine shielding and interference effects, i.e. the manner in which aerodynamic coefficients are influenced by the location and orientation of the ancillary structures on the platform, e.g. living quarters, flare boom, derricks, etc. The present paper addresses the wind tunnel modeling procedures and automated data acquisition and reduction methods. The aerodynamic force and moment coefficients with respect to the body and flow axes were reduced from the experimental measurements for azimuth angles of 0 to 360 degrees at 15-degree intervals. A total of eight configurations were monitored ranging from a platform configuration that included all the ancillary structures to the case where every deck component was removed. The aerodynamic coefficients obtained from the classification society recommended procedures provided conservative estimates in comparison with the measured values for all configurations. The results also illustrate that the interference effects among various ancillary structures on the platform are significant.     

Analysis on Interface Shear Stress of Thermally Insulated Ocean Pipelines Under Installation

1.IntroductionMost of the crude oil producedfromoffshore China has a highcontent of wax,which makesthe oilagglomerate at hightemperature.Heat preservation measures,therefore,must be adopted to maintainthe temperature higher thanthe oil’s pour point,sotha…     

A new facility for studying ocean-structure–seabed interactions: The O-tube

This paper describes a unique new physical testing facility for studying ocean-structure–seabed interactions, and in particular pipeline on-bottom stability on erodible seabed under hydrodynamic loading. The facility, named the O-tube due to its shape, is a fully enclosed flume in which ambient and storm-induced near-seabed flows are generated by a computer-controlled flow pump. Combined steady and oscillatory flow can be generated by alternating pump flow directions in a controlled manner, and computer control also allows irregular flow to be generated. The design of the O-tube combines the capabilities of a conventional open channel flume (which provides steady current) with a U-tube (which provides oscillatory flow). The facility is designed to physically model severe storm conditions, as well as ambient or tidal flows. When studying pipeline stability on erodible seabed under severe hydrodynamic loading conditions, tests can be performed at a relatively large scale (typically 1/5) for large diameter pipelines (e.g. 40 in. gas trunklines) and at full scale for small diameter pipelines (< 8 in.) to minimize potential scaling effects associated with movable bed model tests. The specifications of the O-tube, a model pipe and an actuator system that supports the model pipe are given in detail. Preliminary model testing results show that the facility has met its design expectations.     

Linear genetic programming to scour below submerged pipeline

Genetic programming (GP) has nowadays attracted the attention of researchers in the prediction of hydraulic data. This study presents Linear Genetic Programming (LGP), which is an extension to GP, as an alternative tool in the prediction of scour depth below a pipeline. The data sets of laboratory measurements were collected from published literature and were used to develop LGP models. The proposed LGP models were compared with adaptive neuro-fuzzy inference system (ANFIS) model results. The predictions of LGP were observed to be in good agreement with measured data, and quite better than ANFIS and regression-based equation of scour depth at submerged pipeline.     

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     

Numerical investigation of local scour below a vibrating pipeline under steady currents

Local scour below a vibrating pipeline under steady current is investigated by a finite element numerical model. The flow, sediment transport and pipeline response are coupled in the numerical model. The numerical results of scour depths and pipeline vibration amplitudes are compared with measured data available in literature. Good agreement is obtained. It is found that pipeline vibrations cause increases of scour depth below the pipeline. The scour pit underneath a two-degree-of-freedom vibrating pipeline is deeper than that under a pipeline vibrating only in the transverse flow direction. The effects of water depth are also investigated. The present numerical result shows that water depth has weak effect on the scour depth. However it does affect the time scale of the scour. The shallower the water depth is, the less time it requires to reaches the equilibrium state of scour. It is found that the vibration forces vortices to be shed from the bottom side of the pipeline. Then vortex shedding around a vibrating pipeline is closer to the seabed than vortex shedding around a fixed pipeline. This contributes to the increase of the scour depth.     

Wake studies of a 1/30th scale horizontal axis marine current turbine

A 0.4 m diameter (1:30th scale) horizontal axis marine current turbine (MCT) was tested in a circulating water channel. The turbine performance and wake characteristics were determined over a range of flow speeds and rotor thrust coefficients. Measurements of the water surface elevation profiles indicated increasing variation and surface turbulence with increasing flow speeds. Blockage-type effects (where the measured point velocity was greater than the inflow velocity) occurred around the sides of the rotor for all flow speeds. Although the effects were exaggerated at model scale, it is expected that reasonable variations in water level and flow velocity could also occur over a full scale MCT array.     

A model equation for the transverse forces on cylinders in oscillatory flows

A quasi-steady model is presented to predict the transverse force on cylinders in waves and oscillating flows. The model assumes that the Strouhal number, based on the instantaneous flow velocity, is constant, taking a value of 0.2. It is also assumed that the lift coefficient, based on the instantaneous dynamic pressure of the flow, is constant over a half cycle of the flow. The predictions of the model are compared with measurements taken on a circular cylinder in planar oscillatory flow over the Keulegan Carpenter number, KC, range from 5 to 53. The agreement between predicted and measured transverse forces is good at high KC but deteriorates at low KC. For high KC, it is shown that the model can be further improved if additional variables are introduced into the model equation.     

Estimating the hydrodynamic forces on a mini TLP with computational fluid dynamics and design-code techniques

This paper reports on the prediction of the hydrodynamic forces on a full-scale mini Tension Leg Platform (TLP) of the type typically deployed for deep-sea operation. Two alternative prediction techniques were used: Computational Fluid Dynamics (CFD), which is based on the solution of the fundamental equations that govern turbulent fluid flow; and ‘engineering’ calculations based on force coefficients derived from a design code that is in routine use in the Offshore Industry. The results from these two techniques were compared with each other and with experimental data obtained from wind-tunnel and towing-tank tests on a 1–70 scale model. It was found that the two techniques, while yielding very similar predictions for the front TLP members, give substantially different predictions for the aft members — a result that is consistent with the presence of significant interference effects that are captured only by the CFD. The design code yielded the highest value for the global drag coefficient, followed very closely by the towing-tank result. The wind-tunnel tests produced the lowest value for this parameter. The CFD predictions, which were the first to be obtained in this study, fall in the mid-range of the experimental values. These and other results are discussed in the context of the use of CFD in practical design applications.     

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     

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.     

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.     

Modelling of tidal motion in shoaling waters: The estuary of Milford Haven

An experimental survey of the estuary of Milford Haven has been carried out in which velocity, temperature and salinity have been measured over the full extent of the estuary during a complete spring and a complete neap- tidal cycle. The measurements were taken from three survey vessels, each of which was used to service six or seven survey points so that the measurements comprised a total of about 40 vertical profiles distributed over a grid of 20 survey points for each tide. Tide level measurements at two points were made simultaneously. The experimental measurements of tidal level have been used to calibrate a two-dimensional mathematical model based upon a new numerical representation of the shallow water equations. The predictions of velocity for the model have been compared with vertically integrated velocities calculated from experiments, and good agreement has been found over the full extent of the estuary.The effect of a strong south-westerly wind in the estuary has been examined in numerical simulation.     

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.     

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.     

Numerical modelling of suspended sediment fluxes in estuarine waters

A two-dimensional finite difference numerical model, capable of predicting depth-averaged tidal flow fields in coastal and estuarine waters, has been extended to include tide-induced non-cohesive sediment transport processes. The partial differential equations governing the conservation of mass, momentum and suspended sediment in an incompressible turbulent flow are included in a depth-integrated form in the model. For the representation of the processes of erosion and deposition of sediment from the bed an empirically based source-sink term was refined, based on the results of three mobile bed flume studies. The model has been tested by simulating tidal flows and suspended sediment fluxes in two estuaries, with particular application to the Humber estuary in the U.K. The model was calibrated and found to produce an encouraging degree of agreement between the numerical predictions and corresponding field measurements for this estuary. Furthermore, the predicted gross deposition and erosion features of the estuary were found to be in close agreement with interpretations from Eulerian tidal residual predictions.     

Effect of Rate-Dependent Soil Strength on Cylinders Penetrating Into Soft Clay

This paper presents a predictive model for undrained penetration of cylinders into soft seafloor soils. The penetration depth will depend on the velocity of the cylinder as it touches down at the seafloor, and the net deceleration of the cylinder as it is acted on by forces of self-weight, soil buoyancy, and soil-shearing resistance. The soil-shearing resistance force increases as a function of penetration depth and, due to the dependence of undrained shear strength on strain rate, penetration velocity. This paper presents finite element (FE) simulations that quantify both effects and form the basis of a simplified soil-resisting force model. Strain-rate effects are modeled within a framework of rate-dependent plasticity, with shearing resistance increasing semilogarithmically with increasing strain rate above a certain threshold strain rate. With all forces acting on the cylinder, estimated penetration depths are predicted from simple equations of motion for a single particle. Comparisons to laboratory tests involving penetration of cylinders into soft reconstituted marine clay show reasonable agreement between model predictions and measurements.