Wave induced forces around buried pipelines

This work refers to an experimental investigation carried out to analyze wave induced pressures on a pipeline buried in a permeable seabed. In this investigation, the model tests were performed on a pipeline buried in the soil test bed. The wave flume used was 30 m long, 2 m wide and 1.7 m deep, 96 number of tests were conducted with waves generated for different wave heights. A pipeline 200 mm in diameter was buried in the sandy bed at different burial depth ratios. The pipeline was laid perpendicular to the wave direction, pressure was measured with 12 transducers along the outer circumference of the pipeline. The results show that wave induced pressures are significantly controlled by the wave period analyzed in terms of the scattering parameter (ka). Higher pressures were recorded at the top and the lower pressures were recorded at the bottom.     

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.     

Wave forces on a large, horizontal submerged cylinder

A numerical boundary integral equation method combined with a non-linear time stepping procedure is used for the calculation of wave forces on a large, submerged, horizontal circular cylinder. As the method is based on potential theory, all computations are performed in the inertia dominated domain, that is, for small Keulegan-Carpenter numbers. Computations are carried out for the Eulerian mean current under wave trough level equal to zero. When the cylinder is moved towards the sea bed the computations show that the inertia coefficients increase significantly, which is associated with a blockage effect. Furthermore, the effect of the wave steepness is reduced when the submergence of the cylinder is increased. In the vicinity of the free water surface the vertical inertia coefficient is highly dependent upon the wave steepness, which tends to reduce it, whereas the horizontal inertia coefficient is only slightly dependent on the wave steepness. Computations are also carried out for cylinder diameters comparable with the wave length. Finally, inertia coefficients computed by the present method are compared with some analytical results by Ogilvie [(1963), First and second order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16, 451–472]. As long as the assumptions leading to Ogilvie's theory are fulfilled (cylinder radius small compared to the wave length), the results are quite similar.     

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.     

Wave forces on hemicylinders

Potential solutions describing the flow about two-dimensional marine structures on or near the ocean bottom are formulated, based on Airy's wave model. The solutions for a half-cylinder and semicircular shell are considered in detail and evaluated in the case of deep submergence. The formulation with and without flow underneath the structure is given and, in particular, the existence of a large difference between the two cases in the vertical forces is shown. The effect of introducing vorticity at the edges of the shell is investigated. Numerical results for hemicylinders resting on the bottom and slightly raised off the bottom are presented. The results obtained for the wave forces are compared with experimental results obtained for a slightly raised, open hemicylinder.     

Free spanning analysis of offshore pipelines

A rigorous procedure was established on the free span analysis of offshore pipelines. The closed form solutions of the beam–column equation, considering tension and compressive force, were derived for the various possible boundary conditions. The solutions can be used to find the natural frequencies of the free spans using the energy balance concept. The results can be applied to improve the current design codes. The improved procedure will yield more realistic calculations of the allowable free span lengths of offshore pipelines. Some calculations are included to present the sensitivity of the axial forces on the allowable free spanning lengths.     

Wave diffraction by large offshore structures: an exact second-order theory

An exact second order theory has been formulated in this paper to calculate the wave forces on offshore structures. Lighthill's method for deep water waves has been extended to shallow water waves. Exact expression for linear velocity potential applicable to the circular cylindrical strcutures for shallow water waves have been used in these calculations. These results have been verified with those obtained by direct perturbation technique reported recently by Rahman and Heaps. It is interesting to note that both the methods yield identical results.     

Three-dimensional scour below offshore pipelines in steady currents

This paper presents the results of an experimental investigation on three-dimensional scour below offshore pipelines subject to steady currents. The major emphasis of the investigation is on the scour propagation velocity along the pipeline after the scour initiation. Physical experiments were conducted to quantify the effects of various parameters on scour propagation velocity along the pipeline in a water flume of 4 m wide, 2.5 m deep and 50 m long. Local scour depths directly below the model pipeline were measured using specifically developed conductivity scour probes. Effects of various parameters such as pipeline embedment depth, incoming flow Shields parameter and flow incident angle (relative to the pipeline) on scour propagation velocity along the pipeline were investigated. It was found that scour propagation velocity generally increases with the increase of Shields parameter but decreases with the increase of the pipeline embedment depth. A general predictive formula for scour propagation velocity is proposed and validated against the experimental results.     

A finite volume solution of wave forces on submarine pipelines

In this paper, a numerical model is established for simulating the wave forces on a submarine pipeline. A set of two-dimensional Navier–Stokes equations is discretized numerically with a finite volume method in a moving mesh system. After each time step, the mesh is modified according to the changed wave surface boundary. The deffered correction second-order upwind scheme (SUDC) is adopted here to discretize the convective fluxes. The effects of the clearance between the pipeline and the seabed, water depth and wave height on wave forces are studied, respectively. The results by the numerical simulation agree well with the experimental data and theory value.     

Investigations of ice forces on a conical offshore structure

Conical shapes have been used for a long time to reduce the ice impact forces. For a major Canadian offshore lighthouse in Lake Erie, a nearly conical shape was used as early as 1857. But the actual mode of destruction of an ice sheet colliding with a conical structure is still not fully understood. The measured and theoretical values of the horizontal force calculated by the different methods have been compared. Calculations and field observations suggest that a failure mode transitional between that of crushing and flexure occurs for the steeper cone angles.     

Non-linear restoring forces of an offshore platform

The method of calculation of non-linear restoring forces presented in this paper is simple, concise and feasible to apply easily in the calculation of restoring forces of platforms in order to simulate motion responses of offshore platforms in the time-domain. In this method, hydrostatic restoring forces and moments are related to the translational and/or rotational displacements. Calculations of non-linear yaw, roll and pitch restoring moments are based on the catenary type of moorings. Although the method presented here is a simple one, it is capable of the calculation of restoring forces for use in the time-domain motion simulations of offshore platforms, with an acceptable degree of accuracy when the numerical simulation results were compared with the experimental measurements.     

Wave forces on vertical cylinders upon shoals

An experimental study has been carried out on the forces from plunging breaking regular and irregular waves on a vertical cylinder on a shoal. Total as well as local wave forces have been measured. Engineering formulae for the calculation of the horizontal forces and overturning moments have been derived. The duration of the impact forces have been measured and compares fairly well with theoretical values.     

Wave forces on a seawater intake caisson

The wave force on a seawater intake structure consisting of a perforated square caisson of 400 mm×400 mm size encircling a vertical suction pipe of 160-mm diameter is investigated using physical model studies. The porosity of caisson was varied from 1.6 to 16.9%. Regular and random waves of wide range of heights and periods were used. It is found that the force ratio (ratio of the force on perforated caisson to the force on caisson with zero percent porosity) reduces to an extent of up to 60% with increase in porosity of the caisson from 1.6 to 16.9%. The force ratio was found to increase with increase in relative wave height and reduces with increase in relative width. Multiple regression analysis of the measured data points was carried out and predictive equations for wave force ratios are obtained both for regular and random waves. The results of this investigation can be used in the hydrodynamic design of perforated caissons, which are widely used as seawater intake structures.     

Hydrodynamic forces on partly buried tandem, twin pipelines in current

This study extends the investigations of the forces on a cylinder, laid on, or partly buried in the bed with a parallel twin dummy cylinder nearby and without it, and were determined by measuring the pressure distribution on the cylinder in the case of a steady current. The pressure distribution around the cylinder was measured by using pressure transducers. The forces on the cylinder were calculated by the integration of the measured pressures on the surface of the cylinder. Force coefficients were obtained for the ranges of Re=0.8×10⁴–1.5×10⁴ for the burial depth to diameter RATIO=0:0.7. The distance between axis of the measurement and dummy cylinders to diameter ratio (x/D) was 2, 1.5 and 1. The dummy cylinder was replaced downstream and upstream of the measurement cylinder.     

The cross-over mechanisms of integral buckle arrestors for offshore pipelines

Local buckling of submarine pipelines is unavoidable under extreme conditions and it can propagate along the pipeline. Thus, arrestors are installed in a periodic placement along the pipeline to limit the extent of catastrophic collapse between two adjacent arrestors. Generally, the integral buckle arrestors are crossed by two modes: the flattening mode and the flipping mode. This paper focuses on the cross-over mechanisms of arrestors by analyzing results from experiments and numerical simulations. Fifteen groups of full-scale and reduced-scale physical experiments are conducted to investigate the effect of local ovality of the downstream pipes on the arrestor performance. Furthermore, an extensive parametric study of cross-over modes of arrestors is performed by FE models to supplement the experimental results. It is found that the local ovality of the downstream pipes impacts the cross-over modes of integral buckle arrestors, which is more likely to deform by ovalization in the same sense as the local ovality. On the other hand, a new formula involving the major geometric and material characteristics of pipes and arrestors is proposed to estimate the flattening mode and the flipping mode of arrestors when the downstream pipes are intact. And the switch point of the two cross-over modes is 0.265.     

A numerical model for onset of scour below offshore pipelines

A numerical model is developed to predict the onset of local scour below offshore pipelines in steady currents and waves. The scour is assumed to start when the pressure gradient underneath the pipeline exceeds the floatation gradient of the sediments. In this model, the water flow field above the bed is determined by solving the two-dimensional (2-D) Reynolds-averaged Navier–Stokes equations with a k-ω turbulence closure. The seepage flow below the seabed is calculated by solving the Darcy's law (Laplace's equation) with known pressure distribution along the common boundaries of the flow domains-seabed. The numerical method used for both the turbulent flow around the pipeline and Darcy's flow in the seabed is a fractional finite element method. The average pressure gradient along the buried pipe surface is employed in the evaluation of onset condition with a calibration coefficient. The numerical model is validated against experimental data available in literature. A unified onset condition for steady currents and waves is proposed. Influences of flow parameters, including water depth, embedment depth, boundary layer thickness, Reynolds number (Re) and Keuleagan–Carpenter (KC) number, on the pressure drop coefficient over the pipeline are studied systematically.     

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.