Øivind Asgeir Arntsen

Evaluating wave forces on groups of three and nine cylinders using a 3D numerical wave tank

The evaluation of the complex wave regime due to wave interaction with a large group of cylinders placed in proximity requires an efficient and accurate numerical model. This paper presents the application of a two-phase Computational Fluid Dynamics (CFD) model to carry out a detailed investigation of wave forces and flow around vertical circular cylinders placed in groups of different configurations at low Keulegan-Carpenter (KC) numbers. The 3D numerical wave tank is validated by comparing the numerical results with experimental data. Further, the hydrodynamic effects associated with three cylinders placed in tandem, side by side and in a 3 × 3 square array of nine cylinders are investigated. Wave forces are seen to reduce along the row in a tandem array. In a side-by-side arrangement, the central cylinder experiences the highest force. A combination of these effects is seen in the 3 × 3 square array. The variation of the wave forces on the cylinders in the array for different center-to-center distances and incident wavelengths is evaluated and the results show that the wave forces are the highest on the cylinders when the center-to-center distance is slightly less than half the incident wavelength.

Disturbances, lift and drag forces due to the translation of a horizontal circular cylinder in stratified water

The uniform flow of a fluid with a narrow stratified layer past a horizontal circular cylinder is studied experimentally. This is done through a Galilean transformation of the problem to a situation where the cylinder moves, and the water is at rest. Measurements were made of the interfacial waves formed behind the cylinder towed horizontally at constant speeds. A specially designed stiff force measuring system with a resolution of 0.5 mN measured the drag and lift forces exerted upon the cylinder. When fluid buoyancy forces dominate, it is shown that the increased drag force and other pertinent properties of the problem are efficiently described in terms of a densimetric Froude number, and explicitly independent of the Reynolds number. Lee-waves were detected at all towing speeds less than the speed of long interfacial gravity waves. Maximum wave heights occurred at half of that speed. Vortex shedding was hampered for speeds less than 0.65 of the long interfacial wave speed. Recommended values of increased drag-coefficients are given. The importance of a finite thickness of the stratified layer is documented. The critical densimetric Froude number defining when stratification starts to be important becomes lower with increasing layer thickness. And, with the cylinder located in the stratified layer, the drag-force does not increase although internal waves of appreciable height develop. The situation modelled has its engineering counterpart in the flow past submerged tube bridges.

Energy transfer due to shoaling and decomposition of breaking and non-breaking waves over a submerged bar

ABSTRACT Wave propagation over a submerged bar is simulated using the open source CFD model REEF3D with various incident wave heights to study shoaling, wave breaking features and the process of wave decomposition into higher harmonics for relatively long waves of kd=0.52. The computed free surface elevations are compared with experimental data and good agreement is obtained for both non-breaking and spilling breaking waves for both the wave phase and free surface elevation, which has been difficult to obtain in current literature. The differences in the mode of wave shoaling over the weather side slope and the wave decomposition over the lee side slope of the submerged bar are discussed. The evolution of spilling breakers and plunging breakers over the bar crest is also studied. It is found that the free surface elevation continuously increases due to shoaling in the case of non-breaking waves, whereas breaking waves propagate with much lower free surface elevations after breaking over the bar crest. The power spectra of the free surface elevations at various locations indicate that the wave energy in the fundamental frequency is reduced by 76 for the non-breaking wave with kA=0.015 and by about 90 in other cases with higher incident wave heights with kA=0.023−0.034 due to energy dissipation and energy transfer to higher harmonic components as the wave propagates over the submerged bar.

Lee waves and hydrodynamical loads due to the motion of a submerged horizontal circular cylinder in a three-layer fluid

Laboratory experiments and analytical studies investigating the interaction of two-dimensional, uniform stratified flow with a submerged horizontal circular cylinder are presented. Measurements were made of the interfacial waves formed behind the cylinder towed horizontally at constant speeds, and of the drag and lift forces exerted on the cylinder. An analytical linear model that describes the wave field and the associated wave induced drag force is formulated. In this model, the water is modeled as a uniform flow of three layers of inviscid and immiscible fluids. A solution is found for the case of the cylinder located in the upper layer. The experiments showed that large amplitude first mode internal waves are generated when the cylinder is towed at about one half of the long wave celerity of first mode waves, and that drag and lift forces change significantly with stratification. The analytical model demonstrates the role of a finite stratified layer. For the shorter waves it predicts wave lengths wel...

Calculation of Wave Forces on Cylindrical Piles Using a 3D Numerical Wave Tank

Offshore constructions generally include a large number of vertical cylinders in the support structure. The calculation of wave forces on a vertical cylinder and hydrodynamic effects on it in the presence of neighbouring cylinders is of practical interest. In this paper, a 3D numerical model is used to calculate wave forces on bottom fixed cylindrical piles. Two cases are considered in this study: a single cylinder and a pair of tandem cylinders. A scenario with multiple cylindrical structures in close proximity introduces complex wave-structure interactions and would be of great interest to observe this in detail in a three-dimensional simulation. The wave force exerted on a cylindrical pile is numerically calculated by integrating the pressure and the wall shear stress around the surface of the cylinder. In the case of the single cylinder, the force calculated by the model is compared to the force predicted by the Morison formula and MacCamy-Fuchs theory. In the second case, the pair of cylinders is aligned in the direction of the incoming waves. The numerically calculated inline wave force on each cylinder is compared to the analytical solution for this setup and a good agreement is seen.The Reynolds-Averaged Navier-Stokes equations are used as the governing equations for the fluid flow in the numerical model. The convective terms are discretized using a 5th-order conservative finite difference WENO scheme. A 3rd-order accurate TVD Range-Kutta scheme is used for time discretization. Chorin’s projection method is used to discretize the pressure. The Poisson equation for pressure is solved using a preconditioned BiCGStab algorithm. The level set method is used to obtain a sharp representation of the free water surface. Turbulence in the flow is simulated using the k-ω model. The numerical model is adapted to parallel processing using the MPI library to improve the computing performance of the code.Copyright

Numerical Modeling of Berm Breakwater Optimization With Varying Berm Geometry Using REEF3D

Harbours are important infrastructures for an offshore production chain. These harbours are protected from the actions of sea by breakwaters to ensure safe loading, unloading of vessels and also to protect the infrastructure. In current literature, research regarding the design of these structures is majorly based on physical model tests. In this study a new tool, a threedimensional numerical model is introduced. The open-source CFD (Computational Fluid Dynamics) model REEF3D is used to study the design of berm breakwaters. The model uses the Volume averaged Reynolds Averaged Navier-Stokes (VRANS) equations to solve the porous flows. At first the VRANS approach in REEF3D is validated for flow through porous media. A dam break case is simulated and comparisons are made for the free surface both inside and outside the porous medium. The numerical model REEF3D is applied to show how to extend the database obtained with purely numerical results, simulating different structural alternatives for the berm in a berm breakwater. Different simulations are conducted with varying berm geometry. The influence of the berm geometry on the pore pressure and velocities are studied. The resulting optimal berm geometry is compared to the geometry according to empirical formulations.

Extreme Wave Generation, Breaking and Impact Simulations With REEF3D

An accurate description of extreme waves is necessary in order to estimate maximum wave forces on offshore structures. On several occasions freak waves have been observed in the past, some causing severe damage. In order to model such extreme wave conditions with a computational fluid dynamics (CFD) model, emphasize needs to be put on the wave generation. One possibility is to use focused waves of first or second order based on irregular sea state wave spectra. For focused waves, the wave phase is chosen, so that the waves focus in a predetermined location at a specified time. Numerical tests have shown, that generating extreme waves based on this method is somewhat limited. The individual wave components are steep enough, that they start to break before the focus location. In the current paper, transient wave packets are used for extreme wave generation. This way, extreme waves can be generated that are higher, but only break at the concentration point. The transient wave packets method is implemented in the open-source CFD software REEF3D. This model uses the level set method for interface capturing. For the hydrodynamics, the Navier-Stokes equations are solved in three dimensions. The code employs a staggered Cartesian mesh, ensuring tight pressure-velocity coupling. Complex geometries are handled with a ghost cell immersed boundary method. High-performance computing is enabled through domain decomposition based parallelization. Convection discretization of the different flow variables is performed with the fifth-order WENO (weighted essentially non-oscillatory) scheme. For the explicit time treatment a third-order Runge-Kutta scheme is selected. In order to validate the extreme wave generation, numerical tests in an empty wave tank are performed and compared with experimental data. Then, the extreme wave breaking on a vertical circular cylinder is investigated. ∗Corresponding author, hans.bihs@ntnu.no

Numerical study of irregular breaking wave forces on a monopile for offshore wind turbines

Abstract The substructures of offshore wind turbines are subjected to different types of hydrodynamic loads from sea states. The wave forces exerted by irregular breaking waves are one of the serious concerns because of the uncertainties involved in defining the breaking wave and the resulting force calculations. In the present study, irregular breaking wave forces on a vertical pile structure are investigated using an open-source Computational Fluid Dynamics (CFD) model REEF3D. The Level Set Method (LSM) is used for modelling the free surface. The Bretschneider spectrum is used for the irregular wave generation. This is validated in the numerical wave tank by comparing the numerical wave spectrum with the experimental wave spectrum. The wave free surface is calculated at three wave gauge locations and compared with experiments. It is observed that the peak of spectral wave density is higher for the wave gauge located besides the cylinder due to shoaling, wave run up and reflections from the cylinder and the peak of spectral wave density is lower for the wave gauge located behind the cylinder due to wave breaking. Further, simulations are performed to study the wave forces on a monopile due to the depth-limited breaking waves. A good match is observed with the experimental and numerical results. Numerical wave energy spectra at different locations along the tank are compared to study the changes in the wave surface elevations due to the interaction of irregular breaking waves with a monopile. The statistical parameters for free surface elevation and wave forces are further investigated. The free surface features around the monopile during its interaction with waves are also studied.

3D Numerical modelling of pile scour with free surface profile under waves and current using the level set method in model REEF3D

Wave action stirs up sediments and keeps it in suspension while currents wash it away from the coastal zone. The combined action of the waves and current close to the sediment bed may worsen the situation by creating excessive sediment transport leading to the failure of hydraulic structures. In this study, numerical modeling of local scour under waves and current is carried out using the open source CFD model REEF3D, which solves the Navier-Stokes equation using the finite difference method. The simulated flow field from the Navier-Stokes equations is coupled with sediment transport algorithms in a numerical waves tank. Further, the calculated bedload and suspended load are linked with the Exner formula to calculate bed elevation changes. The free surface and scoured bed surface are captured using the level set method. Two case scenarios, namely scour under waves and scour under current are run until the equilibrium scour condition is achieved. The simulated results are compared with experimental data of Link (2006) and Sumer & Fredsoe (2001). Good comparison between experimental data and simulated results is observed. It is observed that for equal flow velocity in the flume, sediment transport under current only condition is larger than under waves alone.

Analysis of Wave Interaction With Cylinders Using a 3D Numerical Wave Tank

Evaluation of flow around a cylinder placed in waves is a challenging task due to the complex nature of the flow. A good understanding of the flow physics involved here is important as coastal and offshore structures consist of horizontal and vertical cylindrical elements. This paper explores the use of Computational Fluid Dynamics (CFD) to evaluate the flow field around cylindrical structures. A 3D numerical wave tank is employed to study the free surface and fluid velocities around a vertical cylinder placed in waves and the total force acting on the cylinder is evaluated. The numerical results are compared with experimental data. Further, a simple representation of an offshore structure modelled as multiple cylinders in proximity is also simulated in the numerical wave tank. The presence of neighbouring cylinders has an effect on the flow field. This affects the force acting on each of the cylinders in the group. The forces acting on every cylinder in the group are evaluated and the free surface elevation in the flow field is also visualised. The numerical result is compared with the result from an analytical formula.The numerical model uses the Reynolds-Averaged Navier-Stokes equations to evaluate the flow field. The convective terms are discretized using a 5th-order conservative finite difference WENO scheme. Time discretization is carried out using a 3rd-order Runge-Kutta scheme. Pressure discretization is carried out using Chorin’s projection method. The Poisson pressure equation is solved using a pre-conditioned BiCGStab algorithm. A sharp representation of the free surface is obtained using the level set method. Turbulence modeling is carried out using the k-ω model. Computational performance of the numerical model is improved by parallel processing using the MPI library.Copyright