Wave Load and Structural Analysis for a Jack-Up Platform in Freak Waves

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Ould el Moctar ◽  
Thomas E. Schellin ◽  
Thomas Jahnke ◽  
Milovan Peric
Keyword(s):  
Finite Element ◽  
Structural Model ◽  
Stokes Equations ◽  
Breaking Waves ◽  
Wave Loads ◽  
Wave Load ◽  
Two Phase ◽  
Freak Waves ◽  
Highly Nonlinear ◽  
Jack Up

This paper analyzed the effects of freak waves on a mobile jack-up drilling platform stationed in exposed waters of the North Sea. Under freak wave conditions, highly nonlinear effects, such as wave run-up on platform legs and impact-related wave loads on the hull, had to be considered. Traditional methods based on the Morison formula needed to be critically examined to accurately predict these loads. Our analysis was based on the use of advanced computational fluid dynamics techniques. The code used here solves the Reynolds-averaged Navier–Stokes equations and relies on the interface-capturing technique of the volume-of-fluid type. It computed the two-phase flow of water and air to describe the physics associated with complex free-surface shapes with breaking waves and air trapping, hydrodynamic phenomena that had to be considered to yield reliable predictions. Lastly, the finite element method was used to apply the wave-induced loads onto a comprehensive finite element structural model of the platform, yielding deformations and stresses.

Wave Load and Structural Analysis for a Jack-Up Platform in Freak Waves

2007 ◽  
Author(s):  
Ould el Moctar ◽  
Thomas E. Schellin ◽  
Milovan Peric
Keyword(s):  
Structural Model ◽  
Stokes Equations ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Wave Loads ◽  
Wave Load ◽  
Two Phase ◽  
Freak Waves ◽  
Highly Nonlinear ◽  
Jack Up

The paper analyzed effects of freak waves on a mobile jack-up drilling platform stationed in exposed waters of the North Sea. Under freak wave conditions, highly nonlinear effects, such as wave run-up on platform legs and impact-related wave loads on the hull, had to be considered. Traditional methods based on the Morison formula needed to be critically examined to accurately predict these loads. Our analysis was based on the use of advanced CFD techniques. The code used here solves the Reynolds-averaged Navier-Stokes equations and relies on the interface-capturing technique of the volume-of-fluid type. It computed the two-phase flow of water and air to describe the physics associated with complex free-surface shapes with breaking waves and air trapping, hydrodynamic phenomena that had to be considered to yield reliable predictions. Lastly, the FEM was used to apply the wave-induced loads onto a comprehensive finite element structural model of the platform, yielding deformations and stresses.

Wave-in-Deck Load Analysis for a Jack-Up Platform

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Thomas E. Schellin ◽  
Milovan Perić ◽  
Ould el Moctar
Keyword(s):  
Stokes Equations ◽  
Wave Theory ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Design Parameters ◽  
Wave Loads ◽  
Wave Direction ◽  
Two Phase ◽  
Highly Nonlinear ◽  
Jack Up

This paper describes the prediction of environmental loads on a typical three-leg jack-up platform under freak wave conditions. Considered were cases where the air gap is small and the hull is subject to impact-related wave-in-deck loads. The technique to predict wave loads was based on the use of a validated CFD code that solves the Reynolds-averaged Navier–Stokes equations. This code relies on the interface-capturing technique of the volume-of-fluid type to account for highly nonlinear wave effects. It computes the two-phase flow of water and air to describe the physics associated with complex free-surface shapes with breaking waves and air trapping, hydrodynamic phenomena that had to be considered to yield reliable predictions. The Stokes fifth-order wave theory initialized volume fractions of water, velocity distributions in the solution domain, and time-dependent boundary conditions at inlet and outlet boundaries. This paper demonstrates that this technique can be a valuable numerical tool for preliminary designs as well as subsequent safety assessments. In particular, it shows that effects of different operating and design parameters on wave-in-deck loads, such as wave direction, wave height, wave period, and wind speed, can be evaluated with an affordable computing effort.

Wave-Deck-Load Analysis for a Jack-Up Platform

2009 ◽  
Author(s):  
Thomas E. Schellin ◽  
Milovan Peric´ ◽  
Ould el Moctar
Keyword(s):  
Stokes Equations ◽  
Volume Fraction ◽  
Wave Theory ◽  
Breaking Waves ◽  
Design Parameters ◽  
Wave Direction ◽  
Wave Load ◽  
Two Phase ◽  
Highly Nonlinear ◽  
Jack Up

The paper analyzes freak wave-in-deck load effects on a typical three-leg jack-up platform stationed in the North Sea. Considered were cases where the air gap is small and the hull is subject to impact-related wave-in-deck loads. Wave load predictions were based on the use of a validated CFD code that solves the Reynolds-averaged Navier-Stokes equations. The code relies on the interface-capturing technique of the volume-of-fluid type to account for highly nonlinear wave effects. It computes the two-phase flow of water and air to describe the physics associated with complex free-surface shapes with breaking waves and air trapping, hydrodynamic phenomena that had to be considered to yield reliable predictions. Stokes 5th order wave theory was used to initialize volume fraction of water and velocity distribution in the solution domain, as well as to prescribe time-dependent boundary conditions at inlet and outlet boundaries. It was demonstrated that CFD methods can be used to predict the load phenomena under extreme wave conditions and thus serve as a valuable tool for both initial design and subsequent assessment of safety aspects. In particular, we demonstrated that effects of different operating and design parameters on wave-in-deck loads, such as wave direction, wave height, wave period, and wind speed, can be evaluated with an affordable computing effort using personal computers.

Forced Response Assessment Using Modal Force Based Indicator Functions

2008 ◽  
Author(s):  
M. Vahdati ◽  
C. Breard ◽  
G. Simpson ◽  
M. Imregun
Keyword(s):  
Finite Element ◽  
Structural Model ◽  
Stokes Equations ◽  
Linear Time ◽  
Response Assessment ◽  
Element Model ◽  
Forced Response ◽  
Navier Stokes ◽  
Modal Force ◽  
Indicator Functions

This paper will focus on core-compressor forced response with the aim to develop two design criteria, the so-called chordwise cumulative modal force and heightwise cumulative force, to assess the potential severity of the vibration levels from the correlation between the unsteady pressure distribution on the blade’s surface and the structural modeshape. It is also possible to rank various blade designs since the proposed criterion is sensitive to changes in both unsteady aerodynamic loads and the vibration modeshapes. The proposed methodology was applied to a typical core-compressor forced response case for which measured data were available. The Reynolds-averaged Navier-Stokes equations were used to represent the flow in a non-linear time-accurate fashion on unstructured meshes of mixed elements. The structural model was based on a standard finite element representation from which the vibration modes were extracted. The blade flexibility was included in the model by coupling the finite element model to the unsteady flow model in a time-accurate fashion. A series of numerical experiments were conducted by altering the stator wake and using the proposed indicator functions to minimize the rotor response levels. It was shown that a fourfold response reduction was possible for a certain mode with only a minor modification of the blade.

Wave Loads on Floaters of Aquaculture Plants

2008 ◽  
Author(s):  
David Kristiansen ◽  
Odd M. Faltinsen
Keyword(s):  
Stokes Equations ◽  
Model Tests ◽  
Staggered Grid ◽  
Physical Parameters ◽  
Surface Zone ◽  
Two Dimensional ◽  
Wave Loads ◽  
Wave Load ◽  
Constrained Interpolation ◽  
Advection Term

This paper addresses wave loads on horizontal cylinders in the free surface zone by means of model tests and numerical simulations. This has relevance for the design of floating fish farms at exposed locations. Two model geometries were tested, where two-dimensional flow conditions were sought. The cylinders were fixed and exposed to regular wave trains. Wave overtopping the models were observed. A two-dimensional Numerical Wave Tank (NWT) for wave load computations is described. The NWT is based on the finite difference method and solves the incompressible Navier-Stokes equations on a non-uniform Cartesian staggered grid. The advection term is treated separately by the CIP (Constrained Interpolation Profile) method. A fractional and validation of the NWT is emphasized. Numerical results from simulations with the same physical parameters as in the model tests are performed for comparison. Deviations are discussed.

On convergent schemes for two-phase flow of dilute polymeric solutions

2018 ◽  
Vol 52 (6) ◽  
pp. 2357-2408 ◽  
Author(s):  
Stefan Metzger
Keyword(s):  
Finite Element ◽  
Two Phase Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Phase Flow ◽  
Two Phase ◽  
Extra Stress Tensor ◽  
Spring Force ◽  
Polymeric Solutions ◽  
Fokker Planck

We construct a Galerkin finite element method for the numerical approximation of weak solutions to a recent micro-macro bead-spring model for two-phase flow of dilute polymeric solutions derived by methods from nonequilibrium thermodynamics ([Grün, Metzger, M3AS 26 (2016) 823–866]). The model consists of Cahn-Hilliard type equations describing the evolution of the fluids and the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three spatial dimensions for the velocity and the pressure of the fluids with an elastic extra-stress tensor on the right-hand side in the momentum equation which originates from the presence of dissolved polymer chains. The polymers are modeled by dumbbells subjected to a finitely extensible, nonlinear elastic (FENE) spring-force potential. Their density and orientation are described by a Fokker-Planck type parabolic equation with a center-of-mass diffusion term. We perform a rigorous passage to the limit as the spatial and temporal discretization parameters simultaneously tend to zero, and show that a subsequence of these finite element approximations converges towards a weak solution of the coupled Cahn-Hilliard-Navier-Stokes-Fokker-Planck system. To underline the practicality of the presented scheme, we provide simulations of oscillating dilute polymeric droplets and compare their oscillatory behaviour to the one of Newtonian droplets.

scholarly journals Efficient Wave Modeling Using Nonhydrostatic Pressure Distribution and Free Surface Tracking on Fixed Grids

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Hans Bihs ◽  
Arun Kamath ◽  
Ankit Aggarwal ◽  
Csaba Pakozdi
Keyword(s):  
Stokes Equations ◽  
Wave Model ◽  
Offshore Structures ◽  
3D Simulation ◽  
Wave Forces ◽  
Wave Loads ◽  
Two Phase ◽  
New Approach ◽  
2D Simulation ◽  
Numerical Wave

For the estimation of wave loads on offshore structures, relevant extreme wave events need to be identified. In order to achieve this, long-term wave simulations of relatively large scales need to be performed. Computational fluid dynamics (CFD) based numerical wave tanks with an interface capturing two-phase flow approach typically require too large computational resources. In this paper, a three-dimensional (3D) nonhydrostatic wave model is presented, which solves the Navier–Stokes equations and employs an interface tracking method based on the continuity of the horizontal velocities along the vertical water column. With this approach, relatively fewer cells are needed in the vicinity of the air–water interface compared to CFD-based numerical wave tanks. The numerical model solves the governing equations on a rectilinear grid, which allows for the employment of high-order finite differences. The capabilities of the new wave model are presented by comparing the wave propagation in the tank with the CFD approach in a two-dimensional (2D) simulation. Further, a 3D simulation is carried out to determine the wave forces on a vertical cylinder. The calculated wave forces using the new approach are compared to those obtained using the CFD approach and experimental data. It is seen that the new approach provides a similar accuracy to that from the CFD approach while providing a large reduction in the time taken for the simulation. The gain is calculated to be about 4.5 for the 2D simulation and about 7.1 for the 3D simulation.

scholarly journals Capillary effects on wave breaking

2015 ◽  
Vol 769 ◽  
pp. 541-569 ◽  
Author(s):  
Luc Deike ◽  
Stephane Popinet ◽  
W. Kendall Melville
Keyword(s):  
Surface Tension ◽  
Wave Breaking ◽  
Stokes Equations ◽  
Breaking Waves ◽  
Bond Number ◽  
Capillary Waves ◽  
Two Phase ◽  
Wave Regime ◽  
Capillary Effects ◽  
Wave Energy Dissipation

We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier–Stokes equations for a two-phase air–water flow. A parametric study in terms of the Bond number, $\mathit{Bo}$, and the initial wave steepness, ${\it\epsilon}$, is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of $({\it\epsilon},\mathit{Bo})$ is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness ${\it\epsilon}_{c}$ defines the onset of wave breaking. At low Bond number, the influence of surface tension is quantified through two boundaries separating, first gravity–capillary waves and breakers, and second spilling and plunging breakers; both boundaries scaling as ${\it\epsilon}\sim (1+\mathit{Bo})^{-1/3}$. Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter $b$ is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.

Finite Element Implementation of a Planar Soft Tissue Structural Constitutive Model for Heart Valve Simulations

2013 ◽  
Author(s):  
Rong Fan ◽  
Michael S. Sacks
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Soft Tissues ◽  
Structural Model ◽  
Mechanical Response ◽  
Biological Tissues ◽  
Biaxial Test ◽  
Tissue Microstructure ◽  
Highly Nonlinear ◽  
Insight Into

Constitutive modeling is critical for numerical simulation and analysis of soft biological tissues. The highly nonlinear and anisotropic mechanical behaviors of soft tissues are typically due to the interaction of tissue microstructure. By incorporating information of fiber orientation and distribution at tissue microscopic scale, the structural model avoids ambiguities in material characterization. Moreover, structural models produce much more information than just simple stress-strain results, but can provide much insight into how soft tissues internally reorganize to external loads by adjusting their internal microstructure. It is only through simulation of an entire organ system can such information be derived and provide insight into physiological function. However, accurate implementation and rigorous validation of these models remains very limited. In the present study we implemented a structural constitutive model into a commercial finite element package for planar soft tissues. The structural model was applied to simulate strip biaxial test for native bovine pericardium, and a single pulmonary valve leaflet deformation. In addition to prediction of the mechanical response, we demonstrate how a structural model can provide deeper insights into fiber deformation fiber reorientation and fiber recruitment.

Prediction of Hydroplaning Potential Using Fully Coupled Finite Element-Computational Fluid Dynamics Tire Models

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Ashkan Nazari ◽  
Lu Chen ◽  
Francine Battaglia ◽  
John B. Ferris ◽  
Gerardo Flintsch ◽  
...  
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Mesh Size ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Element Size ◽  
Road Surfaces ◽  
Tire Models ◽  
Fully Coupled

Abstract Hydroplaning is a phenomenon that occurs when a layer of water between the tire and pavement pushes the tire upward. The tire detaches from the pavement, preventing it from providing sufficient forces and moments for the vehicle to respond to driver control inputs such as breaking, accelerating, and steering. This work is mainly focused on the tire and its interaction with the pavement to address hydroplaning. Using a tire model that is validated based on results found in the literature, fluid–structure interaction (FSI) between the tire-water-road surfaces is investigated through two approaches. In the first approach, the coupled Eulerian–Lagrangian (CEL) formulation was used. The drawback associated with the CEL method is the laminar assumption and that the behavior of the fluid at length scales smaller than the smallest element size is not captured. To improve the simulation results, in the second approach, an FSI model incorporating finite element methods (FEMs) and the Navier–Stokes equations for a two-phase flow of water and air, and the shear stress transport k–ω turbulence model, was developed and validated, improving the prediction of real hydroplaning scenarios. With large computational and processing requirements, a grid dependence study was conducted for the tire simulations to minimize the mesh size yet retain numerical accuracy. The improved FSI model was applied to hydroplaning speed and cornering force scenarios.

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