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**File Type**

Fourtakas, Georgios (University of Manchester) | Stansby, Peter K. (University of Manchester) | Rogers, Benedict D. (University of Manchester) | Lind, Steven J. (University of Manchester) | Yan, Shiqiang (City University of London) | Ma, Qingwei (City University of London)

This paper presents a two-dimensional, one-way coupling methodology between the quasi-arbitrary Lagrange–Euler finite element method (QALE-FEM) nonlinear potential flow solver and the incompressible smoothed particle hydrodynamics (ISPH) Navier-Stokes equations solver. Nonlinear potential flow solvers such as the QALE-FEM are highly efficient solvers for propagating waves in large domains; however, when extreme nonlinearity takes place, such as fragmentation, breaking waves, and violent interaction with marine structures, the methodology becomes incapable of dealing with these flow features. The particle method ISPH is known to be accurate for such highly nonlinear fragmentized flows and provides near-noise-free pressures. ISPH is thus ideal for near-field flows involving overturning, splashing, and slamming. Herein, we propose a one-way coupling methodology between QALE-FEM and ISPH where the methods are used for the far-field and inner/local regimes, respectively. To validate the one-way coupling algorithm, two sinusoidal waves have been used with satisfactory results. The intention is to extend this approach to the strong coupling of the potential flow solver with ISPH using a two-phase (air–water) solver. The aim is to reliably predict extreme wave forces and slamming on offshore structures such as decks and platforms for marine renewable energy and the oil and gas industry.

Artificial Intelligence, boundary, boundary condition, coupling, finite element potential, free surface, free-surface flow, incompressible sph, interface, ISPH, isph domain, node, nonlinear free-surface, one-way coupling, particle, potential flow, potential flow solver, solver, strong coupling, Upstream Oil & Gas

SPE Disciplines:

ABSTRACT

A numerical study has been undertaken to investigate focusing wave impact on a fixed FPSO-type offshore structure in this paper. The linear wave theory is used to generate a focusing wave from the inlet whereas a two-phase flow model has been employed to study the details of wave-structure interactions. The large-eddy simulation approach has been adopted in this study, where the model is based on the filtered Navier-Stokes equations with the dynamic Smagorinsky sub-grid model being used for the unresolved scales of turbulence. The governing equations have been discretized using the finite volume method, with the air-water interface being captured using a volume of fluid method and the cut cell method being implemented to deal with complex geometry in the Cartesian grid. Numerical results have been presented and compared with the experimental measurements and other numerical simulations using QALE-FEM+OpenFOAM in terms of the wave run-up and pressure on the structure.

INTRODUCTION

It is noticed that extreme waves will become more common in coastal and offshore region due to the impact of climate change. Wave- structure interaction is a key aspect in the safe and cost-effective design of coastal and offshore structures, and marine renewable devices. Understanding the characteristics of the extreme wave climate, its variability, and survivability is an important consideration for sustainable development of coastal and offshore infrastructure.

In order to roughly predict the hydrodynamic loads on structures, the Morison equation and potential flow theory (Ma, *et al.*, 2015) have been widely used in the literatures. However, it is challenged to consider wave impact on the structures by using these two approaches during wave breaking, especially when there are splash-up and air entrainment.

With developments of CFD (computational fluid dynamics) and increases in computer power, recent models for studying wave-structure interaction, solve the Navier-Stokes equations coupled with a free surface calculation. Several methods have been developed by solving Navier-Stokes model by using mesh-based methods (Chen, *et al.*, 2014; Hu, *et al.*, 2016; MartÃnez Ferrer, *et al.*, 2016a; Xie *et al.*, 2017), or alternatively, meshless smoothed particle hydrodynamics (SPH) (Lind, *et al.*, 2012) and the meshless local Petrov-Galerkin (MLPG_R) method (Ma, 2005).

city university, computational, elevation, Engineering, equation of state, Fluid Dynamics, fluid modeling, interaction, interface, numerical result, numerical simulation, Offshore Structure, platform design, reservoir simulation, Simulation, subsea system, two-phase flow, two-phase flow model, University, Upstream Oil & Gas, water surface, wave impact, wave-structure interaction, Xie

SPE Disciplines:

ABSTRACT

This paper reports numerical investigations performed to simulate the free oscillations of floating body in calm water using Improved Meshless Local Petrov-Galerkin method based on Rankine Source function (IMLPG_R). The IMLPG_R method is a mesh-free method for solving the interaction between floating bodies and waves based on the viscous fluid theory. The pressure at each time step is estimated by solving the Pressure Poisson Equation, which is derived from the Navier-Stokes Equation using the fractional step method. The forces and moments acting on the floating body are calculated by integrating the pressure on the body surface. Then using Newton's Second law, the translational and rotational motions of floating body are evaluated. The free heave response and roll response of floating body in calm water are numerically simulated.

INTRODUCTION

Oscillations of floating bodies on the free surface of the viscous fluid are investigated by various researchers because of its application in the design and development of floating bodies such as ships, offshore platforms, barges, floating-breakwater, fish-farms, floating airports etc. Experimental investigations of such events are often laborious and expensive. As an alternative, numerical methods are commonly used for analyzing the response of floating bodies in waves.

The common numerical models used for solving such problems include potential theory and Navier-Stokes (NS) models. The former, especially the fully nonlinear potential theory (FNPT) is suitable for modelling fluid only if the viscosity is insignificant and flow is irrotational. If viscous and turbulence effects are significant, e.g. with wave breaking, it is necessary to use NS models to solve the fluid part. Both mesh-based methods and meshfree methods are utilized for solving the NS models. For the NS models with the Eulerian grid, considerable numerical diffusion caused by the treatment of the convective term in the momentum equations may be observed if the mesh resolution is insufficient. For those with the Lagrangian grid, the mesh distortion may limit its application to the problem with wave breaking, although the numerical diffusion due to the convective term may be minimized. Such constraints in the mesh are released if the mesh-free method is used, since the mesh-free method discretizes the problem domain into randomly distributed nodes to produce appropriate solutions.

SPE Disciplines:

**ABSTRACT**

The paper reports a progress on the development of a hybrid approach coupling the Meshless Local Petrov-Galerkin Method based on Rankine Solution (MLPG-R) and the Quasi Arbitrary Langangian-Eulerian Finite Element Method (QALE-FEM) for modelling nonlinear water waves. The former is to solve the one-phase incompressible Naiver-Stokes model using a fractional step method (projection method), whereas the latter is to solve the Fully Nonlinear Potential Theory (FNPT) using a time-marching procedure. They are fully coupled using a zonal approach. The hybrid approach takes the advantage of the QALE-FEM on modelling fully nonlinear water waves with relatively higher computational efficiency and that of the MLPG-R on its capacity on dealing with viscous effects and breaking waves. The model is validated by comparing the numerical prediction with the experimental data for a unidirectional focusing wave. A good agreement has been achieved.

**INTRODUCTION**

Wave-structure interaction has been a focus for the researches on offshore, coastal and ocean engineering for many years. For safety and survivability of the structures, extreme wave condition must be considered. Accurately modelling such extreme wave condition usually requires a large-scale (~ 10s km) and long-duration (e.g. 3-hour sea state) numerical simulation to capture the spatial-temporal propagation of the ocean wave. On the other hand, the response of the structure in extreme condition is considerably influenced by small-to micro-scale physics, such as the viscous/turbulent effect, hydro elasticity and so on. This implies that an effective numerical model shall be able to deal with both large-scale oceans wave and small-scale near-field physics simultaneously. The presence of the extreme waves invalids the routine wave diffraction analysis based on linear and second-order potential theory in frequency domain and a fully nonlinear analysis shall be considered using time domain analysis.

Advances have been made on the development of fully nonlinear potential theory (FNPT) on modelling highly nonlinear wave waves in large scale and for long duration, e.g. 3-hour sea state. Various numerical models based on the FNPT, e.g. the quasi-arbitrary Lagrange-Euler finite element method (QALE-FEM, Ma and Yan, 2006; Yan and Ma, 2010a) and Spectral Boundary Integral methods (e.g. Wang and Ma, 2015; Wang *et al,* 2016), have been developed and proven to be robust and highly efficient for modelling extreme water waves without breaking. The FNPT assumes that the flow is inviscid and irrotational, therefore, it cannot deal with breaking waves, slamming and other small-scale physics near structures.

SPE Disciplines:

Technology: Information Technology > Artificial Intelligence > Representation & Reasoning > Spatial Reasoning (0.34)

Fourtakas, Georgios (The University of Manchester) | Stansby, Peter K. (The University of Manchester) | Rogers, Benedict D. (The University of Manchester) | Lind, Steven J. (The University of Manchester) | Yan, Shiqiang (School of Engineering and Mathematical Sciences City University of London) | Ma, Qingwei W. (School of Engineering and Mathematical Sciences City University of London)

**ABSTRACT**

This paper presents a 2-D one-way coupling methodology between the quasi-arbitrary Lagrange-Euler finite element method (QALE-FEM) (Ma and Yan 2006) which is a nonlinear potential flow solver and incompressible smoothed particle hydrodynamics (ISPH) (Lind *et al.* 2012), Navier-Stokes equations solver. Nonlinear potential flow solvers such as the QALE-FEM are highly efficient solvers for propagating waves in large domains; however, when extreme nonlinearity takes place such as fragmentation, breaking waves and violent interaction with marine structures, the methodology becomes incapable of dealing with these flow features. A particle method such as ISPH is known to be accurate for such highly nonlinear fragmentized flows with noise-free pressures. ISPH is thus ideal for the near-field and slamming due to its ability to treat highly nonlinear flows and free surface flows with overturning and splashing. Herein, we propose a one-way coupling methodology between QALE-FEM and ISPH where the methods are used for the far field and inner/local regimes respectively. To validate the one-way coupling algorithm a regular wave has been used with satisfactory results. The intention is to extend this approach to strong coupling of the potential flow solver with ISPH using a two-phase (air- water) solver (Lind *et al.* 2016). The aim is to reliably predict extreme wave forces and slamming on offshore structures such as decks and platforms for marine renewable energy and oil and gas industry.

**INTRODUCTION**

Structures for offshore oil and gas and more recently for supporting wind turbines and machines for marine renewable energy conversion have been the subject of sustained research and development for a number of years. These offshore structures are often located in depths where waves may be classed as intermediate with breaking bore-like waves which result in extreme loads. However, impulsive loading and slamming due to extreme waves is not well defined particularly when structural response occurs. The problem is complex: important characteristics such as slamming pressures and loads due to breaking wave impact forces involve two or more phases such as air-water, fluid-structure interaction (Lind *et al.* 2015; Khayyer and Gotoh 2016). As importantly, different scales ranging from the far-field propagation to near-field slamming are significant as highly nonlinear incident waves from the far-field directly determine near-field, possibly breaking wave dynamics (Skillen *et al.* 2013).

SPE Disciplines:

**ABSTRACT**

This paper presents a numerical investigation on the significance of the role of the compressibility of the fluids associated with water entry problems using a multi-phase solver OpenFOAM, in which the water and air are treated as either compressible (compressible solver) or incompressible (incompressible solver). The models are validated by using the experimental data of a 3D plate dropping case, whereas the detailed investigations focus on 2D wedge dropping with different dead-rise angles and/or tilting angles. The effects of the compressibility are examined by comparing the results of the compressible solver and that of the incompressible solver. It is concluded that the free surface profiles during the impact are significantly influenced by the compressibility of the fluids, leading to different patterns of impacts (convective motion between fluids and dropping wedge); even in a case with large dead-rise angle, the incompressible solver may lead to incorrect predictions on the peak pressure and the force acting on the wedge surface.

**INTRODUCTION**

Large impulsive pressure and slamming forces may lead to the damage of the offshore structure, and are of interest for the engineering purposes. Typical examples include breaking wave impacts on quay walls/breakwaters, slamming of the ship bow during extreme weather condition. The experimental (e.g. Miyamoto and Tanizawa, 1985; MOERI, 2013; Mai *et al,* 2015), numerical or analytical studies (either based on the potential theory, e.g. Zhao and Faltinsen, 1993; Zhao *et al.* 1996, or viscous flow theories such as Gao *et al.,* 2012; Oger *et al.,* 2007; Skillen *et al.,* 2013) on the water entry problems, initiated by Von Karman (1929) and Wagner (1932), provides useful references for reliably predicting the slamming loads and exploring associated small-scale physics, such as the air trapping, spray and extreme free surface deformation. Significant advances have been recently made on computational fluid dynamics (CFD) modelling on such problems. Both single-phase (e.g. Gao *et al.,* 2012; Oger *et al.,* 2007; Skillen *et al.,* 2013) and multiphase models (Kleefsman *et al* 2005; Sussman *et al,* 1994; Soulhal *et al,* 2014) have been attempted, and a promising accuracy was demonstrated on predicting slamming loads.

Artificial Intelligence, compressibility, dead-rise angle, Engineering, equation of state, Fluid Dynamics, fluid modeling, free surface, free surface profile, incompressible solver, investigation, maximum pressure, Multiphase, numerical investigation, pressure distribution, Reservoir Characterization, Simulation, solver, Upstream Oil & Gas, Water Entry Problem, water surface, wedge

SPE Disciplines:

**Abstract**

This paper presents a comparative numerical study for the water impact problems due to dropping of triangular wedges or ship sections. In the numerical investigation, both the dynamic mesh technique and immersed boundary method adopting fixed Cartesian grids have been adopted in order to conform to the motion of the structure. For the former, a multiple-phase solver with the volume of fluid for identifying the free surface is implemented. In the simulation using this method, both the compressible and incompressible solvers have been considered to explore the role of the compressibility. For the latter, an in-house immersed boundary method, in which a generalized equation is developed to govern the motion of different phases (air, water and solid) and a level-set method is adopted to identify the free surface & body surfaces. Different cases with different dropping speed have been considered in the investigation and the results are compared with the experimental data for the comparative study on the water impact problem.

**Introduction**

The water entry is a complex, high-speed and nonlinear fluid-structure interaction problem covering many physical phenomena, such as the air trapping, free surface deformations, spray and jet flows. Significant impulsive pressure and slamming forces associated with the water entry problems lead to considerable hydro-elastic issues and, possibly, a severe damage of the offshore structure. Although this problem has been attracting the awareness of industrial and academic communities, the relevant understanding is still developing, in particular the role of the compressibility, aeration and hydro-elasticity, as revealed by recent experimental studies (e.g. Miyamoto and Tanizawa 1985; Okada and Sumi, 2000; Huera-Huarte *et al*. 2011; Ma *et al*, 2014, 2015; Mia *et al*, 2015).

Since Wagner (1932), attempts on deriving analytical solutions or empirical formula have been done to predict the slamming forces, e.g. Dobrovolâ€™skaya (1969), Armand and Cointe (1986), Cointe (1991). Nevertheless, these analytical works were limited to simple-geometry or wedge-type bodies. In fact, the body shapes and impact angles play important roles on the impact pressure development and fluid-structure formation near the impact surface, as confirmed by the experimental observations, e.g. Okada and Sumi (2000) and Huera-Huarte *et al*. (2011). This limits the extension of the above-mentioned analytical works to bodies with more complex geometry, and therefore, initiated a fast growth of the numerical simulations on the water entry problems.

Artificial Intelligence, boundary method, compressibility, computational, convergence, Engineering, experiment, Fluid Dynamics, IBM, interaction, mesh, mesh size, numerical simulation, OpenFOAM, Reservoir Characterization, ship section, Simulation, time history, Upstream Oil & Gas, water entry, wedge

SPE Disciplines:

**Abstract**

The grounded or collided oil tankers are often subjected to periodic motions, which excites the liquid sloshing inside the cargo tanks and influences the oil spilling. This paper presents a systematic numerical investigation of the effects of the tank motions on the oil spilling from damaged oil tanks by using a VOF-based multiphase flow solver with the assistance of dynamic mesh techniques. For simplicity, only the two-dimensional single-hull tank (SHT) subjected to pre-specified periodic motions with different frequencies and amplitudes is considered. The results suggest that the tank motion does not only cause a periodic oscillation of the oil/water flow through the broken hole, but also results in a second long-duration stage of spilling after a quasi-hydrostatic-equilibrium condition occurs, leading to more significant amount of spilled oil.

**Introduction**

A maritime accident of oil tankers usually involves oil spilling as ship hulls are damaged due to collision or grounding. When accidental oil spilling occurs, a quick and adequate accident assessment is a top priority to guide the subsequent emergency response with the purpose of mitigating environmental impact. Although governments, industries and academics have devoted significant efforts to reducing the risk of oil spilling by introducing stricter legislation and operating codes for several decades (Fingas, 2001), such disasters are still inevitable.

Assessing the potential oil spilling is one of the most important indexes for hull designs. However, its complexity emerges when comprehensively considering the integrated system combining the external environment (tide, current and wave), the ship response (damaged ship motion and sloshing) and the oil leakage (Zhang & Suzuki, 2006). However, most of the existing historical (e.g., Kim, 2002; Homan and Steiner, 2008; Glen, 2010; Yip et al. 2011) or probabilistic (e.g. Van de Wiel and Drop, 2009; Goerlandt and Montewka, 2014) researches simplified the scenarios and applied hydrostatic theories, in which the external sea is assumed to be still and the ship motions are ignored. Such theories have been demonstrated to be insufficient due to significant dynamics-dominated factors involved in the oil spilling (e.g., Yamaguchi and Yamanouchi, 1992; Lu et al. 2010; Tavakoli et al. 2011; Yang et al. 2014; Yang et al. 2015).

amplitude, cargo tank, chemical spill, collision, Discharge, Fluid Dynamics, freight & logistics services, frequency, marine transportation, motion amplitude, multiphase flow, oil spilling, oil water, rad, Scenario, SHT, spilling, SQRT, tank, tank motion, time history, Upstream Oil & Gas, Water Basin

Industry:

- Transportation > Marine (1.00)
- Energy > Oil & Gas > Upstream (0.88)
- Transportation > Freight & Logistics Services > Shipping > Tanker (0.54)

SPE Disciplines:

Thank you!