VARANS Equation Research Articles

Impact toughness analysis of offshore wind power structures under the influence of long-period waves

Abstract In this paper, the performance of offshore wind turbine structures under long-period wave impacts is investigated, and a numerical model of long-period waves is developed to simulate the wave motion and fluid seepage in the pore medium by using the VARANS equation with the OlaFlow solver, and various turbulence models such as the model, RNG model, and the VOF method is applied to capture free surfaces, which can accurately simulate wave generation, propagation, reflection, breaking, and fluid seepage in the pore medium. These methods can accurately simulate the wave generation, propagation, reflection, breaking, and fluid seepage in the pore medium, and the accuracy of the numerical simulation is verified by comparing the results with those of the physical experiment. The results show that the wind farm exhibits good impact toughness under the influence of long period waves, and its overturning stability and slip stability are better than the safety coefficient required by the specification.

Numerical Analysis of Dynamic Response and Liquefaction Phenomena in Sandy Seabed Foundation around a Semi-Circular Breakwater under Wave Loading

Understanding the stability of the seabed foundation holds paramount significance in guaranteeing the safety and structural soundness of the breakwater alongside additional offshore structures. This study aimed to investigate the stability of a sandy seabed foundation around a semi-circular breakwater under wave loading in nearshore areas. A coupled numerical model of waves, a semi-circular breakwater, and the seabed was developed based on the OpenFOAM platform. The VARANS equations were used to govern the wave behavior. Meanwhile, the Biot’s partially dynamic model was employed to numerically simulate the seabed response considering both consolidation under self-weight and dynamic response under wave loading. The effects of various wave parameters, seabed properties, and the radius of the structure on the dynamic response of the seabed and the depth of liquefaction were investigated. The numerical results indicate that an increase in wave height, period, and permeability coefficient intensifies the dynamic response of the seabed soil. Furthermore, an increase in water depth weakened the soil’s dynamic response. There was a negative correlation between the radius of the semi-circular breakwater and the dynamic response. The influence of Poisson’s ratio on the dynamic response of the seabed was relatively small. Furthermore, a stronger dynamic pore pressure response was observed at the connection between the semi-circular breakwater and the rubble foundation.

Numerical modelling of wave transformation and runup over rough fringing reefs using VARANS equations

Computational Fluid Dynamics (CFD) models are gaining popularity recently in efforts to understand the complex dynamics of wave interaction with coral reef profiles. To provide an alternative approach to the current CFD models to account for the reef surface with large bottom roughness, a 3D numerical wave tank based on the CFD tool OpenFOAM® is developed in this study. The VARANS equations are solved for two-phase incompressible flow with the k-ω SST model for the turbulence closure and VOF method for tracking the free surface. The reef surface with high friction is modeled by using a porous media model in the VARANS equations. The numerical model is first validated with laboratory experiments. The model is then applied to evaluate the impacts of forcing condition (wave and water level), reef morphology (reef-flat width, fore-reef slope, and back-reef slope), and reef roughness on wave transformation and wave runup. Moreover, an empirical formula is derived from the numerical results to predict wave runup. Subsequently, the simulated cross-reef variations of energy dissipation, wave spectrum, wave shape parameters (skewness and asymmetry) and nonlinearity parameter (Ursell number) are discussed for both the smooth and rough reefs. Finally, the cross-reef variations of the TKE and its dissipation rate are also examined for both reefs via the numerical simulations.

Seabed liquefaction around breakwater heads at a river mouth: An integrated 3D model

In this paper, a 3D model is developed to investigate the foundation stability around breakwaters at a river mouth, where both ocean waves and river currents are considered. The present model consists of flow and seabed sub-models. In the flow sub-model, the VARANS equations is used to describe hydrodynamic process, while the dynamic u−p approximation is employed in the seabed sub-model. Based on the integrated model, both oscillatory and residual liquefaction phenomenon is investigated by adopting the poro-elastic and poro-elastoplastic seabed models, respectively. The numerical results reveal that the breakwaters at the river mouth with the river current significantly alter the hydrodynamic properties around breakwater heads. Furthermore, the dynamic soil responses and liquefaction zones predicted by the poro-elastic and poro-elastoplastic seabed models show the completely different development trend, which the latter seabed has more intense and severe reactions. The parametric study indicates that the breakwater foundation is more likely to be liquefied in a loosely deposited soil under larger waves. The river currents can exacerbate the liquefaction condition in the region near breakwater heads. In addition, the pore pressure is smaller in front of a milder slope of breakwater flank and a round breakwater head with a smooth slope.

Numerical modelling of the fluid–seabed-structure interactions considering the impact of principal stress axes rotations

The principal stresses that occur in soil below ground level often change direction due to engineering activities. A typical example would be the cyclic loading applied by waves and currents onto the foundation of offshore structures. Even though the principal stress rotations (PSR) are recognized as some kind of “loading” that is exerted onto seabed soil, it is ignored in most investigations into how soil around marine structures responds to ocean waves and currents. In response this paper will simulate the fluid-seabed-structure interactions (FSSI) while considering the impact of PSR. This simulation will utilize an integrated numerical model in which VARANS equations are used for the flow motion. A coupled fluid-dynamic framework and a generalized plasticity model will be developed for the saturated porous medium to examine the cyclic loading of seabed and the continuous rotation of principal stress orientations. It is predicted that the stress path in the τxz versus (σx′−σz′) plane around the structure will denote variations in deviator stress in conjunction with the rotations of the principal stress axis. The mechanical impact of PSR becomes most significant in the region beneath the breakwater and up to a depth of the half thickness of the seabed. Ignoring the PSR-induced deformation may lead to an underestimation of (p̄PSR−p̄no−PSR)∕γwd by 35% in this region.

Response of a Porous Seabed around an Immersed Tunnel under Wave Loading: Meshfree Model

Seabed instability surrounding an immersed tunnel is a vital engineering issue regarding the design and maintenance for submarine tunnel projects. In this study, a numerical model based on the local radial basis function collocation method (LRBFCM) is developed to evaluate the seabed behaviour in a marine environment, in which the seabed is treated as the porous medium and governed by Biot’s “ u − p ” approximation. As for the flow field above the seabed, the VARANS equations are used to simulate the fluid motion and properties. The present model is validated with analytical solutions and experimental data which show a good capacity of the integrated model. Both wave and current loading are considered in this study. Parametric studies are carried out to investigate the effects of wave characteristics and soil properties. Based on the numerical results, the maximum liquefaction depth around the immersed tunnel could be deeper under the wave loading with long wave period (T) and large wave height (H). Moreover, a seabed with lower permeability ( K s ) and degree of saturation ( S r ) is more likely to be liquefied.

Numerical Study for Soil Response Around Submerged Breakwaters with Bragg Reflection

A better understanding of soil behavior in a seabed foundation around submerged breakwaters under combined wave and current loadings has become crucial regarding the design and maintenance for such breakwaters. Bragg effect is considered in this study, which is one of the important factors that influence the flow field and soil response in the vicinity of multiple breakwaters. The wave-current induced dynamic soil response (effective stresses, pore pressures and displacements) and its resultant residual liquefaction in a loosely deposited seabed foundation around multiple breakwaters are investigated. In this study, the wave motion is governed by VARANS equation and the Biot’s [Formula: see text]–[Formula: see text] approximation is used to govern soil-fluid interactions in porous medium. The elasto-plastic constitutive model (PZIII) is used to reproduce the plastic soil behavior in seabed foundation under long-term cyclic ocean loading. Numerical results show that the flow motion can be largely changed due to Bragg effects. The construction of breakwaters significantly change the stress field in seabed foundation. Parametric study shows that, under the strongest Bragg effect, the presence of currents, soil properties and wave characteristics have great impact on the liquefaction potential.

Stability analysis of a composite breakwater at Yantai port, China: An application of FSSI-CAS-2D

In offshore areas, quaternary loose seabed soils widely distribute around the world, and a great number of offshore structures actually have been constructed on quaternary seabed floors. In practical engineering, it is highly necessary to evaluate the stability of offshore structures built on quaternary seabed floors under the impact of extreme ocean waves. Based on the VARANS equation and the dynamic Biot's equation, an integrated numerical model FSSI-CAS 2D has been developed by Ye et al. (2013b) to investigate the interaction between ocean waves, marine structures and their seabed foundations. In this study, taking the composite breakwater project in the west harbour zone of Yantai port in China as an engineering case, the integrated numerical model FSSI-CAS-2D is used to evaluate the stability of the composite breakwater under the impact of fortified ocean waves with a 50 years recurrence period. Computational results indicate that the composite breakwater at west harbour zone of Yantai port would be generally stable during its service life. This application demonstrates that the integrated model FSSI-CAS-2D is applicable, and suitable for practical engineering. The case study illustrated in this study can provide ocean engineers with an excellent case demonstration of engineering application, to evaluate the stability of offshore structures under the impact of extreme ocean waves.

Numerical investigation of dynamic soil response around a submerged rubble mound breakwater

A better understanding of physical process of the fluid-seabed-structure interaction (FSSI) is beneficial for engineers involved in the design of marine infrastructures. Most previous studies for the problem of FSSI have considered wave-only conditions, despite the co-existence of wave and current in the real ocean environment. Unlike the previous studies, currents are included in the present study for the numerical modelling of FSSI, using an integrated FVM-FEM scheme, in which the VARANS equation is used to simulate fluid field, while Biot's poro-elastic model is used for porous flow in a seabed. Numerical examples show the important influences of currents on the local hydrodynamic process and the resulting dynamics of seabed foundation around a submerged rubble mound breakwater. The structure is relatively stable in the presence of counter-current waves, whereas the co-current waves would significantly compromise the instability of structure due to potential of shear failure and liquefaction in its sandy seabed foundation.

Nonlinear interaction between wave, breakwater and its loose seabed foundation: A small-scale case

In offshore environment, newly deposited quaternary loose sediments widely exist in the world. Sometimes, coastal engineers cannot avoid choosing these natural loose sediments as the foundation of marine structures. Under this situation, the interaction between ocean wave, marine structures and their loose sand foundation, and the wave-induced pore pressure built-up in loose seabed foundation are the key factors in which coastal engineers would most concern. In this study, the nonlinear interaction mechanism between ocean wave, a composite breakwater and its loose elasto-plastic sand bed foundation is investigated by utilizing a semi-coupled numerical model FSSI-CAS 2D. In the coupled numerical model FSSI-CAS 2D, VARANS equation for wave model, and dynamic Biot׳s equation for soil model are used for the governing equations. The advanced and excellent elasto-plastic constitutive model PZIII proposed by Pastor et al. (1990) is adopted to describe the nonlinear dynamic behavior of loose sand soil under cyclic wave loading. Taking the parameters of Neveda sand determined in the VELACS project funded by NSF as the property parameters for the loose sand bed, a small-scale computational case like the experimental set-up in Mostafa et al. (1999) is taken as a representative case to investigate the wave-structure-loose seabed foundation interaction mechanism. The numerical results indicate that the pore pressure in loose seabed foundation builts up significantly, and the marine structure subsides and tilts under wave loading. The loose sand bed becomes denser and denser due to soil compaction. Parametric studies show that both the wave characteristics and the soil properties can affect the built-up of residual pore pressure in loose seabed foundation.

Validation of a 2-D semi-coupled numerical model for fluid–structure–seabed interaction

A 2-D semi-coupled model PORO-WSSI 2D (also be referred as FSSI-CAS 2D) for the Fluid-Structure-Seabed Interaction (FSSI) has been developed by employing RANS equations for wave motion in fluid domain, VARANS equations for porous flow in porous structures; and taking the dynamic Biot's equations (known as "u − p" approximation) for soil as the governing equations. The finite difference two-step projection method and the forward time difference method are adopted to solve the RANS, VARANS equations; and the finite element method is adopted to solve the "u − p" approximation. A data exchange port is developed to couple the RANS, VARANS equations and the dynamic Biot's equations together. The analytical solution proposed by Hsu and Jeng (1994) and some experiments conducted in wave flume or geotechnical centrifuge in which various waves involved are used to validate the developed semi-coupled numerical model. The sandy bed involved in these experiments is poro-elastic or poro-elastoplastic. The inclusion of the interaction between fluid, marine structures and poro-elastoplastic seabed foundation is a special point and highlight in this paper, which is essentially different with other previous coupled models The excellent agreement between the numerical results and the experiment data indicates that the developed coupled model is highly reliablefor the FSSI problem.

Numerical study of the stability of breakwater built on a sloped porous seabed under tsunami loading

Strong earthquake induced huge tsunami has occurred for three times in Pacific ocean in recent ten years; for example, the tsunami triggered by the Sumatra earthquake in 2004, Chile earthquake in 2010 and Tohoku earthquake (Japan) in 2011. Tsunami carrying huge energy always would bring high risks to the population living near to coastline. Breakwater is widely used to dissipate the wave energy, and protect coastline and ports. However, they are vulnerable when being attacked by tsunami wave. At present, the interaction mechanism between tsunami, breakwater and its seabed foundation is not fully understood. In this study, the dynamics and stability of a breakwater under the attacking of tsunami wave is investigated by adopting an integrated model PORO-WSSI 2D, in which the VARANS equation for wave motion, and the Biot’s dynamic equation for soil are used. Based on the numerical results, it is found that offshore breakwater interacts intensively with tsunami wave when it overtopping and overflowing over a breakwater. The impact force on the lateral side of breakwater applied by tsunami wave is huge. The shear failure is likely to occur in the seabed foundation of breakwater. The liquefaction is unlikely to occur due to the fact that there is basically no upward seepage force in seabed foundation in the process of tsunami wave passing through the breakwater.

Three-dimensional interaction of waves and porous coastal structures: Part I: Numerical model formulation

This paper and its companion paper (Lara et al. (2012)) describe the capability of a new model, called IH-3VOF, to simulate wave–structure interaction problems using a three-dimensional approach, when porous structures are present. The lack of a universal approach for the formulation of porous media flow equations has motivated a new derivation in the present work. Applications dealing with heterogeneous media, where porosity varies along the porous body, such as the study of multilayered rubble-mound breakwaters, are the final objective of the study. In this first paper, a new derivation of the equations, eliminating the limitations imposed by previous approaches is presented. The model integrates a new set of equations which covers physical processes associated with flow interaction with porous structures. The model considers the multiphase VARANS equations, a volume-averaged version of the traditional RANS (Reynolds-Averaged Navier–Stokes) equations. Turbulence is modeled using a k–ε approach, not only at the clear fluid region but also inside the porous media. A VOF technique is used to track the free surface. In this first paper, the model has been validated using laboratory data of a two-dimensional flow. In the companion paper the model is further validated with new experimental data sets, considering porous and solid structures as well as the presence of air. The model predictions present an excellent agreement with the laboratory measurements.

IH-3VOF: A THREE-DIMENSIONAL NAVIER-STOKES MODEL FOR WAVE AND STRUCTURE INTERACTION

This paper describes the capability of a new model, called IH-3VOF to simulate wave-structure interaction problems using a three-dimensional approach. The model is able to deal with physical processes associated with wave interaction with porous structures. The model considers the VARANS equations, a volume-averaged version of the traditional RANS (Reynolds Averaged Navier-Stokes) equations. Turbulence is modeled using a k-ï¥ approach, not only at the clear fluid region (outside the porous media) but also inside the porous media. The model has been validated using laboratory data of free surface time evolution in a fish tank containing a porous dam. Numerical simulations were calibrated by adjusting the porous flow empirical coefficients for two granular material characteristics. Sensitivity analysis of porous parameters has also been performed. The model is proven to reproduce with a high degree of agreement the free surface evolution during the seeping process. Simulations of a three- dimensional porous dam breaking problem has been studied, showing the excellent performance of the model in reproducing fluid patterns around a porous structure. The model is powerful tool to examine the near-field flow characteristics around porous structures in three dimensional flow conditions.