Volume-averaged Reynolds-averaged Navier-Stokes Research Articles

Evaluating wave force and interface fluid velocity distribution at the vicinity of a breakwater by considering consolidation of porous media

Previous studies have successfully simulated the interaction between wave and porous media using volume-averaged Reynolds-averaged Navier-Stokes (VARANS) equations. However, the consolidation of porous media subject to wave loading affects the progressing wave, which is crucial to computation of wave force and wave-porous media interface fluid velocity. Research on this aspect is scarce. This study adopted the u -p approximation for Biot dynamic consolidation theory to quantify the consolidation of porous media. The continuity condition on the interfaces between the wave and porous seabed was considered to achieve their interaction. Coupling algorithms of wave and porous seabed were validated against experimental measurements in the literature. An engineering case of wave traveling over a breakwater was examined, and computation results of wave pressures and interface fluid velocities at the vicinity of a breakwater by VARANS equations and wave-porous seabed coupling algorithm of this study were compared to explore the influence of the consolidation effect on the progressing wave.

Numerical simulations of flow inside a stone protection layer with a modified k-ω turbulence model

A numerical model is developed to investigate the flow in porous media, for the purposes of simulating scour protection around coastal and offshore structures. In the present model, the Volume-Averaged Reynolds Averaged Navier-Stokes (VARANS) equations are solved, coupled with the volume-averaged k-ω turbulence closure. The volume-averaged k-ω equations are derived by taking the spatial average of the standard k-ω equations. The unknown coefficients caused by the averaging procedure are determined by large eddy simulation (LES). The developed model is validated against existing experimental results of flow in stone covers under both oscillatory and steady current conditions. A gradual transition of porosity towards unity at the interface between the porous media and the free flow is assumed in the simulation to fit the irregular interface in practical engineering. In the presence of parabolic porosity variation at the interface, the calculated velocity profile, bed shear stress, and turbulent fluctuations inside the porous medium are compared to measurements. The numerical results match well against the experimental data. Comparison with the volume-averaged k-ε turbulence model shows that the volume-averaged k-ω turbulence model provides more accurate flow behavior within the porous media.

Investigations on the shallow water wave attenuation over continuous porous oyster reef-like structure

Observations over the decades have found that oyster reefs in shallow estuarine environments have the potential to protect shorelines or offshore structures by dissipating wave energy. Laboratory experiments were conducted to observe the shallow water wave attenuation in different terrains of the continuous porous oyster reef-like structures. To better reproduce this process, a numerical wave flume that is within the OpenFOAM scheme was developed in this study. The volume-averaged Reynolds-Averaged Navier–Stokes (VARANS) equations were solved for two-phase incompressible flow around the porous structures and the VOF method was used for tracking the free surface. The model was first validated by the present laboratory experiments. Subsequently, dimensional analysis was conducted to address the factors influencing wave attenuation over continuous porous reef-like structures. The model was then applied to evaluate the impacts of wave factors and morphological factors of porous oyster reef-like structures on the wave attenuation. By the end, an empirical formula was proposed to predict the wave transmission coefficient based on the numerical results and the experimental data.

Numerical investigation of breaking waves impact on vertical breakwater with impermeable and porous foundation

Three different types of breaking waves impact on a vertical breakwater with impermeable and porous foundations are studied using our in-house solver, DUTFOAM. The numerical model is based on the Volume-Averaged Reynolds-Averaged Navier-Stokes (VARANS) method and the numerical results are compared with experimental data to obtain a reasonable agreement. The characteristics of flow fields inside and outside the porous region under different breaking wave conditions are discussed and compared. When considering the impermeable foundation, breaking waves that entrapped small air pockets pose the most extensive pressure and forces, while the broken waves exerted the minimum. The porous foundation, with varying porosity values, dramatically affects the flow field and resulting structural forces. Our findings demonstrate that more considerable peak pressures and higher acting positions with porous foundations than impermeable situations for all three breaking wave conditions. Moreover, a sharp increase in horizontal forces and overturning moments occurs in broken wave conditions when the porosity equals 0.5, which poses a threat to stability and deserves additional attention.

Wave Motion and Seabed Response around a Vertical Structure Sheltered by Submerged Breakwaters with Fabry–Pérot Resonance

This paper presents the results from a numerical simulation study to investigate wave trapping by a series of trapezoidal porous submerged breakwaters near a vertical breakwater, as well as the seabed response around the vertical breakwater. An integrated model, based on the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equations is developed to simulate the flow field, while the dynamic Biot’s equations are used for simulating the wave-induced seabed response. The reflection of the wave energy over the submerged breakwaters, caused by the vertical breakwater, can be reserved, indicating that the existence of the submerged breakwaters in the front of the vertical breakwater can either provide shelter or worsen the hazards to the vertical breakwater. Numerical examples show two different modes under the Fabry–Pérot (F–P) resonance condition of the wave transformation, namely the wave reflection (Mode 1) and the wave trapping (Mode 2). The distance between the submerged breakwaters and the vertical breakwater, is a key parameter dominating the local hydrodynamic process and the resultant dynamic stresses around the vertical breakwater. The numerical results indicated that more submerged breakwaters and a higher porosity of submerged breakwaters will obviously dissipate more wave energy, and hence induce a smaller wave force on the rear vertical breakwater and liquefaction area around the vertical breakwater.

Numerical analysis of seabed liquefaction in the vicinity of two tandem pipelines in a trench

In engineering practice, pipeline trenching has been adopted as one of effective protection options. Most previous studies mainly focused on the prediction of the seabed response around a single pipeline, although two tandem pipelines have been used in engineering practice for transporting hydrocarbons. This study aimed to investigate the wave–current induced liquefaction around two tandem pipes in a trench. A series of simulations were performed to explore the effect of the horizontal gap ratio of dual pipes in a shared trench on the seabed response, and the results were compared with a single trenched pipe. In the numerical model, we used an integrated two-dimensional model that was developed based on the Finite Volume Method (FVM) in OpenFOAM®. In terms of the flow field, VARANS (Volume-Averaged Reynolds Averaged Navier–Stokes) was applied to simulate the fluid motion, while Biot’s consolidation equation was used to govern the seabed model. The numerical examples indicate that twin pipelines semi-buried in close proximity within the same trench significantly impact the flow patterns and seabed response around them. Furthermore, the self-weight of dual pipes, ocean currents and trench configuration have a considerable influence on the evaluation of the liquefaction distribution around two tandem pipelines in a trench.

Computational Fluid Dynamics Investigation of Flow in Scour Protection Around a Mono-Pile With the Volume-Averaged k-ω Model

Abstract The study numerically investigates the flow behavior around a mono-pile with scour protection under steady and oscillatory flow conditions. A hydrodynamic model based on volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equations with the volume-averaged k-ω turbulence closure is developed and implemented in openfoam. Three porosity transition types, i.e., constant, linear and parabolic, near the interface between stone cover and free flow are first evaluated in two-dimensional models. The simulated results, i.e., flow velocities, turbulence levels and bed shear stresses, are compared with previous experiments under steady and oscillatory flow conditions. The parabolic transition shows the best agreement with the measurements and is therefore used in the developed model. Under steady current, a three-dimensional model is validated against experimental measurements including flow features both inside and outside of the scour protection around a mono-pile, and it exhibits relatively good performance. Further, the volume-averaged k-ω model shows better agreement to experiments in porous medium compared to results from k-ω shear stress transport and volume-averaged k-ɛ models. The model is applied to investigate the flow patterns under the oscillatory flow condition. The results show that a horseshoe vortex is formed, and it penetrates the entire scour protection, which generates high flow velocities and bed shear stresses; erosion is most likely to occur at the area in the presence of vortex, which poses a threat to the pile stability. The simulations demonstrate the ability of the developed model to evaluate the flow behavior in scour protection.

Study of wave-induced seabed response around twin pipelines in sandy seabed through laboratory experiments and numerical simulations

Wave-seabed-pipelines interaction is of critical importance in the design of submarine pipelines. Previous studies mainly focus on investigating the characteristics of flow fields and hydrodynamics around a single pipeline. In this study, laboratory experiments and numerical simulations have been performed to examine the effect of burial depth and space between the centers of twin pipelines on the wave-seabed-twin pipelines interaction subject to waves. In the mathematical model, the Volume-Averaged Reynolds-Averaged Navier-Stokes (VARANS) equations are used to describe the wave motion in the fluid domain, while the seabed domain is described by using the Biot's poro-elastic theory. Numerical models are validated using these experimental measurements and available relevant experimental data. Experimental and numerical results indicate that the burial depth and relative position of twin pipelines can significantly affect the wave-averaged flow velocity field and the pore-water pressure distribution as well as effective stress.

Application of a VARANS based resistance-type porosity model on simulating wave interactions with perforated caisson sitting on a rubble-mound foundation

Rubble-mound foundation can be regarded as a form of porous structure that is widely used in engineering practice. Porous medium flow must be considered when simulating wave interactions with perforated caisson sitting on a rubble-mound foundation. In this paper, volume-averaged/Reynolds averaged Navier-Stokes (VARANS) equations are adopted to describe the flow inside and outside the porous structure. Moreover, they are combined with the volume averaged k−ε model to simulate the turbulence effect. In addition, the three-step finite element method is applied to solve VARANS equations numerically, and the CLEAR-VOF method is applied to capture the free fluid surface. The resistance-type porosity numerical model is proposed and verified by several test cases and then used to simulate wave interactions with perforated caisson sitting on a rubble-mound foundation. The porosity model gives reliable results compared to the experiments with respect to the wave height, the pressure distribution, and the total vertical wave force. The model can be adopted to study the wave interaction with perforated caisson sitting on a rubble-mound foundation and used for the design of such caisson in engineering practice.

Seabed foundation stability around offshore detached breakwaters

In this study, a three-dimensional (3D) model is adopted to investigate the problem of fluid-seabed-structure interactions (FSSI) around offshore detached breakwaters. The Volume-Averaged Reynolds-Averaged Navier-Stokes (VARANS) equations are used to simulate the 3D fluid motion in the vicinity of breakwaters, including reflected, diffracted waves and non-linear turbulence. The partially dynamic Biot’s equations (i.e., the u−p approximations) and poro-elastoplastic constitutive model are adopted to describe fluid-seabed interactions in a porous seabed. A one-way coupling algorithm is established to integrate the fluid motion and seabed response. By using the present model, this study addresses the long term cyclic loading induced seabed response and liquefaction potential of a loosely packed foundation. In addition, the effects of the perpendicular longshore currents on the hydrodynamic properties and liquefaction potential are also taken into account. The numerical results reveal that the loose sandy seabed around the offshore detached breakwaters experienced a gradual decrease of stiffness until liquefaction occurs under successive loading cycles. Longshore currents tend to exacerbate the wave field and increase the risk of liquefaction of seabed foundation, especially in the shallow soil layer near the seabed surface.

Influence of Wave-Absorbing Chamber Width on the Wave Attenuation Performance of Perforated Caisson Sitting on Rubble-Mound Foundation

A Jarlan-type perforated caisson consisted of a perforated front wall, a solid rear wall, and a wave-absorbing chamber between them. The wave-absorbing chamber was the main feature of the perforated caisson, and its width had a great effect on wave attenuation performance. In this study, a larger range of the wave-absorbing chamber width was observed in model experiments to investigate the effect on wave attenuation performance including the reflection coefficients and the horizontal wave forces of a perforated caisson sitting on a rubble-mound foundation. A resistance-type porosity numerical model based on the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equations was validated by comparing the present results with those of previously reported and present experiments. The validated numerical model was then used for extended research. It was found that the reflection coefficients, the total horizontal wave force, and its components all tended to oscillate in a decrease ⟶ increase ⟶ decrease manner with increasing the wave-absorbing chamber width. The reflection coefficients and wave forces acting on both sides of the perforated front wall were found to be synchronized regardless of perforation ratio or the rubble-mound foundation height.

CFD/DEM coupled approach for the stability of caisson-type breakwater subjected to violent wave impact

Wave impacts on vertical caissons may cause breakwaters failures. This paper focuses on the analysis of the stability of breakwaters under violent wave impacts by using a triple-coupled Fluid-Porous-Solid model. The fluid model is described by the Volume-Averaged Reynolds-Averaged Navier-Stokes equations in which the nonlinear Forchheimer equations for the porous medium are added to the inertia terms. The solid model, based on the DDA method which is an implicit DEM method, has been used to analyze the movement and the stability of the caisson and armour units by taking into account the shapes of the armor units, as well as the contact between blocks. The developed model has been used for multiple purposes. Firstly, to estimate the variation of the maximum height of the impacting wave with the breakwater slope. A new formula has then been established for this purpose. Secondly, to analyze the influence of the porosity and of the thickness of the porous layer on the Turbulence Kinetic Energy (TKE) distribution around the breakwater structure. The results show that the higher the thickness, the lower the TKE intensity will be. Finally, the model has been used to analyze the stability of shaped armour units placed behind the caisson.

Combined wave–current induced seabed liquefaction around buried pipelines: Design of a trench layer

With the increasing development and utilization of offshore oil and gas resources, seabed instability around pipelines subjected to combined ocean wave and current loadings and protection of the pipelines are becoming increasingly important. As a general practice, it is recommended to use trenching in shallow water region for the protection of submarine pipelines from the danger caused by storm waves and ocean currents changing level of the seabed. For a better understanding of the physical process involved in wave–current–seabed–pipeline interactions (WCSPI), a workable Finite Volume Model (FVM) is proposed to simulate wave–current induced soil responses around offshore pipelines. Based on the established FVM model, this study investigates the momentary soil liquefaction induced by various environmental loadings in ocean environments. In the present model, data exchange is taken place on the seabed surface to couple the flow and seabed sub-models. Unlike most previous studies, ocean currents are included in the present model, in which the Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equation is employed to govern non-linear fluid motions, while Biot’s consolidation equation is used to link solid-pore fluid interactions in porous mediums. Numerical examples demonstrate the significant influence of ocean currents, trench geometry, and self-weight of the pipe on the wave-induced pore pressures and on the resultant seabed liquefaction around the pipeline.

Numerical Simulation of Wave Interaction with Submerged Porous Structures and Application for Coastal Resilience

Srineash, V.K.; Kamath, A.; Murali, K., and Bihs, H., 2020. Numerical simulation of wave interaction with submerged porous structures and application for coastal resilience. Journal of Coastal Research, 36(4), 752–770. Coconut Creek (Florida), ISSN 0749-0208.The study of wave interaction with porous structures is essential as coastal structures are often porous in nature because of their prominent energy dissipation characteristics. The present work is focused on the numerical modeling of wave interaction with submerged porous structures, which are often classified as reef breakwaters and low-crested structures. Numerical modeling of wave interaction with porous structures is considered to be a challenge for researchers because of the complexities associated with it. The present study numerically investigates the wave interaction process through the porous media by representing the porous media using Volume-averaged Reynolds-Averaged Navier–Stokes (VRANS) equations. For the study, an open-source RANS-based computational fluid dynamics tool, REEF3D, has been used for numerical modeling. The study also consists of experiments that are used for validating the numerical model. The numerical results for the free-surface elevation and the hydrodynamic pressure are compared with the experimental measurements and found to be in good agreement. The numerical study is extended to different crest widths of the structure and varying wave parameters to investigate the effects of various dimensionless parameters affecting wave transmission. The frequency-domain analysis is performed to investigate the energy distribution of the incident and transmitted waves. Finally, the utility of the numerical model adopting VRANS equations has been demonstrated for climate-change mitigation studies. This has been carried out by studying the effects of pressure reduction on a vertical seawall due to the presence of a porous reef breakwater in the sea side. Pressure reduction up to 32% is calculated because of the presence of the porous structure in front of the seawall and this demonstrates the application of reef breakwaters for coastal resilience studies. Such investigations are useful in protecting the existing coastal structures prone to severe wave conditions exceeding the design limits.

Advantages of an innovative vertical breakwater with an overtopping wave energy converter

This paper presents an innovative vertical breakwater cross-section integrating an overtopping wave energy converter, named OBREC-V, and the analysis of its hydraulic performance and stability response to hydraulic loading. The structure is composed of a vertically-faced caisson with a sloping ramp on the top, a reservoir and a set-back crown-wall. The analysis of the structure is carried out by performing numerical simulations based on the Volume-Averaged Reynolds Averaged Navier-Stokes (VARANS) equations. The numerical simulations are performed to compare the performance of a traditional and innovative vertical caissons under the action of irregular waves, in terms of wave reflection, overtopping and wave acting forces. Results show that the reflection coefficients are lower than those computed in front of the traditional breakwater, with a reduction of up to the 40%. New formulations are proposed to better estimate the reflection coefficient and the wave overtopping at the rear side of the structure taking into account the non-conventional geometry of the device. The analysis of the forces indicate that the non-conventional geometry of the innovative OBREC-caisson increases the overall stability of the structure. The values of the safety factor against sliding, Cs, on innovative caissons are similar or greater than those calculated on the traditional vertical structure for almost all the tests. The downward force on the ramp and reservoir and the time lag between the vertical and horizontal forces, lead to a significant reduction of the maximum destabilizing forces Fs in the innovative breakwater, whose values range between 60 and 80% of the ones computed on the traditional structure. The obtained results show the co-benefits, in terms of functionality and hydraulic stability, that an OBREC-V entails with respect to a traditional vertical breakwater.

Modeling porous coastal structures using a level set method based VRANS-solver on staggered grids

ABSTRACT Several engineering problems in the field of coastal and offshore engineering involve flow interaction with porous structures such as breakwaters, sediment screens, and scour protection devices. In this paper, the interaction of waves with porous coastal structures using an open-source computational fluid dynamics (CFD) model is presented. The fluid flow through porous media is modeled using the Volume-averaged Reynolds-averaged Navier-Stokes (VRANS) equations. Novel improvements to the numerical grid architecture and discretization schemes are made, with a staggered numerical grid for better pressure-velocity coupling and higher-order schemes for convection and time discretization. New interpolation schemes required for the VRANS equations on a staggered grid are implemented. The flow problem is solved as a two-phase problem and the free surface is captured with the level set function. The model is validated by comparing the numerical results to experimental data for different cases such as flow through crushed rock, solitary, and regular wave interaction with a porous abutment and wave interaction with a breakwater considering the three different porous layers. The numerical results are also seen to be highly grid-independent according to the grid convergence study and show a significantly better agreement to experimental data in comparison to current literature.

Investigation on A Resistance-Type Porosity Model and the Experimental Coefficients

The mathematical model based on the Volume-Averaged/Reynolds-Averaged Navier—Stokes (VARANS) equations has been adopted in recent years to generally simulate the interaction between waves and porous structures. However, it is still hard to determine the two experimental coefficients (α and β) included in VARANS equations. In the present study, VARANS equation is adopted to describe the flow inside and outside the porous structures uniformly, with applying the volume averaged k − e model to simulate the turbulence effect. A new calibration method is used to evaluate the accuracy of numerical simulation of wave motion on porous seabed with different coefficients, by taking the wave damping rate as an index. The calibration is achieved by completing a simulation matrix on two calibration cases. A region can be found in the parameter space to produce a lower error, which means that the simulation results are better consistent with the experimental results.

Stability analysis of a non-conventional breakwater for wave energy conversion

This paper presents the stability analysis of a non-conventional breakwater cross-section integrating an overtopping wave energy converter, named OBREC. The device consists of a traditional rubble-mound breakwater in which the upper part of the armour layer is replaced by a smooth ramp and a reservoir.The analysis of the structure is carried out by combining model scale experiments and numerical simulations based on the Volume-Averaged Reynolds Averaged Navier-Stokes (VARANS) equations.The numerical analysis is used to complete and extend the results of the physical model test campaign, providing a deeper understanding of the pressure distribution and resultant force behaviour in locations where laboratory measurements were difficult to obtain or not available. Results show that the maximum vertical and horizontal total forces on the device are not simultaneous. At the time instant of the maximum total horizontal force, the vertical force is zero or directed downward, due to the significant positive contribution of the force acting on the sloping ramp. Additional numerical simulations show the influence of the submerged ramp length on the forces acting on the structure using the global and local stability analysis. The presence of the shaft contributes positively to the global stability against the sliding failure mode by reducing the uplift force exerted on the horizontal base. Moreover, the stability analysis shows that the critical conditions for the global failure modes occur at different time instants.

A Three-Dimensional Model for the Seabed Response Induced by Waves in Conjunction with Currents in the Vicinity of an Offshore Pipeline Using OpenFOAM

To better understand the physical processes involved in the wave–seabed–pipeline interactions (WSPI), a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. Seabed instability around an offshore pipeline is one of the key factors that need to be considered by coastal engineers in the design of offshore infrastructures. Most previous investigations into the problem of WSPI have only considered wave conditions and have not included currents, despite the co-existence of waves and currents in natural ocean environments. Unlike previous studies, currents are included in the present study for the numerical modeling of WSPI, using an integrated FVM model, in which the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equation is used to solve the mean fluid field, while Biot’s consolidation equation is used to describe the solid–pore fluid interaction in the porous medium. Numerical examples demonstrate a significant influence of ocean current direction and angle on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in two-dimensional (2D) numerical simulation.

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

Harbors are important infrastructures for an offshore production chain. These harbors 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 three-dimensional (3D) numerical model is introduced. The open-source computational fluid dynamics (CFD) 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.