scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

Numerical Simulation of Wave Overtopping of Breakwater Armored with Porous Layers and Water-Structure Impaction

2012 ◽  
Vol 226-228 ◽  
pp. 1255-1259
Author(s):  
Zong Liu Huang ◽  
Peng Zhi Lin
Keyword(s):  
Porous Media ◽  
Numerical Model ◽  
Wave Height ◽  
Stokes Equations ◽  
Water Structure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wave Overtopping ◽  
Impact Forces ◽  
The Impact

A numerical model has been developed to study wave overtopping of permeable units protected breakwater and water-structure impactions. The numerical model solves the Reynolds Averaged Navier-Stokes equations outside of porous media and solves the spatially averaged Navier-Stokes equations in porous media, respectively. The numerical model is first validated by experimental data. The validated model is then employed to investigate the breaking wave overtopping porous media protected breakwater. The overtopping discharge and impact forces on the structures behind the crown wall in different wave conditions are studied. The increase of wave height brings increasing maximum overtopping discharges and different spatial distribution of water behind the crown wall. The impact forces on the structures are determined by both incident wave height and relative positions of the structures.

scholarly journals Wave Interaction With a Shallowly Submerged Step in 2D

2019 ◽  
Author(s):  
Guy J. McCauley ◽  
Hugh Wolgamot ◽  
Scott Draper ◽  
Jana Orszaghova
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Water Wave ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Energy Devices ◽  
Barrier Reefs

Abstract Water wave propagation over shallowly submerged structures is of much interest in the context of submerged wave energy devices, breakwaters or barrier reefs. This work examines waves passing over a two-dimensional shallowly submerged fixed step extending to the seabed. The problem has been modelled in CFD using the open source toolbox OpenFoam utilising the Reynolds Averaged Navier-Stokes Equations. These simulations are compared to experimental work from a previous study as means of validation and extended to larger amplitude waves for a single incident wave frequency. The flow over the step is characterised and examined in the context of developing an efficient hybrid numerical model for the problem.

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

Subsidence of the Ekofisk Platforms: Wave in Deck Impact Study — Various Wave Models and Computational Methods

2002 ◽  
Author(s):  
Bogdan Iwanowski ◽  
Henrik Grigorian ◽  
Ingar Scherf
Keyword(s):  
Computational Methods ◽  
Stokes Equations ◽  
Type Equation ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Wave Loads ◽  
Wave Impact ◽  
Navier Stokes Equations ◽  
Wave Models ◽  
Displacement Approach

Subsidence of the Ekofisk platforms creates several operational challenges. For safety of the platforms, it is of great importance to find the wave impact loads acting on the platforms’ decks. The paper describes how such loads can be computed. Three theoretical wave models are discussed in the paper: the Airy wave, Airy wave modified through Wheeler stretching and the 5th order non-linear Stokes wave. The wave loads for these wave models are computed by various methods. The method based on momentum displacement approach and Morison-type equation developed by Dr. Kaplan is used as a reference point. The loads are also computed through a solution of complete Navier-Stokes equations, with the Volume of Fluid (VOF) method used to trace motion of the fluid’s free surface. Results of different wave models and different computational methods are compared and discussed.

scholarly journals Fluid-kinetic modelling for respiratory aerosols with variable size and temperature

2020 ◽  
Vol 67 ◽  
pp. 100-119 ◽  
Author(s):  
Laurent Boudin ◽  
Céline Grandmont ◽  
Bérénice Grec ◽  
Sébastien Martin ◽  
Amina Mecherbet ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Kinetic Modelling ◽  
Type Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aerosol Dynamics ◽  
Convection Diffusion Equation ◽  
Time Marching ◽  
Branched Structure ◽  
The Impact

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics.

scholarly journals Flow Pressure Behavior Downstream of Ski Jumps

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 168 ◽  
Author(s):  
Agostino Lauria ◽  
Giancarlo Alfonsi ◽  
Ali Tafarojnoruz
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Dynamic Pressure ◽  
Pressure Head ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Free Jet ◽  
Jet Characteristics ◽  
The Impact

Ski jump spillways are frequently implemented to dissipate energy from high-speed flows. The general feature of this structure is to transform the spillway flow into a free jet up to a location where the impact of the jet creates a plunge pool, representing an area for potential erosion phenomena. In the present investigation, several tests with different ski jump bucket angles are executed numerically by means of the OpenFOAM® digital library, taking advantage of the Reynolds-averaged Navier–Stokes equations (RANS) approach. The results are compared to those obtained experimentally by other authors as related to the jet length and shape, obtaining physical insights into the jet characteristics. Particular attention is given to the maximum pressure head at the tailwater. Simple equations are proposed to predict the maximum dynamic pressure head acting on the tailwater, as dependent upon the Froude number, and the maximum pressure head on the bucket. Results of this study provide useful suggestions for the design of ski jump spillways in dam construction.

scholarly journals Experimental and Simulation Study on Validating a Numerical Model for CO2 Density-Driven Dissolution in Water

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 738
Author(s):  
Holger Class ◽  
Kilian Weishaupt ◽  
Oliver Trötschler
Keyword(s):  
Carbon Dioxide ◽  
Numerical Model ◽  
Stokes Equations ◽  
Onset Time ◽  
Navier Stokes ◽  
Grid Refinement ◽  
Navier Stokes Equations ◽  
Laboratory Flume ◽  
Diffusive Processes ◽  
Color Indicator

Carbon dioxide density-driven dissolution in a water-filled laboratory flume of the dimensions 60 cm length, 40 cm height, 1 cm thickness, was visualized using a pH-sensitive color indicator. We focus on atmospheric pressure conditions, like in caves where CO2 concentrations are typically higher. Varying concentrations of carbon dioxide were applied as boundary conditions at the top of the experimental setup, leading to the onset of convective fingering at differing times. The data were used to validate a numerical model implemented in the numerical simulator DuMux. The model solves the Navier–Stokes equations for density-induced water flow with concentration-dependent fluid density and a transport equation, including advective and diffusive processes for the carbon dioxide dissolved in water. The model was run in 2D, 3D, and pseudo-3D on two different grids. Without any calibration or fitting of parameters, the results of the comparison between experiment and simulation show satisfactory agreement with respect to the onset time of convective fingering, and the number and the dynamics of the fingers. Grid refinement matters, in particular, in the uppermost part where fingers develop. The 2D simulations consistently overestimated the fingering dynamics. This successful validation of the model is the prerequisite for employing it in situations with background flow and for a future study of karstification mechanisms related to CO2-induced fingering in caves.

Numerical Modelling of Circulation in Lake Sperillen, Norway

2000 ◽  
Vol 31 (1) ◽  
pp. 57-72 ◽  
Author(s):  
N. R. B. Olsen ◽  
D. K. Lysne
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Field Measurements ◽  
Navier Stokes ◽  
Water Current ◽  
Simple Method ◽  
Vertical Temperature Profile ◽  
Navier Stokes Equations ◽  
Good Agreement

A three-dimensional numerical model was used to model water circulation and spatial variation of temperature in Lake Sperillen in Norway. A winter situation was simulated, with thermal stratification and ice cover. The numerical model solved the Navier-Stokes equations on a 3D unstructured non-orthogonal grid with hexahedral cells. The SIMPLE method was used for the pressure coupling and the k-ε model was used to model turbulence, with a modification for density stratification due to the vertical temperature profile. The results were compared with field measurements of the temperature in the lake, indicating the location of the water current. Reasonably good agreement was found.

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