scholarly journals Simulations of oil spread on a water surface

2000 ◽  
Vol 214 (6) ◽  
pp. 889-900
Author(s):  
Y Liu ◽  
H Liu ◽  
H Zhang ◽  
G Miao
Keyword(s):  
Water Waves ◽  
Wave Reflection ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Advection Equation ◽  
Navier Stokes Equations ◽  
Oil Slick ◽  
Smooth Plane ◽  
Wavy Surfaces ◽  
Set Up

Numerical simulation of an oil slick spreading on still and wavy surfaces is described in this paper. The so-called σ transformation is used to transform the time-varying physical domain into a fixed calculation domain for the water wave motions and, at the same time, the continuity equation is changed into an advection equation of wave elevation. This evolution equation is discretized by the forward time and central space scheme, and the momentum equations by the projection method. A damping zone is set up in front of the outlet boundary coupled with a Sommerfeld-Orlanski condition at that boundary to minimize the wave reflection. The equations for the oil slick are depth-averaged and coupled with the water motions when solving numerically. As examples, sinusoidal and solitary water waves, the oil spread on a smooth plane and on still and wavy water surfaces are calculated to examine the accuracy of simulating water waves by Navier-Stokes equations, the effect of damping zone on wave reflection and the precise structures of oil spread on waves.

Mechanistic Study of Upper Ocean Turbulence Interacting With Surface Waves

2010 ◽  
Author(s):  
Xin Guo ◽  
Di Yang ◽  
Yi Liu ◽  
Lian Shen
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Stokes Equations ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Mechanistic Study ◽  
Navier Stokes Equations ◽  
Random Forcing ◽  
Set Up ◽  
Pseudo Spectral Method

We perform direct numerical simulations to simulate the interaction between surface waves and the turbulence underneath. The Navier–Stokes equations are simulated using a pseudo-spectral method in horizontal directions and a finite-difference method in vertical direction, with fully nonlinear viscous free-surface kinematic and dynamic boundary conditions at the free surface. We set up the turbulence and the waves by a random forcing method in the bulk flow and a pressure forcing method at the surface, which were recently developed by [1]. It is found that there are surface waves generated on the free surface due to the excitation by the turbulence. The surface elevation is sensitive to the effect of gravity and surface tension. In the presence of progressive waves at the free surface, the turbulent vortical structure is turned, stretched, and compressed periodically by the strain field of waves.

scholarly journals COMPARISON OF DIFFERENT METHODS FOR GENERATION AND ABSORPTION OF WATER WAVES

2019 ◽  
Vol 18 (1) ◽  
pp. 71 ◽  
Author(s):  
J. M. P. Conde
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Numerical Models ◽  
Experimental Studies ◽  
Wave Generation ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Wave Absorption ◽  
Water Level Rise

The knowledge of water wave characteristics (generation, propagation, transformation and breaking) is fundamental for hydrodynamic studies and the design of ocean, coastal and port structures. In addition to the small-scale experimental studies, the use of numerical models is also a very important tool in hydrodynamic studies. To have reliable numerical results a proper validation is required. The main objective of this paper is to compare different methods of wave generation and wave absorption in a numerical flume, and to find what is the most suited to simulate non-breaking regular wave propagation in a two-dimensional flume in deep water condition. The numerical simulations were made using the OpenFOAM® software package. Two solvers, waves2Foam and IHFoam/OlaFlow, the utility GroovyBC and a mesh stretching technique are compared. These numerical codes solve the transient Navier-Stokes equations and use a VoF (Volume of Fluid) method to identify the free surface. A solution dependence study with the methods of wave generation and wave absorption is presented. The results are also compared with the theoretical wave and experimental data. The results show that the different methods of generation produce waves similar to the theoretical and the experimental ones, only slightly differences were visible. The three method of wave dissipation considered produce very different results: IHFoam/OlaFlow is not able to dissipate the wave tested; the mesh stretching technique is able to dissipate the waves but produces a water level rise; the waves2Foam solver is able to dissipate properly the wave tested.

An AGARD Working Group Study of 3D Navier-Stokes Codes Applied to Single Turbomachinery Blade Rows

1998 ◽  
Author(s):  
John Dunham ◽  
Georges Meauzé
Keyword(s):  
Working Group ◽  
Stokes Equations ◽  
Transport Model ◽  
Turbulent Transport ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wall Flows ◽  
Dimensional Boundary ◽  
Set Up

Computer codes which solve the Reynolds-averaged Navier-Stokes equations are now used by manufacturers to design turbomachines, but there is no consensus among experts about which grids and which turbulence models are good enough to provide a reliable basis for design decisions. The AGARD Propulsion and Energetics Panel set up a Working Group to help to clarify these issues, by analysing predictions (using as wide a range of codes as possible) of two representative but difficult single blade row test cases: NASA Rotor 37 and an annular turbine cascade tested by DLR. This paper summarises the Group’s results and conclusions. Recommendations are made about the type and density of grid, which depend on many factors. Although mixing-length turbulence models give good results for quasi-two-dimensional boundary layers, they are essentially unsuitable for turbomachines with their complex end wall flows; it is essential to adopt some kind of turbulent transport model.

scholarly journals Recent Results from Analysis of Flow Structures and Energy Modes Induced by Viscous Wave around a Surface-Piercing Cylinder

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Giancarlo Alfonsi ◽  
Agostino Lauria ◽  
Leonardo Primavera
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Flow ◽  
Ocean Engineering ◽  
Navier Stokes Equations ◽  
Pressure Formulation ◽  
The Subject ◽  
Run Up ◽  
Velocity Pressure

Due to its relevance in ocean engineering, the subject of the flow field generated by water waves around a vertical circular cylinder piercing the free surface has recently started to be considered by several research groups. In particular, we studied this problem starting from the velocity-potential framework, then the implementation of the numerical solution of the Euler equations in their velocity-pressure formulation, and finally the performance of the integration of the Navier-Stokes equations in primitive variables. We also developed and applied methods of extraction of the flow coherent structures and most energetic modes. In this work, we present some new results of our research directed, in particular, toward the clarification of the main nonintuitive character of the phenomenon of interaction between a wave and a surface-piercing cylinder, namely, the fact that the wave exerts its maximum force and exhibits its maximum run-up on the cylindrical obstacle at different instants. The understanding of this phenomenon becomes of crucial importance in the perspective of governing the entity of the wave run-up on the obstacle by means of wave-flow-control techniques.

Quantifying Vessel Material Properties Using MRI Under Pressure Condition and MRI-Based FSI Mechanical Analysis for Human Atherosclerotic Plaques

2006 ◽  
Author(s):  
Chun Yang ◽  
Xueying Huang ◽  
Jie Zheng ◽  
Pamela K. Woodard ◽  
Dalin Tang
Keyword(s):  
Material Properties ◽  
Stokes Equations ◽  
Maximum Shear Stress ◽  
Maximum Principal Stress ◽  
Mechanical Analysis ◽  
Navier Stokes ◽  
Atherosclerotic Plaques ◽  
Navier Stokes Equations ◽  
Stenosis Severity ◽  
Set Up

Atherosclerotic plaques may rupture without warning and cause acute cardiovascular syndromes such as heart attack and stroke. Mechanical image analysis using MRI-based models with fluid-structure interactions (FSI) and MRI-determined material properties may improve the accuracy of plaque vulnerability assessment and rupture predictions. A plaque-phantom was set up to acquire plaque MR images under pressurized conditions. The 3D nonlinear modified Mooney-Rivlin (M-R) model was used to describe the material properties with parameters selected to fit the MRI data. The Navier-Stokes equations were used as the governing equations for the flow model. The fully-coupled FSI models were solved by ADINA. Our results indicate that doubling parameter values in the M-R model led to 12.5% decrease in structure maximum principal stress (Stress-P1) and 48% decrease in maximum principal strain (Strain-P1). Flow maximum shear stress (MSS) was almost unchanged. Results from a modified carotid plaque with 70% stenosis severity (by diameter) showed that Stress-P1 at the plaque throat from the wall-only model is 145% higher than that from the FSI model. MSS from a flow-only model is about 40% higher than that from the FSI model. This approach has the potential to develop non-invasive patient screening and diagnosis methods in clinical applications.

A Study of Aerodynamic Effects of High-Speed Trains through Tunnels

2011 ◽  
Vol 94-96 ◽  
pp. 1663-1667
Author(s):  
Jing Zhao ◽  
Ren Xian Li
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Navier Stokes ◽  
High Speed Train ◽  
Navier Stokes Equations ◽  
Geometry Model ◽  
Flow Geometry ◽  
High Speed Trains ◽  
Set Up ◽  
Numerical Calculation Method

In this paper, the aerodynamic effects of high-speed train passing in tunnels are investigated in numerical calculation method of hydromechanics. According to the actual situation of flow filed when the train through the tunnel, the flow geometry model is set up. The flow problem is described by Navier-Stokes equations of unsteady viscous compressible fluid and k-e two equations turbulent model. Thereby the aerodynamic effects of the train through the tunnel are analyzed comprehensively. The changes of the air pressure in tunnel caused by high-speed train entering into the tunnel are mainly analyzed. In addition, the mechanical characteristics of carriages when two train in the tunnel passing through each other are analyzed.

scholarly journals Stokes’s Fundamental Contributions to Fluid Dynamics

2019 ◽  
pp. 115-128
Author(s):  
Peter Lynch
Keyword(s):  
Fluid Dynamics ◽  
Water Waves ◽  
Stokes Equations ◽  
Weather Prediction ◽  
Finite Amplitude ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Basic Equations ◽  
Primary Focus

George Gabriel Stokes made fundamental mathematical contributions to fluid dynamics that had profound practical consequences. The basic equations formulated by him play a central role in numerical weather prediction, in the simulation of blood flow in the body and in countless other important applications. In this chapter the primary focus is on the two most important areas of Stokes’s work on fluid dynamics, the derivation of the Navier–Stokes equations and the theory of finite amplitude oscillatory water waves.

scholarly journals Evidence of Landau Damping in a Fluid Coupled with an Anharmonic Lattice

2018 ◽  
Author(s):  
Andrei Ludu ◽  
Eric Padilla ◽  
M. A. Qaayum Mazumder
Keyword(s):  
Drag Force ◽  
Water Waves ◽  
Stokes Equations ◽  
Collisionless Plasma ◽  
Rogue Waves ◽  
Landau Damping ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Anharmonic Lattice ◽  
Specific Frequency

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.

scholarly journals SHOALING OF FINITE-AMPLITUDE WAVES ON PLANE BEACHES

1970 ◽  
Vol 1 (12) ◽  
pp. 21
Author(s):  
Robert K-C Chan ◽  
Robert L. Street
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Difference Equations ◽  
Rectangular Mesh ◽  
Finite Amplitude Waves ◽  
Large Water ◽  
Marker And Cell Method

This work focuses on the shoaling of large water waves with particular application to storm-generated waves and tsunamis The specific objective is the exact simulation on a digital computer of finite-amplitude waves advancing on a beach of constant slope The study is based on the simulation technique called SUMMAC (the Stanford-University-Modified Marker-And-Cell Method) The flow field is represented by a rectangular mesh of cells and by a line of hypothetical particles which defines the free surface Based on the Navier-Stokes equations, finite-difference equations were derived so that the entire flow configuration could be advanced through a finite increment of time The pressure and velocity components are used directly as the dependent variables Through extensive analyses and numerical experiments, this scheme was found to be computationally stable if the cell size and the time increment are properly selected As a specific example, the dynamics of a solitary wave passing from a zone of constant depth onto a sloping beach were simulated Primary attention was focused on the details of the water particle motions and the changes in the amplitude and shape of the wave as it climbed the slope The computed results are compared with the experiments with good agreement.

Sign in / Sign up

Export Citation Format

Share Document