scholarly journals Coupling Vortical Bulk Flows to the Air–Water Interface: From Putting Oil on Troubled Waters to Surfactants on Protein Solutions

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 198
Author(s):  
Amir H. Hirsa ◽  
Juan M. Lopez
Keyword(s):  
Stokes Equations ◽  
Bulk Flow ◽  
Surface Velocity ◽  
Navier Stokes ◽  
Protein Solutions ◽  
Water Interface ◽  
Interfacial Flows ◽  
Navier Stokes Equations ◽  
Flowing Liquid ◽  
Air Water Interface

The air–water interface in flowing systems remains a challenge to model, even in cases where the interface is essentially flat. This is because even though each side is governed by the Navier–Stokes equations, the stress balance which provides the boundary conditions for the equations involves properties associated with surfactants that are inevitably present at the air–water interface. Aside from challenges in measuring interfacial properties, either intrinsic or flow-dependent, the two-way coupling of bulk and interfacial flows is non-trivial, even for very simple flow geometries. Here, we present an overview of the physics associated with surfactant monolayers of flowing liquid and describe how the monolayer affects the bulk flow and how the monolayer is transported and deformed by the bulk flow. The emphasis is primarily on cylindrical flow geometries, and both Newtonian and non-Newtonian interfacial responses are considered. We consider interfacial flows that are solenoidal as well as those where the surface velocity is not divergence free.

scholarly journals Dynamic Measurements with the Bicone Interfacial Shear Rheometer: Numerical Bench-Marking of Flow Field Based Data Processing

2018 ◽  
Author(s):  
Pablo Sánchez-Puga ◽  
Javier Tajuelo Rodríguez ◽  
Juan Manuel Pastor ◽  
Miguel Ángel Rubio
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Amplitude Ratio ◽  
Numerical Procedure ◽  
Complex Viscosity ◽  
Detailed Comparison ◽  
Interfacial Shear ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Air Water Interface

Flow field based methods are becoming increasingly popular for the analysis of interfacial shear rheology data. Such methods take properly into account the subphase drag by solving the Navier-Stokes equations for the bulk phases flows, together with the Boussinesq-Scriven boundary condition at the fluid-fluid interface, and the probe equation of motion. Such methods have been successfully implemented at the double wall-ring (DWR), the magnetic rod (MR), and the bicone interfacial shear rheometers. However, a study of the errors introduced directly by the numerical processing is still lacking. Here we report on a study of the errors introduced exclusively by the numerical procedure corresponding to the bicone geometry at an air-water interface. In our study we directly input a preset the value of the complex interfacial viscosity and we numerically obtain the corresponding flow field and the complex amplitude ratio for the probe motion. Then we use the standard iterative procedure to obtain the calculated complex viscosity value. A detailed comparison of the set and calculated complex viscosity values is made upon changing different parameters such as real and imaginary parts of the complex interfacial viscosity and frequency. The observed discrepancies yield a detailed landscape of the numerically introduced errors.

scholarly journals Numerical Modeling of Soil Erosion with Three Wall Laws at the Soil-Water Interface

2021 ◽  
Vol 7 (9) ◽  
pp. 1546-1556
Author(s):  
Hatim El Assad ◽  
Benaissa Kissi ◽  
Rhanim Hassan ◽  
Parron Vera Miguel Angel ◽  
Rubio Cintas Maria Dolores ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Soil Water ◽  
Clay Soil ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Water Interface ◽  
Navier Stokes Equations ◽  
Modeling Software ◽  
Wall Shear

In the area of civil engineering and especially hydraulic structures, we find multiple anomalies that weakens mechanical characteristics of dikes, one of the most common anomalies is erosion phenomenon specifically pipe flow erosion which causes major damage to dam structures. This phenomenon is caused by a hole which is the result of the high pressure of water that facilitate the soil migration between the two sides of the dam. It becomes only a question of time until the diameter of the hole expands and causes destruction of the dam structure. This problem pushed physicist to perform many tests to quantify erosion kinetics, one of the most used tests to have logical and trusted results is the HET (hole erosion test). Meanwhile there is not much research regarding the models that govern these types of tests. Objectives: In this paper we modeled the HET using modeling software based on the Navier Stokes equations, this model tackles also the singularity of the interface structure/water using wall laws for a flow turbulence. Methods/Analysis: The studied soil in this paper is a clay soil, clay soil has the property of containing water more than most other soils. Three wall laws were applied on the soil / water interface to calculate the erosion rate in order to avoid the rupture of such a structure. The modlisitation was made on the ANSYS software. Findings: In this work, two-dimensional modeling was carried of the soil.in contrast of the early models which is one-dimensional model, the first one had shown that the wall-shear stress which is not uniform along the whole wall. Then using the linear erosion law to predict the non-uniform erosion along the whole length. The previous study found that the wall laws have a significant impact on the wall-shear stress, which affects the erosion interface in the fluid/soil, particularly at the hole's extremes. Our experiment revealed that the degraded profile is not uniform. Doi: 10.28991/cej-2021-03091742 Full Text: PDF

Heat Transfer of Coupled Fluid Flow Within a Channel With a Permeable Base

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
Rosemarie Mohais ◽  
Balswaroop Bhatt
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Effective Means ◽  
Reynolds Numbers ◽  
Model Systems ◽  
Surface Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Small Reynolds Numbers

We examine the heat transfer in a Newtonian fluid confined within a channel with a lower permeable wall. The upper wall of the channel is impermeable and driven by an accelerating surface velocity. Through a similarity solution, the Navier–Stokes equations are reduced to a fourth-order differential equation; the analytical solutions of which determined for small Reynolds numbers show dependence of the temperature and heat transfer profiles on the slip parameter based on the properties of the porous channel base. For larger Reynolds numbers, numerical solutions for three main groups of solutions show that the Reynolds number strongly influences the heat transfer profile. However, the slip conditions associated with the porous base of the channel can be used to alter these heat transfer profiles for large Reynolds numbers. The presence of a porous base in a channel can thus serve as an effective means of reducing or enhancing heat transfer performance in model systems.

Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals

2001 ◽  
Author(s):  
J. Jeffrey Moore
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Internal Flow ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Navier Stokes Equations ◽  
Rotordynamic Forces

Abstract Labyrinth seals are utilized inside turbomachinery to provide non-contacting control of internal leakage. These seals can also play an important role in determining the rotordynamic stability of the machine. Traditional labyrinth seal models are based on bulk-flow assumptions where the fluid is assumed to behave as a rigid body affected by shear stress at the interfaces. To model the labyrinth seal cavity, a single, driven vortex is assumed and relationships for the shear stress and divergence angle of the through flow jet are developed. These models, while efficient to compute, typically show poor prediction for seals with small clearances, high running speed, and high pressure (Childs, 1993). In an effort to improve the prediction of these components, this work utilizes three-dimensional computational fluid dynamics (CFD) to model the labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations. Unlike bulk-flow techniques, CFD makes no fundamental assumptions on geometry, shear stress at the walls, as well as internal flow structure. The method allows modeling of any arbitrarily shaped domain including stepped and interlocking labyrinths with straight or angled teeth. When only leakage prediction is required, an axisymmetric model is created. To calculate rotordynamic forces, a full 3D, eccentric model is solved. The results demonstrate improved leakage and rotordynamic prediction over bulk-flow approaches compared to experimental measurements.

Wet/Dry Areas Modelling of Interaction Between Wind and Water Waves Under Zero Wind Speed

2012 ◽  
Author(s):  
Xianyun Wen
Keyword(s):  
Shear Stress ◽  
Wind Speed ◽  
Water Waves ◽  
Stokes Equations ◽  
Control Volume ◽  
Integral Form ◽  
Navier Stokes ◽  
Interfacial Flows ◽  
Navier Stokes Equations ◽  
Dry Areas

Accurate prediction of the distribution of shear stress is essential for the numerical investigation of the interaction between the wind and water waves on ocean surface since the shear stress plays a key role in this type of interfacial flows. The numerical velocity distribution provided by the computational fluid dynamics should have high accuracy as the shear stress is computed by the derivative of the numerically predicted velocity. The recently developed wet/dry areas method based on the conservative integral form of the Navier-Stokes equations mathematically reveals that the convection terms in the Navier-Stokes equations should be calculated on the surface of control volume and the mass flux on the surface of the control volume should be calculated by the areas exposed to the water and air. In this paper the new numerical method, the wet/dry areas method, is briefly explained and applied to a two-dimensional viscose air-water flow when the wind speed is zero.

Hydrodynamic Impact of a Falling Body upon a Viscous Incompressible Fluid

1977 ◽  
Vol 21 (03) ◽  
pp. 165-181
Author(s):  
Buford R. Koehler ◽  
C. F. Kettleborough
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Surface Velocity ◽  
Navier Stokes ◽  
Hydrodynamic Impact ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Pressure Distributions

The hydrodynamic impact of a falling body upon a viscous incompressible fluid is investigated by the development and solution of a mathematical model which simulates the impact of a rigid flat-bottomed body upon the quiescent free surface of viscous incompressible water. A one-dimensional compressible air layer exists between the falling body and the water free surface. Velocity and pressure distributions within the air layer are calculated using the continuity equation and the one-dimensional momentum equation derived from the Navier-Stokes equations. The water free surface is allowed to deform as the air pressures acting on it increase. The two-dimensional rectangular coordinate form of the Navier-Stokes equations for an incompressible fluid is applied to the water. A normalization scheme is used which causes the water free surface to appear straight and simplifies the application of free-surface boundary conditions. Water velocities are calculated from the momentum and continuity equations. Pressures are calculated using the pressure equation derived from the Navier-Stokes equations. Air-water interface velocities are obtained from boundary-layer relations. The governing equations of the air layer and water region are expressed in finite difference form and are solved on a high-speed digital computer. The behavior of the air layer before impact is discussed. Air layer velocity and pressure distributions are obtained. The influence of the air layer on the water is studied. Pressure and velocity distributions in the water are obtained before and at the instant of impact. Pressure distributions and pressure histories compare favorably with available experimental data. Corresponding plots of the moving free surface show the actual shape of the compressible air region. A slight variation in the body deadrise angle is found to significantly change impact pressures and the shape of the pressure distributions.

scholarly journals CFD-Based Metamodeling of the Propagation Distribution of Styrene Spilled from a Ship

2020 ◽  
Vol 10 (6) ◽  
pp. 2109
Author(s):  
Chan Ho Jeong ◽  
Min Kyu Ko ◽  
Moonjin Lee ◽  
Seong Hyuk Lee
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Kriging Model ◽  
Surface Velocity ◽  
Navier Stokes ◽  
Ansys Fluent ◽  
Navier Stokes Equations ◽  
Commercial Code ◽  
Velocity Surface ◽  
Over Time

The present study aimed to numerically establish a new metamodel for predicting the propagation distribution of styrene, which is one of the hazardous and noxious substances (HNSs) spilled from ships. Three-dimensional computational fluid dynamics (CFD) simulations were conducted for 80 different scenarios to gather large amounts of data on the spatial distribution of the change in concentration over time. We used the commercial code of ANSYS Fluent (V.17.2) to solve the Reynolds-averaged Navier–Stokes equations, together with the scalar transport equation. Based on the CFD results, we adopted the well-known kriging model to create a metamodel that estimated the propagation velocity and spatial distributions by considering the effect of the current surface velocity, deep current velocity, surface layer depth, and crack position. The results show that the metamodel accurately predicted the changes in the local distribution of styrene over time. This model was also evaluated using the hidden-point test.

Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals

2003 ◽  
Vol 125 (4) ◽  
pp. 427-433 ◽  
Author(s):  
J. Jeffrey Moore
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Internal Flow ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Navier Stokes Equations ◽  
Rotordynamic Forces

Labyrinth seals are utilized inside turbomachinery to provide noncontacting control of internal leakage. These seals can also play an important role in determining the rotordynamic stability of the machine. Traditional labyrinth seal models are based on bulk-flow assumptions where the fluid is assumed to behave as a rigid body affected by shear stress at the interfaces. To model the labyrinth seal cavity, a single, driven vortex is assumed and relationships for the shear stress and divergence angle of the through flow jet are developed. These models, while efficient to compute, typically show poor prediction for seals with small clearances, high running speed, and high pressure.* In an effort to improve the prediction of these components, this work utilizes three-dimensional computational fluid dynamics (CFD) to model the labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations. Unlike bulk-flow techniques, CFD makes no fundamental assumptions on geometry, shear stress at the walls, as well as internal flow structure. The method allows modeling of any arbitrarily shaped domain including stepped and interlocking labyrinths with straight or angled teeth. When only leakage prediction is required, an axisymmetric model is created. To calculate rotordynamic forces, a full 3D, eccentric model is solved. The results demonstrate improved leakage and rotordynamic prediction over bulk-flow approaches compared to experimental measurements.

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