On Offset Placement of a Compound Droplet in a Channel Flow

2021 ◽  
Author(s):  
Jagannath Mahato ◽  
Dhananjay Kumar Srivastava ◽  
Dinesh Kumar Chandraker ◽  
Rajaram Lakkaraju
Keyword(s):  
Viscosity Ratio ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Flow Direction ◽  
Navier Stokes ◽  
Volume Of Fluid Method ◽  
Lateral Migration ◽  
Navier Stokes Equations ◽  
Deformation Patterns ◽  
Compound Droplet

Abstract Investigations on flow dynamics of a compound droplet have been carried out in a two-dimensional fully-developed Poiseuille flow by solving the Navier-Stokes equations with the evolution of the droplet using the volume of fluid method with interface compression. The outer droplet undergoes elongation similar to a simple droplet of same size placed under similar ambient condition in the flow direction, but, the inner droplet evolves in compressed form. The compound droplet is varied starting from the centerline towards the walls of the channel. The simulations showed that on applying an offset, asymmetric slipper-like shapes are observed as opposed to symmetric bullet-like shapes through the centerline. Temporal dynamics, deformation patterns, and droplet shell pinch-off mode vary with the offset, with induction of lateral migration. Also, investigations are done on the effect of various parameters like droplet size, Capillary number, and viscosity ratio on the deformation magnitude and lateral migration.

Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments

2015 ◽  
Vol 767 ◽  
pp. 364-393 ◽  
Author(s):  
P. Lubin ◽  
S. Glockner
Keyword(s):  
Stokes Equations ◽  
Early Stage ◽  
Flow Direction ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Vortex Filaments ◽  
Navier Stokes Equations ◽  
Main Flow Direction

AbstractThe scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier–Stokes equations, in air and water. Recent progress in computational capabilities has allowed us to run fine three-dimensional simulations, giving us the opportunity to study for the first time fine vortex filaments generated during the early stage of the wave breaking phenomenon. To date, no experimental observations have been made in laboratories, and these structures have only been visualised in rare documentary footage (e.g. BBC 2009 South Pacific. Available on YouTube, 7BOhDaJH0m4). These fine coherent structures are three-dimensional streamwise vortical tubes, like vortex filaments, connecting the splash-up and the main tube of air, elongated in the main flow direction. The first part of the paper is devoted to the presentation of the model and numerical methods. The air entrainment occurring when waves break is then carefully described. Thanks to the high resolution of the grid, these fine elongated structures are simulated and explained.

Axisymmetric Low-Reynolds Motion of Drops Through Circular Microchannels

2012 ◽  
Author(s):  
Saira F. Pineda ◽  
Arjan M. Kamp ◽  
D. Legendre ◽  
Armando J. Blanco
Keyword(s):  
Pressure Gradient ◽  
Drop Size ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Flow Dynamics ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
System Pressure ◽  
The Continuum

Flow constituted by drops appears in a wide range of natural, biological and engineering situations. For example, liquid-liquid two phase flow inside capillaries constitutes a model commonly used to represent fluid flow in a petroleum reservoir. The typical modeling approach considers inertial forces negligible in comparison to viscous forces, allowing the use of Stokes equation to study flow dynamics. Very few numerical simulations have been made considering inertial effects. In this project, the flow of a periodic train of drops in a viscous suspending fluid, due to the influence of a fixed pressure gradient, was studied by numerical simulation considering the full Navier-Stokes equations. A numerical approach based on a Volume of Fluid (VOF) formulation was employed using JADIM software, developed by the Institut de Mécanique des Fluides de Toulouse, France. JADIM solves Navier-Stokes equations using a VOF finite volume method, second order in space and time using structured mesh. This two-fluid approach without reconstruction of the interface allows simulating two-phase flows with complex interface shapes. Densities of the drops equal to those of the suspending fluid and a constant interface tension were assumed. The effect of drop size, viscosity ratio, interfacial forces and system pressure gradient on the flow dynamics was studied. Parameters values were chosen to be representative for some particular viscous oil. The result validation shows an excellent agreement between both numerical results. However, there are relative differences between them due to the increase in flow velocity when drop relative size increase and validity of Stokes approach is questionable. Results show non-symmetric eddies in the continuum phase, in a referential frame fixed to the drop. The shape of eddies is strongly influenced by viscosity radio. Drop mobility decreases with increasing size. Additionally, drop mobility also decreases when the viscosity ratio increases. Extra pressure gradient of the system due to the presence of the drop shows a strong dependency on the size ratio between the drop and the pore. For size ratio lower than 0.5, the extra pressure gradient required to move the continuum phase is small. However, when drop to micro-channel ratio exceeds 0.5, the extra pressure gradient significantly increases when the drop size increases. Also, viscosity ratio affects on the system pressure loss, especially in cases where the viscosity ratio is high. The analysis of the capillary number effect on the dynamics of the two-phase system shows that it does not influence drop mobility for the drop sizes considered.

An Improved Volume of Fluid Method for Two-Phase Flow Computations on Collocated Grid System

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Dong-Liang Sun ◽  
Yong-Ping Yang ◽  
Jin-Liang Xu ◽  
Wen-Quan Tao
Keyword(s):  
Two Phase Flow ◽  
Stokes Equations ◽  
Volume Of Fluid ◽  
Vof Method ◽  
Navier Stokes ◽  
Phase Flow ◽  
Volume Of Fluid Method ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Collocated Grid

An improved volume of fluid method called the accurate density and viscosity volume of fluid (ADV-VOF) method is proposed to solve two-phase flow problems. The method has the following features: (1) All operations are performed on a collocated grid system. (2) The piecewise linear interface calculation is used to capture interfaces and perform accurate estimations of cell-edged density and viscosity. (3) The conservative Navier–Stokes equations are solved with the convective term discretized by a second and third order interpolation for convection scheme. (4) A fractional-step method is applied to solve the conservative Navier–Stokes equations, and the BiCGSTAB algorithm is used to solve the algebraic equations by discretizing the pressure-correction equation. The above features guarantee a simple, stable, efficient, and accurate simulation of two-phase flow problems. The effectiveness of the ADV-VOF method is verified by comparing it with the conventional volume of fluid method with rough treatment of cell-edged density and viscosity. It is found that the ADV-VOF method could successfully model the two-phase problems with large density ratio and viscosity ratio between two phases and is better than the conventional volume of fluid method in this respect.

Flow of fluid of non-uniform viscosity in converging and diverging channels

1982 ◽  
Vol 117 ◽  
pp. 283-304 ◽  
Author(s):  
Alison Hooper ◽  
B. R. Duffy ◽  
H. K. Moffatt
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Lubrication Theory ◽  
Navier Stokes ◽  
Volume Flux ◽  
Navier Stokes Equations ◽  
Two Fluid ◽  
Converging And Diverging Channels

It is shown that the well-known Jeffery–Hamel solution of the Navier–Stokes equations admits generalization to the case in which the viscosity μ and density ρ are arbitrary functions of the angular co-ordinate θ. When |Rα| [Lt ] 1, where R is the Reynolds number and 2α the angle of divergence of the planes, lubrication theory is applicable; this limit is first treated in the context of flow in a channel of slowly varying width. The Jeffery–Hamel problem proper is treated in §§ 3–6, and the effect of varying the viscosity ratio λ in a two-fluid situation is studied. In § 5, results already familiar in the single-fluid context are recapitulated and reformulated in a manner that admits immediate adaptation to the two-fluid situation, and in § 6 it is shown that the singlefluid limit (λ → 1) is in a certain sense degenerate. The necessarily discontinuous behaviour of the velocity profile as the Reynolds number (based on volume flux) increases is elucidated. Finally, in § 7, some comments are made about the realizability of these flows and about instabilities to which they may be subject.

scholarly journals Modeling of Particle Deposition in a Two-Fluid Flow Environment

2021 ◽  
Vol 39 (3) ◽  
pp. 1001-1014
Author(s):  
Yap Yit Fatt ◽  
Afshin Goharzadeh
Keyword(s):  
Fluid Flow ◽  
Particle Deposition ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Immiscible Fluids ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rising Bubble ◽  
Lower Viscosity ◽  
Two Fluid

Particle deposition occurs in many engineering multiphase flows. A model for particle deposition in two-fluid flow is presented in this article. The two immiscible fluids with one carrying particles are model using incompressible Navier-Stokes equations. Particles are assumed to deposit onto surfaces as a first order reaction. The evolving interfaces: fluid-fluid interface and fluid-deposit front, are captured using the level-set method. A finite volume method is employed to solve the governing conservation equations. Model verifications are made against limiting cases with known solutions. The model is then used to investigate particle deposition in a stratified two-fluid flow and a cavity with a rising bubble. For a stratified two-fluid flow, deposition occurs more rapidly for a higher Damkholer number but a lower viscosity ratio (fluid without particle to that with particles). For a cavity with a rising bubble, deposition is faster for a higher Damkholer number and a higher initial particle concentration, but is less affected by viscosity ratio.

scholarly journals Simulating Hydraulic Characteristics and Enhance Design of My Lam Spillway-Stilling Basin,Vietnam

2019 ◽  
Vol 8 (10) ◽  
pp. 953-957
Keyword(s):  
3D Model ◽  
Stokes Equations ◽  
Separated Flow ◽  
Navier Stokes ◽  
Volume Of Fluid Method ◽  
Hydraulic Characteristics ◽  
Navier Stokes Equations ◽  
Stilling Basin ◽  
Proper Design ◽  
3D Software

The purpose of this paper is to use a hydrodynamic 3D model to simulate steady flow over spillway-stilling basin of Mylam, Vietnam. A robust and effective tool of Flow 3D software in simulating many complicated phenomena of fluid flow is selected. This model uses Volume of Fluid Method to solve Navier-Stokes equations. The computed water surface elevation at gauges along centerline of weir and chute channel are compared with experimental ones in four working conditions. The reasonable agreement between them are observed. Besides, the detail hydraulic features in each segment is indicated such as: oblique wave on spillway chute; separated flow at curve and enlarge segment and the specific hydraulic energy dissipation in stilling basin of design is carried out. The insufficient construction of dissipated obstacles in stilling basin design is shown. Therefore, a proper design is proposed.

Drag Coefficients of Viscous Drops

2000 ◽  
Author(s):  
Zhigang Feng ◽  
Efstathios E. Michaelides
Keyword(s):  
Drag Coefficient ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Computational Technique ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Viscous Drops

Abstract We have used a finite-difference scheme to solve the Navier-Stokes equations for the steady flow inside and outside viscous spheres in a fluid of different properties. Hence, we obtained the hydrodynamic forces and the steady-state drag coefficient of the spheres. The computational technique we have used enables us to extend the results to Reynolds numbers between 0 and 1,000. The viscosity ratio of the computations ranges between 0 (inviscid bubble) and infinity (solid particle). The method presented here makes use of a two-layer concept for the computational domain outside the sphere. The first layer is a very thin one [O(Re−1/2)] and is positioned at the interface of the sphere. The second layer is based on an exponential function and covers the rest of the domain. The computations yield the friction and the form drag of the sphere. It is observed that both the Reynolds number and the viscosity ratio play a major role on the value of the hydrodynamic force and the drag coefficient. If all other conditions are the same, there is a negligible effect of the density ratio on the drag coefficient of viscous spheres.

Simultaneous Variable Solutions of the Incompressible Steady Navier-Stokes Equations in General Curvilinear Coordinate Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 299-305 ◽  
Author(s):  
G. Vradis ◽  
V. Zalak ◽  
J. Bentson
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Flow Direction ◽  
Solution Algorithm ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Solution Technique ◽  
Algebraic Equations ◽  
Coordinate Systems ◽  
Navier Stokes Equations

A simultaneous variable solution technique for the incompressible, steady, two-dimensional Navier-Stokes equations in primitive formulation and general curvilinear orthogonal and nonorthogonal coordinate systems has been developed. The governing equations are discretized using finite difference approximations. The formulation is fully second order accurate and the well-known staggered grid of Welch and Harlow is used. The solution algorithm is based on an iterative marching technique in which the algebraic equations are linearized by evaluating the coefficients at the previous iteration level. The resulting system of linear equations is solved in a marching fashion by employing a block tridiagonal solution algorithm to obtain the solution along lines transverse to the main flow direction. The strong pressure-velocity coupling inherent in the present formulation results in high convergence rates. Flows in channels of different geometries have been computed and the results have been compared to available data in the literature. In all cases the method has demonstrated to be accurate, robust and computationally efficient.

Vortex-Induced Vibration of Two Side-by-Side Cylinders With a Small Gap in Uniform Flow

2017 ◽  
Author(s):  
Adnan Munir ◽  
Ming Zhao ◽  
Helen Wu
Keyword(s):  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gap Ratio ◽  
Vortex Induced Vibrations ◽  
Lock In

Vortex-induced vibrations of two elastically mounted and rigidly coupled circular cylinders in side-by-side arrangement in steady flow are investigated numerically. The vibration of the cylinders is limited to the cross-flow direction only. The three-dimensional Navier-Stokes equations are solved using the Petrov-Galerkin Finite element method and the equation of motion is solved using the fourth order Runge Kutta method. It is well known that when the gap between two stationary side-by-side cylinders is very small, the flow between the two cylinders is biased towards one cylinder and the lift force on each cylinder is significantly smaller than that of an isolated single cylinder. The aim of this study is to investigate the effect of a small gap ratio of 0.5 between the two cylinders on the lock-in regime and the amplitude of the vibration of two side-by-side cylinders in a fluid flow. Simulations are carried out for a constant mass ratio of 2, a constant Reynolds number of 1000 and a range of reduced velocities. It is found that in the lock-in range of the reduced velocity, the two cylinders vibrate about their balance position with high amplitudes. Outside the lock-in regime the flow from the gap becomes biased towards one cylinder, which is similar to that from the gap between stationary cylinders.

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