Mathematical modeling of steady stratified flows

2003 ◽  
Vol 3 ◽  
pp. 195-207
Author(s):  
A.M. Ilyasov ◽  
V.N. Kireev ◽  
S.F. Urmancheev ◽  
I.Sh. Akhatov
Keyword(s):  
Stokes Equations ◽  
Approximate Model ◽  
Immiscible Liquid ◽  
Stratified Flows ◽  
Navier Stokes ◽  
Flat Channel ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Flow Parameters ◽  
Direct Numerical Solution

The work is devoted to the analysis of the flow of immiscible liquid in a flat channel and the creation of calculation schemes for determining the flow parameters. A critical analysis of the well-known Two Fluids Model was carried out and a new scheme for the determination of wall and interfacial friction, called the hydraulic approximation in the theory of stratified flows, was proposed. Verification of the proposed approximate model was carried out on the basis of a direct numerical solution of the Navier–Stokes equations for each fluid by a finite-difference method with phase-boundary tracking by the VOF (Volume of Fluid) method. The graphical dependencies illustrating the change in the interfase boundaries of liquids and the averaged over the occupied area of the phase velocities along the flat channel are presented. The results of comparative calculations for two-fluid models are also given, according to the developed model in the hydraulic approximation and direct modeling. It is shown that the calculations in accordance with the hydraulic approximation are more consistent with the simulation results. Thus, the model of hydraulic approximation is the most preferred method for calculating stratified flows, especially in cases of variable volumetric content of liquids.

ON THE EXISTENCE AND UNIQUENESS OF TWO‐FLUID CHANNEL FLOWS

2005 ◽  
Vol 9 (1) ◽  
pp. 67-78 ◽  
Author(s):  
J. Socolowsky
Keyword(s):  
Stokes Equations ◽  
Channel Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Free Boundary Value Problems ◽  
Fluid Channel ◽  
Density Ratios ◽  
Steady State Solutions ◽  
Two Fluid

iscous two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations. In this paper the solvability of the related stationary problems is discussed and computational results are presented. Furthermore, it is shown that depending on the flow parameters like viscosity or density ratios and on the fluxes there can happen nonexistence of steady‐state solutions. For other parameter sets the solution is even unique. Dvieju, tekančiu kanale, klampiu skysčiu srauto uždavinys iškyla taikant ivairias skirtingu rušiu paviršiu padengimo technologijas. Atitinkamas matematinis modelis išreiškiamas dvimačiu kraštiniu uždaviniu su laisvu paviršiumi Navje-Stokso lygtims. Straipsnyje nagrinejamas santykinai stacionaraus uždavinio išsprendžiamumas ir pateikiami skaičiavimo rezultatai. Be to parodoma, kad priklausomai nuo sroves parametru kaip ir nuo klampumo ir tankio santykio stacionarus sprendiniai gali neegzistuoti. Su kitais parametrais egzistuoja tiksliai vienas sprendinys.

Two-Fluid Flow Between Rotating Annular Disks

1976 ◽  
Vol 98 (2) ◽  
pp. 214-222 ◽  
Author(s):  
J. E. Zweig ◽  
H. J. Sneck
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Small Clearance ◽  
Annular Disks ◽  
Two Fluid

The general hydrodynamic behavior at small clearance Reynolds numbers of two fluids of different density and viscosity occupying the finite annular space between a rotating and stationary disk is explored using a simplified version of the Navier-Stokes equations which retains only the centrifugal force portion of the inertia terms. A criterion for selecting the annular flow fields that are compatible with physical reservoirs is established and then used to determine the conditions under which two-fluid flows in the annulus might be expected for specific fluid combinations.

Numerical simulation of turbulent flow in a pipe oscillating around its axis

2000 ◽  
Vol 424 ◽  
pp. 217-241 ◽  
Author(s):  
MAURIZIO QUADRIO ◽  
STEFANO SIBILLA
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Streamwise Vortex ◽  
Longitudinal Axis ◽  
Navier Stokes ◽  
Planar Geometry ◽  
Wall Region ◽  
Navier Stokes Equations ◽  
Moving Wall ◽  
Direct Numerical Solution

The turbulent flow in a cylindrical pipe oscillating around its longitudinal axis is studied via direct numerical solution of the Navier–Stokes equations, and compared to the reference turbulent flow in a fixed pipe and in a pipe with steady rotation. The maximum amount of drag reduction achievable with appropriate oscillations of the pipe wall is found to be of the order of 40%, hence comparable to that of similar flows in planar geometry. The transverse shear layer due to the oscillations induces substantial modifications to the turbulence statistics in the near-wall region, indicating a strong effect on the vortical structures. These modifications are illustrated, together with the implications for the drag-reducing mechanism. A conceptual model of the interaction between the moving wall and a streamwise vortex is discussed.

Numerical Analysis of the Sulcus Vocalis Disorder on the Function of the Vocal Folds

2016 ◽  
Vol 33 (4) ◽  
pp. 513-520 ◽  
Author(s):  
A. Vazifehdoostsaleh ◽  
N. Fatouraee ◽  
M. Navidbakhsh ◽  
F. Izadi
Keyword(s):  
Stokes Equations ◽  
Vocal Folds ◽  
Element Model ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Complex Process ◽  
Sulcus Vocalis ◽  
First Time

AbstractSpeaking is a very complex process resulting from the interaction between the air flow along the larynx and the vibrating structure of the vocal folds. Sulcus is a disease missing layers in the vocal folds result in cracks resulting in some disorders in producing sounds. Sulcus and its effects on the vocal cord vibrations are numerically studied for the first time in this paper. An ideal model of healthy vocal folds and Sulcus vocalis has been two-dimensionally defined and the finite element model of vocal folds is solved in a fully coupled form. The proposed calculative model was used in a fluid range of the computational fluid dynamics, arbitrary Lagrangian-Eulerian (ALE), incompressible continuity and Navier-Stokes equations and in a structure range of a three-layer elastic linear model. Self-excited oscillations were presented for vocal folds among type II patients and compared with healthy models. Responses were qualitatively and quantitatively studied. The healthy model was compared with numerical and empirical results. In addition, the effects of the disease on the flow parameters and the vibration frequency of the vocal folds were studied. According to the simulated model, the oscillation frequency decreased 25% and the average and instantaneous volume flux significantly increased compared to healthy samples. Results may help present a guideline for surgery and subsequently evaluate patients’ improvement.

scholarly journals An Assessment of Suitability of a SIMPLE VOF/PLIC-CSF Multiphase Flow Model for Rising Bubble Dynamics

2012 ◽  
Vol 4 (1) ◽  
pp. 65-83 ◽  
Author(s):  
S. Senthil Kumar ◽  
Y. M. C. Delauré
Keyword(s):  
Bubble Dynamics ◽  
Stokes Equations ◽  
Piecewise Linear ◽  
Navier Stokes ◽  
Simple Type ◽  
Two Phase ◽  
Simple Method ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Fluid Properties

A Volume of Fluid (VOF) – Youngs' model for the solution of an incompressible immiscible two-phase flows is presented. The solver computes the flow field by solving the family of Navier Stokes equations on a fixed (Eulerian) Staggered Cartesian grid using the Finite Volume formulation of Semi-Implicit Pressure Linked Equation (SIMPLE) method and tracks the position of interface between two fluids with different fluid properties by Piecewise Linear Interface Construction (PLIC) Method. The suitability of the SIMPLE type implementation is assessed by investigating the dynamics of free rising bubbles for different fluid properties and flow parameters. The results obtained with the present numerical method for rising bubbles in viscous liquids are compared with reported numerical and experimental results.

Multiple Node Breakup of a Liquid Jet Into Drops in Another Immiscible Liquid

2002 ◽  
Author(s):  
Shunji Homma ◽  
Jiro Koga ◽  
Shiro Matsumoto ◽  
Gre´tar Tryggvason
Keyword(s):  
Stokes Equations ◽  
Immiscible Liquid ◽  
Capillary Waves ◽  
Navier Stokes ◽  
Unstable Wave ◽  
Liquid Jet ◽  
Navier Stokes Equations ◽  
Axisymmetric Jet ◽  
Multiple Node ◽  
Liquid Systems

We investigate numerically the breakup of an axisymmetric jet into drops in liquid-liquid systems, specifically focus on multiple node breakup, where more than one node of the most unstable wave becomes one drop. The unsteady Navier-Stokes equations for incompressible Newtonian fluids are solved with a Front-Tracking / Finite Difference method. Various combinations of the non-dimensional numbers (Re = 80, 160, 320; We = 5, 8; Fr = 4, 8, 32, ∞) are examined for constant ratios of density (ρc, ρj = 1.25) and viscosity (µc, µj = 1). Capillary waves grow on the jet surface and the multiple node breakup is observed in all cases examined. A “shoulder” is observed on the jet right behind the bulb when the double-node breakup occurs. Unlike the breakup of a jet in air, vortical motions in the external fluid affect the breakup process.

Numerical Simulation of the Micromixing Induced by Ultrasonic Vibration of Sidewall-Trapped Microbubbles

2013 ◽  
Vol 275-277 ◽  
pp. 618-621
Author(s):  
Su Xia Zheng ◽  
Liang Yao Su ◽  
Chun Hui Li ◽  
Zhong Bin Xu
Keyword(s):  
Stokes Equations ◽  
Simulation Method ◽  
Navier Stokes ◽  
Micro Channel ◽  
Ultrasonic Vibrations ◽  
Navier Stokes Equations ◽  
Mixing Performance ◽  
Two Fluids ◽  
Micro Bubble ◽  
Micrometer Scale

It exist several strategies to mix two fluids in a micro channel. The way micro bubble vibrations influence the mixing flow is still unknown. This paper presents numerical simulations of the mixing within the micro device with and without micro bubble vibrations. A simplified model of the microchannel has been successfully employed, via using moving panels instead of sidewall-trapped bubbles oscillation. The simulation method, which exerted sinusoidal movements on the panels to approximately represent the ultrasonic vibrations of microbubbles, has been used to fully solve the Navier-Stokes equations. The comparison between simulations and previously reported experiments, in terms of flow pattern and the mixing performance within micro channel, exhibits a very good agreement. When ultrasonic vibrations of a frequency of 80 kHz and amplitude of 8 μm were applied, the mixing flow patterns have been reproduced and with a little differences comparing to the experimental results. All of these studies have revealed the mix mechanism under the micrometer scale in a certain way.

Level-Set Computations of Free Surface Rotational Flows

2005 ◽  
Vol 127 (6) ◽  
pp. 1111-1121 ◽  
Author(s):  
Giuseppina Colicchio ◽  
Maurizio Landrini ◽  
John R. Chaplin
Keyword(s):  
Free Surface ◽  
Numerical Method ◽  
Level Set ◽  
Stokes Equations ◽  
Vertical Surface ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Level Set Function ◽  
Rotational Flows

A numerical method is developed for modeling the violent motion and fragmentation of an interface between two fluids. The flow field is described through the solution of the Navier-Stokes equations for both fluids (in this case water and air), and the interface is captured by a Level-Set function. Particular attention is given to modeling the interface, where most of the numerical approximations are made. Novel features are that the reintialization procedure has been redefined in cells crossed by the interface; the density has been smoothed across the interface using an exponential function to obtain an equally stiff variation of the density and of its inverse; and we have used an essentially non-oscillatory scheme with a limiter whose coefficients depend on the distance function at the interface. The results of the refined scheme have been compared with those of the basic scheme and with other numerical solvers, with favorable results. Besides the case of the vertical surface-piercing plate (for which new laboratory measurements were carried out) the numerical method is applied to problems involving a dam-break and wall-impact, the interaction of a vortex with a free surface, and the deformation of a cylindrical bubble. Promising agreement with other sources of data is found in every case.

scholarly journals Inertial dynamics of air bubbles crossing a horizontal fluid–fluid interface

2012 ◽  
Vol 707 ◽  
pp. 405-443 ◽  
Author(s):  
Romain Bonhomme ◽  
Jacques Magnaudet ◽  
Fabien Duval ◽  
Bruno Piar
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Air Bubbles ◽  
Fluid Interface ◽  
Navier Stokes Equations ◽  
Film Drainage ◽  
Two Fluids

AbstractThe dynamics of isolated air bubbles crossing the horizontal interface separating two Newtonian immiscible liquids initially at rest are studied both experimentally and computationally. High-speed video imaging is used to obtain a detailed evolution of the various interfaces involved in the system. The size of the bubbles and the viscosity contrast between the two liquids are varied by more than one and four orders of magnitude, respectively, making it possible to obtain bubble shapes ranging from spherical to toroidal. A variety of flow regimes is observed, including that of small bubbles remaining trapped at the fluid–fluid interface in a film-drainage configuration. In most cases, the bubble succeeds in crossing the interface without being stopped near its undisturbed position and, during a certain period of time, tows a significant column of lower fluid which sometimes exhibits a complex dynamics as it lengthens in the upper fluid. Direct numerical simulations of several selected experimental situations are performed with a code employing a volume-of-fluid type formulation of the incompressible Navier–Stokes equations. Comparisons between experimental and numerical results confirm the reliability of the computational approach in most situations but also points out the need for improvements to capture some subtle but important physical processes, most notably those related to film drainage. Influence of the physical parameters highlighted by experiments and computations, especially that of the density and viscosity contrasts between the two fluids and of the various interfacial tensions, is discussed and analysed in the light of simple models and available theories.

The development of concentrated vortices: a numerical study

1971 ◽  
Vol 48 (1) ◽  
pp. 1-21 ◽  
Author(s):  
L. M. Leslie
Keyword(s):  
Steady State ◽  
Numerical Experiment ◽  
Laboratory Experiments ◽  
Body Force ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Quasi Steady State ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Axis Of Rotation

Amongst the more important laboratory experiments which have produced concentrated vortices in rotating tanks are the sink experiments of Long and the bubble convection experiments of Turner & Lilly. This paper describes a numerical experiment which draws from the laboratory experiments those features which are believed to be most relevant to atmospheric vortices such as tornadoes and waterspouts.In the numerical model the mechanism driving the vortices is represented by an externally specified vertical body force field defined in a narrow neighbourhood of the axis of rotation. The body force field is applied to a tank of fluid initially in a state of rigid rotation and the subsequent flow development is obtained by solving the Navier–Stokes equations as an initial-value problem.Earlier investigations have revealed that concentrated vortices will form only for a restricted range of flow parameters, and for the numerical experiment this range was selected using an order-of-magnitude analysis of the steady Navier–Stokes equations for sink vortices performed by Morton. With values of the flow parameters obtained in this way, concentrated vortices with angular velocities up to 30 times that of the tank are generated, whereas only much weaker vortices are formed at other parametric states. The numerical solutions are also used to investigate the comparative effect of a free upper surface and a no-slip lid.The concentrated vortices produced in the numerical experiment grow downwards from near the top of the tank until they reach the bottom plate whereupon they strengthen rapidly before reaching a quasi-steady state. In the quasi-steady state the flow in the tank typically consists of the vortex at the axis of rotation, strong inflow and outflow boundary layers at the bottom and top plates respectively, and a region of slowly-rotating descending flow over the remainder of the tank. The flow is cyclonic (i.e. in the same sense as the tank) in the vortex core and over most of the bottom half of the tank and is anticyclonic over the upper half of the tank away from the axis of rotation.

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