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.

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.

Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations

Analysis ◽  
2020 ◽  
Vol 40 (3) ◽  
pp. 127-150
Author(s):  
Tania Biswas ◽  
Sheetal Dharmatti ◽  
Manil T. Mohan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stokes Equations ◽  
Minimum Principle ◽  
Immiscible Fluids ◽  
Second Order ◽  
Navier Stokes ◽  
Distributed Optimal Control ◽  
Navier Stokes Equations

AbstractIn this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary conditions of optimality via the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality 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.

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.

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.

Fluid Structure Interaction Modelling for the Vibration of Tube Bundles: Part I—Analysis of the Fluid Flow in a Tube Bundle

2011 ◽  
Author(s):  
Quentin Desbonnets ◽  
Daniel Broc
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Tube Bundle ◽  
Nuclear Industry ◽  
Navier Stokes ◽  
Inertial Effects ◽  
Navier Stokes Equations ◽  
Dissipative Effects ◽  
Tube Bundles ◽  
Interaction Modelling

It is well known that a fluid may strongly influence the dynamic behaviour of a structure. Many different physical phenomena may take place, depending on the conditions: fluid flow, fluid at rest, little or high displacements of the structure. Inertial effects can take place, with lower vibration frequencies, dissipative effects also, with damping, instabilities due to the fluid flow (Fluid Induced Vibration). In this last case the structure is excited by the fluid. Tube bundles structures are very common in the nuclear industry. The reactor cores and the steam generators are both structures immersed in a fluid which may be submitted to a seismic excitation or an impact. In this case the structure moves under an external excitation, and the movement is influence by the fluid. The main point in such system is that the geometry is complex, and could lead to very huge sizes for a numerical analysis. Homogenization models have been developed based on the Euler equations for the fluid. Only inertial effects are taken into account. A next step in the modelling is to build models based on the homogenization of the Navier-Stokes equations. The papers presents results on an important step in the development of such model: the analysis of the fluid flow in a oscillating tube bundle. The analysis are made from the results of simulations based on the Navier-Stokes equations for the fluid. Comparisons are made with the case of the oscillations of a single tube, for which a lot of results are available in the literature. Different fluid flow pattern may be found, depending in the Reynolds number (related to the velocity of the bundle) and the Keulegan-Carpenter number (related to the displacement of the bundle). A special attention is paid to the quantification of the inertial and dissipative effects, and to the forces exchanges between the bundle and the fluid. The results of such analysis will be used in the building of models based on the homogenization of the Navier-Stokes equations for the fluid.

Nanofluidic transport and formation of nano-emulsions

2008 ◽  
Vol 2 (1) ◽  
Author(s):  
P.A. Chando ◽  
S.S. Ray ◽  
A.L. Yarin
Keyword(s):  
Stokes Equations ◽  
Theoretical Calculations ◽  
Ccd Camera ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Fluid Layers ◽  
Pressure Driven Flow ◽  
Two Fluid

The focus of this research is to study fluidic transport through carbon nanotubes. The nanotubes studied were formed by electrospinning Polycaplrolactone (PCL) nanofibers and then using them as channel templates in colyacrylamide blocks which were carbonized. A pressure driven flow is initiated through the nanochannels and the rate of emulsion formation is recorded with a CCD camera. Theoretical calculations are conducted for nanochannels because in many experiments, the nanochannels studied have two-phase flows, which make direct application of Poiseuille law impossible. The model used for the calculations is a slit with two fluid layers in between. In particular, in many experiments, decane-air system is of interest. The calculations are carried out using the Navier-Stokes equations. The results of the model are used to evaluate experimental volumetric flow rates and find the distribution of air and decane in the nanochannels.

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