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.

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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 SIMULATION OF ISOTHERMAL AND THERMAL TWO-PHASE FLOWS USING PHASE-FIELD MODELING

2007 ◽  
Vol 18 (04) ◽  
pp. 536-545 ◽  
Author(s):  
NAOKI TAKADA ◽  
AKIO TOMIYAMA
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Density Ratio ◽  
Navier Stokes ◽  
Phase Field Modeling ◽  
Two Phase Flows ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Field Modeling ◽  
High Density Ratio

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, we examined the applicability of two versions of computational fluid dynamics method, NS-PFM, combining Navier-Stokes equations with phase-field modeling for interface based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

scholarly journals Do the Volume-of-Fluid and the Two-Phase Euler Compete for Modeling a Spillway Aerator?

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 3092
Author(s):  
Lourenço Sassetti Mendes ◽  
Javier L. Lara ◽  
Maria Teresa Viseu
Keyword(s):  
Stokes Equations ◽  
Cost Benefit ◽  
Volume Of Fluid ◽  
Navier Stokes ◽  
Type Model ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Entrained Air ◽  
Computational Resources ◽  
Mesh Convergence

Spillway design is key to the effective and safe operation of dams. Typically, the flow is characterized by high velocity, high levels of turbulence, and aeration. In the last two decades, advances in computational fluid dynamics (CFD) made available several numerical tools to aid hydraulic structures engineers. The most frequent approach is to solve the Reynolds-averaged Navier–Stokes equations using an Euler type model combined with the volume-of-fluid (VoF) method. Regardless of a few applications, the complete two-phase Euler is still considered to demand exorbitant computational resources. An assessment is performed in a spillway offset aerator, comparing the two-phase volume-of-fluid (TPVoF) with the complete two-phase Euler (CTPE). Both models are included in the OpenFOAM® toolbox. As expected, the TPVoF results depend highly on the mesh, not showing convergence in the maximum chute bottom pressure and the lower-nappe aeration, tending to null aeration as resolution increases. The CTPE combined with the k–ω SST Sato turbulence model exhibits the most accurate results and mesh convergence in the lower-nappe aeration. Surprisingly, intermediate mesh resolutions are sufficient to surpass the TPVoF performance with reasonable calculation efforts. Moreover, compressibility, flow bulking, and several entrained air effects in the flow are comprehended. Despite not reproducing all aspects of the flow with acceptable accuracy, the complete two-phase Euler demonstrated an efficient cost-benefit performance and high value in spillway aerated flows. Nonetheless, further developments are expected to enhance the efficiency and stability of this model.

Modeling of Cell Motion in Micro-Scale Hydrodynamic-Electrical Field

2009 ◽  
Vol 74 ◽  
pp. 139-142
Author(s):  
Ting Ye ◽  
Hua Li
Keyword(s):  
Stokes Equations ◽  
Elastic Shell ◽  
Practical Significance ◽  
Cell Manipulation ◽  
Navier Stokes ◽  
Phase System ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Maxwell Stress Tensor ◽  
Cell Motion

A modeling of two-phase system is presented for investigation of the cell motion and deformation in the microchannel subject to the mechanical and electrical coupled forces. In order to evaluate the mechanical force developed by cell membrane, it is treated as an incompressible and elastic shell with uniform thickness capable of shearing and bending deformation. Due to the irregular and complex cell configuration after deformation, the Maxwell stress tensor (MST) method is successfully employed to analyze the dielectrophoretic force. The modified particle binary level set (MPBLS) method is presented to accurately track the moving interface between the two phases, which is vital for a modeling of two-phase system. Afterwards the modified SIMPLER coupled with SIMPLEC is used to numerically solve the incompressible Navier-Stokes equations governing the entire flow field. On basis of the series of methods, the motion and deformation of red blood cell (RBC) in the microchannel under the mechanical and electrical forces are simulated to demonstrate the deformation process and the moving trajectory of RBC. The present study is not only of great value for deeper understanding of some diseases caused by cell abnormality, but also of practical significance for cell manipulation and separation.

Discussion on Clustering Effects in Vertical Gas-Particle Flows

2000 ◽  
Author(s):  
Eivind Helland ◽  
Rene Occelli ◽  
Lounes Tadrist
Keyword(s):  
Gas Phase ◽  
Stokes Equations ◽  
Lagrangian Approach ◽  
Inelastic Collisions ◽  
Navier Stokes ◽  
Coupling Term ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Drag Forces ◽  
Particle Flows

Abstract Simulations of 2D gas-particle flows in a vertical riser using a mixed Eulerian-Lagrangian approach are addressed. The model for the interstitial gas phase is based on the Navier-Stokes equations for two-phase flow with a coupling term between the gas and solid phases due to drag forces. The motion of particles is treated by a Lagrangian approach and the particles are assumed to interact through binary, instantaneous, non-frontal, inelastic collisions with friction. In this paper different particle clustering effects in the gas-particle flow is investigated.

Luminosity calculation of meteor entry based on detailed flow simulations in the continuum regime

2020 ◽  
Vol 635 ◽  
pp. A184 ◽  
Author(s):  
B. Dias ◽  
J. B. Scoggins ◽  
T. E. Magin
Keyword(s):  
Radiation Effects ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Transfer Coefficients ◽  
Coupled Flow ◽  
Navier Stokes Equations ◽  
Lost City ◽  
Flow Simulations ◽  
Chemical Models ◽  
The Continuum

Context. Composition, mass, and trajectory parameters of meteors can be derived by combining observations with the meteor physics equations. The fidelity of these equations, which rely on heuristic coefficients, significantly affects the accuracy of the properties inferred. Aims. Our objective is to present a methodology that can be used to compute the luminosity of meteor entry based on detailed flow simulations in the continuum regime. Methods. The methodology consists in solving the Navier–Stokes equations using state-of-the-art physico-chemical models for hypersonic flows. It includes accurate boundary conditions to simulate the surface evaporation of the molten material and coupled flow-radiation effects. Such detailed simulations allow for the calculation of heat-transfer coefficients and luminous efficiency, which can be incorporated into the meteor physics equations. Finally, we integrate the radiative transfer equation over a line of sight from the ground to the meteor to derive the luminosity magnitude. Results. We use the developed methodology to simulate the Lost City bolide and to derive the luminosity magnitude, obtaining good agreement between numerical results and observations. The computed color index is more prominent than the observations. This is attributed to a lack of refractory elements such as Ca in the modeled flow that might originate from the vaporization of droplets in the trail, a phenomenon currently not included in the model.

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