The sharp-interface limit of the Cahn–Hilliard/Navier–Stokes model for binary fluids

2013 ◽  
Vol 714 ◽  
pp. 95-126 ◽  
Author(s):  
F. Magaletti ◽  
F. Picano ◽  
M. Chinappi ◽  
L. Marino ◽  
C. M. Casciola
Keyword(s):  
Numerical Simulations ◽  
Capillary Waves ◽  
Sharp Interface ◽  
Navier Stokes ◽  
Interface Thickness ◽  
Effective Parameters ◽  
Binary Fluids ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Sharp Interface Limit

AbstractThe Cahn–Hilliard model is increasingly often being used in combination with the incompressible Navier–Stokes equation to describe unsteady binary fluids in a variety of applications ranging from turbulent two-phase flows to microfluidics. The thickness of the interface between the two bulk fluids and the mobility are the main parameters of the model. For real fluids they are usually too small to be directly used in numerical simulations. Several authors proposed criteria for the proper choice of interface thickness and mobility in order to reach the so-called ‘sharp-interface limit’. In this paper the problem is approached by a formal asymptotic expansion of the governing equations. It is shown that the mobility is an effective parameter to be chosen proportional to the square of the interface thickness. The theoretical results are confirmed by numerical simulations for two prototypal flows, namely capillary waves riding the interface and droplets coalescence. The numerical analysis of two different physical problems confirms the theoretical findings and establishes an optimal relationship between the effective parameters of the model.

Unifying binary fluid diffuse-interface models in the sharp-interface limit

2013 ◽  
Vol 736 ◽  
pp. 5-43 ◽  
Author(s):  
David N. Sibley ◽  
Andreas Nold ◽  
Serafim Kalliadasis
Keyword(s):  
Phase Field ◽  
Outer Region ◽  
Mobility Model ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Navier Stokes ◽  
Binary Fluids ◽  
Sharp Interface Limit ◽  
Binary Fluid ◽  
Phase Field Models

AbstractRecent results published by Gugenberger et al. on surface diffusion (Phys. Rev. E, vol. 78, 2008, 016703), show that the sharp-interface limit of the phase field models often adopted in the literature fails to produce the appropriate boundary conditions. With this knowledge, we consider the sharp-interface limit of phase field models for binary fluids, obtained carefully, where hydrodynamic equations are coupled to phase field evolution based on Cahn–Hilliard or Allen–Cahn theories, in a variety of guises, and unify and contrast their forms and behaviours in the sharp-interface limit. In particular, a tensorial mobility model is analysed, which allows the bulk fluids in the outer region to satisfy classical Navier–Stokes type equations to all orders in the Cahn number.

Lattice-Boltzmann Simulation of Two-Phase Fluid Flows

1998 ◽  
Vol 09 (08) ◽  
pp. 1383-1391 ◽  
Author(s):  
Yu Chen ◽  
Shulong Teng ◽  
Takauki Shukuwa ◽  
Hirotada Ohashi
Keyword(s):  
Lattice Boltzmann ◽  
Fluid Flows ◽  
Navier Stokes ◽  
Interface Model ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Lattice Boltzmann Simulation ◽  
Dam Breaking ◽  
Volumetric Stress ◽  
Phase Fluid

A model with a volumetric stress tensor added to the Navier–Stokes Equation is used to study two-phase fluid flows. The implementation of such an interface model into the lattice-Boltzmann equation is derived from the continuous Boltzmann BGK equation with an external force term, by using the discrete coordinate method. Numerical simulations are carried out for phase separation and "dam breaking" phenomena.

scholarly journals Numerical Simulations of the Impact and Spreading of a Particulate Drop on a Solid Substrate

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Hyun Jun Jeong ◽  
Wook Ryol Hwang ◽  
Chongyoup Kim
Keyword(s):  
Numerical Simulations ◽  
Solid Surface ◽  
Reynolds Numbers ◽  
Suspended Particles ◽  
Solid Substrate ◽  
Oscillatory Behavior ◽  
Navier Stokes ◽  
Droplet Spreading ◽  
Navier Stokes Equation ◽  
The Impact

We present two-dimensional numerical simulations of the impact and spreading of a droplet containing a number of small particles on a flat solid surface, just after hitting the solid surface, to understand particle effects on spreading dynamics of a particle-laden droplet for the application to the industrial inkjet printing process. The Navier-Stokes equation is solved by a finite-element-based computational scheme that employs the level-set method for the accurate interface description between the drop fluid and air and a fictitious domain method for suspended particles to account for full hydrodynamic interaction. Focusing on the particle effect on droplet spreading and recoil behaviors, we report that suspended particles suppress the droplet oscillation and deformation, by investigating the drop deformations for various Reynolds numbers. This suppressed oscillatory behavior of the particulate droplet has been interpreted with the enhanced energy dissipation due to the presence of particles.

scholarly journals A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

2020 ◽  
pp. 1-35
Author(s):  
Christian Rohde ◽  
Lars von Wolff
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Solid Phase ◽  
Immiscible Fluids ◽  
Sharp Interface ◽  
Ion Concentration ◽  
Navier Stokes ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Two Phase

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase-field approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase-field model is able to realize Navier-slip conditions for solid–fluid interfaces in the limit.

Numerical simulations using conserved wave absorption applied to Navier–Stokes equation model

2015 ◽  
Vol 99 ◽  
pp. 15-25 ◽  
Author(s):  
Zhe Hu ◽  
Wenyong Tang ◽  
Hongxiang Xue ◽  
Xiaoying Zhang ◽  
Jinting Guo
Keyword(s):  
Numerical Simulations ◽  
Stokes Equation ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Wave Absorption

Filter-Based Unsteady RANS Computations for Single-Phase and Cavitating Flows

Volume 3 ◽  
2004 ◽  
Author(s):  
Jiongyang Wu ◽  
Wei Shyy ◽  
Stein T. Johansen
Keyword(s):  
Eddy Viscosity ◽  
Single Phase ◽  
Experimental Information ◽  
Time Dependent ◽  
Navier Stokes ◽  
Cavitating Flows ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Filter Size ◽  
The Impact

The widely used Reynolds-Averaged Navier-Stokes (RANS) approach, such as the k-ε two-equation model, has been found to over-predict the eddy viscosity and can dampen out the time dependent fluid dynamics in both single- and two-phase flows. To improve the predictive capability of this type of engineering turbulence closures, a consistent method is offered to bridge the gap between DNS, LES and RANS models. Based on the filter size, conditional averaging is adopted for the Navier-Stokes equation to introduce one more parameter into the definition of the eddy viscosity. Both time-dependent single-phase and cavitating flows are simulated by a pressure-based method and finite volume approach in the framework of the Favre-averaged equations coupled with the new turbulence model. The impact of the filter-based concept, including the filter size and grid dependencies, is investigated using the standard k-ε model and with the available experimental information.

Mathematical Simulation of Different Argon Blowing Style in Ladle Furnace

2005 ◽  
Vol 475-479 ◽  
pp. 3211-3214
Author(s):  
San Bing Ren ◽  
Jun Fei Fan ◽  
Zong Ze Huang ◽  
Yi Sheng Chen ◽  
You Duo He
Keyword(s):  
Mathematical Simulation ◽  
Stokes Equation ◽  
Molten Steel ◽  
Navier Stokes ◽  
Ladle Furnace ◽  
Phase Zone ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Flow Variables ◽  
Turbulence Parameters

In the present paper, applied the experiential correlation, the gas holdup and distribution of two phase zone which formed by argon blown were determined. The flow variables of molten steel and turbulence parameters in the Ladle Furnace were estimated utilizing the results of frontal calculation and through numerically solution momentum Navier-Stokes equation in conjunction with k-εturbulence model. Several different spray styles including blowing through single hole, double holes, top lance were simulated and compared in this project.

A Sharp Surface Tension Modeling Method for Capillarity-Dominant Two-Phase Incompressible Flows

2007 ◽  
Author(s):  
Zhaoyuan Wang ◽  
Albert Y. Tong
Keyword(s):  
Surface Tension ◽  
Incompressible Flows ◽  
Jump Condition ◽  
Navier Stokes ◽  
Pressure Jump ◽  
Interfacial Flows ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Numerical Instabilities ◽  
Spurious Currents

A surface tension implementation algorithm for two-phase incompressible interfacial flows is presented in this study. The surface tension effect is treated as a jump condition at the interface and incorporated into the Navier-Stokes equation via a capillary pressure gradient. The interface is tracked by a coupled level set and volume-of-fluid (CLSVOF) method based on the finite-volume formulation on a fixed Eulerian grid. It has been shown in a stationary benchmark test the spurious currents are greatly reduced and the sharp pressure jump across the interface is well preserved. Numerical instabilities caused by the sharp treatment on a fixed grid are avoided. Several dynamic tests are performed to further validate the accuracy and versatility of the present method, the results of which are in good agreement with data reported in the literature.

scholarly journals An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models

1998 ◽  
Vol 09 (08) ◽  
pp. 1393-1404 ◽  
Author(s):  
D. J. Holdych ◽  
D. Rovas ◽  
J. G. Georgiadis ◽  
R. O. Buckius
Keyword(s):  
Multiphase Flow ◽  
Stress Tensor ◽  
Lattice Boltzmann ◽  
Effective Field ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Physical Parameters ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Definition Of

Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.

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