Application of Interface-Tracking Method Based on Phase-Field Model to Numerical Analysis of Isothermal and Thermal Two-Phase Flows

2007 ◽  
Author(s):  
Naoki Takada
Keyword(s):  
Phase Field ◽  
Density Ratio ◽  
Phase Field Model ◽  
Field Method ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Two Phase

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, the applicability of two versions of Navier-Stokes phase-field method (NS-PFM) was examined, combining NS equations for a continuous fluid with a diffuse-interface model 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.

Interface-Tracking Simulation of Two-Phase Flows by Phase-Field Method

2006 ◽  
Author(s):  
Naoki Takada ◽  
Akio Tomiyama
Keyword(s):  
Phase Field ◽  
Density Ratio ◽  
Phase Field Model ◽  
Three Dimensions ◽  
Phase Field Method ◽  
Vapor Flow ◽  
Two Phase Flows ◽  
Two Phase ◽  
Flow Problems ◽  
Aspect Ratios

The purpose of this study is to examine multi-physics computational fluid dynamics method, NS-PFM, which is a combination of Navier-Stokes (NS) equations with phase-field model (PFM) based on the free-energy theory, for interface-capturing/tracking simulation of two-phase flows. First, a new NS-PFM which we have proposed was applied to immiscible, incompressible, isothermal two-phase flow problems with a high density ratio equivalent to that of an air-water system. In this method, a Cahn-Hilliard equation was used for prediction of diffusive interface configuration. The numerical simulations demonstrated that (1) predicted collapse of two-dimensional liquid column in a gas under gravity agreed well with available data at aspect ratios of column = 1 and 2, and (2) coalescence of free-fall drops into a liquid film was successfully simulated in three dimensions. Second, we took heat transfer into account in another NS-PFM which solves a full set of NS equations and the van-der-Waals equation of state. Through a numerical simulation of a non-ideal fluid flow in the vicinity of the critical point, it was confirmed that the NS-PFM is applicable to thermal liquid-vapor flow problems with phase change.

scholarly journals A Phase-Field Method for Interface-Tracking Simulation of Two-Phase Flows

2005 ◽  
Author(s):  
Naoki Takada ◽  
Masaki Misawa ◽  
Akio Tomiyama
Keyword(s):  
Surface Tension ◽  
Free Energy ◽  
Phase Field ◽  
Density Ratio ◽  
Bubble Nucleation ◽  
Computational Method ◽  
Phase Field Method ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Two Phase

For interface-tracking simulation of two-phase flows, we propose a new computational method, NS-PFM, combining Navier-Stokes (NS) equations with phase-field model (PFM). Based on the free energy theory, PFM describes an interface as a volumetric zone across which physical properties vary continuously. Surface tension is defined as an excessive free energy per unit area induced by density gradient. Consequently, PFM simplifies the interface-tracking procedure by use of a standard technique. The proposed NS-PFM was applied to several problems of incompressible, isothermal two-phase flow with the same density ratio as that of an air-water system. In this method, the Cahn-Hilliard (CH) equation was used for predicting interface configuration. It was confirmed through numerical simulations that (1) the flux driven by chemical potential gradient in the CH equation plays an important role in interfacial advection and reconstruction, (2) the NS-PFM gives good predictions for pressure increase inside a bubble caused by the surface tension, (3) coalescence of liquid film and single drop falling through a stagnant gas was well simulated, and (4) collapse of liquid column under gravity was predicted in good agreement with other available data. Then, another version of NS-PFM was proposed and applied to a direct simulation of bubble nucleation of a non-ideal fluid in the vicinity of the critical point, which demonstrated the capability of NS-PFM to capture liquid-vapor interface motion in boiling and condensation.

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.

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