Simulation of immiscible two-phase flows based on a kinetic diffuse interface approach (original) (raw)
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Physics of Fluids
In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the particle distribution functions at cell interfaces are reconstructed using a weighted essentially non-oscillatory scheme. Second, the conservative lower-order Allen–Cahn equation is chosen instead of the higher-order Cahn–Hilliard equation to evolve the free-energy-based phase field governing the dynamics of two-phase interfaces. Five benchmark problems are simulated to demonstrate the capability of the approach in treating two-phase flows at large density ratios and high Reynolds numbers, including three two-dimensional problems (a stationary droplet, Rayleigh–Taylor instability, and a droplet splashing on a thin liquid film) and two three-dimensional problems (binary droplets collision and Rayleigh–Taylor instability). All results agree well wi...
A diffuse-interface model for axisymmetric immiscible two-phase flow
Applied Mathematics and Computation, 2005
A diffuse-interface model is considered for solving axisymmetric immiscible twophase flow with surface tension. The Navier-Stokes (NS) equations are modified by the addition of a continuum forcing. The interface between the two fluids is considered as the half level set of a mass concentration c, which is governed by the Cahn-Hilliard (CH) equation-a fourth order, degenerate, nonlinear parabolic diffusion equation. In this work, we develop a nonlinear multigrid method to solve the CH equation with degenerate mobility and couple this to a projection method for the incompressible NS equations. The diffuse-interface method can deal with topological transitions such as breakup and coalescence smoothly without ad hoc Ôcut and connectÕ or other artificial procedures. We present results for RayleighÕs capillary instability up to forming satellite drops. The results agree well with the linear stability theory.
Fedsm 2006-98536 Interface-Tracking Simulation of Two-Phase Flows by Phase-Field Method
2006
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 interfacecapturing/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 equ...
Mathematical Models and Methods in Applied Sciences
While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier–Stokes–Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompres...
Low-Speed Flow Simulation by the Gas-Kinetic Scheme
Journal of Computational Physics, 1999
This paper extends the gas-kinetic BGK-type scheme to low Mach number flows, and thus shows that incompressible flow solutions are accurately obtained from the BGK scheme in the low Mach number limit. The influence of boundary conditions, internal molecular degrees of freedom K , and the flow Mach number M on the accuracy of the solutions of incompressible or nearly incompressible flow problems is quantitatively evaluated. The gas-kinetic scheme is tested carefully in two numerical examples, namely, the cavity flow problem and the flow passing a backward facing step problem. For the cavity flow problem, the numerical results from the gaskinetic scheme under different Reynolds numbers compare well with Ghia's data. For the backward step problem, the numerical results are compared accurately with previously published experimental data. 18 SU, XU, AND GHIDAOUI incompressible fluid flow equations relates to the proper choice of intermediate boundary conditions [6]. In fact, Ref. [6] provides excellent insight into the problems associated with some intermediate boundary conditions and shows which intermediate boundary is optimal for viscous incompressible flows.
A kinetic model for a two phases flow simulation
ARIMA, 2006
Dans ce travail, nous nous intéressons à la modélisation et la simulation de l'effet d'injection des bulles d'air dans un réservoir d'eau. La phase eau est modélisée par les équations de Navier-Stokes dans lesquelles on intègre l'effet des bulles d'air par un terme source. Ce dernier dépend d'une fonction densité de probabilité qui est décrite par une équation cinétique de type Vlasov. Pour les aspects numériques, on utilise la méthode particulaire pour l'équation cinétique et la méthode des éléments finis mixte pour les équations de Navier-Stokes. Enfin, nous présentons quelques résultats numériques pour illuster les méthodes utilisée. ABSTRACT. This work deals with the modelling and simulation of the air bubble injection effect in a water reservoir. The water phase is modelled by a Navier-Stokes equation in which we integrate the air bubble effect by a source term. This one depends on probability density function described by a kinetic model. For the numerical aspects we used particular method for kinetic equation and mixed finite elements method for Navier-Stokes equations. Finally, we present some numercial results to illustrate the used method. MOTS-CLÉS : Ecoulement diphasique, équation de Vlasov, équations de Navier-Stokes, méthode particulaire, méthode des éléments finis mixtes.
Journal of Nuclear Science and Technology, 2003
A new gas-liquid two-phase flow simulation method has been developed based on the extended two-fluid model, which has capabilities of both the two-fluid and the interface-tracking models. The VOF (Volume of Fluid) technique has been introduced for suitable interface calculations. Interfaces of free surface and large bubbles are calculated directly by solving transport of a steep void fraction gradient corresponding to interface, while averaged behavior of microscopic dispersed bubbles and droplets are calculated in the two-fluid model scheme. It is expected that the present method can treat effects of significant kinetic interaction between the phases directly without empirical correlations. The calculated propagation of wet front in a dam break problem is close to experimental data. The predicted flow patterns of complex gas-liquid two-phase flow in a flat tube are quite similar to observations with a video camera. The present simulation will be a useful tool for predictions of integral behavior of thermal-hydraulic phenomena in large-scale nuclear power plants.
A Numerical Method for Two-Phase Flow Based on a Phase-Field Model
2006
For interface-tracking simulation of incompressible two-phase fluids with high density ratios, a new numerical method was proposed by combining Navier-Stokes equations with a phase-field model based on a van der Waals-Cahn-Hilliard free-energy theory. The method was applied to several benchmark problems. Major findings are as follows: (1) The volume flux derived from a local chemical potential gradient in the Cahn-Hilliard equation leads to accurate volume conservation, autonomic reconstruction of gas-liquid interface, and reduction of numerical diffusion and oscillation. (2) The proposed method gave good predictions of pressure increase inside a bubble caused by the surface tension force. (3) A single liquid drop falling in stagnant gas and merging into a stagnant liquid film was successfully simulated.