Two-phase Flows In Complex Geometries Research Articles

A ternary phase-field model for two-phase flows in complex geometries

In this work, a ternary phase-field model for two-phase flows in complex geometries is proposed. In this model, one of the three components in the classical ternary Cahn–Hilliard model is considered as the solid phase, and only one Cahn–Hilliard equation with degenerate mobility needs to be solved due to the condition of volume conservation, which is consistent with the standard phase-field model with a single-scalar variable for two-phase flows. To depict different wetting properties at the complex fluid–solid boundaries, the spreading parameters in ternary phase-field model are determined based on the Young’s law, in which the liquid–solid surface tension coefficient is assumed to be a linear function of gas–liquid surface tension coefficient and related to the contact angle and the minimum curvature of the solid surface. In addition, to achieve a high viscosity in the solid phase and preserve the velocity boundary conditions on the solid surface, the phase-field variable of the solid phase is also used to derive the modified Navier–Stokes equations. To test the present model, we further develop a consistent and conservative Hermite-moment based lattice Boltzmann method where an adjustable scale factor is introduced to improve the numerical stability, and conduct the numerical simulations of several benchmark problems. The results illustrate that present model has the good capability in the study of the two-phase flows in complex geometries.

A Diffuse-Domain Phase-Field Lattice Boltzmann Method for Two-Phase Flows in Complex Geometries

This study constructs a new diffuse-domain (DD) lattice Boltzmann (LB) method for two-phase flows in complex geometries. We first coupled the DD method with the consistent and conservative phase-field (CCPF) method which can be described by the DD-CC Navier–Stokes–Cahn–Hilliard (NSCH) equations with the consistency of reduction, the consistency of mass and momentum transport, and the consistency of mass conservation. Then we conducted a matched asymptotic analysis and found that the DD-CCNSCH equations would converge to the CCNSCH equations as the thickness of the DD interface approaches to zero. Since the boundary conditions imposed on the complex geometries are incorporated into the DD-CCNSCH equations as the source terms, the system can be implemented more readily in a large and regular domain, and there is no need to treat the complex boundary conditions specially. We further developed a DD-CCPFLB method, and through the Chapman–Enskog analysis, the DD-CCPFLB method can correctly recover the DD-CCNSCH equations for two-phase flows in complex geometries. To quantitatively validate the DD-CCPFLB method, three benchmark problems are considered, and the numerical results are in agreement with those obtained through directly solving the CCNSCH equations combined with the original boundary conditions, the analytical solution, or the reported data. Finally, the present method is used to study the problems of two-phase flows in complex geometries, including the droplet dynamics in the Y-shaped channel and a droplet passing through cylindrical obstacles. The effects of the wettability and viscosity ratio are mainly investigated, and it is found that these two factors have significant impacts on the droplet dynamics.

Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density

Phase-field model has been applied extensively and successfully for simulating two-phase flows with variable density. Several stable numerical methods have been proposed for solving such a highly nonlinear and coupled system. The key issue is to design a method such that it can preserve the (exact or slightly modified) conservative/dissipative law of energy of the fluid system at the discrete level. However, most of the existing energy stable numerical methods are restricted to only the first order accuracy in time for two-phase flow with different density. The design of a temporally second order accurate numerical method for the two-phase flows with variable density still remains challenging. In this paper, we develop several second order, robust and accurate numerical schemes for a quasi-incompressible Navier-Stokes Cahn-Hilliard model of two-phase flows with variable density which is thermodynamically consistent and was originally developed in [1] for simulating two-phase flows in complex geometries. Especially, numerical schemes proposed in this paper can preserve the mass conservation or energy dissipative law. Several numerical examples are presented to validate the robustness and accuracy of our numerical schemes.

3D numerical study of large-scale two-phase flows with contact lines and application to drop detachment from a horizontal fiber

One fundamental problem in understanding two-phase flows in coalescers is determining how large of a drop can attach to and subsequently remain on a fiber. Droplet detachment can be caused by gravity or shear from the cross-flow overcoming the adhesion between the drop and the fiber. Previous studies have found the critical size of a drop on a hydrophilic fiber under gravity and the critical size of a drop on a hydrophobic fiber. In this paper, we present an accurate, conservative, and robust numerical strategy to simulate large-scale two-phase flows in complex geometries, and validate the capability of the proposed approach to predict the critical size of a drop on a cylindrical hydrophilic fiber under gravity and on a hydrophobic fiber without gravity. Then, an exploratory study of the critical size of a drop on a cylindrical fiber with cross-flow is performed.

Simulations of viscoelastic two-phase flows in complex geometries

Abstract A front-tracking/immersed-boundary (FT/IB) method is developed for direct numerical simulations of viscoelastic two-phase flow systems in complex geometries. One set of governing equations is written for the whole computational domain and different phases are treated as a single fluid with variable material and rheological properties. The interface is tracked explicitly using a Lagrangian grid while the flow equations are solved on a fixed Eulerian grid. An immersed boundary method is used to impose the boundary conditions on arbitrarily-shaped solid walls. The surface tension is computed at the interface using the Lagrangian grid and included into the momentum equations as a body force. The viscoelasticity is accounted for using the FENE-CR model. The viscoelastic model equations are solved fully coupled with the flow equations within the front-tracking framework. The FT/IB method is first validated for a single-phase and a two-phase Newtonian flow problems. Then it is applied to study motion and deformation of a viscoelastic drop in a pressure-driven flow through a capillary tube with a smooth and a sharp-edged constrictions. It is shown that the FT/IB method is robust, second order accurate in space and suitable to simulate viscoelastic two-phase flows interacting with a complex geometry.

Numerical simulation of two-phase flows in complex geometries by using the volume-of-fluid/immersed-boundary method

The numerical modeling of two-phase flows in complex geometries is of special relevance in many scientific and industrial applications. In this paper, we describe a numerical method to perform three-dimensional simulations of such flow problems. This method adopts a volume-of-fluid (VOF) approach to capture and advance the fluid interface, and it integrates the fluid solver with the immersed boundary (IB) modeling of arbitrary-shape walls and moving bodies. The shape and movement of solid geometries are efficiently represented by an auxiliary signed distance function (SDF) with local coordinate transformation. Validation tests have been conducted using the present method, and the computational results are in good agreements with reference solutions and experimental data. We further present its application to the simulation of the air–water flow in a twin screw kneader. Hence, the adequacy and suitability of the present VOF–IB method are shown to successfully simulate complicated two-phase flows interacting with general geometries.

Two-phase flow in complex geometries: A diffuse domain approach.

We present a new method for simulating two-phase flows in complex geometries, taking into account contact lines separating immiscible incompressible components. We combine the diffuse domain method for solving PDEs in complex geometries with the diffuse-interface (phase-field) method for simulating multiphase flows. In this approach, the complex geometry is described implicitly by introducing a new phase-field variable, which is a smooth approximation of the characteristic function of the complex domain. The fluid and component concentration equations are reformulated and solved in larger regular domain with the boundary conditions being implicitly modeled using source terms. The method is straightforward to implement using standard software packages; we use adaptive finite elements here. We present numerical examples demonstrating the effectiveness of the algorithm. We simulate multiphase flow in a driven cavity on an extended domain and find very good agreement with results obtained by solving the equations and boundary conditions in the original domain. We then consider successively more complex geometries and simulate a droplet sliding down a rippled ramp in 2D and 3D, a droplet flowing through a Y-junction in a microfluidic network and finally chaotic mixing in a droplet flowing through a winding, serpentine channel. The latter example actually incorporates two different diffuse domains: one describes the evolving droplet where mixing occurs while the other describes the channel.

An improved large eddy simulation of two-phase flows in a pump impeller

An improved large eddy simulation using a dynamic second-order sub-grid-scale (SGS) stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the current second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body-fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbulent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.

ADVANCED THREE-DIMENSIONAL TWO-FLUID POROUS MEDIA METHOD FOR TRANSIENT TWO-PHASE FLOW THERMAL-HYDRAULICS IN COMPLEX GEOMETRIES

A three-dimensional two-fluid model for two-phase flow within tube or rod bundles is presented. The porous media concept is applied in the model statement. Closure laws for interfacial mass, momentum and energy transfer, bundle flow resistance and heat transfer are presented. Correlations for the interfacial drag force are proposed. Some illustrative examples of application (including also verification) to two-phase flows in complex geometries and across vertical and horizontal tube/rod bundles are presented below. The developed model is suitable for the simulation and analyses of complex multidimensional thermal-hydraulics of nuclear fuel rod bundles or shell-and-tube heat exchangers with vapor generation within a tube bundle on the shell side.

Gas–solid flow modelling based on the kinetic theory of granular media: validation, applications and limitations

Improvement of operating conditions of existing circulating fluidised bed combustor units, as well as attempts to scale up present units to larger ones, are mainly based on empirical correlation or simplified scaling laws. Moreover, it is known that the details of the unit geometry (entry and exit design, horizontal cross-section shape, secondary air location and configuration) have a great importance in the overall plant performance. Improvement of our understanding of the complex hydrodynamic behaviours involved in these processes requires refined and local physical models. The approach retained at the Laboratoire National d'Hydraulique of EDF for the prediction of the two-phase flows in complex geometries is based on the two-fluid model formalism, where both phases are characterised by their first velocity moments (volumetric concentration, mean velocity and second order fluctuating velocity correlation tensors). Separate transport equations are written for each moment with appropriate closure assumptions for unknown terms such as the momentum exchange between the two phases and the effective stress tensors of both phases. These closures are based on the existing kinetic theory of dry granular media and on single phase turbulence modelling. The present paper will try to focus on the closure of the solid stress based on the kinetic theory. By starting from the “simplest case” of a dry assembly of spherical particles, with one diameter, we will see that the kinetic theory provides us an appropriate formalism and some practical closures. These can be easily checked by performing some direct simulation of a set of particles. Nevertheless, in industrial applications, the particles size distribution cannot be reduced to a narrow peak distribution (one size) but in some case to a wide Gaussian distribution, the variance sometimes be compared to the mean diameter; in some other cases, the distribution can be compared to well separated picks. For each of these cases, the kinetic theory provides a conceptual formalism but the derivation of practical closures requires some restrictive assumptions leading to important limitations in the range of applicability of these closures. Moreover, another important assumption underlying these closures is that particles are freely moving between collisions. Of course, in real gas–solid flow, the carrier gas acts on each particle through the drag force. By introducing this force in the kinetic theory, it is possible to modify the closures and direct numerical simulations are able to validate these modifications. Another assumption underlying these closures is that colliding particles are not correlated. Nevertheless, the interstitial carrier gas or interparticle forces can introduce a correlation between neighbouring particles. In the present paper, we will try to emphasise these limitations and to indicate some possible way to overcome these limitations.

Macroscopic balance equations for two-phase flow models

The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analyzed. The equations obtained in this report supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. The flow-field model equations required by the balance equations are not discussed nor have applications and numerical solution techniques been considered.