Numerical Simulation Of Two-phase Flow Research Articles

Influence of capillary end effects on steady-state relative permeability estimates from direct pore-scale simulations

We investigate and characterize the influence of capillary end effects on steady-state relative permeabilities obtained in pore-scale numerical simulations of two-phase flows. Our study is motivated by the observation that capillary end effects documented in two-phase laboratory-scale experiments can significantly influence permeability estimates. While numerical simulations of two-phase flows in reconstructed pore-spaces are increasingly employed to characterize relative permeabilities, a phenomenon which is akin to capillary end effects can also arise in such analyses due to the constraints applied at the boundaries of the computational domain. We profile the relative strength of these capillary end effects on the calculation of steady-state relative permeabilities obtained within randomly generated porous micro-structures using a finite volume-based two-phase flow solver. We suggest a procedure to estimate the extent of the regions influenced by these capillary end effects, which in turn allows for the alleviation of bias in the estimation of relative permeabilities.

Numerical simulation of two-phase flow in porous media using a wavelet based phase-field method

An understanding of the transport and dynamics of two fluids in porous media, as well as the bubbly flow regime, is important for many engineering applications, such as enhanced oil recovery (EOR) method, drilling technology, multiphase production system, etc. In this respect, the dependence of capillary stresses on the excess free-energy of a thin interfacial layer formed by two immiscible fluids is not fully clear, particularly in porous media. Of particular interests are the closure models for interphase forces which often hinder the reliable prediction of the homogeneous flow regime. This article presents a multiphase Computational Fluid Dynamics (CFD) study of bubbles in homogeneous porous media to model the flow of oil and gas, and investigates a closure model that is based on the Allen-Cahn phase-field method, where the capillary stress is derived from the excess free-energy. The governing dynamics is simulated with the volume averaged Navier-Stokes equations extended for multiphase flow in porous media. The equations have been discretized by a wavelet transform method to accurately capture the topological change of the fluid-fluid interface. To validate the closure model for interphase forces, the results of the present phase-field method have been compared with that from experiments, as well as from reference numerical models. An excellent agreement among the results from present phase-field simulations, experiments, and some reference numerical simulations has been observed. The terminal velocity of the rising gas bubble in a liquid saturated porous medium, as well as in a pure liquid has been investigated. The bubble rising velocity in both cases have been compared with respect to the theoretical and experimental results. The study illustrates how the bubble dynamics in porous media depend on the excess free energy of a thin interfacial layer formed by two immiscible fluids.

Mathematical modeling and numerical simulation of two-phase flows using Fourier pseudospectral and front-tracking methods: The proposition of a new method

• Formulation and implementation of the Fourier pseudospectral method with: • Coupling of the immersed boundary methods to solve non-periodic problems; • Coupling of the Front-Tracking method for numerical simulation of two phase flow; • Solution to problems involving rising bubble using this new method; • Comparison of numerical results with those from other methods. In the present work, an extension of the Fourier Pseudospectral Method coupled with the Immersed Boudary Method for non-periodic problems (IMERSPEC) applied to numerical simulation of two-phase flow was developed. The proposed method was originally developed for single-phase, incompressible flow. Here, the method is extended to two-phase flows using the front-tracking method (IMERSPEC-FT) to model fluid-fluid interfaces. The proposed method was verified and validated through results involving spurious currents, mass conservation and numerical experiments analysis for rising bubbles. IMERSPEC-FT is shown to be a promising scheme for the two-phase computational fluid dynamics (CFD).

Direct numerical simulations of two-phase flow in an inclined pipe

We study the instability mechanisms leading to slug flow formation in an inclined pipe subject to gravity forces. We use a phase-field approach, where the Cahn–Hillard model is used to model the interface. At the inlet, a stratified flow is imposed with a specified velocity profile. We validate our numerical results by comparing against previous theoretical models and by predicting the various flow regimes for horizontal and inclined pipes, including stratified flow, slug flow, dispersed bubble flow and annular flow. Subsequently, we focus on slug formation in an inclined pipe and connect its appearance with specific vortical dynamics. A two-dimensional channel geometry is first considered. When the heavy fluid is injected as the top layer, inverted vortex shedding emerges, which periodically impacts on the bottom wall, as it develops further downstream. The accumulation of heavy fluid in the bottom wall causes a back flow that induces rolling waves and interacts with the upstream jet. When the heavy fluid is placed as the bottom layer, the heavy fluid accumulates and initially forms a massive slug at the bottom region, close to the inlet. Subsequently, the heavy fluid slug starts to break into smaller pieces, some of which translate along the pipe. During the accumulation phase, a back flow forms also generating rolling waves. Occasionally, a rolling wave can reach the top of the pipe and form a new slug. To describe the generation of vorticity from the two-phase interface and pipe walls in the slug formation, we study the circulation dynamics and connect it with the resulting two-phase flow patterns. Finally, we conduct three-dimensional (3-D) simulations in a circular pipe and compare the differences between the 3-D flow patterns and its circulation dynamics against the 2-D simulation results.

Numerical analysis of tsunami-triggered oil spill from industrial parks in Osaka Bay

Oil storage tanks in industrial parks were heavily damaged by a large-scale tsunami, and large-scale oil spill occurred, which led to a fire. Moreover, it was found that mud samples in these regions had a high level of oil contamination after the disaster, showing that the tsunami triggered high turbid water mixed with spill oil and deposited on the sea bottom. For industrial zones around the coastal line with the potential for tsunamis, the building of a scenario of a tsunami-triggered oil spill from these industrial parks is urgently needed for planning the ship evacuating routes and the evacuation of residences nearby. This was carried out by numerical simulations of two-phase flow around the industrial parks. The results could build a scenario of a tsunami-triggered oil spill from industrial zones and could help to add the oil spill effect in reviewing the risk management of industrial zones around the coastal line.

A weighted multiple-relaxation-time lattice Boltzmann method for multiphase flows and its application to partial coalescence cascades

We present a lattice Boltzmann method (LBM) with a weighted multiple-relaxation-time (WMRT) collision model and an adaptive mesh refinement (AMR) algorithm for direct numerical simulation of two-phase flows in three dimensions. The proposed WMRT model enhances the numerical stability of the LBM for immiscible fluids at high density ratios, particularly on the D3Q27 lattice. The effectiveness and efficiency of the proposed WMRT–LBM–AMR is validated through simulations of (a) buoyancy-driven motion and deformation of a gas bubble rising in a viscous liquid; (b) the bag-breakup mechanism of a falling drop; (c) crown splashing of a droplet on a wet surface; and (d) the partial coalescence mechanism of a liquid drop at a liquid–liquid interface. The numerical simulations agree well with available experimental data and theoretical approximations where applicable.

Simulation of two-phase flow and mass transfer with deformable interface

Two-phase flow and interphase mass transfer are very popular in chemical processes. Rapid development of numerical simulation plays a crucial role in deep understanding of the mechanism of momentum, mass and heat transfer in two-phase systems. However, establishing and solving the mathematical models of two-phase flow and transport processes, especially the accurate description of deformable moving interface, are critical and difficult. This review addresses the level set method and the boundary element method, which are involved with the numerical simulation of two-phase flow of deformable surfaces, and presents a detailed discussion of the limits and advantages of these typical methods. We show the research status and prospect of the mathematical methods of deformation interface of fluid particle coalescence and breakage, micro-fluidics and droplets in two-phase flow field. In the end, we briefly introduce the numerical simulation methods of interphase mass transfer across deformable interface.

A new approach to solve mixture Multi-phase Flow model using Time Splitting Projection Method

This paper was aimed at introducing a new approach to numerical simulation of two-phase flows by solving the mixture model equations. In this approach, an effective numerical algorithm was developed based on the time splitting projection method to solve the mixture model equations for an incompressible two-phase flow. In this study, a new technique was developed to solve the mixture continuity equation based on the time splitting projection method. One of the advantages of the mixture model is that, in addition to determining the velocities of each phase, it solves only one set of momentum equations and calculates the velocity differences between the phases by solving the relative velocity equation. Accordingly, an extended finite volume vertical two-dimensional numerical model was used to determine the pressure distribution, velocity field and volume fraction of each phase at each time step. The model has been used in various tests to simulate unsteady flow problems. Comparison between numerical results, analytical solutions and experimental data demonstrated a satisfactory performance.

Physical and numerical simulation of two-phase flow in the area of mini-channel

The results of physical and numerical modeling to determine the rate of evaporation of ethanol, at a flow of air flow velocities in the range of 0.0139 - 0.139 m/s and temperature in the range of 10 - 45 °C are placed. The time of the establishment of the diffusion equilibrium in the work area and differences in the results of numerical and physical modeling are have determined.

Applying Different Strategies within OpenFOAM to Investigate the Effects of Breakup and Collision Model on the Spray and in-Cylinder Gas Mixture Attribute

In the current study, a 3-D numerical simulation of two-phase flow has been conducted in a direct injection CI engine using the Eularian-Lagrangian approach and a new breakup model. The newly modified breakup scheme has been implemented for simulating the ultra-high pressure diesel injection. The effects of droplet breakup and collision model on the spray and in-cylinder gas characteristics have been examined using the open source code OpenFOAM. Spray penetration and cone angle are investigated as spray properties and surrounding gas motion are studied by in-cylinder gas velocity and pressure distribution for non-evaporating conditions. In addition, vapor penetration of the evaporating spray is presented to study the effects of current scheme on the evaporating condition. The continuous field is described by RANS equations and dynamics of the dispersed droplet is modeled by Lagrangian tracking scheme. Results of the proposed modified KHRT model are compared against other default methods in OpenFOAM and favorable agreement is achieved. Robustness and accuracy of different breakup schemes and collision models are also verified using the published experimental data. It is demonstrated that the proposed breakup scheme and Nordin collision model display very accurate results in the case of ultra-high pressure injection.

Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software

Streamline simulation is developed to simulate waterflooding in fractured reservoirs. Conventional reservoir simulation methods for fluid flow simulation in large and complex reservoirs are very costly and time consuming. In streamline method, transport equations are solved on one-dimensional streamlines to reduce the computation time with less memory for simulation. First, pressure equation is solved on an Eulerian grid and streamlines are traced. Defining the “time of flight”, saturation equations are mapped and solved on streamlines. Finally, the results are mapped back on Eulerian grid and the process is repeated until the simulation end time. The waterflooding process is considered in a fractured reservoir using the dual porosity model. Afterwards, a computational code is developed to solve the same problem by the IMPES method and the results of streamline simulation are compared to those of the IMPES and a commercial software. Finally, the accuracy and efficiency of streamline simulator for simulation of two-phase flow in fractured reservoirs has been proved.

A Ghost Fluid/Level Set Method for boiling flows and liquid evaporation: Application to the Leidenfrost effect

The development of numerical methods for the direct numerical simulation of two-phase flows with phase change, in the framework of interface capturing or interface tracking methods, is the main topic of this study. We propose a novel numerical method, which allows dealing with both evaporation and boiling at the interface between a liquid and a gas. Indeed, in some specific situations involving very heterogeneous thermodynamic conditions at the interface, the distinction between boiling and evaporation is not always possible. For instance, it can occur for a Leidenfrost droplet; a water drop levitating above a hot plate whose temperature is much higher than the boiling temperature. In this case, boiling occurs in the film of saturated vapor which is entrapped between the bottom of the drop and the plate, whereas the top of the water droplet evaporates in contact of ambient air. The situation can also be ambiguous for a superheated droplet or at the contact line between a liquid and a hot wall whose temperature is higher than the saturation temperature of the liquid. In these situations, the interface temperature can locally reach the saturation temperature (boiling point), for instance near a contact line, and be cooler in other places. Thus, boiling and evaporation can occur simultaneously on different regions of the same liquid interface or occur successively at different times of the history of an evaporating droplet. Standard numerical methods are not able to perform computations in these transient regimes, therefore, we propose in this paper a novel numerical method to achieve this challenging task. Finally, we present several accuracy validations against theoretical solutions and experimental results to strengthen the relevance of this new method.

On two-phase flow solvers in irregular domains with contact line

We present numerical methods that enable the direct numerical simulation of two-phase flows in irregular domains. A method is presented to account for surface tension effects in a mesh cell containing a triple line between the liquid, gas and solid phases. Our numerical method is based on the level-set method to capture the liquid–gas interface and on the single-phase Navier–Stokes solver in irregular domain proposed in [35] to impose the solid boundary in an Eulerian framework. We also present a strategy for the implicit treatment of the viscous term and how to impose both a Neumann boundary condition and a jump condition when solving for the pressure field. Special care is given on how to take into account the contact angle, the no-slip boundary condition for the velocity field and the volume forces. Finally, we present numerical results in two and three spatial dimensions evaluating our simulations with several benchmarks.

Numerical study on the wettability dependent interaction of a rising bubble with a periodic open cellular structure

A phase-field method for interface resolving numerical simulations of two-phase flows with OpenFOAM® is validated for the buoyancy-driven rise of a single air bubble through a viscous stagnant liquid using experimental data from literature. The validation encompasses the terminal bubble rise velocity and the instantaneous cutting of the bubble by a solid horizontal cylinder. In the latter process, the numerical method takes into account the equilibrium contact angle of the three-phase system. The numerical method is then used to study the behavior of a single air bubble rising through a representative subdomain of a periodic open cellular structure (POCS) with cubic cell geometry filled with stagnant water. The results indicate that the bubble shape and path do significantly depend on the structure wettability. In the industrial application of POCS for enhancing mass transfer and as catalytic supports, the utilization of structures with high wettability (low contact angles) is expected to be beneficial.

A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows

A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21] ) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a typical chaotic structure in the flow field is observed at a Reynolds number of 10000, which indicates that the proposed model is a promising tool for direct numerical simulation of two-phase flows.

One-dimensional comparison of numerical approaches on two-phase flow in the membrane electrode assembly of PEMFC

Numerical simulation of two-phase flow is important for the performance evaluation of proton exchange membrane fuel cell (PEMFC). Exchange of water between vapor and liquid phases in the gas diffusion layer (GDL) was considered by Nguyen and co-workers (2000) using the evaporation and condensation rate constants. Hsuen and Yin (2011), in which a pseudo-phase-equilibrium function approximates the vapor/liquid phase equilibrium, proposed another two-phase flow approach. Both methods are capable of predicting the cell performance and the species concentration profiles in the membrane electrode assembly (MEA) without the need to track liquid water front in the GDL explicitly. The present study compares the numerical results of these two approaches in detail. In addition, one-dimensional simplified semi-analytical solution based on the instantaneous phase equilibrium assumption is used to validate the numerical calculations. The evaporation/condensation approach allows the existence of super-saturated vapor near the interface of cathode GDL and membrane. Thus, membrane can be better hydrated near the interface once liquid water emerges in the GDL as compared to the pseudo-phase equilibrium method. Consequently, smaller ohmic resistance and hence better cell performance are observed with Nguyen's prediction once liquid water appears in the GDL.

Choice of measure source terms in interface coupling for a model problem in gas dynamics

This paper is devoted to the mathematical and numerical analysis of a coupling procedure for one-dimensional Euler systems. The two systems have different closure laws and are coupled through a thin fixed interface. Following the work of [5], we propose to couple these systems by a bounded vector-valued Dirac measure, concentrated at the coupling interface, which in the applications may have a physical meaning. We show that the proposed framework allows to control the coupling conditions and we propose an approximate Riemann solver based on a relaxation approach preserving equilibrium solutions of the coupled problem. Numerical experiments in constrained optimization problems are then presented to assess the performances of the present method. 1. Introduction The study of large-scale and complex problems exhibiting a wide range of physical space and time scales (see for instance [62, 35, 14]), usually requires separate solvers adapted to the resolution of specific scales. This is the case of many industrial flows. Let us quote, for example, the numerical simulation of two-phase flows applied to the burning liquid oxygen-hydrogen gas in rocket engines [58]. This kind of flow contains both separated and dispersed two-phase flows, due to atomization and evaporation phenomena. This requires appropriate models and solvers for separated and dispersed phases that have to be appropriately coupled. Another example concerns turbomachine flows which can be modeled by the Euler equations of gas dynamics with different closure laws between the stages of the turbine, where the conditions of temperature and pressure are strongly heterogeneous. The coupling of these different systems is thus necessary to give a complete description of the flow inside the whole turbine. The method of interface coupling allows to represent the evolution of such flows, where different models are separated by fixed interfaces. First, coupling conditions are specified at the interface to exchange information between the systems. The definition of transmission conditions generally results from physical consideration, e.g. the conservation or the continuity of given variables. Then, the transmission conditions are represented at the discrete level. The study of interface coupling for nonlinear hyperbolic systems has received attention for several years. In [43], the authors study the scalar case from both mathematical and numerical points of view.

New Leakage Current Particulate Matter Sensor for On-Board Diagnostics

Structure and principle of the new leakage current particulate matter (PM) sensor are introduced and further study is performed on the PM sensor with the combination of numerical simulation and bench test. High voltage electrode, conductive shell, and heaters are all built-in. Based on the principle of Venturi tube and maze structure design, this sensor can detect transient PM concentrations. Internal flow field of the sensor and distribution condition of PM inside the sensor are analyzed through gas-solid two-phase flow numerical simulation. The experiment was also carried out on the whole sensor system (including mechanical and electronic circuit part) and the output signals were analyzed. The results of simulation and experiment reveal the possibility of PM concentration (mass) detection by the sensor.

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.

A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow

A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time energy inequality. An adaptive spatial discretization is proposed that conserves the energy inequality in the fully discrete setting by applying a suitable post processing step to the adaptive cycle. For the fully discrete scheme a quasi-reliable error estimator is derived which estimates the error both of the flow velocity, and of the phase field. The validity of the energy inequality in the fully discrete setting is numerically investigated.