Two-fluid Flow Research Articles

On the Rayleigh-Taylor instability for two uniform viscous incompressible flows

The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eulerian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in (unstable) equilibrium is analyzed. By a general method of studying a family of modes, the smooth (when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized problem. Then, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.

On Dual-Grid Level-Set Method for Computational-Electro-Multifluid-Dynamics Simulation

An axisymmetric Dual-Grid Level-Set Method (DGLSM) is proposed for transient simulation of two-fluid electrohydrodynamic flow. Level-set and electric field equations are solved on a uniform grid which is twice that for Navier-Stokes equations, for accurate computation of interface and forces due to surface tension and electric field. Code validation and performance study is done for two problems: coalescence and electric field-induced deformation of drops (both fluids leaky and perfect dielectrics). The DGLSM gives results of almost the same accuracy as a fine-grid-based traditional level-set method (LSM) in a computational time slightly more than that for a coarse-grid-based LSM.

Global classical solution for a three-dimensional viscous liquid-gas two-fluid flow model with vacuum

This is a continuation of the paper (J. Math. Phys., 52(2011), 093102). We consider the Cauchy problem to the three-dimensional viscous liquid-gas two-fluid flow model. The global existence of classical solution is proved, where the initial vacuum is allowed.

Modelling the non-equilibrium two-phase flow during depressurisation of CO2 pipelines

The development, testing and validation of a two-fluid transient flow model for simulating outflow following the failure of high pressure CO2 pipelines is presented. Thermal and mechanical non-equilibrium effects during depressurisation are accounted for by utilising simple constitutive relations describing inter-phase mass, heat and momentum transfer in terms of relaxation to equilibrium. Pipe wall/fluid heat exchange on the other hand is modelled by coupling the fluid model with a finite difference transient heat conduction model. The two-fluid transient flow model's performance is tested by comparison of the predicted transient pressure and temperature profiles along the pipeline against those based on the simplified homogeneous equilibrium model (HEM) as well as real data captured during the full bore rupture of a 260m long, 233mm internal diameter pipeline containing CO2 at 36bara and 273°C. The two-fluid model is found to produce a reasonably good degree of agreement with the experimental data throughout the depressurisation process. The HEM based flow model on the other hand performs well only near the rupture plane and during the early stages of the depressurisation process.

Integrity of estimates of the two-fluid model and gender impacts

This paper summarizes a research study to develop a methodology for utilizing naturalistic Global Positioning System (GPS) driving data for two-fluid model estimation. The two-fluid vehicular traffic flow model describes traffic flow on a street network as a mix of stopped and running vehicles. The parameters of the model essentially represent ‘free flow’ travel time and the level of interaction among vehicles. These parameters have traditionally been used to evaluate roadway networks and corridors with partially limited access. However, the two-fluid model has been found to be a direct result of driver behavior, and can also be used to represent behavioral aspects of driver populations, e.g., aggressiveness, passiveness, etc. Through these behavioral aspects they can also be related to safety on roadways. Due to which the two-fluid model can be considered to be a safety footprint for a particular road or individual driver. Due to which it is critical to understand factors that influence the two-fluid model. In this study, two-fluid models were estimated using naturalistic driving data collected with GPS data loggers in San Luis Obispo (SLO), California. Linear referencing in ArcMap was used to link the GPS data with roadway characteristic data for each element of the roadway network. The linear referencing methodology is the key to relate the GPS driving data with the elements of roadway network. This study explores two fundamental questions: (1) how sensitive are the estimates of the two fluid parameters to various samples? This question is fundamentally important to help define the integrity of the two-fluid model for planning and operational purposes. To this end we use a random sampling approach to address this question. (2) Are there behavioral differences across gender? This provides important behavioral insights on driving behavior across gender. Significant differences were observed between male and female drivers, with female drivers being more aggressive.

Two-fluid compressible simulations on GPU cluster

In this work we propose an efficient finite volume approximation of twofluid flows. Our scheme is based on three ingredients. We first construct a conservative scheme that removes the pressure oscillations phenomenon at the interface. The construction relies on a random sampling at the interface [6, 5]. Secondly, we replace the exact Riemann solver by a faster relaxation Riemann solver with good stability properties [4]. Finally, we apply Strang directional splitting and optimized memory transpositions in order to achieve high performance on Graphics Processing Unit (GPU) or GPU cluster computations.

Influence of magnetic field and heat transfer on two-phase fluid model for oscillatory blood flow in an arterial stenosis

The unsteady two-fluid blood flow model in an artery with mild stenosis is considered by taking into account of effects of both heat transfer and magnetic field. Such a combination has not been reported in the literature of blood flow. The effects of plasma layer thickness, magnetic field, radiation parameter, thermal conductivity and viscosity ratio on flow variables are discussed and depicted graphically. The phase lag between pressure gradient and flow variables has been predicted and the effects of magnetic and radiation parameters, thermal conductivity, plasma layer thickness and Grashof number on the phase lag are brought out which form new information that are, for the first time, added to the literature. It has been pointed out here that the temperature and shear stress (or wall shear stress) decrease with increasing of plasma layer thickness. The flow resistance decreases with the increase in Grashof number and plasma layer thickness. Hence, the existence of the peripheral plasma layer and the pivotal role of Grashof number could be useful for the functions of the diseased arterial system and hence it is concluded that the present study is believed to yield some good improvement over two-fluid models discussed in the literature.

Sub-harmonic resonant wave interactions in the presence of a linear interfacial instability

This work considers the role of nonlinear sub-harmonic resonant wave interactions in the development of interfacial waves, which may be under the influence of a linear interfacial instability, in an inviscid two-fluid stratified flow through a horizontal channel. We begin by examining the case of resonant interactions between one linearly unstable mode and its sub-harmonic that may be linearly stable or unstable. Using the method of multiple scales, we derive the nonlinear interaction equations governing the time evolution of interacting wave amplitudes. These nonlinear equations account for the combined effects of both the nonlinear resonant interaction and the linear instability. We show that through this nonlinear coupling, the linearly stable sub-harmonic mode can achieve faster than exponential growth. It is found that such a mechanism is capable of generating large-amplitude long waves that are stable by linear stability analysis. The analytical predictions are cross validated by comparisons with direct nonlinear numerical simulations based on a more general perturbation based spectral method. Good agreement between the analytical and numerical solutions is observed. The more complicated case where a single mode is simultaneously involved in multiple (sub-harmonic and triad) resonances is also investigated numerically. The results demonstrate that chains of resonances can permit the energy generated by the linear instability, among high wavenumber components, to be passed across the spectrum to the longest wave components creating an efficient mechanism for the generation of large-amplitude long waves from unstable short waves.

Dynamic Effect of Capillary Pressure in Tight Gas Reservoir

Standard theories for two-fluid flow in porous media assume capillary pressure to be in equilibrium. Numerical simulators often assume that equilibrium capillary pressure-saturation conditions are maintained as changes in fluid satu- ration are taking place. But recent theories indicate that capillary pressure is perhaps not only a function of saturation but also rate change, which is known as the dynamic effect. In order to investigate effects of the dynamic capillary pressure on fluid flow in tight gas reservoirs, standard theory and present novel pore-scale and Darcy-scale theoretical approaches that account for a dynamic capillary pressure were reviewed in this paper. A dynamic capillary pressure relationship was included in the mathematical and numerical schemes were proposed to simulate tight gas reservoir production, which al- lows one to identify previously unreported flow scenarios. The numerical schemes were also to modify the Gray and Has- sanizadeh equation for infiltration to account for a capillary pressure that depends on the flow velocity. This study is of great benefit to finding out the flow law of tight gas reservoir and the subsequent work of exploitation.

Modeling of Heat Transfer Across the Interface in Two-Fluid Flows

A model is presented in this article to deal with heat transfer across the interface separating two immiscible fluids. It is suitable to be incorporated into interface-tracking methods, such as volume-of-fluid (VOF) methods, because a sharp interface is available in these approaches. The temperature at the interface and the heat flux through it are calculated in such a way that the continuity of the two properties at the contact surface is satisfied explicitly. With use of these values, the temperature either at the centroid or on a face of the interface cell can be estimated, which serves as Dirichlet boundary condition for the energy equation. The temperature field is then calculated by solving the energy equations for the two fluids simultaneously in an implicit way. This method is first assessed via testing on two heat conduction problems in which two solids are in contact. Good agreement between numerical solutions and theory is obtained. To demonstrate its capability, it is applied to two kinds of heat transfer problems, one being the collapse of a heated water column in a cavity, and the other the falling of a molten tin droplet in an oil tank. The effect of fluid flow on the heat transfer is clearly illustrated.

The Immersed Interface Method for Simulating Two-Fluid Flows

The Immersed Interface Method for Simulating Two-Fluid Flows

A fast pressure-correction method for incompressible two-fluid flows

We have developed a new pressure-correction method for simulating incompressible two-fluid flows with large density and viscosity ratios. The method's main advantage is that the variable coefficient Poisson equation that arises in solving the incompressible Navier–Stokes equations for two-fluid flows is reduced to a constant coefficient equation, which can be solved with an FFT-based, fast Poisson solver. This reduction is achieved by splitting the variable density pressure gradient term in the governing equations. The validity of this splitting is demonstrated from our numerical tests, and it is explained from a physical viewpoint.In this paper, the new pressure-correction method is coupled with a mass-conserving volume-of-fluid method to capture the motion of the interface between the two fluids but, in general, it could be coupled with other interface advection methods such as level-set, phase-field, or front-tracking. First, we verified the new pressure-correction method using the capillary wave test-case up to density and viscosity ratios of 10,000. Then, we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value. Next, the method is shown to be second-order accurate in space and time independent of the VoF method, and it conserves mass, momentum, and kinetic energy in the inviscid limit. Also, we show that for solving the two-fluid Navier–Stokes equations, the method is 10–40 times faster than the standard pressure-correction method, which uses multigrid to solve the variable coefficient Poisson equation. Finally, we show that the method is capable of performing fully-resolved direct numerical simulation (DNS) of droplet-laden isotropic turbulence with thousands of droplets using a computational mesh of 10243 points.

CFD Simulation of Hydrodynamics and Methanation Reactions in a Fluidized-Bed Reactor for the Production of Synthetic Natural Gas

Numerical investigations of hydrodynamics and kinetic reactions in a fluidized bed methanation reactor are carried out by coupling methanation kinetics with the two-fluid flow model. The gas–solid reacting flow models are implemented within OpenFOAM software. The grid resolution is investigated using two-dimensional and three-dimensional (2D and 3D) meshes. The bed height is reasonably predicted with the Gidaspow and Syamlal models. Simulated results are compared against experimental data in the literature. The simulated axial species concentrations agree well with the measured results at the end of the bed. The effects of different operating parameters are evaluated using the established models. The increase in the gas inlet velocity results in more dilute solid concentration and larger bed expansion. The weak bed expansion results from the methanation reaction with gas volume reduction. The methane concentration is increased when increasing catalyst inventory in the reactor. The addition of water into t...

Engineering Analysis and Design with ALE-VMS and Space–Time Methods

Flow problems with moving boundaries and interfaces include fluid–structure interaction (FSI) and a number of other classes of problems, have an important place in engineering analysis and design, and offer some formidable computational challenges. Bringing solution and analysis to them motivated the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method and also the variational multiscale version of the Arbitrary Lagrangian–Eulerian method (ALE-VMS). Since their inception, these two methods and their improved versions have been applied to a diverse set of challenging problems with a common core computational technology need. The classes of problems solved include free-surface and two-fluid flows, fluid–object and fluid–particle interaction, FSI, and flows with solid surfaces in fast, linear or rotational relative motion. Some of the most challenging FSI problems, including parachute FSI, wind-turbine FSI and arterial FSI, are being solved and analyzed with the DSD/SST and ALE-VMS methods as core technologies. Better accuracy and improved turbulence modeling were brought with the recently-introduced VMS version of the DSD/SST method, which is called DSD/SST-VMST (also ST-VMS). In specific classes of problems, such as parachute FSI, arterial FSI, ship hydrodynamics, fluid–object interaction, aerodynamics of flapping wings, and wind-turbine aerodynamics and FSI, the scope and accuracy of the FSI modeling were increased with the special ALE-VMS and ST FSI techniques targeting each of those classes of problems. This article provides an overview of the core ALE-VMS and ST FSI techniques, their recent versions, and the special ALE-VMS and ST FSI techniques. It also provides examples of challenging problems solved and analyzed in parachute FSI, arterial FSI, ship hydrodynamics, aerodynamics of flapping wings, wind-turbine aerodynamics, and bridge-deck aerodynamics and vortex-induced vibrations.

Visualization of two-fluid flows of superfluid helium-4

Cryogenic flow visualization techniques have been proved in recent years to be a very powerful experimental method to study superfluid turbulence. Micron-sized solid particles and metastable helium molecules are specifically being used to investigate in detail the dynamics of quantum flows. These studies belong to a well-established, interdisciplinary line of inquiry that focuses on the deeper understanding of turbulence, one of the open problem of modern physics, relevant to many research fields, ranging from fluid mechanics to cosmology. Progress made to date is discussed, to highlight its relevance to a wider scientific community, and future directions are outlined. The latter include, e.g., detailed studies of normal-fluid turbulence, dissipative mechanisms, and unsteady/oscillatory flows.

Computational simulation of the interactions between moving rigid bodies and incompressible two-fluid flows

We present a two-dimensional computational flow solver for simulation of two-way interactions between moving rigid bodies and two-fluid flows. The fluids are assumed to be incompressible and immiscible. The two-step projection method along with Graphics Processing Unit (GPU) acceleration is employed to solve the flow equations. The fluid–solid interaction is captured by using the fictitious domain method. A consistent mass and momentum scheme is implemented, which allows for simulation of multiphase flows characterized by large density ratios. The evolution of interfaces in the three-phase system is tracked by using the volume-of-fluid method with two scalar functions, representing the solid domain and one of the fluids. A geometrical approach is employed to reconstruct the interfaces in cells containing three phases and capture the intersection of phase interfaces (triple point). The performance and accuracy of the flow solver are assessed through a set of canonical test cases. Then, it is used to simulate the interactions between a free-floating buoy and waves generated by a bottom-hinged paddle in a wave tank.

Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios

We present the development of a Lattice Boltzmann Method (LBM) for the numerical simulation of multiphase flows with high density ratios, such as found in ocean surface wave and air–sea interaction problems, and its efficient implementation on a massively parallel General Purpose Graphical Processing Unit (GPGPU). The LBM extends Inamuro’s et al.’s (2004) multiphase method by solving the Cahn–Hilliard equation on the basis of a rigorously derived diffusive interface model. Similar to Inamuro et al., instabilities resulting from high density ratios are eliminated by solving an additional Poisson equation for the fluid pressure. We first show that LBM results obtained on a GPGPU agree well with standard analytic benchmark problems for: (i) a two-fluid laminar Poiseuille flow between infinite plates, where numerical errors exhibit the expected convergence as a function of the spatial discretization; and (ii) a stationary droplet case, which validates the accuracy of the surface tension force treatment as well as its convergence with increasing grid resolution. Then, simulations of a rising bubble simultaneously validate the modeling of viscosity (including drag forces) and surface tension effects at the fluid interface, for an unsteady flow case. Finally, the numerical validation of more complex flows, such as Rayleigh–Taylor instability and wave breaking, is investigated. In all cases, numerical results agree well with reference data, indicating that the newly developed model can be used as an accurate tool for investigating the complex physics of multiphase flows with high density ratios. Importantly, the GPGPU implementation proves highly efficient for this type of models, yielding large speed-ups of computational time. Although only two-dimensional cases are presented here, for which computational effort is low, the LBM model can (and will) be implemented in three-dimensions in future work, which makes it very important using an efficient solution.

On Two-Fluid Blood Flow through Stenosed Artery with Permeable Wall

The present investigation concerns the fluid mechanical study on the effects of the permeability of the wall through an axisymmetric stenosis in an artery assuming that the flowing blood is represented by a two-fluid model. The expressions for the blood flow characteristics, the impedance, the wall shear stress distribution in the stenotic region and the shearing stress at the stenosis throat have been derived. Results for the effects of permeability as well as of the peripheral layer on these blood flow characteristics are quantified through numerical computations and presented graphically and discussed comparatively to validate the applicability of the present model.

On Two-Fluid Blood Flow through Stenosed Artery with Permeable Wall

The present investigation concerns the fluid mechanical study on the effects of the permeability of the wall through an axisymmetric stenosis in an artery assuming that the flowing blood is represented by a two-fluid model. The expressions for the blood flow characteristics, the impedance, the wall shear stress distribution in the stenotic region and the shearing stress at the stenosis throat have been derived. Results for the effects of permeability as well as of the peripheral layer on these blood flow characteristics are quantified through numerical computations and presented graphically and discussed comparatively to validate the applicability of the present model.

An Estimation Method of Water Drive Displacement Based on Formation Permeability Distribution and Inverse Problem Modeling

Formation permeability distribution is important in the oil industry since it is a key tool in forecasting oil production performance, a matter of primary concern to oilfield operators. However, the direct problems of reservoir analysis are limited in practice by a lack of input parameters such as reservoir vertical heterogeneity. Therefore, inverse problem modeling is important to achieve reservoir vertical heterogeneity using production profiles, which are always known for existing reservoirs. In this way, what has occurred inside a reservoir can be understood by applying reservoir output in the reverse model. Because formation permeability can frequently be represented by a normal distribution and can describe heterogeneity and water production capability, an inverse problem of formation permeability was modeled to study reservoir vertical heterogeneity and reservoir production performance based on oil-water two-fluid flow theory and optimization problems. Moreover, through establishing an objective function, we obtained an optimal solution for water production rate. Finally, one case is simulated by this model and good results achieved, which are compatible with production and experimental data.