A review of spurious currents in the lattice Boltzmann method for multiphase flows

A spurious current is a small-amplitude artificial velocity field which arises from an imbalance between discretized forces in multiphase/multi-component flows. If it occurs, the velocity field may persist indefinitely, preventing the achievement of a true equilibrium state. Spurious velocities can sometimes be as large as the characteristic velocities of the problem, causing severe instability and ambiguity between physical and spurious velocities. They are typically exacerbated by large values of numerical surface tension or when the two fluids being simulated have large density ratios. The resulting instability can restrict what parameters may be simulated. To varying degrees, spurious currents are found in all multiphase flow models of the lattice Boltzmann method (LBM). There have been many studies of the occurrence of the phenomenon, and many suggestions on how to eliminate it. This paper reviews the three main models of simulating multiphase/multi-component flow in the lattice Boltzmann method, as well as the subsequent modifications made in order to reduce or eliminate spurious currents.     

Performance analysis of a single-wire capacitance sensor for interface level measurement in stratified multiphase flows

A single-wire capacitance sensor can be used to measure the interface level of a conductive liquid in a stratified multiphase flow. This type of capacitive sensor uses the conducting core in an insulated wire as its first electrode, and the conductive fluid as its second electrode, separated by the wire insulation, producing a coaxial capacitor with a variable electrode length linearly correlated to the liquid level. Therefore in theory, there should be a linear relationship between the liquid level and measured capacitance value. However, at low liquid levels, the authors have observed a noticeable departure from the theoretical correlation in the way of an upward offset. The cause for such a departure is investigated by means of a simplified model geometry and attributed to an additional capacitance between the wire conductor and conductive plane provided by the liquid interface. Analytical and numerical modelling have been carried out to better understand this effect. Recommendations are given on how to correct it.     

Numerical simulation of multiphase flows with material interface on an unstructured grid system

Two-dimensional multiphase flows with material interface due to density difference are numerically simulated on an unstructured grid system by a Navier-Stokes solver developed by Myong and Kim (2006), since numerical computation for these flows is still known to be difficult, especially if the interface separates fluids of large different densities. This solver employs an unstructured cell-centered method based on a conservative pressure-based finite volume method, since the unstructured grid approach makes the solver very flexible in dealing with complex boundaries, and adopts a high resolution method (CICSAM) in a volume of fluid (VOF) scheme for the accurate phase interface capturing. The test cases are the Rayleigh-Taylor instability (density ratio of 2), the oil bubble rising in a partially filled container (density ratio of 2), the air bubble rising in a fully filled container with bubble shedding (density ratio of 100) and the droplet splash (density ratio of about 1000), which are typical benchmark problems among multiphase flows with material interface due to density difference. The present results are compared with other numerical solutions found in the literature. The present method (solver) efficiently and accurately simulates complex interface flows such as multiphase flows with material interface due to both density difference and instability.     

A new visualisation and measurement technology for water continuous multiphase flows

This paper reports the performance of a research prototype of a new multiphase flow instrument to non-invasively measure the phase flow rates, with the capability to rapidly image the flow distributions of two- and three-phase (gas and/or oil in water) flows. The research prototype is based on the novel concepts of combining vector Electrical Impedance Tomography (EIT) sensor (for measuring dispersed-phase velocity and fraction) with an electromagnetic flow metre (EMF, for measuring continuous-phase velocity with the EIT input) and a gradiomanometer flow-mixture density metre (FDM), in addition to on-line water conductivity, temperature and absolute pressure measurements. EIT–EMF–FDM data fusion embedded in the research prototype, including online calibration/compensation of conductivity change due to the change of fluids' temperature or ionic concentration, enables the determination of mean concentration, mean velocity and hence the mean flow rate of each individual phase based on the measurement of dispersed-phase distributions and velocity profiles. Results from first flow-loop experiments conducted at Schlumberger Gould Research (SGR) will be described. The performance of the research prototype in flow-rate measurements are evaluated by comparison with the flow-loop references. The results indicate that optimum performance of the research prototype for three-phase flows is confined within the measuring envelope 45–100% Water-in-Liquid Ratio (WLR) and 0–45% Gas Volume Fraction (GVF). Within the scope of this joint research project funded by the UK Engineering & Physical Sciences Research Council (EPSRC), only vertical flows with a conductive continuous liquid phase will be addressed.     

Impedance mapping of particulate multiphase flows

Multiphase flows occur in many operations in the chemical, petroleum and power generation industries, which cover both multi-component and multiphase situations, such air–water, solid–water, steam and air–oil–water as well as their combinations. Due to the correlation of the multiphase and independence of each phase, the correct measuring of multiphase flow, in terms of concentration, local velocity and mass flow rate, is an extremely challenging task. Electrical resistance tomography has been used for visualisation of the concentration profiles and characterisation of fluid dynamics in particulate two-phase systems that have impedance contract between the main fluid and the second phase fluid or component clusters. This paper reviews the author’s and his colleagues’ previous and current work on electrical resistance tomography, particularly on sensing strategies, data collection systems and image reconstruction algorithms. Recent applications on the characterisations of mixing processing, solid–water and the control of a bubble column are introduced.     

Applications of wire-mesh sensors in multiphase flows

This article offers an overview of the applications of the wire-mesh sensor (WMS) in different environments. It presents a critical review of the literature, with relevant and recent implementations, remarkably in gas–liquid and liquid–liquid flow, comparing it with other techniques. In addition, it is shown how the sensor is adapted to each application and its different geometries, showing its flexibility. The advantages and disadvantages of the use of the WMS are analyzed. This technique can provide information about local, chordal, cross-section or in-situ volume profiles/distributions of phase fraction; velocities, size and distributions of droplets/bubbles; frequency of periodic structures; interfacial area; film thickness; flow regimes and thermal distribution.     

Transient analysis for compressible fluid flow in transmission line by the method of characteristics

Transient analysis for compressible fluid flow has been conducted to evaluate the dynamic characteristics of the dead-ended or volume-terminated transmission lines following a sudden pressure change at its entrance. The two partial-differential equations, based on the conservation of mass, energy and momentum, were derived for the one-dimensional adiabatic compressible flow with friction and entrance head loss. The governing equations describing the present transient-state flow are hyperbolic, and the boundary conditions include a fixed volume termination at the exit and sinusoidal disturbance in the sudden pressure change at tube entrance. The method of characteristics is used to transform the partial differential equation into the particular total differential equations, which can be integrated along the characteristic lines. The present result shows good agreements with the existing results. The effects of tube length. tube diameter and end volume are evaluated on the responses of the pressure and on the damping factor.     

A light-erosion method for high-pressure dust-gas-plasma flows generation

A light-erosion method for generating high-pressure dust-gas-plasma flows during ultraviolet (λ = 213 nm) laser ablation of a polymeric matrix ((C₂F₄) _n ) containing dust particles (thin-wall borosilicate glass microspheres with a ∼15- to 80-μm diameter d) is described. The carrying-out of the dust particles by ionized vapors of the substance of the target matrix, their space-time localization in the gas-plasma flow in a period Δτ ∼ 15–75 μs after the laser exposure up to the further spatial separation of the vaporized substance of the target matrix and the dust particle cloud is recorded by laser interferometry and shadow photography methods. The importance of certain selection of the matrix-dust system for realizing the light-erosion method for generating dust-gas-plasma flows, in particular laser exposure conditions, is shown. When condensed media with a low ionization potential (Al, Ce) are used as a dust component, the proposed method for generating heterogeneous gas-plasma flows can be efficient for their further heating by coherent radiation.     

Digital imaging measurement of dense multiphase flows in industrial processes

This paper presents a submersible imaging system for investigations of multiphase flows in various industrial applications. Our objective is to visualize and online monitor complex multiphase flows that take place in industrial process devices (e.g., reactors, channels and flotation tanks) of chemical and paper industries. The system presented, including a laptop computer, CCD camera and pulsed, optical fibre-coupled diode laser, is designed for industry-scale, in situ measurements of dispersed phase particle properties (size, shape and velocity). The system has been successfully tested in a waste water dissolved air flotation (DAF) tank, in a white water de-aeration channel, in a deinking flotation cell Metso OptiCell and in a plastic bead production reactor, where the hot and pressurized plastic bead production process is monitored through a submersed pipe. New image processing techniques and system modifications are presented based on the test experiences.     

Constitutive relations for compressible granular materials using non-Newtonian fluid mechanics

This paper is about constitutive relations which can model the flow of granular materials with cohesion, friction, and collisions between particles. The constitutive model represents compressible viscoplastic fluids with second-order effects, in which the Cauchy stress tensor depends on the velocity components and on the rate of volume distribution. An alternative model employs the maximum volume distribution to take second-order effects into account. It is shown that the simplification of the model in which compressibility and second-order effects are neglected leads to the constitutive model of Diez and Godoy. The formulation is employed to solve the flow through an inclined channel, for which the problem reducesto a one-dimensional situation. Explicit solutions are obtained for this case, and are presented in some detail for different degrees of approximation. The results are compared with theoretical values by other authors and with experimental data available in the literature, by Drake and Walton and by Savage, with excellent agreement. The constitutive equation in which second-order terms are a function of the volume distribution is the most general of the constitutive relations presented.     

Development of separation and blockage in branched converging compressible flows

The development of separation and steady state blockage in three different experiments in which two high speed flows converge on the junction formed by intersecting ducts is compared with calculations of the inviscid flow field. Agreement between the two are satisfactory. The calculated flow field is derived by the Fluid-in-Cell finite difference method.     

A neural network developed in a Foundation Fieldbus environment to calculate flow rates for compressible fluid

This paper proposes the development of an artificial neural network multilayer perceptron, implemented in a Foundation Fieldbus environment, to calculate the flow rate of natural gas by using an orifice plate in a closed pipe. The principal benefit of using neural networks lies in their low computational cost and simplicity of implementation, which allows just standard blocks to be used, making the technology independent of the Foundation Fieldbus system manufacturer. To perform the calculation, the proposed methodology relies on static pressure, temperature and differential pressure measurements, which are typically available in industrial plants. The developed methodology generates highly accurate results, and this approach can be implemented at a relatively low cost for Foundation Fieldbus system users.     

Three-dimensional MHD simulations of the electromagnetic flowmeter for laminar and turbulent flows

The interaction between an electrically conducting fluid and an external magnetic field in an ideal cylindrical electromagnetic flowmeter is numerically investigated for both laminar and turbulent flows. Induced electric potential in the fluid, and the difference in potential at the measuring electrodes are directly obtained by including MHD effects in the CFD simulations. Fully developed laminar and turbulent flows are simulated. The computed electric potential difference on the electrodes agrees with analytical values for small Hartmann number cases, where the induced Lorentz force is small. Turbulent flow produces a more uniform electric potential distribution in the flow meter cross-section than laminar flow. These integrated MHD/CFD simulations couple the MHD effect with flow dynamics without deriving a weighting function with an assumed velocity profile, which will be necessary for electromagnetic flow meters when the Hartmann number is not small.     

Numerical modeling of heat and mass diffusion in compressible low speed flows

Numerical modeling of the heat transfer and molecular mixing in an electrical furnace designed for the spectroscopic study of hydrogen/alkali-metal-vapor mixtures is described. The gases enter the furnace through three concentric tubes, the inner two of which contain the test gases while the outer contains a guard gas to protect the windows. The inner tubes terminate prior to the measurement section to allow the gases to mix. Heating is accomplished through contact with the wall of the outer tube. An implicit time-marching procedure including a preconditioning method is used to compute the coupled gas flows. The results show that optimum flow speeds occur at a Reynolds number of order ten. Higher speeds do not allow adequate heating or mixing and can become unsteady, while lower speeds allow considerable back diffusion in the concentric tubes.     

提高关联成像重构质量的研究

比较基于压缩感知关联成像(CGI)与伪逆关联成像(PGI)两者之间的成像效果差异,探讨形态学权重自适应对关联成像去除噪声的效果。选择不同的图像,通过MATLAB软件开展仿真实验,对目标图像分别采样64、256、512、1 024、2 048、3 000次,首先通过关联成像、基于压缩感知关联成像与伪逆关联成像三种方法重构图像,再对比压缩感知与伪逆两种方法重构图像的效果,以峰值信噪比(PSNR)、相关系数(CC)为量化指标,将基于压缩感知关联成像与伪逆关联成像在不同采样次数下进行对比分析。同时,通过实验分析形态学权重自适应去除关联成像中噪声的效果。伪逆关联成像在低次数采样的情况下比基于压缩感知关联成像的成像效果更好,在高采样次数下,基于压缩感知关联成像的成像效果更好。在实际重构中压缩感知关联成像重构的图像仍有噪声,形态学权重自适应可以有效去除关联成像实验中产生的噪声。     

The effect of second order refraction on optical bubble sizing in multiphase flows

In multiphase flow research and many industrial applications it is important to determine the bubble size and velocity. To achieve this, one of approaches is to utilize laser phase-Doppler anemometry. However, it was found that the second order refraction has great impact on PDA sizing method when the relative refractive index of media is less than one. In this paper, the problem of second order refraction is investigated and a model of phase-size correlation to eliminate the measurement errors is introduced for bubble sizing. As a result, the model relaxes the assumption of single scattering mechanism in conventional phase-Doppler anemometry. The results of simulations based on this new model by using Generalized Lorenz Mie Theory (GLMT) are compared with those based on the conventional method. An optimization method for accurately sizing air-bubble in water has been suggested.     

Ultrasonic speckle correlation imaging of 2D particle velocity profiles in multiphase flows

Two-dimensional ultrasonic speckle correlation velocimetry (USV) is a new technique that allows imaging of moving scattering media, at a high frame-rate. In this paper we apply the technique to determine two-dimensional particle velocity profiles of multiphase flows. Experiments are realized with suspensions of Sonazoid (medical contrast agent) and Magnetite (Fe₃O₄) in water. All measurements are performed in a vertical pipe with the flow moving downwards. The two-dimensional particle velocity profiles are then compared with a reference liquid volume flow velocity. As expected from theory, the heavier Magnetite particles have slightly higher velocity than the liquid, whereas the contrast agent simply follows the liquid motion.The proposed technique can be used in combination with other techniques to measure the mass flow of the solid phase, in solid/liquid multiphase flow. This is generally more interesting than measuring the bulk mass or volume flow.     

A new yield function for compressible materials

A new yield function for compressible materials has been derived based upon a yield criterion postulated by the authors. This function was experimentally verified for the uniaxial state of compressive stress using the aluminum alloy X7091 as a model material, and excellent agreement was found between theoretical and experimental results for the density dependence of the yield and geometrical hardening. Yield surfaces for various density levels have been generated in a three-dimensional principal-stress space using computer graphics.     

Numerical simulations of impact flows with incompressible smoothed particle hydrodynamics

A 2D incompressible smoothed particle hydrodynamics (SPH) method is implemented to simulate the impact flows associated with complex free surface. In the incompressible SPH framework, pressure Poisson equation (PPE) based on the projection method is solved using a semi-implicit scheme to evaluate the correct pressure distribution. In this procedure, the PPE comprises the divergence-free velocity condition and density-invariance condition with a relaxation parameter. To test the accuracy and efficiency of the proposed incompressible SPH method, it was applied to several sample problems with largely distorted free surface, including 2D dam-break over horizontal and inclined planes with different inclination angles, as well as the water entry of a circular cylinder into a tank. We mainly focused on the time history of impact pressure on various positions of the solid boundary and temporal evolution of free surface profiles. The results showed reasonably good agreement with experimental data. However, further improvement is needed for extremely high impact flow.