Particles In Fluid Flow Research Articles

A pressure correction method for fluid-particle interaction flow: Direct-forcing method and sedimentation flow

A direct-forcing pressure correction method is developed to simulate fluid–particle interaction problems. In this paper, the sedimentation flow is investigated. This method uses a pressure correction method to solve incompressible flow fields. A direct-forcing method is introduced to capture the particle motions. It is found that the direct-forcing method can also be served as a wall-boundary condition. By applying Gauss's divergence theorem, the formulas for computing the hydrodynamic force and torque acting on the particle from flows are derived from the volume integral of the particle instead of the particle surface. The order of accuracy of the present method is demonstrated by the errors of velocity, pressure, and wall stress. To demonstrate the efficiency and capability of the present method, sedimentations of many spherical particles in an enclosure are simulated. Copyright © 2010 John Wiley & Sons, Ltd.

Reduction of a Urea Crystallizer Model by Proper Orthogonal Decomposition and Best-Points Interpolation

A reduced model of a urea crystallizer is developed for process control purposes. It is derived from a reference model, which describes the formation of particles in fluid flow and is of very high order. A strong reduction of the system order is achieved by proper orthogonal decomposition (POD). However, it turns out that POD alone does not lead to a satisfactory reduction of the computation time. The reason is the presence of nonlinear terms in the reference model whose evaluation is quite costly in the reduced model. To get a speed-up of the reduced model, the nonlinear terms are approximated by an interpolation technique. The resulting reduced model is 500 times smaller and 100 times faster than the reference model, while the loss of accuracy is marginal.

Waveform interpolation for applications of time-reversal acoustics.

Acoustic waves can force fluids and small objects along the direction of sound propagation (streaming). Potential applications include forcing the flow of fluid and small particles for drug delivery into the brain, or of underground fluids, such as oil, toward a borehole collection point. Well-focused beams are needed for amplitudes to be large enough to be effective. Time-reversal acoustics (TRA) permits focusing of sound in heterogeneous media, but requires a sensor near a point of desired focus. There is a need, addressed in this talk, to send signals off the grid of available sensors so that forces may be delivered in regions between receivers, and no receiver need be at a point where focus is desired. The Acoustic Shepherd introduces interpolation or data matching of TRA-derived Green functions for this purpose. One particular scheme of geometric-mean interpolation is analyzed, and the curve along which the focus moves from one receiver to another as the interpolating weights are varied is shown. General approximation methods from statistical estimation theory are also described. These methods are expected to work better in heterogeneous media (having unknown acoustic properties) than well-known beam forming methods designed for homogeneous media.

A level set approach for dilute non-collisional fluid-particle flows

Gas-particle and other dispersed-phase flows can be described by a kinetic equation containing terms for spatial transport, acceleration, and particle processes (such as evaporation or collisions). However, computing the dispersed velocity is a challenging task due to the large number of independent variables. A level set approach for computing dilute non-collisional fluid-particle flows is presented. We will consider the sprays governed by the Williams kinetic equation subject to initial distributions away from equilibrium of the form ∑i=1Nρi(x)δ(ξ-ui(x)). The dispersed velocity is described as the zero level set of a smooth function, which satisfies a transport equation. This together with the density weight recovers the particle distribution at any time. Moments of any desired order can be evaluated by a quadrature formula involving the level set function and the density weight. It is shown that the method can successfully handle highly non-equilibrium flows (e.g. impinging particle jets, jet crossing, particle rebound off walls, finite Stokes number flows).

Discrete particle simulation of particle–fluid flow: model formulations and their applicability

The approach of combining computational fluid dynamics (CFD) for continuum fluid and the discrete element method (DEM) for discrete particles has been increasingly used to study the fundamentals of coupled particle–fluid flows. Different CFD–DEM models have been used. However, the origin and the applicability of these models are not clearly understood. In this paper, the origin of different model formulations is discussed first. It shows that, in connection with the continuum approach, three sets of formulations exist in the CFD–DEM approach: an original format set I, and subsequent derivations of set II and set III, respectively, corresponding to the so-called model A and model B in the literature. A comparison and the applicability of the three models are assessed theoretically and then verified from the study of three representative particle–fluid flow systems: fluidization, pneumatic conveying and hydrocyclones. It is demonstrated that sets I and II are essentially the same, with small differences resulting from different mathematical or numerical treatments of a few terms in the original equation. Set III is however a simplified version of set I. The testing cases show that all the three models are applicable to gas fluidization and, to a large extent, pneumatic conveying. However, the application of set III is conditional, as demonstrated in the case of hydrocyclones. Strictly speaking, set III is only valid when fluid flow is steady and uniform. Set II and, in particular, set I, which is somehow forgotten in the literature, are recommended for the future CFD–DEM modelling of complex particle–fluid flow.

Modeling of transport phenomena during the coaxial laser direct deposition process

Laser direct deposition is widely used for rapid freeform fabrication of fully dense components with good metallurgical properties directly from computer-aided design drawings. Because of complex physics involved such as laser powder interaction, laser substrate interaction, track interface evolution, and melt-solid interaction, it is important to develop simulation models to better understand the characteristics and mechanisms in the process so that optimization and control of a laser direct deposition process are possible. In this paper, a new comprehensive three-dimensional self-consistent transient model is presented for a coaxial laser direct deposition process, which considers physical behaviors such as laser particle interaction, mass addition, heat transfer, fluid flow, melting, and solidification. A continuum model is built to deal with different phases (gas, liquid, solid, and mushy zone) in the calculation domain. An improved level-set method, which takes the conservative form while being implicitly solved with other governing equations, is proposed to track the evolution of free liquid/gas interface during the deposition process. To make the model more physically complete than those in the literature, a newly derived mass source term, which considers the rate of the gas phase being replaced by the deposited material due to the moving interface in some control volumes, is incorporated into the continuity equation. Corresponding new source terms of enthalpy and momentum due to the moving interface are also derived and embedded in the energy and momentum equations. The governing equations are discretized using the finite volume approach to better predict the fluid motion mainly driven by capillary and thermocapillary forces. The simulated track heights, widths, molten pool depths, and track profiles agree well with the experimental results.

An extension of the hard-sphere particle–particle collision model to study agglomeration

When performing Eulerian–Lagrangian simulations of particle–fluid flows collisions between the particles need to be accounted for. One of the methods used for this is the hard-sphere model. This model, however, does not take into account cohesive forces between the particles, and for this reason it is not able to simulate many aspects of real flows, such as the formation of agglomerates. There have been some attempts in literature to treat cohesive forces in simulations of particulate flows but none of these methods were actually implemented directly into the hard-sphere model but rather have been solved separately as a part of the numerical scheme. In this paper we show how the standard hard-sphere model may be extended to include these important interactions in an efficient and proper way. The extended model is presented in detail and some numerical results are shown.

Relation between segregation patterns and granular flow modes in conical rotating drum

Generally, it is difficult to observe, without any disturbance, flow structures or velocities inside flows such as granular flows, particle-fluid flows and so on. It is effective to use a non-contact and non-destructive measurement method for such flows. In the present paper, an MRI (Magnetic Resonance Imaging) technique is employed to measure the motion and velocity inside the flows. MRI has been applied to granular flows since about 1990. Our group has studied the particle motion inside the rotating drum using MRI. The rotating drum is industrial equipment which is widely utilized in engineering processes. In the cylindrical rotating drum it is well-known that axial and/or radial segregation take place. In the present study, we use a conical rotating drum which is sometimes employed in the granulation process. The conical rotating drum is half-filled with a mixture of two different sizes of spherical particles. We varied the rotational speed. Then we investigated the effect of the rotational speed on the axial segregation pattern and observed the flow mode.

J0502-2-2 高濃度固液混相流中の液体速度のMRI計測([J0502-2]混相流の多次元ビジュアリゼーション～流動場の光・電磁場・超音波センシング～(2))

It is difficult to apply optical techniques to the velocity measurement of the fluid-particle flows, especially when the volume fraction of particles becomes high, hi the present paper, the MRI (Magnetic Resonance Imaging) measurement is applied to dense liquid-particle flows. The velocity distribution of the liquid-particle flow is measured non-invasively by the phase method.

Colloid Retention in Porous Media of Various Porosities: Predictions by the Hemispheres-in-Cell Model

The hemispheres-in-cell model for colloid transport and deposition in simple granular filtration media preserves the utilities provided in the Happel sphere-in-cell but also incorporates features (e.g., grain-to-grain contact) that are shown to drive colloid deposition from experiments and simulations when colloid-surface repulsion exists (Ma, H.; Pedel, J.; Fife, P.; Johnson, W. P. Environ. Sci. Technol., 2009, in press). The capability of the hemispheres-in-cell model to predict colloid deposition in the absence of repulsive energy barriers for different particle sizes and fluid flow velocities was previously examined (Ma, H.; Pedel, J.; Fife, P.; Johnson, W. P. Environ. Sci. Technol., 2009, in press). In this article, we examine the influence of porosity on colloid deposition in terms of theoretical (simulated) collector efficiencies from the hemispheres-in-cell model, as well as existing models, to examine whether expected trends in porosity are similar among the different models. The need for experimentally determined collector efficiencies for porosities outside the range of 0.33-0.42 is highlighted. We demonstrate agreement between existing experimental results and our model predictions, indicating that the hemispheres-in-cell model can potentially serve as a new model geometry to develop a predictive theory of colloid filtration in the presence of energy barriers, a condition that is typical in environmental contexts.

A fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows

A third-order quadrature-based moment method for simulating dilute and moderately dilute fluid–particle flows has been implemented with full coupling in a computational fluid dynamics code. The solution algorithm for the particle phase uses a kinetic-based finite-volume technique to solve the velocity moment equations derived from kinetic theory. The procedure to couple the particle-phase volume-fraction and momentum equations with the Eulerian solver for the fluid phase is explained in detail. As an example application, simulations of a particle-laden vertical channel flow at fluid-phase Reynolds number 1379 and particle Stokes numbers 0.061 and 0.61 were carried out. The fluid and particle velocities, particle-phase volume fraction and granular temperature were observed to reach a steady state in the case of Stokes number 0.061, while instabilities that led to the formation of structures and initiated the particle segregation process were observed in the case with the higher Stokes number. These results are validated against results from a classical two-fluid model derived from the kinetic theory of granular flows in the small Knudsen number limit, and Euler–Lagrange simulations of the same flow.

Averaging method of particulate systems and its application to particle-fluid flow in a fluidized bed

A particulate system can be described through the discrete approach at the microscopic level or through the continuum approach at the macroscopic level. It is very significant to develop the method to link the two approaches for the development of models allowing a better understanding of the fundamentals of particulate systems. Several averaging methods have been proposed for this purpose in the past, but they mainly focused on cohesionless particle systems. In this work, a more general averaging method is proposed by extending it for cohesionless particle systems. The application of the method to the particle-fluid flow in a gas fluidized bed is studied. The density, velocity and stress of this flow are examined. A detailed discussion has been conducted to understand the dependence of the averaged variables on sample size.

Effect of particle and fluid properties on the pickup velocity of fine particles

Systems involving fluid–particle flows are a key component of many industrial processes, but they are not well-understood. One important parameter to consider when designing a conveying system is pickup velocity, the minimum fluid velocity required for particle entrainment. Many theoretical and experimental analyses have been performed to better understand pickup velocity, but there is little consistency with regard to system conditions, fluid properties, and particle characteristics, which makes comparisons between these studies very difficult. Although the proper design of many conveying systems requires the utilization of expressions that are applicable across a broad range of operating parameters, most expressions are system specific, which means that they are not extendable to other conditions. Also, there is currently an absence of a universal expression to predict particle entrainment in both gases and liquids. In this work, the pickup velocity of glass spheres, crushed glass, and stainless steel spheres in water has been measured for particles less than 450 μm. The effects of particle size, particle shape, and particle density are discussed and compared to the pickup velocity trends previously determined for similar gas-phase systems. In addition, the experimental data are used to assess an existing force balance model previously developed for gas-phase systems.

Higher-order quadrature-based moment methods for kinetic equations

Kinetic equations containing terms for spatial transport, body forces, and particle–particle collisions occur in many applications (e.g., rarefied gases, dilute granular gases, fluid-particle flows). The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables. A useful alternative is to reformulate the problem in terms of the moments of the velocity distribution function. Closure of the moment equations is challenging for flows sufficiently far away from the Maxwellian limit. In previous work, a quadrature-based third-order moment closure was derived for approximating solutions to the kinetic equation for arbitrary Knudsen number. A key component of quadrature-based closures is the moment-inversion algorithm used to find the non-negative weights and velocity abscissas. Here, a robust inversion procedure is proposed for three-component velocity moments up to ninth order. By reconstructing the velocity distribution function, the spatial fluxes in the moment equations are treated using a kinetic-based finite-volume solver. Because the quadrature-based moment method employs the moment transport equations directly instead of a discretized form of the kinetic equation, the mass, momentum and energy are conserved for arbitrary Knudsen and Mach numbers. The computational algorithm is tested for the Riemann shock problem and, for increasing Knudsen numbers (i.e. larger deviations from the Maxwellian limit), the accuracy of the moment closure is shown to be determined by the discrete representation of the spatial fluxes.

Current R&D Challenges for Fluidized Bed Processes in the Refining Industry

Fluidized bed processes are widely used in the refining industry, mostly for conversion applications (e.g. fluid catalytic cracking, fluid coking, residue hydroconversion, Fischer-Tropsch Synthesis, etc.). These are large scale processes operating under severe conditions. Fluidized bed processes involve many complex phenomena that need to be considered in order to ensure proper design, operation and reliability. There have been thousands of publications over many years in the field of fluidization, but some of the fundamentals of fluid-particle flows still remain to be clarified. As a consequence, scale-up and industrialization of new technologies or processes remain a difficult, challenging and risky task.IFP is deeply involved with fluidized bed processes used in the refining industry. Over the last twenty years, industrial developments and PhD studies were conducted to explore new concepts, to develop new technologies, to scale-up hydrodynamics, to understand and quantify key phenomena. This paper discusses R&D practices in the field and current challenges encountered, mostly based on IFP experience. It does not intend, however, to provide an extensive literature review of all topics addressed in this paper.Interactions between particles, multiphase flow and reactor geometries are complex issues in fluidized beds. Therefore, experimentation is required to study new concepts such as downflow systems, complex phenomena such as vaporization of droplets in contact with gas-particle systems. The design of the experiment and the development of appropriate instrumentation are never simple and in the absence of simple similarities, anticipation of the main flow features is unavoidable. Modeling of results is then mandatory in order to translate results to industrial perspectives. Over the last 15 years, CFD has appeared as a promising tool to describe multiphase flow phenomena in complex geometries. Unfortunately, the lack of theoretical models to describe gas particle flow, at least for Group A powders, still leads researchers to conduct experiments to validate simulations or to adjust the gas-particle closure equations to validate results. Furthermore, observation in industrial units, during start-up or under steady conditions, when possible, greatly aids in validating research efforts and methodology.Despite its maturity, our industry is moving forward. There are ongoing developments in the energy and fuels market as well as in environmental fields, but also in the scientific background available to describe multiphase flow. Therefore, evolutionary R&D in the field is still needed to progress in the description of complex phenomena in order to optimize reactors and technologies and to face the changes of our industry.

Analysis of Submarine Pipeline Scour Using Large-Eddy Simulation of Dense Particle-Liquid Flows

Using large-eddy simulation technique for dense particle-fluid flows, the current-induced scour is predicted for both the mono- and bidispersed systems below a horizontal submarine pipeline exposed to unidirectional flow. The simulations are four-way coupled, which implies that both solid-liquid and solid-solid interactions are taken into account. Particles are assumed to behave as viscoelastic solids during interactions with their neighboring particles, and their motion are predicted by a Lagrangian method. The interparticle normal and tangential contact forces between particles are calculated using a generalized Hertzian model. The other forces on a particle that are taken into account include gravitational pressure gradient force accounting for the acceleration of the displaced liquid, the drag force resulting from velocity difference with the surrounding liquid, and the Magnus and Saffman lift forces. The predicted scour profiles for monodispersed system are found to compare favorably with the laboratory observations. For the bidispersed system, a seepage flow underneath the pipe (which is a major factor to cause the onset of scour below the pipeline) is found to be weakened using an appropriate size for the sand bed. This fiffnding highlights the importance of the bed particle size distribution on the onset of scour below the pipelines.

Numerical Analysis of a Finite Element/Volume Penalty Method

We present here some contributions to the numerical analysis of the penalty method in the finite element context. We are especially interested in the ability provided by this approach to use Cartesian, non boundary-fitted meshes to solve elliptic problems in complicated domain. In the spirit of fictitious domains, the initial problem is replaced by a penalized one, posed over a simply shaped domain which covers the original one. This method relies on two parameters, namely h (space-discretization parameter) and $\varepsilon$ (penalty parameter). We propose here a general strategy to estimate the error in both parameters, and we present how it can be applied to various situations. We pay special attention to a scalar version of the rigid motion constraint for fluid-particle flows.

A new point-locating algorithm under three-dimensional hybrid meshes

When particles are traced individually in a numerical simulation of particle-fluid flow, a point-locating scheme is necessary to relate the coordinates of a given point to the grid cell containing it. A new point-locating scheme combining the advantages of the existing ones is presented in this paper. The new method is first explained in detail. Then its performance under three-dimensional hybrid meshes is compared with the existing approaches in the literature. The results show that the proposed method is efficient, multifunctional and easy to implement in a structured/unstructured fluid flow solver.

Effect of pulse modulation on particle growth during SiH4 plasma process

The effects of pulse modulation on particle growth by coagulation between particles in a pulsed SiH4 plas- ma reactor were analyzed by using a discrete-sectional method. At the start of the plasma discharge, there is high con- centration of small-sized particles, and, later, the large-sized particles appear and grow by coagulation between small- sized particles. During plasma-off, the monomer generation stops and the particle concentration decreases with time by the effects of particle coagulation and fluid flow. As the pulse frequency decreases or as the duty ratio increases, the large-sized particles grow faster because more monomer particles are generated during longer plasma-on time. These results show that the pulse modulation, the changes of pulse frequency and duty ratio, can play a key role in suppressing the particle growth in the pulsed plasma process efficiently. This study proves that the pulsed plasma process can be applied to reduce the particle contamination in the plasma process for preparation of high quality thin films.

Numerical simulation and experimental study of fluid–particle flows in a spouted bed

In this work, the Eulerian–Eulerian multiphase model is used in the computational simulation of fluid dynamics of spouted beds with two different geometries: conical–cylindrical and conical. For the conical–cylindrical spouted bed, the simulated results of radial velocities of particles with a 1.41 mm diameter along bed heights in the range of 0.022 to 0.318 m are compared with experimental values obtained by He et al. [Y.L. He, C.J. Lim, J.R. Grace and, J.X. Zhu, Measurements of Voidage Profiles in Spouted Beds, Canadian Journal of Chemical Engineering, 72 (1994), 229–234], and show a good agreement. The influence of static bed height on the characteristic curve is assessed through simulations using different airflow rates. The respective minimum spouting velocities are compared with experimental values and with values obtained through empirical correlations reported in the literature. The results of the CFD simulations show a deviation of 3.8% when compared with the experimental data, which is less than the aforementioned correlations. The stages of transition from the condition of static bed to spouting bed are presented through the simulation of solids volume fraction distribution and the radial profile of voidage in the spouting region. The characteristic curve and minimum spouting conditions for a simulated conical bed, with glass particles of 6 mm diameter are compared with the experimental results showing deviations of 12.1% for the pressure drop and 5.6% for the minimum spouting velocity.