Dispersed Multiphase Flows Research Articles

Laminar flow past an infinite planar array of fixed particles: point-particle approximation, Oseen equations and resolved simulations

In the point-particle model of disperse multiphase flow, the particles, assumed to be very small compared with all the scales of the flow, are represented by singular forces acting on the fluid. The hydrodynamic forces are found from standard correlations by interpolating the velocity field from the grid nodes to the particle positions, with the implicit assumption that the computational cells are much larger than the particles. It is argued here that this model has similarities with the Oseen linearization of the Navier–Stokes equation, the most important one being that, in the Oseen context, the particles are also treated, to leading order, as singularities. For this and other reasons addressed in the paper, the Oseen equations can be used as proxies for the point-particle model and the comparison of their solutions with particle-resolved simulations, both of which are presented in this paper, can shed light on the strengths and weaknesses of the point-particle model. The specific situation considered is the laminar, steady, uniform flow normal to a plane of periodically arranged particles exchanging momentum and heat with the fluid.

Resolved particle simulations using the Physalis method on many GPUs

We present a distributed memory many-GPU implementation of the Physalis method for resolving spherical particles in disperse multiphase flow simulations. The current work extends a previous single-GPU computational procedure by implementing a distributed memory Poisson solver and distributed finite-size particle methods using MPI. We document the changes required to move to a distributed memory model for both the fluid and solid phases. We benchmark the code with up to one million resolved particles in a domain size of 19203 on 216 GPUs at the Maryland Advanced Research Computing Center and present strong and weak scaling results. Finally, by taking advantage of the realization that the solution procedure for the pressure Poisson equation can be implemented using a symmetric matrix, we are able to replace the biconjugate gradient stabilized algorithm used in previous work with the conjugate gradient algorithm.

A dynamic spectrally enriched subgrid-scale model for preferential concentration in particle-laden turbulence

A new subgrid-scale (SGS) model for turbulent velocity fluctuations is proposed for large-eddy simulations (LES) of dispersed multi-phase flows. The modeled velocity contains scales smaller than the LES grid resolution, thereby enabling the prediction of small-scale phenomena such as the preferential concentration of particles in high-strain regions. The construction of the spectrally enriched velocity field in physical space is made dynamically, and is based on (1) modeling the smallest resolved eddies of sizes comparable to the LES grid size via approximate deconvolution, and (2) reconstructing the SGS fluctuations via non-linear generation of small-scale turbulence. The model does not contain tunable parameters, can be deployed in non-uniform grids, and is applicable to inhomogeneous flows subject to arbitrary boundary conditions. The performance of the model is assessed in LES of isotropic turbulence laden with inertial particles, where improved agreement with direct numerical simulation results is obtained for the statistics of preferential concentration.

Higher-order moment models for laminar multiphase flows with accurate particle-stream crossing

Modelling of laminar multiphase flow is extremely important in a wide range of engineering and scientific applications. The particle phases are often difficult to model, especially when particles display a range of velocities at each location in space. Lagrangian method can be too costly and many Eulerian methods, though often computationally less taxing, suffer from model deficiencies and mathematical artifacts that lead to non-physical results. In particular, efficient Eulerian models that can accurately predict the crossing of multiple streams of non-interacting particles in laminar flow have traditionally been lacking.The goal of this work is to investigate the predictive capabilities of modern techniques from the kinetic theory of gases to a treatment of disperse multiphase flow. In particular, several moment-methods, including a recently proposed fourteen-moment approximation to the underlying kinetic equation describing particle motion, are applied and their abilities to predict particle-stream crossing are assessed. The derivation, mathematical structure, and physical behaviour of the resulting model are explained. A numerical implementation is presented and results for a flow problem that is designed to demonstrate the fundamental behaviour of each model with respect to particle stream crossing is presented.

Effect of density ratio on velocity fluctuations in dispersed multiphase flow from simulations of finite-size particles

Velocity fluctuations in the carrier phase and dispersed phase of a dispersed multiphase flow are studied using particle-resolved direct numerical simulation. The simulations correspond to a statistically homogeneous problem with an imposed mean pressure gradient and are presented for $${Re}_{m}=20$$ and a wide range of dispersed phase volume fractions $$\left( 0.1 \le \phi \le 0.4 \right) $$ and density ratios of the dispersed phase to the carrier phase $$\left( 0.001 \le \rho _\mathrm{p}/\rho _\mathrm{f} \le 1000 \right) $$ . The velocity fluctuations in the fluid and dispersed phase at the statistically stationary state are quantified by the turbulent kinetic energy (TKE) and granular temperature, respectively. It is found that the granular temperature increases with a decrease in the density ratio and then reaches an asymptotic value. The qualitative trend of the behavior is explained by the added mass effect, but the value of the coefficient that yields quantitative agreement is non-physical. It is also shown that the TKE has a similar dependence on the density ratio for all volume fractions studied here other than $$\phi =0.1$$ . The anomalous behavior for $$\phi =0.1$$ is hypothesized to arise from the interaction of particle wakes at higher volume fractions. The study of mixture kinetic energy for different cases indicates that low-density ratio cases are less efficient in extracting energy from mean flow to fluctuations.

An exploratory study on fluid particles breakup rate models for the entire spectrum of turbulent energy

In this study, the role of turbulence on the formulation of breakup kernels for fluid particles in dispersed multiphase flows is demonstrated. Two pieces of information for model derivations including the turbulent energy spectrum and the second-order structure function are chosen as the main candidates to extend the models for the entire turbulent spectrum, contrary to the original expressions that are limited for the inertial subrange. Further, a two-step validation procedure is proposed to incorporate the effect of turbulence for model validations, that is, the original and the extended models are compared and validated against two sets of experimental data for breakup rates. The first set covers the inertial subrange, while the second set is a dataset that includes direct measurements toward the dissipation subrange of turbulence. The results show that the predictive abilities of breakup kernels can be enhanced by the model extension, when the droplet diameters are outside the inertial subrange of turbulence. This work, thus, answers how the entire spectrum of turbulence can improve the breakup kernels and proposes a validation method to include the effect of turbulence for the validation of breakup kernels.

Reynolds-averaged modeling of turbulence damping near a large-scale interface in two-phase flow

The two-fluid Euler-Euler model can be used for the description of co-existing stratified and dispersed multiphase flow within one flow domain. For realistic engineering applications, turbulence is often modeled in the Reynolds-averaged Navier-Stokes (RANS) framework where closure of the Reynolds stresses is mostly achieved using the turbulent viscosity formulation. It is a well-known problem that at large-scale interfaces between two phases such turbulence modeling breaks down as turbulent viscosity in the vicinity of an interface is over-predicted. To address this issue, we adopt the Egorov approach (Egorov et al., 2014) which locally damps turbulence near the interface. This model is based upon the idea that at a large-scale interface the lighter phase may see the heavier phase much like a solid wall, suggesting a wall-like treatment of turbulent dissipation at the interface. The implementation of the model inside a two-phase formulation of the k–ω model is discussed, and shown to give good predictions of interfacial turbulence in co-current stratified two-phase flow. The Egorov approach is extended to the k–ε model, which may be relevant for a large array of engineering applications in which the k–ε model is more effective than the k-ω model. It is shown that the non-dimensional Egorov approach coefficient is grid dependent. We introduce a new formulation of the interfacial damping term in the two-fluid Euler-Euler model which gives more consistent results for different computational grids in comparison to the original formulation of the Egorov approach. This feature, as well as its straightforward implementation in both the k–ω and k–ε models, make the new model useful to a large array of multiphase engineering problems in which interfacial turbulence damping is relevant.

Shock dispersal of dilute particle clouds

We present experiments and numerical simulations for an elementary paradigm of disperse multiphase flow: highly dilute, homogeneous, finite-dimension clouds of particles (curtains) hit by shock/blast waves in one dimension. In the experiments (particle volume fraction ${<}1\,\%$) the blasts that follow the shocks vary from low subsonic to supersonic, and we report data on curtain expansions and volume fraction distributions. The particle-resolving numerical simulations, run for the supersonic case, yield excellent agreement with all of these experimental data. We find that the essential feature for these good predictions is a flow choking phenomenon that entails a (particle) dispersive character of the flow down a volume fraction gradient (as at the downstream portions of the curtain). A most basic effective-field model is made to capture this gas dynamics by emulating the wake behind each particle, as seen in the particle-resolving direct Euler simulation (DES). On this basis, standard drag laws yield excellent agreement with the dispersive behaviour found in the experiment/DES, thus revealing a physics-based path to eventual well posedness of the mathematical model.

Coupling CFD-DEM with dynamic meshing: A new approach for fluid-structure interaction in particle-fluid flows

Many important engineering applications involve the interaction of free-moving objects with dispersed multi-phase flows, however due to the challenge and complexity of modelling these systems, modelling approaches remain very limited and very few studies have been reported. This work presents a new method capable of addressing these problems. It integrates a dynamic meshing approach, used to explicitly capture the flow induced by free-moving large object(s), with a conventional CFD-DEM method to capture the behaviour of small particles in particle-fluid flow. The force and torque acting on the large object due to the fluid flow are explicitly calculated by integrating pressure and viscous stress acting on the object's surface and the forces due to collisions with both the smaller particles and other structures are calculated using a soft-sphere DEM approach. The developed model has been fully implemented on the ANSYS/Fluent platform due to its efficient handling of dynamic meshing and complex and/or free-moving boundaries, thus it can be applied to a wide range of industrial applications. Validation tests have been carried out for two typical gas-solid fluidization cases, they show good qualitative and quantitative agreement with reported experimental literature data. The developed model was then successfully applied to gas fluidization with a large immersed tube which was either fixed or free-moving. The predicted interacting dynamics of the gas, particle and tube were highly complex and highlighted the value of fully resolving the flow around the large object. The results demonstrated that the capability of a conventional CFD-DEM approach could be enhanced to address free-body fluid-structure interaction problems encountered in particle-fluid systems.

Coherent clusters of inertial particles in homogeneous turbulence

Despite the widely acknowledged significance of turbulence-driven clustering, a clear topological definition of particle cluster in turbulent dispersed multiphase flows has been lacking. Here we introduce a definition of coherent cluster based on self-similarity, and apply it to distributions of heavy particles in direct numerical simulations of homogeneous isotropic turbulence, with and without gravitational acceleration. Clusters show self-similarity already at length scales larger than twice the Kolmogorov length, as indicated by the fractal nature of their surface and by the power-law decay of their size distribution. The size of the identified clusters extends to the integral scale, with average concentrations that depend on the Stokes number but not on the cluster dimension. Compared to non-clustered particles, coherent clusters show a stronger tendency to sample regions of high strain and low vorticity. Moreover, we find that the clusters align themselves with the local vorticity vector. In the presence of gravity, they tend to align themselves vertically and their fall speed is significantly different from the average settling velocity: for moderate fall speeds they experience stronger settling enhancement than non-clustered particles, while for large fall speeds they exhibit weakly reduced settling. The proposed approach for cluster identification leverages the Voronoï diagram method, but is also compatible with other tessellation techniques such as the classic box-counting method.

Pressure evolution equation for the particulate phase in inhomogeneous compressible disperse multiphase flows

Pressure evolution equation for the particulate phase in inhomogeneous compressible disperse multiphase flows

A spatiotemporal tree model for turbulence in dispersed phase multiphase flows: Energy dissipation rate behavior in single particle and binary particles arrays.

In this article, a spatiotemporal dynamical system model (tree model) is utilized for investigating the features of forced and unforced turbulence in a dispersed phase two-phase system. The tree model includes a variable for spatial dimension in addition to variables of wavenumber and time, which display both spatial and temporal intermittencies. The focus of this paper is to study the turbulence modulation due to the presence of rigid particles. The study considers particles with the sizes of 32, 64, and 128 times the Kolmogorov length scale. Specifically, the study of the energy dissipation rate (EDR) at the particle-fluid interface is considered. Two models, namely, A and B with different types of interaction connections between nearby shells, are used first to compare the results of the particle-laden case with decaying turbulence. The number of tree connections in the model is found to affect the amount of augmentation of EDR near the particle surface. Model B is studied further with different sizes of particles in forced turbulence cases and compared to the unladen case with the same parameters. Also, the model expression is studied in the forced turbulence case of dual particles separated by given distances. The results of spatiotemporal shell models provide new approach of handling high Reynolds turbulence in dispersed phase multiphase systems.

Three-dimensional modeling of the separation gradient aerosol technologies.Oil separators of the GTE suction systems with the gas flow rate up to 800 m3/h

There have been implemented separation gradient aerosol technologies which take into account all the forces and effects that influence the deposition of finely dispersed particles. Substantiation is provided for the scientific statement of intensification of the gradient processes of the aerosol media transfer in the boundary layers of multipurpose surfaces during cleaning of the dispersed multiphase flows for the development of technical devices enhancing energy saving and ecological purity of power plants. A sectional design scheme and a three-dimensional model of an oil separator in finite elements were developed for calculating the hydrodynamics and separation. The hydrodynamic situation and the trajectory of the particles in the flow section of the oil separator are calculated. According to the calculation of the velocity distribution in the oil separator at G = 100...200 m3/h, the velocity in the coagulation profile does not exceed 10 m/s. On the basis of the results of the static pressure distribution for G = 100, 200 m3/h, it is established that the pressure difference in the separating coagulators reaches 2.5...3.9 kPa, respectively. The calculation results at G = 100...200 m3/h show that the total pulsation effect of precipitation of the highly dispersed particles makes up 25.1%. Using the calculations, a prototype oil separator was created; its experimental studies were performed on the stand in the form of an open-type wind tunnel. The coefficient of the total purification efficiency is determined, which reaches 99.9%. On the basis of the separation gradient aerosol technologies, it is possible to improve cleaners capturing aerosols in various power plant systems. The performed studies allow further developing a line-up of separators for the gas flow rate from 20 to 2000 m3/h.

A Study of the Soft-Sphere Model in Eulerian-Lagrangian Simulation of Gas-Liquid Flow

AbstractEulerian-Lagrangian method is becoming more and more popular for the simulation of dispersed multiphase flow as the computational ability grows. An important issue in this method is the handle of collisions. Until now, both hard-sphere and soft-sphere models have been used extensively in the simulation of gas-solid systems while in gas-liquid systems only the hard-sphere model is used. This study presents an investigation of the performance of the soft-sphere model in gas-liquid systems. The open source software OpenFOAM is utilized to complete our simulations. We simulated the 2D Becker case to give a preliminary study of the suitability of the soft-sphere model in gas-liquid systems. We tested the normal stiffness coefficient from 50 N/m to 0.01 N/m and found that the coefficient 1 N/m predicted sufficiently accurate flow field. In the simulation of 3D Deen case, we tried more stiffness coefficients and found that the soft-sphere model successfully predicted the fluid velocity, and the result at a normal stiffness coefficient of 1 N/m is the optimum. It can be expected that the soft-sphere model is also suitable in gas-liquid systems.

Migration law of respirable dust on a super-long fully mechanized double-shearer working face

In order to understand the migration law of respirable dust and gain reasonable design parameters for dust control on a super-long double-shearer fully mechanized working face, this paper describes research carried out using a numerical simulation package (Fluent) based on gas-solid coupling dispersed multiphase flow model and field measurement to research different technology modes, dust distribution law at different intervals where shearers work in opposite directions on the lower 9303 face, No. 2 Jining Mine, Yankuang Coal Mining Co. Results show that the concentration of dust 3–6m away from the shearers working in the same directions was large, while the impact area of respirable dust near the shearer increased significantly to 5–6m with the distance between two shearers working in opposite directions. The concentration of dust on a double-shearer face was considerably higher than that of a face with one shear under the combined effect of wind speed on the face and disturbed wind around the shearer, while the dust concentration near the shearer on the return side was considerably higher than that on the inlet side. The concentration of dust on a double-shearer face along the airflow declined slowly so that dust was hard to control. Simulation results confirmed the results of field measurement, which could provide reference for dust prevention design.

Multivariate Gaussian Extended Quadrature Method of Moments for Turbulent Disperse Multiphase Flow

The present contribution introduces a fourth-order moment formalism for particle trajectory crossing (PTC) in the framework of multiscale modeling of disperse multiphase flow. In our previous work, the ability to treat PTC was examined with direct-numerical simulations using either quadrature reconstruction based on a sum of Dirac delta functions denoted as quadrature-based moment methods (QBMM) in order to capture large scale trajectory crossing, or by using low-order hydrodynamics closures in the Levermore hierarchy denoted as kinetic-based moment methods (KBMM) in order to capture small-scale trajectory crossing. Whereas KBMM leads to well-posed PDEs and has a hard time capturing large-scale trajectory crossing for particles with enough inertia, QBMM based on a discrete reconstruction suffers from singularity formation and requires too many moments in order to capture the effect of PTC at both the small scale and the large scale both to small-scale turbulence as well as free transport coupled to drag in an Eulerian mesoscale framework. The challenge addressed in this work is thus twofold: first, to propose a new generation of method at the interface between QBMM and KBMM with less singular behavior and the associated proper mathematical properties, which is able to capture both small-scale and large-scale trajectory crossing, and second to limit the number of moments used for applicability in two-dimensional (2-D) and 3-D configurations without losing too much accuracy in the representation of spatial fluxes. In order to illustrate its numerical properties, the proposed Gaussian extended quadrature method of moments is applied to solve 1-D and 2-D kinetic equations representing finite-Stokes-number particles in a known turbulent fluid flow.

Euler-Euler simulation of mass-transfer in bubbly flows

For practical applications the Euler-Euler two-fluid model relies on suitable closure relations describing interfacial exchange processes. Concerning pure fluid dynamics of dispersed gas-liquid multiphase flow, an ongoing effort has led to a validated set of closures that is applicable under a rather broad range of conditions. Similar results for the technologically even more important field of mass transfer remain to be achieved. Progress so far has been hampered by a lack of spatially resolved data including measurements of concentration, which are suitable for CFD model validation. In addition, correlations proposed to describe the mass transfer coefficient differ widely. Here, a preliminary study of axial concentration profiles in a bubble column is given, based on the available experimental data found in the literature. For this purpose the simplified assumption of a constant mass transfer coefficient throughout the column is made and experimentally determined values are used. New measurements will be needed to come to a final conclusion.

Numerical simulation of mold filling and particulate flow of A356/SiCp indirect squeeze casting

In this investigation, a mathematical model based on the dispersed phase model and multiphase flow principle was introduced, and applied to simulate the mold filling and particulate flow of particulate reinforced metal matrix composites casting. Experiments of spiral-square shaped indirect squeeze castings of A356/50 µm SiCp were conducted to validate the established model. The SiCp fractions in the casting different locations were quantitatively measured with micro digital image analysis system and were compared with the simulation results. It was found that particulate fractions and distribution patterns at different locations were quite different along the filling distance. The experimental and simulated results about the SiCp distribution in the castings show acceptable agreement. Further, the effect of fluid flow and particulate trajectories on the particulate distribution was analyzed and discussed. The research has shown the validity of application of the model for practical particulate reinforced Al-based composites casting.

Inter-phase heat transfer and energy coupling in turbulent dispersed multiphase flows

The present paper addresses important fundamental issues of inter-phase heat transfer and energy coupling in turbulent dispersed multiphase flows through scaling analysis. In typical point-particle or two-fluid approaches, the fluid motion and convective heat transfer at the particle scale are not resolved and the momentum and energy coupling between fluid and particles are provided by proper closure models. By examining the kinetic energy transfer due to the coupling forces from the macroscale to microscale fluid motion, closure models are obtained for the contributions of the coupling forces to the energy coupling. Due to the inviscid origin of the added-mass force, its contribution to the microscale kinetic energy does not contribute to dissipative transfer to fluid internal energy as was done by the quasi-steady force. Time scale analysis shows that when the particle is larger than a critical diameter, the diffusive-unsteady kernel decays at a time scale that is smaller than the Kolmogorov time scale. As a result, the computationally costly Basset-like integral form of diffusive-unsteady heat transfer can be simplified to a non-integral form. Conventionally, the fluid-to-particle volumetric heat capacity ratio is used to evaluate the relative importance of the unsteady heat transfer to the energy balance of the particles. Therefore, for gas-particle flows, where the fluid-to-particle volumetric heat capacity ratio is small, unsteady heat transfer is usually ignored. However, the present scaling analysis shows that for small fluid-to-particle volumetric heat capacity ratio, the importance of the unsteady heat transfer actually depends on the ratio between the particle size and the Kolmogorov scale. Furthermore, the particle mass loading multiplied by the heat capacity ratio is usually used to estimate the importance of the thermal two-way coupling effect. Through scaling argument, improved estimates are established for the energy coupling parameters of each energy exchange mechanism between the phases.

Resolved-particle simulation by the Physalis method: Enhancements and new capabilities

We present enhancements and new capabilities of the Physalis method for simulating disperse multiphase flows using particle-resolved simulation. The current work enhances the previous method by incorporating a new type of pressure-Poisson solver that couples with a new Physalis particle pressure boundary condition scheme and a new particle interior treatment to significantly improve overall numerical efficiency. Further, we implement a more efficient method of calculating the Physalis scalar products and incorporate short-range particle interaction models. We provide validation and benchmarking for the Physalis method against experiments of a sedimenting particle and of normal wall collisions. We conclude with an illustrative simulation of 2048 particles sedimenting in a duct. In the appendix, we present a complete and self-consistent description of the analytical development and numerical methods.