Dilute Particle-laden Flows Research Articles

Online 3D Characterization of Micrometer-Sized Cuboidal Particles in Suspension.

Characterization of particle size and shape is central to the study of particulate matter in its broadest sense. Whilst 1D characterization defines the state of the art, the development of 2D and 3D characterization methods has attracted increasing attention, due to a common need to measure particle shape alongside size. Herein, ensembles of micrometer-sized cuboidal particles are studied, for which reliable sizing techniques are currently missing. Such particles must be characterized using three orthogonal dimensions to completely describe their size and shape. To this end, the utility of an online and in-flow multiprojection imaging tool coupled with machine learning is experimentally assessed. Central to this activity, a methodology is outlined to produce micrometer-sized, non-spherical analytical standards. Such analytical standards are fabricated using photolithography, and consist of monodisperse micro-cuboidal particles of user-defined size and shape. The aforementioned activities are addressed through an experimental framework that fabricates analytical standards and subsequently uses them to validate the performance of ourmultiprojection imaging tool. Significantly, it is shown that the same set of data collected for particle sizing can also be used to estimate particle orientation in flow, thus defining a rapid and robust protocol to investigate the behavior of dilute particle-ladenflows.

Isogeometric large-eddy simulations of turbulent particle-laden flows

In recent years, isogeometric analysis (IGA) has attracted significant attention from the computational mechanics community due to its ability to integrate design and analysis. Besides, IGA is also a higher-order discretization technique for solving partial differential equations, showing high approximation capability per degree of freedom. In this paper, we extend the application realm of IGA to particle-laden flows based on Eulerian–Eulerian description that couples Navier–Stokes equations with a density transport equation through a Boussinesq approximation. The coupled systems are solved by using quadratic non-uniform rational B-spline (NURBS) functions and a recently developed residual-based variational multiscale (VMS) formulation, which introduces coupling between the fine velocity scales and density equation residuals. We deploy the proposed approach to perform large-eddy simulations (LES) of dilute particle-laden flows over a flat surface at Reynolds number = 10,000. We compare the simulation results against direct numerical simulation (DNS) results from the literature. We find that combining VMS and IGA, the proposed approach enables accurate prediction of a wide range of flow/particle statistics with a relatively lower mesh resolution.

Numerical Investigation of the Characteristics of Erosion in a Centrifugal Pump for Transporting Dilute Particle-Laden Flows

Erosion in centrifugal pumps for transporting flows with dilute particles is a main pump failure problem in many engineering processes. A numerical model combining the computational fluid dynamics (CFD) and Discrete Element Method (DEM) is applied to simulate erosion in a centrifugal pump. Different models of the liquid-solid inter-phase forces are implemented, and the particle-turbulence interaction is also defined. The inertial particles considered in this work are monodisperse and have finite size. The numerical results are validated by comparing the results with a series of experimental data. Then, the effects of particle volume fraction, size, and shape on the pump erosion are estimated in the simulations. The results demonstrate that severe erosive areas are located near the inlet and outlet of the pressure side of the impeller blade, the middle region of the blade, the corners of the shroud and hub of the impeller adjoining to the pressure side of the blade, and the volute near the pump tongue. Among these locations, the maximum erosion occurs near the inlet of the pressure side of the blade. Erosion mitigation occurs under the situation where more particles accumulate in the near-wall region of the eroded surface, forming a buffering layer. The relationship between the particle size and the erosion is nonlinear, and the 1 mm particle causes the maximum pump erosion. The sharp particles cause more severe erosion in the pump because both the frequency of particle-wall collisions and the impact angle increase with the increasing sharpness of the particle.

Euler-Lagrange modelling of dilute particle-laden flows with arbitrary particle-size to mesh-spacing ratio

This paper addresses the two-way coupled Euler-Lagrange modelling of dilute particle-laden flows, with arbitrary particle-size to mesh-spacing ratio. Two-way coupled Euler-Lagrange methods classically require particles to be much smaller than the computational mesh cells for them to be accurately tracked. Particles that do not satisfy this requirement can be considered by introducing a source term regularisation operator that typically consists in convoluting the point-wise particle momentum sources with a smooth kernel. Particles that are larger than the mesh cells, however, generate a significant local flow disturbance, which, in turn, results in poor estimates of the fluid forces acting on them.To circumvent this issue, this paper proposes a new framework to recover the local undisturbed velocity at the location of a given particle, that is the local flow velocity from which the disturbance due to the presence of the particle is subtracted. It relies upon the solution of the Stokes flow through a regularised momentum source and is extended to finite Reynolds numbers based on the Oseen flow solution. Owing to the polynomial nature of the regularisation kernel considered in this paper, a correction for the averaged local flow disturbance can be analytically derived, allowing to filter out scales of the flow motion that are smaller than the particle, which should not be taken into account to compute the interaction/drag forces acting on the particle. The proposed correction scheme is applied to the simulation of a particle settling under the influence of gravity, for varying particle-size to mesh-spacing ratios and varying Reynolds numbers. The method is shown to nearly eliminate any impact of the underlying mesh resolution on the modelling of a particle's trajectory. Finally, optimal values for the scale of the regularisation kernel are provided and their impact on the flow is discussed.

Analytical solution of an Eulerian dilute particle-laden flow problem

Dilute particle-laden flows are encountered in various natural processes and manmade applications. To reduce the computational resources used to simulate such flows, the particle phase could be formulated using the Eulerian approach, resulting in a continuum hydrodynamic model. The aim of this paper is to present the analytical solution of a steady two-dimensional flow problem using that model. The dispersed solid particles, considered in this problem, are immersed in a uniform fluid flow field. The solid phase is coupled to the fluid using a linear Stokes-drag, which is valid for low slip velocities. The general solution of the solid phase velocity field is obtained by solving its quasi-linear hyperbolic momentum equations using the method of characteristics. For the case of a uniform inlet particle velocity, the solid phase velocity field is obtained in terms of Lambert W function. Subsequently, this velocity field is substituted in the solid phase continuity equation; transforming it to a semi-linear hyperbolic partial differential equation, which is solved to obtain the solid phase volume fraction field.

Coupling the fictitious domain and sharp interface methods for the simulation of convective mass transfer around reactive particles: Towards a reactive Sherwood number correlation for dilute systems

We suggest a reactive Sherwood number model for convective mass transfer around reactive particles in a dilute regime. The model is constructed with a simple external-internal coupling and is validated with Particle-Resolved Simulation (PRS). The PRS of reactive particle-fluid systems requires numerical methods able to handle efficiently sharp gradients of concentration and potential discontinuities of gradient concentrations at the fluid-particle interface. To simulate mass transfer from reactive catalyst beads immersed in a fluid flow, we coupled the Sharp Interface Method (SIM) to a Distributed Lagrange Multiplier/Fictious Domain (DLM/FD) two-phase flow solver. We evaluate the accuracy of our numerical method by comparison to analytic solutions and to generic test cases fully resolved by boundary fitted simulations. A previous theoretical model that couples the internal diffusion-reaction problem with the external advection-diffusion mass transfer in the fluid phase is extended to the configuration of three aligned spherical particles representative of a dilute particle-laden flow. Predictions of surface concentration, mass transfer coefficient and chemical effectiveness factor of catalyst particles are validated by DLM-FD/SIM simulations. We show that the model captures properly the effect of an internal first order chemical reaction on the overall respective reactive Sherwood number of each sphere depending on their relative positions. The proposed correlation for the reactive Sherwood number is based on an existing non-reactive Sherwood number correlation. The model can be later used in Euler/Lagrange or Euler/Euler modelling of dilute reactive particle-laden flows.

A pseudo point source model based on velocity coupled method for dilute particle-laden flow with dissipation scale particles

The interphase interaction between the particle and fluid is one of the most fundamental issues in the research of particle-laden flow. Neither the conventional point source model nor the particle-resolved method is an appropriate choice to study the interphase interaction when the order of magnitude of particle diameter is the same as the turbulence dissipation length scale or the grid spacing. In the present study, a pseudo point source model is proposed to consider the finite size effect of particles under the limitation of an acceptable calculation consumption. In this model, the feedback effect of particles on the fluid is represented by coupling the particle-induced disturbance flow with the carrier flow. The disturbance flow of the particle is solved by Stokes approximation or Oseen correction based on the particle Reynolds number, and the geometric relationships between the particle along with its disturbance and grid are also considered. Meanwhile, the no-slip boundary condition on the particle surface is reconstructed as much as possible. The free settling of a single particle and the particle-laden turbulent channel flow are applied to verify the pseudo point source model. For each simulation case, the results of the pseudo point source model are compared with that obtained by the conventional point source model. From the preliminary results, it is concluded that the pseudo point source model behaved much better than the conventional point source model in predicting the free settling process when the particle diameter is greater than the grid spacing. In simulations of the particle-laden channel turbulence, the pseudo point source model can obtain more reasonable results, especially in the cases where the particle diameter is larger than the Kolmogorov dissipation scale. Finally, some outlooks which needs further study are discussed.

Turbulence modulation model for gas-particle flow based on probability density function approach**Project supported by the National Natural Science Foundation of China (Grant No. 51176044).

The paper focuses on the turbulence modulation problem in gas–particle flow with the use of probability density function (PDF) approach. By means of the PDF method, a general statistical moment turbulence modulation model without considering the trajectory difference between two phases is derived from the Navier–Stokes equations. A new turbulence production term induced by the dispersed-phase is analyzed and considered. Furthermore, the trajectory difference between two media is taken into account. Subsequently, a new k–ε turbulence modulation model in dilute particle-laden flow is successfully set up. Then, the changes to several terms, including the turbulence production, dissipation, and diffusion terms, are well described consequently. The promoted model provides a more probable explanation for the modification of particles on the turbulence. Finally, we applied the model to simulate a gas–particle turbulence flow case in a wall jet, and found that the simulation results agree well with the experimental data.

Direct Numerical Study on Effect of Interparticle Collision in Particle-Laden Turbulence

Particle-laden turbulent flow is widely seen in the natural world and industrial applications, and thus studies on multiphase flows with particles are of great significance for improving the efficiency of industrial processes and environment protection. In the present study, the Euler–Lagrange direct numerical simulation based on the point-source-in-cell model was employed to calculate the dilute particle-laden flow in a vertical channel. The turbulence flowfield was obtained by directly solving the Navier–Stokes equation. The particle’s motion was described by the Basset–Boussinesq–Oseen equation, and the shear lift force and Magnus lift force were also included in the particle equation of motion. The main purpose was focused on the effect of interparticle collision, which was detected by using a deterministic method. It was found through investigation that interparticle collision has a significant effect on the particle-laden flow even when the particle’s volume fraction is very small [about ]. Interparticle collision increases the near-wall particle velocity. The near-wall particle accumulation is decreased because interparticle collision can not only promote the particle migration from the near-wall region to the channel center but also change interphase forces. It was also found that interparticle collision has little effect on the mean velocity profile and the turbulence intensity of the gas phase. In addition, interparticle collision enhances the fluctuating intensities of particles in the wall-normal direction and spanwise direction. In the streamwise direction, the fluctuating intensity of particles is enhanced in the very-near-wall region and the channel center, while it is reduced in other regions by interparticle collision.

A Lagrangian VOF tensorial penalty method for the DNS of resolved particle-laden flows

The direct numerical simulation of particle flows is investigated by a Lagrangian VOF approach and penalty methods of second order convergence in space for incompressible flows interacting with resolved particles on a fixed structured grid. A specific Eulerian volume of fluid method is developed with a Lagrangian tracking of the phase function while the solid and divergence free constraints are ensured implicitly in the motion equations thanks to fictitious domains formulations, adaptive augmented Lagrangian approaches and viscous penalty methods. A specific strategy for handling particle collisions and lubrication effects is also presented. Various dilute particle laden flows are considered for validating the models and numerical methods. Convergence studies are proposed for estimating the time and space convergence orders of the global DNS approach. Finally, two dense particle laden flows are simulated, namely the flow across a fixed array of cylinders and the fluidization of 2133 particles in a vertical pipe. The numerical solutions are compared to existing theoretical and experimental results with success.

Modelling of pipe bend erosion by dilute particle suspensions

A computational fluid dynamic model coupled to a Lagrangian particle tracking routine and a number of erosion models have been used to predict the solid particle erosion in four different 90° square cross-section bends for dilute particle-laden flow. Comparisons with experimental data over a range of conditions, including particle size, mass loading and flow Reynolds number, demonstrate good agreement with predictions of all the erosion models considered. In particular, the models are able to yield reliable predictions of erosion depth and wear location on the concave and convex walls of the bends. The slight disparities observed are most likely due to uncertainties in the particle–wall collision model employed, and variability in the data. The complexity of the particle–wall collision process precluded the development in this work of a model which accounted for the occurrence of erosion pockets and their subsequent influence on the fluid flow, particle trajectories and the magnitude of wear at secondary wear locations, as well as the dynamic movement of the maximum wear location. Despite this, however, and within experimental uncertainty, the models perform well, although their further extension as noted could potentially lead to improved agreement with data.

Numerical Investigation of Phase Distribution and Liquid Turbulence Modulation in Dilute Particle-Laden Flow

Studies on the motion of particles in turbulence and interactions between particles and turbulence are extremely significant, which can help us to improve the efficiency of industrial processes. In this article, we investigated the particle distribution and particle-turbulence interaction in a solid-liquid channel flow with the Euler-Lagrange two-way model. The liquid phase was solved using direct numerical simulation (DNS), and the particle motion was tracked by Newtonian equations of motion considering effects of drag force, pressure gradient force, and gravity. Two-way coupling was used to explain the effect of particles on the turbulence structure. The results show that the local void fraction of particles indicates the wall-peaked profile, particles scatter uniformly in the spanwise direction, and the injection of particles suppresses the turbulence activities in the near wall region. Suppression of the liquid turbulence is mainly caused by vortexes decay of different sizes.

Time-resolved PIV measurements of the interaction of polystyrene beads with near-wall-coherent structures in a turbulent channel flow

Time-resolved PIV measurements were performed in a dilute particle-laden flow tracking near-neutrally buoyant polystyrene beads and the velocity field of a near wall turbulent boundary layer. Data were taken in a vertical light sheet aligned in the streamwise direction at the center of a horizontal, closed loop, transparent square water channel facility. In addition, low speed measurements were performed characterizing the effects of the dispersed phase on mean and turbulence flow quantities. Reynolds shear stress slightly differed from clear water conditions whereas fluid mean and rms values were not affected. A case study for several beads revealed a clear relation between their movement and near-wall coherent structures. Several structures having 2D vorticity signatures of near-wall hairpin vortices and hairpin packets, directly affected bead movement. A statistical analysis showed that the mean streamwise velocity of ascending beads lagged behind the mean fluid velocity and bead rms values were higher than fluid ones. Particle Reynolds numbers based on the magnitude of the instantaneous relative velocity vector peaked near the wall; values not exceeding 100, too low for vortex shedding to occur. Quadrant analysis showed a clear preference for ascending beads to reside in ejections while for descending beads the preference for sweeps was less.

Preferential concentration of particles by turbulence

Preferential concentration describes the accumulation of dense particles within specific regions of the instantaneous turbulence field. This phenomenon occurs in dilute particle-laden flows with particle time constants of the same order as an appropriately chosen turbulence time scale. The mechanisms which drive preferential concentration are centrifuging of particles away from vortex cores and accumulation of particles in convergence zones. Experimental and numerical studies are reviewed which demonstrate that preferential concentration occurs in a wide range of flows including plane and axisymmetric free shear flows, wall-bounded flows, homogeneous turbulent flows, and complex shear flows. The same basic mechanisms are active in all these flows but the specific effects and the definition of an appropriate time scale change from problem to problem. Preferential concentration has been shown to have a significant effect on droplet combustion, aerosol particle settling and turbulence modification by particles and is expected to be significant in numerous other applications. Current models describing preferential concentration and its global effects on the flow are inadequate.

Turbulence modulation in homogeneous dilute particle-laden flows

Continuous-phase properties were studied for homogeneous dilute particle-laden flows caused by nearly monodisperse glass particles falling in a stagnant water bath. Test conditions included 0.5, 1.0 and 2.0 mm diameter particles (yielding particle Reynolds numbers based on terminal velocities of 38, 156 and 545) with particle volume fractions less than 0.01%. Measurements included mean and fluctuating velocities, as well as temporal spectra and spatial correlations of velocity fluctuations in the streamwise and cross-stream directions, using a two-point phase-discriminating laser velocimeter. Flow properties were also analysed using a stochastic method involving linear superposition of randomly-arriving particle velocity fields.For present test conditions, liquid velocity fluctuations varied solely as a function of the rate of dissipation of particle energy in the liquid. The flows were highly anisotropic with streamwise velocity fluctuations being roughly twice cross-stream velocity fluctuations. Correlation coefficients and temporal spectra were independent of both particle size and the rate of dissipation of particle energy in the liquid. The temporal spectra indicated a large range of frequencies even though particle Reynolds numbers were relatively low, since both mean and fluctuating velocities in the particle wakes contributed to the spectra because particle arrivals were random. The theory predicted many of the features of the flows reasonably well but additional information concerning the mean and turbulent structure of the wakes of freely moving particles having moderate Reynolds numbers in turbulent environments is needed to address deficiencies in predictions of integral scales and streamwise spatial correlations.