Simulation Of Particle-laden Turbulent Flow Research Articles

Evaluation of RANS-DEM and LES-DEM Methods in OpenFOAM for Simulation of Particle-Laden Turbulent Flows

CFD-DEM modelling of particle-laden turbulent flow is challenging in terms of the required and obtained CFD resolution, heavy DEM computations, and the limitations of the method. Here, we assess the efficiency of a particle-tracking solver in OpenFOAM with RANS-DEM and LES-DEM approaches under the unresolved CFD-DEM framework. Furthermore, we investigate aspects of the unresolved CFD-DEM method with regard to the coupling regime, particle boundary condition and turbulence modelling. Applying one-way and two-way coupling to our RANS-DEM simulations demonstrates that it is sufficient to include one-way coupling when the particle concentration is small (O ~ 10−5). Moreover, our study suggests an approach to estimate the particle boundary condition for cases when data is unavailable. In contrast to what has been previously reported for the adopted case, our RANS-DEM results demonstrate that simple dispersion models considerably underpredict particle dispersion and previously observed reasonable particle dispersion were due to an error in the numerical setup rather than the used dispersion model claiming to include turbulence effects on particle trajectories. LES-DEM may restrict extreme mesh refinement, and, under such scenarios, dynamic LES turbulence models seem to overcome the poor performance of static LES turbulence models. Sub-grade scale effects cannot be neglected when using coarse mesh resolution in LES-DEM and must be recovered with efficient modelling approaches to predict accurate particle dispersion.

Modulation of turbulence intensity by heavy finite-size particles in upward channel flow

Abstract

Two-way coupled particle-turbulence interaction: Effect of numerics and resolution on fluid and particle statistics

We show that statistics from simulations of particle-laden turbulent flows modeled by the point-particle Euler-Lagrange methodology diverge with mesh refinement when the undisturbed fluid velocity used in the drag force that couples the dispersed and continuous phases is not properly modeled. For decaying homogeneous isotropic turbulence, fluid and particle energies, particle acceleration, and energy dissipation rates are found to be grid insensitive only when the undisturbed fluid velocity is robustly modelled. Ultimately, this work provides insight into what types of questions are answerable using two-way coupled point-particle methods.

Interface-resolved numerical simulations of particle-laden turbulent flows in a vertical channel filled with Bingham fluids

In this paper, a fictitious domain method is used to perform interface-resolved numerical simulations of particle-laden turbulent flows in a vertical channel filled with Bingham fluids. The interactions between the particles and the turbulence are investigated at a bulk Reynolds number of 8000 (based on the mean velocity and the channel width), a particle/channel size ratio of 0.1 and a particle volume fraction of 2 %. The Bingham number based on the mean velocity and the channel half-width is 0.0, 0.54 and 3.0, respectively. Both neutrally buoyant and weak particle settling effects are considered. Our results indicate that the yield stress of Bingham fluids has drag-reduction effects by weakening the turbulence, and the addition of the particles enhances the flow friction. The Saffman lift force is important to the particle concentration distribution across the channel. Particle sedimentation attenuates the fluctuating velocity and Reynolds stress, resulting in a smaller flow friction compared with the neutrally buoyant case. When the fluid plasticity is strong, the single-phase flow has considerable temporal and spatial intermittencies. The vortex structures in one half-channel can be stronger than those in the other half-channel for a long period, resulting in the asymmetry of the statistics for a long time. The vortices are preferentially concentrated in streamwise-extended bands. The vortex bands and the laminar flow regions are largely segregated in the spanwise directions, and the vortex bands in the two half-channels are also typically staggered in the spanwise direction. The addition of the particles suppresses such vortex structures, the enormous intermittency and the asymmetry during the transition in the single-phase flow.

On random walk models for simulation of particle-laden turbulent flows

In this investigation, the accuracy of the discrete and continuous random walk (DRW, CRW) stochastic models for simulation of fluid (material) point particle, as well as inertial and Brownian particles, was studied. The corresponding dispersion, concentration, and deposition of suspended micro- and nano-particles in turbulent flows were analyzed. First, the DRW model used in the ANSYS-Fluent commercial CFD code for generating instantaneous flow fluctuations in inhomogeneous turbulent flows was evaluated. For this purpose, turbulent flows in a channel were simulated using a Reynolds-averaged Navier–Stokes (RANS) approach in conjunction with the Reynolds Stress Transport turbulence model (RSTM). Then spherical particles with diameters in the range of 30 µm to 10 nm were introduced uniformly in the channel. Under the assumption of one-way coupling, ensembles of particle trajectories for different sizes were generated by solving the particle equation of motion, including the drag and Brownian forces. The DRW stochastic turbulence model of the software was used to include the effects of instantaneous velocity fluctuations on particle motion, and the steady state concentration distribution and deposition velocity of particles of various sizes were evaluated. In addition, the improved CRW model based on the normalized Langevin equation was used in an in-house Matlab code. Comparisons of the predicted results of the DRW model of ANSYS-Fluent with the available experimental data and the DNS simulation results and empirical predictions showed that this model is not able to accurately predict the flow fluctuations seen by the particles in that it leads to unreasonable concentration profiles and time-varying deposition velocities. However, the predictions of the improved CRW model were in good agreement with the experimental data and the DNS results. Possible reasons causing the discrepancies between the DRW predictions and the experimental data were discussed. The improved CRW model was also implemented through user-defined functions into the ANSYS-Fluent code, which resulted in accurate concentration distribution and deposition velocity for different size particles.

Assessment of numerical methods for fully resolved simulations of particle-laden turbulent flows

During the last decade, many approaches for resolved-particle simulation (RPS) have been developed for numerical studies of finite-size particle-laden turbulent flows. In this paper, three RPS approaches are compared for a particle-laden decaying turbulence case. These methods are, the Volume-of-Fluid Lagrangian method, based on the viscosity penalty method (VoF-Lag); a direct forcing Immersed Boundary Method, based on a regularized delta function approach for the fluid/solid coupling (IBM); and the Bounce Back scheme developed for Lattice Boltzmann method (LBM-BB). The physics and the numerical performances of the methods are analyzed. Modulation of turbulence is observed for all the methods, with a faster decay of turbulent kinetic energy compared to the single-phase case. Lagrangian particle statistics, such as the velocity probability density function and the velocity autocorrelation function, show minor differences among the three methods. However, major differences between the codes are observed in the evolution of the particle kinetic energy. These differences are related to the treatment of the initial condition when the particles are inserted in an initially single-phase turbulence. The averaged particle/fluid slip velocity is also analyzed, showing similar behavior as compared to the results referred in the literature. The computational performances of the different methods differ significantly. The VoF-Lag method appears to be computationally most expensive. Indeed, this method is not adapted to turbulent cases. The IBM and LBM-BB implementations show very good scaling.

On the smoothing of point force in the two-way coupling simulation of polymer-laden turbulent flow

Effects of smoothing of point force used in the two-way coupling simulation of particle-laden turbulent flow are examined for one dimensional simple model and for the Eulerian-Lagrangian simulations of polymers in turbulence. We show that the regularization by using Gaussian function yields preferable behavior in evaluating the smoothed point force compared to the conventional methods used in the previous studies. An efficient computational scheme to use the approximated Gaussian function is newly developed for the two-way coupling simulation in which the turbulent field is solved by using the spectral method. This scheme is applied to the Eulerian-Lagrangian simulations for examining polymer-turbulence interactions.

The influence of sub-grid scale motions on particle collision in homogeneous isotropic turbulence

The absence of sub-grid scale (SGS) motions leads to severe errors in particle pair dynamics, which represents a great challenge to the large eddy simulation of particle-laden turbulent flow. In order to address this issue, data from direct numerical simulation (DNS) of homogenous isotropic turbulence coupled with Lagrangian particle tracking are used as a benchmark to evaluate the corresponding results of filtered DNS (FDNS). It is found that the filtering process in FDNS will lead to a non-monotonic variation of the particle collision statistics, including radial distribution function, radial relative velocity, and the collision kernel. The peak of radial distribution function shifts to the large-inertia region due to the lack of SGS motions, and the analysis of the local flowstructure characteristic variable at particle position indicates that the most effective interaction scale between particles and fluid eddies is increased in FDNS. Moreover, this scale shifting has an obvious effect on the odd-order moments of the probability density function of radial relative velocity, i.e. the skewness, which exhibits a strong correlation to the variance of radial distribution function in FDNS. As a whole, the radial distribution function, together with radial relative velocity, can compensate the SGS effects for the collision kernel in FDNS when the Stokes number based on the Kolmogorov time scale is greater than 3.0. However, it still leaves considerable errors for $${ St}_\mathrm{k }<3.0$$ .

Effects of finite-size heavy particles on the turbulent flows in a square duct

A parallel direct-forcing fictitious domain method is applied in fully-resolved numerical simulations of particle-laden turbulent flows in a square duct. The effects of finite-size heavy particles on the mean secondary flow, the mean streamwise velocity, the root-mean-square velocity fluctuation, and the particle concentration distribution are investigated at the friction Reynolds number of 150, the particle volume fraction of 2.36%, the particle diameter of 0.1 duct width, and the Shields number ranging from 1.0 to 0.2. Our results show that the particle sedimentation breaks the up-down symmetry of the mean secondary vortices, and results in a stronger secondary-flow circulation which transports the fluids downward in the bulk center region and upward along the side walls at a low Shields number. This circulation has a significant impact on the distribution of the mean streamwise velocity, whose maximum value occurs in the lower half duct, unlike in the plane channel case. The flow resistance is increased and the turbulence intensity is reduced, as the Shields number is decreased. The particles accumulate preferentially at the face center of the bottom wall, due to the effect of the mean secondary flow. It is observed that the collision model has an important effect on the results, but does not change the results qualitatively.

Numerical Simulations of Particle-Laden Turbulent Flows to Characterize the Two Different Types of Paint Spray; Bell-Cup Atomizer and Powder Spray Gun

Numerical Simulations of Particle-Laden Turbulent Flows to Characterize the Two Different Types of Paint Spray; Bell-Cup Atomizer and Powder Spray Gun

A hybrid stochastic-deconvolution model for large-eddy simulation of particle-laden flow

We develop a hybrid model for large-eddy simulation of particle-laden turbulent flow, which is a combination of the approximate deconvolution model for the resolved scales and a stochastic model for the sub-grid scales. The stochastic model incorporates a priori results of direct numerical simulation of turbulent channel flow, which showed that the parameters in the stochastic model are quite independent of Reynolds and Stokes number. In order to correctly predict the flux of particles towards the walls an extra term should be included in the stochastic model, which corresponds to the term related to the well-mixed condition in Langevin models for particle dispersion in inhomogeneous turbulent flow. The model predictions are compared with results of direct numerical simulation of channel flow at a frictional Reynolds number of 950. The inclusion of the stochastic forcing is shown to yield a significant improvement over the approximate deconvolution model for the particles alone when combined with a Stokes dependent weight-factor for the well-mixed term.

Development of an algebraic-closure-based moment method for unsteady Eulerian simulations of particle-laden turbulent flows in very dilute regime

An algebraic-closure-based moment method (ACBMM) is developed for unsteady Eulerian particle simulations, coupled with direct numerical simulations (DNSs) of fluid turbulent flows, in very dilute regime and up to large Stokes numbers StK (based on the Kolmogorov timescale) or moderate Stokes numbers St (based on the turbulent macroscale seen by the particles). The proposed method is developed in the frame of a conditional statistical approach which provides a local and instantaneous characterization of the dispersed-phase dynamic accounting for the effect of crossing between particle trajectories which becomes substantial for StK>1. The computed Eulerian quantities are low-order moments of the conditional probability density function (PDF) and the corresponding governing equations are derived from the PDF kinetic equation in the general frame of the kinetic theory of gases. At the first order, the computation of the mesoscopic particle number density and velocity requires the modeling of the second-order moment tensor appearing in the particle momentum equation and referred to as random uncorrelated motion (RUM) particle kinetic stress tensor. The current work proposes a variety of different algebraic closures for the deviatoric part of the tensor. An evaluation of some effective propositions is given by performing an a priori analysis using particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal particle-laden turbulent planar jet. Several million-particle simulations are analyzed in order to assess the models for various Stokes numbers. It is apparent that the most fruitful are explicit algebraic stress models (2ΦEASM) which are based on an equilibrium assumption of RUM anisotropy for which explicit solutions are provided by means of a polynomial representation for tensor functions. These models compare very well with Eulerian–Lagrangian DNSs and properly represent all crucial trends extracted from such simulations.

Large-eddy simulation of particle-laden turbulent flow with heat transfer

The influence of solid particles on the heat transfer rate of a non-isothermal turbulent channel flow is studied using large-eddy simulation. An Eulerian–Lagrangian approach is adopted, and the backward effects of particles in both the momentum and energy equations are taken into account. It is shown that at a constant particle mass loading, the heat transfer rate increases proportionally with the particle specific heat. For a constant particle specific heat, however, depending on the value of the particle specific heat, the heat transfer rate may decrease, increase, or stay unchanged with the increase of the mass loading. To further clarify this issue, the total Nusselt number is split into a turbulence contribution and a particles contribution, and the relation of the Nusselt number with the fluid temperature–velocity correlation and the fluid-particles heat transfer is examined in details. In addition, the mean and fluctuating profiles for fluid and particles are reported, and the results are validated against the available data in the literature.

Optimal interpolation schemes for particle tracking in turbulence

An important aspect in numerical simulations of particle-laden turbulent flows is the interpolation of the flow field needed for the computation of the Lagrangian trajectories. The accuracy of the interpolation method has direct consequences for the acceleration spectrum of the fluid particles and is therefore also important for the correct evaluation of the hydrodynamic forces for almost neutrally buoyant particles, common in many environmental applications. In order to systematically choose the optimal tradeoff between interpolation accuracy and computational cost we focus on comparing errors: the interpolation error is compared with the discretization error of the flow field. In this way one can prevent unnecessary computations and still retain the accuracy of the turbulent flow simulation. From the analysis a practical method is proposed that enables direct estimation of the interpolation and discretization error from the energy spectrum. The theory is validated by means of direct numerical simulations (DNS) of homogeneous, isotropic turbulence using a spectral code, where the trajectories of fluid tracers are computed using several interpolation methods. We show that B-spline interpolation has the best accuracy given the computational cost. Finally, the optimal interpolation order for the different methods is shown as a function of the resolution of the DNS simulation.

Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number

AbstractA fictitious domain method is used to perform fully resolved numerical simulations of particle-laden turbulent flow in a horizontal channel. The effects of large particles of diameter 0.05 and 0.1 times the channel height on the turbulence statistics and structures are investigated for different settling coefficients and volume fractions (0.79 %–7.08 %) for the channel Reynolds number being 5000. The results indicate the following. (a) When the particle sedimentation effect is negligible (i.e. neutrally buoyant), the presence of particles decreases the maximum r.m.s. of streamwise velocity fluctuation near the wall by weakening the intensity of the large-scale streamwise vortices, while increasing the r.m.s. of the streamwise fluctuating velocity in the region very close to the wall and in the centre region. On the other hand, the particles increase the r.m.s. of transverse and spanwise fluctuating velocities in the near-wall region by inducing the small-scale vortices. (b) When the particle settling effect is so substantial that most particles settle onto the bottom wall and form a particle sediment layer (SL), the SL plays the role of a rough wall and parts of the vortex structures shedding from the SL ascend into the core region and substantially increase the turbulence intensity there. (c) When the particle settling effect is moderate, the effects of particles on the turbulence are a combination of the former two situations, and the Shields number is a good parameter for measuring the particle settling effects (i.e. the particle concentration distribution in the transverse direction). The average velocities of the particle are smaller in the lower half-channel and larger in the upper half-channel compared to the local fluid velocities in the presence of gravity effects. The effects of the smaller particles on the turbulence are found to be stronger at the same particle volume fractions.

Two-fluid approach for direct numerical simulation of particle-laden turbulent flows at small Stokes numbers

A two-fluid approach is proposed for direct numerical simulation of particle-laden turbulent flows in two-way coupling where the particle Stokes number is small. An Eulerian velocity field is calculated for the particle phase through a truncated series expansion in terms of the velocity and acceleration of the fluid phase [M. R. Maxey, J. Fluid Mech. 174, 441 (1987)]. This expansion is valid for particles with a sufficiently small Stokes number defined as the ratio of particle time constant to the Kolmogorov time scale. The transport equation of the Eulerian concentration field of particles (particle volume fraction) is solved along with the fluid-phase equations for which the effect of the particles on the fluid phase is taken into account through source terms in the momentum equations. For the assessment purposes, particle-laden decaying isotropic turbulence is studied. The results obtained through the proposed two-fluid approach are compared against those obtained by the trajectory approach in which the particle equations are solved in the Lagrangian framework. It is shown that there is a good agreement between various fluid-phase statistics obtained by these approaches for different small Stokes numbers and mean particle concentrations.

A numerical method for fully resolved simulation (FRS) of rigid particle–flow interactions in complex flows

A fictitious-domain based formulation for fully resolved simulations of arbitrary shaped, freely moving rigid particles in unsteady flows is presented. The entire fluid–particle domain is assumed to be an incompressible, but variable density, fluid. The numerical method is based on a finite-volume approach on a co-located, Cartesian grid together with a fractional step method for variable density, low-Mach number flows. The flow inside the fluid region is constrained to be divergence-free for an incompressible fluid, whereas the flow inside the particle domain is constrained to undergo rigid body motion. In this approach, the rigid body motion constraint is imposed by avoiding the explicit calculation of distributed Lagrange multipliers and is based upon the formulation developed by Patankar [N. Patankar, A formulation for fast computations of rigid particulate flows, Center for Turbulence Research Annual Research Briefs 2001 (2001) 185–196]. The rigidity constraint is imposed and the rigid body motion (translation and rotational velocity fields) is obtained directly in the context of a two-stage fractional step scheme. The numerical approach is applied to both imposed particle motion and fluid–particle interaction problems involving freely moving particles. Grid and time-step convergence studies are performed to evaluate the accuracy of the approach. Finally, simulation of rigid particles in a decaying isotropic turbulent flow is performed to study the feasibility of simulations of particle-laden turbulent flows.

Large Eddy Simulation of Particle-Laden Turbulent Channel Flow Considering SGS Coupling

The paper presents a new dynamic SGS model of two-way coupling for large eddy simulation of particle-laden turbulent flow based on Yuu's model (1997). The advantage of this new model is that coupling of fluid-particles SGS components is taken into account and at the same time the coefficient of proposed SGS model can be optimized by Germano's (1991) dynamic procedure. To investigate the capability of this model, numerical simulations of particle-laden turbulent flow at Re=644 in a vertical channel were performed using this new dynamic SGS model and using Van Driest wall function. By comparing the calculation results with that of using single-phase SGS models, in which the coupling of SGS components was not considered, the present dynamic SGS model for two-way coupling was verified. In addition, the roles of particles GS and SGS components played in the turbulence modulation of fluid flow were clarified for particle-laden channel turbulent flows.

209 固気混相乱流の Two Way Coupling LES における Dynamic SGS モデルの提案

The paper presents a dynamic SGS model of Two Way Coupling for Large Eddy Simulation of particle-laden turbulent flow, which based on Yuu's model (2000). The advantage of this new model is that the coefficient of proposed SGS model can be decided by Germano's (1991) dynamic procedure. Then, the numerical simulation was performed with Van Driest wall function model and the present dynamic SGS model, for downward particle laden turbulent flows at Re=644 in a vertical channel. The present dynamic SGS model has been verified through comparison of statistical properties of particle-laden turbulent flow.

LES of Particle-Laden Turbulent Channel Flow Considering SGS Coupling. A Proposal of Dynamic SGS Model.

The paper presents a dynamic SGS model of Two Way Coupling for Large Eddy Simulation of particle-laden turbulent flow, which based on Yuu's model (1997). The advantage of this new model is that the coefficient of proposed SGS model can be decided by Germano's (1991) dynamic procedure. Then, the numerical simulation was performed with Van Driest wall function model and the present dynamic SGS model, for downward particle laden turbulent flows at Re=644 in a vertical channel that was experimentally investigated by Kulick (1994). The present dynamic SGS model has been verified through comparison of statistical properties of particle-laden turbulent flow. In addition, the effect of SGS component coupling on the turbulence modification has been investigated.