Numerical Simulations Of Particle-laden Flows Research Articles

A three-dimensional fictitious domain method for direct numerical simulations of particle-laden flows with heat transfer

In the present work, a three-dimensional fictitious domain method for particulate flows with heat transfer is proposed. For the case of fixed particle temperature, an iterative scheme for the temperature Lagrange multiplier is proposed, in order to determine its initial value and overcome the spurious oscillation of the explicit scheme at the initial time stage for different initial fluid and particle temperatures. Both explicit and implicit schemes are proposed for the solution of coupled fluid and solid temperature equations in the case of freely evolving particle temperature. The implicit scheme is suited to the case of large density ratios, specific heat ratios, or thermal conductivity ratios. Our method for the case of fixed particle temperature is verified via the test problems of a stationary hot sphere heating the surrounding quiescent fluid, a fixed sphere, and spheroid, respectively, in uniform flow, and sedimentation of a sphere and spheroid, respectively, in a vertical channel. We propose a new correlation of particle Nusselt number for an isolated sphere in a relatively small domain. Our code for the case of varying particle temperatures is verified via the effective thermal conductivity of a motionless sphere and the rising of a catalyst particle in an enclosure. Our method is applied to the sedimentation of a sphere at different Grashof numbers, specific heat ratios, and conductivity ratios. In addition, some preliminary results on heat transfer in turbulent channel flows laden with neutrally buoyant spherical and spheroidal particles, respectively, from fully resolved simulations with our method are reported.

Direct numerical simulation of particle-laden flow in an open channel at

We perform two-way coupled direct numerical simulation of particle-laden flow in an open channel at a friction Reynolds number ( $Re_{\tau }$ ) of 5186, which exhibits many characteristics of high-Reynolds-number wall-bounded turbulence, such as the distinct separation of scales in the inner and outer layers. Three representative cases, an unladen case and low- and high-Stokes-number particle-laden cases, are performed to investigate the turbulent modification by particles. To this end, we compare several statistical quantities to understand the particle effect on momentum exchange and interphasial energy transfer. The modulation of large-scale motions (LSMs) and very-large-scale motions (VLSMs) are analysed using spectral information, and we find that the LSMs and VLSMs are generally weakened in the inner and outer layers, which is qualitatively different from similar simulations at lower Reynolds numbers ( $Re_{\tau } \approx 500$ ). The spatial structures are investigated with correlation analysis, and inclined VLSMs are observed in the near-wall region, with decreased inclination angles by particles. The particles tend to widen and shorten the spanwise and streamwise extent of coherent structures, respectively. Furthermore, we find that the vorticity vector displays a preferential alignment with the eigenvector corresponding to the intermediate eigenvalue of the strain-rate tensor, independent of the particle Stokes number.

CP3d: A comprehensive Euler-Lagrange solver for direct numerical simulation of particle-laden flows

We present a comprehensive Euler-Lagrange solver, CP3d, for the direct numerical simulation of particle-laden flows. The solver can handle one-way, two-way, interface-unresolved four-way and interface-resolved coupling regime. To make the solver versatile, different numerical approaches are available for fluid, particle as well as the coupling sub-solver. For the sake of computational accuracy and efficiency, a third-order exponential approximation method is proposed for Basset history force in interface-unresolved regime, and a new simplified lubrication force model based on the averaged integration is utilized in interface-resolved simulation to account for the short-range hydrodynamic force. The volume integration approach is also modified to adapt the staggered mesh configuration. The present solver is intensively validated against several benchmarks. A 2D pencil-like domain decomposition is implemented for parallel communication. The resulting solver is able to simulate large scale cases with billions of grid points and millions of moving particles in interface-resolved four-way regime, using only hundreds of computational cores. In addition, a nearly perfect linear strong scaling performance is achieved. In our test, CP3d is more than ten times faster than other similar solver reported in the literature. Program summaryProgram Title: Channel-Particle 3D, CP3d.CPC Library link to program files:https://doi.org/10.17632/7j6kcf8629.1.Developer's repository link:https://github.com/gongzheng-justin/CP3d.Code Ocean capsule:https://codeocean.com/capsule/0609843.Licensing provisions: MIT License.Programming language: Fortran 95, parallelized using MPI.External libraries: FFTW.Nature of problem:CP3d provides a comprehensive tool to perform the direct numerical simulation for particle-laden flows. One-way, two-way, interface-unresolved four-way and interface-resolved coupling regimes can be conducted.Solution method: the code employs second-/fourth-order finite-difference discretization for the fluid Navier-Stokes equation, and numerically solves the Maxey-Riley equation for the particle phase. In four-way regime, particle collisions are considered by discrete-element method. Immersed boundary method is utilized in the interface-resolved coupling regime.

Experimental and numerical investigation into the effect of surface roughness on particle rebound

Erosion damage and particle deposition are crucial wear phenomena in gas turbine engines. As a result, compressor efficiency decreases, stability margin reduces, and maintenance cost increases. Hence, predicting these phenomena in an accurate manner is of paramount importance for a cost-efficient, safe, and sustainable operation. Erosion and particle deposition in the annulus are affected by particle transportation in the fluid and particle-wall interaction. The latter involves the particle impact, the potential damage of the surface and/or the particle, and the particle rebound. Particle rebounds are statistical in nature due to the target surface roughness, the variability in particle sizes, and superimposed effects caused by particle shapes as well as particle rotation and particle break-up during contact. Multiple studies investigated the statistics of particle rebound, providing empirical-based models for median and spread. However, modeling the particle-wall interaction and its data spread on a transparent physical basis allows separating the effect of target roughness from superimposed effects. The presented article pursues this objective by assessing the statistical spread of particle rebound data through multiple techniques and utilizing their interdependencies. It combines experimental, numerical, and analytical considerations. For the first time, coherent boundary conditions for the experimental, numerical and analytical setup allow the distinction of the effect of roughness from the integral effect of the superimposed phenomena. A sandblast test rig equipped with laser measurement equipment was used to measure particle rebound from flat titanium and stainless steel plates at different angles. The numerical setup is developed under OpenFOAM 6 using a RANS solver for transient simulations with compressible media in combination with one-way coupled particle flows. The numerical model includes the rebound spread model proposed by Altmeppen et al. combined with the quasi-analytical rebound model proposed by Bons et al. The statistical spread of particle rebound is investigated for roughness levels that are similar to the ones of deteriorated high-pressure compressor blades as discussed by Gilge et al. The measured surface roughness of the experimentally investigated targets is used as input parameters to the numerical framework. The rebound statistics obtained in the numerical simulation are compared to the rebound data measured in the experiment. Based on this study, conclusions are drawn about which part of the rebound spread is attributable to surface roughness and which is caused by superimposed effects. It was found that the effect of surface roughness as characterized by Altmeppen et al. contributes in the order of 46 % to the rebound spread for small impact angles. However, the share in spread due to roughness gradually decreases with increasing global impact angles to a level of 13 % for angles close to 90°. The remaining percentage of rebound spread is attributed to superimposing phenomena. In addition to the rolling and sliding of aspherical particles, further phenomena such as plastic deformation and erosion of the roughness peaks during contact and the associated dissipation of energy gain in importance for steeper impact angles. Therefore, the effect of surface roughness should not be neglected in numerical simulations of particle-laden flows. Modeling the superimposed phenomena which are observed to be dominating at high impact angles opens up a further field of research.

Comparative study of the virtual flux method and immersed boundary method coupled with regularized lattice Boltzmann method for suspension flow simulations

Suspension flows are ubiquitous in many fields, and reducing computational costs for numerical simulations of suspension flows remains a great challenge. Numerical simulations of particle-laden flows were performed here using the regularized lattice Boltzmann method (RLBM). RLBM, coupled with the virtual flux method (VFM) or the immersed boundary method (IBM) with the multi-direct forcing approach, conducted a series of three simulations for stationary and moving boundaries. The VFM and IBM results were compared for validation, and the computational efficiency was evaluated. For the two simulations using stationary and moving boundaries (i.e., a steady flow past a stationary cylinder and a plane Poiseuille flow including a single moving circular particle), the results based on the VFM and IBM were qualitatively comparable. The computational time for IBM was longer than that for VFM due to the iterations in its scheme. The pressure-driven suspension flow simulations showed that a dilute suspension's (<5%) relative viscosity was almost equivalent. The difference between the results obtained by the VFM and IBM in the semidilute regime (>10%) was discussed in terms of particle rotational motion. Even though the scalability for parallel computing was comparable between the VFM and IBM, the computational time could be effectively reduced by using the VFM instead of the IBM because of the increased suspension concentration.

Numerical Simulation of Particle-Laden Flow and Soot Layer Formation in Porous Filter

So far, diesel particulate filters (DPFs) have been widely used to collect diesel particulates including soot in the exhaust after-treatment. However, as the soot is continuously collected in the porous filter, the exhaust pressure (pressure drop) increases. To optimize the filter design for reducing its pressure drop, we need a numerical simulation. In this study, we simulated the particle-laden flow across the DPF. Structure of SiC-DPF was obtained by an X-ray CT technique. We conducted the numerical simulation by changing the soot aggregation diameter (simply called soot size), and evaluated the time-variation of the pressure drop. For discussing the soot deposition process, the contributions of the Brownian diffusion and the interception effect were separately estimated. Especially, we focused on the soot deposition region which could affect the pressure drop, together with the soot cake permeability and the soot packing density. Results show that, as the soot size is smaller, more soot is trapped. As a result, the shift from the depth filtration to the surface filtration is observed earlier. Therefore, for discussing the pressure drop, it is important to consider where the soot deposition occurs as well as the deposited soot mass in the filter.

An efficient four-way coupled lattice Boltzmann – discrete element method for fully resolved simulations of particle-laden flows

A four-way coupling scheme for the direct numerical simulation of particle-laden flows is developed and analyzed. It employs a multiple-relaxation-time lattice Boltzmann method with an adapted bulk viscosity to simulate the fluid phase efficiently. The momentum exchange method is used to couple the fluid and the particulate phase. The particle interactions in normal and tangential direction are accounted for by a discrete element method using linear contact forces. All parameters of the scheme are studied and evaluated in detail and precise guidelines for their choice are developed. The development is based on several carefully selected calibration and validation tests of increasing physical complexity. It is found that a well-calibrated lubrication model is crucial to obtain the correct trajectories of a sphere colliding with a plane wall in a viscous fluid. For adequately resolving the collision dynamics it is found that the collision time must be stretched appropriately. The complete set of tests establishes a validation pipeline that can be universally applied to other fluid-particle coupling schemes providing a systematic methodology that can guide future developments.

A Review on Contact and Collision Methods for Multi-Body Hydrodynamic Problems in Complex Flows

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the combustion process, to aerosol deposition in spray medication, along with many others. Due to their strongly nonlinear and multiscale nature, the above complex phenomena still raise a very steep challenge to the most computational methods. In this review, we provide comprehensive coverage of multibody hydrodynamic (MBH) problems focusing on particulate suspensions in complex fluidic systems that have been simulated using hybrid Eulerian-Lagrangian particulate flow models. Among these hybrid models, the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) provides mathematically simple and computationally-efficient algorithms for solid-fluid hydrodynamic interactions in MBH simulations. This paper elaborates on the mathematical framework, applicability, and limitations of various 'simple to complex' representations of close-contact interparticle interactions and collision methods, including short-range inter-particle and particle-wall steric interactions, spring and lubrication forces, normal and oblique collisions, and mesoscale molecular models for deformable particle collisions based on hard-sphere and soft-sphere models in MBH models to simulate settling or flow of nonuniform particles of different geometric shapes and sizes in diverse fluidic systems.

Direct Numerical Simulation of Particle-laden Flow Around an Obstacle at Different Reynolds Numbers

Inspired by the practical operation of the fluid machineries, direct numerical simulation of fluid with a lot of finite-size particles flowing around a large-size obstacle at three different Reynolds numbers is implemented by using a two-way coupled finite-volume, discrete-element and immersed-boundary method. The results show that, for a low Reynolds number Re=20, the flow is dominated by viscosity, and under the circumstances of a small Stokes number, the particles follow fluid streamlines closely. The flow suggests regular movement characteristics of laminar flow, although the vortices behind the obstacle tend to collapse under the perturbation of particles. For a moderate Reynolds number Re=100, the phenomenon of vortex shedding is also observed. Due to the centrifugal force induced by the vortices, particles are distributed around the main vortices behind the obstacle, forming particle-free zones in these vortices. For a high Reynolds number Re=300, the flow is chaotic. The vortices of many sizes appear irregularly in the domain and the distribution of particles tends to be uniform.

A fictitious domain method with distributed Lagrange multipliers on adaptive quad/octrees for the direct numerical simulation of particle-laden flows

In this article, we extend our Distributed Lagrange Multiplier/Fictitious Domain method previously implemented on simple regular Cartesian grids to quadtree/octree adaptive grids. The objective is to improve both the accuracy and efficiency of our DLM/FD particle-resolved simulation method by extending its computing capabilities through dynamic local mesh refinement. The main features of our numerical method, such as a first-order operator splitting time algorithm and a second-order reconstruction of the velocity field close to the boundary of the immersed rigid bodies (of arbitrary shape), are unchanged. We implemented our adaptive DLM/FD algorithm within Basilisk, a parallel platform to solve partial differential equations on dynamic quadtree/octree grids. The quadtree/octree structure of the grid and specific design rules of Basilisk impose a special treatment of some of the operations performed on the grid in the DLM/FD-Uzawa algorithm. The new computational method is then tested and validated on a set of flow configurations including the challenging problem of accurately computing lubrication interaction forces without resorting to using any ad hoc correction. Finally, we illustrate the potential of our code to compute complex particle-laden flow configurations that were not attainable in the past with a DLM/FD algorithm implemented on a simple regular Cartesian grid.

Clustering behaviour and settling velocity of bidisperse inertial particles in turbulent open channel flow

The clustering behaviour and settling velocity of bidisperse inertial particles with sub-millimetre diameters travelling in a turbulent open channel flow are investigated using the simultaneous particle image velocimetry and particle tracking velocimetry measurement technique. Instantaneous images of flow field and inertial particles are separated based on different wavelengths of light emitted by fluorescent seeding particles and inertial particles. Four flow configurations of turbulence are generated by turbulence grids with different sizes in the open channel. The clustering behaviour of monodisperse and bidisperse inertial particles and the discrepancy between them in the different flow cases are studied. We found that bidisperse inertial particles have weaker clustering phenomenon as compared with corresponding monodisperse inertial particles and this weak clustering phenomenon is almost consistent when the Taylor microscale Reynolds number Reλ changes from 90 to 267. The relationship between settling velocity and local concentration of inertial particles is then investigated. The results support the preferential concentration as the mechanism for the enhancement of settling velocimetry when the normalized particle concentration is in the range of 0.1~10. However, the anisotropy property and large eddy effect in turbulence will greatly change the interaction between inertial particles and turbulent flows and further alter their settling velocity, such as the average settling velocity decreasing with increasing Stokes number which depends on the dissipation time scale. Accordingly, we propose a new dimensionless multiscale parameter SvηReL1/2 to take into account the effect of large eddies and turbulence anisotropy on the settling velocity. With the simultaneous measurement of particle settling velocities and fluid velocities, we also analyse the unsteady force term in the particle dynamic equation. When the turbulence intensity is small and/or the particle inertia related to particle diameter and density ratio between inertial particle and fluid is small, the unsteady term can have a large contribution and it should not be neglected in the particle dynamic equation for the point-particle method in the numerical simulations of particle-laden flows.

Numerical simulation of particle-laden flow in an industrial wastewater sedimentation tank

The wastewater of steel production factories consists of a large amount of very small metal particles. The metal particles in this wastewater enter a large sedimentation tank and are deposited on the floor of it. In this study, the turbulence particle-laden flow in the sedimentation tank of a steel rolling company is investigated. The Reynolds Averaged Navier–Stokes equations are solved with SST k-ω and standard k-e turbulence models. Two-phase flow simulation is performed using the discrete phase model. Particle structure is determined by a scanning electron microscope. Based on the range of particle size, the particles are divided into 13 classes. Each class is injected into the continuous phase and then tracked. In order to evaluate the results, the settling efficiency is determined by sampling the input and output wastewater. This efficiency is compared with the results of numerical simulation. The pattern of solid particle motion shows that the nature of particle motion is three-dimensional. Particle tracking indicates that the settling efficiency increases with increasing the particle diameter. The streamlines show that a large and strong eddy is created in the sedimentation tank. This eddy is so strong that acts as a dead zone and reduces the efficiency of tank. In the following, the effect of environmental temperature on the efficiency of sedimentation tank is investigated. Results show that with increasing the temperature of the wastewater, the efficiency of settling tank increases.

Immersed boundary/solid method for the numerical simulation of particle-laden flows

An outlook of computational fluid dynamics methods based on the fixed Cartesian grid, especially the immersed boundary (IB) method and related techniques, is provided. The basic idea of IB methods and the improvements to maintain consistency of boundary condition and mass conservation, that is the consistent projection method, are discussed. Then, recent examples for particle-laden flows are introduced. To deal with many particles, the immersed solid method is picked up as an efficient alternative to the IB method. In particular, we place focus on the flow and heat transfer of dense mixture of particles and liquid. In such a condition, the flow in narrow gap in between solid interfaces is considered by the lubrication equation. Finally, for further development of application in large-scale turbulent flows laden with particles, the importance of explicitly-defined volume averaging is pointed out based on our recent progress.

Drag enhancement and turbulence attenuation by small solid particles in an unstably stratified turbulent boundary layer

Point-particle direct numerical simulations of particle-laden flows have been conducted to investigate the complex coupling between inertial particles, buoyancy force, and strong shear flows in an unstably stratified turbulent boundary layer over a flat plate. Two-way coupling and particle-particle collisions, i.e., four-way coupling, are considered in the dilute gas-solid flows. The simulation results indicate that the presence of inertial particles with diameter smaller than the Kolmogorov length scale tends to reduce the thermal displacement thickness and enthalpy thickness, while increasing the mean skin-friction coefficient and Nusselt number. The feedback force exerted by the particles on the fluid is found to contribute largely to the drag enhancement. The turbulence intensities and temperature fluctuations are significantly attenuated in the particle-laden flows with respect to the unladen flow. The budgets of the turbulent kinetic energy show that the particles have direct and indirect effects on the modulation of turbulence. On the one hand, the production and the viscous dissipation rate are suppressed by the particles in most regions of the boundary layer. On the other hand, the particle-turbulence interactions produce an extra energy source in the inner layer, while causing an additional energy sink in the outer layer of the boundary layer. These combined effects lead to the pronounced turbulence attenuation observed in this study.

Direct numerical simulation of turbulent flow and heat transfer in a spatially developing turbulent boundary layer laden with particles

Direct numerical simulations of particle-laden flows in a spatially developing turbulent thermal boundary layer over an isothermally heated wall have been performed with realistic fully developed turbulent inflow boundary conditions. To the authors’ best knowledge, this is the first time the effects of inertial solid particles on turbulent flow and heat transfer in a flat-plate turbulent boundary layer have been investigated, using a two-way coupled Eulerian–Lagrangian method. Results indicate that the presence of particles increases the mean streamwise velocity and temperature gradients of the fluid in the near-wall region. As a result, the skin-friction drag and heat transfer are significantly enhanced in the particle-laden flows with respect to the single-phase flow. The near-wall sweep and ejection motions are suppressed by the particles and hence the Reynolds shear stress and wall-normal turbulent heat flux are attenuated, which leads to reductions in the production of the turbulent kinetic energy and temperature fluctuations. In addition, the coherence and spacing of the near-wall velocity and temperature streaky structures are distinctly increased, while the turbulent vortical structures appear to be disorganized under the effect of the particles. Moreover, the intensity of the streamwise vortices decreases monotonically with increasing particle inertia.

Local lubrication model for spherical particles within incompressible Navier-Stokes flows.

The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

Uncertainty quantification in numerical simulation of particle-laden flows

Numerical models can help to push forward the knowledge about complex dynamic physical systems. Modern approaches employ detailed mathematical models, taking into consideration inherent uncertainties on input parameters (phenomenological parameters or boundary and initial conditions, among others). Particle-laden flows are complex physical systems found in nature, generated due to the (possible small) spatial variation on the fluid density promoted by the carried particles. They are one of the main mechanisms responsible for the deposition of sediments on the seabed. A detailed understanding of particle-laden flows, often referred to as turbidity currents, helps geologists to understand the mechanisms that give rise to reservoirs, strategic in oil exploration. Uncertainty quantification (UQ) provides a rational framework to assist in this task, by combining sophisticated computational models with a probabilistic perspective in order to deepen the knowledge about the physics of the problem and to access the reliability of the results obtained with numerical simulations. This work presents a stochastic analysis of sediment deposition resulting from a turbidity current considering uncertainties on the initial sediment concentrations and particles settling velocities. The statistical moments of the deposition mapping, like other important features of the currents, are approximated by a Sparse Grid Stochastic Collocation method that employ a parallel flow solver for the solution of the deterministic problems associated to the grid points. The whole procedure is supported and steered by a scientific workflow management engine designed for high performance computer applications.

Direct numerical simulation of a particle-laden flow in a flat plate boundary layer

In this paper, a direct numerical simulation of particle-laden flow in a flat plate boundary layer is performed, using the Eulerian–Lagrangian point-particle approach. This is, as far as we know, the first simulation of a particle-laden spatially-developing turbulent boundary layer with two-way coupling. A local minimum of the particle number density is observed in the close vicinity of the wall. The present simulation results indicate that the inertial particles displace the quasi-streamwise vortices towards the wall, which, in turn, enhance the mean streamwise fluid velocity. As a result, the skin-friction coefficient is increased whereas the boundary layer integral thicknesses are reduced. The presence of particles augments the streamwise fluctuating velocity in the near-wall region but attenuates it in the outer layer. Nevertheless, the wall-normal and spanwise velocity fluctuations are significantly damped, and so is the Reynolds stress. In addition, the combined effect of a reduced energy production and an increased viscous dissipation leads to the attenuation of the turbulent kinetic energy.

Collision modelling for the interface-resolved simulation of spherical particles in viscous fluids

AbstractThe paper presents a model for particle–particle and particle–wall collisions during interface-resolving numerical simulations of particle-laden flows. The accurate modelling of collisions in this framework is challenging due to methodological problems generated by interface approach and contact as well as due to the greatly different time scales involved. To cope with this situation, multiscale modelling approaches are introduced avoiding excessive local grid refinement during surface approach and time step reduction during the surface contact. A new adaptive model for the normal forces in the phase of ‘dry contact’ is proposed, stretching the collision process in time to match the time step of the fluid solver. This yields a physically sound and robust collision model with modified stiffness and damping determined by an optimization scheme. Furthermore, the model is supplemented with a new approach for modelling the tangential force during oblique collisions which is based on two material parameters: a critical impact angle separating rolling from sliding and the friction coefficient for the sliding motion. The resulting new model is termed the adaptive collision model (ACM). All proposed sub-models only contain physical parameters, and virtually no numerical parameters requiring adjustment or tuning. The new model is implemented in the framework of an immersed boundary method but is applicable with any spatial and temporal discretization. Detailed validation against experimental data was performed so that a general and versatile model for arbitrary collisions of spherical particles in viscous fluids is now available.

Modeling mechanical contact and lubrication in Direct Numerical Simulations of colliding particles

We developed a model for inexpensive Direct Numerical Simulations of particle-laden flow by fully resolving the hydrodynamics at all times except when the gap between colliding particles becomes comparable to the grid step. The resolved hydrodynamics were obtained with a previously developed pressure boundary integral method for direct fluid–particle simulations on Cartesian grids. The unresolved part of the lubrication pressure/shear force in the subgrid gap was predicted using theoretical Stokes flow models. Singular lubrication forces were avoided by postulating that contact begins when the gap distance between the particles becomes equal to the size of micro-asperities. The mechanical contact between particles is dynamically resolved and particle interactions are both inelastic and frictional. The proposed numerical model was validated through resolution tests and comparison with experimental data for immersed binary collisions.