Particle-resolved Simulation Research Articles

Deterministic drag modelling for spherical particles in Stokes regime using data-driven approaches

In this paper, we develop a deterministic drag model for stationary spherical particles in a Stokes flow using a cascade of data-driven approaches. The model accounts for the variation in drag experienced by each particle within fixed random arrangements. The developed model is a symbolic expression that offers explainability, ease of implementation, and computational efficiency. Firstly, we generate particle-resolved direct numerical simulation data of the flow past periodic random arrangements of stationary spherical particles with volume fractions between 0.05 and 0.4 using the method of regularized Stokeslets. Secondly, we train graph neural networks (GNs) on the generated data to learn the pairwise influence of neighbouring particles on a reference particle. The GNs are converted to symbolic expressions using genetic programming (GP), unveiling repeated subexpressions. Finally, these subexpressions constitute the foundation of the proposed algebraic model, further refined via non-linear regression. The proposed model can qualitatively mimic the pairwise influences as predicted by the GN and can capture the drag variations with accuracy from 74% and up to 84.7% when compared to the particle-resolved simulations. Due to the interpretability of the proposed model, we are able to explore how neighbour positions alter the drag of a particle in an assembly. The proposed model is a promising tool for studying the dynamics of particle assemblies in Stokes flow.

Particle-resolved simulations and measurements of the flow through a uniform packed bed

The present study focuses on the assessment of the performance of a finite volume method based, particle-resolved simulation approach to predict the flow through a model packed-bed consisting of 21 layers of spheres arranged in the body centered cubic packing. The unsteady flow developing in the freeboard is also considered. Two highly resolved large eddy simulation were preformed, for two Reynolds numbers, 300 and 500, based on the particle diameter, employing a polyhedral, boundary-conforming mesh. The geometry and the flow conditions are set to reproduce the flow conditions investigated in the experiment carried out by Velten and Zähringer [“Flow field characterisation of gaseous flow in a packed bed by particle image velocimetry,” Transp. Porous Media 150, 307 (2023)] using particle image velocimetry. The numerical results compare favorably with the measurements both inside and above the bed. The effect of differences arising between the physical and numerical configurations is thoroughly discussed alongside the impact of meshing strategy on the accuracy of the predictions.

Lattice Boltzmann simulations of homogeneous shear turbulence laden with finite-size particles

As a powerful tool to investigate turbulent flows laden with finite-size particles, the lattice Boltzmann method (LBM)'s capability to contribute to a particle-resolved simulation of particle-laden homogeneous shear turbulence (HST) has yet to be realized. To capture the turbulence-particle interactions more accurately, the interpolated-bounce-back schemes combined with the momentum-exchange method that possesses second-order accuracy are adopted to treat the no-slip condition on particle surfaces and compute the hydrodynamic force/torque. However, this choice brings extra difficulties in enforcing the shear periodic boundaries due to the absence of fluid information in solid regions. The present study resolves these difficulties by designing a scheme to construct the distribution functions in the particle gaps based on the lubrication theory and an algorithm for the “refilling” process near the shear periodic boundaries. With these developments, a direct numerical simulation of particle-laden HST is achieved with LBM. The turbulence modulation effects induced by particles are briefly discussed.

The influence of particle density and diameter on the interactions between the finite-size particles and the turbulent channel flow

Understanding the influence of different particle parameters on the two-way interactions between the particles and wall-bounded turbulence is important in many natural phenomena and engineering applications. In this work, particle-resolved direct simulation of particle-laden turbulent channel flow is performed based on the mesoscopic lattice Boltzmann method (LBM), and the particle–fluid interface is treated using the interpolated bounce back scheme. The friction Reynolds number (Reτ) of the single phase turbulent channel flow is 180, and the particle volume fraction is fixed at 1%. Three particle–fluid density ratios and three particle diameters are considered, and five particle-laden simulations are performed to investigate the influence of particle density and diameter on the interactions between the particles and the carrier turbulence. Results show that the streamwise velocity of the solid phase is larger than that of the fluid phase in the near-wall region, and the velocity difference between the two phases decreases with increasing particle density, but increases with increasing particle diameter. The probability density functions (PDFs) of particle velocity and angular velocity depend on the distance between the particles and the wall, but the PDFs of particle acceleration and angular acceleration are not spatially dependent. The distribution of particle Reynolds number follows the Gamma distribution within the buffer region and viscous sublayer. The solid phase concentration is high in the near-wall region, and the largest solid-phase concentration in this region occurs in the case with particles of intermediate density. Particles with different parameters would lead to different modulation to the carrier flow. Then, two aspects of the turbulence modulation are explored, i.e., the streamwise velocity and the turbulent kinetic energy (TKE). The presence of finite-size particles typically increases the streamwise velocity in the near-wall region and reduce the streamwise velocity outside this region. The trend is similar for TKE, but the TKE attenuation mainly occurs in the buffer region. The modulation to the streamwise velocity is analyzed using the streamwise momentum balance equation. It is found that the streamwise velocity modulation is dominated by the weighted Reynolds stress, but the different modulation in the near-wall region is due to the difference in weighted particle-induced stress, whereas the different modulation outside the near-wall region is due to the change in weighted Reynolds stress. Through TKE budget analysis, it is found that the enhancement of the total TKE source in the viscous sublayer increases with increasing particle density and diameter and the attenuation of total TKE source in the buffer region increases with increasing particle density and diameter, which is consistent with the TKE modulation for different cases.

Porous-media model based particle-resolved simulation of a fixed bed with olefin catalytic cracking reaction

Understanding the interstitial reacting flow in particle packing structure and its relation with the reaction performance is crucial to designing a highly efficient fixed bed reactor. This study uses a particle-resolved approach with a porous-media model-based immersed boundary method to simulate an olefin catalytic cracking (OCC) fixed bed with 150 cylindrical particles by combining a six-lump kinetic model and mass transfer model. The effects of weight hourly space velocity (WHSV) and particle shape are further investigated in analyzing conversion, concentration variation, flow structure and pressure drop. The study reveals a three-stage pattern in variation of product concentration along the packing structure height with different WHSVs, providing the basis for determining the optimal packing height. It also finds that the hollow-cylindrical particle manifests the best reaction performance while the cylindrical particle the worst. The coordination of surface area and pressure drop of the packing structure determines the OCC reaction effectiveness.

Development of Particle Resolved - Subgrid Corrected Simulations: Hydrodynamic force calculation and flow sub-resolution corrections

Particle Resolved - Direct Numerical Simulation (PR-DNS) of fluid–solid particles is conducted to study hydrodynamic interactions at the interface between phases. An original distinction is proposed between Particle Resolved Simulation (PRS) and Particle Resolved - Direct Numerical Simulation (PR-DNS). In PR-DNS, velocity gradients and pressure are fully resolved, which required several dozens of meshes in the diameter of the particles (40 in Stokes configuration), whereas for PRS, with grid resolution of 10 meshes per diameter, the gradients are only partly resolved, resulting in a sub-resolution of hydrodynamic forces exerted by the fluid to the interface of solid particles. The very high computational cost, associated to PR-DNS, limits its application to academic cases, even though, it was originally developed to study the collective physical effects of a fluid–particle assembly. It explains why numerous simulations with a grid resolution of only a dozen meshes in the particle’s diameter – typically between 10 and 16 – referred to here as PRS, can be found in the literature. In these cases, the velocity gradients and pressure are not accurately computed, inducing an error in the hydrodynamic forces exerted by the fluid to the interface of particles. This paper aims to clarify the hydrodynamic interactions at this scale for a single particle settling in an infinite medium under Stokes configuration. For this purpose, an original method, designed for solid particles, is proposed to compute hydrodynamic forces. A mesh-dependent correlation is then built to numerically correct the partially resolved hydrodynamic forces obtained with PRS, in what we call Particle Resolved - Subgrid Corrected Simulations (PR-SCS). Finally, the correction is assessed for various Reynolds numbers and density ratios under the Stokes assumption.

Particle-resolved thermal lattice Boltzmann simulation using OpenACC on multi-GPUs

We utilize the Open Accelerator (OpenACC) approach for graphics processing unit (GPU) accelerated particle-resolved thermal lattice Boltzmann (LB) simulation. We adopt the momentum-exchange method to calculate fluid-particle interactions to preserve the simplicity of the LB method. To address load imbalance issues, we extend the indirect addressing method to collect fluid-particle link information at each timestep and store indices of fluid-particle link in a fixed index array. We simulate the sedimentation of 4,800 hot particles in cold fluids with a domain size of 40002, and the simulation achieves 1750 million lattice updates per second (MLUPS) on a single GPU. Furthermore, we implement a hybrid OpenACC and message passing interface (MPI) approach for multi-GPU accelerated simulation. This approach incorporates four optimization strategies, including building domain lists, utilizing request-answer communication, overlapping communications with computations, and executing computation tasks concurrently. By reducing data communication between GPUs, hiding communication latency through overlapping computation, and increasing the utilization of GPU resources, we achieve improved performance, reaching 10846 MLUPS using 8 GPUs. Our results demonstrate that the OpenACC-based GPU acceleration is promising for particle-resolved thermal lattice Boltzmann simulation.

Particle-resolved simulation of Fe-based oxygen carrier in chemical looping hydrogen generation

Oxygen carrier capability plays an important role in the performance of chemical looping hydrogen generation (CLHG). In this work, particle-scale simulation of oxygen carriers during the CLHG process is carried out, where the coke deposition effect on pore structures is taken into consideration. Meanwhile, the impacts of porosity and active component distribution of oxygen carriers on the CLHG performance are also analyzed. The results demonstrate that the CLHG performance is sensitive to particle porosity and active component distribution, especially for fuel reactor (FR). The increase of particle porosity can promote the carbon formation rate and hydrogen production rate. The flow direction and the diffusion will lead to the discrepancy of temperature between Egg-shell and Egg-yolk particles.

A multiple-time-step integration algorithm for particle-resolved simulation with physical collision time

In this paper, we present a multiple-time-step integration algorithm (MTSA) for particle collisions in particle-resolved simulations. Since the time step required for resolving a collision process is much smaller than that for a fluid flow, the computational cost of the traditional soft-sphere model by reducing the time step is quite high in particle-resolved simulations. In one state-of-the-art methodology, collision time is stretched to several times the flow solver time step for the fluid to adapt to the sudden change in particle motion. However, the stretched collision time is not physical, the hydrodynamic force may be severely underestimated during a stretched collision, and the simulation of sediment transport may be sensitive to the stretched collision time. The proposed MTSA adopts different time steps to resolve fluid flow, fluid-particle interaction, and particle collision. We assessed the MTSA for particle-wall collisions as well as particle-particle collisions, determined the optimal iteration number in the algorithm, and obtained excellent agreements with experimental measurements and reference simulations. The computational cost of the MTSA can be reduced to about one order of magnitude less than that using the traditional soft-sphere model with almost the same accuracy. The MTSA was then implemented in a particle-resolved simulation of sediment transport with thousands of particles. {By comparing the results obtained using the MTSA and a version of the stretching collision time algorithm similar to Costa et al.(2015), we found that stretching the collision time reduced particle stiffness, weakened particle entrainment, and affected some turbulence and particle statistics.

Numerical investigation on the heat transfer of particle arrays in supercritical water

The heat transfer characteristics of particles in supercritical water (SCW) are the research foundation for the development of the technology of coal gasification in SCW. The study encounters two challenging problems: the complexity of particle spatial distribution and the special variation of SCW properties. Therefore, this work focuses on contrasting the particle interaction characteristics between in SCW and conventional fluid, instead of the direct study of particle clusters in SCW. Research is conducted by the particle-resolved numerical simulation method. In the simulations, the SCW inflow is 973 K and 25 MPa which is a usual operating condition, and all particle surface temperatures are constant and uniform with the values of 300 K, 672 K and 973 K which are respectively below, at and beyond the pseudocritical temperature zone. The side-by-side and streamwise distributed arrays, which are simple but representative, are adopted as the research objects firstly. The effects of particle number and inter-particle distance on heat transfer are studied. Results indicate that the effects of particle interaction on heat transfer under all heat transfer states are similar in the side-by-side array; while only the effects under the pseudocritical and supercritical states are similar in the streamwise array. Then the structured packed array is adopted, and the effects of void fraction (ε) under different heat transfer states are studied. Moreover, a new correlation dependent on ε and Re is built for predicting the ratio of the Nu of a particle in the structured packed array and that of a single particle.

Particle-resolved simulation of antidunes in free-surface flows

The interaction of supercritical turbulent flows with granular sediment beds is challenging to study both experimentally and numerically. This challenging task has hampered advances in understanding antidunes, the most characteristic bedform of supercritical flows. This article presents the first numerical attempt to simulate upstream-migrating antidunes with geometrically resolved particles and a liquid–gas interface. Our simulations provide data at a resolution higher than laboratory experiments, and they can therefore provide new insights into the mechanisms of antidune migration and contribute to a deeper understanding of the underlying physics. To manage the simulations’ computational costs and physical complexity, we employ the cumulant lattice Boltzmann method in conjunction with a discrete element method for particle interactions, as well as a volume-of-fluid scheme to track the deformable free surface of the fluid. By reproducing two flow configurations of previous experiments (Pascal et al., Earth Surf. Process. Landf., vol. 46, issue 9, 2021, pp. 1750–1765), we demonstrate that our approach is robust and accurately predicts the antidunes’ amplitude, wavelength and celerity. Furthermore, the simulated wall shear stress, a key parameter governing sediment transport, is in excellent agreement with the experimental measurements. The highly resolved data of fluid and particle motion from our simulation approach open new perspectives for detailed studies of morphodynamics in shallow supercritical flows.

Comprehensive quasi-steady force correlations for compressible flow through random particle suspensions

Models for quasi-steady drag, quasi-steady drag variation, and transverse forces for compressible flows through random, fixed, particle suspensions are presented. Correlations are formulated using drag force measurements obtained from particle-resolved simulation data spanning subsonic to supersonic flow conditions. The newly proposed drag models are extensions of existing models for incompressible dense gas-solid flows to finite Mach numbers, while the transverse particle force model is new and incorporates the covariation between streamwise and transverse forces.

Particle-resolved simulation of antidunes in free-surface flows

Particle-resolved simulation of antidunes in free-surface flows

Effects of particle shape and packing style on ethylene oxidation reaction using particle-resolved CFD simulation

Gaining in-depth insights into the effects of particle shapes and packing style on ethylene oxidation reaction is of paramount industrial importance. In this work, reactor models of five packing structures with different particle shapes and three packing structures with different packing styles are established by employing software Blender and COMSOL Multiphysics to explore how the reaction-diffusion behaviors affect ethylene oxidation process. The reliabilities of rigid body dynamics model and particle-resolved reactor model are verified by comparing simulated and experimental pressure drops and ethylene conversions. In all the five packing structures with laminar flow conditions, the high bed porosity and low total particle surface area for the trilobe packing structure give rise to the lowest pressure drop of 27.8 Pa/m, while the internal voids cutting mode provides the excellent heat transfer capacity for the Raschig ring packing structure and the highest ethylene conversion and thereby the highest bed temperature rise of 25.1 K for the four-hole cylinder packing structure. Based on these analyses, changing the packing style to the bottom-up Raschig ring - four hole cylinder packing structure would be a good strategy for the effectively lowered reactor temperature rise by 4.8 K together with the slightly reduced ethylene conversion.

The competition/inhibition effect of H2O/CO2-char gasification in typical in situ gasification-chemical looping combustion (iG-CLC) conditions via particle-resolved simulation

In the fuel reactor of in-situ gasification chemical looping combustion (iG-CLC), the solid fuel (e.g., coal, biomass) goes through two typical processes: devolatilization and char gasification. Then the pyrolysis and gasification products react with oxygen carrier to produce CO2 and H2O ideally. The slow char gasification rate during iG-CLC is responsible for combustion efficiency. Therefore, a deeper understanding of char conversion characteristics is required to optimize iG-CLC conditions. In this paper, a particle-resolved simulation with detailed heterogeneous reactions is conducted, in which the effects of char particle size and reaction temperature on char conversion characteristics are carefully studied. To understand the competition between CO2 gasification and H2O gasification, single-particle simulations are carried out under mixed and separate atmospheres. The char gasification rate in CO2/H2O mixtures (rmix) is lower than the sum of the char-H2O gasification rate (rH2O) and the char-CO2 gasification rate (rCO2). We find that the competition for active sites between char-H2O gasification and char-CO2 gasification is not significant, while the inhibition of gasification products play an important role in char-CO2 gasification, particularly the inhibition of CO (from char-H2O or char-CO2 gasification), due to the accumulation of H2 and CO inside the char particle. The inhibition effect is quantified via particle-resolved simulations and then a quantitative formula is attained to describe the complex relationship between H2O gasification and CO2 gasification. Then the point-source model for H2O/CO2-char gasification is developed for computational fluid dynamics simulations. Straightforward cloud diagrams are presented to explore the relationship between conversion rate characteristics and physicochemical properties of char, providing useful information for the optimization of iG-CLC conditions.

An immersed boundary/multi-relaxation time lattice Boltzmann method on adaptive octree grids for the particle-resolved simulation of particle-laden flows

We present an immersed boundary/multi-relaxation time lattice Boltzmann method for the particle-resolved simulation of particle-laden flows. The no-slip boundary condition is handled by an explicit feedback immersed boundary method for fixed and moving particles with arbitrary shape. Two special treatments are applied to improve the simulation stability and accuracy: (i) a smoothed discrete delta function (Yang et al. (2009) [47]) is adopted to suppress the spurious force oscillations and (ii) a multi-relaxation time collision operator is utilized to fix the viscosity-dependent numerical slip error of the immersed boundaries. To further reduce the computational effort, we extend the method from fixed and uniform Cartesian grids to adaptive quadtree/octree grids by implementing it in the open-source software Basilisk. A Lax-Wendroff streaming operator is adopted in our method to retain second-order accuracy in both space and time on non-uniform grids, as well as to maintain a unified time scale over the entire computational domain. Consequently, one collision-streaming operation only is required per time step at all grid levels. We test our proposed method on a set of validation cases corresponding to assorted incompressible flows with fixed and moving rigid particles in both 2D and 3D. The accuracy and robustness of our method are demonstrated via thorough comparison with the analytical, experimental and numerical data provided in the literature.

A particle resolved simulation approach for studying shock interactions with moving, colliding solid particles

This work applies a new combination of techniques for the fully resolved simulation of compressible, gas–particle multiphase flows. The adaptive wavelet collocation method is used to dynamically, and efficiently, adapt the computational grid to localized flow features and the particles. A characteristic-based volume penalization method that imposes arbitrary Dirichlet, Neumann, or Robin-type immersed boundary conditions, is used to enforce the no-slip condition at particle surfaces. A hard-sphere collision model is applied to capture the particle–particle collisions. Proof of concept test cases are presented, showcasing the dynamic grid adaptation and fully resolved two-way coupling between the phases that is possible with this approach. Results for a shock-driven single cylinder under viscous and inviscid conditions are presented along with a demonstration of a shock interacting with a cloud of randomly distributed cylinders and spheres.

Computational Methods for Simulating Dynamics of Particles at Fluid–Fluid Interface

This review gives a brief description of major computational methods to simulate the dynamics of particles at liquid–liquid or liquid–vapor interfaces. The particle-resolved simulation models based on the direct numerical simulation of Navier–Stokes equation and the lattice Boltzmann method (LBM) are surveyed. In addition, we explain a numerical model based on the smoothed-profile LBM for the treatment of moving solid particles in a fluid and the free-energy LBM for the description of a liquid-vapor system. Typical simulation results presented here indicate that the particle-resolved simulations can be an effective approach to explore the particle–fluid–fluid systems.

Effect of large temperature difference on drag coefficient and Nusselt number of an ellipsoidal particle in compressible viscous flow

Particle-resolved simulation which fully considers the temperature-dependence of fluid properties is performed to study the momentum and heat transfer between a high-temperature ellipsoidal particle and the fluid. A non-Boussinesq regime is first identified with the Richardson number larger than unity. The drag coefficient CD and Nusselt number Nu increase significantly with particle temperature. The increased pressure difference and the increased friction drag play the dominant role in the increase of CD at small and large incident angles, respectively. The increase of Nusselt number is mainly due to the increase of the thermal conductivity. The relationship between CD and the incident angle φ satisfies sin2φ, while Nu evolves as sinmφ, where m is a function of Reynolds number and aspect ratio. The values of CD and Nu at φ = 0° and φ = 90° are fitted from simulation results and values at any incident angle can be predicted based on functions of sin2φ and sinmφ.

Particle resolved simulation of sediment transport by a hybrid parallel approach

Sediment transport over an erodible sediment bed is studied by particle resolved simulations with a hybrid parallel approach. To overcome the challenges of load imbalance in the traditional domain decomposition method when encountering highly uneven distributions of particles in sediment transport, the parallel approach of Darmana et al. (2006) originally developed for point particle simulations is modified and implemented into particle resolved simulations. A novel memory optimization technique is proposed to reduce the memory requirement of the hybrid approach for spherical particles with equal size. The present hybrid parallel approach shows good scalability and high parallel efficiency in a challenging sediment transport test case with more than a million spherical particles. Our code is validated by several benchmark cases, and the results show good agreement with experimental and computational data in the literature. Furthermore, a turbulent flow over an erodible sediment bed is simulated. An extraction method is proposed to distinguish the saltating and rolling particles and extract impact and rebound information of the particle–mobile bed interaction. The probability distribution functions (PDF) of several saltation parameters such as velocity, angle, and spanwise angular velocity of impact and rebound events are presented. Splash functions are established for the particle–mobile bed interaction in the turbulent flow, which was rarely investigated in the experiments and is helpful to model the complex particle–bed interactions in turbulent flow.