Fluid-particle Systems Research Articles

A hybrid method for the direct numerical simulation of phase change heat transfer in fluid–particle systems

A hybrid method for the direct numerical simulation of phase change heat transfer in fluid–particle systems

Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation

Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation

Particle-resolved direct numerical simulation and bottom-up statistical analysis on solid-phase pressure in particle–fluid systems

Solid-phase stress is a major factor shaping the complex behaviors of particle–fluid systems. However, uncertainties and inconsistencies can be found among the various models proposed. This work pays attention to the effect of mesoscale structures, that is, the heterogeneity of particle distribution at a scale of statistical meaning but no significant flow field variation, on the solid-phase normal stress, or pressure. Using a bottom-up statistical method, the solid-phase pressure in liquid- and gas–solid flows is investigated by particle-resolved direct numerical simulation (PR-DNS). It is found that, in almost uniform liquid–solid flows, the solid-phase pressure is not well predicted by classical kinetic theory of granular flow (KTGF) due to the presence of interphase force, although KTGF applies much better to single-phase granular flows. In gas–solid flows, with increasing heterogeneity described by structural functions, the statistical solid-phase pressure becomes significantly larger than that in corresponding homogeneous flows. It reveals that mesoscale structures strongly affect solid-phase pressure, and suggests the deviation from classical KTGF in heterogeneous gas–solid flows can be attributed to both the interphase forces (mainly drag) and mesoscale structures. The coefficients in the solid-phase pressure models in KTFG are modified, fitting the statistical results of both homogeneous and heterogeneous particle–fluid flows.

Active particle motion in Poiseuille flow through rectangular channels.

We investigate the dynamics of a pointlike active particle suspended in fluid flow through a straight channel. For this particle-fluid system, we derive a constant of motion for a general unidirectional fluid flow and apply it to an approximation of Poiseuille flow through channels with rectangular cross- sections. We obtain a 4D nonlinear conservative dynamical system with one constant of motion and a dimensionless parameter describing the ratio of maximum flow speed to intrinsic active particle speed. Applied to square channels, we observe a diverse set of active particle trajectories with variations in system parameters and initial conditions which we classify into different types of swinging, trapping, tumbling, and wandering motion. Regular (periodic and quasiperiodic) motion as well as chaotic active particle motion are observed for these trajectories and quantified using largest Lyapunov exponents. We explore the transition to chaotic motion using Poincaré maps and show "sticky" chaotic tumbling trajectories that have long transients near a periodic state. We briefly illustrate how these results extend to rectangular cross-sectionswith a width-to-height ratio larger than one. Outcomes of this paper may have implications for dynamics of natural and artificial microswimmers in experimental microfluidic channels that typically have rectangular cross sections.

Discrete magnification lens model: A new hybrid multi-scale modelling method for fluid-particle systems

We present a novel hybrid multi-scale model, referred to as “discrete magnification lens” method, which utilizes a computational fluid dynamics coupled to discrete element method (CFD-DEM) approach within a specific region of interest in a two-fluid model (TFM) simulation. We applied the discrete magnification lens to the crossing jet problem, where the TFM fails due to lack of considering bi-modal velocity distribution in its formulation. It was observed that adopting the discrete magnification lens, can effectively alter the non-physical behavior of the TFM to obey the behavior seen from CFD-DEM simulations. Moreover, the ability of the discrete magnification lens in reproducing particle clusters and improving the TFM predictions in case of unbounded fluidization simulations was further shown. We found that the discrete magnification lens can effectively enhance the TFM predictions in a complex fluid-particle system while requiring less numerical costs compared to the full-scale CFD-DEM simulations.

An LSTM-enhanced surrogate model to simulate the dynamics of particle-laden fluid systems

The numerical treatment of fluid–particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although an accurate mathematical modelling is available to address this kind of applications, the computational cost of the numerical simulations is very expensive. The use of the most modern high performance computing infrastructures could help to mitigate such an issue but not completely to fix it. In this work we develop a non intrusive data-driven reduced order model (ROM) for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations. The ROM is built using the proper orthogonal decomposition (POD) for the computation of the reduced basis space and the Long Short-Term Memory (LSTM) network for the computation of the reduced coefficients. We are interested to deal both with system identification and prediction. The most relevant novelties rely on (i) a filtering procedure of the full order snapshots to reduce the dimensionality of the reduced problem and (ii) a preliminary treatment of the particle phase. The accuracy of our ROM approach is assessed against the classic Goldschmidt fluidized bed benchmark problem. Finally, we also provide some insights about the efficiency of our ROM approach.

General drag correlations for subsonic to supersonic flow past ordered particle arrays at low and moderate Reynolds numbers

The drag coefficient (CD) is an important and fundamental parameter for particle-fluid systems. In this study, we employed pseudo-particle modeling (PPM), which integrates a time-driven algorithm with the hard-sphere model, to investigate subsonic to supersonic flows past ordered particle arrays with three typical configurations, i.e., simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC), at low and moderate Reynolds numbers. The relationships between the drag coefficient and various factors including Reynolds number (Re), Mach number (Ma), solid volume fraction (εs) and array configuration were analyzed. The study found: 1) Under identical conditions, the drag coefficient varies with configurations. In most cases, CD of SC is the smallest and that of FCC is the largest. 2) At low and moderate Re (Re≤20), the CD decreases with increasing Re and Ma; when Ma≤1.0, the CD increases with increasing εs; when Ma>1.0, the variation of CD with εs differs qualitatively for the SC and BCC particle arrays. 3) For Re≤20, the CD for FCC particle arrays can be tentatively expressed as CD(Re, Ma, εs)=CD(Re) [aexp(-bMa)+(1-a)](1 + Kεsn), while the coefficients a and b are related to Re and K and n are related to Re and Ma. This study fills the absence of drag data for multi-particles in slip flow and transitional flow, thereby providing drag laws for a wide range of particle-fluid systems important for micro-chemical-engineering and aero-space technologies.

A dual-grid approach to speed up large-scale CFD-DEM simulations

With the development of heterogeneous computing, the coupling of discrete element method (DEM) and computational fluid dynamics (CFD) has become an effective approach to simulate large-scale particle–fluid systems. With various models and algorithms accelerating the DEM part significantly, the CFD part becomes an efficiency bottleneck, especially for large-scale simulations. A dual-grid approach is proposed to address this issue. On the fine grid, the fluid velocity and particle–fluid interaction are solved without compromising accuracy in capturing flow details, and the pressure is solved on the coarse grid to ensure mass conservation to boost the CFD part. This approach is validated by simulating several gas–solid fluidized beds, demonstrating a performance speedup of 2.6 for low workload and 10.1 for high workload.

Vibrationally driven particle formations in fluid systems with bimodal thermal inhomogeneities

This study builds on and extends an earlier investigation [Santhosh and Lappa, “On the relationship between solid particle attractors and thermal inhomogeneities in vibrationally-driven fluid-particle systems,” Phys. Fluids 35(10), 103316 (2023)]. As the predecessor work, it can be placed in a wider theoretical context, that is, a line of inquiry started a decade ago [Lappa, “The patterning behavior and accumulation of spherical particles in a vibrated non-isothermal liquid,” Phys. Fluids 26(9), 093301 (2014)] about the surprising ability of high-frequency vibrations imposed on a non-isothermal fluid containing dispersed solid particles to support the self-emergence of ordered particle structures. Here, the non-trivial relationship between the number and shape of the particle formations and the nature of the thermal conditions along the boundary of the fluid container is further explored by probing in detail the role of thermal spot multiplicity. The problem is approached in the framework of a hybrid Eulerian–Lagrangian numerical approach. The results indicate that completely new morphologies become accessible, which are not possible when only two walls are thermally active. Moreover, on increasing the angle ϕ formed by vibrations with the direction perpendicular to the adiabatic walls of the cavity, the compact surfaces formed by particles for ϕ = 0° are taken over by more complex formations, which give the observer the illusion of a flexible fabric formed by the intersection of many independent filamentary structures.

Enhanced fully resolved CFD-DEM-PBFM simulation of non-spherical particle–fluid interactions during hydraulic collection

The interactions between non-spherical particles and fluids are commonplace in both nature and engineering applications, such as deep-sea nodules hydraulic collection. However, accurately simulating granular particles with non-spherical shapes and gaining a deep understanding of the intricate mechanisms involved in fluid–particle interactions still pose significant challenges. In this study, the superquadric model and the Gaussian curvature model are introduced in the Discrete Element Method to describe particle shapes and characterize their nonlinear contact behavior, respectively. Simultaneously, the Fictitious Domain-Immersed Boundary Method (FD-IBM) and the Particle Boundary Field Method (PBFM) are employed to enhance the stability and accuracy of numerical simulations. Building upon these advancements, an extended resolved CFD-DEM-PBFM method is developed. The validation and superiority of this resolved CFD-DEM-PBFM method are rigorously verified by comparing its results with the experimental and other research results across various scenarios, including non-spherical particle collision and packing, particle settling, drafting-kissing-tumbling test, and flow around non-spherical particles. Subsequently, the application of our novel model has been further conducted by a case study that simulates the hydraulic collection of nodules with different aspect ratios l/d. Concurrently, the influences of the nodule shapes on the hydraulic collection mechanism of the hydraulic collection are unveiled in terms of suction forces, trajectory of the particle, and flow field characteristics. Our findings demonstrate that the extended resolved CFD-DEM-PBFM method excels at accurately characterizing multiphase interaction mechanisms at both macro and micro scales, presenting considerable advantages in simulating fluid-particle systems involving non-spherical particles.

Cohesive particle–fluid systems: An overview of their CFD simulation

AbstractSolid particles may experience different kinds of cohesive forces, which cause them to form agglomerates and affect their flow in multiphase systems. When such systems are simulated through computational fluid dynamics (CFD) programs, appropriate modelling tools must be included to reproduce this feature. In this review, these strategies are addressed for various systems and scales. After an introduction of the different forces (van der Waals, electrostatic, liquid bridge forces, etc.), the modelling approaches are categorized under three methodologies. For diluted slurries of very fine particles, many researchers succeeded with pseudo‐single phase approaches, employing a model for the non‐Newtonian rheology. This was especially popular for sludges in anaerobic digestions or certain types of soils. In other cases, continuum‐based approaches seem to be more adequate, including cohesiveness in the kinetic theory of granular flows or the restitution coefficient. Geldart‐A particles experiencing van der Waals forces are the primary focus of such studies. Finally, when each particle is modelled as a discrete element, the cohesive force can be directly specified; this is especially widespread for the wet fluidization case. For each of these approaches, a general overview of the main strategies, achievements, and limits is provided.

GPU-accelerated CFD-DEM modeling of gas-solid flow with complex geometry and an application to raceway dynamics in industry-scale blast furnaces

The coupling of Computational Fluid Dynamics (CFD) and Discrete Element Model (DEM) is a powerful tool for simulating dense particulate systems, yet the conventional CFD-DEM has limits for systems with large particle numbers and complex geometry. This paper reports a novel GPU-based CFD-DEM model to simulate the gas–solid flow with large particle numbers and complex geometry. A novel coupling strategy between the CFD solver and DEM solver is developed, featuring high efficiency and stability. The developed model is validated against the experimental measurements, and its efficiency is compared to the previous CFD-DEM simulations. Then, for demonstration, the model is employed to simulate the dynamic behavior of gas–solid flow in the raceway in ironmaking blast furnaces by considering complex tuyere structure details and the huge particle numbers involved. This model allows to study the effect of the tuyere angle in terms of raceway formulation and tuyere erosion. The results show that the largest and most stable raceway volume can be reached at 5° downward tuyere, although the −5° tuyere nose experiences more wear than 10° downward tuyere. The model provides a cost-effective tool to overcome the longstanding challenge of simulating dense fluid-particle systems with huge particle numbers and complex geometry.

Energy budget of cold and hot gas–solid fluidized beds through computational fluid dynamics-discrete element method simulations

Direct energy budget is carried out for both cold and hot flow in gas–solid fluidization systems. First, the energy paths are proposed from thermodynamic viewpoints. Energy consumption means total power input to the specific system, and it can be decomposed into energy retention and energy dissipation. Energy retention is the variation of accumulated mechanical energy in the system, and energy dissipation is the energy converted to heat by irreversible processes. Then based on the computational fluid dynamics-discrete element method framework, different energy terms are quantified from the specific flow elements of fluid cells and particles as well as their interactions with the wall. In order to clarify the energy budget, it is important to identify which system is studied: the particle-fluid system or the particle sub-system. For the cold flow, the total energy consumption of the particle sub-system can well indicate the onset of bubbling and turbulent, while the variation of local energy consumption terms can reflect the evolution of heterogeneous structures. For the hot flow, different heat transfer mechanisms are analyzed and the solver is modified to reproduce the experimental results. The impact of the heat transfer mechanisms and heat production on energy consumption is also investigated. The proposed budget method has proven to be energy-conservative and easy to conduct, and it is hopeful to be applied to other multiphase flow systems.

Multi-scale study of turbulent mass transfer process in different shaped-adsorbent packed bed

Insufficient consideration of the coupled effect of multi-scale and turbulent mass transfer impedes thorough understanding of the dynamic adsorption process in the fixed bed. To solve this problem, a novel PR-CMT model, integrated particle resolution method and computational mass transfer theory, is proposed and verified to simulate the gas adsorption process on particles by combining the computational mass transfer method and the particle dissolution method. The proposed model not only rigorously accounts for the turbulent diffusion by incorporating the equation of concentration variance c2‾ and concentration variance dissipation εc, but also establishes connections between different scales of fixed-bed particle-fluid systems. Through this work, it is found that there is a preferred fluid path in the particle filling structure, which can lead to significant changes in local mass transfer performance. Additionally, the turbulent diffusion enhances the mass and heat transfer between the gas and particles, resulting in a more uniform distribution in the radial direction. Using the proposed model, the effects of the adsorbent characteristics on the multi-scale adsorption process, such as the adsorbent porosity and shape, are further examined. The results indicate that increasing the adsorbent porosity leads to enhanced overall adsorption rate in the fixed bed, and the turbulent diffusion is strongest in the fixed bed with cylinder adsorbents.

An immersed moving boundary for fast discrete particle simulation with complex geometry

An immersed moving boundary (IMB) scheme in LBM-DEM is proposed for discrete particle simulation with arbitrarily complex geometry. Momentum exchange between fluid and unresolved particles can be exerted by a modified weighting function with drag force and a new solid operator in IMB, which can describe both particle–fluid interaction and complex geometry, and requires only local information in perspective of solution. Combined with stereolithography (STL) format for describing complex geometry, a GPU-based LBM-DEM-IMB is implemented, and its ability and accuracy for complex geometry from STL model is verified by simulating flow past a stationary sphere. Compared with CFD-DEM in discrete particle simulations of both fluidized bed with immersed tube and aerosol transporting in human nasal, proposed method has much higher efficiency and maintains comparable accuracy in dense and dilute particle–fluid systems with complex geometry, which demonstrates it to be a promising computational strategy for particle–fluid two-phase flows.

A resolved SPH-DEM coupling method for analysing the interaction of polyhedral granular materials with fluid

Hybrid fluid–particle systems are prevalent in nature and engineering practices, but accurately simulating the dynamic behaviour is challenging due to their inherent strong non-linearity. This study proposes a three-dimensional resolved numerical framework for analysing complex shape polyhedron–fluid interaction. The weakly compressible smoothed particle hydrodynamics (SPH) is employed to describe the complex hydrodynamic behaviour, and the discrete element method (DEM) is applied to solve the motion of irregular polyhedral granular materials. An accurate contact collision algorithm is implemented in the coupling model to address the dynamic response of polyhedral particles. The high-fidelity modelling of the complex morphology of granular materials is realised. Hence, the coupling code is developed based on two high-performance open-source platforms, and an efficient two-way coupling scheme is designed to manage the fluid–particle interaction under a unified time framework. The reliability and the applicability of the SPH-DEM solver are demonstrated through extensive validations based on existing experimental and numerical data involving violent free-surface flow impacting multiple rigid bodies and cube deposition. Furthermore, a more complex case of wave-flow impact on rock piles is conducted, exhibiting great potential to employ this model in real-life engineering problems.

Particle-resolved direct numerical simulation of particle-laden turbulence modulation with high Stokes number monodisperse spheres

Graphic processing units (GPU)-accelerated direct numerical simulations of particle–fluid systems based on lattice Boltzmann method combined with discrete element method are successfully performed. This method is validated to be accurate and efficient in the four-way coupling simulation of particle–fluid systems. Particle-laden homogeneous isotropic turbulence under particle size dp=30.1η (the Kolmogorov length scale), a wide range of solid volume fraction ϕV=2%−20% and particle Stokes number St=503.87−50 387 are systematically studied. The additional energy dissipation rate εaddi induced by particles is quantitatively calculated. One criterion for turbulence enhancement or attenuation based on energy balance is proposed and successfully used in different particle-laden turbulence. The relative magnitude of two-way coupling rate ψ and particle-induced dissipation εaddi is the direct factor determining the modulation effect on turbulence. Turbulence laden with high Stokes number particles is enhanced. Turbulence laden with high volume fraction particles transited rapidly from enhancement to attenuation, which is attributed to the more rapid decay of ψ relative to εaddi in the freely decaying turbulence.

On the relationship between solid particle attractors and thermal inhomogeneities in vibrationally driven fluid-particle systems

The present analysis extends earlier authors' work [Crewdson et al., “Two-dimensional vibrationally-driven solid particle structures in non-uniformly heated fluid containers,” Chaos 32, 103119 (2022); M. Lappa, “Characterization of two-way coupled thermovibrationally driven particle attractee,” Phys. Fluids 34(5), 053109 (2022); M. Lappa and T. Burel, “Symmetry breaking phenomena in thermovibrationally driven particle accumulation structures,” ibid.32(5), 053314 (2020); and M. Lappa, “The patterning behavior and accumulation of spherical particles in a vibrated non-isothermal liquid,” ibid.26(9), 093301 (2014)] on the existence of solid particle attractee in thermovibrational flow in order to identify new physical principles and enable increased control over the ability of particles to target desired locations into the host fluid. The causality between the thermal boundary conditions and the multiplicity and morphology of emerging particle structures is discussed, and new fundamental topological concepts are harnessed through the combination of two-dimensional and three-dimensional simulations. It is shown that the threefold relationship among the inclination of vibrations, the multi-directional nature of the imposed temperature gradient, and the dimensionality of the system itself can open up new pathways for additional classes of attractors. These can manifest themselves as compact particle structures or completely disjoint sets, apparently behaving as they were driven by different clustering mechanisms (coexisting in the physical space, but differing in terms of characteristic size, shape, and position). A variety of new solutions are presented for a geometry as simple as a cubic enclosure in the presence of localized spots of temperature on otherwise uniformly heated or cooled walls. In order to filter out possible asymmetries due to fluid-dynamic instabilities induced by the back influence of the solid mass on the fluid flow, the analysis is conducted under the constraint of one-way coupled phases.

Numerical investigation of the particle flow behaviors in a fluidized-bed drum by CFD-DEM

The fluidized-bed drum technology involving the combination of a fluidized bed and a rotating drum is used for the granulation and coating of particles, which has been successfully applied in industry. Nevertheless, there should be few published fundamental studies for exploring the particle flow behaviors in a fluidized-bed drum, particularly in the particle level. Consequently, the particle-scale DEM (Discrete Element Method) was coupled with CFD (Computational Fluid Dynamics) in this work to simulate the particle-fluid flow system in a fluidized-bed drum. The experiments in a small horizontal fluidized-bed drum were also carried out to validate the accuracy of our CFD-DEM model. Subsequently, the particle flows in a large inclined fluidized-bed drum were simulated by CFD-DEM, and the relatively comprehensive investigation for the influences of operational conditions (including the gas inlet velocity, drum rotation speed, drum inclination angle and fluidized-bed inclination angle) on the particle flow behaviors (e.g., the particle holdup, particle velocity and particle residence time) was carried out. According to the simulation results, the particle flow behaviors would be significantly affected by these operational conditions. However, increasing the gas inlet velocity could weaken the effects of drum rotation speed, drum inclination angle and fluidized-bed inclination angle.

An analytical energy-balance model for restitution coefficient of a dry particle when impacting on a wet plane

The restitution coefficient of particle is a key parameter for simulations of particle-fluid systems. An analytical model based on particle energy balance is proposed for a system of a dry particle impacting on a wet plane. The proposed model incorporates typical mechanisms of particle energy dissipation. For the cases from F. Gollwitzer, et al. (Phys. Rev. E 86 (2012), 011303), dominant dissipation originates from viscous force, whereas energy loss, due to liquid film inertia, cannot be neglected and even takes over system of Reynolds number higher than 90; energy dissipation induced by capillary force is commonly negligible with capillary number of 0.12–4.6. With consideration of particle roughness effects, the model achieves a good agreement with experimental data widely collected from literature. Using more than 800 points from literature, an artificial neural network tool is also developed. As inputs, Stokes, Weber, Reynolds, Bond, and capillary numbers could provide the best prediction.