Point-particle Model Research Articles

Convective heat transfer coefficients models for biomass cylindrical particles from low to high aspect ratio

This study investigates the heat transfer of co-firing biomass in coal-fired power station boilers, with a focus on practical application for realistic particle shapes. At present, there are no heat transfer or Nusselt number (Nu) correlations available for biomass particles of cylindrical shape such as straw particles. In this study, a direct numerical simulation (DNS) of the heat transfer between cylindrical particles in a heated flow are performed with OpenFOAM-using a body-fitted mesh. The impact of the Reynolds number Re, aspect ratio AR, and angle of incidence θ in the range of (10 ≤ Re ≤ 2000, 1 ≤ AR ≤ 18, 0° ≤ θ ≤ 90°) on the Nusselt number are determined using a systematical analysis of the thermal flow characteristics for different particle temperature fields. The results show that the aerodynamics and geometrical factors of the cylindrical shape play a dominant role in the heat transfer. A model for the Nusselt number is proposed based on a curve fit of the simulation results, which has a root mean square error (RMSE) of 2.2 × 10-2 and an average relative error of 1.15 %. The independence test of the model has an average error of 5.1 %, indicating a high prediction accuracy. Compared to experimental and simulated data from the literature, the model demonstrates reasonable accuracy within its range of applicability, with a relative error of only 5.05 %. This study provides insights into the heat transfer of biomass particles with cylindrical shape and presents a new mathematical model for the Nusselt number, which can be used to improve the accuracy of the heat transfer prediction using point particle models.

Effect of fluid motions on finite spheres released in turbulent boundary layers

This paper extends the work in Tee et al. (Intl J. Multiphase Flow, vol. 133, 2020, 103462) to investigate the effect of turbulent fluid motions on the translation and rotation of lifting and wall-interacting spheres in boundary layers. Each sphere was released from rest in smooth-wall boundary layers with $Re_\tau =670$ and 1300 ( $d^+=56$ and 116, respectively) and allowed to propagate with the incoming fluid. Sphere and surrounding fluid motions were tracked simultaneously via three-dimensional particle tracking velocimetry and stereoscopic particle image velocimetry in streamwise–spanwise planes. Two-point correlations of sphere and fluid streamwise velocities yielded long positive regions associated with long fast- and slow-moving zones that approach and move over the spheres. The related spanwise correlations were shorter due to the shorter coherence length of spanwise fluid structures. In general, spheres lag the surrounding fluid. The less-dense lifting sphere had smaller particle Reynolds numbers varying from near zero up to 300. Its lift-offs coincided with oncoming fast-moving zones and fluid upwash. Wall friction initially retarded the acceleration of the denser sphere. Later, fluid torque associated with approaching high-velocity regions initiated forward rotation. The rotation, which was long-lived, induced sufficient Magnus lift to initiate repeated small lift-offs, reduce wall friction, and accelerate the sphere to higher sustained velocity. Particle Reynolds numbers remained above 200, and vortex shedding was omnipresent such that the spheres clearly altered the fluid motion. Spanwise fluid shear occasionally initiated wall-normal sphere rotation and relatively long-lasting Magnus side lift. Hence the finite sphere size contributed to multiple dynamical effects not present in point-particle models.

Neural-network-based drag force model for polydisperse assemblies of irregular-shaped particles

In this study, a drag force model of irregular-shaped particles in gas-solid flows is investigated using neural network approaches. Pre-developed variational autoencoder, multi-layer perceptron model, and transpose convolutional neural-network model are utilized to obtain intermediate parameters of a pair-wise interaction point-particle (PIEP) model. These parameters are utilized to predict individual drag force coefficients of polydisperse, particulate flows. To apply the PIEP-based model to medium-concentration flows, the average drag force coefficients are obtained through an in-house particle-resolved direct numerical simulation, and a regressed model is developed to predict solid volume fraction factors. With the regression model, the PIEP-based model using the neural-network approaches shows good prediction in particulate systems from low to intermediate concentrations. This study provides computationally efficient models of practical, realistic particulate systems for large scale fluid dynamics simulation, in that it allows predicting the drag forces of polydisperse particles with a small amount of data.

Correlations in strong-field-emitted ultrashort electron pulses from metal needle tips

When two electrons are emitted from a metal needle tip with the help of femtosecond laser pulses, they show a strong anticorrelation signal in the energy domain. Depending on the wavelength and intensity of the driving laser pulses, the electron emission process can be either in a perturbative regime, like single- or multi-photon photoemission, or in the strong-field regime, where emission is dominated by the instantaneous electric field of the laser pulse, or in the intermediate regime. Here, we report on the two-electron anticorrelation signal and how it evolves from the multiphoton toward the strong-field emission regime. We show that in both cases, the resulting anticorrelation signal can be well explained by semi-classical simulations using a point-particle model, thus the dynamics is dominated by the center-of-mass dynamics of the individual electrons. However, the actual emission process of multiple interacting electrons requires improved quantum mechanical models and therefore remains the subject of future work.This paper is part of the Special Topic Collection: papers from the 31th Annual International Laser Physics Workshop 2023 (LPHYS 2023).

Wall-resolved large eddy simulation of mixed-size sand-laden flow

Most of the existing numerical studies on wind-blown sand flow simplify sands into single-size particles, whereas natural wind-blown sand flow is a two-phase flow with mixed-size particles, thus, the simulation of mixed-size sand-laden flow is necessary. In the present work, wall-resolved large eddy simulations of mixed-size sand-laden flows are realized. Each sand in the wind field is tracked using the Lagrangian point-particle model. The transport characteristics of sand particles in mixed-size sand-laden flow are investigated under the premise of considering bed erosion. Considering the significant influence of sand-bed collision on simulation, the splash function is modified in the present simulation according to the previous experimental results. It reveals that in mixed-size sand-laden flow, the fraction of rebound sand particles in all the saltation particles is approximately 0.6, which is twice times of the ejected sand particles, and the modification of the sand rebound angle greatly affects the simulation results of mixed-size sand-laden flow. Meanwhile, the mean size of the saltation sand particles decreases with height and is 20% lower at the top of the saltation layer than that near the sand bed in the present simulation. Further analysis by grouping of sands with their size shows that the sand transport intensity of small sands decreased more rapidly with increasing height. The volume fraction and sand transport intensity of small sand particles exceed those of medium and large sand particles at heights y/δ = 0.05 and y/δ = 0.1.

Evolution of a shock-impacted reactive liquid fuel droplet with evaporation effects: A numerical study

We describe detailed numerical simulations of a liquid fuel droplet impacted by a Mach 5 shock wave, considering the effects of chemical reactions and phase change due to evaporation. In our baseline case, a 5μm, n-Dodecane fuel droplet is preheated to 460K, and surrounded by preheated O2 gas at 700K. The simulations investigate the low Ohnesorge number regime (Oh<0.1), where viscous effects are insignificant and therefore not considered in this work. The fuel droplet undergoes significant deformation and morphological changes following shock impingement, as the droplet surface becomes unstable to the Kelvin-Helmholtz instability. The droplet core is also observed to eject a thin sheet near the equatorial plane, which is then stretched by the high-speed post-shock gas flow, affecting the late-time behavior. We find the observed dominant modes associated with the Kelvin–Helmholtz instability are in reasonable agreement with inviscid linear theory (Chandrasekhar, 1981; Jepsen et al., 2006), when the local conditions at the droplet surface are considered. Furthermore, an evaporation-induced Stefan flow is established which blows off the hot post-shock gases surrounding the droplet, leading to droplet cooling. As the fuel vapors react, a diffusion flame is formed on the droplet-windward side, leading to intense droplet heating and enhanced vapor production in this region. We investigated the effect of the Damkohler number on droplet evolution by varying the fuel reactivity, and found the flame thickness decreased with increasing reactivity in agreement with trends predicted by laminar diffusion flame theory. At the highest reactivity, secondary burning of fuel vapors was observed in the droplet wake, while the resulting flame eventually reattached to the droplet surface. Our results show significant spatial inhomogeneities are present in the droplet flowfield in all the cases investigated, which must be considered in the development of reduced order point-particle models for system-level simulations of detonation engines.

Numerical investigation of particle dispersion and collision in a liquid jet flow

A numerical simulation with the Eulerian–Lagrangian point-particle approach is used to study the dispersion of nanoparticles in liquid jet flows. The volume of fluid method is used to simulate the motion of the gas–liquid interface. The particle motion is resolved by the Lagrangian point-particle model, and the collisions among particles are considered. According to the simulation results, the liquid jet atomization process can be divided into four different periods. Moreover, the nanoparticles lead to an increase in the liquid density and viscosity. The influence of the particle motion on the liquid jet breakup process is discussed. The simulation results show that the collisions would restrain particle dispersion. However, the motions and collisions of the particles would help the breakup of the liquid jet.

Feeding of planktotrophic squirmers: Effects of mobility and elongation of planktonic particles

Ciliated micro-organisms feed on small planktonic and inorganic particles. Investigating their feeding ability is valuable for understanding corresponding ecodynamics. However, how the feeding ability is affected by the motility and elongation of their food particles remains unknown. In this study, we carry out numerical simulations based on a squirmer model and a point-particle model to represent the ciliated micro-organisms and planktonic particles, respectively. The feeding of the squirmer is accomplished by generating a flow field that attracts particles nearby. This squirmer-induced flow is described by the sum of multiple modes of Legendre polynomials. We adopt a 2-mode model, formed by the first mode and any other one, to investigate the influence of the flow structure on the feeding ability. The latter mode identifies the flow field under the two constraints of the constant maximum surface speed and the fixed vortex size. We find that the dependency of the feeding ability on the flow field varies with the mobility of food particles significantly. For non-motile particles, the feeding ability is little disturbed by the flow mode. While for motile particles, the feeding ability is negatively correlated with the flow mode, which suggests an efficient feeding strategy where the squirmer prioritizes enhancing swimming over attraction to capture more particles. Meanwhile, the elongation of food particles also plays an important role, as more elongated motile particles are more likely to be captured by the flows with high modes. This investigation advances the understanding of feeding on motile and elongated particles.

On the surface chemisorption of oxidizing fine iron particles: Insights gained from molecular dynamics simulations

Molecular dynamics (MD) simulations are performed to investigate the thermal and mass accommodation coefficients (TAC and MAC, respectively) for the combination of iron(-oxide) and air. The obtained values of TAC and MAC are then used in a point-particle Knudsen model to investigate the effect of chemisorption and the Knudsen transition regime on the combustion behavior of (fine) iron particles. The thermal accommodation for the interactions of Fe with N2 and FexOy with O2 is investigated for different surface temperatures, while the mass accommodation coefficient for iron(-oxide) with oxygen is investigated for different initial oxidation stages ZO, which represents the molar ratio of O/(O+Fe), and different surface temperatures. The MAC decreases fast from unity to 0.03 as ZO increases from 0 to 0.5 and then diminishes as ZO further increases to 0.57. By incorporating the MD-informed accommodation coefficients into the single iron particle combustion model, the oxidation beyond ZO=0.5 (from stoichiometric FeO to Fe3O4) is modeled. A new temperature evolution for single iron particles is observed compared to results obtained with previously developed continuum models. Specifically, results of the present simulations show that the oxidation process continues after the particle reaching the peak temperature, while previous models predicting that the maximum temperature was attained when the particle is oxidized to ZO=0.5. Since the rate of oxidation slows down as the MAC decreases with an increasing oxidation stage, the rate of heat loss exceeds the rate of heat release upon reaching the maximum temperature, while the particle is not yet oxidized to ZO=0.5. Finally, the effect of transition-regime heat and mass transfer on the combustion behavior of fine iron particles is investigated and discussed.

Modeling and Experiments of Droplet Evaporation with Micro or Nano Particles in Coffee Ring or Coffee Splat.

Experimental and numerical experiments were carried out to study the coffee rings or coffee splats formed by droplet evaporation with micro or nano polystyrene sphere particles (Dp = 10 μm or 100 nm). Particle image velocimetry (PIV) and a high-resolution camera were used in this experiment, along with a temperature-controlled heater and a data-acquisition computer. The results showed that a nano particle could form a homogeneous coffee splat, instead of the common coffee ring formed when using micro particles. In order to account for this phenomenon, this paper developed a complex multiphase model, one which included the smooth particle hydrodynamics (SPH) fluid model coupled with the van der Waals equation of state for droplet evaporation, the rigid particle model of finite-size micro particles, and the point-particle model of the nanometer particles. The numerical simulation was operated on a GPU-based algorithm and tested by four validation cases. A GPU could calculate 533 times the speed of a single-core CPU for about 300,000 particles. The results showed that, for rigid solid particles, the forms emerged spontaneously on the wall, and their structure was mainly affected by the boundary wettability, and less affected by the fluid flow and thermal condition. When the wall temperature was low, it was easier for the particles to be deposited on the contact line. At high wall temperature, the coffee ring effect would be weakened, and the particles were more likely to be deposited in the droplet center. The hydrophilic surface produced a larger coffee ring compared to the hydrophobic surface. The experimental and numerical results proved that particle size could play a significant role during the particle deposition, which may be a possible route for producing uniform-distributed and nano-structure coatings.

New aspects of the [formula omitted]-graded 1D superspace: Induced strings and 2D relativistic models

A novel feature of the Z2×Z2-graded supersymmetry which finds no counterpart in ordinary supersymmetry is the presence of 11-graded exotic bosons (implied by the existence of two classes of parafermions). Their interpretation, both physical and mathematical, presents a challenge. The role of the “exotic bosonic coordinate” was not considered by previous works on the one-dimensional Z2×Z2-graded superspace (which was restricted to produce point-particle models). By treating this coordinate at par with the other graded superspace coordinates new consequences are obtained.The graded superspace calculus of the Z2×Z2-graded worldline super-Poincaré algebra induces two-dimensional Z2×Z2-graded relativistic models; they are invariant under a new Z2×Z2-graded 2D super-Poincaré algebra which differs from the previous two Z2×Z2-graded 2D versions of super-Poincaré introduced in the literature. In this new superalgebra the second translation generator and the Lorentz boost are 11-graded. Furthermore, if the exotic coordinate is compactified on a circle S1, a Z2×Z2-graded closed string with periodic boundary conditions is derived.The analysis of the irreducibility conditions of the 2D supermultiplet implies that a larger (β-deformed, where β≥0 is a real parameter) class of point-particle models than the ones discussed so far in the literature (recovered at β=0) is obtained. While the spectrum of the β=0 point-particle models is degenerate (due to its relation with an N=2 supersymmetry), this is no longer the case for the β>0 models.

Point-particle drag, lift, and torque closure models using machine learning: Hierarchical approach and interpretability

Point-particle closure models that are utilized in Euler-Lagrange simulations play an important role in replicating true dynamics of particle-laden flows. The accuracy of these point-particle models depends on how well they incorporate the local microstructural information of neighboring particles. The current work presents a physics-based hierarchical machine learning approach for developing robust N-body closures. The inclusion of ternary interactions, in addition to binary interactions, enabled by the hierarchical approach leads to improved predictions.

Deep learning for drag force modelling in dilute, poly-dispersed particle-laden flows with irregular-shaped particles

This study applies machine learning-based approaches to develop a drag force model for irregular-shaped particles in incompressible flows. The particle-laden flows are studied through an in-house particle-resolved direct numerical simulation (PR-DNS) at low-intermediate Reynolds numbers (Re). We utilize the PR-DNS to obtain drag force coefficients and flow fields of single particles. A variational auto-encoder model is used to obtain latent vectors to represent the geometrical features of the particles, and artificial neural networks (ANN) are developed to predict drag force coefficients and flow fields of the single particles. This study applies a pairwise interaction extended point-particle (PIEP) model to obtain the coefficients assuming the flow fields of neighboring particles can be linearly superposed. The PIEP method shows significant improvement on prediction for a few neighbored particles. In addition, the results reveal R2 scores of 0.56-0.62 and errors of 9.1-10.0 % for the dilute, polydispersed systems with a volume fraction of 0.5 %.

Heat Transfer in a Non-Isothermal Collisionless Turbulent Particle-Laden Flow

To better understand the role of particle inertia on the heat transfer in the presence of a thermal inhomogeneity, Eulerian–Lagrangian direct numerical simulations (DNSs) have been carried out by using the point–particle model. By considering particles transported by a homogeneous and isotropic, statistically steady turbulent velocity field with a Taylor microscale Reynolds number from 37 to 124, we have investigated the role of particle inertia and thermal inertia in one- and two-way coupling collisionless regimes on the heat transfer between two regions at uniform temperature. A wide range of Stokes numbers, from 0.1 to 3 with a thermal Stokes-number-to-Stokes-number ratio equal to 0.5 to 4.43 has been simulated. It has been found that all moments always undergo a self-similar evolution in the interfacial region between the two uniform temperature zones, the thickness of which shows diffusive growth. We have determined that the maximum contribution of particles to the heat flux, relative to the convective heat transfer, is achieved at a Stokes number which increases with the ratio between thermal Stokes and Stokes number, approaching 1 for very large ratios. Furthermore, the maximum increases with the thermal Stokes-to-Stokes number ratio whereas it reduces for increasing Reynolds. In the two-way coupling regime, particle feedback tends to smooth temperature gradients by reducing the convective heat flux and to increase the particle turbulent heat flux, in particular at a high Stokes number. The impact of particle inertia reduces at very large Stokes numbers and at larger Reynolds numbers. The dependence of the Nusselt number on the relevant governing parameters is presented. The implications of these findings for turbulence modelling are also briefly discussed.

Improvement of heat- and mass transfer modeling for single iron particles combustion using resolved simulations

ABSTRACT In this work, we use a boundary layer resolved model to improve a Lagrangian point particle model to simulate the combustion of single iron particles. By resolving the full boundary layer, mass and heat transfer are accurately modeled, including Stefan flow. Therefore, the model is suitable to improve point particle models. This work focuses on the first stage of iron combustion, which lasts up to the maximum temperature. Temperature- and composition-dependent properties are used and phase transitions from solid to liquid and liquid to gas are taken into account. The Nusselt and Sherwood correlations are investigated in conditions typical for iron particle combustion. It is found that the 1 / 2 -film temperature is the best film rule to use to model heat- and mass transfer for iron particle combustion. The boundary layer resolved model is used to validate the point particle models. Then, the model is systematically elaborated by including a temperature-dependent particle density, slip velocity and Stefan flow. The individual and combined effect of these phenomena on the burn duration are investigated. Including all these effects decreases the time to maximum temperature by around 25 % . Furthermore, it is shown that if one neglects physical phenomena like slip and Stefan flow, but uses the 1 / 3 -film rule instead of the 1 / 2 -film rule, errors cancel and still reasonable agreement is obtained with experiments.

Physics-inspired architecture for neural network modeling of forces and torques in particle-laden flows

We present a physics-inspired neural network (PINN) model for direct prediction of hydrodynamic forces and torques experienced by individual particles in stationary arrays of randomly distributed spheres. In line with our findings, it has recently been demonstrated that conventional fully connected neural networks (FCNN) are incapable of making accurate predictions of force variations in a stationary random array of spheres. The problem arises due to the large number of input variables (i.e., the locations of individual neighboring particles) leading to an overwhelmingly large number of training parameters in a fully connected architecture. Given the typically limited size of training datasets that can be generated by particle-resolved simulations, the NN becomes prone to missing true patterns in the data, ultimately leading to overfitting. Inspired by our observations in developing the microstructure-informed probability-driven point-particle (MPP) model in a previous work, we incorporate two main features in the architecture of the present PINN model: (1) superposition of pairwise hydrodynamic interactions between particles, and (2) sharing training parameters between NN blocks that model neighbor influences. These strategies helps to substantially reduce the number of free parameters and thereby control the model complexity without compromising accuracy. We demonstrate that direct force and torque prediction using NNs is indeed possible, provided that the model structure corresponds to the underlying physics of the problem. For a Reynolds number range of 2⩽Re⩽150 and solid volume fractions of 0.1⩽ϕ⩽0.4, the PINN’s predictions prove to be as accurate as those of other currently available microstructure-informed models.

Aperiodic bursting dynamics of active rotors.

We report experiments on an active camphor rotor. A camphor rotor is prepared by infusing camphor on a regular rectangular paper strip. It performs self-propelled motion at the air-water interface due to Marangoni driven forces. After some transient (periodic) dynamics, the rotor enters into the aperiodic bursting regime, which is characterized as an irregularly repeated rest (halt) and run (motion) of the rotor. Subsequently, this aperiodic (irregular) rotor is entrained to a periodic (regular) regime with the help of a suitable external periodic forcing. Furthermore, we conducted experiments on two such coupled aperiodic camphor rotors. In this set of experiments, synchronized bursting was observed. During this bursting motion, one rotor follows the movement of the other rotor. A numerical point particle model, incorporating excitable underlying equations, successfully replicated experimentally observed aperiodic bursting.

Mechanism of collision model for bedload transport

The current study introduces a new particle–particle collision model as well as a classical particle–wall collision model to simulate the process of bedload transport. Large eddy simulation and two-way coupling Lagrangian point–particle models also are applied. Flow conditions for all simulations are done based on previous experiments and four comparison cases are studied. The bedload function result obtained using this model agrees with the previous studies, which proves that the model is reasonable and effective in dealing with bedload transport in turbulent flow. Otherwise, failure to consider the particle–particle collision, Basset force, or Saffman lift force in the model lead to underestimating the bedload transport rate.

Particle Reynolds number effects on settling ellipsoids in isotropic turbulence

Recently developed drag correlations for ellipsoidal particles are applied in a Lagrangian point-particle model. The results are directly compared against a popular Lagrangian model based on the dynamic equations valid for Stokes flow for the canonical case of settling ellipsoids in isotropic decaying turbulence. For increasing terminal velocities, the pitching torque due to fluid inertia dominates the torque contribution due to the fluid velocity gradient. Consequently, the major axis is preferentially oriented perpendicular to the settling direction. The opposite is predicted, if the new correlations for ellipsoidal particles are not included in the Lagrangian model. The combined effect of the pitching torque and the drag correlations leads to significantly different settling velocities for the varying correlations. The results based on a constant particle relaxation time for various particle diameters show that the particle Reynolds number is a relevant parameter in a multiphase system even for relatively moderate particle Reynolds numbers Rep≤4.

Intervortex forces in competing-order superconductors

The standard Ginzburg-Landau model of competing-order superconductors, applicable to various high ${T}_{c}$ cuprates, is studied. It is observed that this model possesses two distinct species of vortex, and consequently has two distinct integer valued topological charges. A simple point particle model of long-range forces between (anti)vortices of any species is developed and compared with numerical simulations of the full field theory, excellent agreement being found. Some of the results are quite counterintuitive. For example, a parameter regime exists where vortices of one species repel both vortices and antivortices of the other.