Particle-wall Collision Model Research Articles

Experimentally trained hybrid machine learning algorithm for predicting turbulent particle-laden flows in pipes

A hybrid learning algorithm consisting of a preprocessor, a k-nearest neighbors regressor, a noise generator, and a particle–wall collision model is introduced for predicting features of turbulent single-phase and particle–liquid flows in a pipe. The hybrid learning algorithm has the ability to learn and predict the behavior of such complex fluid dynamic systems using experimental dynamic databases. Given a small amount of typical training data, the algorithm is able to reliably predict the local liquid and particle velocities as well as the spatial distribution of particle concentration within and without the limits of the range of training data. The algorithm requires an order of magnitude less training data than a typical full set of experimental measurements to give predictions on the same level of accuracy (typically, 20 cf. 100 trajectories for phase velocity distribution and 40 cf. 500 trajectories for phase concentration distribution), thus leading to huge reductions in experimentation and simulation. A feature importance analysis revealed the effects of the different experimental variables on the particle velocity field in a two-phase particulate flow, with particle–liquid density ratio and particle vertical radial position being the most influential and particle concentration the least. The algorithm is amenable to extension by using more complex databanks to address a much more comprehensive range of flow situations.

A novel particle–particle and particle–wall collision model for superellipsoidal particles

AbstractIn the framework of computational studies of particulate multiphase flow systems, either dilute or dense, particle–particle as well as particle–wall collisions need to be considered, which in the case of nonspherical particle shapes still presents a computational challenge. In this study, we present an efficient numerical implementation of a novel superellipsoidal particle collision model that can be used in general fluid flows. The superellipsoid shape formulation can be viewed as an extension of spherical or ellipsoidal shapes and can be used to represent spherical, ellipsoidal, cylindrical, diamond-like and cubic particles by varying solely five shape parameters. In this context, we present a fast, stable Newton–Raphson-based method for modeling frictional collisions of nonspherical superellipsoidal particles, and demonstrate the performance of our algorithms.

A data-driven stochastic model for velocity field and phase distribution in stirred particle-liquid suspensions

A computationally efficient Lagrangian stochastic model driven by short 3D experimental trajectories determined by a technique of positron emission particle tracking, has been developed to study two-phase particle-liquid flow in a mechanically agitated vessel and unravel the complex behaviour of both phases. Using a small set of trajectory driver data, the stochastic model is used in conjunction with a particle-wall collision model to simulate the full velocity field and spatial distribution of particles. The performance of a first and a second order model is evaluated in particle suspensions of various concentrations. Both models are able to predict local phase velocities to a high degree of accuracy. Predictions of spatial particle distribution are reasonable by the first order model but very accurate by the second order model. Furthermore, the latter is able to accurately predict the two-phase velocity field and spatial phase distribution under flow conditions outside the experimental range. • Deterministic multiphase flow models are challenging and computationally costly • A stochastic model accurately predicts 3D two-phase flow field in a stirred vessel • The stochastic model is driven by a small set of Lagrangian input data • The stochastic model is capable of extrapolating flow predictions • The stochastic model is highly computationally efficient

Improvement and application of a two-dimensional fractal particle-wall collision model

The present work is devoted to applying the fractal particle-wall collision model to general numerical procedures. First, a three-dimensional (3D) collision model is developed to overcome the inability of a two-dimensional (2D) model to deal with the normal incidence of particles. The 3D model uses fractal theory to construct the rough wall and a return-to-subdivision method to determine the contact point between the particle and wall. However, the 3D model consumes relatively high computational resources and is less continuous. Second, an improved 2D model is proposed by setting a random azimuth angle that follows a uniform distribution to consider the normal incidence of particles to the wall. The improved 2D model is applied to the numerical procedure because of its better continuity and lower computational cost. The numerical procedure is well verified by comparison with experimental data available in the literature. • The process of particle-wall collision is described using fractal theory. • The 2D fractal particle-wall collision model is extended to a 3D model. • The fractal collision model is applied to general numerical procedures.

Fractal characteristics of a worn wall and the influence on the particle-wall collisions

A new particle-wall collision model is proposed to analyse the random rebound process of particles after collision with a rough wall. The new model includes two parts. First, the wear caused by particle collisions and the self-similarity of the wall microstructure are considered. The topography of a rough wall is constructed using fractal theory combined with an empirical erosion formula. Second, a return-to-subdivision method is used to determine the contact point between the particle and wall. The hard ball model is used to analyse the motion state of the rebound particles. The present model is numerically implemented through the Monte Carlo method and validated by comparison with the experimental data available in the literature. The possible reasons for the deviation between the predicted and measured results are presented. In addition, the compatibility of the present model with classical models is discussed in detail.

Investigating the n = 1 and n = 2 error fields in W7-X using the newly accelerated FIELDLINES code

No fusion device can be created without some uncertainty; there is always a slight deviation from the geometric specification. These deviations can add up create a deviation of the magnetic field. This deviation is known as the (magnetic) error field. Correcting these error fields is desired as they cause asymmetries in the divertor loads and can thus cause damage to the device if they grow too large. These error fields can be defined by their toroidal (n) and poloidal number (m). The correction of the n = 1 and n = 2 fields in Wendelstein 7-X (W7-X) is investigated in this work. This investigation focuses on field line diffusion to the divertor, a proxy for divertor heat flux. Such work leverages the 25× speedup obtained through the implementation of a new particle-wall collision model. The n = 1 and n = 2 error fields of the as-built coils model of W7-X are corrected by scanning phase and amplitude of the trim and control coils. Reductions in the divertor load asymmetry by factors of four are demonstrated using error field correction. It is found that the as-built coils model has a significantly lower error field than found in experiments (Bozhenkov et al 2018 Nucl. Fusion 59 026004).

Modelling of three-dimensional particle rebound from an anisotropic rough wall

In gas-solid confined flows, particle rebound on a rough wall may have a great influence on the macroscopic properties of both phases. Existing simulation methods use simplified approaches where surface roughness is modelled as two-dimensional or isotropic. To improve the accuracy of such simulations, an anisotropic virtual rough wall statistical approach and the corresponding Lagrangian stochastic particle-wall collision model are proposed. From deterministic simulations of the impact of particles on the anisotropic virtual wall given as correlated bi-Gaussian surface, wall-normal vector angle statistics are used for model development. Rebound angle statistics computed from deterministic simulations and using the proposed stochastic model are in very good agreement. Incident particles in vertical planes not collinear with one of the principal directions of the anisotropic rough surface are bouncing with a mean transverse angle towards the principal direction of lower roughness.

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.

Derivation and validation of a hard-body particle-wall collision model for non-spherical particles of arbitrary shape

In this work an extended three-dimensional model to describe the process of wall collisions of arbitrary shaped non-spherical particles is developed. This model is derived as the generalized solution of the hard-sphere wall collision model described in Crowe et al. (2012) [1]. The validation of the new model is performed versus experimental results of the collision between cylindrical particles and a flat plate ((Sommerfeld et al., 2015 [2]), Sommerfeld and Lain (2018) [3]). The agreement between the measurements of linear normal and tangential velocities and the model predictions was found to be very good while the rotational velocities forecasted by the model showed also a satisfactory agreement with the experiments.

Numerical analysis of dilute gas-solid flows in a horizontal pipe and a 90° bend coupled with a newly developed drag model

The influence of particle concentration on the drag force of a particle deserves attention when using the Lagrangian Particle Tracking methods for the prediction of industrial type gas-solid flows. The Lagrangian approach is best suited to applications where the solids volume fraction is low, and the effect of particle concentration can be ignored. In the present work, a 3D time dependent numerical analysis is performed to study the effect of Lagrangian model improvements to replicate experimental studies of straight horizontal pipe flow and flow through a 90° horizontal-to-vertical bend. The present predictions are compared with published experimental data of Tsuji and Morikawa (1982), and Yilmaz (1997). Special attention is paid to influence of particle mass-flow rates and conveying velocity on the particle motion within the system. This study used a CFX-4 package, where the ability to modify the code was necessary to include particle model improvements. These improvements included implementing a newly drag force model developed as a part of this research work. Particle-wall collision and particle-particle collision models developed by Sommerfeld (1992), and Sommerfeld (2001) are also implemented in the CFD model. The standard k–ε dispersed turbulence model was utilized as the predictions for the gas phase only gave similar predicted axial velocity compared to the more computationally demanding Reynolds stress model. The results showed that the inclusion of the various improvements lead to reasonable predicted particle velocities in both the upper and lower regions of the straight horizontal pipe which denote the dilute and dense regions respectively. It was also found that the inclusion of the rough-wall particle wall collision model decreases the axial particle velocity in the lower region where the bulk of the particle wall collisions occur. While the inclusion of the particle collision models tends to disperse the particles away from the lower region resulting in a less dense lower section and a distinctly more homogenous particle distribution compared with the standard model predictions. Further, the increase in particle concentration leads to a reduction in axial velocity due to a loss of momentum through particle-wall and particle-particle collisions. Finally, the improved CFD model best predicted both the reduction and increase in the particle velocities in the different regions.

Particle trajectories in pipe flow considering particle–wall collisions

Particle–wall collision behaviors have strong effects on confined particle-laden pipe flows, which are important in pneumatic conveying and pulverized coal combustion. In this paper, a numerical simulation of a pipe flow was conducted to analyze the effects of different initial conditions and particle–wall collision model parameters. The results show that a realistic collision model with coefficients provided by experiments can predict accurate particle exit velocity distributions. The effects of the initial motion of the particles diminish at the exit as long as the pipe length and the number of wall collisions are sufficient, and larger particles require the length to be longer. A simplified collision model with an arbitrary constant restitution coefficient e and a friction coefficient f leads to inaccurate results of the particle exit velocity probability density function, and using constant coefficients from data of a single collision angle will make the model ineffective. It is better to apply a normal distribution for e and a constant f if available collision data are limited, which gets reasonably accurate statistical results despite small distribution deviations.

A large eddy simulation study of cyclones: The effect of sub-models on efficiency and erosion prediction

In this study, first, the effect of different state-of-the-art dispersion and particle-wall collision models on the efficiency and erosion prediction are investigated. Second, the influence of particle size on the erosion pattern is explored. These assessments require reliable sub-model inputs, e.g. velocity statistics, which are provided through a large eddy simulation. The results reveal that a dispersion model for cyclone applications should account for the effect of anisotropic normal and shear Reynolds stresses and the “drift correction”. Furthermore, the erosion inside a cyclone can have four critical zones based on the particle size. It is also proven that the accurate prediction of erosion pattern necessitates the inclusion of the Saffman and Magnus lift forces on particles and realistic variable restitution coefficients in the particle-wall collision model. Finally, wall roughness increases the erosion rate of large particles through the combined impact of the “shadow effect” and energetic inner vortex on particles.

The modelling of carrier-wall collision with drug particle detachment for dry powder inhaler applications

The paper proposes a novel particle-wall collision model for calculating temporal changes of particle velocities and forces acting on the particle during the collision between an elastic particle and a plane solid wall. The purpose is to determine the maximum inertia force acting on the particle in connection with an accurate prediction of the transition between the sliding and non-sliding periods. This method is successfully applied to the calculation of drug detachment probability via particle-wall collisions within dry powder inhalers, in which fine drug particles are usually blended with larger carrier particles as one particle cluster for better dispersion. The present novel model is firstly verified in the micro-scale simulation of a single collision between the particle cluster and the wall. The simulation results reveal that the inertia force acting on drug particles is much larger than the fluid dynamic force and dominates the drug detachment. The detachment can occur through lift-off, sliding or rolling. Nearly half of the drug particles on the carrier surface can be detached by lift-off, and most of the remaining drug particles follow up with a sliding or rolling detachment. Based on these studies, a Lagrangian particle tracking algorithm is developed and is used to predict drug detachment probability within an inhaler device through one inhalation. By tracking 1024 particle clusters moving through the inhaler (i.e. the macro-scale simulation), the influence of different flow rates (i.e. 100 l/min and 70 l/min), friction coefficients between the carrier and the wall (i.e. 0.1 and 0.2), and carrier sizes (i.e. 100 μm and 500 μm) on drug detachment are investigated. The improved understanding of particle-wall collision detachment study will be the basis for optimising inhaler design.

A model for evaluating the particle penetration efficiency in a ninety-degree bend with a circular-cross section in laminar and turbulent flow regions

Understanding particle penetration losses in a bent section is useful for quantitatively evaluating the aerosol sampling error in a sampling system. This study intended to examine the physical factors that contribute to sampling error in a 90° bend installed in a sampling line and to evaluate current models that are used to predict penetration losses in continuous emission sampling (CPS).·The particle penetration characteristics of seven size groups (0.1, 0.5, 1.0, 5.0, 10 and 20μm) were numerically investigated via a Lagrangian particle-tracking model in a 90° bend with a circular cross-section. A particle–wall collision model was adopted to consider the particle–wall collision effect. Good agreement was achieved between gas mean velocity and particle penetration efficiency predictions and experimental data in the literature. An analysis was performed to study the particle penetration characteristics in pipes with different bend curvature ratios, geometries and various Re numbers. Our results indicated that approximately 20% particle losses for ≥5μm particles occur if the sampling line is bent. In addition, particle losses can typically be reduced by lowering the air velocity in the sampling line or by using a sampling line with a larger inner diameter. Models based on numerical data were developed as a function of related parameters to further predict the particle penetration efficiency. In a laminar flow, the model η=α⋅e−λ⋅St is given with an error of 2.6%–4.3%. In a turbulent flow system, however, the St and the Dean Number (De) both affect the particle penetration efficiency and the corresponding model η=α⋅e−λ⋅St+κ⋅De is suggested. In comparison to the EPA recommended model, which may contain approximately 3.9%–16.95% sampling error, the new models show better agreement with the experimental data.

Numerical Analysis of Carrier Particle Motion in a Dry Powder Inhaler

The efficiency of dry powder inhalers (DPIs) for drug delivery is still very low and is therefore the objective of intensive research. Thus, numerical calculations (computational fluid dynamics (CFD)) using the Euler/Lagrange approach without coupling are being performed in order to analyze flow structure and carrier particle motion within a typical inhaler device. These computations are being performed for a steady-state situation with a flow rate of 100 l/min. Essential for the detachment of the very fine drug powder (i.e., between 1 and 5 μm) from the carrier particles are the fluid stresses experienced by such particles (i.e., relative velocity, turbulence, and fluid shear) as well as wall collisions, which are both evaluated in the present study. Since the carrier particles are rather large (i.e., normally 50–100 μm), first the importance of different relevant fluid forces, especially transverse lift forces, is investigated. Moreover, the significance of the parameters in the particle–wall collision model is highlighted and a statistical analysis of particle–wall collisions in an inhaler is conducted. The improved understanding of particle motion in the normally very complex flows of inhalers will be the basis for optimizing inhaler design.

Two-phase Turbulence Models in Eulerian-Eulerian Simulation of Gas-particle Flows and Coal Combustion

Eulerian-Eulerian (two-fluid) simulation of gas-particle flows and coal combustion are widely used because of its convenience in simulating large-size facilities. The key point is that it needs more complex closure models, compared to those in Eulerian gas-Lagrangian DEM modeling of particles. This keynote lecture will give a brief review on our many-year studies to solve these problems. The first one is the particle turbulence model. To overcome the shortcomings of the Hinze-Tchen's “particle-tracking-fluid” model, about 20 years ago, a transport equation of particle turbulent kinetic energy and transport equations of both gas and particle Reynolds stresses were proposed by us and subsequently constitute the so-called “k-ɛ-kp”, “unified second-order moment (USM)” and “non-linear k-ɛ-kp” two-phase turbulence models. Furthermore, for simulating reacting gas-particle flows and coal combustion, a full two-fluid model and a combined two-fluid-trajectory model, accounting for both particle turbulent diffusion and particle history effect due to moisture evaporation, devolatilization and char oxidation were proposed. The next is the particle-rough wall interaction. A particle-wall collision model accounting for wall roughness was proposed. Then, to overcome the limitation of the well-known kinetic theory of dense gas-particle flows, an anisotropic two-phase turbulence model, called “USM-Θ” model, accounting for both particle turbulence (large-scale fluctuation) and inter-particle collision (small-scale fluctuation) was proposed. Next, the particle-wake effect on gas turbulence modulation was studied to construct a sub-model and was added to the two-fluid modeling. At last, in recently developed two-fluid large-eddy simulation of gas-particle flows and combustion the particle sub-grid-scale (SGS) stress model is insufficiently studied. Some of them are based on a simple extension of the gas Smagorinsky SGS model without theoretical justification. Therefore, a USM-SGS two-phase stress model was proposed by us, properly accounting for the anisotropy of two-phase SGS stresses and the interaction between them.

Modelling of pipe bend erosion by dilute particle suspensions

A computational fluid dynamic model coupled to a Lagrangian particle tracking routine and a number of erosion models have been used to predict the solid particle erosion in four different 90° square cross-section bends for dilute particle-laden flow. Comparisons with experimental data over a range of conditions, including particle size, mass loading and flow Reynolds number, demonstrate good agreement with predictions of all the erosion models considered. In particular, the models are able to yield reliable predictions of erosion depth and wear location on the concave and convex walls of the bends. The slight disparities observed are most likely due to uncertainties in the particle–wall collision model employed, and variability in the data. The complexity of the particle–wall collision process precluded the development in this work of a model which accounted for the occurrence of erosion pockets and their subsequent influence on the fluid flow, particle trajectories and the magnitude of wear at secondary wear locations, as well as the dynamic movement of the maximum wear location. Despite this, however, and within experimental uncertainty, the models perform well, although their further extension as noted could potentially lead to improved agreement with data.

CFD Simulation of Dilute Gas-Solid Flow in 90<sup>o</sup>Square Bend

Gas-solid two-phase flow in a 90? bend has been studied numerically. The bend geometry is squared cross section of (0.15 m × 0.15 m) and has a turning radius of 1.5 times the duct's hydraulic diameter. The solid phase consists of glass spheres having mean diameter of 77 µm and the spheres are simulated with an air flowing at bulk velocity of 10 m/s. A computational fluid dynamic code (CFX-TASCflow) has been adopted for the simulation of the flow field inside the piping and for the simulation of the particle trajectories. Simulation was performed using Lagrangian particle-tracking model, taking into account one-way coupling, combined with a particle-wall collision model. Turbulence was predicted using k-ε model, wherein additional transport equations are solved to account for the combined gas-particle interactions and turbulence kinetic energy of the particle phase turbulence. The computational results are compared with the experimental data present in the literature and they were found to yield good agreement with the measured values.

A computational investigation of particle distribution and deposition in a 90° bend incorporating a particle–wall model

This paper investigates the particle flow movement and deposition in a 90° bend after a straight duct, utilizing the Lagrangian particle-tracking model incorporated with a particle–wall collision model. Particle turbulent dispersion is introduced by employing the ‘eddy lifetime’ model, and particle deposition velocity in the bend is proposed by counting the number of deposited trajectories in a time period. The developed models are validated for both airflow and particle flow by previous experimental data. Particle distribution and deposition behavior at five size groups (1, 3, 5, 9, and 16 μm) are investigated. The simulation results show that, compared with traditional ‘Trap’ model, the particle–wall collision model postpones the emergence and slows the increase of the ‘particle free zone’ as the particle diameter increases. Particle deposition velocity in the duct bend is also generally predicted by the proposed estimation equation under the simulated conditions. This reveals that adopting the particle–wall collision model obtains a reasonable prediction of particle distribution and deposition in the duct bend. This work will benefit the understanding and application of microparticle flow in curved duct systems.

Extension of the hard-sphere particle-wall collision model to account for particle deposition

Numerical simulations of flows of fluids with granular materials using the Eulerian-Lagrangian approach involve the problem of modeling of collisions: both between the particles and particles with walls. One of the most popular techniques is the hard-sphere model. This model, however, has a major drawback in that it does not take into account cohesive or adhesive forces. In this paper we develop an extension to a well-known hard-sphere model for modeling particle-wall interactions, making it possible to account for adhesion. The model is able to account for virtually any physical interaction, such as van der Waals forces or liquid bridging. In this paper we focus on the derivation of the new model and we show some computational results.