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Detailed process and equipment knowledge is crucial for the successful production of biopharmaceuticals. An essential part is the characterization of equipment for which Computational Fluid Dynamics (CFD) is an important tool. While the steady, Reynolds-averaged Navier–Stokes (RANS) k − ε approach has been extensively reviewed in the literature and may be used for fast equipment characterization in terms of power number determination, transient schemes have to be further investigated and validated to gain more detailed insights into flow patterns because they are the method of choice for mixing time simulations. Due to the availability of commercial solvers, such as M-Star CFD, Lattice Boltzmann simulations have recently become popular in the industry, as they are easy to set up and require relatively low computing power. However, extensive validation studies for transient Lattice Boltzmann Large Eddy Simulations (LB LES) are still missing. In this study, transient LB LES were applied to simulate a 3 L bioreactor system. The results were compared to novel 4D particle tracking (4D PTV) experiments, which resolve the motion of thousands of passive tracer particles on their journey through the bioreactor. Steady simulations for the determination of the power number followed a structured workflow, including grid studies and rotating reference frame volume studies, resulting in high prediction accuracy with less than 11% deviation, compared to experimental data. Likewise, deviations for the transient simulations were less than 10% after computational demand was reduced as a result of prior grid studies. The time averaged flow fields from LB LES were in good accordance with the novel 4D PTV data. Moreover, 4D PTV data enabled the validation of transient flow structures by analyzing Lagrangian particle trajectories. This enables a more detailed determination of mixing times and mass transfer as well as local exposure times of local velocity and shear stress peaks. For the purpose of standardization of common industry CFD models, steady RANS simulations for the 3 L vessel were included in this study as well.

The trajectories of energetic particles trapped by the geomagnetic field, as those composing the Earth’s Van Allen radiation belts, are usually defined by three cyclic motions: gyration, bounce along field lines and drift around the Earth, which are all controlled by this field. The geomagnetic dipole, in turn, has been declining at a rate of ∼5% every hundred years since at least ∼1840. Even with the possibility of a recovery without an extreme event, the global field intensity will very probably continue to decrease in the near future with a consequent weakening of our planet’s magnetic shield capacity. The expected variations in trapped particle trajectories are analyzed in the present work through an analytical approach considering the observed axial dipolar geomagnetic field component and its secular variation. The variations expected on the mirror point altitude and on the boundary of Störmer forbidden zone are assessed along the period 1900-2020. The structures here analyzed could approximate plausible radiation belt changes for a continuously weakening geomagnetic dipole which might have numerous consequences for technologies that operate in space.

In this article, we introduce a new method to detect transient trapping events within a single particle trajectory, thus allowing the explicit accounting of changes in the particle’s dynamics over time. Our method is based on new measures of a smoothed recurrence matrix. The newly introduced set of measures takes into account both the spatial and temporal structure of the trajectory. Therefore, it is adapted to study short-lived trapping domains that are not visited by multiple trajectories. Contrary to most existing methods, it does not rely on using a window, sliding along the trajectory, but rather investigates the trajectory as a whole. This method provides useful information to study intracellular and plasma membrane compartmentalisation. Additionally, this method is applied to single particle trajectory data of β2-adrenergic receptors, revealing that receptor stimulation results in increased trapping of receptors in defined domains, without changing the diffusion of free receptors.

The restitution coefficient is one of the microphysical properties that must be specified for a discrete element model simulation. The more accurate the input, the more accurate the simulation results are. Due to the differences in shape and surface roughness between the corn stalk particle model built-in EDEM software and the actual corn stalk, the simulation will be distorted if the measured recovery coefficients are directly introduced into the EDEM software for simulation. To address this issue, this paper presents experimental measurements of the collision behavior between the intermodal tissue, pith, and nodal tissue particles and the horizontal substrate based on kinematic principles and with the aid of high-speed camera technology to reconstruct the trajectory of the particles during free fall and bounce. Utilizing EDEM software to simulate the free fall and bounce processes, a quadratic polynomial prediction model of the recovery coefficient input values and calculated values was established. Combined with the simulation and physical tests, the coefficients of restitution between the pith and the iron plate and pith surface are 0.559, 0.767. The collision restitution coefficients were determined to be 0.767, 0.616, and 0.784 for the collision between the rind and the iron plate, rind surface, and pith surface, respectively. 0.549, 0.705, 0.687, and 0.723 for the collision restitution coefficients between the node and the rind surface, pith surface, and node surface, respectively. The calibration restitution coefficient was input to EDEM software for the simulation test, and the relative error between the simulation results and the physical examination was within 4.15%. The particle model created and the restitution coefficients calibrated can be used as a reference for designing a corn stalk processing machine and the discrete-element study on the motion of corn stalk particles inside such devices.Graphic abstract

Axial fans are vital accessories in aircraft ventilation systems, but, they may experience erosion from particulate flows, causing a decline in effectiveness over time. This study investigated the trajectories of two types of sand particles and erosion in an axial fan stage, considering the relative position of the blades facing the inlet guide vanes. The movement of particles was simulated using an in-house code that implements a Lagrangian approach along with a stochastic particle-eddy interaction model. The flow field was solved separately and the flow data was transferred to the particle trajectory code. The finite element method allowed for the tracking of particles through the computational cells and accurate determination of their impact positions. A semi-empirical erosion correlation was used to evaluate the local erosion rates, mass removal, and geometry deterioration. As a result, the rotor exhibits a high frequency of impacts and significant erosion on the leading edge of the blade, extending to the upper corner of the pressure side and blade tip, as well as the front of the suction side. In the inlet guide vane, the erosion is spread out along the entire pressure side but at lower erosion rates compared to the rotor blade. The erosion patterns obtained at different pitch-wise positions were cumulated to get better representation of erosion patterns. After being exposed to MIL-E5007E sand (0–1000 $\\unicode{x03BC}$ m) at the highest concentration for 10 hours, the blade experienced a reduction of a 0.29% in mass, a 0.45% decrease in tip chord, and a 0.23% increase in tip clearance. On the other hand, AC-coarse sand (0–200 μm) resulted in a 0.23% decrease in blade mass, a 0.4% reduction in tip chord, and a 0.16% increase in tip clearance. The data that is available can be used to monitor the lifespan of axial fans of similar design and select appropriate coatings to protect against erosion.

The discharge of sediment plumes, which occurs mainly in the two depth zones, has a critical impact on assessing the deep-sea environment. Therefore, it is necessary to establish the corresponding physical oceanography for the evolution of these sediment plumes. For a more accurate evolution estimation of the plumes, the model in this research is concerned with the dynamic interaction between the deep-sea mining vehicle (DSMV) and the sediment plumes on small scales (t ≤ 2 s), contributing to a focus on the vital physical mechanics of controlling the extent of these plumes. The sediment concentration and particle trajectories of the plume emissions were determined using the Lagrangian discrete phase model (DPM). The results show that (1) the wake structure of the DSMV wraps the plume vortex discharged from the rear of the vehicle and inhibits the lateral diffusion of the plume, (2) the length of the entire wake (Lw) increases exponentially as the relative discharge velocity of the plume (U*) increases, where U* is defined as the dimensionless difference between the traveling velocity of the DSMV and the discharge velocity of the plume, and (3) at the same traveling speed of the DSMV and U* less than 0.75, the dispersion of the sediment particles in the early discharge stage of the plume does not vary with the plume discharge rate. This will be beneficial for the more accurate monitoring of ecological changes in deep-sea mining activities and provide theoretical guidance for the green design of DSMVs.

Purpose This paper aims to study the effects of the processing parameters in the reciprocating magnetorheological polishing (RMRP) on abrasive particle trajectory by the simulation analysis, which provides a basis for the machining uniformity of the workpiece. Design/methodology/approach The principle of the RMRP method is discussed, and a series of simulation analysis of the abrasive particle trajectory are performed to evaluate the effects of the workpiece’s rotational speed, the eccentric wheel’s rotational speed, the eccentricity and the frame gap on abrasive particle trajectory by using the RMRP method. Findings The processing parameters have a significant influence on the abrasive particle trajectory, and then the machining uniformity of the workpiece is affected. Under certain experimental conditions, the height difference of workpiece measuring points varies between 4 and 11 µm, and the height difference of equal radial measuring points is less than 1.5 µm by optimizing processing parameters. Originality/value In this study, the optimal processing parameters can be obtained by the simulation analysis of abrasive particle trajectory, which can replace the experimental methods to obtain the reasonable processing parameters for the machining uniformity of the workpiece. It provides references for the selection of processing parameter values in magnetorheological polishing process.

This paper presents a comprehensive numerical study of a truncated conical precipitator. The main objective was to enhance the efficiency of the precipitator by exploring the influence of several parameters on particle trajectories and the evolution of the collection efficiency. The studied parameters include the cone coefficient (D), flow velocity, applied voltage, conduit diameter and length, as well as relative permeability. For each parameter, analyses were conducted on the evolution of the collection efficiency for particles with various diameters, ranging from 0.01 to 10 μm. The results obtained from the numerical simulation on COMSOL Multiphysics® indicate that, regardless of the value of D, the precipitator exhibits optimal efficiency in collecting particles with extreme diameters (0.01 and 10 μm) due to the dominance of the electrical force. In contrast, particles with intermediate diameters (0.1–1 μm) present a challenge, as the drag and electric forces are too weak to ensure effective particle collection. The study highlights that a sharper tip at the top of the precipitator significantly enhances its efficiency. Increasing the applied voltage and selecting lower inner radii of the collecting electrode reinforce the electrical force and enhance particle collection. Furthermore, increasing the height of the precipitator directs particle trajectories more effectively toward the collecting electrode. The results provide valuable insights for the design of more efficient precipitators and propose practical guidelines for improving their effectiveness. These contributions are particularly important for air pollution control technologies, offering significant advancements in this field.

This study investigated the effect of the angle between the blade and the inclined disc on particle trajectory correction during ejection from an organic fertilizer side-throwing device. Using the inclined disc device as the test subject, a blade-based coordinate system was established to model the complex relative particle motion under combined disc and blade inclination. Particle dynamics and blade forces were analyzed quadrantally, enabling the development of a mechanical model and the derivation of displacement equations. Numerical simulation, virtual simulation, and experimental testing yielded the following results: Under the current device parameters, the relative velocity between particles and the blade reaches its maximum when the angle between the blade and the inclined disc is 80°. Within the angle range from 65° to 85°, as the angle increases, the scattering angle of single-sided discs monotonically decreases, while that of dual-sided discs monotonously increases. At an angle of 65°, the trajectories of the dual-sided disc flows tend to converge. At 80°, the flow is at the critical point between convergence and divergence. The effective throwing distance first increases and then decreases, reaching a maximum at an angle of 80°. This study clarifies the relationship between the angle correction of blade–disc inclination and particle velocity and trajectory on the blade, providing a reliable mathematical model and simulation method for similar studies in the field of inclined disc centrifugal material ejection.

Microfluidics has shown great potential in cell analysis, where the flowing path in the microfluidic device is important for the final study results. However, the design process is time-consuming and labor-intensive. Therefore, we proposed an ANN method with three dense layers to analyze particle trajectories at the critical intersections and then put them together with the particle trajectories in straight channels. The results showed that the ANN prediction results are highly consistent with COMSOL simulation results, indicating the applicability of the proposed ANN method. In addition, this method not only shortened the simulation time but also lowered the computational expense, providing a useful tool for researchers who want to receive instant simulation results of particle trajectories.