Particle-free Zones Research Articles

A Level-Set/FEM approach for particle bed growth in Stokes–Darcy suspension filtration

This article presents an innovative approach to modeling particle bed growth through suspension dead-end filtration, a process of paramount importance in various industrial and environmental contexts. More precisely, it focuses on the numerical formulation of a continuous approach based on a Stokes–Darcy coupling. In a Level-Set/FEM frame, this model effectively captures the dynamic evolution of particle beds (cake), taking into account the interaction between suspended particles and porous media. Model validation is also a key focus of this paper. Numerical tests are carried out under various conditions, and their results are compared with analytical solutions and experimental data drawn from the literature. This permits corroboration of the predictive capabilities of the model, confirming the robustness and accuracy of the proposed approach. Firstly, Stokes–Darcy coupled flows are investigated in simplified cases such as rectangular geometries and coaxial cylinders. These scenarios serve as benchmarks to assess the model performance under simple and varied conditions. Additionally, the more challenging case of a three-dimensional anisotropic flow between two ellipsoids is addressed, where the evolution of the cake takes place in three dimensions. Through rigorous analysis and comparison with analytical solutions, the model is proved efficient in capturing the inherent complexities of such scenarios. Finally, richer two-dimensional Stokes–Darcy flows are considered, in the presence of both impermeable and permeable obstacles, representing a crucial step towards modeling real industrial processes. This last study highlights not only the formation of particle-free zones but also the practical relevance of this work.

Exploring high-temperature deformation and damage behaviour in high-performance ferritic (HiperFerSCR) steel with Laves phase particles

The mechanical behaviour at high temperatures and the corresponding microstructural characteristics of a newly developed high-performance ferritic, salt-corrosion-resistant (HiperFerSCR) steel containing Laves phase particles were studied to investigate the active deformation mechanisms and the evolution of damage. A series of tensile tests were conducted at both room temperature and elevated temperatures (550, 600, and 650 °C), along with detailed microstructural analyses using scanning electron microscopy and electron backscatter diffraction. The tensile flow characteristics of HiperFerSCR at room temperature exhibit significant strain hardening, which is due to the Laves phase particles that encourage planar slip, demonstrated by the formation of numerous slip bands and low-angle grain boundaries. The intersections of these slip bands with grain boundaries appear to be the initiation sites for cracks, which then propagate intergranularly as well as within grain interiors along the slip bands. At high temperatures, the flow characteristics show strain softening, which is attributed to a dynamic recovery (DRV) mechanism, evident in the formation of subgrain boundaries decorated with Laves phase particles. During high-temperature deformation, damage initiates in the particle-free zone (PFZ), which expands at higher temperatures, leading to strain localisation, void formation along the grains, and eventually, grain boundary decohesion.

Influence of the strain rate on the fatigue behaviour of fully ferritic high chromium steel and P91 steel at high temperatures

Fully ferritic, high-chromium HiperFer alloy presents a promising option, providing a combination of both, high corrosion resistance and material strength above 600 °C. Although these steels show improved strength at creep and thermomechanical loading compared to conventionally used 9–12 % Cr-steels, a comprehensive understanding of their fatigue behaviour and the influence of different strain rates is required. Hence, in this study the fatigue behaviour of HiperFer-17Cr2 was analysed in stress-controlled fatigue tests performed at temperatures above 600 °C and at 0.05 Hz and 5 Hz. Moreover, a martensitic steel P91 was investigated as a reference. The results obtained for HiperFer–17Cr2 reveal an increase in fatigue strength with a decrease in frequency and an increase in stress. Additionally, an influence of the frequency on the cyclic deformation behaviour of HiperFer-17Cr2 was observed, which is characterized by cyclic hardening. This cyclic hardening correlates with an increase in hardness, which is associated with the deformation induced formation of Laves phase particles. After LCF load with lower frequency a stronger hardness increase as well as a higher amount of Laves phase particles and smaller particle-free zones at the grain boundaries were observed, contributing to the higher fatigue strength obtained at lower strain rate.

Preparation of ultra-high ductility and high strength Mg-Sn-Zn-Zr alloy by differential thermal ECAP (DT-ECAP) induced heterogeneous structure

Developing high-ductility magnesium (Mg) alloys has become an imminent issue for their wide application. In this work, a new Mg-Sn-Zn-Zr alloy with ultra-high ductility (elongation, El. over 40 %) and high ultimate tensile strength (UTS, ∼309–354 MPa) was prepared by a novel differential thermal equal-channel angular pressing (DT-ECAP). Heterogeneous structures, including bimodal grain structures and inhomogeneous distribution of second phases composed of banded structure and particle free zone (PFZ), were induced by DT-ECAP process. Based on the results of electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), high-resolution TEM (HRTEM), and selected area electron diffraction (SAED), the bimodal grain structure originated from incomplete dynamic recrystallization (DRX) dominated by Zener pinning, strain-induced grain boundary migration (SIBM) and the limitation of polycrystallization due to lower dislocation density. Meanwhile, the bimodal distribution of second phases was highly associated with the defect density and initial structure. More importantly, the enhanced strength of DT-ECAPed alloys can be primarily attributed to hetero-deformation induced (HDI) strengthening, grain boundary strengthening, and precipitation strengthening. Moreover, HDI hardening, texture weakening or randomizing activation of non-basal slip, high density of dislocations in sub-structures, and twining induced superior work-hardening effect, which was highly responsible for the ultra-high ductility in sixth pass (6P) alloy. The current work provides a novel DT-ECAP process for inducing heterogeneous structure and offers beneficial insight into the development of ultra-high ductility and high strength for rare-earth-free Mg alloys via a combination of HDI strengthening and hardening and other vital mechanisms.

Impact of Laval nozzle structure on the flow characteristics of supersonic gas-solid two-phase flow

This study introduces a mathematical coupling model within the Euler-Lagrange framework to conduct numerical simulations for supersonic gas-particles flow. After validating the model, the gas flow characteristics and particle dynamics within supersonic gas-particle flow under various nozzle configurations are investigated. The findings are as follows: (1) A Laval nozzle with a smoothly connected throat suppresses the generation of fan-shaped Prandtl-Meyer expansion waves and other complex wave systems, effectively mitigating significant changes in gas pressure at the throat and enhancing the stability of supersonic jets. (2) The presence of a particle-free zone in the nozzle divergent segment reduces the collision frequency between particles and the walls, thereby restricting the radial expansion of particles. (3) Utilizing an internally smooth-lined nozzle and expanding the radial divergence angle to 2.5–2.8 times, while ensuring particles maintain consistent axial penetration performance, increases the reflective contact area. This leads to an improvement in the utilization efficiency of particles. These findings provide valuable insights for optimizing nozzle configurations and enhancing the performance of supersonic gas-particle systems.

Enhancing strength and ductility of Al-matrix composite via a dual-heterostructure strategy

Aluminum matrix composites (AMCs) often have low ductility, which has been a long-lasting issue in the last few decades. This problem arises largely from the non-deformability of reinforcement particles, which leads to premature failure of the matrix-particle interfaces. Here we propose a new microstructural design strategy for AMCs: distribute the reinforcement particles non-uniformly to form dual-heterostructured AMCs. The zones with high-density particles are recognized as the hard zones, which carry less plastic strain than the particle-free zones to prevent premature interfacial failure. A dual-heterostructured Al-matrix nanocomposite is fabricated, in which AlN nanoparticles are distributed in a dual-level hierarchy: first level heterogeneous nanoparticle distribution and second level heterogeneous zones with different grain sizes. The dual heterostructure produced a unique dual level hetero-deformation induced (HDI) strengthening and hardening to produce high strength and ductility. The dual level HDI strengthening effect has been revealed by the inflection points on the loading-unloading-reloading stress-strain curves. Furthermore, the evolution of local strain fields during the in-situ tensile deformation directly proved the occurrence of strain partitioning, in which the ductile particle free zones have carried a larger strain than the hard particle rich zones. Dispersive shear strain bands are observed for the first time in AMCs. These findings are expected to help design other metal matrix composites with superior mechanical properties.

Microstructural and electrochemical behavior of spark plasma sintered (Cu-10Zn) + Al2O3 nanocomposites

The present work deals with developing Al2O3 reinforced α-brass (Cu-10Zn) nanocomposites through spark plasma sintering and evaluated its electrochemical properties in a 3.5% NaCl aqueous solution. Microstructural analysis revealed the uniform dispersion of Al2O3 particles with inter-particle spacing ∼2.45 µm in 3 wt.% Al2O3 nanocomposites. The initiation of Al2O3 clustering and vast clustering of particles with wide particles-free-zone were observed in 6 and 9 wt.% Al2O3 nanocomposites. X-ray diffraction peaks confirm the crystallinity and incorporation of Al2O3 in the α-brass matrix. The corrosion behavior was studied by measuring the change in open-circuit potential values, electrochemical impedance spectroscopy (EIS), linear sweep voltammetry (LSV), and potentiodynamic polarization (PDP) studies in 3.5% NaCl solution. The 3 wt.% Al2O3 nanocomposites exhibited lower icorr value than the Cu-10Zn matrix and other Al2O3 reinforced nanocomposites. The EIS results confirm the surface layer enhancement and resistance to charge transfer in 3 wt.% Al2O3 nanocomposites due to their uniform distribution in the matrix. The uniformly embedded reinforcement particles abridged the prospects of galvanic coupling, which resulted in the upliftment of corrosion resistance and passivation behavior. An increase in the icorr value beyond 3 wt.% Al2O3 nanocomposites was due to the clustering of reinforced nanoparticles and vast particle-free zones and caused intergranular corrosion.

Improving the stress corrosion resistance of 7075 matrix composites through combination of nanoparticle incorporation and retrogression re-aging treatment

7xxx aluminum matrix composites reinforced with ceramic nanoparticles are expected to possess advantageous comprehensive performance. However, further applications of these composites remain in doubt because it is likely that introducing these extrinsic phases could impair the resistance to stress corrosion crack (SCC). In this work, we used 7075 as the matrix, and TiB2 nanoparticles as the reinforcement, to study the influences of the retrogression and re-aging (RRA) treatment and nanoparticle incorporation on the SCC behavior of 7075 aluminum alloy. The intergranular corrosion test (IGCT) and slow strain rate test (SSRT) results show that both TiB2 and RRA are conducive to the improvements in the SCC resistance. The positive effects of RRA can be two-fold: (i) the lattice distortion is alleviated during the RRA temper; (ii) the coarse and discrete grain boundary precipitates (GBPs). The accumulation of active solute elements, however, also occurs at the grain boundaries, leading to severe intergranular corrosion. Surprisingly, some coarse TiB2 particles larger than the thickness of particle-free zones (PFZs) could obstruct the mass transportation, reducing the susceptibility to intergranular corrosion. In conclusion, the strength and SCC resistance of 7075 alloy can be concurrently improved by the combination of particle incorporation and RAA treatment.

Laves Phase Precipitation Behavior in HiperFer (High Performance Ferritic) Steel with and without Boron Alloying

High-chromium ferritic stainless HiperFer steels were developed for high-temperature applications in power conversion equipment. The presented research describes the precipitation behavior of the Laves phase after the thermomechanical treatment of Fe-17Cr-0.6Nb-2.4W HiperFer alloys with and without the addition of 55 ppm boron. The boron-alloyed variant was produced with the aim of enhancing grain boundary strengthening and consequently increasing creep resistance. The focus is set on the effect of boron on the thermomechanically induced precipitation of (Fe,Cr,Si)2(Nb,W) Laves phase at grain boundaries. The addition of boron modifies the diffusion conditions in the area of grain boundaries. Consequently, the formation of Laves phase is promoted and the particle growth and coarsening process are suppressed. The impact of boron addition was validated by performing creep and thermomechanical fatigue testing in the standard processing state of HiperFer steel. In the B-alloyed variant, increased creep ductility through the modification of the particle-free zone widths at high-angle grain boundaries was encountered. Nevertheless, an optimized thermomechanical treatment is necessary to fully utilize the increased ductility effect for the creep strength optimization of the B-alloyed grade.

High electromagnetic absorption ratio in TiB2/AZ80 composite

TiB2/AZ80 Mg matrix composite containing particle rich zone (PRZ) and particle free zone (PFZ) was parpred by simple stiring casting and cross-rolling. The percolation structure of the PRZ endows the composite with local metamaterial properties, which introduces a new electromagnetic wave (EMW) absorption mechanism, namely plasma oscillation, for Mg matrix composite. Likewise, the multiple internal reflection and the TiB2–Mg interface polarization also contribute to the high EMW absorption capacity. As a result, the electromagnetic interference (EMI) shielding performances measured by vector network analysis shows that the X-band EMI shielding performance of the as-rolled composite is significantly improved than that of the AZ80 alloy, especially its absorption shielding efficiency ratio exceeds 70%.

Modelling of Red-Mud Particle-Solid Distribution in the Feeder Cup of a Thickener Using the Combined CFD-DPM Approach

The paper evaluates the behavior of a red-mud solid fraction in a thickener feeder cup, aiming to identify the main characteristics of particle distribution in the flocculation zone and to determine the dependencies affecting the further process taking place in the particle-free sedimentation zone in the thickener-thickening unit. This work used mathematical and numerical modeling to study the influence of such parameters as the flow rate of the feed pulp in the thickener, the flow rate of the flocculant, the density of pulp at the inlet to the unit, and the viscosity and temperature of the pulp on the particle-size distribution from under the feeder cup. The results and dependencies obtained are intended to be used as nominal values in the red-mud thickening process performed on a lab-scale unit.

Investigation of microstructure and tribological performances of high-fraction TiC/graphene reinforced self-lubricating Al matrix composites

Al-10.0 vol% (TiC and GNPs) composites were fabricated with different volume ratios of TiC and GNPs from 10.0:0.0–8.0:2.0 by powder metallurgy. The results show particle free zones (PFZs) in as-sintered composites decrease and distributions of reinforcements become more uniform, and the hardness and wear resistance of hybrid composite increase as TiC-to-GNPs ratio decreases. Al-8.5 vol% TiC-1.5 vol% GNPs has the highest hardness at 200.5 HV and the best wear resistance with a wear rate of 4.99 × 10−4 mm3/Nm based on the collaborative effects of TiC and GNPs, respectively. However, as the GNPs fraction increases to 2.0 vol%, the hardness and wear resistance of the composite drop drastically because of GNPs agglomeration.

Modelling of liquid film migration in Al-Cu alloys.

Microstructural evolution in the presence of liquid film migration (LFM) is simulated for Al-Cu alloys using a cellular automaton (CA) model. Simulations are performed for the microstructural evolution and concentration distribution in an Al-4 wt.%Cu alloy with initially equiaxed grain structures holding in a temperature gradient. A slight deviation from local equilibrium, estimated from experimental data, is considered to be the driving force for LFM. The direction of LFM is triggered by concentration fluctuations setting a concentration gradient as a further driving force. The simulation successfully reproduces the experimentally observed microstructures generated by LFM accompanied by a particle free zone behind the liquid film. The solid concentration in the particle free zone is found to be the equilibrium solid concentration. The simulated concentration profile across the migrating liquid film agrees well with experimental measurements. The simulated grain structure becomes coarser and highly elongated after holding in the temperature gradient. The results reveal that the increase in transversal grain width is mainly controlled by LFM, while the grain elongation in longitudinal direction is attributed to both LFM and temperature gradient zone melting. The solid concentration decreases from the initial (supersaturated) composition to the local equilibrium solid concentration corresponding to the local temperature. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

A numerical study of particle-laden flow around an obstacle: flow evolution and Stokes number effects

Three-way coupled numerical simulations of particle-laden fluid flow around a square obstacle are performed by a coupled finite-volume and discrete-element method, taking account of the collisions between particles. The fluid flow is described by the Eulerian formalism, while the Lagrangian formalism is used for the solid particles. The dynamics of each phase and the modulation mechanism of the flow field by the inertial particles are explored. The Reynolds number based on the side length of the obstacle is 100, which leads to a typical periodic flow pattern of vortex shedding. Under the action of particles, the flow tends to be chaotic even in the upstream region, and the vortex shedding occurs earlier. The intensity of the vortex is attenuated due to particle dissipation. At sufficiently small Stokes numbers, the particles exhibit flow tracer behavior with relatively high fidelity. However, as the Stokes number and mass loading increase, the interaction between the particles and fluid becomes important, especially in the core region of the channel. With the increase of the particle response time, the spanwise velocity fluctuation is attenuated, while the influence on the streamwise velocity fluctuation seems complicated. No particles are observed to hit the rear surface of the obstacle or deposit in the domain during the flow. When the Stokes number and mass loading are elevated from 0.0036 and 0.065 to 0.5 and 9.024, respectively, the distribution of the particles near the channel centerline varies from being filled in the shedding vortices to surrounding them. Meanwhile, the particle-free zones centered on these vortices become larger. For the Stokes number and mass loading up to 1.5 and 27.073, respectively, the particles are scattered in the downstream area, and the flow pattern of the Kármán vortex street is modified. Within the range of the Stokes number considered, the drag and lift coefficients, and the Strouhal number also show a certain trend of variation.

Particle-free zone of the two-phase flow in a convergent-divergent nozzle

The gas-particle two-phase flow in a convergent-divergent nozzle is encountered in many applications like solid-propellant rocket motors (SRMs). The “Particle-free Zone” adjacent to the nozzle wall is crucial for the nozzle performance which is closely related to the specific impulse of the motor. Though it has been usually observed by many investigators, the existence of the particle-free zone in different nozzles and its effect on nozzle performance are still ambiguous. In this research, we investigated the two-phase flow with monodispersed micron particles in a nozzle using a two-way coupled Eulerian-Lagrangian model and found that the particle-free zone does not exist for smallest particles (dp = 1.0 μm). Moreover, we built a theoretical model for predicting the extent of the particle-free zone by calculating the trajectory of the particle closest to the nozzle wall. The effects of the particle size, total pressure, total temperature and nozzle geometry on the particle-free zone were studied. Finally, we analyzed the nozzle performance and found that the gas velocity at the outlet and the thrust do not change with particle size monotonously, and the medium-sized particles cause the largest thrust loss.

Прогнозування енергетичного стану нерівноважних термодинамічних систем в умовах деградації їхньої внутрішньої будови та функціональних властивостей

A general approach is developed to individual analytic prediction of an energy state indexes for thermodynamic systems (TS) working under the nonequilibrium service conditions that cause determined and random degradation of the TS structures and performance: losses nominal levels of structure components and service properties characteristics. The following TS were proposed to be considered as relevant ones for the analysis: heat-resistant alloys; technology processes; climate, ecology and biology systems. Based on the energy conservation law, analytic relations were obtained for the TS service parameters calculations to specify conditions for the TS maximum performance reaching based on the TS individual structure features and a random factor values. The values have to be used in the relations may be rigorously experimentally or theoretically specified for each TS. The approach developed in the work was applied to predict creep temperature interval for industrial, austenite, particle hardened ASTM A316 steel. The basic possible strengthening mechanisms in the steel were taking into account: dislocation gliding with the particles and forest dislocations overcoming together with typical for the steel type structural inhomogeneities existence: the particle free zones. Proceeding from the steel real structure features, the particle overcoming by mobile dislocations was concluded to be the dominant strengthening mechanism in the steel. Hence the steel starting creep temperature was calculated which value is in accordance with the known for the Fe based alloys minimal temperature of the dislocation climbing beginning. Based on the obtained results and their fundamental theoretical background, possibility is emphasized to apply the approach in science, technology control, medicine etc

Direct Numerical Simulation of Particle-laden Flow Around an Obstacle at Different Reynolds Numbers

Inspired by the practical operation of the fluid machineries, direct numerical simulation of fluid with a lot of finite-size particles flowing around a large-size obstacle at three different Reynolds numbers is implemented by using a two-way coupled finite-volume, discrete-element and immersed-boundary method. The results show that, for a low Reynolds number Re=20, the flow is dominated by viscosity, and under the circumstances of a small Stokes number, the particles follow fluid streamlines closely. The flow suggests regular movement characteristics of laminar flow, although the vortices behind the obstacle tend to collapse under the perturbation of particles. For a moderate Reynolds number Re=100, the phenomenon of vortex shedding is also observed. Due to the centrifugal force induced by the vortices, particles are distributed around the main vortices behind the obstacle, forming particle-free zones in these vortices. For a high Reynolds number Re=300, the flow is chaotic. The vortices of many sizes appear irregularly in the domain and the distribution of particles tends to be uniform.

Microstructural and mechanical characterizations of stir cast aluminum 356–Nb2O5 composite

Stir casting and heat treatment was applied to manufacture wear-resistant aluminum 356 matrix composites with niobium pentoxide particle reinforcement. Regular scattering of matrix phase and uniform distribution of particles were achieved through stirring fully liquid aluminum melt and Nb2O5 mixture. A normal solidification rate and T6 heat treatment guarantied the fine microstructure, low porosity content, minimum particle-free zones, very small primary/secondary dendritic arm spacings, and needle-like Si2Fe2Al9 phase. Composite formation increased the macro/microhardness from 27 to 66.5 and 33 to 88.7 kgf/mm2 for macro- and microhardness, respectively. It also decreased the wear mass loss considerably and improved the fatigue limit and the forming capabilities due to the moderate tensile/bending strength and ductility.

Superplastic Deformation Mechanisms in Fine-Grained 2050 Al-Cu-Li Alloys.

The deformation behavior and microstructural evolution of fine-grained 2050 alloys at elevated temperatures and slow strain rates were investigated. The results showed that significant dynamic anisotropic grain growth occurred at the primary stage of deformation. Insignificant dislocation activity, particle-free zones, and the complete progress of grain neighbor switching based on diffusion creep were observed during superplastic deformation. Quantitative calculation showed that diffusion creep was the dominant mechanism in the superplastic deformation process, and that grain boundary sliding was involved as a coordination mechanism. Surface studies indicated that the diffusional transport of materials was accomplished mostly through the grain boundary, and that the effect of the bulk diffusion was not significant.

Influence of Substrate Surface Finish Metallurgy on Lead-Free Solder Joint Microstructure with Implications for Board-Level Reliability

Solder joints can experience fatigue cracking at the interface between the solder and substrate during thermal cycling due to the difference in thermal expansion between joined components. In order to strengthen the interfacial region and prevent cracking, two Cu pad surface treatments were studied on Sn-3Ag-0.5Cu solder, and on matte Sn plate and Ni plate coatings. The resulting intermetallic microstructures were characterized using scanning electron microscopy and energy-dispersive spectroscopy. Mechanical testing was performed using nano-indentation on the solder joints. The matte Sn plate on Cu sample formed an uneven distribution of Ag3Sn particles and a planar Cu6Sn5 interfacial intermetallic. The Ni-plated sample formed a needle-like Ni-rich interfacial intermetallic and uniform dispersion of Ag3Sn particles. The rough intermetallic compound (IMC)/solder interface and even IMC particle distribution cause the Ni-plated sample to experience reduced damage under board-level thermomechanical cycling because the interfacial structure reduces the Sn matrix recrystallization that contributes to fatigue cracking. In contrast, the matte Sn-plated sample exhibited an Ag3Sn particle-free zone adjacent to a planar Cu6Sn5 IMC layer which allows for rapid Sn recrystallization and fatigue crack propagation.