Solid Fraction Distribution Research Articles

Excellent hydrophobicity and high mobility of condensate droplets on hierarchical nanostructured surfaces: Insights from MD simulations

Comprehending the fundamental physical mechanisms behind condensation and the formation of suspended droplets on hierarchical structured surfaces is of paramount importance in the design of anti-frosting surfaces. In this study, we characterize the nucleation, growth and dynamic wetting behaviors of condensate droplets on hierarchical nanostructured surfaces by molecular dynamics simulation, and reveal that hierarchical structures facilitate the rapid formation and high mobility of suspended droplet during condensation. The mechanism underlying the formation of suspended droplets on hierarchical surfaces is unveiled, which can be attributed to the spontaneous dewetting transition induced by confined growth of individual droplets. Additionally, the impact of solid fraction and secondary structure distribution on condensation and dynamic wetting is systematically discussed. The results indicate that an increase in solid fraction or the number of secondary structures enhances the stability of suspended droplets and improves the droplet mobility. In particular, the presence of bottom secondary structures on sidewalls plays a crucial role in the formation of suspended droplets on hierarchical surface. It is expected that the above findings could provide valuable guidance for optimizing the design of functionalized surfaces with anti-frosting and self-cleaning performance.

A computational study of binary eutectic system with convection under volumetric freezing: A Moving Boundary Problem

A reduction in the operating time during the solidification of an eutectic alloy is one of the prime demands in front of the investigators. The classical theory of solidification was not able to offer rapid solidification of an alloy due to not account the structural property of the material. To account convection and external heat sink effect, an external volumetric heat sink is considered and it depends on the distance and time. The thermal conductivity, density, and specific heat of the mushy zone are assumed to be the linear combination of solid and liquid regions properties with a solid fraction distribution. The mathematical model accounts for the solid fraction distribution, which has a linear relationship with the temperature of the mushy zone. The analytical solution of the problem has been determined via similarity transformation. To explore the current study, numerical data of the Copper-Aluminum alloy with 5% Copper is presented. It has been found that with a volumetric heat sink, the rate of solidification becomes faster than usual. Further, the rate of heat removal from the surface accelerates. Convection enhances the rate of freezing of the eutectic alloy. The temperature of the mushy region is going up for the increasing value of the solid fraction in mushy zone, which is lying in [0,1] and when we increase the strength of volumetric heat, then the temperature profile decreases and, the first-interface and second-interface increase gradually in the whole medium. We compared the current result with Tien and Geiger’s result, and it is found in good compliance. It is expected that the current study will improve the fundamental understanding of the solidification of an eutectic alloy and reduce the time for freezing, which is useful to design industrial freezing devices for alloys.

Extended kinetic theory applied to pressure-controlled shear flows of frictionless spheres between rigid, bumpy planes.

We numerically investigate, through discrete element simulations, the steady flow of identical, frictionless spheres sheared between two parallel, bumpy planes in the absence of gravity and under a fixed normal load. We measure the spatial distributions of solid volume fraction, mean velocity, intensity of agitation and stresses, and confirm previous results on the validity of the equation of state and the viscosity predicted by the kinetic theory of inelastic granular gases. We also directly measure the spatial distributions of the diffusivity and the rate of collisional dissipation of the fluctuation kinetic energy, and successfully test the associated constitutive relations of the extended kinetic theory, i.e., a kinetic theory which includes the role of velocity correlations. We then phrase and numerically integrate a system of differential equations governing the flow, with suitably modified boundary conditions. We show a remarkable qualitative and quantitative agreement with the results of the discrete simulations. In particular, we study the effect of (i) the coefficient of collisional restitution, (ii) the imposed load and (iii) the bumpiness of the planes on the profiles of the hydrodynamic fields, the ratio of shear stress-to-pressure and the gap between the bumpy planes. Finally, we predict the critical value of the imposed load above which crystallization occurs, based on the value of the solid volume fraction near the boundaries obtained from the numerical solution of the kinetic theory. This notably reproduces what we observe in the discrete simulations.

3D coarse-grained DPM simulation of the MIP reaction-regeneration loop

The reactor-regenerator loop is the core facility of the maximizing iso-paraffin (MIP) process. Although the discrete particle method (DPM) simulation can provide detailed information at the particle scale, it has been unable to simulate such a complex loop system due to limitations of coarse-grained (CG) models, computing software, and hardware. In this study, a newly proposed soft-shell CG-DPM model with a CG ratio of up to 800 is used to simulate a 3.5 Mt/a industrial-scale MIP reactor-regenerator loop. The solid fraction distribution obtained is found to agree well with in-situ measurements. Hydrodynamic properties including the distribution of solid fraction, gas and solid velocity, standard derivation of solid fraction with time, temporal distribution of the flow field, and particle residence time distribution are measured in the simulation, which are meaningful to better design and operate such systems in the future.

Microstructure Design of Semi-Solid Slurry for Metal Direct Writing

Metal direct writing in semi-solid slurry is an innovative technology to realize low-cost printing of load-bearing parts in contrast to laser-based additive manufacturing. However, it is challenging to achieve near net-forming of 3D parts in the current stage because of the out of controlled microstructure and hence the unstable macro extrusion of the used semi-solid slurry. Here, mixed powder remelting (MPR) is introduced to actively design the characteristics of solid phases, i.e., solid fraction, shape factor, and size distribution. Specifically, high-melting-point pure Al powder served as the dispersed solid phases in the liquid phase that transformed from Al-Si alloy powder after remelting, leading to hypoeutectic Al-Si semi-solid slurry. The effectiveness of this approach was experimentally examined and kinetically modelled, to prepare semi-solid slurry with pre-set microstructure. The improved extrusion stability of semi-solid slurry can be anticipated, and it is universal for manufacturing of metal matrix composites slurry.

Slurry preparation for semi-solid metal direct writing by a novel approach of mixed powder remelting

Extrusion-based metal direct writing is a promising metal additive manufacturing technology due to its high efficiency and low cost. However, fabricating parts with high integrity and complex geometry remains challenging. The most critical factor is the unavailable of semi-solid slurries with uniform and nearly spherical solid particles, resulting in uncontrollable extrusion and printing. Currently, mixed powder remelting (MPR) is reported to preset the features of the solid phases, including volume fraction, morphology, and size distribution. Specifically, the semi-solid slurries of hypoeutectic AlSi alloys were obtained by preheating and shearing the mixed powder composed of eutectic AlSi alloy powder and pure aluminum powder. Their microstructural characteristics and rheological behavior were investigated, demonstrating the microstructure tailoring (controllable solid fraction and size distribution, high shape factor of about 0.9) and the reduced viscosity fluctuation by a factor of 7 compared with traditional processes. MPR shows unparalleled advantages for further engineering applications of metal direct writing.

Optimisation of melt pouring temperature and low superheat casting of Al-15Mg2Si-4.5Si composite

ABSTRACT In this study, a computational fluid dynamics (CFD) model is employed to optimise the melt pouring temperature during Low superheat casting (LSC) of the Al-15 Mg2Si-4.5Si composite. The die cavity considered to perform the die filling simulations corresponds to the as-cast tensile specimens, as per ASTM B557 guidelines. The findings of the study include melt temperature distribution, solid fraction distribution during filling as well as during solidification, velocity distribution of the melt and surface defect concentration. Experimentation is performed to develop low superheat cast composite based on the numerically estimated optimum melt pouring temperature of 650°C. Mixture of irregular dendritic, polygonal and equiaxed shaped primary Mg2Si grains are observed within the cast parts, whereas primary Al grains are found to be of dendritic morphology with occasional presence of spheroids. Marked improvements in microstructure and mechanical properties have been evidenced in the LSC composite compared to its conventional cast counterpart.

Rotary hearth furnace for steel solid waste recycling: Mathematical modeling and surrogate-based optimization using industrial-scale yearly operational data

The presence of zinc in byproduct dust produced during steel production poses a challenge to resource management and can have adverse environmental effects. This study investigates the dezincification behavior of a commercial-scale rotary hearth furnace used to recycle the byproduct dust. A mathematical model of iron-ore/carbon-composite pellets was developed, incorporating a one-dimensional dynamic model to examine the non-uniform distribution of temperature and solid weight fraction. The Arrhenius kinetics of the ZnO reduction reaction (ZnO + CO → Zn + CO2) was fitted using operational data yielding estimated parameters of 163.6 kJ mol−1 and 868.6 m s−1. The simulation results of our study showed good agreement with the operational data from the furnace, with a relative error of 10%. Six factors were identified as having an impact on the dezincification ratio, with the most significant being operational time, particle size, temperature, C/O ratio, porosity, and emissivity in descending order. The mathematical model was used to examine two scenarios of environmental problems and derive optimal solutions for each. Our results show that extreme gradient boosting using operating temperature, operating duration, and C/O ratio as trained variables was the most accurate in predicting dezincification and metallization, resulting in a 33% increase in waste recycling through surrogate-based optimization. The Pareto front analysis highlights the importance of considering the net impact of carbon emissions, total production cost, and solid waste penalties together.

Simulation of energy storage unit in existence of sinusoidal obstacles considering nanomaterial

To attain a unit for air conditioning in a building with less entropy generation and high thermal performance, a present system has been introduced in which cylinders of paraffin have been utilized. The problem of pure-paraffin is low conductivity and it can be improved with adding nanoparticles. For attaining the features of nanomaterial, single phase – based formulation have been implemented. The types of paraffin and nano-powders are RT25 and TiO2. In outputs, the components of irreversibility and distribution of solid fraction and temperature have been described. The efficacy of temperature and speed of air flow, distance of cylinders and fraction of additive have been examined. Both irreversibility and thermal productivity of the unit have been scrutinized. The higher temperature of air leads to the conversion of paraffin to liquid. Augmenting the fraction of additives may boost the melting rate around 6.79 %. With augment of “b”, the charging time alters from 17,888 s to 11,479 s. With elevation of inlet speed and temperature, melting rate enhances.

Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous Media

A method was developed to integrate the truncated power-law distribution of solid volumetric fraction into the widely used Kozeny–Carman (KC)-type equations to assess the potential uncertainty of permeability. The focus was on the heterogeneity of porosity (or solid volumetric fraction) in the KC equation. The truncated power-law distribution simulates a heterogeneous scenario in which the solid volumetric fraction varies over different portions of porous media, which is treated as stationary, so its spatial mean can be replaced by the ensemble mean. The model was first compared with the experimental results of 44 samples from the literature and a recent model of KC equation modification that targets the coefficients in the equation. The effects of the fractal dimension of characteristic length of the solid volumetric fraction on the mean and standard deviation of permeability are calculated and discussed. The comparison demonstrates that the heterogeneous solid volumetric fraction can have similar effects as adjusting the empirical constant in the KC equation. A narrow range smaller than mean ± standard deviation from the model agreed with the experimental data well. Incorporating the truncated power-law distribution into the classical KC model predicts a high mean permeability and uncertainty. Both the mean and standard deviation of the permeability decrease with an increasing fractal dimension.

Numerical Prediction of Turbulent Drag Reduction with Different Solid Fractions and Distribution Shapes over Superhydrophobic Surfaces

The exploration of superhydrophobic drag reduction has been and continues to be of significant interest to various industries. In the present work, direct numerical simulation (DNS) is utilized to investigate the effect of the parameters on the drag-reducing performance of superhydrophobic surfaces (SHS). Simulations with a friction Reynolds number of 180 were carried out at solid fraction values of ϕs=116,111, and 14, and three distribution shapes: aligned, staggered, and random. The top wall is the smooth one, and the bottom wall is a superhydrophobic surface (SHS). Drag reduction and Reynolds stress profiles are compared for all cases. The turbulent kinetic energy budget, including production, dissipation, and diffusion, is presented with respect to the solid fraction and type of distribution to investigate the drag reduction mechanism. The sizes of the longitudinal vortices and formation of hairpin vortices are investigated through the observation of coherent structures. The simulation of a post model is a useful method to study the drag reduction for different solid fraction values and distribution geometries. Our study demonstrates that the drag reduction could acquire 42% with the solid fraction value ϕs=116 and an aligned distribution shape for post superhydrophobic surface geometry. Our study also showed the relationship of the Reynolds stress component (R11, R22, and R33) to the drag reduction with the differences in the solid fraction values and distribution geometry. In which, the R11 component has the most change between an aligned distribution and a random one. The peak value of R11 tends to shift away from the SHS wall. In addition, the analysis of the TKE budget over the superhydrophobic surface was performed, which can be adopted as a useful resource in turbulence modeling based on RANS methodology.

Convection-induced bridging during alloy solidification

In this work, the effect of solute expansion coefficient on the natural convection and freezing front propagation is investigated by performing three-side cooled solidification experiments. Four different aqueous salt solutions, and different compositions thereof, were employed for experimentation. The mixtures were solidified to analyze the effect of solute expansion coefficients on the convection currents and the composition distribution in the bulk. The initial compositions were chosen such that all cases have the same primary solid fraction at eutectic temperature, for obtaining similar compositional changes in the bulk liquid at various stages. Similar cooling conditions were also maintained to ensure that the variation in convection strength is primarily caused by different solute expansion coefficients. A distinct observation of the free surface freezing before the bulk, termed bridging, is reported in certain cases. Further analysis revealed that the bridging could be attributed to a difference in solute convection caused by the solute expansion coefficient. Numerical simulations were performed to further ascertain the plausible initiation mechanisms for bridging. The predicted compositional and solid fraction distribution revealed lesser solute accumulation near the surface, for the lower solute expansion cases, and the resulting increase in the tendency of freezing at the top. An upper limit for the ratio of solutal to thermal Rayleigh numbers in the experimental conditions has been identified for the occurrence of bridging in high Prandtl number fluids.

Simulation for discharging of phase change material within a porous duct utilizing multi layers

Effect of nanoparticles on solidification within a duct with multi air layer was scrutinized in current research. Impose of wavy canal and nanoparticles can augment the solidification rate and these factor were checked in current unsteady modeling. Exergy drop and solid fraction distributions were analyzed. As mass of liquid reduces, exergy drop declines and impose of sinusoidal wall can augment the exergy drop. Cold air make the liquid PCM convert to solid and its temperature augments. With use of sinusoidal wall, better exchange of heat occurs and solidification occurs in lower time. Air temperature reduces as mass of liquid decreases and same behavior was reported for temperature of NEPCM. At t = 1.4hr, Tair of two cases were the same and after this time, temperature of flat plate is greater than another case. After full solidification, temperatures of air for two cases become equal. Solidification time reduces about 26.6% with utilizing wavy surface.

Simulation of spiral tube during melting utilizing multi-type nanoparticles

In current storage unit, spiral tubes were employed which is full of hot hybrid nanomaterial. The hybrid fluid become hot due to existence of sun and to use such heat the pipe was employed in storage unit which is full of RT82. To make it more effective, instead of straight pipe, spiral one was utilized. Two types of configurations were implemented with equal PCM volume. The difference of two cases is position where hybrid fluid exits the system. For validation, LF was evaluated and data were compared with experimental data. Outputs in term of temperature and solid fraction distribution as well as velocity distribution can help us to find which style is more applicable. Using spiral pipe is very common in industry because of lower sedimentation. In taype1, changing time from 10 to 30 min leads to change in solid fraction from 0.638 to 0.094.

A 2D Numerical Simulation of Binary Alloy Solidification: Effect of Mesh Resolution on Formation of Channel Segregates

Mesh refinement is crucial for capturing the complex phenomena that governs the formation of channel segregates during binary alloy solidification. In this article, the influence of mesh size on the formation of channel segregates during the solidification of Sn-5wt%Pb alloy is numerically investigated. A solver is developed in OpenFOAM for solving the coupled transport equations of mass, momentum, energy and species. Subsequently, the simulations are performed for different mesh sizes to predict the flow field, temperature, species and solid fraction distribution including the morphology of channel segregates. From this study, it is observed that the mesh size significantly affects the morphology and the strength of channel segregates. For very fine mesh size, having sufficient number of grid point along their width, the formed channels are more continuous and the flow inside channels is resolved.

A study of solidification on binary eutectic system with moving phase change material

A one-dimensional moving boundary problem describing solidification of a eutectic system under imposed material movement occupying a semi-infinite medium is solved for two different cases of solid fraction distribution within the mushy zone. In the first case it is assumed that the solid fraction distribution has a linear relationship with temperature and in the second case solid fraction distribution is varying linearly with distance within the mushy zone. An exact solution of the problem is obtained with the help of a similarity technique. To demonstrate the current study experimental data of Al-Cu solidification are presented. All the thermal-physical properties of each part are discussed in detail for both models. The temperature profile in each region and moving interfaces are calculated for different Peclet number Pe. In the present study it is shown that the moving interfaces are enhanced, growing relatively faster and assisting in the process of phase-transition when material moves in the direction of freeze but transition is delayed when material moves in the reverse direction. It is also shown that mushy zone becomes thinner when surface temperature is lower than the solidus temperature for different Peclet numbers. In addition, the heat removal Q at the surface ξ=0 is shown with respect to time for different Peclet numbers. To validate our study, we compare our results with a previous published work and they are found to be close.

A simple numerical method to simulate the flow through filter media: Investigation of different fibre allocation algorithms

AbstractFlow patterns and pressure‐drop through three fine‐fibre air filter media were simulated using the lattice Boltzmann method. The geometry for the flow domain was two‐dimensional, with fibres having truncated log‐normal diameter distributions matching SEM photograph measurements on the actual media. The influence of the strategy in positioning the fibres inside the computational domain on the pressure drop of the filter media was investigated. Two different schemes were proposed to position the fibres into a cross section of the filter medium: a random distribution algorithm and the Mitchell's best candidate algorithm. Furthermore, no‐slip and free‐slip boundary conditions were tested for the fluid‐fibre interaction. The comparison between numerical and experimental data shows that the random allocation of fibres better predicted the filter media behaviour. Simulated data suggest that the free‐slip boundary condition must be used when studying the interaction of the fluid with small fibres similar to the size of the fibres used in this study. This study allowed the development of a simple strategy to estimate the pressure drop of a filter medium by having little information of its physical structure, such as solid fraction and diameter distribution.

Heat transfer analysis for the solidification of a binary eutectic system under imposed movement of the material

The current article deals with a moving boundary problem describing solidification of a eutectic alloy in a semi-infinite medium. The process of solidification of a eutectic alloy is considered under imposed movement of material in the mushy zone in place of liquidus zone due to imposing an insulated boundary condition at liquidus front. It is assumed that solid fraction $$f_{\text {s}}$$ has a linear, quadratic and cubic relationship with distance within the mushy zone between the solidus and liquidus. An exact solution of the problem is obtained with the help of similarity transformation. A numerical example of the solidification of Al–Cu alloy is presented to demonstrate the application of the current analysis. Solidification of eutectic system is discussed in the absence of material movement and in the presence of material movement in each case of solid fraction distribution. Thus, the temperature profile and moving interfaces in each region are shown for different Peclet numbers Pe. In addition, heat extraction Q from the surface $$x=0$$ is shown with respect to the time for different Pe. The novelty of the current study is transition process becomes fast when material moves in the direction of freeze and hence time for complete freezing of the alloy reduces. Moreover, mushy zone becomes thinner when material moves in the direction of freeze. A comparative study and error analysis between the present work and Tien and Geiger (ASME J Heat Transf 89:230–233, 1967)[9] in linear case of solid fraction are presented in figure and tables. The application of the present analysis is useful for both eutectic and solid solution alloys.

3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

BackgroundExperimental analyses of the 3D strain field evolution during loading allows for better understanding of deformation and failure mechanisms at the meso- and microscale in different materials. In order to understand the auxetic behaviour and delamination process in paperboard materials during tensile deformation, it is essential to study the out-of-plane component of the strain tensor that is, in contrast to previous 2D studies, only achievable in 3D.ObjectiveThe main objective of this study is to obtain a better understanding of the influence of different out-of-plane structures and in-plane material directions on the deformation and failure mechanisms at the meso- and microscale in paperboard samples.MethodsX-ray tomography imaging during in-situ uniaxial tensile testing and Digital Volume Correlation analysis was performed to investigate the 3D strain field evolution and microscale mechanical behaviour in two different types of commercial paperboards and in two material directions. The evolution of sample properties such as the spatial variation in sample thickness, solid fraction and fibre orientation distribution were also obtained from the images. A comprehensive analysis of the full strain tensor in paperboards is lacking in previous research, and the influence of material directions and out-of-plane structures on 3D strain field patterns as well as the spatial and temporal quantification of the auxetic behaviour in paperboard are novel contributions.ResultsThe results show that volumetric and deviatoric strain, dominated by the out-of-plane normal strain component of the strain tensor, localize in the out-of-plane centre already in the initial linear stress-strain regime. In-plane strain field patterns differ between samples loaded in the Machine Direction (MD) and Cross Direction (CD); in MD, strain localizes in a more well-defined zone close to the notches and the failure occurs abruptly at peak load, resulting in angular fracture paths extending through the stiffer surface planes of the samples. In CD, strain localizes in more horizontal and continuous bands between the notches and at peak load, fractures are not clearly visible at the surfaces of CD-tested samples that appear to fail internally through more well-distributed delamination.ConclusionsIn-plane strain localization preceded a local increase of sample thickness, i.e. the initiation of the delamination process, and at peak load, a dramatic increase in average sample thickening occurred. Different in-plane material directions affected the angles and continuity of the in-plane strain patterns as well as the sample and fracture properties at failure, while the out-of-plane structure affected how the strain fields distributed within the samples.

Numerical investigation on the scale-up rules of a supercritical water fluidized bed reactor using the two-fluid model

The supercritical water fluidized bed reactor (SCWFBR) is a novel hydrogen production technique, so the understanding on its scale-up is limited. In this regard, the trial-and-error procedure is not an option for traditional experimental research because it is costly and high risk. To overcome these problems, numerical simulations were carried out in this study based on the two-fluid model (TFM) to examine the capability of different scale-up rules for the SCWFBR. The numerical model was first validated based on experimental results. Then, four different-sized SCWFBRs were designed, in which numerical simulations for both air–solid and supercritical water (SCW)–solid systems were conducted following different scale-up rules. The distributions of solid volume fraction, solid velocity and pressure in these reactors were fully investigated. Comparisons among the numerical results showed that keeping the Reynolds number, Froude number and dimensional inlet velocity constant is critical for the scale-up of both SCWFBRs and traditional gas–solid fluidized bed reactors (FBRs). Moreover, keeping the particle diameter constant is helpful in obtaining the similarity of the multiphase flow behavior. For the SCWFBR, but not for the traditional gas–solid FBR, a constant density ratio between solid and fluid should be kept during the scale-up. Finally, for the SCW–solid system with more active particle motions, the effect of the interparticle collisions should be considered in the scaling parameters at high Reynolds numbers.