Solid Velocity Research Articles

A novel mechanistic model for predicting shrinkage kinetics in plant-based foods by integrating solid matrix mobility and viscoelasticity

Deformation during drying is a major physical change influencing drying kinetics and final product quality. Therefore, accurate prediction of shrinkage kinetics is essential for determining the optimal drying conditions for these foods. Shrinkage kinetics is greatly influenced by their structural mobility (rubbery-glassy transition) and viscoelastic properties. The current deformation models lack a comprehensive integration of structural mobility and viscoelasticity concepts, resulting in limitation in attaining insights on physiochemical state variations and viscoelastic stresses developed during drying. In order to overcome this limitation, this study proposes a novel mechanistic shrinkage model that combines solid matrix mobility-based shrinkage velocity and viscoelasticity consideration, incorporating variable mechanical properties to simulate deformation arising from moisture loss and pressure gradient respectively. Comparison between predicted drying kinetics and shrinkage evolution with experimental observation yielded close agreement, achieving low mean absolute error values. As the drying process progressed, a distinct anisotropic shrinkage pattern emerged, which is attributed to varied structural mobility based on temperature and moisture distribution across the food sample. Notably, shrinkage driven by moisture loss significantly outweighed that induced by pressure, exerting a predominant influence on overall volume change. Furthermore, the model demonstrated heightened sensitivity to water transport parameters compared to mechanical factors, which indicates the significance of moisture dynamics in shaping the drying process. Combined consideration of physiochemical changes and viscoelastic concept in the developed deformation model extends new possibility towards optimizing the drying process as well as quality aspect evaluation.

Atmospheric Bubbling Fluidized Bed Risers: Effect of Cone Angle on Fluid Dynamics and Heat Transfer

Abstract In this paper, a comparative study of fluid flow behavior and thermal characteristics of sand particles has been carried out numerically and experimentally in bubbling fluidized beds for five-cone angles of the riser wall having 0 deg, 5 deg, 10 deg, 15 deg, and 20 deg. An Eulerian model with a k–ε turbulence model is used to explore the numerical analysis, and the findings are compared to those of the experiments. For the study, the inlet air velocity is fixed at 1.5 m/s with sand particles filled up to 30 cm to maintain bubbling conditions in the risers. The results indicate that increasing the cone angle up to 10 deg while maintaining the amount of bed materials constant leads to a reduction in pressure drop. The expansion of particles along the riser is observed to decrease with the increase in the cone angle up to 10 deg. The radial solid volume fraction profile transforms to a U shape from the W-type profile as the cone angle increases up to 10 deg. Correspondingly, the solid velocity is found to have an inverted U-type and W-shaped profile for the risers. The granular temperature is also found to increase with a decrease in the solid percentage at any location. The average bed temperature, interphase, and bed-to-wall heat transfer coefficient at a location of 10 cm axial height also increase with the cone angle increase up to 10 deg. As a result, the conical riser, when designed with a greater cone angle up to 10 deg, exhibits more efficiency in terms of heat transfer characteristics. The 3D simulation results are in strong concurrence with the experimental results in all investigations.

A formulation for fluid–structure interaction problems with immersed flexible solids: Application to splitters subjected to flow past cylinders with different cross-sections

In the finite element method framework, a fluid–structure formulation is developed by coupling an Eulerian fixed-mesh fluid approach with a Lagrangian deforming-mesh description for a flexible solid. The coupled formulation is solved using a staggered scheme during time. For the fluid solution stage, the solid walls are considered as a time-variable internal boundary. The velocity and pressure fields are obtained by solving the weak form of the fluid dynamic equations in which the solid velocity is imposed on the internal boundary via a penalization term. For the solid solution stage, the displacement field is obtained by solving the discrete solid dynamic equations which consider traction forces computed by integrating pressures and viscous stresses on the nodes belonging to the solid walls. This novel technique is firstly applied to analyze a flexible splitter under the shedding of a flow past square cylinder due to this problem is considered as a benchmark in the literature. The present solutions agree with those computed using body-fitted techniques, thus validating the proposal. Secondly, flexible splitter motions under the shedding of flow past cylinders with different cross-sections and splitter lengths are comprehensively studied. Overall, the computed results confirmed that the hydrodynamic coefficients on the cylinders were reduced because of the presence of the splitter.

A sub-grid gas–solid interaction model for coarse-grained CFD–DEM simulations

Computational fluid dynamics has been coupled with coarse-grained discrete element method (CFD–CGDEM) to study industrial-scale gas–solid fluidized beds. However, solving the fluid flow at a grid size of several coarse-grained particles (CGPs) cannot accurately predict the gas–solid interaction, and thus reasonable correction model is required. This study develops a sub-grid model to correct the gas–solid interaction and thereby improve the accuracy of coarse-grid CFD–CGDEM simulation. First, the fluid grids with the size of several CGPs are divided into the auxiliary three-dimensional sub-grids. Then, the CGPs are mapped onto the sub-grids by the weight function to reconstruct the local solid velocities and solid fractions of the sub-grids. After that, the simplified mass and momentum conservation equations are solved to resolve the local gas velocities of sub-grids. Finally, the drag on each CGP is corrected based on the local gas-phase hydrodynamics of sub-grids. Results show that the sub-grid model resolving the local gas velocity in all the three directions works better than that just in the main stream direction. The coarse-grid CFD–CGDEM simulations with this sub-grid model agree well with the experiment for the bubbling, turbulent and rapid fluidized beds. Besides, by solving the simplified conservation equations with graphics processing units, the coarse-grid CFD–CGDEM coupled with the sub-grid model achieves 674 times speedup compared to the fine-grid simulation, demonstrating a much more efficient method to study industrial-scale gas–solid fluidized beds.

Solutions to a two-phase mass flow model with generalized drag

Drag plays a dominant role in the interfacial momentum exchange in mixture mass flows. In this study, we examine a general two-phase mass flow model formulated by Pudasaini [1], which incorporates drag. This model describes the mass flow comprising a mixture of solid particles and viscous fluid moving downhill under the influence of gravity. We construct explicit, analytical, and numerical solutions to the model using the Lie symmetry method. These new solutions disclose the role of generalized drag in the dynamics of both solid particles and viscous fluid. The solutions show that solid and fluid phases undergo nonlinear evolution in a coupled manner. Additionally, the solutions demonstrate that increased drag results in a tighter binding between solid and fluid components. We also analyze the role of pressure gradients. The solutions reveal that when solid pressure dominates fluid pressure, solid velocity increases faster than fluid velocity. These findings align with our expectations, emphasizing the importance of analytical solution techniques in understanding the complex process of mixture mass transport in mountain slopes and valleys, thereby enhancing our understanding.

Coupled finite element analysis of the dynamics of poroelastic media considering the relative fluid acceleration

AbstractThis paper mainly discusses the dynamics of poroelastic media using the finite element analysis based on the u‐v‐p full formulation, where , , and p denote the solid displacement, relative fluid velocity with respect to solid velocity, and pore fluid pressure. It incorporates the effect of relative fluid acceleration with respect to solid acceleration on soil dynamic response. The ‐‐p formulation is first verified through the comparison with the analytical solution. After that, the response of one‐dimensional saturated soil column and two‐dimensional partially saturated soil layer subjected to vertical loading with different combinations of soil permeability and loading frequency are investigated using the analyses with the ‐‐p and ‐p formulations, based on which the effect of relative pore fluid motion is discussed and the differences in the soil response between two kinds of analysis approaches are examined. Results reveal that the rapid fluid flow has a pronounced effect on soil dynamics and the soil with a greater degree of saturation is more sensitive to the increase of loading frequency and soil permeability. The soil dynamic response can basically be divided into two main categories that represent insignificant and significant flow motion depending on loading frequency and soil permeability. Furthermore, despite vertical loading, horizontal soil response can also be affected by the large relative pore fluid flow when loading frequency and soil permeability are large. In addition, the simplified formulation can still be applicable to predict dynamics of poroelastic media in cases with high loading frequency and low soil permeability.

A bilateral semi-resolved CFD-DEM approach for cost-effective modelling in a rotary drum

It is of significance to numerically describe particle-flow interphase flow details at a feasible computational cost. Inspired by the semi-resolved Computational Fluid Dynamics-Discrete Element Method (CFD-DEM), an improved bilateral semi-resolved CFD-DEM approach (BSM) approach is developed in this work. Compared with the conventional divided particle volume method (DPVM) and recent semi-resolved CFD-DEM (SM) approach, the BSM approach allows a higher-resolution mesh and achieves higher accuracy as well as applicability when simulating the transient flow with sharp gradients of solid volume fraction and velocity etc. Then the BSM approach is applied to a rotary drum to demonstrate the effectiveness by investigating the internal hydrodynamics details. The typical flow behaviours are detailed; then the effects of the restitution and friction on the internal flow are analysed with details to demonstrate its effectiveness in terms of repose angle, active–passive zone, solid residence time, particle mixing and axial dispersion. The results show a positive correlation of the active depth, mixing degree, and particle dispersion with the friction, while restitution increasing depicts no significant effects on this particulate flow. This work provides an improved numerical tool for understanding the multiphase transient flows involving sharp gradients.

Investigation on gas–liquid–solid three-phase flow model and flow characteristics in mining riser for deep-sea gas hydrate exploitation

In response to the problem of gas–liquid–solid three-phase flow in deep-sea hydrate extraction pipelines, a gas–liquid–solid three-phase flow model considering the dynamic decomposition of hydrates is established using continuity equations, momentum equations, and energy equations. The numerical solution of the theoretical model is achieved using the finite difference method. Comparing the theoretical model with the experimental results, the results showed that the average error of gas holdup, liquid holdup, solid phase content, gas phase velocity, liquid phase velocity, and solid phase velocity obtained from the theory and experiment are 8.24%, 0.41%, 1.88%, 5.80%, 2.81%, and 2.22%, respectively, which verified the correctness of the theoretical model. On this basis, the influences of hydrate abundance, liquid phase displacement, and wellhead backpressure on the gas–liquid–solid three-phase flow characteristics in the pipeline were investigated, and it was found that the gas holdup rate will increase with the increase in hydrate abundance, liquid phase displacement, and wellhead backpressure, with the influence of hydrate abundance being more sensitive. The liquid holdup rate increases with the increase in hydrate abundance and liquid phase displacement, but decreases first and then increases toward the wellhead position with the increase in wellhead backpressure. The solid phase content decreases with the increase in hydrate abundance, and first increases and then decreases toward the wellhead position as the liquid phase displacement and wellhead backpressure increase. The influence of gas phase velocity on the abundance of hydrates is relatively small, but it increases with the increase in liquid phase displacement. When the wellhead backpressure increases, the instantaneous increase then tends to flatten out. The influence of hydrate abundance on the liquid phase velocity is also relatively small, but it increases with the increase in liquid phase displacement and decreases with the increase in wellhead backpressure. The solid phase velocity will increase with the increase in hydrate abundance and liquid phase displacement, but it will not show significant changes with the change of wellhead backpressure. The research results can provide a theoretical basis for the safety of hydrate mining.

Numerical investigation on solids settling in a non-Newtonian slurry inside a horizontal flume

Slurry transportation is always crucial for many industrial processes. This study numerically investigates the settling behavior of multisize solid particles in a non-Newtonian slurry inside a semicircular open channel (flume). The non-Newtonian slurry is modeled using a three-dimensional unsteady Eulerian–Eulerian (E–E) model coupled with the Hershel–Bulkley rheological model. A detailed sensitivity analysis of drag models is performed to establish the solid–fluid interaction in the slurry flow. The numerical model is validated with the experimental data from the literature and shows a fair agreement. The validated model is used to simulate the settling behavior of the slurry in the flume. The mean particle diameter of the solid particles in the slurry is in the range of 75–296 μm with a median diameter of 188 μm. The effect of particle size distributions (PSDs), flume inclination, bubble size, and bubble volume fraction on the particle settling inside the flume is investigated in the parametric study. The analysis of our results revealed that the settling of solids is significantly affected by PSDs in the open channel system. In particular, the increase in flume inclination progresses the settling and dissipation of fine and coarse particles, respectively. Additional simulations showed that the inception of bubbles influences the settling velocity of solids, which changes the settling behavior of multisize solids inside the flume. The presented study can be used as a valuable guideline for the optimization of intermediate exclusion of water from thickened slurry in order to ensure the stability of tailing storage facility.

MFIX–DEM simulation of gas-solid flow dynamics in a dual fluidized bed system

Abstract To overcome the operational difficulties associated with bubbling and circulating fluidized bed gasifiers, a new gasification technology termed dual fluidized bed gasification (DFBG) has evolved. To strengthen the understanding of the gasification and combustion processes in the DFBG system, a thorough analysis of bed hydrodynamics is of paramount importance. Furthermore, the complexity of the hydrodynamics escalates while incorporating diverse fuels like biomass and coal, along with bed materials fluidized in a single reactor due to its nonlinearity and transience. As a result, the study of hydrodynamics in such a system is indispensable. The present study focuses on the discrete element model (DEM) simulation of the bed hydrodynamic behaviour within the gasifier of a DFBG system. The simulation was conducted using Multiphase Flow with Interphase eXchanges (MFiX) software. The influence of superficial velocity on the number of particles in a gasifier was analyzed using the 2-D discrete element model (DEM). In this numerical investigation, transient variation of pressure drop, axial and radial solid volume fraction, and particle velocity was evaluated, and the data were analyzed using the ParaView software. The simulation results of the gasifier indicated an increase in the bed pressure drop with the rise in inlet air velocity. The effective height of solid volume fraction also increased with the surge in superficial velocity. The solid velocity profile and streamlines were also investigated to understand its variation pertaining to the location within the fluidized bed.

MFiX-TFM simulation of hydrodynamics of a dual fluidized bed system

The abundance and replenishable nature of biomass make it a suitable fuel for power generation. Among the various technologies, dual fluidized bed gasification (DFBG) is a suitable technology to generate high-quality syngas from biomass. However, the complexity of hydrodynamics and heat transfer with bed geometry, flow conditions as well as feedstock demands effective research for the design of such system. This study, therefore, focuses on the simulation of hydrodynamics of a dual fluidized bed gasification system. The 2-D two-fluid model (TFM) simulations were performed using Multiphase Flow with Interphase eXchanges (MFiX) software by varying the superficial air velocities for both the gasifier and riser. The influence of superficial air velocity on static pressure, pressure drop, axial and radial voidage, solid velocities, and granular temperature was evaluated. From the simulations, it was observed that with the increase in superficial air velocities, there was an increase in the effective height of pressure drop (66%), voidage, and solid velocities of the gasifier. For the simulation of the riser, similar trends in the profile of hydrodynamic parameters were also observed. The optimum velocity for the gasifier and riser has been suggested to be between 0.15 and 0.35 m/s and 6–7 m/s, respectively.

A machine learning-based simplified collision model for granular flows

This study aims to create an efficient, rapid, and reliable particle collision model utilizing machine learning techniques for granular flow simulations. A simplified surrogate collision model developed in the framework of a Hybrid Euler–Lagrange (HEL) technique was successfully applied to model particle interactions for flows with a low fraction of the granular phase. The precision of the simplified collision model was evaluated using experimental data obtained from the in-house, two-stream particle collision test rig, focusing on solid phase velocity profiles. The implemented model demonstrates strong concordance with the experimental results. The simulations carried out highlight the relation between the simulation time step and the collision rate, which affects the cost of the numerical simulation. The execution time for both the conventional Discrete Element Method (DEM) on a CPU and the streamlined collision HEL model saw a reduction exceeding 70%.

Mitigation of Erosion Wear Produced by Fly-Ash Slurry on 90<sup>0</sup> Elbow by Changing the Cross-Section Shape and Area Ratio

The predominant method of transporting fly ash involves conveying it in slurry form through pipelines within diverse industrial facilities. The key elements of slurry conveyance encompass bends, pumps, and valves. These components of the pipeline endure significant erosion and wear due to the impact of discrete particles. In this investigation, the study assessed the wear induced by slurry erosion in conventional 900 pipe bend and 900 square section elbows of different area ratios using ANSYS Fluent. The discrete phase model was used to estimate the slurry erosion wear for the fly ash-water suspension. From the investigation, the outcomes from the standard k-turbulence model were discovered to be in agreement with the experimental data. This study also looked at a number of other influencing factors, such as the solid concentration and velocity. The analysis reveals that the average erosion wear is lower in the square cross-section elbow compared to the standard elbow. Furthermore, the erosion wear is observed to decrease further with an increase in the cross-sectional area of the square section elbow.

Uncertainty Quantification in Modeling Mold Heat Transfer in Steel Continuous Slab Casting with CON1D

Computational models are powerful tools to quantify physical phenomena to gain valuable insights into a manufacturing process. Their accuracy is hindered, however, by uncertainty in the input data. Furthermore, when calibrating models with plant measurements, it helps to understand which variables have greatest effect on the critical model outputs. This work applies uncertainty quantification and sensitivity analysis to determine the most influential input parameters in the CON1D model of heat transfer and solidification in steel continuous casting with slag. Results show that the slag rim greatly affects heat flux near the meniscus, so control of its size is important. Heat flux and temperature down the mold depend greatly on velocity of the solid slag layer, and slag solidification temperature, which control the slag layer thickness, which in turn affects the interfacial resistance that controls heat transfer in the process. Scale formation on the mold coldface greatly increases mold temperatures. Based on the results presented here, models of heat transfer in continuous casting such as CON1D would benefit from plant measurements such as slag rim size and solid slag velocity, and lab measurements such as slag viscosity at lower temperatures, to better characterize this important slag property.

Prediction of gas–solid erosion wear of bionic surfaces based on machine learning and unimodal intelligent optimization algorithm

Solid particle erosion wear is an inevitable phenomenon in industrial production, with erosion removal mass serving as a crucial metric for assessing the wear rate per unit area on the impacted surface. Developing predictive models to estimate the degree of mass removal is crucial for effectively controlling, evaluating, and preventing severe damage resulting from solid particle erosion wear. In this study, we constructed a comprehensive dataset comprising smooth and bionic surfaces, encompassing inner, outer, and planar surfaces. The dataset was used in a multifactorial erosion experiment, considering adjustable erosion angles, solid particle incident gas velocities, and solid particle diameter sizes. Through visualization and analysis of the obtained dataset, we identified optimal scenarios for bionic surface erosion resistance, offering insights for structural design against bionic erosion resistance. Furthermore, we compared machine learning algorithms to address the prediction problem, resulting in the selection of the best-performing regression algorithm, SVR (Support Vector Regression). Additionally, we compared the performance of other advanced intelligent optimization algorithms using unimodal benchmark functions, finding that HHO (Harris Hawks Optimization) emerged as the optimal choice for unimodal optimization. Building on HHO, we developed the IHHO (Improved Harris Hawks Optimization)-SVR model, using experimental data from erosion tests as the training dataset. This model can predict gas–solid two-phase flow erosion patterns, encompassing various wall types, solid particle sizes, solid incident gas velocities, and impact angles. Due to its robustness and rapid prediction capabilities, the model is expected to serve as a cost-effective tool for predicting erosion removal mass in gas–solid two-phase flow scenarios.

Impact of several coarse-graining models on a pilot-scale fluidized bed behavior using discrete element method–computational fluid dynamics

Impact of several coarse-graining models on a pilot-scale fluidized bed behavior using discrete element method–computational fluid dynamics

Two-Fluid and Discrete Population Balance Model for Simulation of Batch Sedimentation Relevant to Plutonium Reconversion

There are widespread occurrence and application of solid-liquid sedimentation processes among different industries. Therefore, it becomes important to understand the hydrodynamic inside the process equipment and particle agglomeration characteristics. In the present work, solid-liquid sedimentation is analyzed, which will be helpful for the design of continuous process equipment in plutonium (Pu) reconversion. Experiments were carried out in a batch settler to understand solid sedimentation in suspension in terms of varying the overall solid fractions. Euler-Euler two-fluid simulations were performed to investigate the local and overall solid phase volume fraction distributions, position of the active interface (AI) (settling curve), axial solid phase velocity, and pressure distributions during settling, and selected data were compared with the measured data. Further, the discrete population balance model (PBM) with different agglomeration kernels was used with the two-fluid computational fluid dynamics (CFD) model to understand and further improve predictions in terms of the AI position. The variation in number density of the different particles in the settler with time was investigated. The predicted results show that agglomeration is dominant during the sedimentation process and application of the discrete PBM with the CFD model enhances the predictive capability in comparison with the predictions obtained from only the two-fluid model. The results reported using CFD+PBM will aid in the design of continuous process equipment (thickener/precipitator) for Pu reconversion.

Dynamic α-factor models for fine-bubble- and surface aeration – impact of settleability and implications on N2O emission

In water resource recovery facilities (WRRF), aeration efficiency and N2O greenhouse gas emission are affected by the variability of the α-factor. Dynamic calibration of α using sensor data represents a significant knowledge gap this contribution aims to address. To assess factors influencing oxygen and N2O gas mass-transfer, a continuous flow laboratory-scale reactor system was operated to encourage the proliferation of filamentous bacteria. Gas mass-transfer was assessed using fine-bubble and surface aeration. Significant impacts of solid settling velocity on the α-factor – relative to that by MLSS concentration – is obtained. The feasibility of using solid settling velocity and concentration, as α-factor predictors, is tested. The theoretical approach of using relative diffusivity to dissolved oxygen – as an effective predictor of N2O liquid–gas mass-transfer stripping – is experimentally validated, for the first time. Plant-wide WRRF simulations show that surface aeration is inferior to fine-bubble aeration in terms of greenhouse gas emission and treated water quality.

Upscaling mass adsorption and momentum transport in the crown of trees

Airborne chemical species transport and adsorption in the crown of trees are relevant processes with many crucial environmental consequences. This multiphase and multiscale process requires incorporation of momentum transport both in the air and in the solid phases composing the biomass (leaves and branches) and coupling with species mass transport. In this work, an upscaled model for momentum transport and adsorption of chemical species in tree crowns is derived using the method of volume averaging. The model comprises four effective-medium equations, namely: the macroscopic balance equation for momentum transport in the air, which has a Darcy-like structure; the macroscopic equations for total mass and momentum transport, considering the air and deformable leaves and branches; and an unsteady upscaled equation for species mass (diffusive and convective) transport and adsorption at the surface of leaves and branches. These equations are written in terms of effective-medium coefficients that capture the essential microscale information by solving ancillary closure problems in periodic unit cells in the Laplace domain. This allowed evaluating the dynamic functionality of the unsteady adsorption and dispersion coefficients in terms of the Reynolds number, the solid velocity and the adsorption rate. The macroscopic model predictions of the average chemical species concentration were found to be in excellent agreement with direct numerical simulations (i.e., with a relative percent difference smaller than 1%), thus providing a first validation of the upscaled model. Extensions to other systems are briefly discussed.

Enhancing the performance of thermal energy storage by adding nano-particles with paraffin phase change materials

Abstract Phase change materials (PCMs) are now being extensively used in thermal energy storage (TES) applications. Numerous researchers conducted experiments using various circumstances and materials to optimize storage performance. A study was conducted to compare the numerical research of the melting process of paraffin wax using a hybrid nano-integrated paraffin PCM with graphene oxide (GO) and single-walled carbon nanotubes (SWCNTs) in a TES unit. Hence, this research focuses on a sustainable TES system using hybrid nanomaterials (PCM + GO, PCM + SWCNTs, PCM + GO + SWCNT) with varying concentrations of nanoparticles. The objective is to improve the thermal characteristics of PCMs. The main aim of this study is to examine the numerical analysis of the system inside a TES that has a rectangular form. The numerical experiments were conducted using the finite-volume solver Ansys Fluent. The obtained findings show the thermophysical characteristics fluctuations with respect to the solid volume fractions, liquid fraction, temperature, and velocity inside the TES system. Implementing an effective heat transfer mechanism from the point of capture to storage and later consumption necessitates the employment of a heat transfer fluid. The inclusion of SWCNT particles at a concentration of just 10% has been seen to expedite the melting phenomenon. Furthermore, incorporating GO in conjunction with SWCNT alleviates this phenomenon, resulting in a melting behavior that resembles that of unadulterated paraffin. Additionally, the introduction of just 1% GO, combined with SWCNT, leads to a rapid alteration in surface heat transfer coefficient compared to the scenario with single SWCNT and paraffin. These insights hold practical relevance for the development of TES systems in various applications.