Interphase Momentum Research Articles

Optimisation of a converging-diverging nozzle for the wet-to-dry expansion of the siloxane MM

Wet-to-dry expansion within the nozzle guide vane of an ORC turbine has been proposed as a means to improve the power output of ORC systems for waste-heat recovery (<250 °C). However, given the rapid fluid acceleration in the stator, the phases can develop significant velocity and temperature disparity due to density difference and finite rate of interphase heat transfer. Since these factors can significantly affect the phase-change process, wet-to-dry nozzle design techniques must account for non-equilibrium effects. The first part of this paper aims to further verify a previously developed quasi-1D inviscid non-equilibrium nozzle design tool by comparing it to non-equilibrium CFD simulations, which, unlike the design model, account for lateral flow variations, viscous and turbulence effects, along with secondary momentum forces. Within the CFD model, the interphase mass, momentum, and energy exchange models have been updated using correlations better tailored to evaporating droplet flows and a corrected drag equation. Moreover, the definition of the vapour mass fraction has been modified, while a simplified droplet breakup model has been used to predict the droplet size. The results from the CFD simulations indicate that the outlet vapour mass fraction is approximately 10 to 15% lower than that predicted by the quasi-1D tool. However, the overall flow behaviour and phase-change pattern were in satisfactory agreement, justifying the use of the design tool for 1D optimisation. As such, the quasi-1D tool is coupled to a gradient-based optimiser to optimise the nozzle pressure profile and enhance evaporation of siloxane MM for expansions with an inlet pressure ranging from 450 to 650 kPa, and inlet vapour quality of 0.3. CFD simulations of the optimised geometries indicate an increase of 3.3 to 5.7% in the outlet vapour mass fraction, which was raised from 84.9, 87.7 and 90.5% to 88.2, 93.4 and 95.7% for 450, 550 and 650 kPa inlet pressures respectively. However, a more abrupt expansion in the optimised nozzles resulted in the development of a shock and led to deterioration in nozzle efficiency compared to the baseline nozzles. Finally, a CFD-based shape optimisation was conducted, which demonstrated that it may be difficult to further enhance the vapourisation rate. However, the optimised geometry did mitigate the effect of the oblique shock that appears in the diverging section of the nozzle, raising the expansion efficiency by around 3%.

Modeling two-phase gas-solid flow in axisymmetric diffusers using cut cell technique: an Eulerian-Eulerian approach

Axisymmetric diffusers find wide applications in various industrial processes, including combustion systems, pneumatic conveying, and fluidized bed reactors. Understanding and accurately modeling the behavior of two-phase flows in these devices are critical for optimizing their performance and efficiency. Various aspects of the two-phase gas-solid flow, including particle-particle and particle-wall interactions, interphase momentum transfer, and phase segregation, are investigated. Our currently developed technique, which uses a cut-cell technique, is an established new method to handle the inclined wall of an axisymmetric diffuser. The near-wall cells are treated as five faces for the new grid; one is the inclined wall. This helps treat the boundary condition at the wall in an accurate physical way. The code FORTRAN, developed in-house, was used to solve the axisymmetric diffuser using a cut-cell technique. The results of this study will provide valuable insights into the behavior of gas-solid two-phase flows in axisymmetric diffuser. A parametric study of the impact of particles diameters (100,200,and300μm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$100,\\ 200,\\ \ ext{and} \\ 300\\mu m$\\end{document}), the solid volume loading ratios (0.005,0.008,0.01)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(0.005,\\ 0.008,\\ 0.01)$\\end{document}, and cant angle (4.5∘,7∘,9.5∘)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(4.5^{\\circ},\\ 7^{\\circ},\\ 9.5^{\\circ}) $\\end{document} effect of axisymmetric diffuser on the local skin friction, pressure, velocity, turbulent kinetic energy, and separation zone.

Universal phase-field mixture representation of thermodynamics and shock-wave mechanics in porous soft biologic continua.

A continuum mixture theory is formulated for large deformations, thermal effects, phase interactions, and degradation of soft biologic tissues suitable at high pressures and low to very high strain rates. Tissues consist of one or more solid and fluid phases and can demonstrate nonlinear anisotropic elastic, viscoelastic, thermoelastic, and poroelastic physics. Under extreme deformations or shock loading, tissues may fracture, tear, or rupture. Existing models do not account for all physics simultaneously, and most poromechanics and soft-tissue models assume incompressibility of some or all constituents, generally inappropriate for modeling shock waves or extreme compressions. Motivated by these prior limitations, a thermodynamically consistent formulation that combines a continuum theory of mixtures, compressible nonlinear anisotropic thermoelasticity, viscoelasticity, and phase-field mechanics of fracture is constructed to resolve the pertinent physics. A metric tensor of generalized Finsler space supplies geometric insight on effects of rearrangements of microstructure, for example degradation, growth, and remodeling. Shocks are modeled as singular surfaces. Hugoniot states and shock decay are analyzed: Solutions account for concurrent viscoelasticity, fracture, and interphase momentum and energy exchange not all contained in previous analyses. Suitability of the framework for representing blood, skeletal muscle, and liver is demonstrated by agreement with experimental data and observations across a range of loading rates and pressures. Insight into previously unresolved physics is obtained, for example importance of rate sensitivity of damage and quantification of effects of dissipation from viscoelasticity and phase interactions on shock decay.

Numerical study on Fe3O4 nanoparticle separation from water flow using magnetic field: A 3D simulation

The development of magnetic separation technology using magnetic nanoparticles offers a promising avenue for targeted drug delivery and dealing with the upcoming water crises, environmental pollution and the gradual mineral resource depletion. In this study, a three-dimensional Lagrangian Discrete Phase Model (DPM) is carried out to simulate the performance of Fe3O4 nanoparticles to improve the separation process under the influence of an external magnetic field within a horizontal pipe. The crucial role of the drag force in capture efficiency (CE) prompted its examination, simulating various drag models for groups of particles. The Stokes-Cunningham model, showing a 3.59% average error is a suitable choice compared to experimental results. The research examines the impact of effective parameters, including flow velocity, magnetic field intensity, wire location, particle size and mass flow rate, and pipe diameter on CE and flow pattern. The results show that increasing nanoparticle concentration reshapes the flow pattern due to secondary flows without significantly changing separation efficiency. Moreover, decreasing flow velocity, diminishes drag force and enhances magnetic force impact. Specifically, reducing the velocity to a third increases CE by 37%. Furthermore, capture capacity varies approximately linearly with electric current. Due to the magnetic force’s role as a volumetric force in interphase momentum transfer, the increase in particle size from 200 to 500 nm at 3 × 105 A enhances CE by nearly 50%. However, increasing the pipe diameter diminishes particle capture, attributed to higher Reynolds numbers. According to the results, the impact of increasing magnetic field intensity and particle size on CE improvement is notably more pronounced compared to the effect of flow velocity reduction. A comparative analysis of three injection types reveals that using the group injection type helps to select an appropriate injection location to increase CE and identify the final positions of nanoparticles.

Investigation of geometrical hopper and initial packing state on the inter-phase momentum transfer with granular flow in vertical packed bed

Abstract For the specific application of vertical packed bed design, the main task is to optimize and improve the granular flow pattern, since a worse granular flow pattern is detrimental to the performance of heat transfer and flow in vertical packed bed. To improve the uniformity of granular flow profiles, an application of the discrete element method is used to investigate the granular flow pattern in a vertically packed bed under the condition of different tapered hopper angles and initial packing states. The uniformity of granular dramatically decreases with an increase in the fluctuation of granular velocity distribution. The variation of structural parameters has a positive influence on enhancing the stability of the granular layer. Coefficient of variation and relative fluctuation kinetic energy are introduced as criteria to describe the stability of the granular layer. This study numerically reveals the evolution of initial packing states has a slight influence on improving the stability of granular flow.

Global nonlinear stability of bidispersive porous convection with throughflow and depth-dependent viscosity

The linear instability and the nonlinear stability analyses have been performed to examine the combined impact of a uniform vertical throughflow and a depth-dependent viscosity on bidispersive porous convection using the Darcy theory with a single temperature field. The validity of the principle of exchange of stability is proved. The eigenvalue problems resulting from both linear instability and nonlinear stability analyses with variable coefficients are numerically solved using the Chebyshev pseudo-spectral method. The equivalence of linear instability and nonlinear stability boundaries is established in the absence of throughflow, while in its presence, the subcritical instability is shown to be evident. The stability of the system is independent of the direction of throughflow in the case of constant viscosity, whereas upflow is found to be more stabilizing than downflow when the viscosity is varying with depth. While the viscosity parameter offers a destabilizing influence on the onset of convection in the absence of throughflow, it imparts both stabilizing and destabilizing effects on the same in its presence. The influence of the ratio of permeabilities and the interphase momentum transfer parameter is to make the system more stable. The findings of a mono-disperse porous medium are presented as a specific case within the broader context of this investigation.

Numerical Two-Phase Simulations of Alkaline Water Electrolyzers

Alkaline water electrolyzers (AWE) have several advantages over other types of electrolyzers, including their high efficiency and especially their relatively low cost due to the usage of non-precious metal catalysts, such as nickel and iron, for the electrodes. Information about local quantities and physical phenomena such as the formation of gas bubbles, current densities, temperatures or local species concentrations within a running cell are important for their improvement. Multiphysical computational fluid dynamics (CFD) simulations of electrochemical components using detailed three-dimensional models can provide valuable insight on local behaviors and characteristics that are difficult or impossible to measure experimentally.This work extends the CFD library openFuelCell2 1, which has been implemented using the open-source platform OpenFOAM®, to simulate AWE cells. The model considers the major transport phenomena, including two-phase fluid flow, heat and mass transfer, electrochemical reactions, species transfer and charge transfer in the various functional regions of the cell. It employs an Eulerian-Eulerian approach to characterize the behavior of each phase comprising interphase mass transport, momentum exchange and heat transfer. Appropriate mapping functions are used to couple the physically distinct regions together. A Butler-Volmer equation characterizes the electrochemical reactions that are assumed to occur in electrodes of finite thickness.This model is used to simulate a single zero-gap AWE cell, depicted in Fig. 1, for different operating conditions such as varying temperatures and volumetric flow rates. The conducted studies provide insight into the local formation of the created gas phase (bubbles), the distribution of species within the gas and electrolyte and their impact towards the performance of the running cell. These numerically obtained results are compared to in-house available and gathered experimental data. Figure 1 demonstrates that the polarization curves obtained at various temperatures are in good agreement with the experimental data. Figure 1

A novel relaxation drift model for simulating liquid-vapor momentum non-equilibrium in two-phase ejectors

A novel relaxation drift model (RDM) was proposed to simulate the interphase momentum non-equilibrium (slip) inside two-phase work-recovery CO2 ejectors. The RDM was validated using the experimental data of 5 different ejectors under 15 trans-critical conditions in total. The proposed model was compared with the existing homogeneous model (HM) and algebraic slip model (ASM) through case studies. The effects of ejector mixer design and nozzle expansion state were also disclosed. The results showed that the prediction errors of ejector performance by the RDM were within 17 %, which was smaller than the maximum error of 23 % predicted by the HM and the ASM. The numerical results demonstrated that the liquid droplets had lower velocities than the vapor when the liquid-vapor mixture accelerated, but the droplets travelled faster than the vapor during deceleration of the mixture. It was also revealed that the velocity slip would affect the shock pattern at the diffuser inlet if the mixer was choked. The effects of slip, however, became insignificant when the mixer was designed too large. In addition, the RDM might overestimate the ejector performance if the motive nozzle was strongly under-expanded. This study facilitates understanding of interphase velocity slip in two-phase CO2 ejector flow.

Euler-Euler LES of bubble column bubbly flows by considering sub-grid scale turbulent dispersion effect on modulating bubble transport

It has now been recognised and generally accepted that turbulent dispersion may be modelled using the time average of the fluctuating part of the interphase momentum, employing the drag the Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows. As the turbulent eddies in the surrounding of bubbles interact strongly with the bubbles in bubbly flow, the bubble trajectories and bubble oscillation take place accordingly as the consequence of continuous deformation of the bubble surfaces. When using large eddy simulation for modelling bubbly flow, the sub-grid scale (SGS) filtered velocity fluctuations of liquid phase can be interpreted as many small eddies that may act on the surface of bubbles, consequently giving rise to bubble shape variations and the dispersion of bubbles. This study employs Euler/Euler large-eddy simulation (LES) modelling to demonstrate that the turbulent dispersion force model can be used to effectively indicate the influence of turbulent eddies on bubble dynamics, in particular the bubble cluster oscillations, which leads to remarkable improvements in the prediction of bubble lateral dispersion behaviour. The use of spatial filtering to model the SGS bubble dispersion is proposed with a modification on SGS eddy viscosity to reflect turbulent dispersion due to bubble induced turbulence. The results of the time-averaged LES modelled bubble velocities and bubble volume fraction profiles are in good agreement with the experimental data while the turbulent kinetic energy spectrum obtained at different locations on the centreline of the bubble column still exhibits the conventional −5/3 scaling for shear induced turbulence and a −3 scaling for bubble induced turbulence.

Effect of Stokes number and particle-to-fluid density ratio on turbulence modification in channel flows

Two-way momentum-coupled direct numerical simulations of a particle-laden turbulent channel flow are addressed to investigate the effect of the particle Stokes number and of the particle-to-fluid density ratio on the turbulence modification. The exact regularised point-particle method is used to model the interphase momentum exchange in presence of solid boundaries, allowing the exploration of an extensive region of the parameter space. Results show that the particles increase the friction drag in the parameter space region considered, namely the Stokes number $St_+ \in [2,80]$ , and the particle-to-fluid density ratio $\rho _p/\rho _f \in [90,5760]$ at a fixed mass loading $\phi =0.4$ . It is noteworthy that the highest drag occurs for small Stokes number particles. A measurable drag increase occurs for all particle-to-fluid density ratios, the effect being reduced significantly only at the highest value of $\rho _p/\rho _f$ . The modified stress budget and turbulent kinetic energy equation provide the rationale behind the observed behaviour. The particles’ extra stress causes an additional momentum flux towards the wall that modifies the structure of the buffer and of the viscous sublayer where the streamwise and wall-normal velocity fluctuations are increased. Indeed, in the viscous sublayer, additional turbulent kinetic energy is produced by the particles’ back-reaction, resulting in a strong augmentation of the spatial energy flux towards the wall where the energy is ultimately dissipated. This behaviour explains the increase of friction drag in particle-laden wall-bounded flows.

Iterative screening methodology for optimal modeling of bubble coalescence/breakup and interphase force in CMFD simulation of flow boiling

The Euler–Euler two fluid approach has been widely adopted in computational multi-fluid dynamic (CMFD) simulation of nucleate boiling flow. Accurate prediction of bubble size and interphase forces are desired to properly model interphase momentum transfer in the CMFD simulation. Bubble dynamics, including nucleation, coalescence/breakup and condensation, should be modeled to calculate bubble size variation. In the meantime, modeling of interphase forces is crucial to predict distribution of void fraction. Numerous closure models have been developed for bubble dynamics and interphase forces. Diverse model combinations were reported depending on the specific application. As a step forward to converge the diversity, efforts are dedicated to establish a methodology to iteratively screen the closure models for nucleate flow boiling at elevated pressures based on the DEBORA experiment. In the proposed methodology, the closure models for each physics are first evaluated and sorted based on the predicted value in fixed-point analysis and its effect on CMFD results observed in separate-effect analysis. The second part of the methodology is iterative screening. To achieve accurate bubble size prediction, the optimal coalescence model is identified for each breakup model. With the optimal coalescence counterpart, the optimal breakup model is then identified. For the interphase force models, the optimal lift force model is first determined based on the CMFD simulation with the same drag force model and without wall lubrication force model. The optimal wall lubrication force and drag force model are selected in sequence. Utilized one single case of DEBORA experiments, the optimal set of the coalescence/breakup models, i.e., Prince et al.’s and Luo et al.’s models, and the interphase models, i.e., Tomiyama et al.’s models for drag and lift force, Lubchenko et al.’s model for wall lubrication force and Burns et al.’s model for turbulence dispersion force has been selected. Validation of the model combination based on more DEBORA experiment datasets and Bartolomei et al.’s experiment shows promising prediction accuracy.

CFD investigation on the effect of ring-type internals on oxy-fuel combustion in pilot-scale circulating fluidized bed

The effect of internals in the riser of circulating fluidized bed on the oxy-fuel combustion is in lack. Consequently, the multiphase particle-in-cell (MP-PIC) method, which belongs to the Eulerian-Lagrangian framework, is used to investigate the influence of ring-type internals on the particle-scale characteristics, including particle velocity, temperature, heat transfer coefficient (HTC), slip velocity, and Reynolds number. The results show that the incorporation of ring-type internals significantly affects the distribution and motion of gas and particles. Increasing the internal number or reducing the aperture ratio slightly improve the sand temperature in the riser by facilitating improved interphase momentum exchange and heat transfer. Increasing internal number from two to six improves the sand temperature and HTC in the riser of about 13 K and 61 W/m2·K. While increasing the aperture ratio from 0.7 to 0.9 decreases the sand temperature of about 17 K. The incorporation of internals within the riser also induces fluctuations in particle variables nearby. The horizontal feeder of coal leads to asymmetrical distribution of local particle HTC. Sand and coal particles exhibit similar distributions in key parameters such as size, temperature, HTC and Reynolds number. The consistent trend in Reynolds number and HTC between sand and coal particles can be attributed to the primary factors influencing these parameters, such as interphase momentum exchange and heat transfer.

Direct numerical simulations of polypropylene gasification in supercritical water

In order to reduce environmental pollution by plastic wastes, supercritical water gasification (SCWG) appears as a promising technology. The present study investigates the SCWG process of polypropylene (PP) plastic waste using particle-resolved direct numerical simulations (PR-DNS). A directional ghost-cell immersed boundary method has been used to solve the reacting boundary condition, including detailed molecular diffusion models. To validate the procedure, SCWG of a coal particle has been first investigated as a benchmark, analyzing in detail interphase momentum and heat and mass transfer, and chemical reactions are analyzed. Surface reactions and the resulting Stefan flow expand the boundary layer around the particle, impacting the efficiency of heat and mass transfer. Adding then a suitable reaction mechanism, SCWG of PP plastic wastes leading to combustible gases is analyzed by PR-DNS and found to be very efficient. The gasification temperature is an important parameter to control SCWG efficiency. To the authors' knowledge, this is the first PR-DNS study investigating the SCWG process for plastic wastes, and it provides interesting information regarding transfer processes and their limitations.

MFIX-Exa: CFD-DEM simulations of thermodynamics and chemical reactions in multiphase flows

MFIX-Exa is a CFD-DEM code for the numerical solution of chemically reacting multiphase flows (fluid and solids phases), specifically targeted for flows in complex reactor geometries. The fluid is modeled using a low Mach number formulation with a multicomponent ideal gas equation of state, which is imposed as a constraint of the velocity field. The fluid equations are discretized using an embedded boundary (EB) aware Godunov scheme with an approximate projection. The particles (that constitute the solids phase) are represented by a soft-sphere spring-dashpot model and evolved using a forward Euler method with subcycling. The fluid and particles models are coupled through a volume fraction field in addition to interphase mass, momentum, and energy transfer. The mathematical model and numerical approach are benchmarked against three different verification tests and validated with two separate tests. Also, a scaling analysis is provided. This manuscript represents the current state-of-the-art of MFIX-Exa and describes the major extensions to the previous work presented in Musser et al. (2021), including the Godunov time integration algorithm for the fluid phase and the inclusion of thermodynamics and chemistry modeling to both the fluid and solids phases.

Study of biomass gasification in an industrial-scale dual circulating fluidized bed (DCFB) using the Eulerian-Lagrangian method

Dual circulating fluidized bed (DCFB) has emerged as an efficient reactor for biomass gasification due to its unique feature of high gas-solid contact efficiency and separated reactions in two reactors, yet the understanding of complex in-furnace phenomena is still lacking. In this study, biomass gasification in an industrial-scale DCFB system was numerically studied using a multiphase particle-in-cell (MP-PIC) method featuring thermochemical sub-models (e.g., heat transfer, heterogeneous reactions, and homogeneous reactions) under the Eulerian-Lagrangian framework. After model validation, the hydrodynamics and thermochemical characteristics (i.e., pressure, temperature, and species) in the DCFB are comprehensively investigated. The results show that size-/density-induced segregation makes solid fuels concentrate on the bed surface. Interphase momentum exchange leads to the continuous decrease of the gas pressure axially. In the gasifier and combustor, the lower heating value (LHV) of the gas products is 5.56 MJ/Nm3 and 0.2 MJ/Nm3 and the combustible gas concentration (CGC) is 65.5% and 1.86%, respectively. The temperature in the combustor is about 100 K higher than that in the gasifier. A higher solid concentration results in a smaller value of particle heat transfer coefficient (HTC). The HTCs range from 50 to 150 W/(m2 K) for a solid concentration larger than 0.3 in the combustor while the HTCs range from 100 to 200 W/(m2 K) in the gasifier. The Reynolds number of biomass particles is two orders of magnitude larger than that of the sand particle. The numerical results shed light on the reactor design and process optimization of biomass gasification in DCFBs.

Two-particle method for liquid–solid two-phase mixed flow

Liquid–solid two-phase flows are a very important class of multiphase flow problems widely existing in industry and nature. This paper establishes a two-phase model for liquid–solid two-phase flows considering multiphase states of granular media. The volume fraction is defined by the solid phase, determining the material properties of the two phases, and momentum is exchanged between the phases by drag and pressure gradient forces. On this basis, a two-particle method for simulating the liquid–solid two-phase flow is proposed by coupling smoothed particle hydrodynamics with smoothed discrete particle hydrodynamics. The coupling framework for the two-particle method is constructed, and the coupling between the algorithms is realized through interphase momentum exchange, volume fraction constraint, and field variable sharing. The liquid phase density changes are divided into two types. One is caused by weak compressibility, and the other is caused by changes in the solid phase volume fraction. The former is used to calculate the liquid-phase flow field, and the latter is used to calculate the two-phase coupling to solve the problem of sudden bulk density changes in the liquid phase caused by changes in particle volume fractions. The two-particle method maintains the dual advantages of the particle method for free interface tracking and material point tracking for particles. The new method is validated using a series of fundamental test cases, and comparison with experimental results shows that the new method is suitable for resolving liquid–solid two-phase flow problems and has significant practical value for future simulations of mudflow motions, coastal breakwaters, and landslide surges.

Interface-resolved direct numerical simulations of interphase momentum, heat, and mass transfer in supercritical water gasification of coal

Interactions between a reacting particle and the surrounding fluid are complex due to the interplay between flow dynamics, heat and mass transfer, and chemical reactions. In the present work, particle–fluid transport processes in supercritical water gasification of coal are studied using high-fidelity interface-resolved direct numerical simulations. The impact of different factors on the particle–fluid interactions are evaluated by performing simulations of the flow around two-dimensional particles considering different numerical configurations. The outgoing Stefan flow from the particle surface is found to cause expanded boundary layers for velocity, heat, and species. The temperature-induced changes in transport properties around a heated particle lead to a higher drag force and decreased heat/mass transport; those differences are further enlarged when taking into account the volumetric expansion of the fluid. Transport limitation for coal gasification in a realistic configuration is finally investigated. Temperature-induced fluid dilatation is then the major factor affecting drag force and heat transfer around the reacting particle, and mass transport is significantly impacted by species production or consumption in the boundary layer. Reaction heat release and variations in fluid composition within the thermal boundary layer lead to a slight enhancement of heat transfer. This work reveals and quantifies the main mechanisms affecting the exchanges between a reacting coal particle and surrounding supercritical water regarding both thermal and chemical aspects. It also provides high-fidelity data to later fit the reduced models needed for simulations of large-scale supercritical water gasification installations.

An improved direct-forcing immersed boundary method for simulations of flow and heat transfer in particle-laden flows

In studies of particle-laden flow, the direct-forcing immersed boundary (IB) method is commonly utilized to fully resolve the flow around the particles. With the use of interpolation functions, the effective diameter of a particle is typically larger than the actual diameter, resulting in an erroneous flow field, an overestimated drag force, and an inaccurately estimated interphase heat transfer rate when the grid resolution is insufficient. Relatively high grid resolutions (typically dp/h > 20) are required to ensure accurate estimations of the momentum and heat transfer between fluid and particles, leading to high computational cost when simulating cases with numerous particles. To address these issues, we propose an improved direct-forcing IB method involving retraction of the Lagrangian points, which considers the interphase momentum and heat transfer simultaneously. The method establishes two sets of Lagrangian points for computing the drag force and heat transfer rate, respectively. Based on the optimal retraction distance of the two sets of Lagrangian points, two retraction functions of the Reynolds number and grid resolution are formulated. Using the developed retraction functions, we simulate the DKT process, non-isothermal flow past three in-line spheres, and gravitational settling of a sphere with variable temperature to validate the improved IB method. It is found that the drag force and Nusselt number can be accurately reproduced using the improved IB method with a relatively small grid resolution (dp/h = 10).

Euler/Euler large eddy simulation of bubbly flow in bubble columns under CO2 chemisorption conditions

It has been generally recognised that the turbulent dispersion force plays an important role in interphase momentum transfer. However, the effect of the added mass stress on the momentum and mass transfer in bubble column bubbly flow has not been addressed appropriately. As the turbulent eddies in the surroundings of bubbles interact strongly with the rising bubbles in bubble column bubbly flow, such interactions will bring out the change of interfacial areas between the bubbles and carrier fluid, consequently leading to changes in the interfacial mass transfer. When employing large eddy simulation for modelling bubbly flow coupled with the chemisorption process, the SGS filtered velocity fluctuations of liquid phase can be interpreted as the turbulent eddies that continuously hit the surfaces of bubbles, causing bubble deformation and the variation of bubble interfacial areas, which give rise to the turbulent dispersion and added mass stress forces. The present study will demonstrate through Euler/Euler large-eddy simulations (LES) modelling that by considering the turbulent dispersion force (SGS-TDF) and added mass stress (SGS-AMS), the bubble dynamics and mass transfer under the chemisorption conditions can be better indicated, which leads to remarkable improvements in the prediction of bubble lateral dispersion and the interfacial mass transfer. The turbulent dispersion and added mass stress related to the spatially filtering were proposed with a modification on SGS eddy viscosity to reflect turbulent dispersion due to bubble-induced turbulence. A comprehensive assessment of the effects of these additional filtered stress terms on the time-averaged velocity and bubble volume fraction profiles, flow patterns, mass transfer and the pH variation during CO2 chemisorption and the turbulent kinetic energy and species concentration spectra was conducted.

Linear and Non-Linear Stability Analysis for Thermal Convection in A Bidispersive Porous Medium with Thermal Non-Equilibrium Effects

The linear instability and nonlinear stability analyses are performed for the model of bidispersive local thermal non-equilibrium flow. The effect of local thermal non-equilibrium on the onset of convection in a bidispersive porous medium of Darcy type is investigated. The temperatures in the macropores and micropores are allowed to be different. The effects of various interaction parameters on the stability of the system are discussed. In particular, the effects of the porosity modified conductivity ratio parameters, and , with the inter-phase momentum transfer parameters and, on the onset of thermal Convection are also considered. Furthermore, the nonlinear stability boundary is found to be below the linear instability threshold. The numerical results are presented for free-free boundary conditions.