Mass Transfer Equations Research Articles

Optimization of convective drying performance of multiple porous moist objects in a 3D channel

In this study, a procedure for optimizing the convective drying performance of multi porous moist objects in a three dimensional channel is proposed. The numerical simulation is performed by using the finite element method and COBYLA optimization algorithm is used to find the optimum spacing between the objects without mass transfer in the first stage. Then, heat and mass transfer equations for the porous moist objects are coupled with the channel flow equations at the optimum spacing which delivers the best convective drying performance. It is observed that the flow recirculation and flow reversal in the inter-spacing with various distances between the objects resulted in thermal gradient variations along the multi object surfaces. The average Nusselt number rises for second block while it shows non-monotonic behavior for the first block when the distance between the first and second group objects are varied. Distance between the second and third objects also affected the average Nu variation for all of the objects. The lateral distance between first and second group objects resulted in up to 50% variation in the average Nu for the second block. The optimum spacing between the objects for the maximum Nusselt number of the objects are obtained as d1=5.93hc, d2=7hc and d3=0.584hc. The moisture reduction amounts for each of the object at the optimums spacing are found higher as compared to parametric variation of unsteady simulation results. The computational cost for the parametric unsteady coupled heat and mass transport equations in the channel and in the porous moist objects is 75 h 12 min while the optimization assisted simulation results reduced the computational cost to 2 h 33 minutes. Also, artificial neural networks are utilized to obtain the dynamic feature of convective drying at the optimum spacing considering various values of hot dry air temperature which delivers fast and accurate prediction results when compared to high fidelity computational fluid dynamics simulation results.

Heat transfer under conditions of operation of a gas infrared emitter and an air exchange system

In this work, the processes of heat transfer in a premise heated by a gas infrared emitter (GIE) are studied on the basis of numerical solution of the heat and mass transfer equations in a two-dimensional formulation. Calculations are carried out taking into account the presence of supply and exhaust ventilation in the considered area. Ventilation is required during the operation of high-intensity type GIE. The analysis of the main heat and mass transfer parameters by radiant and convective flows is carried out.

A third-order two-step numerical scheme for heat and mass transfer of chemically reactive radiative MHD power-law fluid

A two-stage third-order numerical scheme is proposed for solving ordinary differential equations. The scheme is explicit and implicit type in two stages. First, the stability region of the scheme is found when it is applied to the linear equation. Further, the stability conditions of the scheme are found using a linearized homogenous set of differential equations. This set of equations is obtained by applying transformations on the governing equations of heat and mass transfer of incompressible, laminar, steady, two-dimensional, and non-Newtonian power-law fluid flows over a stretching sheet with effects of thermal radiations and chemical reaction. The proposed scheme with an iterative method is employed in two different forms called linearized and non-linearized. But it is found that the non-linearized approach performs better than the linearized one when residuals are compared through plots. Additionally, the proposed scheme is compared to the second-order central finite difference method for second-order non-linear differential equations and the Keller-Box/trapezoidal method for a linear differential equation. It is determined that the proposed scheme is more effective and computationally less expensive than the standard/classical finite difference methods. Moreover, the impact of magnetic parameter, radiation parameter, modified Prandtl and Schmidt numbers for power-law fluid, and chemical reaction rate parameter on velocity, temperature, and concentration profiles are displayed through graphs and discussed. The power-law fluid’s heat and mass transfer simulations are also carried out with varying flow behavior index, sheet velocity, and mass diffusivity. We hoped that this effort would serve as a guide for investigators tasked with resolving unresolved issues in the field of enclosures used in industry and engineering.

Strong Acids or Bases Displaced by Weak Acids or Bases in Aerosols: Reactions Driven by the Continuous Partitioning of Volatile Products into the Gas Phase

Aerosols are ubiquitous in the atmosphere and profoundly affect climate systems and human health. To gain more insights on their broad impacts, we need to comprehensively understand the fundamental properties of atmospheric aerosols. Since aerosols are multiphase, a dispersion of condensed matter (solid particles or liquid droplets, hereafter particles) in gas, partitioning of volatile matter between the condensed and the gas phases is one defining characteristic of aerosols. For example, water content partitioning under different relative humidity conditions, known as aerosol hygroscopicity, has been extensively investigated in the past decades. Meanwhile, partitioning of volatile organic or inorganic components, which is referred to as aerosol volatility, remains understudied. Commonly, a bulk solution system is treated as a single phase, with volatility mainly determined by the nature of its components, and the composition partitioning between solution and gas phase is limited. Aerosols, however, comprise an extensive gas phase, and their volatility can also be induced by component reactions. These reactions occurring within aerosols are driven by the formation of volatile products and their continuous partitioning into the gas phase. As a consequence, the overall aerosol systems exhibit prominent volatility. Noteworthily, such volatility induced by reactions is a phenomenon exclusively observed in the multiphase aerosol systems, and it is trivial in bulk solutions due to the limited extent of liquid-gas partitioning. Take the chloride depletion in sea salt particles as an example. Recent findings have revealed that chloride depletion can be caused by reactions between NaCl and weak organic acids, which release HCl into the gas phase. Such a reaction can be described as a strong acid displaced by a weak acid, which is hardly observed in bulk phase. Generally, this unique partitioning behavior of aerosol systems and its potential to alter aerosol composition, size, reactivity, and other physicochemical properties merits more attention by atmospheric community.This Account focuses on the recent advancements in the research of component reactions that induce aerosol volatility. These reactions can be categorized into four types: chloride depletion, nitrate depletion, ammonium depletion, and salt hydrolysis. The depletion of chloride or nitrate can be regarded as a displacement reaction, in which a strong acid is displaced by a weak acid. Such a reaction releases highly volatile HCl or HNO3 into the gas phase and leads to a loss of chloride or nitrate within the particles. Likewise, ammonium depletion is a displacement reaction in which a strong base is displaced by a weak base, resulting in release of ammonia and substantial changes in aerosol hygroscopicity. In addition, aerosol volatility can also be induced by salt hydrolysis in a specific case, which is sustained by the coexistence of proton acceptor and hydroxide ion acceptor within particles. Furthermore, we quantitatively discuss these displacement reactions from both thermodynamic and kinetic perspectives, by using the extended aerosol inorganic model (E-AIM) and Maxwell steady-state diffusive mass transfer equation, respectively. Given the ubiquity of component partitioning in aerosol systems, our discussion may provide a new perspective on the underlying mechanisms of aerosol aging and relevant climate effects.

Influence of permeability on the hydrothermal system at Vulcano Island (Italy): inferences from numerical simulations

Volcano-hydrothermal systems are governed by complex interactions between fluid transport, and geochemical and mechanical processes. Evidence of this close interplay has been testified by distinct spatial and temporal correlations in geochemical and geophysical observations at Vulcano Island (Italy). To understand the interaction between fluid circulation and the geochemical and geophysical manifestations, we perform a parametric study to explore different scenarios by implementing a hydro-geophysical model based on the equations for heat and mass transfer in a porous medium and thermo-poroelastic theory. Numerical simulations allow us to define the controlling role of permeability distribution on the different modeled parameters as well as on the geophysical observables. Changes in the permeability within the highly fractured crater area could be responsible for the fluctuations in gas emission and temperature recorded during the crisis periods, which are accompanied by shallow volcano-seismicity in the absence of significant deformation and gravity variations. Despite the general medium permeability of the volcanic edifice, the presence of more highly permeable pathways, which allow the gas to rapidly escape, as testified by the presence of a well-developed fumarolic field, prevents the pressure buildup at shallow depths.Graphic abstract

Unsteady conjugate model of fluid mechanics and mass transfer for butanol pervaporation process by non-porous membrane

A diffusion-convective mass transfer mathematical conjugated model of butanol recovery from a re-circulating aqueous solution by pervaporation using a polydimethylsiloxane (PDMS) membrane was developed based on computational fluid dynamics. Discretized continuity, linear momentum, and convective-diffusion mass transfer equations were solved by an in-house code based on the finite volume method for a laminar flow with a flat attached non-porous membrane. In addition, a novel numerical procedure to determine the butanol diffusivity in the PDMS membrane was developed based on the solution of the conjugate unsteady convection-diffusion model that included five coupled partial differential equations. The evolution of the distribution of the velocity profile in the fluid flow and the transient variation of butanol concentration in the feed solution and inside the PDMS membrane were determined. Variations in time and space of the dimensionless mass flux along the length of the pervaporation module were calculated from the conjugate convection-diffusion mass transfer model. The numerical predictions of the butanol mass flux in the feed solution exhibited good agreement with the experimental results with an error smaller than 3%. Understanding the mechanisms of mass and fluid transport phenomena by computational modeling can be helpful for improving the design of pervaporation processes.

SIMULATION OF A WATER CURTAIN APPLICATION TO PROTECT WORKERS FROM THERMAL INJURIES

Problem statement. The problem of evaluating the effectiveness of using the water curtain to reduce the risk of thermal injury to people in a fire is considered. The problem is to determine the temperature fields when supplying water for air cooling. The purpose of the article. Development of a numerical model for calculating the process of propagation of water droplets in the air, their evaporation to reduce the temperature of heated air due to fire. Methodology. For mathematical modeling of the process of propagation of water droplets in air, thermal air pollution, the convective-diffusion equation of mass transfer, the energy equation and the equation describing the motion of an ideal liquid (potential flow model) are used. The potential flow model allows you to quickly determine the field of air flow velocity in areas with a complex geometric shape. Implicit difference splitting schemes are used for numerical integration of the convective-diffusion mass transfer equation and the energy equation. Physical splitting of basic equations is used to construct a difference analogue of modeling equations. The Richardson method and the conditional approximation scheme are used to solve the aerodynamics problem of determining the velocity potential field and the components of the air velocity vector. An engineering method for calculating the process of evaporation of a drop of water based on Sreznevsky's law has been developed. Scientific novelty. An effective numerical model has been developed that allows the method of computational experiment to determine the efficiency of using the water curtain to reduce the level of thermal pollution of atmospheric air due to fire. The numerical model is based on the integration of the fundamental equations of aerodynamics, heat and mass transfer. The model takes into account the most significant physical factors that affect the process under study: the movement of heated air, the movement of water droplets in the air, evaporation of the droplet, and so on. Practical significance. Based on the built model, a computer code has been created that allows you to quickly determine the temperature fields in the air when using a water curtain. The numerical model will be useful when conducting computational experiments for the purpose of scientifically sound choice of the location of the water curtain in case of fire. Conclusions. A computer code has been created that allows a computational experiment to investigate the effectiveness of using a water curtain in a fire. The developed computer program can be implemented on low and medium power computers. The results of a computational experiment are presented.

Strip load on transversely isotropic elastic double porosity media with strong permeability contrast

In double porosity media, fluid could flow through the distributed micro-fractures at a larger scale as well as through the nanopores of the organic matrix at a smaller scale, while fluid mass could be transferred between them. Besides, the solid deformation acts as an important coupling term and leads to the two-way coupled process. However, these processes are not well presented in previous studies. In this work, a new coupled modeling approach was proposed for saturated double porosity media with strong permeability con-trast. Specifically, the transversely isotropic equivalent fracture permeability is considered for the preferentially oriented micro-fractures at the micro-scale or meso-scale; while at the nano-scale, the non-Darcy flow and mass transfer equations are employed to consider the interaction between fluid particles and the solid pore wall. Finally, the stabilized finite element method is developed to investigate the settlement and pressure dissipation behaviors of the strip load problem. Cited as: Zhang, Q. Strip load on transversely isotropic elastic double porosity media with strong permeability contrast. Advances in Geo-Energy Research, 2021, 5(4): 353-364, doi: 10.46690/ager.2021.04.02

Physics‐based numerical simulation of heat and moisture transport in red chili subjected to mix‐mode solar drying with phase change energy storage

AbstractIn this study, a coupled heat and mass transfer model was developed using a finite element (FE) simulation approach to describe solar drying of red chili integrated with Na2SO4∙10H2O as phase change material thermal storage. The coupled heat and mass transfer equation solution was achieved by using COMSOL multiphysics with three‐dimensional (3D) axisymmetric geometry mesh generation. The Lagrange triangular FEs of very fine size were employed in obtaining the geometry of the mesh. This study adopts a time‐dependent study that shows the variation of time within 0, 2, 3, 4, and 5 hours, respectively, for continuous drying of red chili in the solar dryer. The effect of air temperature and thermal storage on temperature and moisture distribution on drying of red chili was investigated. The temperature distribution was not uniform and heat transfer at the base was higher than the tip while there is a clear moisture gradient for different drying times, though this moisture moves from the base to the tip and more uniform distribution was obtained after 4 hours of drying. Drying temperature increased from a side to the core of the sample as the drying progresses. Although thermal storage accelerated the drying process, solar radiation showed a greater influence on the drying process. The developed numerical model with the experimental results showed the same trend with the values of MAE and SE for temperature found to be 0.48132 and 0.000842 for the without thermal storage (NTS) sample, 0.2266 and 30.000551 for thermal storage (TS). Also, the values of MAE and SE are 0.0051 and 0.006048 for NTS, 0.00212 and 0.00538 for TS, respectively for moisture profile. The lower values of these errors specify a better prediction capability of the model code.

Numerical modelling of study the effect of the entrainment velocity, the number of Nusselt and the thickness of the non-convective zone on the stability of the pond solar

In this paper, the effect of the entrainment velocity, the Nusselt number, and the thickness of the salinity gradient zone $(NCZ)$ on the stability of the solar pond are studied. The modelling equations of thermal energy and mass transfer in a salt gradient solar pond are discretized by finite difference methods in the transient regime. A new border condition applicable near the equilibrium of interface between the $(NCZ)$ and the $(LCZ)$ region is proposed. We take account of the effects of both turbulent entrainment and diffusion on the growth or erosion of the gradient zone $(NCZ)$. The obtained numerical results show an additional condition of solar pond's stability which links between the salinity gradient $\left( \Delta C\right) \ $ and the temperature gradient $\left( \Delta T\right)$ in the $(NCZ)$ region.

Heat and mass transfer in the grain under variable conditions

The article describes the drying process in the formulation of the internal problem, the main equations of internal heat and mass transfer of potentials are considered. The process of removing moisture from the surface of the grain, which is determined by the transfer of moisture and the diffusion-convective transfer of heat and moisture through the boundary layer, is studied. The movement of heat in the boundary layer was determined by the molecular thermal conductivity. It is established that the speed of the drying process depends on the rate of removal of water vapor from the surface of the grain. It was found that the change in the quality of the seed material did not depend on the absolute removal of moisture. The first drying period is shown, when the temperature of the grain surface rises from the temperature of the adiabatic air saturation, when the drying agent at the boundary of the grain surface is saturated with water vapor, and the drying speed depends on the speed of their removal from the evaporation surface. At this point, the moisture evaporated, the vapors were removed by the drying agent. At the initial moment, the movement of the evaporation line did not occur, but then it was fixed inside the grain. In the course of research, the process of removing moisture from the seeds is fast, but it has little effect on their quality. The removal of grain moisture reached up to 3 % from the upper layers of the seeds, which did not affect their quality. An analytical expression is considered for calculating the heat transfer coefficient and the drying agent velocity, taking into account the allowed moisture content, as well as the heat flux density. The permissible speed of the drying agent in a dense layer of grain is determined, which depends on the height of the layer, the specific surface of the grain, its temperature and the proportion of heat supplied to heat the material. For drying conditions typical for grain dryers, the drying speed should not exceed 0.6 m/s.

Multi-field coupling deformation of rock and multi-scale flow of gas in shale gas extraction

Shale is a kind of multi-scale medium to store shale gas. The analysis of its structural changes during gas extraction is helpful to increase shale gas production. In this study, the shale reservoir is divided into three systems according to the scale: kerogen system, pore system and fracture system. Based on the fractal geometry theory, the fractal permeability models of the pore system and fracture system are established according to the fracture length and pore diameter geometric characteristics. The diffusion model of kerogen system was established according to the nano-pore structure characteristic of kerogen with adsorption and desorption mechanism. A multi-scale fluid-solid coupling model was established by combining the gas mass transfer equation with the matrix deformation equation. The accuracy of the model is verified by the horizontal well gas production data. The results show that:(1) the effective stress causes the evolution of reservoir internal structure and permeability; (2) local mechanical property changes of the reservoir will spread to the entire reservoir; (3) adsorption effect dominates the storage capacity of shale structure. This study provides a new method for revealing the mechanism of gas flow in rock and improving gas extraction rate.

Numerical Simulation of the Water Vapor Separation of a Moisture-Selective Hollow-Fiber Membrane for the Application in Wood Drying Processes.

In this study, a simplified two-dimensional axisymmetric finite element analysis (FEA) model was developed, using COMSOL Multiphysics® software, to simulate the water vapor separation in a moisture-selective hollow-fiber membrane for the application of air dehumidification in wood drying processes. The membrane material was dense polydimethylsiloxane (PDMS). A single hollow fiber membrane was modelled. The mass and momentum transfer equations were simultaneously solved to compute the water vapor concentration profile in the single hollow fiber membrane. A water vapor removal experiment was conducted by using a lab-scale PDMS hollow fiber membrane module operated at constant temperature of 35 °C. Three operation parameters of air flow rate, vacuum pressure, and initial relative humidity (RH) were set at different levels. The final RH of dehydrated air was collected and converted to water vapor concentration to validate simulated results. The simulated results were fairly consistent with the experimental data. Both experimental and simulated results revealed that the water vapor removal efficiency of the membrane system was affected by air velocity and vacuum pressure. A high water vapor removal performance was achieved at a slow air velocity and high vacuum pressure. Subsequently, the correlation of Sherwood (Sh)–Reynolds (Re)–Schmidt (Sc) numbers of the PDMS membrane was established using the validated model, which is applicable at a constant temperature of 35 °C and vacuum pressure of 77.9 kPa. This study delivers an insight into the mass transport in the moisture-selective dense PDMS hollow fiber membrane-based air dehumidification process, with the aims of providing a useful reference to the scale-up design, process optimization and module development using hollow fiber membrane materials.

Computer model of drying behaviour of ceramic green bodies with particular reference to moisture content dependent properties

A numerical model was developed to predict the drying behavior of ceramic green bodies. Resolution of the simultaneous heat and mass transfer equations involved finite elements and the Backward Euler method. Based on experimental data, the model uses equivalent moisture diffusivity, water activity, thermal conductivity and heat capacity as input parameters which depend on moisture content. In particular, the equivalent moisture diffusivity is a key parameter controlling water transport from the body interior to the surface. A simple method was used to estimate the effect of shrinkage on drying rate during the initial drying stage. Predictions of the internal moisture distribution, drying rate and surface temperature as a function of time gave good agreement to experiment for green bodies of alumina paste. External conditions of convection coefficient and relative humidity are shown to sensitively control drying rate and surface temperature evolution during the constant rate period.

Numerical simulation on the terminal rise velocity and mass transfer rate of single sub-millimeter bubbles

Gas–liquid reactors containing bubbles are intensively used in the chemical industry. However, the gas–liquid mass transfer is usually the rate-limiting step. One possible way to intensify the mass transfer is the application of sub-millimeter bubbles (1–1000 μm) which efficiently increase interfacial area. Literature usually focused on bubbles larger than 1000 μm, and it still needs to be studied whether the frequently-used literature equations for terminal rise velocity and mass transfer can accurately predict the behavior of sub-millimeter bubbles. Therefore, the terminal rise velocity and mass transfer rate of single sub-millimeter bubbles were obtained by numerical simulation. It was found that the literature equations could not accurately predict the behavior of sub-millimeter bubbles over the whole size range. New equations were proposed to improve calculation accuracy, with which the terminal rise velocity and mass transfer rate of sub-millimeter bubbles can be accurately predicted.

A Review of Modeling Rotating Packed Beds and Improving Their Parameters: Gas–Liquid Contact

The aim of this review is to investigate a kind of process intensification equipment called a rotating packed bed (RPB), which improves transport via centrifugal force in the gas–liquid field, especially by absorption. Different types of RPB, and their advantages and effects on hydrodynamics, mass transfer, and power consumption under available models, are analyzed. Moreover, different approaches to the modeling of RPB are discussed, their mass transfer characteristics and hydrodynamic features are compared, and all models are reviewed. A dimensional analysis showed that suitable dimensionless numbers could make for a more realistic definition of the system, and could be used for prototype scale-up and benchmarking purposes. Additionally, comparisons of the results demonstrated that Re, Gr, Sc, Fr, We, and shape factors are effective. In addition, a study of mass transfer models revealed that the contact zone was the main area of interest in previous studies, and this zone was not evaluated in the same way as packed beds. Moreover, CFD studies revealed that the realizable k-ε turbulence model and the VOF two-phase model, combined with experimental reaction or mass transfer equations for analyzing hydrodynamic and mass transfer coefficients, could help define an RPB system in a more realistic way.

Gas/liquid mass transfer phenomena in micellar multiphase systems

Micellar multiphase systems are versatile examples for smart solvent systems, which can be applied to intensify important process aspects like reaction rate and product separation. Choosing different temperatures and compositions, the phase behaviour of micellar multiphase systems can be changed, and the reaction conditions altered. Due to the changing phase behaviour, mass transfer is affected, i.e., by altered interfacial areas which can influence the rate of a reaction. Up to two liquid dispersed phases can appear. For fast reactions with a gaseous component, the dispersion conditions and mass transfer are, therefore, complex. In this work, the gas/liquid mass transfer in two and three-phase micellar multiphase systems was observed to gain a better understanding of the transport mechanisms in such systems. The phase behaviour was found to influence the mass transfer strongly. When a microemulsion formed the continuous phase, the mass transfer was enhanced by a factor up to 2.4. Whenever a second liquid phase appeared, the volumetric mass transfer coefficient was decreased. While the mass transfer of the gas to a pure single liquid phase could be predicted by known theory, current mass transfer equations fail to capture the effect in micellar multiphase systems.

SIMULATION OF WASTE WATER TREATMENT BASED ON CFD MODEL: EXPRESS CALCULATION

Purpose. Development of CFD model to evaluate the efficiency of wastewater treatment in a horizontal settler. The CFD model can be used to calculate flow hydrodynamics and mass transfer in settlers with complex geometric shape in the area of wastewater flow. Methodology. For numerical simulation of the process of wastewater movement in a horizontal settler, two mathematical models are used. The first model is based on the motion equations of a viscous incompressible fluid – the Navier-Stokes equations. The Navier-Stokes equations are written in the variables «vorticity - flow function». A two-dimensional mass transfer equation is used to calculate the concentration of a pollutant in a horizontal settler. To numerically integrate the two-dimensional mass transfer equation, a finite-difference splitting scheme is used. The splitting of the modeling equation of mass transfer is carried out so that at each fractional step to determine the unknown value of the pollutant concentration by an explicit formula. For numerical integration of the vortex transfer equation and the equation for the flow function (the Navier-Stokes system of equations), finite-difference splitting schemes are used. Findings. Based on the developed CFD model, a complex of computer programs has been developed, which makes it possible to determine the efficiency of water treatment in a horizontal settler with additional elements. The results of a computational experiment to assess the efficiency of water treatment in a horizontal settler with additional elements in the form of plates are presented. Originality. An efficient CFD model has been created, which allows to quickly evaluate the efficiency of wastewater treatment in a horizontal settler with additional elements. The developed CFD model takes into account the geometric shape of the facility and the most significant physical factors, that influence the efficiency of the waste water treatment in horizontal settler: non-uniform flow velocity, diffusion, different position of inlet and outlet openings. Practical value. The developed CFD model belongs to the class of «diagnostic models» and can be used to assess the efficiency of treatment facilities at the stage of their preliminary design.

COMPUTER SIMULATION OF BIOLOGICAL WASTEWATER TREATMENT PROCESSES IN AEROTANKS WITH PLATES

Purpose. Efficiency determination of the aeration tank at the stage of design or reconstruction of bioreactors in which biological wastewater treatment is carried out requires the use of special mathematical models and calculation methods. The main purpose of the article is to develop CFD models for evaluating the operation efficiency of aeration tanks. Methodology. A numerical model has been developed for the computer calculation of the biological wastewater treatment process in aerotanks, taking into account hydrodynamics. The model is based on two-level mass conservation equations for the substrate and activated sludge and the velocity potential equation. The process of biological transformation of the substrate is calculated based on the Monod model. For the numerical integration of the mass transfer equations of activated sludge and substrate, the alternating-triangular difference splitting scheme is used. In this case, the basic equations are divided into two equations of a more simplified form. For the numerical integration of the equations for the velocity potential, it is split into two one-dimensional equations. Further, each equation is solved according to explicit scheme. For the numerical integration of equations that describe the process of substrate transformation based on the Monod model, the Euler method is used. Findings. The software implementation of the constructed numerical model has been carried out. The results of a computational experiment on the study of the wastewater treatment process in an aeration tank with plates are presented. This leads to the conclusion that the quality control of wastewater treatment in aeration tanks is possible with the help of plates. Originality. A multivariate CFD model has been developed, which makes it possible to quickly assess the efficiency of the aeration tank. A feature of the model is the ability to evaluate the operation of the aeration tank, taking into account its geometric shape and location of additional plates in the construction. Practical value. The constructed numerical model can be used during calculations in the case of designing aeration tanks, or in determining the efficiency of wastewater treatment under new operating conditions.

Stability criteria and convective mass transfer from the falling spherical drops, part I: Bingham plastic fluids

AbstractThis work deals with the flow and mass transfer around a falling spherical drop in Bingham plastic fluids. Bubbles, drops, and particles are often dispersed in a suspending fluid of non‐Newtonian nature. For example, suspensions of particles in a polymer solution are used in hydraulic fracturing slurries and swarms of bubbles are used in airlift bioreactors containing various biomacromolecules, as well as in foam production, degassing, and de‐volatilization of polymer melts. Governing equations for momentum and mass transfer and the Bingham constitutive equation are solved over a wide range of dimensionless groups as Reynolds number, ; Schmidt number, ; Bingham number, ; and viscosity ratio (0.1 and 10). The local underline transport processes are expressed using streamlines, concentration contours, and sheared and un‐sheared regions, whereas the average transport quantities are reported in terms of drag coefficient, critical yield‐stress parameter, and Sherwood number. A co‐existence of sheared and un‐sheared regions occurs within the flow domain due to the fluid‐yield stress. The sheared regions progressively diminish with the increasing value of the Bingham number. On the other hand, inertial effects (increasing ) promotes the expansion of the sheared region in the flow domain. The new modified dimensionless groups are defined by re‐scaling the governing equations based on the effective viscosity of the fluid. Finally, the present numerical values of the drag and average Sherwood number are correlated using the new modified dimensionless numbers.