A numerical model of gas flow in a direct-flow cyclone of two different configurations is presented. The main task of the simulation was to determine the gas velocity field in the apparatus and analyze the presence of a turbulent wake of the stabilizer swirled, which can have a negative impact on the efficiency of the apparatus. During the study, it was found that when the gas flow is disrupted by the stabilizer of the swirler, a turbulent wake is formed, into which trapped particles can fall. The solution to this problem is to lengthen the stabilizer and increase its diameter. The article also discusses numerical studies of cyclones, devices for purifying gases from dust known in the literature. The review showed the popularity of such topics among scientific teams, which confirms its relevance. Publications include numerical models of vehicles, which are obtained using various turbulence modeling methods. The most significant result of numerical modeling is the gas velocity field, on the basis of which the efficiency of the devices is determined, and their design is optimized and modernized. A brief overview of the most well-known turbulence models is given, and their main advantages and disadvantages are described. It has been shown that the ratio of accuracy and demand for computing resources of RANS models is justified in most cases. Based on a review of models, the choice of a turbulence model for the ongoing numerical study of a new design of a direct-flow cyclone is justified.

A model was proposed for determining the efficiency of fractional separation in a uniflow cyclone. The model includes parameters that characterize the motion of a particle in the cyclone and, hence, the degree of separation, namely, the distance that the particle travels when moving in a helical path, and this path itself. The separation efficiency in a uniflow cyclone of a new design was experimentally studied. The experiments were carried out with quartz flour of four particle size fractions: 15, 20, 30, and 50 μm. The efficiency of the cyclone in the separation of small particles was high for apparatuses of this type. The separation efficiency curves were analyzed.

Numerical solutions of the equations of the flow of a gas–solid suspension in the separation chamber of a uniflow cyclone are found using the FlowVision software. The solutions make it possible to characterize the dependence of the main hydrodynamic characteristics and the concentration profile of solid-phase particles on the geometrical parameters of the separation chamber. It is shown that the main phenomena that have a negative impact on the efficiency of the cyclone are the the circulating gas flows and the turbulent wake downstream of the swirler. The results of the analysis are used to develop recommendations for choosing the geometric parameters of the camera that minimize the influence of these phenomena.

A mathematical model is presented that describes the movement of gas in a direct-flow cyclone. The equations of motion of the gas phase were solved and profiles for the tangential and axial components of gas velocity were derived based on them. The results obtained are compared with the results of numerical simulation. The latter was carried out in the FlowVision software using the SST turbulence model. Via numerical calculations the change in the tangential and axial components of the gas velocity was determined at distances of 110, 150, 200, and 250 mm from the plate turbulator, or cyclone swirler.

A mathematical model is presented that describes the movement of gas in a direct-flow cyclone. The equations of motion of the gas phase were solved and profiles for the tangential and axial components of gas velocity were derived based on them. The results obtained are compared with the results of numerical simulation. The latter was carried out in the FlowVision software using the SST turbulence model. Via numerical calculations the change in the tangential and axial components of the gas velocity was determined at distances of 110, 150, 200, and 250 mm from the plate turbulator, or cyclone swirler.

The applicability of various mathematical models of turbulence for simulation of gas motion in reverse-flow cyclones was evaluated. Out of very numerous turbulence models, only those demonstrating the greatest efficiency in modeling complex flows were selected for the analysis. It is known that, among the models using the Reynolds equations supplemented with parameter equations expressing turbulent viscosity, the standard k –ε model does not provide an accurate description of the gas velocity field in reverse-flow cyclones. For this reason, the suitability of the shear stress transport (SST) turbulence model, as well as of the nonlinear k –ε model, which includes quadratic and cubic terms in the expression for the so-called Reynolds stresses and is advisable for swirling flow simulation, was examined. Also performed were calculations using Smagorinsky model representing a popular choice for large eddy simulations. The results of the calculations were compared with the published experimental data from measuring the gas velocity components inside the cyclone using a laser Doppler anemometer. It was shown that the best results were provided by the Smagorinsky model, which therefore may be usable for modeling gas cleaning processes in cyclones. Modeling will enable eliminating the need to perform time-consuming experiments for optimizing the geometric parameters of cyclones. Moreover, establishing a reliable method for calculating the aerodynamics of a cyclone allows using the calculations for optimizing the operating conditions of a cyclone under specified working parameters.

dispersion of 1 μm -10 μm.To conduct the experiments, the researchers assembled an experimental setup that includes a cyclone, a dispenser, a fan, and a number of auxiliary devices.Aslamova V.S and others [5] developed a direct-low cyclone for use in the production of mineral wool.

We investigated the operation of an axial-flow cyclone as the most promising dust-cleaning equipment based on energy consumption. Numerical solutions were obtained for the gas-solids suspension flow equations in axial flow cyclones with different separation chambers' geometry using FlowVision software. The chamber's geometrical features determined the nature of the gas-solids suspension flow, directly affecting the dusty gases' purification degree. The circulating gas flows and the turbulent "trace" after the swirl generator were found to negatively influence the cyclone efficiency and the hydraulic resistance values. A high chamber height also negatively affected the gas purification since the bulk of dust particles were removed from the gas-solids flow at the initial section. The initial section's length coincided with the gas-solids suspension's jet flow zone due to the flow coming off the swirl vanes' edges. Due to turbulent mixing, the particles' secondary entrainment and return to the gas flow began to manifest outside this zone. Based on this analysis, it is possible to develop recommendations for choosing the chamber's geometric parameters, minimizing the influence of the indicated factors. On the basis of this research, it will be possible to ensure cyclones' high efficiency with significantly lower hydraulic resistance when designing axial-flow cyclones relative to other types of cyclone.

A quantitative description of the evolution of the dispersed composition of the solid phase in technological processes in which the particle size does not remain constant is proposed.Considering the stochastic nature of elementary mass transfer events in individual particles, the methods of the theory of probability are applied.The analysis of the change in the dispersed composition is based on the balance equation for the particle mass distribution function.The equation accounts for all possible physical mechanisms that effect changes in particle size during chemical and technological processes.Examples of solutions to this equation for specific processes of practical importance are given.The solutions obtained are in good agreement with experimental data, which indicates the adequacy of the proposed approach.Its effectiveness has been confirmed during the analysis and calculation of the processes of granulation of various solutions and disposal of oil-containing waste to obtain a granular mineral additive.

A mathematical model of the change in the solid-phase particle size (mass) distribution was developed, according to which the rate of this change in a complex process can be represented as a superposition of the rates of less complex processes, such as coagulation, breakup, abrasion, etc. The proposed approach allows one to determine the particle size (mass) distribution function of the end product of both continuous-flow, and batch processes. Examples of using the proposed approach for solving specific, practically important problems were given, indicating its efficiency.

The features of various types of microstructure of manganese dioxide and the area of its industrial application at present and the prospects for its possible use in the near future were considered. The possible usage of manganese dioxide of active crystalline structure as a sorbent in the purification of exhaust gases from nitrous gases and sulfur dioxide was noted. That usage is of particular importance for solving ecological issues.

This article presents a methodological approach to modeling the processes of changing the dispersed composition of solid phase particles, such as granulation, crystallization, pyrolysis, and others. Granulation is considered as a complex process consisting of simpler (elementary) processes such as continuous particle growth, agglomeration, crushing and abrasion. All these elementary processes, which are also complex in themselves, usually participate in the formation of the dispersed composition of particles and proceed simultaneously with the predominance of one process or another, depending on the method of its organization and the physicochemical properties of substances. A quantitative description of the evolution of the dispersed composition of the solid phase in technological processes in which the particle size does not remain constant is proposed. Considering the stochastic nature of elementary mass transfer events in individual particles, the methods of the theory of probability are applied. The analysis of the change in the dispersed composition is based on the balanced equation of the particle mass distribution function. The equation accounts for all possible physical mechanisms that effect changes in particle size during chemical and technological processes. Examples of solutions to this equation for specific processes of practical importance are provided. The obtained analytical solutions are of independent interest and are in good agreement with the experimental data, which indicates the adequacy of the proposed approach. These solutions can also be used to analyze similar processes. The effectiveness has been confirmed during the analysis and calculation of the processes of granulation of various solutions and disposal of oil-containing waste to obtain a granular mineral additive.

The main sources of emissions of industrial nitrogen oxides have been reviewed. A promising method for the absorption of nitrogen monoxide by a reusable sorbent based on manganese dioxide with the possibility subsequent use of the absorbed products has been suggested.

The article is devoted to the development of a mathematical model for the classification of dispersed materials in a multisection, vertical air classifier. The analysis of the work of the multisection vertical air classifier was carried out using the apparatus of the theory of probability. It is assumed that the probability that a particle from a given section gets into an adjacent, overlying section is the same for all sections. The problem of the sequential motion of a particle from section to section, formulated in this way, exactly corresponds to the Bernoulli scheme of independent tests with two outcomes: a transition to an overlying section and a transition to an underlying section. In this scheme, all probabilities are calculated based on the Bernoulli distribution. This approach made it possible to obtain a calculated ratio for the probability of particles entering the upper product of the classifier, depending on the number of the section into which the source material is fed. This ratio also takes into account the size of the particles, their density and gas velocity. The calculation results are in good agreement with the experimental data on the fractionation of quartz sand particles and manganese dioxide powder in a seven-section apparatus, which confirms the adequacy of the proposed mathematical model. The calculated ratios obtained in the work make it possible to solve the main problem of the classification process, namely, by the known distribution density of the particles of the initial material by size and the given working gas velocity, to determine the dispersed composition of particles at the exit from the classifier. In addition, by selecting the working gas velocity and the place of introduction of dispersed material into the apparatus, it is possible to purposefully control the granulometric composition of the material at the exit from the apparatus.

In this work, gas velocity profiles in the separating chamber of a direct-flow cyclone are obtained, and a method for calculating its efficiency is proposed. The method allows us to trace the influence of the geometric parameters of the chamber, the particle size and the gas flow rate on the degree of its purification. The calculation results are confirmed by numerous experiments

The process of particle attrition in an apparatus with a fluidized bed of material has been investigated. A mathematical model of the process of particle attrition was proposed, which makes it possible to determine the density of the distribution function of particles by weight, as well as the degree of attrition depending on the average residence time in the bed. An experimental study of the particle attrition was carried out on the example of granules of ammonium sulfate in an apparatus with a spouted bed and the adequacy of the proposed model to the actual process was confirmed.

Introduction. Vibration cavitation homogenizers are increasingly used in various industries, including the pharmaceutical industry – for the preparation of creams, gels to give them a homogeneous composition, and more recently for the extraction of valuable substances from plant materials. As we have shown earlier, a comparison of the extraction of dioscin from fenugreek seeds, carried out in devices of various designs, under the same conditions for organizing the process showed that the most effective method was the extraction method in a vibro-cavitation field. Obviously, this is due to the fact that cavitation reduces the diffusion resistance of the process and, thus, increases the intensity of the process of transferring the mass of a substance from the solid phase to the solution. However, the extraction process in apparatus of this type is complex and is accompanied by crushing of seeds, which leads to a change in the dispersed composition of the solid phase.Aim. Conduct a theoretical and experimental analysis of the process of grinding hay fenugreek seeds particles in a vibrocavitation homogenizer, accompanied by the extraction of biologically active substances, as well as obtaining dependences that allow evaluating the contribution of grinding to the formation of the dispersed composition of the meal in this apparatus and determining the average particle size as a result of crushing. In earlier works, using the example of the extraction of dioscin from fenugreek seeds, it was shown that an increase in the rotor speed increases the yield of biologically active substances. However, fine grinding of raw materials often leads to the formation of a sediment layer that pollutes the solution with ballast substances and complicates its purification, and also reduces the yield of biologically active substances, therefore, the study of this process is necessary to control the dispersed composition in order to ensure the highest extraction efficiency in devices of this type.Materials and methods. The first stage of the study was the theoretical analysis of the grinding process, since it is a special case of a large class of processes in which the dispersed composition of the solid phase is not constant. Therefore, in this work, for the mathematical description of particle grinding, a model is used that takes into account the kinetic features of the process under consideration. An experimental study of the extraction of valuable components from plant raw materials was carried out in a laboratory setup with a vibro-cavitation homogenizer of periodic action. As a raw material, we used fenugreek seeds purchased from LLC «Stoing», Moscow (Russia), which we used for research. Commodity analysis showed the compliance of raw materials with the requirements of the GF XIV edition. The initial, aqueous solution of ethanol (volume concentration 60 %) with fenugreek seeds was loaded into glass 6, in a volume of 0.2 liters, then the rotor of the apparatus was brought into rotation and brought to a given rotation frequency. The experiments were carried out at a rotation frequency of 1000, 3000 and 5000 rpm (16.7; 50 and 83.3) 1/s. At each value of the rotor speed, the process time varied in the range from 0 to 50 minutes, and the process was carried out for 60, 120, 180, 240 and 300 seconds. Studies carried out for 5 minutes or more showed that the dispersed composition of the meal practically does not change over time, but significantly depends on the rotor speed. Thus, after 5 minutes, a certain stabilization of the dispersed composition occurs and further residence of the material in the apparatus does not lead to a noticeable change in the dispersed composition. After each experiment, the meal was taken, dried, and sieve analysis of the dispersed composition was carried out.Results and discussion. Based on the results obtained by processing the experimental data according to the equation, the values of the average probability of particle crushing were calculated and, as it turned out, it practically does not depend on time, but depends only on the rotor speed. The dependence of the change in the average probability of particle grinding at different rotor speed was obtained. The analysis of these results showed that the value of the average probability of particle grinding in the cavitation homogenizer increases with an increase in the rotor speed, which is quite expected, since the frequency of contacts of particles with the working organs of the apparatus increases. In addition, the obtained dependence for the average probability of particle crushing is linear. This Expression quite accurately describes the values of the change in time of the relative mass of particles in the working range n = 16.7 – 83.3 1/s. Taking these values into account, the experimental and calculated results are in good agreement.Conclusions. The proposed approach and the results obtained can be used to assess the dispersed composition of particles obtained in other designs of devices of similar action.

Introduction. In recent years, substances extracted from plant materials have been widely used in the pharmaceutical, cosmetic and food industries. Such substances are used as solutions, dry extracts for the manufacture of medicines, dietary supplements, cosmetic creams, food additives in various forms – tablets, capsules, solutions, granular powders. The extraction of valuable substances from plant materials is carried out using the extraction process, which is carried out by various methods and in apparatuses of various designs. Earlier, a comparative study of the extraction of dioscin from fenugreek by various methods was carried out: in devices with a stirrer, in an ultrasonic field, supercritical, fluid CO2 extraction, and in a vibro-cavitation homogenizer. It is shown that the most effective method is the extraction carried out in a vibrocavitation homogenizer.Aim.To analyze the kinetics of the extraction of dioscin from fenugreek seeds, to determine the optimal values of the required degree of grinding of the raw materials, working temperature, the concentration of ethyl alcohol in the solution and the rotational speed of the rotor of the vibrocavitation homogenizer. Determine the effective mass transfer coefficient responsible for the intensity of mass transfer inside the particles.Materials and methods. An experimental study of the extraction of valuable components from plant materials was carried out in a laboratory unit with a vibrocavitation homogenizer of periodic action. As raw materials were used seeds of hay fenugreek, ecotype of Morocco, acquired in the company Fitokasa, Casablanca (Morocco), which we used for research. Commodity analysis showed that raw materials comply with the requirements of the State Pharmacopoeia XIVth edition. As extractants, aqueous solutions of ethanol with an alcohol concentration of 40, 50, 60, 70, 80, and 90 %. The analysis of the kinetics of the process was based on the following ideas. Extraction begins with the surface of the particles of plant material. As the extracted component moves into the volume of the solution, the extractant penetrates into the internal pores of the particles, and the surface on which the extractant and the extracted component interact is gradually shifted into the individual particles. In this case, the resistance to mass transfer in the region between the specified surface and the outer surface of the particle increases over time.Results and discussion. An analysis of the results shows that the rotor speed significantly intensifies the process. In addition, the influence of the rotor speed is most pronounced at the initial stage of the process, when the surface layers of particles of plant material are extracted. It was also found that the resistance to mass transfer inside particles increases significantly as it approaches the final stage of the process, and with an increase in the rotor speed, it increases, especially at the initial stage of the process, which is associated with the intensity of cavitation and the weakening of its effect as the process deepens inward particles.Conclusions. The obtained dependences are necessary to determine the duration of the extraction process in a batch mode, or the average residence time of seeds in the working volume when organizing the process in a continuous mode.