Леонид Миньков - Academia.edu (original) (raw)
Papers by Леонид Миньков
Computer Research and Modeling, 2012
В данной работе на основе численного моделирования исследуются особенности закрученного турбулент... more В данной работе на основе численного моделирования исследуются особенности закрученного турбулентного течения монодисперсной суспензии в гидроциклоне с инжектором. Для описания турбулентного поля течения суспензии используется модель рейнольдсовых напряжений и модель смеси для описания параметров частиц в двумерном осесимметричном приближении. Особое внимание уделяется выяснению механизмов воздействия вида инжекции на перестройку гидродинамических полей и в конечном итоге на механизмы классификации. Показано, что тангенциальный способ инжекции сильнее влияет на сепарационную кривую по сравнению с радиальным способом.
Journal of Physics: Conference Series, 2019
In the paper we solve the problem of supersonic gas flow in a two-dimensional channel with the mo... more In the paper we solve the problem of supersonic gas flow in a two-dimensional channel with the moving upper wall making oscillations according to the harmonic law. In order to obtain a numerical solution for gas dynamics equations we have implemented two difference schemes: the scheme with the space and time approximation of the first order and the scheme with the space approximation of the second order. The fluxes were computed using Van Leer's method. A special form of fluxes in the gas dynamics equations is given, which enables to calculate fluxes on cell faces of difference mesh using Van Leer's method. Depending on a type of the harmonic law and initial gas inflow conditions, the peculiarities of oblique-shock wave propagation in moving curvilinear domains have been investigated. It has been determined that under a particular oscillation frequency the presence of wall oscillation practically doesn't have an effect on the flow regime inside the domain. The convergence of the obtained solution is shown by calculations using difference grids with different numbers of cells. While comparing the numerical solution obtained due to our program with the one obtained with Ansys Fluent solver we found that the constructed code operates correctly.
Key Engineering Materials, 2016
This paper reports on the ways of allocating the metal particles in the propellant grain of tube ... more This paper reports on the ways of allocating the metal particles in the propellant grain of tube cross-sectional type to provide maximum combustion efficiency of metal. Two-dimensional flow field and the burning rate law govern a transport of the burning metal particles. The analytical correlation for the optimum allocation of metal particles in the case-bounded propellant grain of tube cross-sectional type under the assumption of equilibrium two-phase flow is deduced.
Key Engineering Materials, 2016
Two approaches for simulating the burning surface in gas dynamics by means boundary conditions an... more Two approaches for simulating the burning surface in gas dynamics by means boundary conditions and right sides in the equations involving Dirac delta function are discussed. A comparison of numerical steady-state solutions and the exact ones in one-dimensional approximation is performed for two approaches. It is shown that the numerical solutions obtained with the finite-difference scheme of first order accuracy on the base of two considered approaches converge to each other when the mesh refinement is applied. The numerical solution for the steady state problem coincides with the analytical one, if the pressure at the boundary cell face is set equal to the pressure in the center of the boundary cell.
DESCRIPTION In hydrocyclones, the particle separation efficiency is limited by the suspended fine... more DESCRIPTION In hydrocyclones, the particle separation efficiency is limited by the suspended fine particles, which are discharged with the coarse product in the underflow. It is well known that injecting water in the conical part of the cyclone reduces the fine particle fraction in the underflow. This paper presents a mathematical model that simulates the water injection in the conical part of apparatus. The model accounts for the fluid flow and the particle motion. The model includes: the turbulent particle diffusion and particle settling. Particle interactions, due to hindered settling caused by increased density and viscosity of the suspension, and fine particle entrainment by settling coarse particles are also included in the model. Water injection in the conical part of the hydrocyclone is performed in an experiment to reduce fine particle discharge in the underflow. This added water transports the fine particles of the sediment to the center, where they are directed to the ove...
Biofizika
A model is proposed that describes the growth and destruction of a biofilm due to the consumption... more A model is proposed that describes the growth and destruction of a biofilm due to the consumption of contaminants dissolved in the water being purified. The mathematical solution involves equations describing the balance of biomass, the delivery and uptake of substrate, and the dynamics of biofilm thickness. The effect of erosion on the characteristics of the steady-state regime was shown. The concentrations of the substrate and biomass, the flow of the substrate into the film, and changes in biofilm thickness were calculated.
Minerals Engineering, 2014
This contribution is dedicated to the direct modelling the non-monotonic course of the separation... more This contribution is dedicated to the direct modelling the non-monotonic course of the separation function of a hydrocyclone. To calculate the separation curve it is necessary to know the concentration field of particles of each size fraction in the apparatus. The system of equations describing the steady-state turbulent flow of a polydisperse suspension consisting of a liquid phase (water) and N fractions of the dispersed phase (particles) in the hydrocyclone, in line with the ''mixtures model'' can be written in a form of conservation equations. This system is investigated numerically. The main feature of these calculations is that previously developed model for the settling velocity of a polydisperse suspension in a centrifugal field is used. The results can be summarised as following: The consideration of the interaction of particles in a polydisperse suspension can explain the non-monotonic character of the separation curve (the Fish-Hook-effect) by the deviation of the particles' sedimentation rate from the law of Stokes. The magnitude of the Fish-Hook-effect depends on the concentration of the solid phase.
A simplified model of operation of a flow classification apparatus of finite length for the case ... more A simplified model of operation of a flow classification apparatus of finite length for the case of a low-concentrated suspension has been analyzed. An analytical and numerical analysis of the behavior of the separation function has been made. Particular emphasis has been placed on such characteristics of classification as the size and sharpness of separation. A self-similar solution for the concentration of particles in each phase has been obtained and compared to the numerical solution. Introduction. Classification processes in technology are often based on the action of a force directed transversely to the flow of a suspension which is allowed to pass through the apparatus [1, 2]. The drift of particles which is caused by this force leads to their deposition on the wall. The drift velocity grows with particle size and, consequently, large particles are deposited faster than small ones. Therein, in essence, lies the classification effect. In the absence of accompanying phenomena (unequal inlet conditions for different particles and the complexity of flow including turbulence), the sharpness of separation would be absolute; all particles smaller than a certain critical d j * in size would escape from the apparatus, whereas large ones with d j > d j * would be trapped. Below, we consider a schematic classifier of the type of hydrocyclones [1-4] for which one has currently developed quite reliable calculation methods and for which there are numerous computational formulas of empirical character [2, 4]. The approximate-analytical methods have been summarized in [2, 3, 5] and a numerical analysis of the processes in the apparatus has been performed in [6]. At the same time, a number of important aspects of the classification process have yet to be included into consideration. One can establish their significance by modeling the process in a formulation not involving numerous accompanying details which make the analysis more difficult. One such problem is the significance of the finiteness of the time of residence of particles in the apparatus. In the present work, we analyze the influence of the nonequilibrium of the transport of particles on the characteristics of classification based on the ideas of a diffusion-turbulent model of the process in the apparatus [2, 7, 8]; according to this model, the transfer of particles to the exterior wall due to the centrifugal force is opposed by the diffusion flow caused by the high level of turbulence. It takes a certain time or, in terms of the stationary regime, a certain apparatus length to attain such an equilibrium of forces; clearly, this equilibrium does not have to exist for fairly short apparatuses. A similar formulation of the problem was proposed in [8] and was considered further in [9], but it was not adequately analyzed. A substantially close model was developed in [10]. In this work, the stochastic Kolmogorov-Fokker-Planck equation for the probability density of stay of a particle at a certain point of flow at a certain instant of time was used instead of the introduction of a forward diffusion particle flux. Clearly, it is possible and expedient to pass to the terms of diffusion theory, since this circumvents the difficulties of formulating boundary conditions. Unlike [10], we have abandoned the special properties of a centrifugal classifier, setting (following [8, 9, 11]) all the hydrodynamic velocities inside the apparatus to be coordinate-independent, which gives us an approach to obtaining analytical solutions. Formulation of the Problem. Classification-Apparatus Model. We consider a classification apparatus (Fig. 1) into which a two-phase mixture flows with a constant velocity U on the left (liquid with solid-particle fractions) and
Journal of Engineering Physics and Thermophysics, 2001
Journal of Engineering Physics and Thermophysics, 2002
Journal of Engineering Physics and Thermophysics, 2012
ABSTRACT In the context of the mechanics of interpenetrating continua, numerical modeling of sepa... more ABSTRACT In the context of the mechanics of interpenetrating continua, numerical modeling of separation of a polydisperse suspension in a hydrocyclone is carried out. The so-called "mixture model" valid for a low volume fraction of particles and low Stokes numbers is used for description of the suspension and particle motion. It is shown that account taken of the interaction between large and small particles can explain the nonmonotonic behavior of the separation curve.
Minerals Engineering, 2004
In many cases, finest particles in hydrocyclones present higher separation efficiencies than can ... more In many cases, finest particles in hydrocyclones present higher separation efficiencies than can be expected when considering the theory of single particle sedimentation. The analysis of sedimentation of polydisperse particle systems shows that particle movement is influenced remarkably by solids concentration and particle size distribution. Sedimentation experiments with a special centrifuge confirm the action of combined effects, of particle entrainment, of countercurrent flow of displaced water and of elevated values of pulp density and viscosity due to the disperse solid phase. These influences can be summarized in a sedimentation model which allows better calculation of the separation result of the hydrocyclone. As a consequence, the typical course of the separation curve of the hydrocyclone indicates a more or less marked so-called fish-hook in the fine particle range.
Combustion, Explosion, and Shock Waves, 1998
The basic equations of combustion hydrodynamics are formulated on the basis of notions such as th... more The basic equations of combustion hydrodynamics are formulated on the basis of notions such as the "normal flame velocity" and the "combustion surface." In the general case of turbulent combustion, the combustion surface is represented as a fractal. It is shown that such a representation and the method of constructing the basic equations do not contradict the previous results obtained within the framework of the classical theory of combustion and the statistical theory of turbulence. The slow deflagration-to-detonation transition upon ignition at a closed end of a tube is studied. The results obtained correspond in order of magnitude to experimental data.
Mining of Mineral Deposits, 2021
Purpose. Although the hydrocyclone separator has many advantages, it still has some limitations w... more Purpose. Although the hydrocyclone separator has many advantages, it still has some limitations which decrease its separation efficiency in many mineral processing applications because of fine particles which are miss separated to the coarse product in the underflow. Water injection in the conical part of the cyclone was recently implemented to solve this problem. The water injection mechanism and the way in which the injected water affects the separation are still not clear and need to be more investigated. Methods. New design of water injection hydrocyclone was tried using a modified conical part with a water injection range consist of five equal distance injection openings open directly on the periphery of the cone part. Findings. This study presents a mechanical mathematical model that simulates the water injection to give a clear indication of the injection mechanism impact on the classification process. It could also predict the dependence of the basic characteristics of the c...
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In this paper, a simplified cellular model of particle sedimentation under gravity in bidisperse ... more In this paper, a simplified cellular model of particle sedimentation under gravity in bidisperse suspension is proposed. To determine the average settling velocity of fine particles, their residence time in the cylindrical cell surrounding the large ones is evaluated. The flow field of a viscous incompressible fluid around the large particle is described based on the approximate Oseen solution. The fine particles are assumed to be inertialless, which allows one to determine the trajectory of these particles by solving only kinematic equations. The influence of the Reynolds number and the size of the cylindrical cell on the average velocity of the fine particles is assessed. A formula for determining the sedimentation velocity of fine particles settling in the presence of large ones with allowance for the volume fraction of coarse particles, particle size ratio, and the Reynolds number is derived. It is shown that the increase in the Reynolds number tends to reduce the effect of the ...
Computer Research and Modeling, 2011
The paper is an example of computer simulation in mechanical engineering. Velocity field in a hyd... more The paper is an example of computer simulation in mechanical engineering. Velocity field in a hydrocyclone are determined numerically, because for direct measurements it is difficult to achieve them. The numerical simulation of 3D fluid dynamics based on the k-eps RNG model of turbulence in the hydrocyclone with the injector, containing 5 tangentially directed nozzles is considered. It is shown that the direction of movement of injected fluid in the hydrocyclone depends on the water flow rate through the injector. The calculations show in accordance with the experiments that the dependence of the Split-parameter on the injected water flow rate has a non-monotone character associated with the ratio of power of the main flow and the injected fluid.
Computer Research and Modeling, Mar 1, 2011
The paper is an example of computer simulation in mechanical engineering. Velocity field in a hyd... more The paper is an example of computer simulation in mechanical engineering. Velocity field in a hydrocyclone are determined numerically, because for direct measurements it is difficult to achieve them. The numerical simulation of 3D fluid dynamics based on the k-eps RNG model of turbulence in the hydrocyclone with the injector, containing 5 tangentially directed nozzles is considered. It is shown that the direction of movement of injected fluid in the hydrocyclone depends on the water flow rate through the injector. The calculations show in accordance with the experiments that the dependence of the Split-parameter on the injected water flow rate has a non-monotone character associated with the ratio of power of the main flow and the injected fluid.
The circulation zone formed behind a spherical partide under a flow around it in incompressible f... more The circulation zone formed behind a spherical partide under a flow around it in incompressible fluid is investigated on the base of numerical simulation. The ^rcase in the settling verity of fine partides in joint sedimentation of small and large partides due to the fiction of small partides that are in the hydro-dynamic wake of large ones is estimated.
Computer Research and Modeling, 2012
В данной работе на основе численного моделирования исследуются особенности закрученного турбулент... more В данной работе на основе численного моделирования исследуются особенности закрученного турбулентного течения монодисперсной суспензии в гидроциклоне с инжектором. Для описания турбулентного поля течения суспензии используется модель рейнольдсовых напряжений и модель смеси для описания параметров частиц в двумерном осесимметричном приближении. Особое внимание уделяется выяснению механизмов воздействия вида инжекции на перестройку гидродинамических полей и в конечном итоге на механизмы классификации. Показано, что тангенциальный способ инжекции сильнее влияет на сепарационную кривую по сравнению с радиальным способом.
Journal of Physics: Conference Series, 2019
In the paper we solve the problem of supersonic gas flow in a two-dimensional channel with the mo... more In the paper we solve the problem of supersonic gas flow in a two-dimensional channel with the moving upper wall making oscillations according to the harmonic law. In order to obtain a numerical solution for gas dynamics equations we have implemented two difference schemes: the scheme with the space and time approximation of the first order and the scheme with the space approximation of the second order. The fluxes were computed using Van Leer's method. A special form of fluxes in the gas dynamics equations is given, which enables to calculate fluxes on cell faces of difference mesh using Van Leer's method. Depending on a type of the harmonic law and initial gas inflow conditions, the peculiarities of oblique-shock wave propagation in moving curvilinear domains have been investigated. It has been determined that under a particular oscillation frequency the presence of wall oscillation practically doesn't have an effect on the flow regime inside the domain. The convergence of the obtained solution is shown by calculations using difference grids with different numbers of cells. While comparing the numerical solution obtained due to our program with the one obtained with Ansys Fluent solver we found that the constructed code operates correctly.
Key Engineering Materials, 2016
This paper reports on the ways of allocating the metal particles in the propellant grain of tube ... more This paper reports on the ways of allocating the metal particles in the propellant grain of tube cross-sectional type to provide maximum combustion efficiency of metal. Two-dimensional flow field and the burning rate law govern a transport of the burning metal particles. The analytical correlation for the optimum allocation of metal particles in the case-bounded propellant grain of tube cross-sectional type under the assumption of equilibrium two-phase flow is deduced.
Key Engineering Materials, 2016
Two approaches for simulating the burning surface in gas dynamics by means boundary conditions an... more Two approaches for simulating the burning surface in gas dynamics by means boundary conditions and right sides in the equations involving Dirac delta function are discussed. A comparison of numerical steady-state solutions and the exact ones in one-dimensional approximation is performed for two approaches. It is shown that the numerical solutions obtained with the finite-difference scheme of first order accuracy on the base of two considered approaches converge to each other when the mesh refinement is applied. The numerical solution for the steady state problem coincides with the analytical one, if the pressure at the boundary cell face is set equal to the pressure in the center of the boundary cell.
DESCRIPTION In hydrocyclones, the particle separation efficiency is limited by the suspended fine... more DESCRIPTION In hydrocyclones, the particle separation efficiency is limited by the suspended fine particles, which are discharged with the coarse product in the underflow. It is well known that injecting water in the conical part of the cyclone reduces the fine particle fraction in the underflow. This paper presents a mathematical model that simulates the water injection in the conical part of apparatus. The model accounts for the fluid flow and the particle motion. The model includes: the turbulent particle diffusion and particle settling. Particle interactions, due to hindered settling caused by increased density and viscosity of the suspension, and fine particle entrainment by settling coarse particles are also included in the model. Water injection in the conical part of the hydrocyclone is performed in an experiment to reduce fine particle discharge in the underflow. This added water transports the fine particles of the sediment to the center, where they are directed to the ove...
Biofizika
A model is proposed that describes the growth and destruction of a biofilm due to the consumption... more A model is proposed that describes the growth and destruction of a biofilm due to the consumption of contaminants dissolved in the water being purified. The mathematical solution involves equations describing the balance of biomass, the delivery and uptake of substrate, and the dynamics of biofilm thickness. The effect of erosion on the characteristics of the steady-state regime was shown. The concentrations of the substrate and biomass, the flow of the substrate into the film, and changes in biofilm thickness were calculated.
Minerals Engineering, 2014
This contribution is dedicated to the direct modelling the non-monotonic course of the separation... more This contribution is dedicated to the direct modelling the non-monotonic course of the separation function of a hydrocyclone. To calculate the separation curve it is necessary to know the concentration field of particles of each size fraction in the apparatus. The system of equations describing the steady-state turbulent flow of a polydisperse suspension consisting of a liquid phase (water) and N fractions of the dispersed phase (particles) in the hydrocyclone, in line with the ''mixtures model'' can be written in a form of conservation equations. This system is investigated numerically. The main feature of these calculations is that previously developed model for the settling velocity of a polydisperse suspension in a centrifugal field is used. The results can be summarised as following: The consideration of the interaction of particles in a polydisperse suspension can explain the non-monotonic character of the separation curve (the Fish-Hook-effect) by the deviation of the particles' sedimentation rate from the law of Stokes. The magnitude of the Fish-Hook-effect depends on the concentration of the solid phase.
A simplified model of operation of a flow classification apparatus of finite length for the case ... more A simplified model of operation of a flow classification apparatus of finite length for the case of a low-concentrated suspension has been analyzed. An analytical and numerical analysis of the behavior of the separation function has been made. Particular emphasis has been placed on such characteristics of classification as the size and sharpness of separation. A self-similar solution for the concentration of particles in each phase has been obtained and compared to the numerical solution. Introduction. Classification processes in technology are often based on the action of a force directed transversely to the flow of a suspension which is allowed to pass through the apparatus [1, 2]. The drift of particles which is caused by this force leads to their deposition on the wall. The drift velocity grows with particle size and, consequently, large particles are deposited faster than small ones. Therein, in essence, lies the classification effect. In the absence of accompanying phenomena (unequal inlet conditions for different particles and the complexity of flow including turbulence), the sharpness of separation would be absolute; all particles smaller than a certain critical d j * in size would escape from the apparatus, whereas large ones with d j > d j * would be trapped. Below, we consider a schematic classifier of the type of hydrocyclones [1-4] for which one has currently developed quite reliable calculation methods and for which there are numerous computational formulas of empirical character [2, 4]. The approximate-analytical methods have been summarized in [2, 3, 5] and a numerical analysis of the processes in the apparatus has been performed in [6]. At the same time, a number of important aspects of the classification process have yet to be included into consideration. One can establish their significance by modeling the process in a formulation not involving numerous accompanying details which make the analysis more difficult. One such problem is the significance of the finiteness of the time of residence of particles in the apparatus. In the present work, we analyze the influence of the nonequilibrium of the transport of particles on the characteristics of classification based on the ideas of a diffusion-turbulent model of the process in the apparatus [2, 7, 8]; according to this model, the transfer of particles to the exterior wall due to the centrifugal force is opposed by the diffusion flow caused by the high level of turbulence. It takes a certain time or, in terms of the stationary regime, a certain apparatus length to attain such an equilibrium of forces; clearly, this equilibrium does not have to exist for fairly short apparatuses. A similar formulation of the problem was proposed in [8] and was considered further in [9], but it was not adequately analyzed. A substantially close model was developed in [10]. In this work, the stochastic Kolmogorov-Fokker-Planck equation for the probability density of stay of a particle at a certain point of flow at a certain instant of time was used instead of the introduction of a forward diffusion particle flux. Clearly, it is possible and expedient to pass to the terms of diffusion theory, since this circumvents the difficulties of formulating boundary conditions. Unlike [10], we have abandoned the special properties of a centrifugal classifier, setting (following [8, 9, 11]) all the hydrodynamic velocities inside the apparatus to be coordinate-independent, which gives us an approach to obtaining analytical solutions. Formulation of the Problem. Classification-Apparatus Model. We consider a classification apparatus (Fig. 1) into which a two-phase mixture flows with a constant velocity U on the left (liquid with solid-particle fractions) and
Journal of Engineering Physics and Thermophysics, 2001
Journal of Engineering Physics and Thermophysics, 2002
Journal of Engineering Physics and Thermophysics, 2012
ABSTRACT In the context of the mechanics of interpenetrating continua, numerical modeling of sepa... more ABSTRACT In the context of the mechanics of interpenetrating continua, numerical modeling of separation of a polydisperse suspension in a hydrocyclone is carried out. The so-called "mixture model" valid for a low volume fraction of particles and low Stokes numbers is used for description of the suspension and particle motion. It is shown that account taken of the interaction between large and small particles can explain the nonmonotonic behavior of the separation curve.
Minerals Engineering, 2004
In many cases, finest particles in hydrocyclones present higher separation efficiencies than can ... more In many cases, finest particles in hydrocyclones present higher separation efficiencies than can be expected when considering the theory of single particle sedimentation. The analysis of sedimentation of polydisperse particle systems shows that particle movement is influenced remarkably by solids concentration and particle size distribution. Sedimentation experiments with a special centrifuge confirm the action of combined effects, of particle entrainment, of countercurrent flow of displaced water and of elevated values of pulp density and viscosity due to the disperse solid phase. These influences can be summarized in a sedimentation model which allows better calculation of the separation result of the hydrocyclone. As a consequence, the typical course of the separation curve of the hydrocyclone indicates a more or less marked so-called fish-hook in the fine particle range.
Combustion, Explosion, and Shock Waves, 1998
The basic equations of combustion hydrodynamics are formulated on the basis of notions such as th... more The basic equations of combustion hydrodynamics are formulated on the basis of notions such as the "normal flame velocity" and the "combustion surface." In the general case of turbulent combustion, the combustion surface is represented as a fractal. It is shown that such a representation and the method of constructing the basic equations do not contradict the previous results obtained within the framework of the classical theory of combustion and the statistical theory of turbulence. The slow deflagration-to-detonation transition upon ignition at a closed end of a tube is studied. The results obtained correspond in order of magnitude to experimental data.
Mining of Mineral Deposits, 2021
Purpose. Although the hydrocyclone separator has many advantages, it still has some limitations w... more Purpose. Although the hydrocyclone separator has many advantages, it still has some limitations which decrease its separation efficiency in many mineral processing applications because of fine particles which are miss separated to the coarse product in the underflow. Water injection in the conical part of the cyclone was recently implemented to solve this problem. The water injection mechanism and the way in which the injected water affects the separation are still not clear and need to be more investigated. Methods. New design of water injection hydrocyclone was tried using a modified conical part with a water injection range consist of five equal distance injection openings open directly on the periphery of the cone part. Findings. This study presents a mechanical mathematical model that simulates the water injection to give a clear indication of the injection mechanism impact on the classification process. It could also predict the dependence of the basic characteristics of the c...
[
In this paper, a simplified cellular model of particle sedimentation under gravity in bidisperse ... more In this paper, a simplified cellular model of particle sedimentation under gravity in bidisperse suspension is proposed. To determine the average settling velocity of fine particles, their residence time in the cylindrical cell surrounding the large ones is evaluated. The flow field of a viscous incompressible fluid around the large particle is described based on the approximate Oseen solution. The fine particles are assumed to be inertialless, which allows one to determine the trajectory of these particles by solving only kinematic equations. The influence of the Reynolds number and the size of the cylindrical cell on the average velocity of the fine particles is assessed. A formula for determining the sedimentation velocity of fine particles settling in the presence of large ones with allowance for the volume fraction of coarse particles, particle size ratio, and the Reynolds number is derived. It is shown that the increase in the Reynolds number tends to reduce the effect of the ...
Computer Research and Modeling, 2011
The paper is an example of computer simulation in mechanical engineering. Velocity field in a hyd... more The paper is an example of computer simulation in mechanical engineering. Velocity field in a hydrocyclone are determined numerically, because for direct measurements it is difficult to achieve them. The numerical simulation of 3D fluid dynamics based on the k-eps RNG model of turbulence in the hydrocyclone with the injector, containing 5 tangentially directed nozzles is considered. It is shown that the direction of movement of injected fluid in the hydrocyclone depends on the water flow rate through the injector. The calculations show in accordance with the experiments that the dependence of the Split-parameter on the injected water flow rate has a non-monotone character associated with the ratio of power of the main flow and the injected fluid.
Computer Research and Modeling, Mar 1, 2011
The paper is an example of computer simulation in mechanical engineering. Velocity field in a hyd... more The paper is an example of computer simulation in mechanical engineering. Velocity field in a hydrocyclone are determined numerically, because for direct measurements it is difficult to achieve them. The numerical simulation of 3D fluid dynamics based on the k-eps RNG model of turbulence in the hydrocyclone with the injector, containing 5 tangentially directed nozzles is considered. It is shown that the direction of movement of injected fluid in the hydrocyclone depends on the water flow rate through the injector. The calculations show in accordance with the experiments that the dependence of the Split-parameter on the injected water flow rate has a non-monotone character associated with the ratio of power of the main flow and the injected fluid.
The circulation zone formed behind a spherical partide under a flow around it in incompressible f... more The circulation zone formed behind a spherical partide under a flow around it in incompressible fluid is investigated on the base of numerical simulation. The ^rcase in the settling verity of fine partides in joint sedimentation of small and large partides due to the fiction of small partides that are in the hydro-dynamic wake of large ones is estimated.