scholarly journals MATHEMATICAL MODELING OF PROCESSES OF SEPARATION OF COMPONENTS OF GRAIN MATERIAL IN THE COMBINED VIBRATION-AIR SEPARATOR

2020 ◽  
pp. 51-59
Author(s):  
Sergey Stepanenko ◽  
Borys Kotov
Keyword(s):  
Mathematical Modeling ◽  
Equations Of Motion ◽  
Air Flow ◽  
Flow Speed ◽  
Material Point ◽  
Experiment Planning ◽  
Theoretical Studies ◽  
Fluidized Layer ◽  
Aerodynamic Properties ◽  
Air Separator

Development of a mathematical model and calculated analytical dependencies for determining the trajectories and parameters of grain movement in a vibro-fluidized layer of grain material components under the action of a pulsating air flow. They are based on the methods of deterministic mathematical modeling and theoretical mechanics based on the equations of motion of a material point at a variable air flow speed and the action of a pulsating air flow. Theoretical studies were carried out using the methods of mathematical analysis and modeling. The research results were processed using elements of the theory of probability and mathematical statistics using software packages; to determine the rational parameters of the process, the method of statistical experiment planning was used. A mathematical description of the motion of the grain material particles in a combined vibration-air separator under the action of a pulsating air flow of variable speed is given. The trajectories of motion of particles with different sizes are obtained. The obtained equation of motion of a particle under the influence of a pulsating air flow makes it possible to determine the dependence of the speed of movement of the material in a vibro-fluidized layer of grain material on a number of factors: the geometric parameters of the sieve-free sieve, the feed angle of the material, the initial kinematic mode of the material, the index of the kinematic mode of the sieve-free sieve, as well as the coefficient of windage of the grain. On the basis of theoretical studies, the possibility of separating particles of grain material into fractions according to aerodynamic properties with vibropneumatic loading of grain into the channel has been determined. The use of a pulsating air flow as a separating carrier, and taking into account the deflecting forces, made it possible to significantly increase the splitting of the trajectories and the criterion for dividing the grain into fractions.

scholarly journals Analytical studies of the technological parameters of the curved channel of the pneumatic separator

2019 ◽  
pp. 89-100
Author(s):  
S. Stepanenko
Keyword(s):  
Air Flow ◽  
Theoretical Studies ◽  
Technological Parameters ◽  
Material Particle ◽  
Fractionation Process ◽  
Basic Principles ◽  
Aerodynamic Properties ◽  
Air Speed ◽  
Trajectory Stability ◽  
Air Separator

Purpose. Establishment of the laws governing the movement of particles in the air flow with an uneven distribution of flow velocity and the action of additional forces arising from this. Methods. Theoretical studies are based on the basic principles of theoretical mechanics, in particular dynamics, as well as the theory of differential equations of the first and second order Results. A mathematical description is obtained of the movement of particles of the grain mixture in the chamber of a gravity-air separator during the action of air flows of variable speed, as well as the trajectory of particles with different sizes. With certain assumptions, the obtained patterns of change in the velocity of a material particle (point) from coordinates. Conclusions 1.Based on theoretical studies, taking into account deflecting forces, the possibility of separating particles of grain material into fractions by aerodynamic properties in vertical channels and with a lower discharge is determined. 2.The use of air flow as a separating carrier can significantly increase the value of the splitting of the trajectories and the criterion for the separation of grain into fractions. 3.Created simplified mathematical models of the movement of the components of the grain material in air separators with vertical channels, which allow us to determine the rational modes of operation of new technical means. Keywords: air flow, variable air speed, trajectory, stability of forces, fractions, fractionation process, grain mixture, air separator, pneumatic circular flow.

scholarly journals Analysis of the influence of non-uniformity of air flow velocity on the trajectory of grain particles motion in a pneumatic inertial separator

2019 ◽  
pp. 66-77
Author(s):  
B. Kotov ◽  
S. Stepanenko
Keyword(s):  
Flow Velocity ◽  
Air Flow ◽  
Kinetic Equations ◽  
Horizontal Channel ◽  
Uniform Field ◽  
Air Velocity ◽  
Aerodynamic Properties ◽  
Air Flow Velocity ◽  
Separation Of Components ◽  
Air Separator

Purpose. Determination of influence of non-uniform velocity field of air in horizontal channel of pneumatic inertial separator on efficiency of separation of components of grain material into fractions by aerodynamic properties. Methods. The specificity of the issue under consideration determines the analytical method of study based on the compilation and analysis of kinetic equations of motion of a particle, in the form of a ball in the air flow of a horizontal channel with uneven distribution of air flow velocity over the height of the pneumatic channel. Results. The mathematical description of the motion of particles of the grain mixture in the chamber of the gravitational-air separator under the action of air flow of variable speed air is given. The trajectories of motion of particles of different size were obtained. The obtained equation of motion of a particle under the action of air flow allows to determine the dependence of the speed of movement of the material in the layer of grain material on a number of factors: geometric parameters of the separator, the angle of feed of the material, the initial kinematic mode of the material, as well as the coefficient of sail of the particle. The technological possibilities of the proposed method of grain separation under the action of air flow are theoretically substantiated and the influence on the technological parameters of the basic parameters: air velocity, coefficient of live section taking into account the layer thickness of the material entering the channel is established. Conclusions 1.On the basis of the analysis of the force interaction of the grain material particle with the air stream, an advanced mathematical model of particle motion in a non-uniform field of air flow velocity in the horizontal channel was obtained. 2.The real possibility of controlling the process of separation of components of grain material by aerodynamic properties by changing the plot of the air flow velocity along the height of the horizontal channel is determined. Keywords: variable air velocity, trajectory, resistance of forces, fractions, air flow, wind factor, fractionation process, grain mixture, air separator.

Nonlinear Bending-Torsion Flutter of a Cantilever Wing Subjected to Parametric Excitation

2005 ◽  
Author(s):  
R. A. Ibrahim ◽  
S. C. Castravete
Keyword(s):  
Parametric Excitation ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Air Flow ◽  
Parametric Instability ◽  
Flow Speed ◽  
Nonlinear Bending ◽  
Nonlinear Flutter ◽  
Nonlinear Equations Of Motion

This study deals with the nonlinear flutter of a cantilever wing in the absence and presence of parametric excitation that acts in the plane of highest rigidity. The nonlinear equations of motion in the presence of an incompressible fluid flow are derived using Hamilton’s principle. The regions of parametric instability are obtained for different values of flow speed. In the neighborhood of combination parametric resonance, the nonlinear response is determined using the multiple scales method for different values of flow speed. In the absence of parametric excitations, numerical simulation is performed for flow speeds at the critical flutter speed. It is found that the nonlinear flutter of the two modes depends on initial conditions, and exhibits symmetric periodic oscillations. Under parametric excitation and in the absence of air flow, each mode oscillates at its own natural frequency. In the presence of air flow, the two modes possess the same frequency response. Depending on the flow speed the response could be periodic, quasi-periodic, or chaotic.

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

scholarly journals Approbation of the Laser Doppler Anemometer Lad-08 on the Secondary Standard Test Rig for Air Flow Speed

2020 ◽  
Vol 1675 ◽  
pp. 012082
Author(s):  
I K Kabardin ◽  
V G Meledin ◽  
S V Dvoinishnikov ◽  
V A Pavlov ◽  
G V Bakakin ◽  
...  
Keyword(s):  
Air Flow ◽  
Flow Speed ◽  
Standard Test ◽  
Laser Doppler Anemometer ◽  
Laser Doppler ◽  
Secondary Standard ◽  
Test Rig

A Model for Otolith Dynamic Response with a Viscoelastic Gel Layer

1991 ◽  
Vol 1 (2) ◽  
pp. 139-151
Author(s):  
J.W. Grant ◽  
J.R. Cotton
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Equations Of Motion ◽  
Otolith Organs ◽  
Major Contributor ◽  
Viscoelastic Solid ◽  
Gel Layer ◽  
Element System ◽  
Experimental Data Analysis ◽  
Finite Difference Techniques

The otolith organs were modeled mathematically as a 3-element system consisting of a viscous endolymph fluid in contact with a rigid otoconial layer that is attached to the skull by a gel layer. The gel layer was considered to be a viscoelastic solid, and was modeled as a simple Kelvin material. The governing differential equations of motion were derived and nondimensionalized, yielding 3 nondimensional parameters: nondimensional density, nondimensional viscosity, and nondimensional elasticity. The equations were solved using finite difference techniques on a digital computer. By comparing the model’s response with previous experimental research, values for the nondimensional parameters were found. The results indicate that the inclusion of viscous and elastic effects in the gel layer are necessary for the model to produce otoconial layer deflections that are consistent with physiologic displacements. Future experimental data analysis and mathematical modeling effects should include viscoelastic gel layer effects, as this is a major contributor to system damping and response.

scholarly journals Theoretical Studies of a Centrifugal Pneumatic Separator with Horizontal Air Flow

2021 ◽  
Vol 852 (1) ◽  
pp. 012017
Author(s):  
A V Chernyakov ◽  
V S Koval ◽  
M A Begunov ◽  
D N Algazin ◽  
K A Boytsov
Keyword(s):  
Air Flow ◽  
Theoretical Studies

scholarly journals CONSTRUCTION OF EQUATIONS OF MOTION OF MULTIBODY SYSTEMS AND COMPUTER MODELING

2018 ◽  
pp. 74-81
Author(s):  
Darina Hroncová
Keyword(s):  
Mathematical Model ◽  
Computer Modeling ◽  
Computer Model ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Ideal Gas ◽  
Material Point ◽  
Operating Conditions ◽  
Contact Friction ◽  
Knowledge Process

Urgency of the research. Computer models mean new quality in the knowledge process. Using a computer model, the properties of the subject under investigation can be tested under different operating conditions. By experimenting with a com-puter model, we learn about the modelled object. We can test different machine variants without having to produce and edit prototypes. Target setting. The development of computer technology has expanded the possibility of solving mathematical models and allowed to gradually automate the calculation of mathematical model equations. It is necessary to insert appropriate inputs of the mathematical model and monitor and evaluate the output results through the computer output device The target was to describe the mathematical apparatus required for mathematical modeling and subsequently to compile a model for computer modeling. Actual scientific researches and issues analysis. When formulating a mathematical model for a computer, the laws and the theory we use are always valid under more or less idealized conditions, and operate with fictitious concepts such as, material point, ideal gas, intangible spring, and the like. However, with these simplifications, we describe a realistic phenomenon where the initial assumptions are only met to a certain extent. In order for the results not to be different from the modeled reality, it is to be assumed that a good computer model arises gradually, by verifying and modifying it, which is one of the advantages of MSC Adams. Uninvestigated parts of general matters defining. The question of building a real manipulator model. Based on the above simulation, it is possible to build a real model. The research objective. Using MSC Adams to simulate multiple body systems and verify its suitability for simulating ma-nipulator and robot models. In various versions of the assembled model we can monitor its behavior under different operating conditions. The statement of basic materials. In computer simulation, MSC Adams-View is used to simulate mechanical systems. It has an interactive environment for automated dynamic analysis of parameterized mechanical systems with an arbitrary struc-ture of rigid and flexible bodies with geometric or force joints, in which act gravity, inertia, experimentally designed contact, friction, aerodynamic, hydrodynamic or electromechanical forces and have integrated control, hydraulic, pneumatic or elec-tromechanical circuits. Conclusions. Working with a mathematical model on a computer opens space for specific synthesis of empirical and ana-lytical method of scientific knowledge. Working with the computer model carries the characteristic features of classical experi-mentation. It represents a qualitatively new way of solving tasks that can not be experimented with on a real object. The result is the equivalence of the computer model and the object being investigated with the features and expressions chosen as essen-tial, with accuracy sufficient to the exact purpose.

Weyl–Euler–Lagrange equations on twistor space for tangent structure

2016 ◽  
Vol 13 (07) ◽  
pp. 1650095
Author(s):  
Zeki Kasap
Keyword(s):  
Mathematical Modeling ◽  
Dynamical System ◽  
Classical Mechanic ◽  
Twistor Space ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Equation System ◽  
Lagrange Equations ◽  
Four Manifolds ◽  
Riemannian Geometries

Twistor spaces are certain complex three-manifolds, which are associated with special conformal Riemannian geometries on four-manifolds. Also, classical mechanic is one of the major subfields for mechanics of dynamical system. A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space for classical mechanic. Euler–Lagrange equations are an efficient use of classical mechanics to solve problems using mathematical modeling. On the other hand, Weyl submitted a metric with a conformal transformation for unified theory of classical mechanic. This paper aims to introduce Euler–Lagrage partial differential equations (mathematical modeling, the equations of motion according to the time) for the movement of objects on twistor space and also to offer a general solution of differential equation system using the Maple software. Additionally, the implicit solution of the equation will be obtained as a result of a special selection of graphics to be drawn.

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