Analytical description of the solid phase particle distribution in a mechanically agitated system

1988 ◽  
Vol 53 (6) ◽  
pp. 1198-1216
Author(s):  
Marie Sýsová ◽  
Ivan Fořt ◽  
Vladimír Kudrna
Keyword(s):  
Mathematical Model ◽  
Diffusion Equation ◽  
Particle Distribution ◽  
Draft Tube ◽  
Solid Phase ◽  
Phase Particle ◽  
Analytical Description ◽  
Random Motion ◽  
Solid Phase Particle ◽  
Calculated Distribution

A mathematical model of the solid particle random motion in a turbulent liquid flow was developed which resulted in an unconventional form of diffusion equation. The diffusion equation derived describes quantitatively the local extremes of the solid phase concentrations in the charge mixed which were verified experimentally. The comparison of the experimental and calculated distribution of local concentrations in the system shows an adequate qualitative agreement. The system consisted of a cylindrical conical-bottomed vessel with baffles and cylindrical draft-tube. A six-blade impeller with inclined (at α = 45° plane blades was used for agitating.

A probability form of the diffusion equation and its use to describe the distribution of the solid phase particle concentrations in a mechanically agitated charge

1986 ◽  
Vol 51 (9) ◽  
pp. 1910-1924 ◽  
Author(s):  
Vladimír Kudrna ◽  
Marie Sýsová ◽  
Ivan Fořt
Keyword(s):  
Markov Process ◽  
Diffusion Equation ◽  
Incompressible Liquid ◽  
Chemical Engineering ◽  
Solid Phase ◽  
Phase Particle ◽  
Local Concentration ◽  
Diffusion Term ◽  
Solid Phase Particle ◽  
Made In

An attempt is made in this paper to describe the solid particle motion in a flowing (agitated) incompressible liquid on the assumption that this motion may be considered as a diffusion Markov process. It is shown that such a procedure leads to a relation which differs from the diffusion equation commonly used in chemical engineering by the form of diffusion term. The expression proposed, unlike the relation usually used, makes it possible to describe the local concentration extremes of solid phase in the charge mixed.

Model of Powder Material Plastic Transformation during Plasma Coating Application

2016 ◽  
Vol 685 ◽  
pp. 685-689 ◽  
Author(s):  
Valery I. Bogdanovich ◽  
Mikhail G. Giorbelidze
Keyword(s):  
Plastic Deformation ◽  
Powder Material ◽  
Solid Phase ◽  
Phase Particle ◽  
Plasma Coating ◽  
Material Particle ◽  
Coating Application ◽  
Solid Phase Particle ◽  
Impact Interaction ◽  
Plastic Transformation

The process of impact interaction of a powder material particle with sprayed-on surface is described. A mathematical simulation is developed for the process of plastic deformation of a solid-phase particle to a disk-shaped cluster. The paper considers the influence of thermal and kinetic factors on the degree of plastic transformation of a particle.

CFD Simulation of Large Dust Collection Cyclones Positioned Vertically in Staggered Downward Cascade Arrangement

2013 ◽  
Author(s):  
Eugen-Dan Cristea ◽  
Pierangelo Conti
Keyword(s):  
Cfd Simulation ◽  
Solid Phase ◽  
Phase Particle ◽  
High Mass ◽  
Cfd Modeling ◽  
Cement Kiln ◽  
Dust Collection ◽  
Dry Process ◽  
Cascade Arrangement ◽  
Simulation Results

Three dimensional, time dependent Euler-Euler simulation approach for numerical calculation of multiphase strongly swirling turbulent gas-heavy laden particulate flow in large industrial collection cyclones, positioned vertically, in staggered downward cascade arrangement has been performed. The multiphase flow was featured high mass loading. This paper specifically addresses a CFD modeling of a “suspension preheater”, typical equipment for dry process cement kiln. Big sized cyclone separator is a key component of this device. The simulation case study was developed in the frame of the commercial general-purpose code ANSYS-Fluent R13. In cyclone separators the swirling gas motion induces a centrifugal force on the solid particulate phase which is the driving force behind the separation process. The turbulence disperses the solid particulates and enhances the probability that particles are discharged, as reject. Both phenomena are related to solid phase particle size distribution (PSD) and flow pattern into the collection cyclones. The multiphase turbulence was modeled using the RSM Mixture Turbulence Model. The simulation results were validated against industrial measurements carried out on an industrial suspension preheater, in the frame of heat and mass balance of cement kiln energy audit. The numerical simulation results were found in reasonable agreement with the collected industrial measurements. This CFD simulation represents a powerful engineering tool on behalf of the cement process engineer either for new cutting-edge design or for performance verification of an existing plant.

scholarly journals Modelling Macrophage Infiltration into Avascular Tumours

2002 ◽  
Vol 4 (1) ◽  
pp. 21-38 ◽  
Author(s):  
C. E. Kelly ◽  
R. D. Leek ◽  
H. M. Byrne ◽  
S. M. Cox ◽  
A. L. Harris ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Spatial Structure ◽  
Random Motion ◽  
Numerical Results ◽  
Macrophage Infiltration ◽  
Numerical Techniques ◽  
Model Predictions ◽  
Independent Experimental Data

In this paper a mathematical model that describes macrophage infiltration into avascular tumours is presented. The qualitative accuracy of the model is assessed by comparing numerical results with independent experimental data that describe the infiltration of macrophages into two types of spheroids: chemoattractant-producing (hepa-1) and chemoattractant-deficient (or C4) spheroids. A combination of analytical and numerical techniques are used to show how the infiltration pattern depends on the motility mechanisms involved (i.e. random motion and chemotaxis) and to explain the observed differences in macrophage infiltration into the hepa-1 and C4 spheroids. Model predictions are generated to show how the spheroid's size and spatial structure and the ability of its constituent cells influence macrophage infiltration. For example, chemoattractant-producing spheroids are shown to recruit larger numbers of macrophages than chemoattractant-deficient spheroids of the same size and spatial structure. The biological implications of these results are also discussed briefly.

scholarly journals Mathematical modeling and algorithm for calculation of thermocatalytic process of producing nanomaterial

2021 ◽  
Vol 23 (3) ◽  
pp. 1590
Author(s):  
Bakhtiyar Ismailov ◽  
Zhanat Umarova ◽  
Khairulla Ismailov ◽  
Aibarsha Dosmakanbetova ◽  
Saule Meldebekova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Phase ◽  
Nonlinear Effects ◽  
Operating Characteristics ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Wide Range ◽  
The Laplace Transform ◽  
Complex Mathematical Model

<p>At present, when constructing a mathematical description of the pyrolysis reactor, partial differential equations for the components of the gas phase and the catalyst phase are used. In the well-known works on modeling pyrolysis, the obtained models are applicable only for a narrow range of changes in the process parameters, the geometric dimensions are considered constant. The article poses the task of creating a complex mathematical model with additional terms, taking into account nonlinear effects, where the geometric dimensions of the apparatus and operating characteristics vary over a wide range. An analytical method has been developed for the implementation of a mathematical model of catalytic pyrolysis of methane for the production of nanomaterials in a continuous mode. The differential equation for gaseous components with initial and boundary conditions of the third type is reduced to a dimensionless form with a small value of the peclet criterion with a form factor. It is shown that the laplace transform method is mainly suitable for this case, which is applicable both for differential equations for solid-phase components and calculation in a periodic mode. The adequacy of the model results with the known experimental data is checked.</p>

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