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.

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.

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.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Diffusional Change of Solid Particle Size

1996 ◽  
Vol 61 (4) ◽  
pp. 536-563
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal
Keyword(s):  
Particle Size ◽  
Solid Particle ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Granular Systems ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Diffusion Term ◽  
Population Balances ◽  
And Diffusion

To the description of changes of solid particle size in population, the application was proposed of stochastic differential equations and diffusion equations adequate to them making it possible to express the development of these populations in time. Particular relations were derived for some particle size distributions in flow and batch equipments. It was shown that it is expedient to complement the population balances often used for the description of granular systems by a "diffusion" term making it possible to express the effects of random influences in the growth process and/or particle diminution.

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 Solid-Phase Assay for Luteinizing Hormone in Mouse Plasma

1976 ◽  
Vol 29 (2) ◽  
pp. 105 ◽  
Author(s):  
AA Gidley-Baird ◽  
BM Bindon
Keyword(s):  
Luteinizing Hormone ◽  
Sensitivity And Specificity ◽  
Solid Phase ◽  
Cross Reaction ◽  
Assay System ◽  
Mouse Plasma ◽  
Pregnant Mice ◽  
Solid Phase Assay ◽  
Made In ◽  
Pituitary Homogenate

A solid-phase tube assay for measuring LH levels in mouse plasma is described. The assay utilizes an antiserum to ovine LH and ovine LH standards and it measures LH levels in 20 III of plasma with a sensitivity of less than 0�6 ng/m!. Various parameters affecting the sensitivity and specificity of the assay were investigated. Serial dilutions of plasma from pregnant mice, a pituitary homogenate from mice and plasma from hypophysectomized mice, injected subcutaneously with ovine LB, ran parallel with ovine LH standards in plasma from hypophysectomized mice and plasma with low LH levels from intact mice. Ovine TSH showed about 12 % cross reaction in the assay system, whilst rat FSH and prolactin and also ovine FSH, prolactin and GH showed practically no cross reaction. Measurements of plasma LH levels have been made in hypophysectomized mice after injection with different vehicles containing 10 or 50llg LH or 50llg FSH per animal. Daily measurements of LH levels throughout pregnancy in the mouse show a rise in LH level prior to implantation and a further rise around mid-pregnancy which drops off sharply to levels which remain fairly constant until parturition when there is another rise.

Erosion Evaluation of Gas-Turbine Grade CMC’s at Room and Elevated Temperatures

2021 ◽  
Author(s):  
Amirhossein Eftekharian ◽  
Ragav P. Panakarajupally ◽  
Gregory N. Morscher ◽  
Dade Huang ◽  
Frank Abdi ◽  
...  
Keyword(s):  
Erosion Rate ◽  
Elevated Temperatures ◽  
Solid Phase ◽  
Phase Particle ◽  
Crack Density ◽  
Smooth Particle Hydrodynamic ◽  
Ceramic Matrix Composites ◽  
Glass Beads ◽  
Erosion Process ◽  
Fiber Matrix

Abstract The objective of this study is to predict ceramic matrix composites (CMCs) erosion behavior and Retained Strength (RS) under environmental conditions using an Integrated Computational Material Engineering (ICME) physics-based approach. The state-of-the-art erosion analysis using phenomenological algorithms and Finite Element Models (FEM) models follows a test duplication methodology and is not able to capture the physics of erosion. In this effort, two CMC systems are chosen for Erosion evaluation: (a) Oxide/Oxide N720/alumina; and (b) MI SiC/SiC. Experiments are conducted at room and elevated temperatures (RT/ ET). Erosion testing considers: (i) a high velocity oxygen fuel (HVOF) burner rig for ET, and (ii) a pressurized helium impact gun for RT. Erodent particles are chosen as alumina and garnet. Experimental observations show that the type of erodent materials affects CMC erosion degradation at ET. Alumina exhibits to be an effective erodent for maintaining a solid phase particle erosion, while Garnet, experiences some degree of melting. Erosion of the oxide/oxide composite is more severe for the same erodent, temperature, mass, and velocity conditions than the MI SiC/SiC composite for all conditions tested. In general, increasing erosion temperature results in increasing erosion rate for the same erodent mass/velocity condition. In conjunction with experiments, a computational Multi-Scale Progressive Failure Analysis (MS-PFA) is also used to predict erosion of the above-mentioned material systems at RT/ET. The MS-PFA augments FEM by a de-homogenized material modeling that includes micro-crack density, fiber/matrix, interphase, and degrades both fiber and matrix simultaneously during the erosion process. Erodent particles are modeled by Smooth Particle Hydrodynamic (SPH) elements. Erosion evolution in CMCs considering strain rate effect predicts a) spallation, b) mass-loss, and c) damages in fiber, matrix, and their interphase. ICME modeling is capable of predicting the erosion process and reproducing the test observation for the MI SiC/SiC at RT, where: a) erodent particles break up the layer of matrix covering fiber due to interlaminar shear (delamination); b) fiber is fractured because of brittle behavior; c) the process (erosion tunneling) continues till it gets to the next thick matrix layer that slows down the tunneling; and d) Erosion tunnel widens as exposed fiber layers are removed (eroded). Simulations are also performed for erosion of the oxide/oxide due to glass beads at RT and ET. Predictions show that erosion rate is lower at ET because voids in the CMC vanish and the glass beads are less effective at ET. Finally, prediction of retained strength of eroded CMC test specimens is predicted by MS-PFA.

Predictive Erosion Modeling in an ESP Pump

2014 ◽  
Author(s):  
Sahand Pirouzpanah ◽  
Gerald L. Morrison
Keyword(s):  
Solid Phase ◽  
Phase Particle ◽  
Flow Behavior ◽  
Primary Flow ◽  
Ansys Fluent ◽  
Electrical Submersible Pumps ◽  
Computational Fluid Dynamics Cfd ◽  
Operating Lifetime ◽  
Two Stages ◽  
Particle Laden Flow

Electrical Submersible Pumps (ESPs) are widely used in upstream oil production. The presence of a low concentration solid phase, particle-laden flow, in the production fluid may cause severe damage in the internal sections of the pump which reduces its operating lifetime. To better understand the ESP pump’s endurance, an ESP-WJE1000, manufactured by Baker Hughes Company was studied numerically to determine the pump’s flow behavior at its best efficiency point. Computational Fluid Dynamics (CFD) analysis was conducted on two stages of the pump’s primary flow path employing Eulerian-Granular scheme in ANSYS-Fluent. The key parameters affecting the erosion phenomena within the pump such as turbulence kinetic energy, local sand concentration and near wall relative sand velocity were identified. The predictive erosion model applicable to pumps was developed by correlating the erosion key parameters with available experimental results.

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