scholarly journals Computing Concentration Distribution of Lump Additives in Argon-stirred Melt

2021 ◽  
pp. 440-445
Author(s):  
Kyrylo S. Krasnikov
Keyword(s):  
Mathematical Model ◽  
Numerical Experiment ◽  
Concentration Distribution ◽  
Total Mass ◽  
Three Dimensional ◽  
Average Diameter ◽  
Navier Stokes ◽  
Horizontal Position ◽  
Lagrange Equations ◽  
Temperature Exchange

To modify easily chemical consistence of molten steel metallurgical plants usually add alloys in a form of lumps through a hopper at ladle`s top. The problem is a large variety of adjusted technological conditions for this process, which leads to iterative discovery of rational ones. The article presents synthesis of a mathematical model for the mentioned process using Navier-Stokes and Euler-Lagrange equations. It is designed for researching of process modes depending on: a horizontal position of addition hopper relatively to argon plug at ladle bottom, an average diameter of spherical addition lumps, a total mass of addition heap, a necessity of the second hopper, a temperature of the melt. It takes into account interconnected three-dimensional fluid and solids dynamics, temperature exchange between melt and lump, also it computes level of concentration homogenization. A numerical experiment shows a significantly better addition homogenization when two hoppers are simultaneously used for a feeding. Adequacy checks are performed using ice balls in air-stirred water.

The eruptive regime of mass-transfer-driven Rayleigh–Marangoni convection

2016 ◽  
Vol 791 ◽  
Author(s):  
Thomas Köllner ◽  
Karin Schwarzenberger ◽  
Kerstin Eckert ◽  
Thomas Boeck
Keyword(s):  
Concentration Distribution ◽  
Marangoni Convection ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Navier Stokes ◽  
Flow Structures ◽  
Rayleigh Convection ◽  
Marangoni Effects ◽  
Validation Experiments

The transfer of an alcohol, 2-propanol, from an aqueous to an organic phase causes convection due to density differences (Rayleigh convection) and interfacial tension gradients (Marangoni convection). The coupling of the two types of convection leads to short-lived flow structures called eruptions, which were reported in several previous experimental studies. To unravel the mechanism underlying these patterns, three-dimensional direct numerical simulations and corresponding validation experiments were carried out and compared with each other. In the simulations, the Navier–Stokes–Boussinesq equations were solved with a plane interface that couples the two layers including solutal Marangoni effects. Our simulations show excellent agreement with the experimentally observed patterns. On this basis, the origin of the eruptions is explained by a two-step process in which Rayleigh convection continuously produces a concentration distribution that triggers an opposing Marangoni flow.

Calculations of three-dimensional viscous flow in a multiblade centrifugal fan by modelling blade forces

2003 ◽  
Vol 217 (3) ◽  
pp. 287-297 ◽  
Author(s):  
S-J Seo ◽  
K-Y Kim ◽  
S-H Kang
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Complex Flows ◽  
Flow Through ◽  
Volume Method ◽  
The Mathematical Model

A numerical study is presented for Reynolds-averaged Navier-Stokes analysis of three-dimensional turbulent flows in a multiblade centrifugal fan. Present work aims at development of a relatively simple analysis method for these complex flows. A mathematical model of impeller forces is obtained from the integral analysis of the flow through the impeller. A finite volume method for discretization of governing equations and a standard k-ɛ model as turbulence closure are employed. For the validation of the mathematical model, the computational results for velocity components, static pressure, and flow angles at the exit of the impeller were compared with experimental data. The comparisons show generally good agreement, especially at higher flow coefficients.

Three-Dimensional Sediment Numerical Simulation of Wenzhou Oufei Tidal Flat Sea Area

2012 ◽  
Vol 535-537 ◽  
pp. 1775-1779
Author(s):  
Jia Rui Li ◽  
Lei Mo ◽  
Wen Hu Zhang
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Tidal Flat ◽  
Concentration Distribution ◽  
Three Dimensional ◽  
Sediment Concentration ◽  
Basic Law ◽  
Open Sea ◽  
Calculation Results ◽  
Sea Area

A flow and sediment mathematical model was built under three-dimensional hybrid coordinate to simulate Wenzhou Oufei tidal flat and its neighboring sea area, and the verification was down. The calculation results and the observed data are identical well. In estuary area, the sediment concentration is the highest, then outside the estuary. In Oufei tidal flat area, the sediment concentration is relatively high, and it decreases gradually towards the open sea. Through the simulation, the characteristics and the basic law of sediment concentration distribution was reproduced.

scholarly journals Increasing the efficiency of highly concentrated coal-water fuel based on the simulation of non-Newtonian fluid flow

2019 ◽  
Vol 294 ◽  
pp. 01009 ◽  
Author(s):  
Nataliya Chernetskaya-Beletskaya ◽  
Andriy Rogovyi ◽  
Igor Baranov ◽  
Alexander Krut ◽  
Maria Miroshnikova ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Energy Consumption ◽  
Transport System ◽  
Three Dimensional ◽  
Transport Systems ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Industrial Enterprises ◽  
Energy Consumption Optimization ◽  
The Mathematical Model

The analysis of further prospects for increasing the efficiency of transportation of coal-water fuel in hydro-transport systems of industrial enterprises is carried out. The mathematical model of the spatial three-dimensional flow of coal-water fuel was developed on the basis of SST turbulence model based on the solution of Navier-Stokes equation. As a result of the calculation, the values of pressure loss, flow rate and velocity distribution over the cross section of the pipeline in the straight section and in the turn were determined, which allowed determining the energy consumption during coal-water fuel transportation in the industrial hydro-transport system. The performed studies allowed us to refine the mathematical model of water-coal suspension flow and, thus, improve the patterns of influence of hydro-transportation scheme and parameters of coal-water fuel on energy consumption for its supply to enterprise consumers. By means of mathematical model of non-Newtonian fluids flow, the patterns of influence of hydro-transport system parameters and transportation modes of coal-water fuel on its energy indicators in industrial hydro-transport systems are determined. The obtained results are related to reduction of energy consumption, optimization of enterprise transport network configuration and increase of efficiency of coal-water fuel transportation to enterprise energy facilities.

scholarly journals DEVELOPMENT OF A MATHEMATICAL MODEL FOR RESEARCHING THE PROCESS OF REDUCTION OF TUNGSTEN HEXAFLUORIDE BY GASEOUS HYDROGEN

2021 ◽  
pp. 225-230
Author(s):  
А.К. Шубин
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Tungsten Hexafluoride ◽  
Numerical Studies ◽  
Cylindrical Coordinate ◽  
Transfer Equations ◽  
Flow Motion

В работе рассмотрена математическая модель, описывающая движение течения стационарной, ламинарной, вязкой, несжимаемой смеси газа в трехмерном осесимметричном канале. Математическая модель, описывающая этот процесс, состоит из уравнений Навье – Стокса, уравнения неразрывности и массообмена, которые записаны в безразмерной форме с учетом осесимметричности в цилиндрической системе координат. Решение уравнений осуществляется в физических переменных «скорость – давление» на разнесенной разностной сетке. Показано влияние характерных параметров на распределение концентрации смеси газа гексафторида вольфрама и водорода в канале. Полученная математическая модель позволяет проводить численные исследования по выбору оптимальных условий осуществления процесса восстановления гексафторида вольфрама водородом. The paper considers a mathematical model describing the flow motion of a stationary, laminar, viscous, incompressible gas mixture in a three-dimensional axisymmetric channel. The mathematical model describing this process consists of the Navier-Stokes equations, the continuity and mass transfer equations, which are written in dimensionless form taking into account axisymmetry in a cylindrical coordinate system. The equations are solved in the physical variables "velocity - pressure" on a spaced difference grid. The influence of characteristic parameters on the concentration distribution of a mixture of tungsten hexafluoride gas and hydrogen in the channel is shown. The obtained mathematical model makes it possible to conduct numerical studies on the choice of optimal conditions for the process of reduction of tungsten hexafluoride with hydrogen.

Mathematical modeling of electron irradiation of oil

2018 ◽  
Vol 35 (5) ◽  
pp. 1998-2009
Author(s):  
Assylzhan Kizbayev ◽  
Dauren Zhakebayev ◽  
Ualikhan Abdibekov ◽  
Askar Khikmetov
Keyword(s):  
Mathematical Model ◽  
Electron Irradiation ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Hydrocarbon Mixture ◽  
Navier Stokes Equation ◽  
Content Type ◽  
The Matrix ◽  
Crank Nicolson

Purpose This paper aims to propose a mathematical model and numerical modeling to study the behavior of low conductive incompressible multicomponent hydrocarbon mixture in a channel under the influence of electron irradiation. In addition, it also aims to present additional mechanisms to study the radiation transfer and the separation of the mixture’s components. Design/methodology/approach The three-dimensional non-stationary Navier–Stokes equation is the basis for this model. The Adams–Bashforth scheme is used to solve the convective terms of the equation of motion using a fourth-order accuracy five-point elimination method, and the viscous terms are computed with the Crank–Nicolson method. The Poisson equation is solved with the matrix sweep method and the concentration and electron irradiation equations are solved with the Crank–Nicolson method too. Findings It shows high computational efficiency and good estimation quality. On the basis of numerical results of mathematical model, the effect of the separation of mixture to fractions with various physical characteristics was obtained. The obtained results contribute to the improvement of technologies for obtaining high-quality oil products through oil separation into light and heavy fractions. Mathematical model is approbated based on test problem, and has good agreement with the experimental data. Originality/value The constructed mathematical model makes developing a methodology for conducting experimental studies of this phenomenon possible.

scholarly journals MATHEMATICAL MODEL OF THE MULTI-CHANNEL SPIRAL CYCLONE / DAUGIAKANALIO SPIRALINIO CIKLONO ORO GREIČIŲ TYRIMAS

2013 ◽  
Vol 5 (4) ◽  
pp. 349-355
Author(s):  
Justina Danilenkaitė ◽  
Aleksandras Chlebnikovas ◽  
Petras Vaitiekūnas
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Differential Equations ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Cylindrical Part ◽  
Navier Stokes ◽  
Laminar And Turbulent Flow

The article deals with a problem of experimental investigation and numerical simulation of gas aerodynamics of a multi-channel spiral cyclone with a tangential inlet. The paper presents an overview of experimental and theoretical works on the cyclones having a particularly complex turbulent flow and focuses on three-dimensional transport differential equations for a non-compressible laminar and turbulent flow inside the cyclone. The equations have been solved applying the numerical finite volume method using the RNG (Re–Normalisation Group) k-ε turbulence model. The numerical simulation of the flow cyclone has been carried out. The height of the cyclone is 0.80 m with 0.33 m in diameter, the height of the spiral–cylindrical part – 0.098 meters and that of the cone – 0.45 m. Inlet dimensions (cylindrical part on the side), in accordance with drawings makes a×b = 28×95 mm. The mathematical model for the air traffic movement cyclone has accounted for Navier-Stokes (Reynolds) three-dimensional differential equations. The simulation results have been obtained with reference to the cyclone of tangential velocity profiles using RNG k-ε turbulence model. The inlet velocity of 5.1 m/s slightly differs from experimental results, thus making an error of 7%. Article in Lithuanian. Santrauka Nagrinėjama dujų aerodinamikos daugiakanaliame spiraliniame ciklone eksperimentinio tyrimo ir skaitinio modeliavimo problema. Apžvelgti eksperimentiniai ir teoriniai ciklonų, kuriuose susidaro ypač sudėtingas sūkurinis srautas, tyrimai. Pateiktos nespūdžiojo laminarinio ir turbulentinio srauto tekėjimo ciklono viduje diferencialinės trimatės pernašos lygtys. Jos skaitiškai spręstos baigtinių tūrių metodu taikant RNG (Re – Normalisation Group) k–ε turbulencijos modelį. Atliktas skaitinis oro srauto judėjimo ciklone modeliavimas. Ciklono aukštis 0,80 m, skersmuo 0,33 m, spiralinės-cilindrinės dalies aukštis 0,098 m, kūginės – 0,45 m, įtekėjimo angos matmenys (cilindrinės dalies šone) pagal brėžinius yra a×b = 28×95 mm. Oro srauto judėjimo ciklone matematinį modelį sudaro Navjė ir Stokso (Reinoldso) trimačių diferencialinių lygčių sistema. Modeliavimo rezultatai, t. y. taikant RNG k–ε turbulencijos modelį (įtekėjimo greitis 5,1 m/s) gauti tangentinio greičio ciklone kitimo duomenys, nežymiai (su 7 % paklaida) skyrėsi nuo eksperimentinių rezultatų.

Imaging of platinum-shadowed macromolecular complexes in dark field

1984 ◽  
Vol 42 ◽  
pp. 146-147
Author(s):  
D.W. Andrews ◽  
F.P. Ottensmeyer
Keyword(s):  
Thin Film ◽  
Three Dimensional ◽  
Average Diameter ◽  
Dark Field ◽  
Bright Field ◽  
Field Mode ◽  
Macromolecular Complexes ◽  
Average Mass ◽  
Topological Features ◽  
Projection Images

Shadowing with heavy metals has been used for many years to enhance the topological features of biological macromolecular complexes. The three dimensional features present in directionaly shadowed specimens often simplifies interpretation of projection images provided by other techniques. One difficulty with the method is the relatively large amount of metal used to achieve sufficient contrast in bright field images. Thick shadow films are undesirable because they decrease resolution due to an increased tendency for microcrystalline aggregates to form, because decoration artefacts become more severe and increased cap thickness makes estimation of dimensions more uncertain.The large increase in contrast provided by the dark field mode of imaging allows the use of shadow replicas with a much lower average mass thickness. To form the images in Fig. 1, latex spheres of 0.087 μ average diameter were unidirectionally shadowed with platinum carbon (Pt-C) and a thin film of carbon was indirectly evaporated on the specimen as a support.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Experimental and Numerical Analysis of a Motorcycle Air Intake System Aerodynamics and Performance

2020 ◽  
Vol 17 (1) ◽  
Author(s):  
M. A. Abd Halim ◽  
N. A. R. Nik Mohd ◽  
M. N. Mohd Nasir ◽  
M. N. Dahalan
Keyword(s):  
Combustion Process ◽  
Three Dimensional ◽  
Engine Performance ◽  
Internal Flow ◽  
Rapid Expansion ◽  
Navier Stokes ◽  
Turbulent Fluctuation ◽  
Ansys Fluent ◽  
Induction System ◽  
Acceleration And Deceleration

Induction system or also known as the breathing system is a sub-component of the internal combustion system that supplies clean air for the combustion process. A good design of the induction system would be able to supply the air with adequate pressure, temperature and density for the combustion process to optimizing the engine performance. The induction system has an internal flow problem with a geometry that has rapid expansion or diverging and converging sections that may lead to sudden acceleration and deceleration of flow, flow separation and cause excessive turbulent fluctuation in the system. The aerodynamic performance of these induction systems influences the pressure drop effect and thus the engine performance. Therefore, in this work, the aerodynamics of motorcycle induction systems is to be investigated for a range of Cubic Feet per Minute (CFM). A three-dimensional simulation of the flow inside a generic 4-stroke motorcycle airbox were done using Reynolds-Averaged Navier Stokes (RANS) Computational Fluid Dynamics (CFD) solver in ANSYS Fluent version 11. The simulation results are validated by an experimental study performed using a flow bench. The study shows that the difference of the validation is 1.54% in average at the total pressure outlet. A potential improvement to the system have been observed and can be done to suit motorsports applications.

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