Mathematical modeling of aluminum degassing by the impeller injector technique validated by a physical modeling

2014 ◽  
Vol 1611 ◽  
pp. 49-54 ◽  
Author(s):  
M. Hernández-Hernández ◽  
W. F. Cruz-Mendez ◽  
C. Gonzalez-Rivera ◽  
M. A. Ramírez-Argáez
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Gas Flow ◽  
Process Analysis ◽  
Liquid Aluminum ◽  
Bubble Diameter ◽  
Operating Parameter ◽  
Gas Flow Rate ◽  
The Mathematical Model ◽  
Kinetics Of

ABSTRACTA mathematical model is developed to describe deoxidation of water in a physical model of a batch aluminum degassing reactor equipped with the rotor-injector technique, assuming that deoxidation kinetics of water is similar to dehydrogenization of liquid aluminum. Degassing kinetics is described by using mass transport and mass balance principles by assuming that degassing kinetics can be characterized by a mass transfer coefficient, which depends on the process variables. The transport coefficient and the average bubble diameter are estimated with correlations reported in the literature for similar gas-injection systems. The water physical model helped to validate the mathematical model and to perform a process analysis by varying: 1) Gas flow rate (20 and 40 l/min); and 2) Impeller’s angular velocity (290 and 573 rpm). Results from the model agree well with measurements of deoxidation kinetics at low impeller rotating speeds. At high rotating speeds the model is still valid but less reliable because it does not take into account the formation of the vortex at the free surface. Nevertheless, the model provides predictions of the influence of every operating parameter and it can be used as a good approximation for real systems.

Study of Aluminum Degasification with Impeller-Injector Assisted by Physical Modeling

2012 ◽  
Vol 1485 ◽  
pp. 41-46
Author(s):  
M. Hernández-Hernández ◽  
E. A. Ramos-Gómez ◽  
M. A. Ramírez-Argáez
Keyword(s):  
Physical Model ◽  
Gas Flow ◽  
Liquid Aluminum ◽  
Gas Injection ◽  
The Novel ◽  
Rotating Speed ◽  
Novel Method ◽  
Purge Gas ◽  
Efficiency And Productivity ◽  
Kinetics Of

ABSTRACTA full-scale water physical model of a degassing unit is built and used to evaluate the performance of several impeller designs. Four impeller designs are tested: a) one smooth not commercial impeller for reference purposes, b) a commercial design by FOSECO®, called standard impeller in this work, c) a commercial design by FOSECO® with notches, and d) a new design proposed in this work. Since the physical model is easy and safe to operate, a full experimental design is performed to evaluate the effect of the most important process variables, such as impeller rotating speed, gas flow rate, impeller design and the point of gas injection (a conventional gas injection through the shaft and a novel method of injecting gas through the bottom of the ladle) on the kinetics of oxygen desorption of water which is similar to dehydrogenation of liquid aluminum. The new design of impeller proposed in this work shows the best performance in degassing of all impellers tested in this study. It is found that the rotor speed and its design are the most significant variables affecting degassing kinetics, and therefore the analysis of the existing commercial impeller designs may be useful to optimize the fluid dynamics of the process, which in turn would increase efficiency and productivity of the process. Finally, the novel gas injection method through the bottom, proposed by our own group, presents slightly faster degassing kinetics than the conventional injection of purge gas in the conventional way through the impeller.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

Mass Transfer Coefficients during Steel Decarburization in a RH Degasser

2008 ◽  
Vol 273-276 ◽  
pp. 679-684
Author(s):  
Roberto Parreiras Tavares ◽  
André Afonso Nascimento ◽  
Henrique Loures Vale Pujatti
Keyword(s):  
Mass Transfer ◽  
Reynolds Number ◽  
Transfer Coefficient ◽  
Mass Transfer Coefficient ◽  
Gas Flow ◽  
Vacuum Chamber ◽  
Volumetric Mass Transfer Coefficient ◽  
Gas Flow Rate ◽  
Rh Process ◽  
Kinetics Of

The RH process is a secondary refining process that can simultaneously attain significant levels of removal of interstitial elements, such as carbon, nitrogen and hydrogen, from liquid steel. In the RH process, the decarburization rate plays a very important role in determining the productivity of the equipment. The kinetics of this reaction is controlled by mass transfer in the liquid phase. In the present work, a physical model of a RH degasser has been built and used in the study of the kinetics of decarburization. The effects of the gas flow rate and of the configurations of the nozzles used in the injection of the gas have been analyzed. The decarburization reaction of liquid steel was simulated using a reaction involving CO2 and caustic solutions. The concentration of CO2 in the solution was evaluated using pH measurements. Based on the experimental results, it was possible to estimate the reaction rate constant. A volumetric mass transfer coefficient was then calculated based on these rate constants and on the circulation rate of the liquid. The logarithm of the mass transfer coefficient showed a linear relationship with the logarithm of the gas flow rate. The slope of the line was found to vary according to the relevance of the reaction at the free surface in the vacuum chamber. A linear relationship between the volumetric mass transfer coefficient and the nozzle Reynolds number was also observed. The slopes of the lines changed according to the relative importance of the two reaction sites, gas-liquid interface in the upleg snorkel and in the vacuum. At higher Reynolds number, the reaction in the vacuum chamber tends to be more significant.

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

Dynamics of Shock Waves in the Cylindrical Channel With Confusers

2009 ◽  
Vol 4 (2) ◽  
pp. 13-18
Author(s):  
Igor Anufriev ◽  
Aleksandr Golovanov ◽  
Aleksandr Tsimbalyuk ◽  
Oleg Sharypov
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Shock Wave ◽  
Shock Wave Front ◽  
Gas Flow ◽  
Cylindrical Channel ◽  
Maximal Pressure ◽  
The Mathematical Model ◽  
Forest Combustible ◽  
Gunpowder Charge

Current work covers experimental and theoretical investigation of conic confusers impact on the intensity shock wave, generated in the shock tube by explosion of gunpowder charge. For given conditions optimal geometric characteristics of the confuser, providing maximal pressure in the shock wave front, were found experimentally. The mathematical model was developed and numerical simulation of the axisymmetric shock-wave gas flow in the channel was carried out. Experimentally was shown, that the application of the optimal confuser provides significant increase of the efficiency gasdynamic effect on the combustion of forest combustible materials.

scholarly journals Bifurcation phenomena and statistical regularities in dynamics of forced impacting oscillator

2019 ◽  
Vol 98 (3) ◽  
pp. 1795-1806 ◽  
Author(s):  
Sergii Skurativskyi ◽  
Grzegorz Kudra ◽  
Krzysztof Witkowski ◽  
Jan Awrejcewicz
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Physical Model ◽  
Dry Friction ◽  
Stepper Motor ◽  
Nonlinear Phenomenon ◽  
Hertz Contact ◽  
Bifurcation Phenomena ◽  
Statistical Regularities ◽  
The Mathematical Model

Abstract The paper is devoted to the study of harmonically forced impacting oscillator. The physical model for oscillator is a cart on a guide connected to the support with springs and excited by the stepper motor. The support also is provided with limiter of motion. The mathematical model for this system is defined with the second-order piecewise smooth differential equation. Model’s nonlinearity is connected with the incorporation of dry friction and generalized Hertz contact law. Analyzing the classical Poincare sections and inter-impact sequences obtained experimentally and numerically, the bifurcations and statistical properties of periodic, multi-periodic, and chaotic regimes were examined. The development of impact-adding regime as a new nonlinear phenomenon when the forcing frequency varies was observed.

scholarly journals A Mathematical Model Combined with Radar Data for Bell-Less Charging of a Blast Furnace

Processes ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 239 ◽  
Author(s):  
Meng Li ◽  
Han Wei ◽  
Yao Ge ◽  
Guocai Xiao ◽  
Yaowei Yu
Keyword(s):  
Mathematical Model ◽  
Blast Furnace ◽  
Gas Flow ◽  
Radar Data ◽  
Radar System ◽  
Utilization Efficiency ◽  
Burden Distribution ◽  
Gas Utilization ◽  
Reduce Energy Consumption ◽  
The Mathematical Model

Charging directly affects the burden distribution of a blast furnace, which determines the gas distribution in the shaft of the furnace. Adjusting the charging can improve the distribution of the gas flow, increase the gas utilization efficiency of the furnace, reduce energy consumption, and prolong the life of the blast furnace. In this paper, a mathematical model of blast furnace charging was developed and applied on a steel plant in China, which includes the display of the burden profile, burden layers, descent speed of the layers, and ore/coke ratio. Furthermore, the mathematical model is developed to combine the radar data of the burden profile. The above model is currently used in Nanjing Steel as a reference for operators to adjust the charging. The model is being tested with a radar system on the blast furnace.

Experimental and Theoretical Study on Melting Kinetics of Spherical Aluminum Particles in Liquid Aluminum

2015 ◽  
Vol 1765 ◽  
pp. 139-144
Author(s):  
Marco Ramírez-Argáez ◽  
Enrique Jardón ◽  
Carlos González-Rivera
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Transfer Coefficient ◽  
Process Analysis ◽  
Convective Heat Transfer Coefficient ◽  
Melting Process ◽  
Solid Particles ◽  
Melting Time ◽  
Melting Kinetics ◽  
Kinetics Of

ABSTRACTIn this study a process analysis of the melting process of solid particles in a bath of same composition is performed using both experimental information and theoretical computations. An experimental setup was used to measure the thermal histories and to follow the evolution with time of the size of solid metallic spherical particles being melted in a metallic bath of same composition. For such a purpose, pure aluminum was used during the experiments for both solid particles and liquid bath. A mathematical model was also developed based on first principles of heat transfer to simulate the melting kinetics of a cold metallic spherical particle immersed in a hot liquid bath of same composition. The mathematical model was reasonably validated when compared against the experimental results obtained in this work. A process analysis of the melting process was performed to determine the effect of the initial temperature and size of the solid particle, the bath temperature and the convective heat transfer coefficient on the melting time and on the energy consumption.The analysis showed that the variable presenting the most significant effect on both the melting time and the energy consumption is the convective heat transfer coefficient between the particle and the bath, since an increment in such a parameter accelerates the melting process and saves energy. Therefore, proper stirring of the bath is highly recommended to enhance the melting of metallic alloying additions in the metallic baths.

Mathematical Modeling of Impingement of an Air Jet in a Liquid Bath

2010 ◽  
Vol 1276 ◽  
Author(s):  
J. Solórzano-López ◽  
R. Zenit ◽  
M. A. Ramírez-Argáez
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Free Surface ◽  
Gas Flow ◽  
Two Phase ◽  
Arc Furnaces ◽  
Air Jet ◽  
Image Velocimetry ◽  
Oxygen Gas ◽  
The Mathematical Model

AbstractPhysical and mathematical modeling of jet-bath interactions in electric arc furnaces represent valuable tools to obtain a better fundamental understanding of oxygen gas injection into the furnace. In this work, a 3D mathematical model is developed based on the two phase approach called Volume of Fluid (VOF), which is able to predict free surface deformations and it is coded in the commercial fluid dynamics software FLUENTTM. Validation of the mathematical model is achieved by measurements on a transparent water physical model. Measurements of free surface depressions through a high velocity camera and velocity patterns are recorded through a Particle Image Velocimetry (PIV) Technique. Flow patterns and depression geometry are identified and characterized as function of process parameters like distance from nozzle to bath, gas flow rate and impingement angle of the gas jet into the bath. A reasonable agreement is found between simulated and experimental results.

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