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.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

scholarly journals Mathematical Modeling of Pollution Transfer in Open Channel

2019 ◽  
pp. 49-50
Author(s):  
Petro Martyniuk ◽  
Oksana Ostapchuk ◽  
Vitalii Nalyvaiko
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Water Flow ◽  
Numerical Experiments ◽  
Open Channel ◽  
Computational Algorithm ◽  
The Mathematical Model

The problem of pollution transfer by water flow in open channel was considered. The mathematical model of the problem was constructed. The numerical solution of the onedimensional boundary problem was obtained. The computational algorithm for solving the problem was programmed to implement. A series of numerical experiments with their further analysis was conducted.

scholarly journals THE MATHEMATICAL MODELING OF METALS CONTENT IN PEAT

2015 ◽  
Vol 1 ◽  
pp. 249
Author(s):  
Edmunds Teirumnieks ◽  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Harijs Kalis
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Inductively Coupled Plasma ◽  
Optical Emission ◽  
Peat Bog ◽  
Inductively Coupled ◽  
Pollution Loading ◽  
The Mathematical Model ◽  
Optical Emission Spectrometer

Metals deposition in peat can aid to evaluate impact of atmospheric or wastewaters pollution and thus can be a good indicator of recent and historical changes in the pollution loading. For peat using in agriculture, industrial, heat production etc. knowledge of peat metals content is important. Experimental determination of metals in peat is very long and expensive work. Using experimental data the mathematical model for calculation of concentrations of metals in different points for different layers is developed. The values of the metals (Ca, Mg, Fe, Sr, Cu, Zn, Mn, Pb, Cr, Ni, Se, Co, Cd, V, Mo) concentrations in different layers in peat taken from Knavu peat bog from four sites are determined using inductively coupled plasma optical emission spectrometer. Mathematical model for calculation of concentrations of metal has been described in the paper. As an example, mathematical models for calculation of Pb concentrations have been analyzed.

On the correctness of a phenomenological model of equilibrium phase transitions in a deformable elastic medium

1992 ◽  
Vol 3 (2) ◽  
pp. 181-191
Author(s):  
A. M. Meirmanov ◽  
N. V. Shemetov
Keyword(s):  
Mathematical Model ◽  
Continuous Medium ◽  
Equilibrium Phase ◽  
Elastic Solid ◽  
Complementary Energy ◽  
Structure Of Solutions ◽  
Two Phase ◽  
Pure Phase ◽  
The Mathematical Model ◽  
Uniqueness Of A Solution

In this paper we investigate the mathematical model of the equilibrium of a finite volume in ℝn (n = 1,2, 3) of a two-phase continuous medium, under the assumption that each pure phase is an isotropic elastic solid. The main results in this paper are:(i) the existence and uniqueness of a solution of this mathematical model;(ii) a discussion of the stress-strain law associated with the free energy of this two-phase continuous medium, which is multiple-valued due to the non-smoothness of the Gibbs potential (complementary energy);(iii) a description of the structure of solutions in plane strain.

scholarly journals Mathematical modeling and harmonic analysis of SISFCL

2017 ◽  
Vol 36 (1) ◽  
pp. 258-270
Author(s):  
Debraj Sarkar ◽  
Debabrata Roy ◽  
Amalendu Bikash Choudhury ◽  
Sotoshi Yamada
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Harmonic Analysis ◽  
Voltage Drop ◽  
Element Model ◽  
Iron Core ◽  
Content Type ◽  
Hysteresis Characteristic ◽  
The Core ◽  
The Mathematical Model

Purpose A saturated iron core superconducting fault current limiter (SISFCL) has an important role to play in the present-day power system, providing effective protection against electrical faults and thus ensuring an uninterrupted supply of electricity to the consumers. Previous mathematical models developed to describe the SISFCL use a simple flux density-magnetic field intensity curve representing the ferromagnetic core. As the magnetic state of the core affects the efficient working of the device, this paper aims to present a novel approach in the mathematical modeling of the device with the inclusion of hysteresis. Design/methodology/approach The Jiles–Atherton’s hysteresis model is utilized to develop the mathematical model of the limiter. The model is numerically solved using MATLAB. To support the validity of model, finite element model (FEM) with similar specifications was simulated. Findings Response of the limiter based on the developed mathematical model is in close agreement with the FEM simulations. To illustrate the effect of the hysteresis, the responses are compared by using three different hysteresis characteristics. Harmonic analysis is performed and comparison is carried out utilizing fast Fourier transform and continuous wavelet transform. It is observed that the core with narrower hysteresis characteristic not only produces a better current suppression but also creates a higher voltage drop across the DC source. It also injects more harmonics in the system under fault condition. Originality/value Inclusion of hysteresis in the mathematical model presents a more realistic approach in the transient analysis of the device. The paper provides an essential insight into the effect of the core hysteresis characteristic on the device performance.

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.

Mathematical Modeling of Steppe Fires

2020 ◽  
pp. 48-62 ◽  
Author(s):  
Valeriy Afanasievich Perminov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Wind Speed ◽  
Vegetation Cover ◽  
Meteorological Conditions ◽  
Condensed Phases ◽  
Pyrolysis Products ◽  
Rate Of Spread ◽  
The Mathematical Model ◽  
Steppe Fires

The chapter presents a mathematical model of the initiation and spread of the steppe fire. The mathematical model is based on the laws of mechanics of multiphase reacting media. The main physicochemical processes describing the drying, pyrolysis, and combustion of gaseous and condensed pyrolysis products are taken into account. As a result of the numerical solution, the distributions of the velocity, temperature, and concentration fields of the components of the gas and condensed phases were determined. The dependence of the rate of spread of the steppe fire on the main parameters of the state of vegetation cover and wind speed was studied. The mathematical model presented in the chapter can be used to predict the spread of steppe fires for various types of steppe vegetation and meteorological conditions, as well as for preventive measures.

Results of Mathematical Modeling to Study the Influence of Accounting the Process Moisture on Energy Indicators of Cogeneration Steam Turbines

2015 ◽  
Vol 792 ◽  
pp. 370-374 ◽  
Author(s):  
Natalia Tatarinova ◽  
Dmitry Suvorov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Energy Efficiency ◽  
Steam Turbines ◽  
Moisture Measurement ◽  
Energy Indicators ◽  
The Mathematical Model

The article proposes and being tested a methodology that allows using the mathematical model developed to clarify the possible impact of a precise process moisture measurement on the performance of energy efficiency of the cogeneration turbines.

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