Modelling the Wear Process of Inhomogeneous Bodies

2005 ◽  
Author(s):  
I. G. Goryacheva
Keyword(s):  
Mathematical Model ◽  
Phase Composition ◽  
Contact Mechanics ◽  
Two Phase ◽  
Wear Process ◽  
Substrate Interface ◽  
Inhomogeneous Bodies ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
Local Hardening

The approaches of contact mechanics are used to evaluate the evolution of the contact characteristics in wear process of inhomogeneous bodies (coated bodies, two-phase composition, bodies with inclusions, etc.). The mathematical model is formulated and used to study the kinetics of the wear process depending on the parameters of inhomogeneity such as size and density of inclusions, waviness at the coating-substrate interface, local hardening parameters, etc.

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.

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 Modeling and Analysis of Magnetic Nanoparticles Injection in Water-Oil Two-Phase Flow in Porous Media under Magnetic Field Effect

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed F. El-Amin ◽  
Ahmed M. Saad ◽  
Amgad Salama ◽  
Shuyu Sun
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Porous Media ◽  
Magnetic Nanoparticles ◽  
Additional Term ◽  
Flow In Porous Media ◽  
Phase System ◽  
Two Phase ◽  
The Mathematical Model ◽  
Nanoparticles Suspension

In this paper, the magnetic nanoparticles are injected into a water-oil, two-phase system under the influence of an external permanent magnetic field. We lay down the mathematical model and provide a set of numerical exercises of hypothetical cases to show how an external magnetic field can influence the transport of nanoparticles in the proposed two-phase system in porous media. We treat the water-nanoparticles suspension as a miscible mixture, whereas it is immiscible with the oil phase. The magnetization properties, the density, and the viscosity of the ferrofluids are obtained based on mixture theory relationships. In the mathematical model, the phase pressure contains additional term to account for the extra pressures due to fluid magnetization effect and the magnetostrictive effect. As a proof of concept, the proposed model is applied on a countercurrent imbibition flow system in which both the displacing and the displaced fluids move in opposite directions. Physical variables, including water-nanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat concentrations of deposited nanoparticles, are investigated under the influence of the magnetic field. Two different locations of the magnet are studied numerically, and variations in permeability and porosity are considered.

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.

Regularity of Dust Distributing in Fully Mechanized Caving Face and Negative Pressure Spray Dust-Settling Technology

2012 ◽  
Vol 246-247 ◽  
pp. 624-628 ◽  
Author(s):  
Wen Nie ◽  
Wei Min Cheng
Keyword(s):  
Mathematical Model ◽  
Negative Pressure ◽  
Lagrangian Model ◽  
Dust Particles ◽  
Phase Flow ◽  
Dust Pollution ◽  
Two Phase ◽  
Fluent Software ◽  
The Mathematical Model ◽  
Hydraulic Supports

The mathematical model of solving two-phase flow of gas and dust particles was built by established the k-ε equation. Moreover, by basing on Eulerian-Lagrangian model and using FLUENT software, the diffusion rule of dust pollution in full-mechanized caving face was confirmed. Based on negative pressure spray dust-settling mechanism, negative pressure spray technology was developed between hydraulic supports, in drawing opening position and shearer, and it was determined by the optimal spray pressure for 4 MPa. After negative pressure spray technology was applied in fully mechanized caving face, the dust concentration was down significantly.

scholarly journals A SIMPLIFIED OXIDATION MODEL FOR TWO-PHASE FLOW IN POROUS MEDIA

2002 ◽  
Vol 1 (2) ◽  
pp. 09
Author(s):  
J. C. Da Mota ◽  
A. J. De Souza ◽  
D. Marchesin ◽  
P. W. Teixeira
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Wave Structure ◽  
Thermal Recovery ◽  
Flow In Porous Media ◽  
Low Temperature Oxidation ◽  
Two Phase ◽  
Temperature Oxidation ◽  
Physical Effects ◽  
The Mathematical Model

This paper describes a simplified mathematical model for thermal recovery by oxidation for flow of oxygen and oil in porous media. Some neglected important physical effects include gravity, compressibility and heat loss to the rock formation, but heat longitudinal conduction and capillary pressure difference between the phases are considered. The mathematical model is obtained from the mass balance equations for air and oil, energy balance and Darcy's law applied to each phase. Based on this model some typical features in low temperature oxidation concerning the wave structure are captured. Numerical simulations showing saturations and temperature profiles are reported.

scholarly journals Drying kinetics of Chinese garlic (Allium tuberosum) and its effect on color

2020 ◽  
Vol 42 ◽  
pp. e8
Author(s):  
Paula De Almeida Rios ◽  
Ednilton Tavares De Andrade ◽  
Kátia Soares Moreira ◽  
Filipe Da Silva De Oliveira ◽  
Bárbara Lemes Outeiro Araújo
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Air Temperature ◽  
Linear Regression Analysis ◽  
Drying Kinetics ◽  
Allium Tuberosum ◽  
Thin Slices ◽  
The Mathematical Model ◽  
Quasi Newton ◽  
Kinetics Of

Dehydrated garlic is an important component both for culinary and medicinal purposes. However, there is a scarcity of studies that characterizes its drying kinetics. Thus, the objective of this work was to study the drying kinetics of Chinese garlic (Allium tuberosum), as well as to analyze the color effect resulting from each treatment. The garlic bulbs were cut into thin slices with a width of 2 and 3 mm, subjected to the drying air temperature of 35, 45, 55 and 70 °C in a mechanical dryer of a fixed layer with forced convection. Was performed a non-linear regression analysis by the Quasi-Newton method, for adjustment to 11 mathematical models to the experimental data of drying. The Midilli equation was the mathematical model that best characterized all the drying temperatures, for the experimental data. The diffusion coefficient presented values between 1.46 x 10-11 and 7.32 x 10-11 m2.s-1. The increase of the drying air temperature caused the dimming of the samples with a reduction of the L* coordinate and reduction of the yellow of the samples according to the coordinate results h*. The temperature of 70 °C was detrimental to the maintenance of the Chinese garlic coloration. 

scholarly journals Modelling and thermodynamic analysis of ejector flow for application at design and off design operating conditions in an ejector air conditioner

2021 ◽  
Vol 12 (3) ◽  
pp. 3455-3467
Author(s):  
Anoop Kumar. M Et.al
Keyword(s):  
Mathematical Model ◽  
Heat Input ◽  
Flow Analysis ◽  
Cooling Capacity ◽  
Two Phase ◽  
Entrainment Ratio ◽  
Air Conditioning System ◽  
The Mathematical Model ◽  
Minimum Quality

Ejector flow in an ejector air conditioning system using R245fa is analysed for entrainment ratio and potential refrigeration effect, at varying temperature and heat input conditions in  the generator ranging from 60C to 100C and 2kW to 5kW respectively. The effect of varying generator temperature in cooling capacity of the system when the vapour ejectoris operating at design evaporator and condenser temperatures of 10C and 35C respectively is investigated. The mathematical model of the vapour ejector with optimum area ratio is developed and validated. A critical entrainment ratio of 0.385 is obtained corresponding to generator temperature of 100C. When the generator temperature is varied from 60C to 100C, the cooling capacity range from 0.3kW at generator heat input of 2 kW to 1.78 kW at 5 kW heat input. Further, the operation of the system is analysed for off design operating condition corresponding to reduced heat input rate in the generator. In that case the state of primary refrigerant flow in ejector inlet will be two phase and a mathematical model for two-phase ejector flow is developed and validated. Ejector flow analysis revealed the minimum quality of flow at ejector inlet to maintain adequate backpressure for condensation to occur range from 0.72 at 60C to 0.22 at 100C. The corresponding refrigeration refrigeration effect produced is less than the respective designed operation value byits  12.2% to 8%. Further, analysis of the system shows that at least 7 kW heat input at 100C is required to produce 1 ton of cooling effect. Ejector flow in an ejector air conditioning system using R245fa is analysed for entrainment ratio and potential refrigeration effect, at varying temperature and heat input conditions in  the generator ranging from 60C to 100C and 2kW to 5kW respectively. The effect of varying generator temperature in cooling capacity of the system when the vapour ejectoris operating at design evaporator and condenser temperatures of 10C and 35C respectively is investigated. The mathematical model of the vapour ejector with optimum area ratio is developed and validated. A critical entrainment ratio of 0.385 is obtained corresponding to generator temperature of 100C. When the generator temperature is varied from 60C to 100C, the cooling capacity range from 0.3kW at generator heat input of 2 kW to 1.78 kW at 5 kW heat input. Further, the operation of the system is analysed for off design operating condition corresponding to reduced heat input rate in the generator. In that case the state of primary refrigerant flow in ejector inlet will be two phase and a mathematical model for two-phase ejector flow is developed and validated. Ejector flow analysis revealed the minimum quality of flow at ejector inlet to maintain adequate backpressure for condensation to occur range from 0.72 at 60C to 0.22 at 100C. The corresponding refrigeration refrigeration effect produced is less than the respective designed operation value byits  12.2% to 8%. Further, analysis of the system shows that at least 7 kW heat input at 100C is required to produce 1 ton of cooling effect.

scholarly journals МАТЕМАТИЧЕСКАЯ МОДЕЛЬ И МЕТОД РАСЧЕТА ДИНАМИКИ СУШКИ И ТЕРМОДЕСТРУКЦИИ БИОМАССЫ

2018 ◽  
Vol 82 (1) ◽  
Author(s):  
Наталья Николаевна Сороковая ◽  
Дмитрий Николаевич Коринчук
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Thermal Decomposition ◽  
Numerical Method ◽  
Heat And Mass Transfer ◽  
The Body ◽  
Physical Factors ◽  
Deformation Equation ◽  
The Mathematical Model ◽  
Kinetics Of

Разработана математическая модель и численный метод расчета динамики тепломассопереноса, фазовых превращений и усадки при сушке коллоидных капиллярно-пористых тел цилиндрической формы в условиях равномерного обдува теплоносителем. Математическая модель строилась на базе дифференциального уравнения переноса субстанции (энергии, массы, импульса) в деформируемых системах. Проведены экспериментальные исследования кинетики обезвоживания частиц энергетической вербы в потоке воздуха с целью верификации математической модели. Обоснована возможность ее использования для расчета совместных процессов сушки и начального этапа термического разложения биомассы. С использованием ранее полученных данных по значениям энергии активации Аэф(Т) для различных видов биомассы проведено математическое моделирование динамики и кинетики высокотемпературной сушки в потоке дымовых газов энергетической вербы, которая сопровождается термодеструкцией гемиоцеллюлозы. Результаты численных экспериментов свидетельствуют об адекватности предложенного подхода, эффективности математической модели и метода ее реализации. На их основе возможно проводить исследование динамики тепломассопереноса при сушке частиц различных видов измельченной биомассы; определение температуры начала и окончания первой стадии термического разложения; момента достижения равновесного влагосодержания в зависимости от свойств материала и сушильного агента. Эти данные позволяют выбирать оптимальные с точки зрения сохранения энергии и качества высушиваемого продукта  режимные параметры процесса.         A mathematical model and a numerical method for calculating the dynamics of heat and mass transfer, phase transformations and shrinkage during the drying of colloidal capillary-porous cylindrical bodies under conditions of equitable winding by a coolant are developed. The mathematical model was based on the differential equation of substance (energy, mass, impulse) transfer in deformable systems. It includes the equations diffusion-filtration transfer of energy for the system as a whole, and the mass transfer of the liquid, vapor and air phases in the pores of the body. Expressions for the intensity of evaporation of a liquid, capillary pressure, and the diffusion coefficients are presented. The relative volume strain was found by means of an analytical solution of the thermoconcentration deformation equation. Based on the explicit three-layer counting difference scheme and the procedure splitting of algorithm  by physical factors, a numerical method for realizing this mathematical model is developed.Experimental studies of the kinetics of dehydration of energy willow particles in the airflow were carried out to verify the mathematical model. Its applicability for calculating combined processes of drying and of the initial stage of thermal decomposition of biomass is substantiated. Using the previously obtained data on the activation energy values for various types of biomass, a mathematical simulation of the dynamics and kinetics of high-temperature drying in the flue gas flow of energy willow was carried out, which is accompanied by thermal destruction of hemiocellulose. The results of numerical experiments indicate the adequacy of the proposed approach, the effectiveness of the mathematical model and the method of its implementation. On their basis, it is possible to study the dynamics of heat and mass transfer when drying particles of different types of ground biomass; determination of the temperature of the beginning and ending of the first stage of thermal decomposition; the moment when the equilibrium moisture content is reached, depending on the properties of the material and the drying agent. These data allow choosing the process parameters that are optimal in terms of energy saving and quality of the dried product.

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