Combustion in Ni–Al system with Cu additive (powder or rod) Experiment and mathematical model

2020 ◽  
pp. 33-43
Author(s):  
O. V. Lapshin ◽  
A. M. Shul’pekov ◽  
R. M. Gabbasov ◽  
V. D. Kitler
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Relative Density ◽  
Aluminum Matrix ◽  
Kinetic Constants ◽  
Model Parameters ◽  
Nickel Aluminum ◽  
Copper Melt ◽  
Analytical Formulas ◽  
The Mathematical Model

Experimental studies were carried out with theoretical calculations of wave synthesis in the Ni–Al–Cu system were performed using the mathematical model developed. Approximate analytical formulas were obtained for synthesis performance evaluation. The inverse problem method was used to get kinetic constants that determine process dynamics based on the experimental data and analytical relationships. It is shown that the combustion front propagation velocity increases monotonically with an increase in the reaction sample relative density in the range of relative density values of 0.4 to 0.6. The depth of copper melt penetration from the center of the sample into the nickel-aluminum matrix depends on the relative density of the sample and copper wire diameter: higher densities and larger diameters lead to an increase in the liquid-phase impregnation area. The rate of nickel and aluminum powder frame wetting with copper melt is limited by the synthesis wave speed. Based on the experimental data and analytical ratios, we estimated the effective kinetic constants describing the high-temperature synthesis of the Ni + Al reaction mixture in the presence of copper additives. The thermal effect of the NiAl intermetallic formation reaction and the preexponential factor in the chemical transformation equation are calculated, the exponent value in the ratio for the mixture thermal conductivity is established; a constant determining the process of nickel-aluminum matrix impregnation with copper melt is found. The macroscopic approach used to analyze the NiAl intermetallic synthesis makes it possible to determine all the desired physicochemical characteristics and model parameters. The mathematical model is suitable for predictive estimates and experimental data analysis in the macroscopic approximation. Approximate analytical formulas are obtained for calculating the NiAl intermetallic synthesis characteristics. They allow for calculating the through channel characteristics and can be used in the design of NiAl products.

scholarly journals Experimental studies of iron transformations kinetics and autocatalysis during its physicochemical removal from underground water

2021 ◽  
Author(s):  
S. Yu Martynov ◽  
V. L. Poliakov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Experimental Studies ◽  
Underground Water ◽  
Model Parameters ◽  
Kinetic Coefficients ◽  
Transfer Equations ◽  
The Mathematical Model ◽  
Autocatalytic Effect ◽  
Forms Of Iron

Abstract The mathematical model of physicochemical iron removal from groundwater was developed. It consists of three interrelated compartments. The results of the experimental research provide information in support of the first two compartments of the mathematical model. The dependencies for the concentrations of the adsorbed ferrous iron and deposited hydroxide concentrations are obtained as a result of the exact solution of the system of the mass transfer equations for two forms of iron in relation to the inlet surface of the bed. An analysis of the experimental data of the dynamics of the deposit accumulation in a small bed sample was made, using a special application that allowed to select the values of the kinetic coefficients and other model parameters based on these dependencies. We evaluated the autocatalytic effect on the dynamics of iron ferrous and ferric forms. The verification of the mathematical model was carried out involving the experimental data obtained under laboratory and industrial conditions.

Development and automation of algorithm for determining basis of nonlinear parameter functions of kinetic constants

2019 ◽  
Vol 19 (4) ◽  
pp. 252-257
Author(s):  
A. S. Ismagilova ◽  
Z. A. Khamidullina ◽  
S. I. Spivak
Keyword(s):  
Mathematical Model ◽  
Kinetic Parameters ◽  
Platinum Catalyst ◽  
Hydrogen Oxidation ◽  
Nonlinear Parameter ◽  
Kinetic Constants ◽  
Model Parameters ◽  
Functional Relations ◽  
The Mathematical Model ◽  
Theoretical Issues

Mathematical modeling of catalytic processes is necessary for the complete and accurate description, as well as for controlling the quality and physicochemical studied of catalysts. In the paper, theoretical issues of industrial catalysis are discussed. The work is devoted to theoretical graph analysis of informativity of kinetic parameters of the model of a complex chemical reaction. The aim is the development and automation of algorithm for determining basis of nonlinear parameter functions in solving inverse problems of chemical kinetics in order to define the number and form of independent combinations of rate constants of elementary stages. A program package for analysis of informativity of kinetic parameters of the mathematical model of a complex catalytic reaction is developed and described. The obtained functional relations between the kinetic parameters can be useful for experimentalists in physicochemical interpretation and analysis of mechanisms of chemical reactions. In other words, the proposed method allows independent combinations of kinetic constants to be distinguished that results in shortening the number of the model parameters and, as a consequence, enhance the accuracy of the mathematical model. The mechanism of hydrogen oxidation over a platinum catalyst is given as an example of the use of the software.

Development and validation of mathematical model of hydrotropic-reactive extraction of lignin

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Indah Hartati ◽  
Wahyudi Budi Sediawan ◽  
Hary Sulistyo ◽  
Muhammad Mufti Azis ◽  
Moh Fahrurrozi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Effective Diffusivity ◽  
Reaction Rate Constant ◽  
Reactive Extraction ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Explicit Finite Difference ◽  
The Mathematical Model

AbstractHydrotropes have been largely explored as reactive extraction agent for lignin separation. In this paper, a mathematical model of hydrotropic-reactive extraction of sugarcane bagasse lignin was proposed and validated by experimental data from literature. The mathematical model was developed by assuming the particle is in slab shape, and by considering simultaneous processes of hydrotrope intra particle diffusion, second order reaction of lignin-hydrotrope, and intra-particle soluble delignification product diffusion. The proposed model results in a set of partial differential equations which were then solved by explicit finite difference approximation method. The mathematical model parameters were determined by fitting the model to the hydrotropic reactive extraction experimental data reported by Ansari and Gaikar (2014). Simulations show that the mathematical model of the hydrotropic-reactive extraction were well fitted to the experimental data with the obtained hydrotrope effective diffusivity (DeA) of 5.0 × 10−11 m2/s, effective diffusivity of soluble lignin product (DeC) of 9.0 × 10−12 m2/s and reaction rate constant (kr) of 1.78 × 10−10 m3/(g.s). It was also observed that the reaction was first order to the hydrotrope (n = 1), and one half order to the lignin (m = 0.5). Meanwhile the pseudo-stoichiometric mass ratio of hydrotrope to lignin was 6.4 g hydrotrope/g lignin.

Application of a Bubble-Induced Turbulence Model to Subcooled Boiling in a Vertical Pipe

1999 ◽  
Author(s):  
Mahmut D. Mat ◽  
Yüksel Kaplan ◽  
Olusegun J. Ilegbusi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Liquid Phase ◽  
Turbulence Model ◽  
Transport Equations ◽  
Subcooled Boiling ◽  
Vertical Pipe ◽  
Void Fractions ◽  
Turbulence Production ◽  
The Mathematical Model

Abstract Subcooled boiling of water in a vertical pipe is numerically investigated. The mathematical model involves solution of transport equations for vapor and liquid phase separately. Turbulence model considers the turbulence production and dissipation by the motion of the bubbles. The radial and axial void fractions, temperature and velocity profiles in the pipe are calculated. The estimated results are compared to experimental data available in the literature. It is found that while present study satisfactorily agrees with experimental data in the literature, it improves the prediction at lower void fractions.

Analytical Study of Hydro-Pneumatic Processes for Gorlov's Power System

1994 ◽  
Vol 208 (1) ◽  
pp. 67-70
Author(s):  
A I Ryazanov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Power System ◽  
Analytical Study ◽  
Model Tests ◽  
Air Pressure ◽  
Pneumatic Power ◽  
Time Required ◽  
The Mathematical Model

This paper describes the aerohydrodvnamics of processes in chambers of Gorlov's hydro-pneumatic power system. The mathematical model is developed to determine the main parameters of the processes: water and air velocities, air pressure in the chamber, the periods of time required to fill and empty the chambers and the output of energy during the cycle. The results obtained are in agreement with experimental data and model tests.

scholarly journals MATHEMATICAL MODELING OF LEACHING PROCESS OF RED MUD IN ORDER TO OBTAIN THE KINETICS PARAMETERS

2015 ◽  
Vol 14 (2) ◽  
pp. 90 ◽  
Author(s):  
K. L. M. Dos Passos ◽  
B. M. Viegas ◽  
E. N. Macêdo ◽  
J. A. S. Souza ◽  
E. M. Magalhães
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Red Mud ◽  
Mineralogical Composition ◽  
Raw Material ◽  
Data Conversion ◽  
Kinetics Parameters ◽  
Leaching Process ◽  
Iron Leaching ◽  
The Mathematical Model

The use of the waste of the Bayer process, red mud, is due to its chemical and mineralogical composition that shows a material rich in oxides of iron, titanium and aluminum. Some studies conducted show that this waste can be applied as a source of alternative raw material for concentration and subsequent recovery of titanium compounds from an iron leaching process, which is present in higher amounts, about 30% by weight. To obtain a greater understanding about the leaching kinetics, the information of the kinetic data of this process is very important. In this context, the main objective of this work is the development of a mathematical model that is able to fit the experimental data (conversion / extraction iron, titanium and aluminum) of the leaching process by which is possible to obtain the main kinetic parameters such as the activation energy and the velocity of chemical reactions as well as the controlling step of the process. The development of the mathematical model was based on the model of core decreasing. The obtained model system of ordinary differential equations was able to fit the experimental data obtained from the leaching process, enabling the determination of the controlling step, the rate constants and the activation energies of the leaching process.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

scholarly journals A mathematical model of common-cold epidemics on Tristan da Cunha

1971 ◽  
Vol 69 (3) ◽  
pp. 423-433 ◽  
Author(s):  
B. J. Hammond ◽  
D. A. J. Tyrrell
Keyword(s):  
Mathematical Model ◽  
Common Cold ◽  
Average Duration ◽  
Model Parameters ◽  
Epidemic Threshold ◽  
Tristan Da Cunha ◽  
Simulation Techniques ◽  
Time Courses ◽  
The Mathematical Model ◽  
Computer Simulation Techniques

SUMMARYRecords of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

Development of a Mathematical Model for Performance Prediction of Planing Catamaran in Calm Water

2019 ◽  
Vol 161 (A2) ◽  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Performance Prediction ◽  
Data Evaluation ◽  
Empirical Equations ◽  
Calm Water ◽  
Semi Empirical ◽  
The Mathematical Model ◽  
Comparison With Experimental Data

In this paper, an attempt has been made to predict the performance of a planing catamaran using a mathematical model. Catamarans subjected to a common hydrodynamic lift, have an extra lift between the two asymmetric half bodies. In order to develop a mathematical model for performance prediction of planing catamarans, existing formulas for hydrodynamic lift calculation must be modified. Existing empirical and semi-empirical equations in the literature have been implemented and compared against available experimental data. Evaluation of lift in comparison with experimental data has been documented. Parameters influencing the interaction between demi-hulls and separation effects have been analyzed. The mathematical model for planing catamarans has been developed based on Savitsky’s method and results have been compared against experimental data. Finally, the effects of variation in hull geometry such as deadrise angle and distance between two half bodies on equilibrium trim angle, resistance and wetted surface have been examined.

scholarly journals The generation of a mathematical model of the biogas production process from organic municipal solid waste

2020 ◽  
Vol 180 ◽  
pp. 02019 ◽  
Author(s):  
Marzhan Temirbekova ◽  
Madina Aliyarova ◽  
Iliya Iliev ◽  
Aliya Yelemanova ◽  
Saule Sagintayeva
Keyword(s):  
Mathematical Model ◽  
Municipal Solid Waste ◽  
Solid Waste ◽  
Anaerobic Fermentation ◽  
Biogas Production ◽  
Biogas Plant ◽  
Model Parameters ◽  
Biochemical Processes ◽  
Biogas Plants ◽  
The Mathematical Model

This paper justifies the efficiency of the biogas collection and utilization at the MSW (municipal solid waste) landfill in Almaty with the installation of several modern biogas plants. The optimal mode of processes occurring in a biogas plant is determined by computer generated simulations. Mathematical model parameters were identified to describe biochemical processes occurring in a biogas plant. Two approaches are used to resolve the mathematical model: the finite-difference method for solving the system of differential equations and simulation modeling by using the Any Logic package. A program is written in the algorithmic language C ++. Numerous calculations were carried out, the results of which are presented in curves and their qualitative picture is consistent with the ongoing processes. The created computer program allows to make a preliminary forecast of anaerobic fermentation occurring in the bioreactor depending on volume of the substrate, methane microorganisms and temperature conditions.

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