Papers by Keyword: Mathematical Modeling

Abstract: The article describes the development of a mathematical model for a condenser-evaporator, which occupies a central position in chlorine liquefaction process. The model describes the key processes in the equipment unit: freon evaporation, chlorine condensation, change in freon level and in equipment pressure. The model is based on the equations characterizing the processes mentioned above, which makes it possible to use the model for design and calculations of non-contact heat transfer equipment with phase transitions of heat carriers of various characteristics. The simulation was carried out with the aim of further development of a condenser-evaporator control system.

Abstract: The paper presents a numerical simulation of combustion of a metallized composite solid propellant with additives of micron-and nanosized aluminum particles. The model takes into account the thermal effect of decomposition of the condensed phase, convection, diffusion, the exothermic chemical reaction in the gas phase, heating and combustion of aluminum particles in the gas flow, the flow of combustion products, the particle velocity lag relative to the gas. The effect of the Al particle size and mass fraction, emitted from the burning surface, on the burning rate is also taken into consideration.

Abstract: This paper discusses the mathematical model of powder material particles heating in the gas flow when applying plasma gas and thermal coatings. It has been assumed that while moving in the plasma, the particle is heated by convective heat transfer and radiative heat transfer. To ensure accuracy and validity of calculation, two characteristic regions have been outlined: Core, where the temperature, density, and viscosity of plasma, as well as the other parameters are assumed as constant; and the region from the core to the coated surface (substrate), where these parameters are the functions of the plasma flow coordinates. One of the assumptions is that the shape of the particles is near-spherical, and the thermal flow’s action to the particles’ surface is uniform. Special attention has been paid to correct selection of criteria , which allowed to simplify the solution and reduce it to the ordinary first-order differential equation derived from the particle heat balance equation.

Abstract: Knowledge of human potential and especially labor resources implies a system of indicators, a quantitative and qualitative analysis that is complex and truthful at all levels. Human resources are changing in size and features in an organization. We intend to represent the human resources of an organization and the changes they undergo by using mathematical modeling, differential equations and even default probabilities.

Abstract: The blanking operation have several die design parameters which affect the quality of the blank and its productivity. The main input parameters are sheet thickness and the punch and die clearance and the dependent output parameters are tool life and the burr height. The selected values should be in optimal value. The optimum value is achieved by using the genetic algorithm. The genetic algorithm is an optimization process to find the better results as an output. Then the development of mathematical modeling by using the equations derived from the multiple regression analysis is performed. It is achieved by converting the linear equations into the matrix form and then solving it using mathematical relations. This output is compared with the genetic algorithm results, to get the better results.

Abstract: Cooling has been used for the preservation of fresh produce such as fruit and vegetables due to its low cost and high effectiveness in maintaining the product quality. Recently, several researchers have conducted theoretical and experimental studies for obtaining the kinetics of cooling and cooling time for fruits with different geometries. Present work, therefore, aims to simulate the cooling of fruits with particular reference to banana, orange, strawberry and Tahiti lemon. The transient heat conduction equation and its analytical solution using Galerkin based integral method are presented. It has been found that the strawberry has lower dimensionless cooling time compared with time required to cool other fruits, which is due to its higher surface area/volume ratio value. In orange and lemon the temperature distribution was found to be homogeneous in the angular direction, while in banana and strawberry it was two-dimensional due to shape of the fruits.

Abstract: This work presents a mathematical modeling and numerical solution of dispersion of pollutants in the atmosphere. The equations of conservation of mass, amount of movement, energy and a chemical species are solved by the Finite Volume Method in Cartesian coordinates and the turbulence closure is based on the Reynolds averages (RANS models), using the model k-ε for the determination of the fields of velocity, temperature and, in a specific case, concentration of pollutant. The numerical results are compared with data from the classic Prairie Grass experiment, showing excellent agreement.

Abstract: Current work is devoted to the problems of mathematical modeling of electrically polarized nanomaterials using LAMMPS software. There are next methods in this software for modeling of such kind: the fluctuating charge method; the adiabatic core-shell method; the thermalized Drude dipole method. This work provides information on advantages and disadvantages of each method; well-structured scripts for LAMMPS software. As our primary research is devoted to the crystalline elastic materials, much attention is given to the 1st and 2nd methods. Main purpose of research is to build models for zinc oxide (ZnO) for identification of elastic and piezoelectric constants and behavior of nanostructures in different fields. Results for analysis are given in figures and tables.

Abstract: The results of theoretical and experimental studies of the synthesis process by the electric sintering of aluminum is a matrix composite. The mathematical model takes into account the conjugate heat transfer and porosity evolution.

Abstract: To describe the explosive flow in thin tubes the model of vapor-liquid mixture with heat and mass transfer in two-dimensional axisymmetric formulation is employed. The phase transformation is significantly amplified with increasing of initial saturation temperature. The radial expansion of the jet outflow occurs due to the intensification of vaporization from cylindrical to conical form and parabolic form for supercritical initial state. Another problem applied to the outflow of a detonation wave in liquid filled with chemically active gas bubbles from the thin cylindrical tube. Modeling shows the important role of the opening angle of the outflow jet, which can either support the detonation or put it down.