Наведена методика визначення температури заготовок печі графітування Кастнера. Сформоване рівняння енергетичного балансу печі, в якому враховується кількість підведеної електричної енергії з урахуванням її втрат в пічних трансформаторах, випрямлювачах і супутньому обладнанні; корисні витрати енергії на нагрівання заготовок; паразитні витрати на прямий нагрів теплоізоляції, компенсаційної вставки та струмовідводу; витрати на нагрів та випаровування вологи з теплоізоляції, втрати з поверхні заготовок в навколишнє середовище і витрати енергії на ендотермічну реакцію газифікації. Розрахунками на чисельній моделі механічного та теплоелектричного стану печей Кастнера визначені температурні залежності коефіцієнта пропорційності паразитних витрат теплоти і ефективного коефіцієнта теплопередачі від поверхні заготовок в навколишнє середовище.

The method of the temperature determination of the blanks of the Castner furnace of graphitization is shown. The equation of the energy balance of the furnace, which takes into account the amount of electrical energy supplied, taking into account its losses in furnace transformers, rectifiers and additional equipment; useful energy consumption for heating the blanks; parasitic consumption for direct heat the thermal insulation, compensated insertion and lead-out of current; the cost of heating and evaporation of moisture from the thermal insulation, losses from the surface of the blanks to the environment and energy costs for the endothermic reaction of gasification are formed. The useful energy expenses for heating blanks for any time since the beginning of the campaign are determined from the heat balance equation Parasitic expenses of active electric energy for direct heating of the thermal insulation, compensation insertion and lead-in of current are determined depending on the amount fed to the furnace of electricity and an effective proportionality factor. The loss of active energy from the surface of the blanks through the layer of the thermal insulation into the environment is determined taking into account the effective heat transfer coefficient, change in the temperature and the time since the beginning of the graphing campaign, and includes the energy consumption for heating and evaporation of moisture from the thermal insulation ,also on the endothermic reaction of gasification. To determine the temperature dependence of the effective coefficient of proportionality and effective heat transfer coefficient from the surface of the blanks, the results of a series of calculated estimates of the heat-power state of the Castner furnace, which are executed on a numerical model of their mechanical and heat-electric state were used. The named model was tested on the data of field experiments on the Castner furnace and takes into account the losses of electricity to the furnace entrance, the heat consumption for heating the thermal insulation, the evaporation of moisture from it, and the endothermic reaction of gasification. Depending on the effective coefficient of proportionality from temperature, three areas are distinguished: the first one is in the range of 0...1500 °C, which is characterized by a decrease in this coefficient, which is associated with a sharp decrease in the specific electrical resistance of the array (billet-insulation); the second is - in the temperature range of 1501...2250 °C and the third is in the temperature range of 2251...3000 °C, in which the coefficient of proportionality increases with temperature, which is associated with an increase in the specific electrical resistance. In the temperature dependence of the effective heat transfer coefficient, two regions are distinguished: the first one is in the range of temperatures up to 250 °C, in which the heat transfer coefficient, which is associated with the constant evaporation of moisture from the thermal insulation; the second (the temperature range 251...1800 °C), in which the effective heat transfer coefficient slightly increases with increasing temperature. For the practical determination of the average mass temperature of the blanks in the Castner furnace, the method of time discretization is used for the time-scale sampling, where the unknown value of the average temperature T for any time interval from the beginning of the graphing campaign is determined by the chord method. The output data includes the characteristics of coal blanks, the initial average mass temperature of the furnace and the electrical characteristics of the furnace. The practical calculations of the average mass temperature of the blanks in the furnace of graphite are executed by one of the Castner technology campaigns, which coincide well with the results obtained on the numerical model of the mechanical and heat-electric state of the furnace. This allows us to recommend the developed methodology for practical use in the development of the automated control system of the process of grapheming in the Castner furnace

Наведено методику й алгоритм розв’язання нелінійних нестаціонарних задач теплопровідності з внутрішніми джерелами теплоти методом скінченних елементів (МСЕ). На базі програмного забезпечення Mathcad розроблено авторський програмний код для розв’язання поставленої задачі, за результатами виконання якого проведено порівняльний аналіз з даними точних розв’язків та з результатами числових розв’язків, отриманими за допомогою програмних продуктів Matlab

Methodology and effective solving algorithm of non-linear dynamic problems of thermal and electric conductivity with significant temperature dependence of thermal and physical properties are given on the basis of finite element method (FEM) and Newton linearization method. Discrete equations system FEM was obtained with the use of Galerkin method, where the main function is the finite element form function. The methodology based on successive solving problems of thermal and electrical conductivity has been examined in the work in order to minimize the requirements for calculating resources (RAM. in particular). Having used Mathcad software original programming code was developed to solve the given problem. After investigation of the received results, comparative analyses of accurate solution data and results of numerical solutions, obtained with the use of Matlab programming products, was held. The geometry of one fourth part of the finite sized cylinder was used to test the given numerical model. The discretization of the calculation part was fulfilled using the open programming software for automated Gmsh nets with tetrahedral units, while ParaView, which is an open programming code as well, was used to visualize the calculation results. It was found out that the maximum value violation of potential and temperature determination doesn`t exceed 0,2-0,83% in the given work according to the problem conditions

We have experimentally studied the thermal and electric state of the Castner furnace, which allows adjusting and verifying the numerical data-based model. The analyzed physical experiment findings show that the billets which contact with a large volume of insulation material within a certain temperature range have a slightly reduced heating rate, which is probably due to the fact that some heat is spent on evaporation and further gasification of the carbon material. We have also found that the use of a ring-shaped inter-electrode gasket affects the temperature distribution in the fore part of the electrode billets since the shape of the gasket allows reducing the temperature difference along the axis of the central pieces. The obtained values of the water temperature spent on cooling of the electrical shunt allowed calculating an effective coefficient for the heat transfer from the surface of the graphite shunt to the cooling belt. The study has proved that the effective heat transfer coefficient has a constant value till the shunt surface temperature reaches the rate of 140 °C. If the temperature exceeds this level, the coefficient value grows because of the lower thermal contact resistance between the cooling belt and the graphite shunt due to the thermal expansion of the latter.

The results of numeric modeling of the nature of supersonic turbulent flows interaction in the field of inclined from the windward side plane of the step for thecanting angle β = 8, 25, 90° and Mach numbers M∞ = 2,9, 2,94. The Navier-Stokes equations averaged by Reynolds with the usage of turbulent model were used as a mathematical model k-ω SST for viscous compressed environment. Comparative analysis of the pressure distribution and surface friction with gained experimental data was held.

The study suggests that the problems of interactions of turbulent flows at the supersonic flow around aircraft elements be solved by numerical analysis methods aided by a mathematical model that is based on the system of the Reynolds-averaged Navier-Stokes equations. The system includes the k-ω SST turbulence model for viscous compressible medium (with two scalar equations of turbulent kinetic energy and relative velocity of its dissipation with the modification that takes into account the transfer of shear stress). The paper presents applied testing and verification of the model along with examples of the problems on supersonic flows around a flat wall and a sphenoid superstructure as well as a perpendicular gas stream. We have identified physical characteristics of interactions between the condensation wave and the boundary turbulent layer, which manifest themselves in the formation of a complex structure of disconnecting and connecting zones of a boundary turbulent layer, which are characterized by respective lines of separation and joining on the wrap surface. The solutions adequately reflect the pattern of the supersonic flow of a compressible medium, condensation waves and vortex zones that are commonly observed during field studies. The comparative analysis of the results of numerical modeling and experimental data confirms the applicability of the mathematical model for complex tasks of the supersonic gas-dynamic state.

Проаналізовано ефективність застосування печей графітування Кастнера й потреби сучасного ринку виробництва графітованих електродів. Показано основні тенденції розвитку нової технології на вітчизняному ринку