Mathematical Model For Calculation Research Articles

Mathematical model and method of solving the generalized Dirichle problem of heat exchange of a cut count

The choice of thermal protection of the rocket fairing is approached with special care, because the fairing must protect against aerodynamic heating, radiation, temperature changes. Currents with large Mach numbers are accompanied by gas-dynamic and physicochemical effects. When flowing around the blunt body, a shock wave is formed, which departs from the body, remaining in the vicinity of the frontal point almost equidistant to its surface. Physico-chemical effects are due to rising temperatures caused by the inhibition of gas by the shock wave. At the same time there is a transition of kinetic energy of a stream rushing in thermal, fluctuating degrees of freedoms of gas molecules are excited, its dissociation and even ionization begins. Therefore, among the problems of great theoretical and practical interest is the problem of studying the temperature fields arising in the fairings for missiles in the form of a truncated cone, which rotate around its axis, given the finiteness of the rate of heat propagation. In the article the mathematical model of calculation of temperature fields for a truncated cone is constructed for the first time which approximately models distribution of temperature fields which arise in fairings for rockets, with taking into account the angular velocity and the final speed heat distribution in the form of a boundary value problem of mathematical physics for hyperbolic equation of thermal conduc-tivity with boundary conditions Dirichlet. A new integral transformation for a two-dimensional finite space is constructed, in the application of which the temperature field in the form of a convergent series is found. The solution found can be used to predict the possible value of thermomechanical stresses, to promote the correct choice of technological parameters, objective control, allows to identify ways to improve the thermal protection of fairings for missiles.

Accounting for arterial and capillary blood gases for calculation of cerebral blood flow in preterm infants

One of the most feared neurological complications of premature birth is intraventricular hemorrhage, frequently triggered by fluctuations in cerebral blood flow (CBF). Although several techniques for CBF measurement have been developed, they are not part of clinical routine in neonatal intensive care. A promising tool for monitoring of CBF is its numerical assessment using standard clinical parameters such as mean arterial pressure, carbon dioxide partial pressure (pCO2) and oxygen partial pressure (pO2). A standard blood gas analysis is performed on arterial blood. In neonates, capillary blood is widely used for analysis of blood gas parameters. The purpose of this study was the assessment of differences between arterial and capillary analysis of blood gases and adjustment of the mathematical model for CBF calculation to capillary values. The statistical analysis of pCO2 and pO2 values collected from 254 preterm infants with a gestational age of 23–30 weeks revealed no significant differences between arterial and capillary pCO2 and significantly lower values for capillary pO2. The estimated mean differences between arterial and capillary pO2 of 15.15 mmHg (2.02 kPa) resulted in a significantly higher CBF calculated for capillary pO2 compared to CBF calculated for arterial pO2. Two methods for correction of capillary pO2 were proposed and compared, one based on the mean difference and another one based on a regression model.Conclusion: Capillary blood gas analysis with correction for pO2 as proposed in the present work is an acceptable alternative to arterial sampling for the assessment of CBF.What is Known:• Arterial blood analysis is the gold standard in clinical practice. However, capillary blood is widely used for estimating blood gas parameters.• There is no significant difference between the arterial and capillary pCO2values, but the capillary pO2differs significantly from the arterial one.What is New:• The lower capillary pO2values yield significantly higher values of calculated CBF compared to CBF computed from arterial pO2measurements.• Two correction methods for the adjustment of capillary pO2 to arterial pO2that made the difference in the calculated CBF insignificant have been proposed.

CFD-МОДЕЛИРОВАНИЕ ПОТОКОВ В НЕПОДВИЖНОМ СЛОЕ АДСОРБЕНТА ДЛЯ ПРОЦЕССА КОРОТКОЦИКЛОВОЙ БЕЗНАГРЕВНОЙ АДСОРБЦИИ ПРИ ОЧИСТКЕ ВОДОРОДА

The paper presents the results of numerical studies of the aerodynamic structure of the flow in a fixed layer of granular adsorbent in the adsorber of a pressure swing adsorption (PSA) unit for synthesis gas separation and hydrogen purification. Сomputational experiments were conducted in COMSOL Multiphysics software using 1-D and 2-D mathematical models to calculate the velocity field in the bulk layer of the 13X adsorbent for the PSA process of hydrogen purification. When assessing the accuracy of calculating the aerodynamic structure of the gas flow in the adsorbent, it was found that the use of a 2-D mathematical model provides an increase in the accuracy of calculations by an average of ~ 1-2% compared with the 1-D model. It is determined that when using an adsorbent with a particle diameter of more than 2 mm in the PSA unit, the use of 2-D and 3-D mathematical models for calculations is promising at speeds of more than 0.3 m/s, due to an increase in the velocity divergence in the center of the vertical cylindrical adsorber and on its walls

Mathematical simulation of the economic-energy parameters of the engine 4DC-125/110 supplied with mixed fuel based on thermal calculation

The article presents a mathematical model of thermodynamic calculation of compression ignition engines. The 4DC-125/110 engine was chosen as an example, and on the basis of the mathematical model, its energy and economic performances were simulated supplying various types of fuel to identify the best operation results.

ЧИСЛЕННАЯ МОДЕЛЬ ОГНЕНЕПРОНИЦАЕМОСТИ ЭЛЕМЕНТОВ ГАЗОТУРБИННЫХ ДВИГАТЕЛЕЙ ИЗ АЛЮМИНИЕВЫХ СПЛАВОВ

For the early stages of design, a numerical model of fire resistance and fire permeability of GTE elements made of alu-minum alloys is proposed. The numerical model is based on the solution of three-dimensional Navier-Stokes equations, closed by a two-parameter isotropic SST – turbulence model. We used an implicit pressure solver and a scheme of second-order accuracy in High Resolution space, which allows lowering the approximation order to the first in the areas of solution discontinuities and high gradients to increase the monotonicity and stability of the solution. Additionally, to achieve the solution stability, the High Speed Numerics solver option was used, activating the solver settings Gradient Factor Relaxation = 0.1 and Blend Factor Relaxation = 0.1. The mathematical model for the thermal-hydraulic calculation was set up in the formulation of the coupled heat transfer, taking into account radiation based on the discrete transfer model of the Participating Media. The influ-ence of the degree of blackness on the results of the numerical model is investigated and the most rational radiation model is chosen. The numerical model was validated according to the results of engineering tests on the fire permeability of the plate not cooled by the air flow using a kerosene burner NexGen of the bench Ts17-G3 of FAU P.I. Baranov TsIAM. The obtained results of calculations on fire permeability are comparable with the experimental data both quantitatively and qualitatively. The developed un-steady numerical model of fire permeability of flat plates of aluminum alloys under conditions of free convection can be used in the de-sign of the fan housing by selecting the most rational structural and layout solutions, such as the thickness of the housing, the presence of fire protection coating, cooling intensity, etc.

РАЗРАБОТКА РАСЧЕТНОЙ МОДЕЛИ НАПРЯЖЕННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ ПОЛУСФЕРИЧЕСКОЙ ЗАГОТОВКИ НА НАЧАЛЬНОЙ СТАДИИ ПРОЦЕССА ВЫТЯЖКИ

The automotive industry is developing at a fairly high pace. At the present stage of development of our society, the demands of consumers for these products are increasing more and more. In turn, this forces vehicle manufacturers to improve paint coatings, expand the color gamut, in order to increase the competitiveness of their products. The more modern the generation of the car, the more difficult the paintwork, therefore, the restoration operations. In this regard, the role of the importance of the quality of bodywork performance comes to the fore. Currently, car repair is a profitable business. If the repair of components and assemblies, as well as maintenance, many motorists perform on their own, then the repair of body parts is not for everyone. In addition to specific equipment that allows you to give the original shape to the details, you need work experience, knowledge of modern materials and features of their use. The technological process of modern bodywork has become much more complicated. The main task is the process of reducing labor intensity, financial costs, as well as optimizing the process. When cars collide, folds form on the body parts as a result of bending forces or as a result of loss of stability from compressive forces. Therefore, almost all automotive deformations can be characterized as metal folds of different radius of curvature. This article discusses the calculated assessment of stresses and deformations at the initial stage of a new extraction method using a hemispherical workpiece, which allows to provide favorable deformation conditions and, consequently, to increase the extraction coefficient (K= D/d). A mathematical model of stress and strain calculation implemented on a computer is proposed.

Mathematical Models for Calculation of the Parameters of the Bank and the Borrower in the Mortgage Lending

The article covers the consideration of the issues of analysis and development of mathematical models to improve the efficiency of the mortgage lending system. The relevance of the study is due to the fact that the current mechanisms of mortgage lending in Russia do not correspond to global trends: by interest rates level; in terms of the volume of loans issued and other conditions. However, it is one of the main tools that allows to improve the population’s living conditions and, as a result, to release the socio-economic tension caused by this factor, as well as to attract additional input in the investment and construction sector, which in modern conditions is one of the most important problems. As a result of the research carried out, the article offers a mathematical model for calculating the parameters of the bank and the borrower, in order to form the most acceptable conditions for the loan. In the mathematical model, such parameters of the borrower and the lender as the price of the apartment, the percentage of the down payment from its price, the mortgage loan rate, the total debt and the loan term, as well as the share of the borrower's income allocated to monthly payments are interconnected. This model will allow the bank to determine the most suitable loan conditions regarding the payment amount, term, and available credit limit, and the borrower to calculate the parameters of the loan in order to make an informed decision on attracting it. All this, in the end, will allow banks to reduce the level of risk on issued mortgage loans, and the borrower — confidence in the ability to pay off the mortgage loan.

A simplified mathematical model for total temperature rise calculation in non-oriented silicon steel cold rolling deformation zone

In tandem cold rolling, the control of the temperature of high-grade non-oriented silicon steel is a difficult problem for its large deformation resistance and the preheating procedure before rolling. And it is complicated to calculate the total temperature rise of rolling deformation zone due to the comprehensive influence of the plastic deformation heat, the friction heat and the contact heat loss. So, to precisely calculate the total temperature rise, firstly, based on the four classical cold rolling force formulas, the initial total temperature rise calculation models are established correspondingly by theoretically analyzing the temperature rise of deformation heat, the temperature rise of friction heat and the temperature drop of contact heat loss; then, the model based on the improved Lian rolling force formula is adopted, which leads to calculated best matching the measured temperature; finally, considering the complex formula calculation of the initial model, based on the influences of different rolling parameters on the total temperature rise, a simplified model for convenient calculation is proposed by the nonlinear regression analysis of the initial model calculation results and main rolling parameters, which is convenient for the actual application by the field technicians.

Method of multiscale coincidence of pulses for measuring temporary loads from moving vehicles in bridges and overpasses

Modern development of road transport is characterized by constant updating of the nomenclature of cars (including heavy-duty vehicles), by increasing of intensity and speed of their movement, especially in large metropolises and on roads of national and local significance. This complicates the operating conditions of spans of highway bridges to some extent, leads to their damage and early wear. The deterioration of the technical condition of the structures of the spans is largely due to the increased dynamic impact of the cars on the bridges. The purpose of this article is to measure the amplitude of oscillations of a bridge structure from temporary loads of rolling stock with non-periodic long-term loading by optical methods. In accordance with this goal, it is necessary to develop a technique and device for measuring the amplitude of oscillations of the bridge structure by converting the amplitude of oscillations in time intervals and their subsequent measurement by multi-scale pulse coincidence. In a number of works, digital deployment systems that use number systems with different bases, represented by a family of deployment functions, are considered in detail.
 Such digital systems in general, are described by the corresponding operating scheme. According to this operating scheme, a method of multiscale matching for measuring time intervals was developed, which formed the basis for measuring the vibration amplitude of the bridge structure. The given mathematical model of calculation of the number of measurement channels was used in the synthesis of velocity transducers and linear displacements based on optical (laser) deployment systems, information conversion devices of radar velocity sensors based on the Doppler effect. Similarly, a frequency comparison device, a digital frequency meter, a digital phase meter, and a number of other frequency-time group devices were synthesized.

Elastic shear buckling coefficients for diagonally stiffened webs

In this paper, the characterisation of the elastic shear buckling behaviour of simply supported plates diagonally stiffened excluding the influence of direct stresses is made. Two broad numerical parametric studies consisting of linear buckling analysis by the finite element method are performed, covering the entire practical range of critical parameters like the aspect ratio and the stiffener’s mechanical properties. In the first parametric study, attention is given to the influence of each parameter in the elastic critical shear stress. For that reason, a beam FE is chosen to model the stiffener, allowing the variation of each parameter individually. As it is systematically disregarded in previous studies, particular attention is given to the effect of the stiffener’s torsional rigidity. The numerical models used in the second parametric study consist of full-shell FE, and the results are used to perform regression analysis that ultimately allowed to proposed two mathematical models for the analytical calculation of the elastic shear buckling coefficient: for open stiffeners over the compression diagonal and for closed cross-section stiffeners over the compression diagonal. The proposed mathematical models present excellent accuracy.

Model of pulsating current traction motor taking into consideration magnetic losses in steel

The aim of the work is to develop a mathematical model of the traction motor of the pulsating current of an electric locomotive taking into account the magnetic losses in the motor steel to determine the starting parameters depending on the voltage of the armature winding. Methodology. Mathematical modeling of electromagnetic processes in a traction motor of pulsating current is applied taking into account the nonlinear nature of the armature inductance, the inductance of the excitation winding and the nonlinear nature of the universal magnetic characteristic. The magnetic losses in the steel of the traction motor were taken into account by establishing the dependence of these losses on the frequency of reversal, the magnetic flux in the magnetic circuit of the motor and the geometric dimensions of the motor. Results. The mathematical model of calculation of starting parameters of the traction engine of the pulsating current of the traction drive of the electric locomotive of alternating current taking into account the equation of instantaneous value of losses in engine steel is developed. The dynamic characteristics of the traction motor with pulsating current are obtained. It allows to investigate starting parameters of the traction engine on the basis of the received mathematical model and to design elements of the traction drive of the electric locomotive according to the specification, to choose optimum design parameters. Originality. For the first time a comprehensive study of the pulsating current traction motor was carried out taking into account the nonlinear nature of the armature inductance, excitation winding inductance and nonlinear nature of the universal magnetic characteristic and taking into account the magnetic losses in the motor steel. Practical significance. The model of the traction motor of pulsating current taking into account losses in steel of the engine on the basis of the carried-out calculation is developed. Experimental studies have confirmed the adequacy of the model, which allows to apply the obtained model to develop a mathematical model of an AC electric locomotive to study the electrodynamic processes in it at different modes of operation of the electric locomotive.

Error analysis of the cutting machine step adjustable drive

The implementation precision of a number of adjustment bodies of a metal-cutting machine is also the most important indicator of its quality, a strictly standardized industry standard, technical conditions for manufacturing and acceptance. Moreover, the standard for limiting the error is set depending on the used denominator of the series. An essential feature of the precision of the series being implemented is that it is determined not by an error in parts’ manufacturing, but by the disadvantages of the used method of kinematic calculation. The established modes largely determine the efficiency of processing on metal-cutting machines. If the setting is set to an underestimated mode, then the performance is reduced accordingly. In the case of the mode overestimation, this leads to a decrease in durability and losses due to increased regrinding and tool changes. Creation of a complex of mathematical models for the design kinematic calculation of the metal-cutting machines’ main movement drive, which allows reducing the error in the implementation of a series of preferred numbers and increasing machining precision. The article provides a mathematical complex for analyzing the total error components, which allows determining and evaluating the total error of the drive of a metal-cutting machine by analyzing its constituent values with high precision: errors of a permanent part, errors of a multiplier part, rounding errors of standard numbers, errors in the electric motor and belt transmission. The presented complex helps to identify the role of the rounding error of preferred numbers in the total relative error formation and makes it possible to reduce it, which allows solving the problem of increasing the step adjustable drive precision. When using a mathematical complex, a fundamentally new opportunity for creating a scientific base appears, developing algorithms and programs for engineering calculation of tables that facilitate the selection of the numbers of teeth for multiple groups, structures and guaranteeing high precision of the implemented series.

Research of the reasons of increased drop in cotton seeds after generation with reduced density of raw roller

Results of researches on definition of influence of density of the raw roller on pubescence of cotton seeds are given in article. The received mathematical model for calculation of contact pressure and movement of the raw roller in the form of a system from six equations with six unknown. The numerical results calculated on the computer. Sizes of shift and contact pressure for the set physic-mechanical and geometrical parameters of a system are determined. It is established that contact pressure significantly depends on elasticity (density) and angular speed of the raw roller. On the basis of the graphic data of contact pressure and contact movement of the raw roller received results of calculations the conclusion that with reduction of density of the raw roller conditions of capture of a short cotton slice worsen. The fact that the contact pressure and movement fluctuate during time is the reason of it, i.e. in the beginning the short cotton slice contacts to a saw, but during fractions of a second this contact is lost, also contact pressure similarly changes. Results of theoretical researches proved increase in a full pubescence of seeds after gin with reduction of density of the raw roller, i.e. one of the reasons of it is deterioration in conditions of capture of short cotton slices a saw - fluctuations of contact pressure and contact movement of the raw roller.

Methods Improving Energy Efficiency of Photovoltaic Systems Operating under Partial Shading

This article is devoted to the relevant problem of increasing the efficiency of PV systems. The presented analysis discusses the available methods for improving the power generation of PV modules under partial shading. Mathematical models for power loss calculation were compiled based on the results of this analysis. The proposed approach minimizes the negative impact of partial shading on the energy production of PV modules. It is based on the equalization of voltages of parallel-connected arrays of modules by installing additional power elements in them. The proposed solution is promising for various areas; it allows for the minimization of the unfavorable influence of existing urban objects (buildings, trees, communications, etc.) on the energy efficiency of PV modules. The obtained results are useful for the sustainable development of the urban environment in the context of digital transformation. They are the basis for the promising methodology of the parametric optimization of power plants using renewable energy sources.

Mathematical model for reliability indicators calculation of tethered UAV hybrid navigation system

The mathematical model for reliability indicators calculation of the hybrid navigation system containing microwave and technical vision subsystems is proposed in this paper for the first time. The proposed method is based on the translation matrix concept of solutions to the Kolmogorov equation system and it allows us to obtain the mathematical expression of availability factor, downtime ratio, and other reliability indicators. Also the presented approach allows finding the reliability indicators for the cases of jump change of transition intensities caused by external influences. Besides the analytical method can be used for investigation of hybrid navigation system transient mode functioning. The results of the numerical calculations clearly demonstrated correctness of the proposed approach.

Analysis of main affecting factors about automobile fuel consumption testing based on ultrasonic technology

In view of the problems existing in automobile fuel consumption testing, ultrasonic technology is used to study automobile fuel consumption testing technology. Based on the mathematical calculation model of automobile fuel consumption testing as ultrasonic jet lag method, a detailed analysis is carried out from the temperature and ultrasonic flow sensors receive uneven and asymmetric signal strength and ultrasonic downstream and counter current experience time-test errors and the distributed fuel flow speed in the supply line, and improvement measures are proposed. The results show that a comprehensive analysis of the main factors that affect automobile fuel consumption testing, and optimization measures are proposed, which can further optimize the mathematical model of automobile fuel consumption testing, and the accuracy of the vehicle fuel consumption sound test can reach 10 ns.

MODEL OF EVALUATION THE FEASIBILITY OF INDUSTRIAL CUSTOMERS TO HOURLY ACCOUNTING OF RETAIL ELECTRICITY MARKET


 
 
 The main differences in pricing and tariffing for industrial consumers of electricity with different forms of electricity metering are considered. Based on the analysis of tariff formation for the final consumer of electricity, components are identified that have a significant impact on the results of solving the problem of assessing the feasibility of the consumer's transition to hourly electricity metering. Such components include the cost of purchasing electricity in the market segment "day ahead" and the cost of accrued imbalances. The relative daily profile of electricity consumption is considered in order to study the influence of the features of the daily load schedule on the weighted average daily market price of electricity. The importance of estimating the cost of daily load profiles when comparing the cost of electricity for the consumer in the group with integrated electricity metering and in terms of individual hourly metering is substantiated. The effect of underestimation of volumes and value of imbalances in the group with integrated electricity metering in comparison with hourly accruals of volumes and value of imbalances is theoretically substantiated. The main components for comparative assessment of the expediency of the consumer's exit from the group with integrated metering of electricity and the transition to its hourly metering according to the individual daily load schedule are identified. Mathematical models for comparative calculations are developed. The use of these models allows to make an economically justified decision on the expediency of the consumer leaving the group without hourly metering of electricity to the model of purchasing electricity with hourly metering. The main approaches to such an assessment are demonstrated on the example of calculations for an industrial enterprise in some regions of Ukraine. Bibl. 15, fig. 3.
 
 

Theoretical study on the leakage characteristics of Disc-Seal Single Screw Pump used in oily sludge waste heat source absorption refrigeration system

The disc-seal single screw pump (DSSP) used in the field of oily sludge transport has a huge advantage. However, there is no research on the leakage characteristics of the DSSP at present, which makes its application limited. Therefore, the mathematical calculation model of leakage amount of each leakage channel was established in this paper according to the geometric model of the leakage channel. By using this mathematical model, the influence rule of working parameters on the leakage characteristics was analyzed. The results show that the total leakage amount per unit time of the DSSP varies periodically with the rotation of the screw, and the total leakage per unit time of the DSSP will increase with the increase of outlet pressure and screw rotation velocity. When the dynamic viscosity coefficient of the medium increases, the corresponding leakage will be reduced, in which the transmission medium dynamic viscosity is the main factor affecting the total leakage of the DSSP. The study of the leakage characteristics of the DSSP can provide a theoretical basis for the optimal design of its structure in the future.

Environmental Impact of District Heating System Retrofitting

Retrofitting of district heating systems is a comprehensive process which covers all stages of district heating (DH) systems: production, distribution and consumption. This study quantitatively shows the effect of retrofitting measures and represents strengths and weaknesses of different development scenarios. Improvements in production units show improvements in fuel use efficiency and thus indirectly reduce CO2 emissions due to unburned fuel. For this purpose, validated district planning tools have been used. Tool uses mathematical model for calculation and evaluation of all three main components of the DH system. For the quantitative evaluation, nine efficiency and balance indicators were used. For each indicator, recommended boundary values were proposed. In total, six simulation scenarios were simulated, and the last scenario have shown significant reduction in CO2 emissions by 40% (from 3376 to 2000 t CO2 compared to the actual state), while share of biomass has reached 47%.

Heat Transfer Simulation Study of Hot Oil Tubes Based on COMSOL

Heat insulation board is added on the adjacent side of hot oil pipeline and other pipelines to increase thermal resistance and reduce the influence of hot oil pipeline on the temperature of the pipeline. Because the heat conduction problem of the soil around the hot oil pipeline after the addition of eat insulation board becomes very complex, this paper studies and analyzes the heat transfer process of the hot oil pipeline through constructing an equivalent simplified mathematical calculation model and heat transfer simulation based on COMSOL.