Mathematical Model For Calculation Research Articles

A Revised Model for Calculating HV Cable Sheath Current Under Short-Circuit Fault Condition and Its Application for Fault Location—Part 1: The Revised Model

This two-part paper proposes a revised method for calculating high voltage (HV) cable sheath currents, and for fault location of cross-bonded HV cable systems. The equivalent circuit and the cable impedance per unit length under short-circuit fault conditions are revised from those under non-fault conditions. Part 1 of this paper proposes a revised phasor domain mathematical model for the sheath current calculation under fault conditions, following demonstration that short-circuit faults can cause changes in the equivalent circuit of the cable metal sheath, and cause changes in the cable impedance per unit length. The calculation results, as given in a case study, show that there exists a unique relation between the fault position and the sheath fault currents, making it possible to locate a fault by analyzing the characteristics of the sheath currents during a fault. Part 2 of the paper focuses on the fault location method via sheath current monitoring.

Math modeling of heat and mass transfer processes during coal-water fuel gasification

In article the current state of gasification technologies in Russia and in the world is analysed. The perspective directions of development of process – entrained flow gasification of coal-water fuel for the purpose of producing syngas for further catalytic conversion and producing chemicals are defined. The mathematical model of thermophysical characteristics calculation of process is presented. Determination results of design parametrs of a gasifier are given.

Carbon footprint of the photovoltaic power supply chain in China

With the increasing consumption of fossil fuels, environmental problems are becoming increasingly serious. To solve these problems, we must vigorously develop clean energy. To this end, China has promulgated many policies to support the development of photovoltaic energy. To study the carbon footprint of the photovoltaic power supply chain and calculate the reduction of carbon emissions, this article establishes a carbon emission mathematical calculation model for photovoltaic power generation systems during the production, transportation and waste treatment processes. The carbon emission reduction model is established by calculating the power consumption of the photovoltaic power supply chain and power generation throughout the life cycle and by using the 1 kW photovoltaic power generation system as an example to analyse the data. The results show that from the perspective of the supply chain, it can effectively reduce carbon emissions from photovoltaic power supply chains by improving raw material development technology to provide high development efficiency, optimizing parts production processes, replacing transportation vehicles with electric vehicles gradually, increasing waste recycling efficiency, and improving waste disposal methods. In 2017, compared with thermal power generation in China, photovoltaic power generation systems were used in areas where the solar radiation is effective for 1000 h–3000 h, the CO2 emission reduction could be considered to be between 1.738 GT and 3.078 GT, which have shown good carbon emission reduction effect.

Surface residual stress distribution for face gear under grinding with a long-radius disk wheel

Face gear transmission has been widely used because of its unique technical advantages. The residual stress of a tooth surface after grinding is the key factor affecting the surface quality of gear teeth. To improve the performance of tooth surfaces and better guide the grinding test, it is necessary to develop a method to analyse the residual stress of face gear after grinding with a long-radius disk wheel. First, a mathematical model of the grinding face gear with a long-radius disk wheel is established. Then, the basic parameters affecting face gear grinding are studied, and mathematical calculation models, including the grinding force and grinding heat, are established. On this basis, the three processes of elastic loading, plastic deformation and stress release are studied, and a mathematical model of the residual stress of face gear grinding is established. Finally, face gear grinding tests are carried out; the residual stress is determined, and the model is verified by experimental data. Through the study of the surface residual stress distribution of face gear under grinding with a long-radius disk wheel, the grinding process can be further guided to improve the grinding quality and can be extended to the analysis of residual stress distribution after grinding of other complex surface parts.

A mathematical calculation model of replacement fluid and citric acid infusion in continuous veno-venous hemofiltration

To design a mathematical calculation model for better understanding and grasping the logical problem of replacement fluid and citric acid anticoagulant infusion in continuous veno-venous hemofiltration (CVVH). (1) Parameter definition: A, B, and T were respectively called the main part of pre-replacement fluid, 5% sodium bicarbonate solution, and 4% sodium citrate infused before filter. And a and b were respectively called the main part of post-replacement fluid, and 5% sodium bicarbonate solution infused after filter. (2) Logic conversion: The liquid in back terminal (Z) was artificially divided into two parts. One (X) was the original residual plasma after filtration. The second (Y) was the part excluding the plasma, including the left part of pre-replacement fluid with sodium citrate, and the post-replacement fluid. (3) The mathematical formulas of liquid volume and electrolyte concentration at X, Y and Z in unit time were listed according to the principle of CVVH and the screening coefficient of filter for different substances. (4) The calculation formulas were entered into Excel form, and a mathematical calculation model was made, and a simulation calculation with examples was carried out. An Excel model was established by inserting the calculation formulas of volume, electrolyte, and total calcium at X, Y and Z. And it was found that the concentration of Na+, K+, Cl-, HCO3- at Y point remained unchanged only when A, B and (or) a, b was kept in same side and proportion even with the change of blood flow and other parameters without sodium citrate as anticoagulant. Once any of the parameters (such as blood flow, replacement fluid volume, etc.) were adjusted in other infusion methods (such as different ratios, different directions of the same year, etc.), the calculation results at Y would vary, and the electrolyte concentration at Z would change accordingly. A change of dilution model or parameter would result in the change of the electrolyte concentration at Y and Z with sodium citrate as anticoagulant. The concentration of total calcium scarcely changed no matter in what model and parameters. All kinds of infusion ways could be included in the Excel model. The infusion results of all kinds of infusion matching could be intuitively evaluated. It is helpful for the medical staff to make a logical analysis and risk prediction in CVVH.

Параметрическое исследование конвективного теплообмена при обтекании затупленного конуса сверхзвуковым воздушным потоком

The paper focuses on a mathematical model for the parametric calculation of convective heat transfer on the surface of a blunted cone with the supersonic airflow around it. We compared the computational data with the known experiments on the cone airflow with Mach number М∞ = 8, and found the parameters of the computational grid, which allow us to have less deviation in calculation results from the experimental data. Taking into account the recommendations developed for the selection of the computational grid, we carried out the parametric study of the supersonic airflow around cones with the different half - angels in the range of Mach numbers from 4 to 10. According to the findings of the study, we made the database that describes the influence of the parameters on the coefficient of heat transfer from the supersonic airflow to the cone surface. The data obtained can be used to optimize the geometric configuration and flight modes of high-speed aircraft.

The novel approach for electric power system simulation tools validation

The reliability and efficiency of electric power system (EPS) operation depends on the adequacy of the information about processes in the EPS. The complexity of obtaining this information lies in the need to use large-scale EPS mathematical model for calculations. Within the framework of numerical integration, a satisfactory solution of such model is hardly to be ensured; consequently, the simplifications and limitations are applied. In this regard, every obtained solution should be validated. The most reliable way of validation is to compare simulation results with field data. However, it is not always possible to receive the necessary amount of field data. The paper proposes an alternative approach for validation: the adequate reference model (RM) usage instead of field data. The prototype of hybrid real-time power system simulator having the necessary properties and capabilities is used as the RM in this paper. The adequacy of proposed approach is illustrated by the fragments of the experimental studies.

IMPROVMENT THE MATHEMATICAL MODEL FOR THE HYDRATES FORMATION CALCULATING IN THE GAS GATHERING NETWORK

Background Most gas fields are characterized by complex and branched systems for collecting and inter-field gas transportation. It should be noted that the main characteristics of gas fields are well cluster location and an extensive plume system from wells to the integrated gas treatment unit (GTU) for transportation, as well as the complex network structure of the inter-field collector. Such systems form a complex hierarchical structure, in which field information has a high degree of inaccuracy, and often there are a large number of errors in the measurements of technological parameters, such as measurements of flow, pressure and temperature. In some nodes of the gas gathering network, these data are not displayed at all or the corresponding parameters are not measured due to the lack of instrumentation. All this leads to increased consumption of chemical reagent methanol. Aims and Objectives To improve gas collection systems and reduce the consumption of chemical reagents during operation, it is necessary to analyze existing mathematical models and, based on this analysis, create a more sophisticated mathematical model of calculation that takes into account the optimal number of factors affecting the formation of hydrates in field systems. Especially this problem is relevant in the conditions of operation of wells at negative ambient temperatures, that is, in the winter period or for the fields of the Far North. Results A completely new mathematical model has been developed that allows to diagnose the formation of hydrates in the plumes of the gas gathering network prior to the integrated gas treatment unit. A formula is proposed for calculating the temperature in gas pipelines, which reflects two independent (physically meaningful) parameters that take into account the presence of a thermal boundary layer and the temperature variation along the length of the pipeline. A flowchart of the proposed mathematical model has been developed, which can be easily realized and obtained a system for diagnosing and preventing the formation of hydrates for the control units of the GTU.

The Complex Torque Coefficient Applied in Subsynchronous Oscillation Caused by HVDC

Subsynchronous oscillation is an unstable state in power system, which may damage rotors of turbine generators and break the steady operation of the power system. In China, some accidents of subsynchronous oscillations had happened in the power stations where there are HVDC projects nearby. So that it is necessary to study the Subsynchronous oscillation caused by HVDC. After analysis of the principle of subsynchronous oscillation, the mathematical calculation model of the system containing HVDC is built and analysed in method of complex torque coefficient. And the simulation model is established in PSCAD/EMTDC to prove the validation of the method of complex torque coefficient used for the system containing HVDC, which combines calculation and simulation of the method for the system.

Horizontal Bending Angle Optimization Method for Scraper Conveyor Based on Improved Bat Algorithm

The horizontal bending angle of scraper conveyor has a great influence on the running resistance, the current consumption, coal winning efficiency of the working surface, etc. Approximately 1–3° is usually the range of horizontal bending angle, but does not indicate the optimum bending angle of the coal mining face. To find the optimal horizontal bending angle, an optimization method is proposed. A mathematical calculation model of the running resistance of the scraper is established based on the direction of the shearer operation. Then, a method of adjusting the step size of the search by inertia weight and expanding fly distance range obeying the t-distribution is proposed based on the basic bat algorithm (BA). Finally, an industrial application was conducted in 21220 Changcun fully mechanized coal mining face, Henan Province. The results show that the current consumption by the scraper conveyor was reduced by 31% when the horizontal bending angle of the S-bending area was 0.66°. Meanwhile, the theoretical current has good consistency with the experimental data, and the average absolute error was 3%.

Influence factors and an evaluation method about breakthrough pressure of carbonate rocks: An experimental study on the Ordovician of carbonate rock from the Kalpin area, Tarim Basin, China

There are many oil and gas fields around the world that are sealed by tight carbonate caprocks. Compared with gypsum rocks and shales, tight carbonate caprocks are characterized by brittleness and ease of structural fracturing and dissolving in acidic groundwater. The breakthrough pressure (BP) is a significant indicator that indicates the sealing capacity of the caprocks. Therefore, we conducted a series of experiments, including effective porosity, permeability, casting thin-sections, BP, mineral composition, microstructural characteristics and clay minerals contents on carbonate samples from Ordovician system in the Kalpin area, Tarim Basin, China to research factors that affect the BP of carbonate caprocks. According to the experimental data analysis, the BP deceases with macropore proportions and increases with proportions of micropore and mesopore volume. Due to the large macropore proportion and low clay content (<10%), expansion of clay minerals with water hardly reduces effective porosity and permeability. Pore throat and cement influence effective porosity and permeability, and thus influence the BP. Generally, the BP decreases with the increase of effective porosity and permeability, and linear correlations exist between the reciprocal of effective porosity (A), −0.48 power of permeability (B) and the BP. Due to the interdependency between A and B, a principal component regression procedure (PCRP) is implemented with the statistical analysis system (SAS) software to eliminate the interdependencies and obtain a fitting formula of BP. The calculated BP with depth by this method matches gas logging results. This study provides a research idea and a mathematical calculation model of the BP of carbonate caprocks to further evaluate and predict carbonate caprocks behaviour.

Valuing the socio-economic benefits of built heritage: Local context and mathematical modeling

Abstract Socio-economic benefits of built heritage are undoubtable and identified in many research works and reports. However, their integration into actual heritage preservation processes remains a challenge due to the lack of comprehensive application methodologies. This research aims at developing the methodology for the assessment of socio-economic benefits of built heritage. As built heritage is linked with its context, the case of Lithuania was selected as an exemplary ground for methodology development. The methodology development process involves the analysis of the cost-benefit approach in heritage assessment, the analysis of classifications of social-economic benefits and values of the built heritage, the analysis of the existing institutionalized heritage assessment tools and the legal context for the built heritage assessment in Lithuania, the development of the classification of socio-economic benefits of the built heritage for the Lithuanian context and the proposals for their estimation. The proposed mathematical model for calculation of socio-economic benefits of the built heritage is spatial technique enabling to capture the synergetic effects of co-existing heritage objects using sum of scaled kernel functions that can be used in cost-benefit analysis in different contexts. The methodology was developed based on the example of Lithuania; however, the overall approach can be adapted to various contexts.

DETERMINING ZONES OF CHEMICAL POLLUTION IN THE CITIES AND ASSESMENT OF CHRONIC DISEASES RISKS

Purpose. The scientific paper is aimed at creating a methodology of chemical pollution zones in the territories of industrial cities and accounting the possibility of assessing the risks of chronic diseases. Methodology. The method of numerical calculation of nitrogen dioxide concentration in atmospheric air is based on the solution of three-dimensional impurity transfer equations, which directly comes from a permanently stationary source (industrial enterprise) and a linearly distributed source (highway). The method takes into account the process of chemical transformation of impurities and photolysis in the atmosphere. The numerical model is based on the splitting of model equations and their solution using an implicit difference scheme. Findings. The created software allows conducting computational experiments to calculate the areas of atmospheric air pollution with nitrogen dioxide, taking into account the interaction of impurities coming from various types of pollution sources and meteorological parameters. On the basis of the obtained field of nitrogen dioxide concentration, an assessment of the change in the risk of chronic intoxication associated with atmospheric air pollution with nitrogen dioxide over 50 years was carried out. Originalitys. For the first time the regularities of changes in the level of atmospheric air pollution with nitrogen dioxide have been established with due regard to the mutual influence of emissions from the industrial enterprise and highway and their chemical transformation in the atmosphere. The risk of chronic intoxication has been calculated and its changes have been analyzed with due regard to the interaction of emissions from the industrial enterprise and highway, it leads up to 10% of risk increasing. Practical value. Authors developed a mathematical model and method of numerical calculation. Software created on their base allows obtaining quickly quantitative results necessary in developing the system for monitoring the man-made loaded regions of the city. The obtained patterns of impurities dispersion allow us to estimate the levels of pollution in urban areas of the city by emissions from industrial enterprises and highways. Accounting of the mutual impact of emissions and the calculation of risks of intoxication allows solving environmental problems arising in the development of transport strategy in cities.

Features of the mathematical model for the control forces calculation of the four-wheeled robot

The article discusses the issue of determining program forces in drives of a four-wheel robotic platform - the issue of opening the uncertainty of the equations system. The motion laws are synthesized on the basis of application of the calculus of variations. The method of determining the program forces is based on the compilation of equations of the dynamics of a rigid body motion and additional equations - “zero-functions” (displacements) of the points of the application of redundant reactions.

Economic and mathematical model for calculation of preliminary production costs of multidimensional products for objects of protection having complex geometric shape

AnnotationThe research presents a description of the operational and economic indicators of the protective multidimensional product. The structure of the protective product and the classification system of its model range depending on the type of protection object are described. The estimation of development dynamics of the protective products market is carried out. The process of formation of the industrial enterprise pricing policy on the basis of ABC method and the method of cutting by “Mueller and son” is presented, the mechanism of preliminary calculation of material consumption for the production of protective products on individual order is visualized

Stature Estimation of Sichuan Han Females Based on X-ray Photography of Total Lower Limbs.

To establish a mathematical model of stature estimation for Sichuan Han females on the basis of the relationship between lower limbs and individual height, thus to provide evidence for forensic identification. Samples were collected from 171 Sichuan Han females. Large flat panel multi-function digital photography system was used to take the full-body X-ray films of the lower limbs. Indexes of long bones and stature of the subjects were measured, respectively. A linear regression analysis was carried out on the correlation between them, and a mathematical model of the stature calculation was established. Then the mathematical model was used to calculate the stature of another 29 Sichuan Han females to test its accuracy. The maximum length of femur （x1） had the highest correlation with stature. A total of 13 linear regression equations were established （P<0.05）, with the correlation coefficient （R） 0.821-0.897 and the standard error of the estimation （SEE） 2.994-3.812 cm. The backtesting showed that the equation y=41.604+1.205 x1+1.318 x6+2.444 x12+1.852 x13-2.388 x14 had the smallest mean absolute deviation （2.485 years old） and the highest accuracy of ±2SEE （92.9%）, and that the equation y=48.783+2.568 x1 had the highest accuracy of ±1SEE （60.7%）. The stature estimation is high by using the long bones of the lower limbs has high accuracy.

RESEARCH OF THE MAGNETOELECTRIC LINEAR OSCILLATORY MOTOR CHARACTERISTICS DURING OPERATION ON ELASTOVISCOUS LOADING

Purpose. To development of mathematical model for calculation of the magnetoelectric linear vibration motor performance with elastoviscous loading and research of machine characteristics in the different operational modes depending on loading parameters. Methodology. Experimental results by means of the developed test setup according to the specified methods are obtained. Moreover we have correlated the experimental data obtained by means of the development experimental setup with the simulated results using analytical model of the linear oscillatory motor with elastoviscous loading. In the analytical model of the linear vibration motor a one-mass vibration system with equivalent parameters of stiffness and viscous friction is considered. Results. Calculations of performance data for three operating modes of the oscillatory motor - for constant value of current, constant amplitude and acceleration of vibrations are carried out. Results of calculation by means of analytical model are coordinated with the experimental data obtained with help of a prototype of the linear motor and the load machine. Originality . Analytical expressions for performance data of the linear vibration motor which are based on the analytical model and an equivalent circuit with the lumped parameters are obtained. It is shown that for calculation of performance data depending on parameters of loading it is possible to use analytical model which is based on an equivalent circuit with constant inertial parameters of the linear motor. Practical value. Results of the work can be used for designing new and improvements of the existing vibration devices on the basis of linear motors with the specified performance data.

Combustion Efficiency of Boron-Containing Particles of the Condensed Phase in Channels with Distributed Injection of Air

A mathematical model and results of calculations of combustion of boron-containing particles of the condensed phase in channels with distributed injection of air are presented. Combustion in channels with discrete and continuously distributed injection of air is considered. Basic effects of the air-to-fuel ratio, place of air injection, and air temperature at the channel inlet on the combustion efficiency are analyzed. Conditions that ensure enhancement of the efficiency of particle combustion in the channel owing to distributed injection of air are determined. The data obtained in the present study can be used at the stage of design and experimental investigations of promising propulsion systems with the use of boron-containing high-energy-density materials as a fuel.

Load capacity of foil gas dynamic bearings with conical surfaces lubricated with low-viscosity cryogenic fluids

The present paper features a mathematical model of load capacity and static characteristics calculation of foil gas dynamic bearings with conical surfaces lubricated with cryogenic fluids based on equations of thermophysics, hydrodynamic and elasticity theory. Algorithmic model is presented. Original software is presented that is used to calculate load capacity and static characteristics of the bearings in question.

Progress and challenges with local approaches to cleavage fracture

Local approaches (LA) to cleavage fracture incorporate microstructure information and failure mechanisms into mathematical models for calculation of component failure probability. They offer a promising mechanistic alternative to global approaches and have been successfully applied to predict cleavage fracture toughness (CFT) changes due to material degradation and geometry effects. Predicting the dependence of CFT on temperature, specifically in the ductile-to-brittle transition (DBT) regime, remains a challenge. This work offers one avenue for addressing the challenge by revisiting the mathematical basis of LA and demonstrating that changes in continuum mechanical fields due to changes of deformation properties with temperature are insufficient to deliver predictions in agreement with experimentally measured CFT dependence on temperature. This suggests that the process by which cleavage initiators are generated is dependent on temperature separately from the dependence of the deformation properties on temperature. The temperature dependence of the generation process is derived for the material studied in the work. A methodology is described for predicting CFT in the DBT regime, using deformation and fracture toughness properties at one temperature and deformation properties at any other temperature of interest.