
Main / mathematical modeling
Keyword: "mathematical modeling"
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘ResearchandProduction Association ‘Mars’, Doctor of Science in Engineering; graduated from the Faculty of Physics at Irkutsk State University, completed his postgraduate study at Bauman Moscow Technical School, doctoral study at Ulyanovsk State Technical University; Chief Staff Scientist of FRPC JSC 'RPA 'Mars'; an author of monographs, text book, articles in the field of the mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]I. Egorov,
Vladimir Aleksandrovich Baboshin, St. Petersburg National Guard Forces Command Military Institute, Candidate of Sciences in Engineering, Associate Professor; graduated from Ulyanovsk Higher Military Command College of Communications; Associate Professor at the Department of Informatics and Mathematics of St. Petersburg National Guard Forces Command Military Institute; an author of articles and inventions in the field of the analysis and synthesis of information systems and mathematical modeling. [email: boboberst@mail.ru.]A. Moiseev,


Models for Creating the SpecialPurpose Mathematical Support of ComputerAided Control Systems
Authors provide reasons to a promising outlook for creating a technology for the development of specialpurpose mathematical support of the computeraided control system in order to improve the management based on process automation of contentrelated information processing and decisionmaking support. Different specialpurpose software components as well as their development stages are analyzed. A block diagram of specialpurpose mathematical support creating that includes production volume data at each stage and intensity of its growth and decrease. Linear differential equations build the mathematical models for creating the specialpurpose mathematical support. Analytical decisions have been made, curves demonstrating the production volume change at all stages are provided. For mathematical modelling the processes of specialpurpose mathematical support creating and decisionmaking support, authors use the LotkaVolterra equations that demonstrate the creative behavior of designers’ work. The equations obtained are examined for stability. Authors detect approximate decisions. The models built are designed for optimal source distribution among development stages of all the specialpurpose software types. Specialpurpose mathematical support, design technology, mathematical modelling.



Sections: Automated control systems
Subjects: Automated control systems, Mathematical modeling. 
Valerii Vladimirovich Kozhevnikov, Scientific Research Technological Institute of Ulyanovsk State University, Candidate of Science in Engineering; graduated from the Pushkin Higher Command School of Radioelectronics; Senior Researcher at the Scientific Research Technological Institute of Ulyanovsk State University; an author of articles in the field of microelectronic system design theory.[email: vvk28061955@mail.ru]V. Kozhevnikov


The Method of Mathematical Modeling of Cognitive Digital Automata
An approach to solving the problem of mathematical modeling of cognitive digital automata (CDA) is proposed. The task of formalizing the concept of the cognitive nature of the CDA mathematical model comes to the fore. The cognitiveness (cognition) of the mathematical model is determined by the possibility of learning and generating solutions that are not provided for in the learning process. A special feature of CDA is that the description of the neural network (NN) structure is used as a structural circuit of the automata, and the logical function "NOTANDOR" is used as the model of the neuron. In the case of the feedbacks formation from the output to the inputs of the neurons, the model of the neuron is a binary trigger with a logical function "NOTANDOR" at the input. As a tool for constructing a mathematical model of CDA, a mathematical apparatus of Petri nets (PNs) is proposed: marked graphs, inhibitory PNs and PNs with programmable logic. The mathematical model is builton the basis of the representation of the CDA in the form of the state equation of the PNs from the class of Murat equations (matrix equations) or a system of linear algebraic equations. The task of formalizing the concept of cognitiveness (cognition) is solved as a result of the logic synthesis (learning) of the initial structural circuit of CDA or the formation of the formula (network algorithm) of CDA. At the same time, the possibility of forming a formula (network algorithm) of CDA depends on the critical mass (quality) of training sets and training algorithms. Hence, the task of generating the minimum set of training sets for a given CDA function or experimentally determined function takes on particular importance. Forecasting or generation of solutions, in turn, is performed on the basis of the mathematical model of CDA obtained in the learning process. intellectual control system, cognitive digital automata, artificial intelligence, neural networks, machine learning, cognition, Petri nets, equation of states, mathematical modeling, synthesis, generation, analysis, logic.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Artificial intelligence. 
Vladislav Nikolaevich Kovalnogov, Ulyanovsk State Technical University, Doctor of Science in Engineering; graduated from Kazan State University; Head of the Department of Heat Power Engineering at Ulyanovsk State Technical University; an author of articles, monographs, and inventions in the field of modeling, research and optimization of hydrogasodynamic processes in power plants and manufacturing equipment. [email: kvn@ulstu.ru]V. Kovalnogov,
Ruslan Vladimirovich Fedorov, Ulyanovsk State Technical University, Candidate of Science in Engineering; graduated from Ulyanovsk State Technical University; Associate Professor of the Department of Heat Power Engineering of UlSTU; an author of articles and inventions in the field of numerical modeling of hydrogasodynamic processes. [email: r.fedorov@ulstu.ru]R. Fedorov,
Larisa Valerievna Khakhaleva, Ulyanovsk State Technical University, Candidate of Science in Engineering; graduated from Ulyanovsk State Technical University; Associate Professor of the Department of Heat Power Engineering of UlSTU; an author of articles and inventions in the field of numerical modeling of hydrogasodynamic processes. [email: larvall@mail.ru]L. Khakhaleva,
Andrei Valentinovich Chukalin, Ulyanovsk State Technical University, graduated from Ulyanovsk State Technical University; Postgraduate Student at the Department of Heat Power Engineering of UlSTU; an author of articles and inventions in the field of numerical modeling of hydrogasodynamic processes. [email: chukalin.andrej@mail.ru]A. Chukalin


Mathematical Modeling and Numerical Analysis of Thermal Protection Effectiveness With Hemispherical Damping Cavities
The gas turbine engine performance improvement is linked inextricably with the increase of the intensity of dynamic, aeromechanical and thermal processes, which, in turn, requires the development of systems and devices allowing to protect the most loaded equipment components. The most effective ways to protect surfaces from overheating are a convective cooling; the absorption and accumulation of heat by condensed substances; the cooling that operates on mass transfer principle; the radiation and electromagnetic cooling; heatshielding coatings. One of the most effective ways to protect surfaces from overheating is a thermal protection in the form of filmlike surface cooling based on the masstransfer surfacecooling principle. This method is widely distributed and it proved to be effective. The paper considers the possibility of improving this method of cooling due to the impact on the boundary layer with hemispherical damping cavities behind the injection section of the cooler. A mathematical model is proposed, the numerical study of the thermal protection effectiveness by the use of hemispherical damping cavities is carried out. The possibility of a significant decrease of the turbulent heat exchange in the boundary layer and of the efficiency improvement of the thermal surface protection of ? by0.06 due to the use of hemispherical damping cavities has been established. The proposed method of thermal protection intensifying and numerical analysis of its efficiency will improve the gas turbine engines that are available for different applications of domestic industry for example in power generation sector, aircraft engineering as well as in shipbuilding. Hemispherical damping cavities, turbulent transport, mathematical modeling, boundary layer, thermal protection.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Vladislav Nikolaevich Kovalnogov, Ulyanovsk State Technical University, Doctor of Engineering; Head of the Department of Heat Power Engineering of Ulyanovsk State Technical University; graduated from Kazan State University; an author of articles, monographs, and inventions in the field of simulation, research, and optimization of thermal and hydrogasdynamic processes in power installations and processing equipment. [email: kvn@ulstu.ru]V. Kovalnogov, Dmitrii Aleksandrovich Generalov, Ulyanovsk State Technical University, Senior Lecturer at the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modelling of hydrogasdynamic processes. [email: dmgeneralov@mail.ru]D. Generalov, Andrei Valentinovich Chukalin, Ulyanovsk State Technical University, Postgraduate Student at the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modelling of hydrogasdynamic processes. [email: chukalin.andrej@mail.ru]A. Chukalin, Ruslan Vladimirovich Fedorov, Ulyanovsk State Technical University, Candidate of Engineering, Associate Professor at the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modelling of hydrogasdynamic processes. [email: r.fedorov@ulstu.ru]R. Fedorov, Anna Alekseevna Plekhanova, Ulyanovsk State Technical University, Forth Year Student of the Thermal and Heat Engineering Course of the Power Faculty at Ulyanovsk State Technical University. [email: nyutka73@mail.ru]A. Plekhanova


New Engineering Solutions Based on Mathematical Modelling of the Turbine Blade System
The article deals with a method for studying the thermal state of turbomachine blades and a numerical investigation method taking into account the phenomenon of gasdynamic temperature stratification. The authors consider the possibility of increasing the efficiency of cooling turbine blades due to the phenomenon of gasdynamic temperature stratification, the possibility of improving the accuracy of the calculated forecasting of the thermal state of the blades by obtaining reliable data by developing a mathematical model and a unique software and information complex for modelling. Mathematical modelling, numerical methods, thermal protection, film cooling, software and information complex, dispersed flow.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Vladislav Nikolaevich Kovalnogov, Ulyanovsk State Technical University, Doctor of Engineering, Head of the Department of Heat Power Engineering of Ulyanovsk State Technical University; graduated from Kazan State University; an author of articles, monographs, and inventions in the field of simulation, research, and optimization of thermal and hydrogasdynamic processes in power installations and processing equipment. [email: kvn@ulstu.ru]V. Kovalnogov, Andrei Valentinovich Chukalin, Ulyanovsk State Technical University, Postgraduate Student at the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modelling of hydrogasdynamic processes. [email: chukalin.andrej@mail.ru]A. Chukalin, Larisa Valerevna Khakhaleva, Ulyanovsk State Technical University, Candidate of Engineering, Associate Professor at the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modelling of hydrogasdynamic processes. [email: larvall@mail.ru]L. Khakhaleva, Ruslan Vladimirovich Fedorov, Ulyanovsk State Technical University, Candidate of Engineering, Associate Professor at the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modelling of hydrogasdynamic processes. [email: r.fedorov@ulstu.ru]R. Fedorov, Anna Alekseevna Plekhanova, Ulyanovsk State Technical University, Third Year Student of the Thermal and Heat Engineering Course of the Power Department at Ulyanovsk State Technical University. [email: nyutka73@mail.ru]A. Plekhanova


Researching the Influence of the Number of Damping Cavities on Frictional Resistance of Turbulent Flow
As a result of experimental and numerical research of turbulent flow with effects on the basis of the modified model of the Prandtl mixing length with the use of pressure pulsation analysis, the structure and resistance of turbulent flow frictional resistance were calculated. The developed model of turbulent exchange and the calculation method allow to take adequately into account the features of the metabolic processes in the presence of damping cavities and predict the frictional resistance with the help of preliminary calculation. The possibility of reduction of the frictional resistance coefficient of a turbulent flow to 35 % was experimentally set with the use of damping cavities. The generalization of the influence of the amount of damping cavities on the frictional resistance was carried out. Damping cavities, mathematical modelling, frictional resistance, turbulent flow.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Irina Aleksandrovna Sedykh, Lipetsk State Technical University, Candidate of Physics and Mathematics, graduated from the Faculty of Automatization and Information Technologies of Lipetsk State Technical University (LSTU); Associate Professor at the Department of Mathematics of Lipetsk State Technical University; an author of monographs and articles, holds State Registration Certificates of computer programs in the field of neighborhood modelling of dynamic systems. [email: sedykhirina@yandex.ru]I. Sedykh, Dmitrii Sergeevich Demakhin, Lipetsk State Technical University, graduated from the Faculty of Physics and Technology of Lipetsk State Technical University; Candidate for the Master’s Degree at LSTU; an author of articles, holds State Registration Certificates of computer programs in the field of neighborhood modelling of dynamic systems. [email: dimademahin@mail.ru]D. Demakhin


Flexible Control of Traffic Lights System on the Basis of Neural Networks
The traditional algorithm of crossroad traffic management with fixed order and switchingon duration was described in the article. Neural networksbased kind of control for crossroad group of traffic lights was offered as an alternative. The appropriate algorithm has been developed and realized in C++. The basic characteristics of designed neural network for crossroad traffic lights control were described. They include the architecture, assignment of neurons for input and output layers, the number of intermediate layer neurons, the activation function of neurons, the learning method. The realized neural networkbased algorithm allows to put in practice flexible control of coordination traffic lights in case of the nonfixed order of traffic lanes priorities. Herewith, the possibility of change in green time of traffic light signal within predetermined limits with the aim of increasing capacity of crossroads in most problematic directions of transport movements was foreseen. Also, restrictions for prevention of blocking segregate streams for too long including blocking pedestrians in crosswalks were provided. Traffic lights systems, mathematical modelling, neural networks, crossroad traffic management.



Sections: Artificial intelligence
Subjects: Artificial intelligence. 
Aleksandr Kupriianovich Ivanov, Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’, Doctor of Engineering, Honoured Worker of Science and Engineering of the Ulyanovsk Region; graduated from the Faculty of Physics at Irkutsk State University; completed his postgraduate studies at Bauman Moscow Higher Technical School and his doctoral studies at Ulyanovsk State Technical University; Chief Staff Scientist at Federal ResearchandProduction Center Joint Stock Company ‘Research and Production Association ‘Mars’; an author of monographs, articles, and a manual in the field of mathematical modeling of hierarchical realtime computeraided control systems. [email: mars@mv.ru]A. Ivanov


Differential Models of Information Processing in Hierarhical Computeraided Control System Authorities
The analysis of information processing in hierarchical computeraided control system authorities is the foundation on which the differential reporting situation and planning models have been constructed. The model of situation report represents heterogeneous differential equation of degree one with constant coefficients and describes the speed of creating output information resources by processing input data originating from subordinate bodies. The equation is solved by applying the method of indefinite coefficients. The analytical results for one, two, and three information sources have been obtained. The planning model represents inhomogeneous combined differential equations with constant coefficients. The combined equations describe the speed of creating routine documents by authorities for subordinate bodies. The solution can be found by applying the method of variation of fundamental system constants. The analytical results for two subordinate bodies have been obtained. The results of calculating output data amount in situation report depending on time and the amount of input data from two or three subordinate bodies were given. The parameters of the differential equation solution for four subordinate bodies have been calculated. Mathematical modeling, information resources, control systems, differential equations.



Sections: Automated control systems
Subjects: Automated control systems, Architecture of ship's system. 
Maria Mikhailovna Dubinina, DesignTheoretical Department at Ulyanovsk Instrument Manufacturing Design Bureau (UIMDB) JointStock Company, Postgraduate Student of the Department of Measuring and Computing Complexes; got the Master’s Degree in Instrument Engineering of Ulyanovsk State Technical University; a designengineer of the DesignTheoretical Department at Ulyanovsk Instrument Manufacturing Design Bureau (UIMDB) JointStock Company; an author of articles and inventions in the field of sensors for pressure perception of aircraft aerometric systems. [email: masha_dubinina.73@mail.ru]M. Dubinina, Mikhail Iurievich Sorokin, Ulyanovsk Instrument Manufacturing Design Bureau (UIMDB) JointStock Company, Candidate of Engineering, Associate Professor at the Department of Measuring and Computing Complexes; graduated from the Faculty of Information Systems and Technologies of Ulyanovsk State Technical University; Head of a department at Ulyanovsk Instrument Manufacturing Design Bureau (UIMDB) JointStock Company; an author of articles and inventions in the field of sensors for pressure perception of aircraft aerometric systems. [email: rto@ukbp.ru]M. Sorokin


A Mathematical Model of Pressure Traverse of a Pitotstatic System Cross Section
The article considers the results of researching pitotstatic systems. The authors have been created mathematical model of pressure traverse of a pitotstatic system crosssection. The model has shown that shifting the arrangements of static pressure tap holes along the receiver length has no effect on pressure distribution over the receiver surface essentially. From the results of mathematical modelling, the authors have obtained the data array for a model of a pitotstatic system in order to detect surface pressure. The method of pressure perception compensation on the basis of mass balance has been suggested. Due to this, improvement of static pressure perception accuracy can be provided not only by shifting the arrangements of static pressure tap holes along the receiver cross section perimeter but also by changing the diameter of holes. This can eventually help to achieve required characteristics of static pressure perception of a chamfer angle and incident flow speed. Mathematical modelling, pitotstatic system, pressure traverse, air consumption.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksandr Nikolaevich Zolotov, Postgraduate Student at the Department of HeatandPower Engineering of Ulyanovsk State Technical University; graduated from Ulyanovsk State Technical University; graduated from Ulyanovsk State Technical University; an author of articles in the field of the numerical modeling of gasdynamic processes. [email: anzolotov@bk.ru]A. Zolotov, Vladislav Nikolaevich Kovalnogov, Ulyanovsk State Technical University, Doctor of Engineering, Head of the Department of HeatandPower Engineering of Ulyanovsk State Technical University; an author of articles, monographs, and inventions in the field of simulation, research, and optimization of thermal and gasdynamic processes in power installations and processing equipment. [email: kvn@ulstu.ru]V. Kovalnogov, Maria Igorevna Kornilova, Ulyanovsk State Technical University, a secondyear student of Ulyanovsk State Technical University; an author of articles in the field of the numerical modeling of gasdynamic processes. [email: masha.kornilova.1995@mail.ru]M. Kornilova


Modeling and Researching the Technique of Thermal Protection of Turbomachines Blades With the Use of Gasdynamic Temperature Stratification
Raising the initial temperature and pressure of the working fluid is one of the simplest and most effective ways of improving fuel efficiency and reducing metal consumption of turbines. Traditional technology of turbine blades production is quite cost and time consuming in production. Therefore, their creation requires the use of mathematical models which serve as a tool for analysis, improvement and selecting the most promising solutions of the refrigeration and increase of the prediction accuracy at the design stage of their effectiveness. Mathematical modeling of the thermal state is widely used in the creation of modern gas turbines [1]. An important objective is the numerical simulation of the spatial flow of the heat transfer in subsonic and transonic lattices. In order to create effective ways of thermal protection, it is necessary to know the distribution of nonstationary temperature fields on the surface and in the body of the scapula. For this purpose, the heat flows from the gas to the blades must be accurately determined taking into account the impact of the mode of flow, thermals, pressure gradient, and other factors [2]. In the paper, the proposed mathematical model and method of numerical investigation of the thermal state of blades of turbomachines streamlined by a supersonic dispersed flow with regard to the phenomenon of gasdynamic temperature stratification was proposed. With the aim to increase the accuracy of the settlement prediction of the thermal state of blades due to obtaining reliable data as well as improve the efficiency of cooling systems to increase the service life of the blades, the authors have developed the programinformational complex which will take into account the results of studies of gasdynamic processes in high speed, disperse flows including the phenomenon of gasdynamic temperature stratification carried out at the Department of Heat Power Engineering at Ulyanovsk State Technical University. Mathematical modeling, numerical methods, thermal protection, convectivefilm cooling, software and information complex, dispersed flow, gasdynamic temperature stratification.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Computeraided engineering. 
Vladislav Nikolaevich Kovalnogov, Doctor of Engineering, Head of the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles, monographs, and inventions in the field of simulation, research, and optimization of thermal and hydrogasdynamic processes in power installations and processing equipment. [email: kvn@ulstu.ru]V. Kovalnogov, Ruslan Vladimirovich Fedorov, Ulyanovsk State Technical University, Candidate of Engineering, Associate Professor at the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modeling the hydrogasdynamic processes. [email: r.fedorov@ulstu.ru]R. Fedorov, Larisa Valerievna Khakhaleva, Ulyanovsk State Technical University, Candidate of Engineering, Associate Professor at the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modeling the hydrogasdynamic processes. [email: larvall@mail.ru]L. Khakhaleva, Andrei Valentinovich Chukalin, Ulyanovsk State Technical University, Postgraduate Student at the Department of Heat Power Engineering of Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modeling the hydrogasdynamic processes. [email: chukalin.andrej@mail.ru]A. Chukalin


Mathematical Modeling and Numerical Analysis of Flow Laminarization in a Perforated Tube With Damping Cavities
The authors have experimentally established the possibility of the partial turbulent flow laminarization in a perforated tube with damping cavities which leads to reduction of up to 35% of frictional resistance. The effect of the number of perforations in the damping cavity on the velocity profile and the frictional resistance has been revealed. The model of turbulent transfer in a boundary layer near the perforated surface with damping cavities and the method of calculating the flow pattern and frictional resistance were proposed. Flow laminarization manifested itself as the decrease of turbulent transfer intensity in the boundary layer due to external or internal influences plays an important role in engineering. Apparently, for the first time the possibility of a reverse transition of a turbulent flow in a laminarization one under the influence of a negative longitudinal pressure gradient was noted in the article [1]. Further researches overviewed in the paper [2] have demonstrated that laminarization in flows with negative longitudinal pressure gradient is accompanied by a substantial (up to 35 ... 50%) decrease of the intensity of heat and a simultaneous increase in the frictional resistance. The model of laminarization in the streams with different influences proposed in the paper [2] has allowed to predict the possibility of its implementation and anear perforated surface with damping cavities. As this takes place, in contrast to the laminarization under the influence of a negative longitudinal pressure gradient there must be a reduction of both the intensity of heat transfer and friction resistance. The purposes of this work are experimental investigation of frictional resistance in the perforated tube with damping cavities with a different number of perforations, the development of turbulent transfer process models and the calculation method of friction resistance. Perforated pipe, a damping cavity, turbulent transfer, mathematical modeling, friction resistance.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Aleksandr Sergeevich Andreev, Ulyanovsk State University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Tashkent State University; Dean of the Faculty of Mathematics and Information Technologies at Ulyanovsk State University; Head of the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [email: AndreevAS@ulsu.ru]A. Andreev, Ekaterina Alekseevna Kudashova, Ulyanovsk State University, graduated from the Faculty of Mathematics and Information Technologies of Ulyanovsk State University; Junior Researcher at the Department of Scientific Research of Ulyanovsk State University; an author of articles in the field of the motion control of mechanical systems. [email: katherine.kudashova@yandex.ru]E. Kudashova


On Modeling the Control Structure of the Omnidirectional Mobile Robo
Nowadays, requirements to modeling and researching selfdirected robotic systems are extremely high. In order to improve maneuverability and control efficiency, new mobile robots with omniwheels are developed. Such robots are able to move in either direction without turning around. They have these features due to the fact of increase of construction and control rules complexity. Three and fourwheeled mobile robots with rollercarrying wheels have become more widespread. The article deals with the problem of theoretical control establishing to provide arbitrary program motion of threewheeled robots with omniwheels. The computer model of valid control efficiency analysis was developed. For developing this model, .the numerical modeling method that turns the continuous model into the corresponding numerical one was used. Practical application of the introduced stabilizing control algorithm for mechanical systems was demonstrated by the example of threewheeled robot motion stabilization. Mathematical modeling, threewheeled robot, stabilization, control, digitization.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Artificial intelligence. 
Petr Alexandrovich Velmisov, Ulyanovsk State Technical University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Saratov State University; Head of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles and monographs in the field of aerohydromechanics, aerohydroelasticity, and mathematical modeling. [email: velmisov@ulstu.ru]P. Velmisov, Sergei Vladimirovich Kireev, Ulyanovsk State Technical University, Candidate of Physics and Mathematics; graduated from the Faculty of Mechanics and Mathematics of Moscow State University (Branch at Ulyanovsk); Associate Professor at the Department of Higher Mathematics of Ulyanovsk State Technical University; an author of articles and a monograph in the field of aerohydroelasticity and mathematical modeling. [email: ksv1511@yandex.ru]S. Kireev


Numerical Method for Solving a Class of Nonlinear Boundary Value Problems of Aerohydroelastity
On the basis of nonlinear models proposed and a numerical method developed for solving corresponding boundary value problems in nonlinear integrodifferential equations static instability (divergence) of the pipeline with the fluid flowing in it is investigated. A numerical method for solving the bifurcation problem includes the RungeKutta 6th order method with the error control at each step, Newton's method for solving nonlinear equations and integration with the use of NewtonKotesa quadrature formulas. Solving the boundary value problem is reduced to solving a Cauchy problem. The complexity of a Cauchy problem is that there is an integral term in the equation. Calculation of this term needs values of the whole integration interval. It makes the direct application of the RungeKutta method impossible. To solve this problem (integration) a special iterative process was developed. Numerical realization is provided with the use of a program written in Delphi 7. Bifurcation diagrams showing the dependence between maximal element bending and the inflow velocity are obtained. Moreover, the element’s forms of deflection are specified. The obtained numerical solutions were compared with analytical ones. Stability, divergence, elastic element, pipeline, nonlinear model, differential equations, boundary value problem, mathematical modeling, numerical method.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Petr Alexandrovich Velmisov, Ulyanovsk State Technical University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Saratov State University; Head of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles and monographs in the field of aerohydromechanics, aerohydroelasticity, and mathematical modeling. [email: velmisov@ulstu.ru]P. Velmisov, Andrei Viktorovich Korneev, Ulyanovsk State Technical University, graduated from the Faculty of Information Systems and Technologies at Ulyanovsk State Technical University; PostGraduate Student at the Department of Higher Mathematics of Ulyanovsk State Technical University; an author of articles in the field of aerohydroelasticity, optimal control, and algorithms development. [email: a.korneev1@gmail.com]A. Korneev


Mathematical Modeling in the Problem of Dynamic Stability of a Pipeline
The paper presents mathematical models for a viscoelastic pipeline that is a hollow rod containing flowing the fluid (gas). The article is devoted to the problem of the dynamic stability of a pipeline. Linear and nonlinear models describe partial differential equations for an unknown function (the displacement of the pipeline points from the equilibrium state). By means of Lyapunov functionals designed stability theorems are formulated and analytical stability conditions for the parameters of the mechanical system and different types of initial conditions are found. The obtained stability conditions are sufficient but not necessary. A mathematical software package is developed to solve this problem. It allows to find an approximate numerical solution of differential equation for describing pipeline vibration and to plot a stability area appropriate to both sufficient and necessary stability conditions. A numerical experiment of stability areas designing is conducted on the basis of the software package. The obtained numerical results are interpreted and compared with analytical stability conditions. The influence of the model parameters variation on the stability is researched. Mathematical modeling, viscoelastic pipeline, aerohydroelasticity, stability, functional, partial differential equations, numerical methods, galerkin method.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Ruslan Vladimirovich Fedorov, Ulyanovsk State Technical University, Candidate of Engineering, Associate Professor at the Department of Heat Power Engineering at Ulyanovsk State Technical University; graduated from Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modeling the hydrogasdynamic processes. [email: r.fedorov@ulstu.ru]R. Fedorov, Dmitrii Aleksandrovich Generalov, Ulyanovsk State Technical University, PostGraduate Student at the Department of Heat Power Engineering at Ulyanovsk State Technical University; graduated from Ulyanovsk State Technical University; an author of articles and inventions in the field of numerical modeling the hydrogasdynamic processes. [email: dmgeneralov@mail.ru]D. Generalov, Maria Igorevna Kornilova, , a second year student at Ulyanovsk State Technical University; an author of articles in the field of numerical modeling the hydrogasdynamic processes. [email: masha.kornilova.1995@mail.ru]M. Kornilova


Mathematical Modeling and Numerical Analysis of a Thermal State of Turbomashine Blades Affected By a Supersonic Dispersed Flow
The development of the advanced gasturbines must ensure their operation under the conditions of an increasing temperature of a working body to improve the efficiency during in a reliable and efficient operation. In this paper, a mathematical model and a method of a numerical research of a thermal state of turbomachine blades affected by a supersonic dispersed flow including a gasdynamic temperature stratification phenomenon are introduced. The adequacy of a turbulent dispersed boundary layer model was verified by comparing the calculation of the heat transfer coefficients of the dispersed flow in the nozzles with the experimental data. In order to improve the accuracy of the calculated prediction of the thermal state of the blades due to obtaining the reliable data, as well as the efficiency of cooling systems for the increasing resource of the blades, a software and information complex integrated into the Solid Works package is currently being developed on the base of the Turbo Works package at the Department of Heat Power Engineering of Ulyanovsk State Technical University. The research results of the temperature stratification will be included into this software and information complex as a unique information base. As the analysis of the numerical study results shows, the application of the developed convectivefilm cooling temperature provides the temperature reduction to the trailing edge of the turbo machine blade by 1.6 times compared with the convection cooling. Mathematical modeling, numerical methods, thermal protection, convectivefilm cooling, software and information complex, dispersed flow.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Anna Aleksandrovna Tcynaeva, Samara State University of Architecture and Civil Engineering, Candidate of Engineering; graduated from Ulyanovsk State Technical University; Associate Professor at the Department of Heatandgas Supply and Ventilation of Samara State University of Architecture and Civil Engineering; an author of development works and articles in the field of mathematical modeling of heatexchange processes in engineering. [email: a.tsinaeva@rambler.ru]A. Tcynaeva


Numerical Investigation of the Temperature Stratification
The intensity of heat and mass transfer in devices based on the gasdynamic temperature stratification, for example, in a supersonic pipe temperature stratification (in the Leontief’s pipe) is determined by the heat flow through the separation wall between subsonic and supersonic flows. This paper presents the mathematical modeling and numerical study of heat transfer in devices of gasdynamic temperature stratification using passive stimulation techniques. The efficiency of heat pipes (HP) and the metal edges of the same configuration were researched. Mathematical modeling was performed using a mathematical model. The mathematical model includes differential equations that describe the motion and heat transfer in the boundary layer; equations for calculation of heat transfer processes in heat pipes; equations to calculate the heat flow between subsonic and supersonic flows in the device of gasdynamic temperature stratification.It was found that the intensification of heat transfer devices based on the gasdynamic temperature stratification (in the Leontief’s pipe) through the use of heat pipes is increasing up to 3 times. It was established that the use of heat pipes with a wick of material copperwater is more of using efficiency of heat pipes with the working material in the aluminumacetone up to 1.05 ... 1.12 times. Mathematical modeling, numerical investigation, temperature stratification, intensification, heat pipes.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Petr Alexandrovich Velmisov, Ulyanovsk State Technical University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Saratov State University; Head of the Department of Higher Mathematics at Ulyanovsk State Technical University; an author of articles, textbooks, and monographs in the field of mathematical modeling, aerohydroelasticity, aerohydrodynamics, differential equations. [email: velmisov@ulstu.ru]P. Velmisov, Sergey Vladimirovich Kireev, Ulyanovsk State Technical University, Candidate of Physics and Mathematics; graduated from the Faculty of Mechanics and Mathematics of Moscow State University (Branch at Ulyanovsk); Associate Professor at the Department of Higher Mathematics of Ulyanovsk State Technical University; an author of articles and a monograph in the field of aerohydroelasticity and mathematical modeling. [email: ksv1511@yandex.ru]S. Kireev


Mathematical Modelling in Instability Problems of Elastic Structural Elements in Gas Flow
On the basis of the proposed nonlinear models and developed numerical method for the solution to the corresponding nonlinear boundaryvalue problems, the static instability (divergence) of the elastic element of the design streamlined and supersonic flow of ideal gas is investigated. A numerical procedure for the bifurcationproblem solution includes the 6th order RungeKutta method with the error control at the step, the Newton's method required for solving nonlinear equations, and integration using NewtonKotesa quadrature. The solution to the boundaryvalue problem is reduced to the Cauchy problem solution, the complexity of which is that the integral term is present in the equation. In order to calculate this integral term the values of the integrand function on the whole interval of integration are required. It makes impossible the direct application of the RungeKutta Method. A special iterative process was developed to solve this problem as integral evaluation. Numerical implementation is carried out by the program written in Delphi 7. Bifurcation diagrams are given that showing the maximal element dependence on incident stream velocity. Element bendingforms are defined. The comparison of obtained numerical solutions against analytical solutions is carried out. The dynamic stability of the elastic structural element in a supersonic gas flow is researched by the Galerkin’s method. The element bending dependences on time in a fixed point are obtained. Stability, divergence, elastic element, plate, supersonic flow, nonlinear model, differential equations, boundaryvalue problem, mathematical modelling, numerical method.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Vladimir Nikolaevich Moiseev, FRPC OJSC ‘RPA ‘MARS, a postgraduate student at Ulyanovsk State Technical University; graduated from the Faculty of Economics and Mathematics of Ulyanovsk State Technical University with a specialty in Applied Mathematics; a software engineer at the department of FRPC OJSC ‘RPA ‘MARS; an author of articles, inventions in the field of air pressure probes of aircraft airdata measuring systems. [email: v.n.moiseev@mail.ru]V. Moiseev, Mikhail Yuryevich Sorokin, Ulyanovsk Instrument Manufacturing Design Bureau, PJSC, Candidate of Engineering; graduated from the Faculty of Information Systems and Technologies of Ulyanovsk State Technical University; a head of a department at Ulyanovsk Instrument Manufacturing Design Bureau, PJSC; an author of articles, inventions in the field of air pressure probes of aircraft airdata measuring systems. [email: rto@ukbp.ru]M. Sorokin, Ivan Petrovich Efimov, Ulyanovsk State Technical University, Candidate of Engineering, graduated from the Ulyanovsk Polytechnical Institute with a specialty in Aircraft Instrument Engineering; Associate Professor of Measuring and Computing Complexes Department of Ulyanovsk State Technical University; an author of articles, inventions in the field of primary pressure sensors of aircraft airdata measuring systems. [email: eip@ulstu.ru]I. Efimov, Nikolay Nikolayevich Makarov, Public Joint Stock Company Ulyanovsk Instrument Manufacturing Design Bureau, Doctor of Engineering, Candidate of Economics; graduated from the Faculty of Aircraft Control Systems and Equipment at Kazan Aiviation Institute named after F. Tupolev, Director General of Public Joint Stock Company Ulyanovsk Instrument Manufacturing Design Bureau; an author of articles and inventions in the field of air pressure probes of aircraft airdata measuring systems. [email: ukbplkv@mv.ru]N. Makarov


Mathematical Model for Pitotstatic Probe
The article deals with mathematical modeling problems of the air pressure probes composed of the front cylindrical receiving tube having inside conical flow stagnation chamber and static pressure holes. Basic mathematical models for the air pressure probes were derived from the mathematical modeling intended for determination of static pressure, dynamic pressure, velocity, velocity and altitude errors. The adequacy of the received mathematical models is checked by comparison against the experimental research findings. Experimental studies were carried out in the T129 wind tunnel of TsAGI with nozzlejet simulator. These models allow to get true data at such parameters as the cylindrical tube radius over the range 6.5 to 8.5 mm, start tube distance to the static pressure holes of 45 to 70 mm, downwash angle of 0 to 90 degrees, incident airflow velocity at 50 to 250 kmh. The received mathematical models enable to automate the engineering process of Pitotstatic probe with metrological performance predictions. This gives the ability to make a quick selection of probes with design parameters required for a specific control object at the initial development stage. Mathematical modeling, pitotstatic probe, mathematical model.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Anna Alexandrovna Tcynaeva, Samara State University of Architecture and Civil Engineering, Candidate of Engineering; graduated from Ulyanovsk State Technical University; Associate Professor at the Deartment of Heatandgas Supply and Ventilation of Samara State University of Architecture and Civil Engineering; author of development works and articles in the field of mathematical modeling of heatexchange processes in engineering. [email: a.tsinaeva@rambler.ru]A. Tcynaeva, Ekaterina Alexandrovna Tcynaeva, Ulyanovsk State Technical University, Candidate of Engineering; graduated from Ulyanovsk State Technical University; Associate Professor at the Deartment of Heatandpower Engineering of Ulyanovsk State Technical University; author of articles in the field of mathematical modeling of heatexchange processes in engineering. [email: tsinaevakate@rambler.ru]E. Tcynaeva, Evgeny Vladimirovich Shkolin, Ulyanovsk State Technical University, Student at the Deartment Heatandpower Engineering of Ulyanovsk State Technical University. Research interests are heat engineering, heat pipes. [email: shkoline@ya.ru]E. Shkolin


Mathematical Modeling of the Temperature Stratification of the Modified Leontief Pipe With Heat Pipes
Mathematical modeling and numerical investigation of the temperature stratification of the modified Leontief's pipe with heat pipes are conducted. A possibility of intensification of turbulent flows temperature stratification by means of using heat pipes is considered. It is identified that an application of heat pipes enables to increase the efficiency of the temperature stratification of up to three times. Mathematical modeling, numerical investigation, temperature stratification, heat pipes.



Sections: Mathematical modeling, calculi of approximations and software systems
Subjects: Mathematical modeling. 
Aleksandr Sergeevich Andreev, Ulyanovsk State University, Doctor of Physics and Mathematics; Professor; graduated from the Faculty of Applied
Mathematics and Mechanics of Tashkent State University; holds the Chair of Information Security and Management
Theory at Ulyanovsk State University; author of articles, textbooks, a monograph in the field of theory of stability and
control of motion [email: mtu@ulsu.ru]A. Andreev, Alexandera Olegovna Artemova, Ulyanovsk State University, postgraduate student; graduated from the Faculty of Mathematics and Information
Technology of Ulyanovsk State University; assistant lecturer at the Chair of Information Security and Management
Theory of Ulyanovsk State University; author of articles in the field of modeling of controlled systems [email: sasenka.05@mail.ru]A. Artemova, Yulia Vladimirovna Petrovicheva, Ulyanovsk State University, postgraduate student; graduated from the faculty of Mathematics and
Information Technology of Ulyanovsk State University; author of articles in the field of mathematical modeling of
controlled mechanical systems [email: mtu@ulsu.ru]Y. Petrovicheva


Modeling of Controlled Motionof Coupled Rigidbody System
Many mechanical systems can be represented as systems of rigid bodies and elastic solids interconnected by means of different
elements: springs, dampers, ball joints or cylindrical hinges, etc. The present paper provides a modeling of a controlled system
of coupled rigid bodies in matrix form of nonlinear differential equations. Mathematical modeling, motion control, systems of coupled rigid bodies.



Sections: Mathematical modeling, calculi of approximations and software systems
Subjects: Mathematical modeling. 
Anatoly Alexanderovich Kupriyanov, Federal ResearchandProduction
Center ResearchandProduction Association Mars, Candidate of Engineering, Associate Professor; graduated from the Faculty
of Radioengineering of Ulyanovsk Polytechnic Institute; leading staff scientist at Federal ResearchandProduction
Center ResearchandProduction Association Mars; is interested in the field of the methodology of the creation and
building of distributed computer systems; author of a monograph, papers and articles in design and development of
local and corporate networks, computeraided packages, and special and generalpurpose computeraided control
systems [email: aakupr1828@rambler.ru]A. Kupriyanov, Andrey Evgenyevich Kukin, Federal ResearchandProduction Center ResearchandProduction Association Mars, postgraduate student of the Chair Telecommunications Technologies and Networks at
Ulyanovsk State University; graduated from the Faculty of Information Technology of Ulyanovsk State University;
programmer at Federal ResearchandProduction Center ResearchandProduction Association Mars; is interested
in the field of development of mathematical models and software systems for interoperability of computeraided
systems [email: mars@mv.ru]A. Kukin


Performance Evaluation for Interoperated Systems
The article deals with a comprehensive approach to selection of optimal design solutions for system architecture of hierarchical
computeraided control system. The approach consists in combination of mathematical modeling and experimental researches
using simulators of interacting systems. The mathematical models based on the experimental dependencies, enable to
evaluate the performance of universal computeraided packages taking into account different requirements for processing
of information flows. Mathematical modeling, simulator of computeraided system, flow of information, performance of universal computeraided packages, experimental research.



Sections: Mathematical modeling, calculi of approximations and software systems
Subjects: Automated control systems, Mathematical modeling. 
Dmitry Alexanderovich Istomin, PJSC 'Ulyanovsk Instrument Manufacturing Design Bureau', Postgraduate student at Ulyanovsk State Technical University; graduated from the Faculty of RadioEngineering of Ulyanovsk State Technical University; head of a department of PJSC 'Ulyanovsk Instrument Manufacturing Design Bureau'; author of articles, inventions in the field of probes for pressure perception of aerometric systems of aircraft. [email: nio24@ukbp.ru]D. Istomin, Ivan Petrovich Efimov, Ulyanovsk State Technical University, Candidate of Engineering; graduated from Ulyanovsk Polytechnic Institute in the profession 'Aircraft Instrument Making'; Associate Professor at the Chair 'Measuring and Computational Systems' of Ulyanovsk State Technical University; author of articles, inventions in the field of primary pressure transducers of aerodynamic systems of aircraft. [email: eip@ulstu.ru]I. Efimov, Mikhail Iurievich Sorokin, PJSC 'Ulyanovsk Instrument Manufacturing Design Bureau', Candidate of Engineering; graduated from the Faculty of Information Systems and Technology of Ulyanovsk State Technical University; head of a department of PJSC 'Ulyanovsk Instrument Manufacturing Design Bureau'; author of articles, inventions in the field of probes for pressure perception of aerometric systems of aircraft. [email: rto@ukbp.ru]M. Sorokin


A Study of Air Pressure Probes With Aerodynamic Compensation
The paper presents results of trials and a mathematical modeling of air pressure probes with corrugated surface aerodynamic compensation, and gives a rationale to use mathematical modeling for further design of such air pressure probes. Static pressure, mathematical modeling, air pressure probe, aerodynamic compensation.



Sections: Mathematical modeling, calculus of approximations and software systems
Subjects: Mathematical modeling. 
