ISSN 1991-2927

## Keyword: "mathematical modeling"

 V. Kovalnogov, R. Fedorov, L. Khakhaleva, 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; heat-shielding coatings. One of the most effective ways to protect surfaces from overheating is a thermal protection in the form of film-like surface cooling based on the mass-transfer surface-cooling 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.
 2018_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V. Kovalnogov, D. Generalov, A. Chukalin, R. Fedorov, 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 gas-dynamic temperature stratification. The authors consider the possibility of increasing the efficiency of cooling turbine blades due to the phenomenon of gas-dynamic 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.
 2017_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V. Kovalnogov, A. Chukalin, L. Khakhaleva, R. Fedorov, 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.
 2017_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 I. Sedykh, 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 switching-on duration was described in the article. Neural networks-based 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 network-based algorithm allows to put in practice flexible control of coordination traffic lights in case of the non-fixed 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.
 2017_ 1

Sections: Artificial intelligence

Subjects: Artificial intelligence.

 A. Ivanov
 Differential Models of Information Processing in Hierarhical Computer-aided Control System Authorities The analysis of information processing in hierarchical computer-aided 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.
 2015_ 4

Sections: Automated control systems

Subjects: Automated control systems, Architecture of ship's system.

 M. Dubinina, M. Sorokin
 A Mathematical Model of Pressure Traverse of a Pitot-static System Cross Section The article considers the results of researching pitot-static systems. The authors have been created mathematical model of pressure traverse of a pitot-static system cross-section. 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 pitot-static 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, pitot-static system, pressure traverse, air consumption.
 2015_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A. Zolotov, V. Kovalnogov, M. Kornilova
 Modeling and Researching the Technique of Thermal Protection of Turbomachines Blades With the Use of Gas-dynamic 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 . 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 . 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 gas-dynamic 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 program-informational complex which will take into account the results of studies of gas-dynamic processes in high- speed, disperse flows including the phenomenon of gas-dynamic temperature stratification carried out at the Department of Heat Power Engineering at Ulyanovsk State Technical University.Mathematical modeling, numerical methods, thermal protection, convective-film cooling, software and information complex, dispersed flow, gas-dynamic temperature stratification.
 2015_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling, Computer-aided engineering.

 V. Kovalnogov, R. Fedorov, L. Khakhaleva, 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 . Further researches overviewed in the paper  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  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.
 2015_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A. Andreev, E. Kudashova
 On Modeling the Control Structure of the Omni-directional Mobile Robo Nowadays, requirements to modeling and researching self-directed robotic systems are extremely high. In order to improve maneuverability and control efficiency, new mobile robots with omni-wheels 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 four-wheeled mobile robots with roller-carrying wheels have become more widespread. The article deals with the problem of theoretical control establishing to provide arbitrary program motion of three-wheeled robots with omni-wheels. 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 three-wheeled robot motion stabilization.Mathematical modeling, three-wheeled robot, stabilization, control, digitization.
 2015_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Artificial intelligence.

 P. Velmisov, 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 integro-differential 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 Runge-Kutta 6-th order method with the error control at each step, Newton's method for solving nonlinear equations and integration with the use of Newton-Kotesa 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 Runge-Kutta 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.
 2015_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 P. Velmisov, 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 non-linear 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.
 2015_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 R. Fedorov, D. Generalov, M. Kornilova
 Mathematical Modeling and Numerical Analysis of a Thermal State of Turbo-mashine Blades Affected By a Supersonic Dispersed Flow The development of the advanced gas-turbines 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 turbo-machine blades affected by a supersonic dispersed flow including a gas-dynamic 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 convective-film 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, convective-film cooling, software and information complex, dispersed flow.
 2014_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A. Tcynaeva
 Numerical Investigation of the Temperature Stratification The intensity of heat and mass transfer in devices based on the gas-dynamic 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 gas-dynamic 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 gas-dynamic temperature stratification.It was found that the intensification of heat transfer devices based on the gas-dynamic 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 copper-water is more of using efficiency of heat pipes with the working material in the aluminum-acetone up to 1.05 ... 1.12 times.Mathematical modeling, numerical investigation, temperature stratification, intensification, heat pipes.
 2014_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 P. Velmisov, S. Kireev
 Mathematical Modelling in Instability Problems of Elastic Structural Elements in Gas Flow On the basis of the proposed non-linear models and developed numerical method for the solution to the corresponding non-linear boundary-value 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 bifurcation-problem solution includes the 6-th order Runge-Kutta method with the error control at the step, the Newton's method required for solving non-linear equations, and integration using Newton-Kotesa quadrature. The solution to the boundary-value 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 Runge-Kutta 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 bending-forms 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, boundary-value problem, mathematical modelling, numerical method.
 2014_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V. Moiseev, M. Sorokin, I. Efimov, N. Makarov
 Mathematical Model for Pitot-static 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 T-129 wind tunnel of TsAGI with nozzle-jet 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 Pitot-static 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, pitot-static probe, mathematical model.
 2014_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A. Tcynaeva, E. Tcynaeva, 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.
 2013_ 2

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Mathematical modeling.

 A. Andreev, A. Artemova, Y. Petrovicheva
 Modeling of Controlled Motionof Coupled Rigid-body 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.
 2012_ 4

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Mathematical modeling.

 A. Kupriyanov, 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 computer-aided 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 computer-aided packages taking into account different requirements for processing of information flows.Mathematical modeling, simulator of computer-aided system, flow of information, performance of universal computer-aided packages, experimental research.
 2012_ 3

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Automated control systems, Mathematical modeling.

 D. Istomin, I. Efimov, 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.
 2011_ 4

Sections: Mathematical modeling, calculus of approximations and software systems

Subjects: Mathematical modeling.

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