scholarly journals Modeling of the Free-Surface-Pressurized Flow of a Hydropower System with a Flat Ceiling Tail Tunnel

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 699
Author(s):  
Jianxu Zhou ◽  
Yongfa Li
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Water Surface ◽  
Wave Speed ◽  
Water Levels ◽  
Water Diversion ◽  
Design Stage ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Hydropower System

For a water diversion hydropower system with a flat ceiling tail tunnel with high elevation, during transient states with relatively low tail water levels, free-surface-pressurized flow inevitably appears and its transient characteristics have obvious effects on the system’s operating stability. Using Newton–Raphson linearization in the characteristic implicit format for modeling of the free-surface-pressurized flow in the tail tunnel, the mathematical models for necessary boundary conditions were derived and linear algebraic equations with a band coefficient matrix were grouped for further transient simulation. Then, a unified mathematical model was established for hydraulic transient analysis of the hydropower system with free-surface-pressurized flow. Combined with experimental research and numerical simulation, the wave speed for the free-surface-pressurized flow was experimentally analyzed for further correctness in the unified model, and by comparative analysis the hydraulic characteristics of the free-surface-pressurized flow in the flat ceiling tail tunnel were investigated. It was found that the derived mathematical model can basically represent water behaviors in the water-surface-pressurized flow, the wave speed for the mixed water-surface-pressurized flow can be set to approximately 50m/s, and with this correctness the numerical results are in good agreement with the experimental results. Therefore, the obtained mathematical model combined with an experimental wave speed or a reference wave speed of 50 m/s for the free-surface-pressurized flow is preferable during the design stage of the hydropower system.

scholarly journals Numerical simulation of the non-regular mode of cooling a high-temperature metal billet by the flow of a gas-liquid medium

2018 ◽  
Vol 224 ◽  
pp. 04003
Author(s):  
Sergey Makarov ◽  
Vyacheslav Dement’yev ◽  
Tat’yana Makhneva ◽  
Elena Makarova
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
High Temperature ◽  
Liquid Medium ◽  
Liquid Flow ◽  
Control Volume ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Gas Liquid Flow ◽  
Regular Mode

A mathematical model of heat transfer at cooling a high-temperature metal billet from structural steel by the flow of a gas-liquid medium in a vertical circular channel is presented. The model has been built with the use of the continuum mechanics approaches and the theory of heat-mass transfer. The non-regular mode of cooling is considered. The results of the numerical parametric investigations of the heat transfer at cooling a metal billet are obtained for a standard regime of thermomechanical strengthening on the basis of the mathematical model of conjugate heat transfer in a two-dimensional nonstationary formulation accounting for the symmetry of the cooling medium flow relative to the longitudinal axis of a cylinder. The control volume approach is used for solving the system of differential equations. The flow field parameters are computed by an algorithm SIMPLE. For the iterative solution of the systems of linear algebraic equations the Gauss-Seidel method with under-relaxation is used. Taking into account evaporation in the liquid, the intensity of the change of the rate of cooling the material of the metal cylindrical billet by the laminar gas-liquid flow is analyzed depending on the time of cooling and the velocity of the gas-liquid flow.

scholarly journals MATHEMATICAL MODELING IN SOCIAL AND ECONOMIC SYSTEMS

T-Comm ◽  
2021 ◽  
Vol 15 (5) ◽  
pp. 38-45
Author(s):  
Mikhail I. Grachev ◽  
◽  
Vyacheslav G. Burlov ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Synthesis Method ◽  
Control Process ◽  
Economic Systems ◽  
Algebraic Equations ◽  
Managerial Decision ◽  
Linear Algebraic Equations ◽  
The Social ◽  
New Variables

In the modern rapidly changing world, there are constant changes in all spheres of human activity, including in the social and economic systems, such as education, law, health care. All areas require study for improving management and decision-making mechanisms in order to increase the efficiency of their functioning and further logic of action improving the process of functioning of processes in social and economic systems. The introduction of the sites of educational organizations into educational institutions of higher education (UHE) has led to the need for the person in charge of the site (LOU) of the organization to have a mathematical model of management decisions to counter emerging threats. In this paper, we will consider the process of forming a mathematical model of an administrative decision, which is obtained on the basis of synthesis from the transition states of the system using the Kolmogorov differential equations, by further transforming them into a system of linear algebraic equations (SLAE) and solving them by the Gauss method. Mathematical modeling is based on synthesis processes using the law of preserving the integrity of the object (ZSCO) and the natural science approach (ESA). The use of the synthesis method allows you to achieve the control goal based on the required performance indicators. The proposed mathematical model helps in solving three processes aimed at monitoring the occurrence of a problem in a controlled system, the process of recognizing the problem and the process of implementing a managerial decision to eliminate the problem. The final obtained mathematical solution for modeling the situation in the social and economic system helps to establish a model of LOU behavior depending on the current situation, which will lead to saving time resources and the possibility of its redistribution for solving other problems. The resulting mathematical model can be further complicated by adding new variables and conditions for the implementation of the control process.

scholarly journals Thermistor Temperature Measurement Network with a Small Number of Wires

2019 ◽  
pp. 284-292
Author(s):  
Vladimir V. Shaydurov ◽  
Anna A. Korneeva
Keyword(s):  
Mathematical Model ◽  
Computational Experiment ◽  
Computational Algorithm ◽  
Model Problem ◽  
Algebraic Equations ◽  
Multiple Points ◽  
Power Sources ◽  
Linear Algebraic Equations ◽  
Sequential Solution ◽  
Thermistor Temperature

The article proposes a new measuring circuit for temperature control at multiple points of the product using a sequence of thermistors and diodes with three connecting wires and two voltage sources. A mathematical model and a computational algorithm for calculating the resistance of thermistors are presented which consist in the formation and sequential solution of systems of linear algebraic equations for different ratios of voltages of two power sources. A model problem and the results of a computational experiment are considered

Performance of a Jet-Flapped Hydrofoil Near a Free Surface

1967 ◽  
Vol 11 (04) ◽  
pp. 224-234
Author(s):  
G. R. Hough ◽  
J. P. Moran ◽  
J. C. Erickson
Keyword(s):  
Free Surface ◽  
Differential Equations ◽  
Surface Effects ◽  
Chord Length ◽  
Pitching Moment ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Jet Blowing ◽  
Submergence Depth

The problem of a two-dimensional jet-flapped hydrofoil operating near a free surface at infinite and zero Froude numbers is treated using thin-airfoil theory. The pair of coupled integro-differential equations which governs the system is derived and is reduced to a set of linear algebraic equations by assuming appropriate series forms for the vortex distributions representing the hydrofoil and the jet. A collocation procedure is then used to solve these algebraic equations. The variation of the hydrofoil lift and pitching moment with submergence depth is calculated for several jet blowing configurations. The results indicate that free-surface effects on jet-flapped hydrofoil performance appear to be significant only for operating depths of less than about one chord length for all of the configurations studied.

scholarly journals Method of integro-differential equations for interpreting the results of vertical electrical sounding of the soil

2021 ◽  
pp. 67-70
Author(s):  
D. G. Koliushko ◽  
S. S. Rudenko ◽  
A. N. Saliba
Keyword(s):  
Mathematical Model ◽  
Relative Error ◽  
Power Plants ◽  
Current Source ◽  
Soil Surface ◽  
Observation Point ◽  
Practical Significance ◽  
Maximum Relative Error ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

The paper is devoted to the problem of determining the geoelectric structure of the soil within the procedure of testing the grounding arrangements of existing power plants and substations to the required depth in conditions of dense development. To solve the problem, it was proposed to use the Schlumbergers method , which has a greater sounding depth compared to the Wenner electrode array. The purpose of the work is to develop a mathematical model for interpreting the results of soil sounding by the Schlumberger method in the form of a four-layer geoelectric structure. Methodology. To construct a mathematical model, it is proposed to use the solution of a particular problem about the field of a point current source, which, like the observation point, is located in the first layer of a four-layer soil. Based on this expressions, a system of linear algebraic equations of the 7-th order with respect to the unknown coefficients ai and bi was compiled. On the basis of its analytical solution, an expression for the potential of the electric field was obtained for conducting VES (the point current source and the observation point are located only on the soil surface). Results. Comparison of the results of soil sounding by the Schlumberger installation and the interpretation of its results for the same points shows a sufficient degree of approximation: the maximum relative error does not exceed 9.7 % (for the second point), and the average relative error is 3.6 %. Originality. Based on the obtained expression, a test version of the program was implemented in Visual Basic for Applications to interpret the results of VES by the Schlumberger method. To check the obtained expressions, the interpretation of the VES results was carried out on the territory of a 150 kV substation of one of the mining and processing plants in the city of Kriviy Rih. Practical significance. The developed mathematical model will make it possible to increase the sounding depth, and, consequently, the accuracy of determining the standardized parameters of the grounding arrangements of power stations and substations.

Using computer vision to monitor varying water levels: an exploratory laboratory experience

2021 ◽  
Author(s):  
Jorge Isidoro ◽  
Ricardo Martins ◽  
João de Lima
Keyword(s):  
Computer Vision ◽  
Free Surface ◽  
Water Surface ◽  
Free Water ◽  
Water Levels ◽  
High Temporal Resolution ◽  
Piping System ◽  
Measuring Device ◽  
Spatial And Temporal Scales ◽  
Free Water Surface

<p>Monitoring water levels is fundamental in a variety of fields within geosciences, hydraulics, and hydrology. Examples of this can be found in the field in rivers, reservoirs, or surface runoff while, at a much lower scale, in the laboratory, e.g., open channel flow. This is an area of ​​great complexity, due to the large diversity of spatial and temporal scales of hydraulic systems and phenomena such as the non-linearity of fluid mechanics, sediment or pollutant transport, turbulence, the interactions between water and solid surfaces (natural or artificial), or atmospheric boundary conditions. The last decade has brought important advances in techniques associated with the acquisition and analysis of images, techniques encompassed in what is currently called “computer vision”.</p><p>In this work, a methodology based on image treatment and segmentation techniques was developed, which allows the detection of the free flow water surface over time in laboratory conditions using simple video equipment.</p><p>The objective of this work was to develop and validate an algorithm for detecting the free water surface with high temporal resolution. Other specific objectives were: (i) to validate the algorithm against measurements in a steady-state flow; (ii) to test the algorithm for accentuated oscillations of the free surface resulting from different bed geometries, slope, and discharge; and (iii) to assert the feasibility of the systematic use of non-specialized and inexpensive video equipment as a level measuring device, without compromising its accuracy.</p><p>All laboratory work took place at the Laboratory of Hydraulics, Water Resources and Environment of the Department of Civil Engineering of the Faculty of Sciences and Technology of the University of Coimbra. The channel has dimensions of 4.00m × 0.15m (L×W) and the slope is adjustable. Water is supplied to the channel, in a closed circuit, from a reservoir by means of a pump and piping system, and the flow controlled by a ball valve. The algorithm developed for detecting the free surface is based on the acquisition, treatment, analysis, and segmentation of images. MATLAB® was used to code functions to recognize the edges present in an image by the image intensity gradient as well as the best-defined segment present in the image, which, in this case, corresponds to the free water surface.</p>

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

FEATURES OF APPLICATION OF SMALL RECONNAISSANCE ROBOT

2019 ◽  
pp. 29-38 ◽  
Author(s):  
R. Zinko ◽  
P. Kazan ◽  
D. Khaustov ◽  
O. Bilyk
Keyword(s):  
Mathematical Model ◽  
Armed Forces ◽  
Climatic Conditions ◽  
Design Stage ◽  
Experimental Sample ◽  
Single Trial ◽  
Test Cycle ◽  
Military Equipment ◽  
The Mathematical Model ◽  
Human Losses

A small intelligence robot (SSR) is a special military intelligence means. It is used to obtain information about the enemy - the collection of intelligence, the search for targets and target indication, observation of the situation, etc. The use of a small intelligence robot is assumed in various natural and climatic conditions: in temperate terrain, on soils with low bearing capacity, at low temperatures, in the desert, on sandy and marshy soils, on rocky soils, in elevated temperature and dustiness of air, and also in conditions highlands In the article an overview of modern developments of remotely controlled robotic military complexes, principles of their construction and perspective directions of development in the armed forces are reviewed. The issues of robotization of existing weapons and military equipment are considered. Every sample of a SSR used in combat action must possess all combat characteristics at once in an optimal ratio between them, ensuring its maximum effectiveness. Ignoring any of the properties or enhancing one property at the expense of others will not enable the full realization of the small surveillance robot. It is reasonable to select the relevant properties at the design stage, using the possibilities of mathematical modeling. The set of tactical and technical characteristics of the SSR allowed forming this. Its characteristics determine the scope and possibilities of application. The mathematical model of the SSR motion is written in the Matlab Simulink environment. Recorded mathematical model of SSR motion, formed single test cycle and input data allowed to conduct computer simulation of motion in possible conditions of operation of small surveillance robot.The single trial cycle presented contains a set of individual sites and reproduces the testing test cycle of a real polygon. On the basis of the developed tactical and technical characteristics of the SSR, the experimental sample was made. An example of the use of SSR for the intelligence of the settlement and at keeping the node of barriers has been provided. The efficiency of performing intelligence units’ tasks and reducing the risk of human losses are shown.

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