Study on the Mathematical Model of Vacuum Breaker Valve for Large Air Mass Conditions

The mathematical model of vacuum breaker valve is significant to the protection scheme. The more accurate the vacuum breaker valve model, the more reliable the calculation results. In this study, the application conditions of the air valve model are analyzed according to the assumptions used in the derivation, and the contradictions between these assumptions are proposed. Then, according to the different working characteristics between the vacuum breaker valve on the siphon outlet pipe and the air valve, the vacuum breaker valve model is deduced based on the modified assumptions. In the derivation process, the thermodynamic change of the gas in the vacuum breaker valve is assumed to follow the isentropic process rather than an isothermal process, and the water level in the vacuum breaker valve is considered to be changeable. An engineering case is introduced, and the results calculated according to the vacuum breaker valve model are compared with those resulting from the air valve model. The results indicate that the vacuum breaker valve model is suitable for large air mass conditions and can provide a theoretical basis for the numerical simulation and settings of vacuum breaker valves.

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Mathematical Model for Charpy Impact Energy of V-Notch Specimens

Advances in Materials Science and Engineering ◽

10.1155/2021/5330068 ◽

2021 ◽

Vol 2021 ◽

pp. 1-7

Author(s):

Wei Wang ◽

Ping Wang ◽

Xuesong Liu ◽

Zhibo Dong ◽

Hongyuan Fang

Keyword(s):

Mathematical Model ◽

Impact Energy ◽

Material Properties ◽

Theoretical Basis ◽

Impact Resistance ◽

Charpy Impact ◽

The Impact ◽

The Mathematical Model ◽

The Relationship ◽

Derivation Process

Firstly, by analyzing the response of Charpy V-notch specimen impacted by pendulum, the relationship between specimen geometry, material properties, and impact energy is established and simplified, and the mathematical model for evaluating impact energy of specimens with different sizes is established. Then, the effectiveness of the model through a series of impact tests is verified. Theoretical analysis and experimental results show that the relationship between ligament length and impact energy is quadratic, while the relationship between ligament thickness and impact energy is linear. In the derivation process, the intrinsic impact toughness is used to evaluate the toughness of materials. The mathematical model makes it possible to evaluate the impact energy of specimens with different sizes and provides a theoretical basis for evaluating the impact resistance of structures.

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ПОБУДОВА МАТЕМАТИЧНОЇ МОДЕЛІ СКЛАДНОГО РУХУ ФЛАКОНІВ НА ЛІНІЯХ РОЗЛИВУ ЛІКІВ ФАРМАЦЕВТИЧНОЇ ПРОМИСЛОВОСТІ

Medical Informatics and Engineering ◽

10.11603/mie.1996-1960.2010.4.146 ◽

2012 ◽

Author(s):

N. О. Kravets

Keyword(s):

Mathematical Model ◽

Experimental Evaluation ◽

Theoretical Dependence ◽

Complex Product ◽

Lateral Lines ◽

Calculation Results ◽

The Mathematical Model

The mathematical model of the complex product motion along the lateral lines at the plate conveyers of the bottle lines is presented in the artcle. The experimental evaluation of the gained theoretical dependence is suggested. The calculation results coordinate well with the modelling and experiment resuls.

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KINEMATIC WAVE EQUATIONS FOR MOVABLE RIVERBEDS

Meteorologiya i Gidrologiya ◽

10.52002/0130-2906-2021-6-43-54 ◽

2021 ◽

pp. 43-54

Author(s):

A. N. Krutov ◽

◽

S. Ya. Shkol’nikov ◽

Keyword(s):

Mathematical Model ◽

Numerical Method ◽

Wave Equations ◽

Simple Wave ◽

Kinematic Wave ◽

Calculation Results ◽

Self Similar ◽

Аpplication of the mathematical model of human torso for modeling abbreval influence in wound ballistics

Vestnik of Russian military medical Academy ◽

10.17816/brmma50549 ◽

2020 ◽

Vol 22 (3) ◽

pp. 132-139

Author(s):

A. V. Denisov ◽

M. D. Stepanov ◽

N. A. Haraldin ◽

A. V. Stepanov ◽

A. I. Borovkov ◽

...

Keyword(s):

Mathematical Model ◽

Element Model ◽

Mechanical Action ◽

Calculation Model ◽

Calculation Results ◽

Automated Processing ◽

Original Calculation ◽

Using Data ◽

The Mathematical Model ◽

Selection Of

Abstract. In the work, a review of scientific articles on the behavior of tissues and organs of the human body under local mechanical effects on it, as well as a description of the physico-mechanical properties of biological materials. The selection of mechanical behavior for each biological material as part of a mathematical model of the human torso was carried out, its finite element model was created, validation experiments were modeled using data presented in the literature. An original calculation model of a human torso with a tuned interaction of organs with each other was developed. Contact interaction parameters are determined. The developed computational model of a human torso was verified based on data from open sources for an experiment with mechanical action by a cylindrical impactor. An algorithm for processing pressure and acceleration graphs has been implemented in order to obtain tolerance curves. A specialized modular program has been created for the automated processing of calculation results and the output of the main results. 42 numerical tests were carried out simulating the entry of a steel ball into each of 21 zones for power engineers of 40 and 80 J. According to the results of the tests for each organ, pressure and acceleration tolerance curves were obtained, animations of the behavior of organs under shock were created, visualization of the pressure field propagation in organs was obtained torso.

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Effect of a Commercial Air Valve on the Rapid Filling of a Single Pipeline: a Numerical and Experimental Analysis

Water ◽

10.3390/w11091814 ◽

2019 ◽

Vol 11 (9) ◽

pp. 1814 ◽

Cited By ~ 6

Author(s):

Óscar E. Coronado-Hernández ◽

Mohsen Besharat ◽

Vicente S. Fuertes-Miquel ◽

Helena M. Ramos

Keyword(s):

Mathematical Model ◽

Air Water Interface ◽

Water Pipelines ◽

Polytropic Equation ◽

Pipeline Failure ◽

Air Valve ◽

Thermodynamic Variables ◽

Air Pockets ◽

The Mathematical Model ◽

Oscillation Equation

The filling process in water pipelines produces pressure surges caused by the compression of air pockets. In this sense, air valves should be appropriately designed to expel sufficient air to avoid pipeline failure. Recent studies concerning filling maneuvers have been addressed without considering the behavior of air valves. This work shows a mathematical model developed by the authors which is capable of simulating the main hydraulic and thermodynamic variables during filling operations under the effect of the air valve in a single pipeline, which is based on the mass oscillation equation, the air–water interface, the polytropic equation of the air phase, the air mass equation, and the air valve characterization. The mathematical model is validated in a 7.3-m-long pipeline with a 63-mm nominal diameter. A commercial air valve is positioned in the highest point of the hydraulic installation. Measurements indicate that the mathematical model can be used to simulate this phenomenon by providing good accuracy.

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Design Method of Self-Loading Device of the Side-Crane Used for Container

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.466-467.951 ◽

2012 ◽

Vol 466-467 ◽

pp. 951-955

Author(s):

Jun Qing Zhan ◽

Xiao Mei Feng ◽

Li Shun Li ◽

Xiang De Meng

Keyword(s):

Mathematical Model ◽

Structural Design ◽

Design Method ◽

The Self ◽

Design Calculation ◽

Force Analysis ◽

Loading Device ◽

Calculation Results ◽

The Mathematical Model ◽

Flat Ground

The self-loading device used for side-crane is put forward. Its structure is presented. Based on the force analysis when the side-crane works at flat ground, the mathematical model is established when the crane working at uneven ground. And the design calculation is performed. The self-loading device’s optimal design is accomplished. Based on the above calculation results, the self-loading prototype is manufactured. And the design method can be adopted to the similar equipment’s structural design.

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Research on the Convergence Condition of Iterative Solution for the Mathematical Model of Reservoir Power Generation Optimization

10.5194/egusphere-egu2020-1992 ◽

2020 ◽

Author(s):

Anqi Tan ◽

Senlin Chen

Keyword(s):

Mathematical Model ◽

Power Generation ◽

Iterative Process ◽

Iterative Solution ◽

Scheduling Optimization ◽

Convergence Conditions ◽

Generation Scheduling ◽

Solution Convergence ◽

Calculation Results ◽

The Mathematical Model

<p>Discrete differential dynamic programming algorithm is widely used in reservoir power generation dispatching, but the problem of "dimensional disaster" still exists, and there are different degrees of limitations such as premature convergence and uncertainty of convergence. In the existing monographs and literature, there is little research on the algorithm itself. The iterative solution convergence conditions, initial parameters, and initial trajectory selection of the mathematical model for reservoir power generation scheduling optimization have important effects on the iterative process and results. The convergence conditions directly determine when the iterative process converges and its calculation results. In this paper, the solution convergence conditions are studied. Based on the calculation results of the mathematical model of reservoir power generation scheduling optimization, the method of iteratively solving the convergence conditions when different state quantities are used as control factors is systematically studied. Shuibuya Hydropower Station Scheduling results show that using this method to determine the termination step size can shorten the calculation time and obtain an optimization result close to the ideal value, avoid the randomness of the convergence process of the iterative solution, and improve the accuracy of the DDDP algorithm and the efficiency of the target value.</p>

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Mathematical model of management of recirculation of motor aggregates

Informacionno-technologicheskij vestnik ◽

10.21499/2409-1650-2017-2-25-35 ◽

2017 ◽

Vol 12 (2) ◽

pp. 25-35 ◽

Cited By ~ 1

Author(s):

A. E. Abbasov

Keyword(s):

Mathematical Model ◽

Combustion Temperature ◽

Three Dimensional ◽

Motor Units ◽

Toxic Substances ◽

Model Of Management ◽

Calculation Results ◽

Control Dependence ◽

Maximum Combustion Temperature ◽

The Mathematical Model

A mathematical model of management of recirculation of motor units is developed. It is shown that the efficiency of recirculation control is achieved with a decrease in the content of toxic substances in the exhaust; Limiting the maximum combustion temperature of the fuel and the pressure in the combustion chamber; Speed control. Based on the mathematical model, an algorithm is developed for calculating the control dependence for the regulation of the position of the electromechanical recirculation valve in specialized graphic computer environments with three-dimensional and two-dimensional visualization of analysis and calculation results. Calculation of the amount of emissions of harmful substances without the developed algorithm and using the developed algorithm is carried out.

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Critical Length and Collapse of Interlayer in Rock Salt Natural Gas Storage

Advances in Civil Engineering ◽

10.1155/2018/8658501 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8

Author(s):

Yingjie Wang ◽

Jianjun Liu

Keyword(s):

Mathematical Model ◽

Rock Salt ◽

Critical Length ◽

Gas Storage ◽

Mechanical Instability ◽

Calculation Results ◽

The Stability ◽

Salt Cavern Gas Storage ◽

The Mathematical Model ◽

Physical And Mechanical Characteristics

The existence of an interlayer has a significant effect on the stability of a rock salt gas storage cavity; therefore, an uncontrollable collapse of the interlayer would cause a series of issues. In this study, three types of mechanical instability criteria are comprehensively calculated. The limit radius of the interlayer is computed under different criteria, and the collapse radius of the interlayer is obtained by comparison. The calculation results of the mathematical model are highly accurate with respect to actual engineering logging data, in general with over 90% of accuracy. It is demonstrated that, besides the physical and mechanical characteristics of the sandwich, the location of the interlayer in the cavity and concentration of the brine also have an important effect on the collapse of the interlayer. The brine at the bottom of the cavity is nearly saturated. Therefore, an interlayer at this location does not easily collapse. The mathematical model established in this study is used in the seismic design and prediction of interlayer collapse during the construction of salt-cavern gas storage facilities in China.

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Life Prediction of Bearings Based on Fuzzy Theory

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.455.422 ◽

2010 ◽

Vol 455 ◽

pp. 422-426 ◽

Cited By ~ 1

Author(s):

X.Q. Wang ◽

F.K. Cui ◽

G.B. Wang

Keyword(s):

Mathematical Model ◽

Case Studies ◽

Influencing Factors ◽

Life Prediction ◽

Fuzzy Theory ◽

Membership Degree ◽

Fuzzy Reliability ◽

Calculation Results ◽

The Mathematical Model ◽

Full Consideration

Based on the fuzzy theory and universal calculation equations, the mathematical model is established for predicting life of a bearing by analyzing various factors. And the fuzzy reliability life can be calculated according to the model. The case studies show that for the proposed method takes full consideration of all the influencing factors and their function of membership degree, the calculation results are very close to the actual ones.

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