scholarly journals Development of mathematical models for calculating parameters during transportation of a steam-water mixture

2021 ◽  
pp. 94-109
Author(s):  
А.А. Чермошенцева ◽  
А.Н. Шулюпин
Keyword(s):  
Mathematical Model ◽  
Geothermal Energy ◽  
Stream Water ◽  
Hydraulic Calculation ◽  
Water Mixture ◽  
Program Model ◽  
Flow Parameters ◽  
Geothermal Fields ◽  
New Challenges ◽  
The Stability

В практике освоения геотермальных месторождений возникает необходимость нахождение взаимосвязи между параметрами потока. При транспортировке пароводяной смеси требуется определение условий, обеспечивающих стабильную работу трубопровода. На отечественных объектах геотермальной энергетики гидравлический расчет трубопроводов пароводяной смеси проводился с использованием компьютерной программы MODEL, разработанной авторами данной работы. Новые вызовы и появление теории устойчивости привели к созданию математической модели SWIP (Steam-Water Inclining Pipeline). В данной статье представлены этапы разработки авторами новой модели, отвечающей современным требованиям In the practice of developing geothermal fields, there is a need to find the dependence between the flow parameters. When transporting a steam-water mixture, it is necessary to determine the conditions that ensure the stability in the pipeline. At domestic geothermal energy, the hydraulic calculation of steam-water mixture pipelines was carried out using the computer program MODEL created by the authors of this work. New challenges and the emergence of the theory of stability led to the creation of a mathematical model SWIP (Stream-Water Inclining Pipeline). This article presents the stages of creating a new model by the authors that meets modern requirements.

scholarly journals Comparative analysis of computer programs for hydraulic calculation of steam-water mixture in pipelines

2021 ◽  
Vol 895 (1) ◽  
pp. 012011
Author(s):  
A Chermoshentseva ◽  
A Shulyupin
Keyword(s):  
Comparative Analysis ◽  
Geothermal Energy ◽  
Hydraulic Calculation ◽  
Stable Operation ◽  
Water Mixture ◽  
Program Model ◽  
Flow Parameters ◽  
Geothermal Fields ◽  
New Challenges ◽  
The Mathematical Model

Abstract In the practice of developing geothermal fields, it is necessary to forecast the flow parameters of the well and the pressure drop in the pipeline and need to decide on the optimal design for stable operation of the pipeline. At domestic facilities of geothermal energy, the hydraulic calculation of the steam-water mixture pipelines was carried out using the computer program MODEL developed by the authors of this work. New challenges and the emergence of stability theory led to the creation of the mathematical model SWIP (Steam-Water Inclining Pipeline). This paper presents a comparative analysis of two options for implementing the new model.

scholarly journals Influence geometry of the pipeline at the stability of steam-water flow during the exploitation of a geo-power station

2020 ◽  
pp. 143-153
Author(s):  
А.Н. Шулюпин ◽  
А.А. Чермошенцева ◽  
Н.Н. Варламова
Keyword(s):  
Water Flow ◽  
Flow Instability ◽  
Gravitational Effect ◽  
Hydraulic Calculation ◽  
Water Mixture ◽  
Two Phase ◽  
Gravitational Forces ◽  
Geothermal Fields ◽  
The Stability ◽  
Carrier Transportation

Исследуются случаи существования неустойчивости потока, вызванной влиянием гравитационных сил в трубопроводах пароводяной смеси на геотермальных месторождениях. Представлена новая разработанная авторами математическая модель пароводяного течения, учитывающая гравитационный эффект и удовлетворяющая новым вызовам при освоении геотермальных месторождений с двухфазной транспортировкой теплоносителя. Показано влияние наклона трубопровода и рельефа трассы на гравитационную устойчивость течения. Даны рекомендации по гидравлическому расчету и строительству трубопроводов пароводяной смеси. Cases of flow instability caused by the influence of gravitational forces in pipelines of steam-water mixture in geothermal fields are investigated. A new mathematical model of the steam-water flow was developed by authors, taking into account the gravitational effect and satisfying new requirements in the development of geothermal deposits with two-phase heat carrier transportation. The influence of the pipeline incline at the gravitational stability of the flow is shown. Recommendations on hydraulic calculation and construction of steamwater mixture pipelines are given.

scholarly journals A new program for the hydraulic calculation of steam-water mixture pipelines in geothermal fields

2020 ◽  
Vol 192 ◽  
pp. 04004
Author(s):  
Aleksandr Shulyupin ◽  
Alla Chermoshentseva ◽  
Natalia Varlamova
Keyword(s):  
Gravitational Effect ◽  
Water Velocity ◽  
Hydraulic Calculation ◽  
Water Mixture ◽  
Two Phase ◽  
Drift Model ◽  
Geothermal Fields ◽  
Proposed Model ◽  
Empirical Coefficients ◽  
Positive Results

A new mathematical model of steam-water flow in a pipeline, which takes into account the gravitational effect and satisfies new challenges in the development of geothermal fields with two-phase transportation of the heat carrier is presented. Taking into account the gravitational effect in the upstream flows, a method based on the “drift model”, which determines the steam velocity averaged over the crosssection was used. A similar method is proposed for downstream flows, but it determines the water velocity averaged over the cross-section. In this case, analogs of empirical coefficients were used. These coefficients determined from the condition of equality of parameters calculated using different approaches in a horizontal flow. The model was verified, which showed positive results. The proposed model significantly expands the possibilities of hydraulic calculation of steam-water mixture pipelines in geothermal fields.

scholarly journals Transportation of steam-water mixture during development of steam-water fields.

2018 ◽  
Vol 56 ◽  
pp. 01008 ◽  
Author(s):  
Alexander Shulyupin ◽  
Natalia Varlamova
Keyword(s):  
Hydraulic Resistance ◽  
High Flow ◽  
Low Flow ◽  
Water Mixture ◽  
Flow Rates ◽  
Foreign Experience ◽  
Scientific Principles ◽  
New Challenges ◽  
The Stability

The main problems of transporting the steam-water mixture revealed during steam-water fields development: pulsations of parameters at low flow rates and considerable hydraulic resistance at high flow rates. The domestic experience of the calculation of steam-water mixture pipelines, oriented to the dispersed-ring flow, is considered. Based on the analysis of domestic and foreign experience in the steam-water fields development, new challenges have been identified that make it urgent to develop scientific principles for the transport of steam-water mixture at low rates, taking into account modern concepts of the stability of steamwater flows.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

Resonance in a mathematical model of baroreflex control: arterial blood pressure waves accompanying postural stress

2005 ◽  
Vol 288 (6) ◽  
pp. R1637-R1648 ◽  
Author(s):  
Peter E. Hammer ◽  
J. Philip Saul
Keyword(s):  
Blood Pressure ◽  
Mathematical Model ◽  
Blood Volume ◽  
Low Frequency ◽  
Pressure Waves ◽  
Central Blood Volume ◽  
Arterial Baroreflex ◽  
Arterial Blood ◽  
Gain Margin ◽  
The Stability

A mathematical model of the arterial baroreflex was developed and used to assess the stability of the reflex and its potential role in producing the low-frequency arterial blood pressure oscillations called Mayer waves that are commonly seen in humans and animals in response to decreased central blood volume. The model consists of an arrangement of discrete-time filters derived from published physiological studies, which is reduced to a numerical expression for the baroreflex open-loop frequency response. Model stability was assessed for two states: normal and decreased central blood volume. The state of decreased central blood volume was simulated by decreasing baroreflex parasympathetic heart rate gain and by increasing baroreflex sympathetic vaso/venomotor gains as occurs with the unloading of cardiopulmonary baroreceptors. For the normal state, the feedback system was stable by the Nyquist criterion (gain margin = 0.6), but in the hypovolemic state, the gain margin was small (0.07), and the closed-loop frequency response exhibited a sharp peak (gain of 11) at 0.07 Hz, the same frequency as that observed for arterial pressure fluctuations in a group of healthy standing subjects. These findings support the theory that stresses affecting central blood volume, including upright posture, can reduce the stability of the normally stable arterial baroreflex feedback, leading to resonance and low-frequency blood pressure waves.

Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

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