NUMERICAL SIMULATION OF THE PROPAGATION OF A GAS SHOCK WAVE IN ELECTRICALLY CHARGED AND NEUTRAL GAS SUSPENSION IN A FLAT CHANNEL

Author(s):  
D.A. TUKMAKOV

In this paper, we consider the propagation of a shock wave from a pure gas into a heterogeneous mixture consisting of solid particles suspended in a gas and having an electric charge. The applied mathematical model takes into account the speed and thermal interaction of the carrier and dispersed components of the mixture. The force interaction of particles and gas was described by the Stokes force. The carrier medium was described as a viscous compressible heat–conducting gas. The equations of the mathematical model were solved by the explicit finite–difference method of the second order of accuracy, using the non–linear correction of the grid function. The system of equations of the mathematical model was supplemented by boundary and initial conditions for the desired functions. As a result of numerical simulation, it was found that in an electrically charged gas suspension there is a difference in gas pressure and velocity, “average density” and velocity of the dispersed component, compared with similar values in a gas suspension with an electrically neutral dispersed component. The revealed differences in the dynamics of neutral and electrically charged dusty media can be explained by the fact that the dispersed component of an electrically charged gas suspension is affected by both aerodynamic drag forces and Coulomb forces. Due to interfacial interaction, the dynamics of the carrier medium changes.

2009 ◽  
Vol 4 (2) ◽  
pp. 13-18
Author(s):  
Igor Anufriev ◽  
Aleksandr Golovanov ◽  
Aleksandr Tsimbalyuk ◽  
Oleg Sharypov

Current work covers experimental and theoretical investigation of conic confusers impact on the intensity shock wave, generated in the shock tube by explosion of gunpowder charge. For given conditions optimal geometric characteristics of the confuser, providing maximal pressure in the shock wave front, were found experimentally. The mathematical model was developed and numerical simulation of the axisymmetric shock-wave gas flow in the channel was carried out. Experimentally was shown, that the application of the optimal confuser provides significant increase of the efficiency gasdynamic effect on the combustion of forest combustible materials.


2020 ◽  
Vol 4 (97) ◽  
pp. 77-88
Author(s):  
DMITRII A. TUKMAKOV

The paper presents a mathematical model of an electrically charged suspension of particles, as well as numerical calculations related to the dynamics of the dispersed component of a mixture moving both under the influence of aerodynamic forces and under the influence of the Coulomb force. The author used a mathematical model of a nonequilibrium multiphase medium motion to describe the aerodynamics of suspensions. The mathematical model took into account the force interaction of the carrier and dispersed phases and interphase heat transfer, as well as the internal electric field generated by electrically charged solid particles. Using the software implementation of the mathematical model, a numerical study of the velocity slip of phases was carried out.


Author(s):  
Д.А. Тукмаков ◽  
Н.А. Тукмакова

В работе моделируется течение однородного газа и неоднородной среды. Целью работы является изучение влияния размера частиц дисперсной компоненты смеси на истечение дисперсной среды в вакуум и выявление отличий от процесса истечения в вакуум однородного газа. Математическая модель, примененная в данной работе, реализует континуальную методологию моделирования течения неоднородной среды, такого рода методика моделирования движения смеси предполагает решение полной гидродинамической системы уравнений движения для каждой из компонент смеси, системы уравнений движения компонент смеси связаны слагаемыми, отвечающими за межфазное силовое и тепловое взаимодействие. Система уравнений включает уравнения непрерывности для плотности несущей среды и средней плотности дисперсной компоненты смеси. Для описания сохранения импульса несущей среды решалось уравнение Навье-Стокса, для дисперсной компоненты смеси также записывалось уравнение сохранения импульса с учетом слагаемых отвечающих за межкомпонентное взаимодействие. Уравнения сохранения энергии компонент смеси решались с учётом межкомпонентного теплообмена. Система уравнений математической модели дополненная краевыми условиями решалась явным конечно-разностным методом второго порядка точности. В результате моделирования выявлены отличия в распределении параметров сплошной среды при распространении в вакуум чистого газа и газовой взвеси частиц. Также выявлено влияние размера частиц дисперсной фазы на процесс истечение несущей среды и дисперсной компоненты газовзвеси в вакуум. The work simulates the flow of a homogeneous gas and an inhomogeneous medium. The aim of the work is to study the influence of the particle size of the dispersed component of the mixture on the outflow of the dispersed medium into vacuum and to identify differences from the process of outflow of a homogeneous gas into the vacuum. The mathematical model used in this work implements a continuous methodology for modeling the flow of an inhomogeneous medium, this kind of methodology for modeling the mixture motion involves solving the complete hydrodynamic system of equations of motion for each of the components of the mixture, the systems of equations of motion of the components of the mixture are connected by terms responsible for the interphase force and thermal interaction. The system of equations includes continuity equations for the density of the carrier medium and the average density of the dispersed component of the mixture. To describe the momentum conservation of the carrier medium, the Navier-Stokes equation was solved for the dispersed component of the mixture, the equation of momentum conservation was also written taking into account the terms responsible for the intercomponent interaction. The energy conservation equations for the mixture components were solved taking into account inter-component heat transfer. The system of equations of the mathematical model supplemented by boundary conditions was solved by an explicit finite-difference method of the second order of accuracy. As a result of the simulation, differences in the distribution of the parameters of a continuous medium during the propagation of pure gas and gas suspension of particles into a vacuum are revealed. The effect of the particle size of the dispersed phase on the process of the outflow of the carrier medium and the dispersed component of the gas suspension into vacuum was also revealed.


Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.


Author(s):  
Yu Zhao ◽  
Yingying Wang ◽  
Liwei Li ◽  
Chao Yang ◽  
Yang Du ◽  
...  

The sheave installation method (SIM) is an effective and non-conventional method to solve the installation of subsea equipment in deep water (>1000m), which has been developed to deploy the 175t Roncador Manifold I into 1,885 meters water depth in 2002. With the weight increment of subsea cluster manifold, how to solve its installation with the high reliability in the deep sea is still a great challenge. In this paper, the installation of the 300t subsea cluster manifold using the SIM is studied in the two-dimensional coordinate system. The mathematical model is established and the lumped mass method is used to calculate the hydrodynamic forces of the wireropes. Taking into account the complex environment loads, the numerical simulation of the lowering process is carried out by OrcaFlex. The displacement and vibration of the subsea cluster manifold in the z-axis direction and the effective tension at the top of the wireropes can be gotten, which can provide guidance for the installation of the cluster manifold in the South China Sea.


2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .


2021 ◽  
Vol 2090 (1) ◽  
pp. 012049
Author(s):  
N V Kovalenko ◽  
A V Smirnov ◽  
O A Ryabushkin

Abstract The mathematical model that describes the local heating of biological tissues by optical radiation is introduced. Changes of the electric properties of biological tissues in such process can be used as a reliable tool for analyzing heating and damage degrees of tissues.


2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Qixin Zhu ◽  
Hongli Liu ◽  
Yiyi Yin ◽  
Lei Xiong ◽  
Yonghong Zhu

Mechanical resonance is one of the most pervasive problems in servo control. Closed-loop simulations are requisite when the servo control system with high accuracy is designed. The mathematical model of resonance mode must be considered when the closed-loop simulations of servo systems are done. There will be a big difference between the simulation results and the real actualities of servo systems when the resonance mode is not considered in simulations. Firstly, the mathematical model of resonance mode is introduced in this paper. This model can be perceived as a product of a differentiation element and an oscillating element. Secondly, the second-order differentiation element is proposed to simulate the resonant part and the oscillating element is proposed to simulate the antiresonant part. Thirdly, the simulation approach for two resonance modes in servo systems is proposed. Similarly, this approach can be extended to the simulation of three or even more resonances in servo systems. Finally, two numerical simulation examples are given.


2011 ◽  
Vol 4 (2) ◽  
pp. 435-449 ◽  
Author(s):  
P. E. Farrell ◽  
M. D. Piggott ◽  
G. J. Gorman ◽  
D. A. Ham ◽  
C. R. Wilson ◽  
...  

Abstract. Verification is a process crucially important for the final users of a computational model: code is useless if its results cannot be relied upon. Typically, verification is seen as a discrete event, performed once and for all after development is complete. However, this does not reflect the reality that many geoscientific codes undergo continuous development of the mathematical model, discretisation and software implementation. Therefore, we advocate that in such cases verification must be continuous and happen in parallel with development: the desirability of their automation follows immediately. This paper discusses a framework for automated continuous verification of wide applicability to any kind of numerical simulation. It also documents a range of test cases to show the possibilities of the framework.


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