Numerical Study on the Mathematical Model of the Cardiac Electrical Conduction

A numerical study is presented for Reynolds-averaged Navier-Stokes analysis of three-dimensional turbulent flows in a multiblade centrifugal fan. Present work aims at development of a relatively simple analysis method for these complex flows. A mathematical model of impeller forces is obtained from the integral analysis of the flow through the impeller. A finite volume method for discretization of governing equations and a standard k-ɛ model as turbulence closure are employed. For the validation of the mathematical model, the computational results for velocity components, static pressure, and flow angles at the exit of the impeller were compared with experimental data. The comparisons show generally good agreement, especially at higher flow coefficients.

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Numerical study of the effect of droplet coagulation intensity on polydisperse aerosol fraction distribution

Izvestiya MGTU MAMI ◽

10.31992/2074-0530-2021-47-1-73-80 ◽

2021 ◽

Vol 1 (1) ◽

pp. 73-80

Author(s):

D.A. Tukmakov ◽

Keyword(s):

Mathematical Model ◽

Boundary Conditions ◽

Volume Content ◽

Fine Particles ◽

Stokes Equations ◽

Numerical Study ◽

Dispersed Phase ◽

Mass Force ◽

Carrier Medium ◽

The Mathematical Model

The paper is devoted to the study of the effect of the intensity of aerosol fluctuations on the dis-tribution of fractions of the dispersed component of the coagulating aerosol. Oscillations of aerosol in closed channel are numerically modeled in operation. To describe the dynamics of the carrier medium, a two-dimensional non-stationary system of Navier-Stokes equations for compressed gas is used. They are written taking into account interfacial power interaction and interfacial heat ex-change. To describe the dynamics of the dispersed phase, a system of equations is solved for each of its fractions. It includes an equation of continuity for the “average density” of the fraction, equa-tions of preservation of spatial components of the pulse and an equation of preservation of thermal energy of the fraction of the dispersed phase of the gas suspension. Phase-to-phase power interac-tion included Archimedes force, attached mass force, and aerodynamic drag force. Heat exchange between the carrier medium-gas and each of the fractions of the dispersed phase was also taken into account. The mathematical model of dynamics of polydisperse aerosol was supplemented by the mathematical model of collision coagulation of aerosol. For the velocity components of the mixture, uniform Dirichlet boundary conditions were set. For the remaining functions of the dynamics of the multiphase mixture, uniform Neumann boundary conditions were set. The equations were solved by the explicit McCormack method with a nonlinear correction scheme that allows to obtain a mono-tone solution. As a result of numerical calculations, it was determined that in the vicinity of the os-cillating piston, an area with an increased content of coarse particles is formed. The coagulation process results in a monotonous increase in volume content of the coarse particle fraction and a mo-notonous decrease in volume content of fine particles. Increasing the intensity of gas fluctuations leads to intensification of the process of coagulation of aerosol droplets.

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Study of Macrosegregation Defects Formation Caused by Double Diffusive Convective Flow during Solidification of a Binary Alloy

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.283-286.340 ◽

2009 ◽

Vol 283-286 ◽

pp. 340-345 ◽

Cited By ~ 2

Author(s):

Farid Mechighel ◽

Mahfoud Kadja ◽

Mohammed El Ganaoui ◽

Bernard Pateyron

Keyword(s):

Mathematical Model ◽

Finite Volume ◽

Binary Alloy ◽

Convective Flow ◽

Continuum Model ◽

Numerical Study ◽

Finite Volume Approach ◽

The Mathematical Model ◽

Double Diffusive

Numerical study of both the solidification of the binary alloy Al-4.1%wtCu and macrosegregation defects formation have been carried out. The mixture continuum model was used in the development of the mathematical model representing the solidification phenomena. This model included the conservative equations (mass, momentum, energy and species); these equations were numerically solved by using a finite volume approach.

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A Model for Drilled Cooling in the Valve Bridge of Cylinder Head

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.52-54.338 ◽

2011 ◽

Vol 52-54 ◽

pp. 338-342

Author(s):

Xiao Liu ◽

Wei Zheng Zhang ◽

Chang Hu Xiang

Keyword(s):

Heat Transfer ◽

Mathematical Model ◽

Heat Transfer Coefficient ◽

Diesel Engine ◽

Theoretical Analysis ◽

Transfer Coefficient ◽

Cylinder Head ◽

3D Model ◽

Numerical Study ◽

The Mathematical Model

To evaluate the efficiency of drilled cooling in the valve bridge of cylinder head, theoretical analysis for the drilled cooling is carried out, and a mathematical model for the enhanced cooling is presented based on a simplified 3D model. The mathematical model is validated by numerical study on the heat transfer with and without drilled cooling, which is carried out through fluid-solid coupling. The correlation between the velocity in the drilled passage and heat transfer coefficient was also analyzed. The results can be used to solve the heat transfer in enhanced diesel engine.

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Numerical Study of Being Forced Leather Cap Type Pig in Straight Gas Pipeline

The Open Civil Engineering Journal ◽

10.2174/1874149501610010141 ◽

2016 ◽

Vol 10 (1) ◽

pp. 141-148

Author(s):

Liqiong Chen ◽

Yunyun Li ◽

Xiaoxiao Chen ◽

Yilan Zhan ◽

Meijuan Dang

Keyword(s):

Mathematical Model ◽

Finite Element ◽

Numerical Study ◽

Geometric Model ◽

Gas Pipeline ◽

Average Force ◽

Oil Pipeline ◽

Finite Element Software ◽

Operation Rules ◽

The Mathematical Model

The research on pipeline pigging technology is significant for the operation and management of pipeline. Domestic and foreign scholars usually research the operation rules of pigging in oil pipeline. There are few studies about gas pipeline pigging running because of running rate. The author established the force calculating model and corresponding numerical methods of leather cap type pig in gas pipeline. The model is based on geometric model of oil pipeline pigging. Combining pigging operation parameters with records in September 2013 and February 2014 at Bei Neihuan, the thesis used mathematical method and finite element software respectively to verify the mathematical model. The mathematical results described the average force of cup. The results indicated that the reason of the breaking of the cup is the force, instead of the cup material, temperament extrinsic reasons, etc. The force is larger than the tensile strength of the cup. The results of ANSYS finite element software simulation described the force of different parts of the cup. It is found that the force exceeding of the cup anti-pull force strength in the upper and lower sides of the cup is larger. Both results showed that using the mathematical model can quickly calculate cup pigging force conditions and determine the cause of damage to the cup. It can improve the efficiency of pigging.

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Mathematical model of the elastoplastic shell collapse, taking into account the possible development of the process instability

Engineering Journal Science and Innovation ◽

10.18698/2308-6033-2019-5-1874 ◽

2019 ◽

Author(s):

А.S. Novoseltsev ◽

A.V. Babkin

Keyword(s):

Mathematical Model ◽

External Surface ◽

Numerical Study ◽

Nonstationary Problem ◽

Tangential Direction ◽

Initial Time ◽

Explosive Load ◽

Adjustment Procedure ◽

Elastoplastic Shell ◽

The Mathematical Model

The mathematical model for the subsequent numerical study of the shaped charge liner collapse affected by external surface forces simulating an explosive load is presented. The basic liner was considered as an originally cylindrical compressible elastoplastic shell within the framework of a two-dimensional flat nonstationary problem of continuum mechanics. To ensure the rationality of the modeling and numerical calculation at the initial time the design fragment was discriminated in the liner by central beams. Deformation of the fragment being a part of the shell was taken into account by the boundary conditions of cyclic repeatability in the tangential direction. For numerical solving the well-known Wilkins Lagrangian method was used, which was refined in terms of the relations describing the mechanical behavior of an elastoplastic medium. Additionally, a self-developed grid adjustment procedure was used, excluding the appearance of highly elongated cells in the calculation. The instability of the shell deformation was initiated by harmonic surface perturbations, initially assigned on the outer or inner surfaces. The degree of instability was assessed by the deviation of the disturbed surface (or the boundary of the so-called stream-forming layer) from the cylindrical one. The used finite-difference algorithms are implemented in the form of appropriate calculation programs. A number of computational verification measures was performed proving the viability of the developed mathematical model and the possibility of its further use

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Numerical study of a modified Trombe wall solar collector system

Thermal Science ◽

10.2298/tsci0901195d ◽

2009 ◽

Vol 13 (1) ◽

pp. 195-204 ◽

Cited By ~ 5

Author(s):

Snezana Dragicevic ◽

Miroslav Lambic

Keyword(s):

Mathematical Model ◽

Numerical Study ◽

Operational Parameters ◽

Collector System ◽

Fast Running ◽

Simulation Techniques ◽

Solar Radiation Intensity ◽

Trombe Wall ◽

Solar Wall ◽

The Mathematical Model

The paper presents numerical analysis of efficiency of the modified Trombe wall with forced convection. The analyzed system comprises a double glass glazing, and a massive wall with opening and central channel in it. In order to increase the efficiency, a fan is provided at the bottom vent of the wall. It is more advanced as compared with simple Trombe solar wall with a relatively low thermal resistance, which is taken as a reference in experimental analysis. The mathematical model, composed for the massive solar wall efficiency, is usually very complicated and assessment of the thermal behavior requires the use of thermal simulation techniques. This paper presents steady-state and one-dimensional mathematical model for simplified analysis of thermal efficiency of modified Trombe solar wall. The results from presented model were analyzed to predict the effects of variations in the operational parameters on the solar wall efficiency: solar radiation intensity, air velocity in the entrance duct, and room air temperature. The results have been compared with the available experimental study, and the comparison has shown satisfactory agreement. The obtained results have be used for simple and fast running design tools that designers can use in the early phases of the design process for approximate calculations of efficiency of the passive solar heating systems.

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A MATHEMATICAL STUDY ON THE VELOCITY SLIP OF PHASES DURING THE INTERACTION BETWEEN A SHOCK WAVE OF LIMITING LOW INTENSITY AND AN ELECTRICALLY CHARGED GAS SUSPENSION

Cherepovets State University Bulletin ◽

10.23859/1994-0637-2020-4-97-7 ◽

2020 ◽

Vol 4 (97) ◽

pp. 77-88

Author(s):

DMITRII A. TUKMAKOV

Keyword(s):

Mathematical Model ◽

Numerical Study ◽

Velocity Slip ◽

Coulomb Force ◽

Solid Particles ◽

Internal Electric Field ◽

Interphase Heat Transfer ◽

Dispersed Phases ◽

The Mathematical Model ◽

Electrically Charged

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.

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WIND DISTURBANCE CANCELLATION FOR SMALLER ALT-AZIMUTH TELESCOPES

Revista Mexicana de Astronomía y Astrofísica Serie de Conferencias ◽

10.22201/ia.14052059p.2021.53.07 ◽

2021 ◽

Vol 53 ◽

pp. 29-34

Author(s):

A. C. Unal ◽

G. Kararsiz ◽

C. T. Yilmaz ◽

O. Keskin ◽

C. Yesilyaprak

Keyword(s):

Mathematical Model ◽

Asymptotic Stability ◽

Numerical Study ◽

Adaptive Controller ◽

Wind Gust ◽

Wind Disturbance ◽

Lyapunov Approach ◽

Unknown Amplitude ◽

Disturbance Cancellation ◽

The Mathematical Model

This study focuses on eliminating unknown amplitude wind disturbance for 2-DOF alt-azimuth configuration small telescopes. An adaptive controller is designed to overcome wind disturbance as a set and forget system. The mathematical model is derived based on 2-DOF alt-azimuth configuration. The wind disturbance is modeled as a sum of sinusoidal with unknown amplitude, frequency and phase by using Wind-Gust model. The controller aims to cancel the effect of the disturbance on the altitude and azimuth angles of the telescope while positioning or staying static on a dedicated configuration. The asymptotic stability is proven with the Lyapunov approach. The numerical study is illustrated to success of the proposed controller.

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Modelling and numerical study of the physicochemical laws of 1,4-cis-polyisoprene obtained in the presence of modified catalytic systems

Вычислительные технологии ◽

10.25743/ict.2020.25.3.002 ◽

2020 ◽

pp. 7-17

Author(s):

Эльдар Наилевич Мифтахов ◽

Светлана Анатольевна Мустафина ◽

Семен Израилевич Спивак

Keyword(s):

Mathematical Model ◽

Numerical Study ◽

Continuous Process ◽

Kinetic Equations ◽

Molecular Characteristics ◽

Batch Reactors ◽

Active Centers ◽

Catalytic Systems ◽

Continuous Mixing ◽

The Mathematical Model

Построена математическая модель, описывающая процесс получения полиизопрена в присутствии микрогетерогенных титансодержащих каталитических систем с учетом динамики активных центров. Построение модели носило поэтапный характер, при котором модель, описывающая периодический процесс, была дополнена рекуррентными соотношениями с целью описания процесса в каскаде реакторов идеального перемешивания. Численное решение прямой задачи позволило провести анализ молекулярно-массового распределения получаемого продукта в зависимости от исходной загрузки. The aim of this work is building a mathematical model that describes the process of producing polyisoprene in the presence of microheterogeneous titanium-containing catalytic systems, taking into account the dynamics of active centers and numerical calculation of the main physicochemical properties of the resulting product. The main methodology for compiling the mathematical model is the application of the kinetic approach, which consists of compiling and numerically solving the kinetic equations for all types of particles involved in the process. Previously, the distribution of active centers of the applied catalytic system was studied. The confirmed polycentricity of the used catalyst, represented by two types of active centers, is reflected in the nature of the description of the mathematical model. To reduce the system of differential equations to the final form, the method of moments was applied, which allows evaluating the complex properties of the obtained product by its averaged molecular characteristics. A model that permits describing the scale of batch reactors was modified by a macrokinetic module that takes into account possible energy and hydrodynamic laws of the process. For this, recurrence relations were introduced that are valid for the description of continuous mixing reactors. The software package developed by the authors of the work allows carring out a computational experiment for various technological conditions for conducting a continuous process. Based on the results of its launch, the dependences of conversion and averaged molecular characteristics on time in the context of each polymerizer were obtained. Thus, the numerical solution of the direct problem is capable analyzing the molecular weight distribution of the obtained product depending on various parameters of the initial load, for both the batch and continuous modes of the process. The dependences obtained by calculation showed satisfactory agreement with experimental data

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