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

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.

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

2020 ◽  
Vol 2 ◽  
pp. 9-18
Author(s):  
D.A. TUKMAKOV
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Shock Wave ◽  
Solid Particles ◽  
Grid Function ◽  
Heat Conducting ◽  
Gas Suspension ◽  
Carrier Medium ◽  
The Mathematical Model ◽  
Electrically Charged

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.

The Improvement and Simulation on the Dynamic Model of Hydraulic AGC System

2012 ◽  
Vol 271-272 ◽  
pp. 1178-1182
Author(s):  
Juan Juan Xing
Keyword(s):  
Mathematical Model ◽  
Dynamic Model ◽  
Object Oriented ◽  
Coulomb Force ◽  
Rolling Process ◽  
Modeling Method ◽  
Practical Application ◽  
Operation Mechanism ◽  
The Mathematical Model

The paper uses the object-oriented modeling method to analysis the hydraulic AGC system and the operation mechanism about a strip mill. It discusses the Coulomb force and roll eccentricity which usually were ignored on rolling process. And improves the mathematical model that reflect the actual AGC system. By simulation, we compared it with the actual rolling process and verified the correction of the mathematical model. And, it will make the good foundation for on-the-spot practical application.

Calculations of three-dimensional viscous flow in a multiblade centrifugal fan by modelling blade forces

2003 ◽  
Vol 217 (3) ◽  
pp. 287-297 ◽  
Author(s):  
S-J Seo ◽  
K-Y Kim ◽  
S-H Kang
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Complex Flows ◽  
Flow Through ◽  
Volume Method ◽  
The Mathematical Model

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.

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

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.

scholarly journals Validation of friction factor predictions in vertical slurry flows with coarse particles

2020 ◽  
Vol 68 (2) ◽  
pp. 119-127 ◽  
Author(s):  
Artur Bartosik
Keyword(s):  
Mathematical Model ◽  
Reynolds Number ◽  
Friction Factor ◽  
Particle Diameter ◽  
Solid Particles ◽  
Coarse Particles ◽  
Carrier Liquid ◽  
Different Types ◽  
Slurry Flows ◽  
The Mathematical Model

AbstractThe paper presents validation of a mathematical model describing the friction factor by comparing the predicted and measured results in a broad range of solid concentrations and mean particle diameters. Three different types of solids, surrounded by water as a carrier liquid, namely Canasphere, PVC, and Sand were used with solids density from 1045 to 2650 kg/m3, and in the range of solid concentrations by volume from 0.10 to 0.45. All solid particles were narrowly sized with mean particle diameters between 1.5 and 3.4 mm. It is presented that the model predicts the friction factor fairly well. The paper demonstrates that solid particle diameter plays a crucial role for the friction factor in a vertical slurry flow with coarse solid particles. The mathematical model is discussed in reference to damping of turbulence in such flows. As the friction factor is below the friction for water it is concluded that it is possible that the effect of damping of turbulence is included in the KB function, which depends on the Reynolds number.

Numerical study of velocity slip of phases during the passage of a shock wave of low intensity from a pure gas to a dusty medium

2019 ◽  
Vol 14 (2) ◽  
pp. 125-131 ◽  
Author(s):  
D.A. Tukmakov
Keyword(s):  
Shock Wave ◽  
Particle Size ◽  
Numerical Study ◽  
Leading Edge ◽  
Velocity Slip ◽  
Fold Increase ◽  
Dispersed Phase ◽  
Grid Function ◽  
Dynamic Force ◽  
Dispersed Phases

In this paper, the process of the movement of a direct shock wave from a pure gas into a dusty medium is numerically modeled. The mathematical model took into account the viscosity, compressibility and thermal conductivity of the carrier phase. Also, the modeling technique made it possible to describe the interphase force interaction, which included the Stokes force, the dynamic force of Archimedes, the strength of the attached masses. In addition, interfacial interaction included heat transfer between the carrier and dispersed phases. The numerical solution was carried out using the explicit finite-difference method, with the subsequent application of the nonlinear correction scheme for the grid function. As a result of numerical calculations, it was revealed that with an increase in the linear particle size of the gas suspension, the velocity slip between the carrier and dispersed phases increases. Numerical modeling also showed that the absolute value of the difference between the velocities of the carrier and the dispersed phase reaches the largest value at the leading edge of the compression wave. The revealed regularities can be explained by the fact that the particles of the dispersed phase are assumed to be spherical in shape. Due to this, a multiple increase in particle size leads to a three-fold increase in their mass, a twofold increase in the area of one particle and a three-fold decrease in the number of particles. Thus, an increase in particle size leads to a decrease in the area of interfacial contact and an increase in the inertia of the particles, which in turn affects the interfacial velocity slip.

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

2009 ◽  
Vol 283-286 ◽  
pp. 340-345 ◽  
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.

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

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.

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

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.

Sign in / Sign up

Export Citation Format

Share Document