scholarly journals Modelling Liquid Steel Motion Caused by Electromagnetic Stirring in Continuous Casting Steel Process

2014 ◽  
Vol 59 (2) ◽  
pp. 487-492 ◽  
Author(s):  
M. Rywotycki ◽  
Z. Malinowski ◽  
J. Giełżecki ◽  
A. Gołdasz
Keyword(s):  
Liquid Steel ◽  
Stokes Equations ◽  
Computation Time ◽  
Electromagnetic Stirring ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Navier Stokes Equations ◽  
Stationary Heat Conduction ◽  
Casting Steel ◽  
Reduce Computation Time

Abstract The paper presents an attempt of modelling liquid steel motion triggered off by electromagnetic stirring. Steel viscosity was calculated on the basis of temperature field determined with the use of stationary heat conduction equation. Velocity field was determined using Navier-Stokes equations and stream continuity equation. Solution was obtained using the finite element method. The developed model allows to carry out quick simulating calculations of fluid flow. Stationary solution was employed, and this allowed to reduce computation time substantially.

Flow in Cavities With Curved Boundaries

2009 ◽  
Author(s):  
Guillermo E. Ovando ◽  
Juan C. Prince ◽  
Sandy L. Ovando
Keyword(s):  
Stokes Equations ◽  
Operator Splitting ◽  
Vortex Formation ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Curved Boundaries ◽  
Navier Stokes Equations ◽  
Vertical Walls ◽  
Curved Walls

Fluid dynamics for a Newtonian fluid in the absence of body forces in a two-dimensional cavity with top and bottom curved walls was studied numerically. The vertical walls are fixed and the curved walls are in motion. The Navier-Stokes equations were solved using the finite element method combined with the operator splitting scheme. We analyzed the behaviour of the velocity fields, the vorticity fields and the velocity profiles of the fluid inside the cavity. The analysis was carried out for two different Reynolds numbers of 50 and 500 with two ratios (R = 1, −1) of the top to the bottom curved lid speed. For these values of parameters the flow is characterized by vortex formation inside the cavity. The spatial symmetry on the flow patterns are also investigated. We found that when the velocities of the top and bottom walls have opposite direction only one cell is formed in the central part of the cavity; however when the velocities of the top and bottom walls have the same direction the vortex formation inside the cavity is more complex.

Simulation of Mold Filling for Non-Newtonian Fluids - Part 2

2006 ◽  
Vol 3 (2) ◽  
pp. 52-60
Author(s):  
Venkatesh M. Kulkarni ◽  
Chu Wee Liang ◽  
C.W. Tan ◽  
P.A. Aswatha Narayana ◽  
K.N. Seetharamu
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Molding Process ◽  
Algebraic Form ◽  
Design Guideline ◽  
Navier Stokes Equations ◽  
Transfer Molding ◽  
Encapsulation Process ◽  
Parametric Studies

This paper deals with the flow in the resin transfer molding process commonly used for IC chip encapsulation in the electronic packaging industry. A solution algorithm is presented for modeling the flow of a non-Newtonian fluid obeying a Power-Law model and the algorithm is used to conduct parametric studies in transfer molding. The flow model uses the Hele-Shaw approximation to solve the Navier-Stokes Equations and a pseudo-concentration algorithm for tracking the interface between the resin and the air. The Finite Element Method is employed to reduce the governing partial differential equations to algebraic form. The model is used to study the flow from the transfer ram into the cavity for different dimensions of transfer molding tools. Parametric studies are carried out to obtain balanced filling for transfer molding configuration. Parametric studies could provide a design guideline to optimize the encapsulation process prior to the setting up of an actual manufacturing set.

Numerical Simulation of Electromagnetic Stirring Effect on Flow Pattern of Metal Melt

2011 ◽  
Vol 264-265 ◽  
pp. 1574-1579
Author(s):  
H. Namaki ◽  
S. Hossein Seyedein ◽  
M.R. Afshar Moghadam ◽  
R. Ghasemzadeh
Keyword(s):  
Flow Pattern ◽  
Maxwell Equations ◽  
Flow Model ◽  
Stokes Equations ◽  
Electromagnetic Stirring ◽  
Navier Stokes ◽  
Simultaneous Solution ◽  
Navier Stokes Equations ◽  
Stirring Effect ◽  
Good Agreement

In this study, a mathematical model was developed to simulate 2-D axisymmetric melt flow under magnetic field in a cylindrical container. The modeling of this process required the simultaneous solution of the turbulent Navier-Stokes equations together with Maxwell equations. The flow pattern in liquid bath was obtained using a two-equation κ-є turbulent flow model, which was further used to obtain the solute distribution. The governing differential equations were solved numerically using finite volume based finite difference method. The computed results, were found to be in good agreement with the measurements reported in the literature. The effect of stirring parameters on temperature homogeneity of the melt have been discussed and presented.

scholarly journals Effect of Inlet Temperature Non-Uniformity on High-Pressure Turbine Performance

2010 ◽  
Author(s):  
Craig I. Smith ◽  
Dongil Chang ◽  
Stavros Tavoularis
Keyword(s):  
High Pressure ◽  
Heat Load ◽  
Stokes Equations ◽  
Computation Time ◽  
Radial Pressure ◽  
Navier Stokes ◽  
Inlet Temperature ◽  
High Pressure Turbine ◽  
Navier Stokes Equations ◽  
Hot Streak

The temperature of the flow entering a high-pressure turbine stage is inherently non-uniform, as it is produced by several discrete, azimuthally-distributed combustors. In general, however, industrial simulations assume inlet temperature uniformity to simplify the preparation process and reduce computation time. The effects of a non-uniform inlet field on the performance of a commercial, transonic, single-stage, high-pressure, axial turbine with a curved inlet duct have been investigated numerically by performing URANS (Unsteady Reynolds-Averaged Navier-Stokes equations) simulations with the SST (Shear Stress Transport) turbulence model. By adjusting the alignment of the experimentally-based inlet temperature field with respect to the stator vanes, two clocking configurations were generated: an aligned case, in which each hot streak impinged on a vane and a misaligned case, in which each hot streak passed between two vanes. In the aligned configuration, the hot streaks produced higher time-averaged heat load on the vanes and lower heat load on the blades. As the aligned hot streaks impinged on the stator vanes, they also spread spanwise due to the actions of the casing passage vortices and the radial pressure gradient; this resulted in a stream entering the rotor with relatively low temperature variations. The misaligned hot streaks were convected undisturbed past the relatively cool vane section. Relatively high time-averaged enthalpy values were found to occur on the pressure side of the blades in the misaligned configuration. The non-uniformity of the time-averaged enthalpy on the blade surfaces was lower in the aligned configuration. The flow exiting the rotor section was much less non-uniform in the aligned case, but differences in calculated efficiency were not significant.

A parallel partition of unity method for the nonstationary Navier-Stokes equations

2017 ◽  
Vol 27 (8) ◽  
pp. 1675-1686 ◽  
Author(s):  
Guangzhi Du ◽  
Liyun Zuo
Keyword(s):  
Stokes Equations ◽  
Partition Of Unity ◽  
Navier Stokes ◽  
Computational Time ◽  
The Finite Element Method ◽  
Partition Of Unity Method ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Standard Galerkin Method

Purpose The purpose of this paper is to propose a parallel partition of unity method (PPUM) to solve the nonstationary Navier-Stokes equations. Design/methodology/approach This paper opted for the nonstationary Navier-Stokes equations by using the finite element method and the partition of unity method. Findings This paper provides one efficient parallel algorithm which reaches the same accuracy as the standard Galerkin method but saves a lot of computational time. Originality/value In this paper, a PPUM is proposed for nonstationary Navier-Stokes. At each time step, the authors only need to solve a series of independent local sub-problems in parallel instead of one global problem.

scholarly journals METHOD OF PARALLELIZATION OF NUMERICAL ALGORITHMOF NAVIER-STOKES EQUATIONS COMPLETE SYSTEM

2016 ◽  
pp. 92-98
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Thermal Conductivity ◽  
Gas Flow ◽  
Stokes Equations ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Computation Time ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Comparison Of The Results

The article considers the features of numerical construction of solutions of the Navier-Stokes equations full system describing a three-dimensional flow of compressible viscous heat-conducting gas under the action of gravity and Coriolis forces. It is shown that accounting of dissipative properties of viscosity and thermal conductivity of the moving continuum, even with constant coefficients of viscosity and thermal conductivity, as well as the use of explicit difference scheme calculation imposes significant restrictions on numerical experiments aimed at studying the arising complex flows of gas or liquid. First of all, it is associated with a signifi- cant complication of the system of equations, the restrictions on the value of the calculated steps in space and time, increasing the total computation time. One of the options is proposed of algorithm parallelization of numerical solution of the complete Navier - Stokes equations system in the vertical spatial coordinate. This parallelization option can significantly increase the computing performance and reduce the overall time of counting. A comparison of the results of calculation of one of options of gas flow in the upward swirling flow obtained by serial and parallel programs is presented.

Flow in Rectangular Cavities With Two Vertical Oscillating Walls

2008 ◽  
Author(s):  
Guillermo E. Ovando ◽  
Alberto Beltran ◽  
Sandy L. Ovando
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Navier Stokes Equations ◽  
Cell Structures ◽  
Lower Reynolds Number ◽  
Constant Displacement ◽  
Vertical Walls

Fluid dynamics in a two-dimensional rectangular cavity with vertical oscillatory walls out of phase was studied numerically. The Navier-Stokes equations were solved using the finite element method. We analyzed the behaviour of the velocity fields, the vorticity fields and we also obtained the streaklines of the fluid at the bottom left corner of the domain for one and two cycles, which is associated with the mixing of the fluid. The analysis was carried out for three different Reynolds numbers of 50, 500 and 1000 with constant displacement amplitude of the moving boundaries of 0.2. For this range of parameters the flow is characterized by two kind of symmetries. We found that for lower Reynolds number there is a good local mixing given by cell structures and the smooth behavior of the fluid inside the cavity; however for higher Reynolds number these structures disappear due to the fluid near the vertical walls impinges against the corner of the cavity, then this fluid is dispersed through the whole cavity during the cycle, increasing the global mixing of the fluid.

A Finite Element Analysis of the Navier-Stokes Equations Applied to High Speed Thin Film Lubrication

1987 ◽  
Vol 109 (1) ◽  
pp. 71-76 ◽  
Author(s):  
J. O. Medwell ◽  
D. T. Gethin ◽  
C. Taylor
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Thin Film Lubrication ◽  
Element Analysis ◽  
Navier Stokes Equations ◽  
Film Lubrication

The performance of a cylindrical bore bearing fed by two axial grooves orthogonal to the load line is analyzed by solving the Navier-Stokes equations using the finite element method. This produces detailed information about the three-dimensional velocity and pressure field within the hydrodynamic film. It is also shown that the method may be applied to long bearing geometries where recirculatory flows occur and in which the governing equations are elliptic. As expected the analysis confirms that lubricant inertia does not affect bearing performance significantly.

Sign in / Sign up

Export Citation Format

Share Document