The Calculation of Transport Phenomena in Electromagnetically Levitated Metal Droplets

1981 ◽  
Vol 9 ◽  
Author(s):  
N. El-Kaddah ◽  
J. Szekely
Keyword(s):  
Temperature Field ◽  
Fluid Flow ◽  
Flow Field ◽  
Force Field ◽  
Electromagnetic Force ◽  
Stokes Equations ◽  
Concentration Field ◽  
Metal Droplet ◽  
Convective Transport ◽  
Mathematical Representation

ABSTRACTA mathematical representation has been developed for the electromagnetic force field, the fluid flow field, the temperature field (and for transport controlled kinetics) in a levitation melted metal droplet. The technique of mutual inductances was employed for the calculation of the electromagnetic force field, while the turbulent Navier-Stokes equations and the turbulent convective transport equations were used to represent the fluid flow field, the temperature field and the concentration field. The governing differential equations, written in spherical coordinates, were solved numerically.The computed results were found to be in good agreement with measurements reported in the literature, regarding the lifting force and the average temperature of the specimen.

scholarly journals The turbulent recirculating flow field in a coreless induction furnace, a comparison of theoretical predictions with measurements

1983 ◽  
Vol 133 ◽  
pp. 37-46 ◽  
Author(s):  
N. El-Kaddah ◽  
J. Szekely
Keyword(s):  
Fluid Flow ◽  
Flow Field ◽  
Force Field ◽  
Body Force ◽  
Induction Furnace ◽  
Stokes Equations ◽  
Measurement Techniques ◽  
Mathematical Representation ◽  
Recirculating Flow ◽  
Coreless Induction Furnace

A mathematical representation has been developed for the electromagnetic force field and the fluid-flow field in a coreless induction furnace. The fluid flow field was represented by writing the axisymmetric turbulent Navier–Stokes equations, containing the electromagnetic body-force term. The electromagnetic body force field was calculated by using a technique of mutual inductances. The k-ε model was employed for evaluating the turbulent viscosity, and the resultant differential equations were solved numerically.The theoretically predicted velocity fields were in reasonably good agreement with the experimental measurements reported by Hunt & Moore; furthermore, the agreement regarding the turbulence intensities was essentially quantitative. These results indicate the k-ε model does provide a good engineering representation of the turbulent recirculating flows occurring in induction furnaces. At this stage it is not clear whether the discrepancies between measurements and the predictions, which were not very great in any case, are attributable either to the model or to the measurement techniques employed.

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

scholarly journals Numerical Simulation of Temperature and Fluid Fields in Solidification Process of Ferritic Stainless Steel under Vibration Conditions

Crystals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 174
Author(s):  
Wenli Wang ◽  
Jing Chen ◽  
Miaomiao Li ◽  
Along Wang ◽  
Mengyao Su
Keyword(s):  
Stainless Steel ◽  
Temperature Field ◽  
Flow Field ◽  
Ferritic Stainless Steel ◽  
Stokes Equations ◽  
Solidification Process ◽  
Crystal Formation ◽  
Positive Temperature ◽  
Vibration Direction ◽  
Casting Mold

A three-dimensional model of a circular casting mold with a vibrating nucleus generator was established, and the characteristics of temperature and flow fields during the solidification process of ferritic stainless steel Cr17 in the casting mold were analyzed using finite element and finite difference methods. A standard k-ε turbulent current model was adopted to simulate the temperature field, and a standard k-ε model in Reynolds-averaged Navier–Stokes equations (RANS) was employed to deal with the flow field. The temperature field diffuses outward with a positive temperature gradient. Low degrees of undercooling can prevent solidified shells from forming rapidly on the surface of the nucleus generator. The temperature perpendicular to the direction of vibration is lower than that in the direction of vibration. The flow field exhibits a heart-shaped distribution and spreads gradually outward. The uniform distribution of grains can be achieved at three different frequencies of vibration. The results show that the degree of undercooling affects the distribution of the temperature field while the frequency of vibration affects the flow field significantly. Under the conditions of undercooling of 540 K and vibration frequency of 1000 Hz, the region perpendicular to the vibration direction of the nucleus generator is the optimum area for equiaxed crystal formation.

scholarly journals Effect of Draw Blank Velocity on Steel Fluid Flow Field in Blank Continuous Caster Crystallizer

2011 ◽  
Vol 2-3 ◽  
pp. 673-677
Author(s):  
Ze Ning Xu ◽  
Hong Yu Liu ◽  
Yan Ping Lu ◽  
Lei Gang Liu
Keyword(s):  
Temperature Field ◽  
Fluid Flow ◽  
Heat Conduction ◽  
Flow Field ◽  
Field Distribution ◽  
Thickness Distribution ◽  
Continuous Caster ◽  
Impurity Content ◽  
Three Dimensions ◽  
Steel Blank

As the heart of continuous caster, crystallizer is the cradle of most surface deficiencies and inside quality problems in steel blank. Steel blank surface quality, nonmetal impurity content and relevant distribution rely on the steel fluid solidification behavior namely steel fluid flow field distribution on great extent. For the high temperature steel fluid has big kinetic energy, so, the immixture dregs, solidification heat conduction, temperature field distribution in crystallizer, solidification blank shell thickness distribution and continuous caster blank quality were influenced by steel fluid flow. The numerical simulation analysis on flow field and temperature field in crystallizer were conducted in this paper. Three dimensions turbulent flow model was adopted to computate flow field. The heat conduction was ignored on draw blank direction in temperature field. The conjugate heat conduction model of ANSYS CFX was adopted to analyze temperature field, which can consider heat conduction in solid layer and convection heat conduction between solid shell face and fluid simultaneity. The draw blank velocity was found by setting crystallizer water gap insertion depth and crystallizer water gap angle, which can obtain reasonable flow field in blank crystallizer.

Coupled Numerical Simulation Study on Electromagnetic Field, Flow Field and Heat Transfer in ø210mm Round Billet Mold with M-EMS

2013 ◽  
Vol 651 ◽  
pp. 722-727
Author(s):  
Wei Chen ◽  
Bao Xiang Wang ◽  
Na Zheng ◽  
Ying Chen ◽  
Yong Ping Feng
Keyword(s):  
Electromagnetic Field ◽  
Temperature Field ◽  
Flow Field ◽  
Magnetic Induction ◽  
Electromagnetic Force ◽  
Recirculation Zone ◽  
Current Intensity ◽  
Distribution Law ◽  
Element Analysis ◽  
Round Billet

aking the ∅210mm round billet M-EMS as study subject, a mathematical model coupling electromagnetic field, flow field and temperature field is established by use of Finite Element Analysis Software ANSYS. The distribution law of magnetic induction and electromagnetic force is investigated in mold; the effects of current intensity and frequency on magnetic induction, electromagnetic force, flow and temperature field is studied. The results show that: the values of magnetic induction and electromagnetic force reach its maximum near the edge of billet and became smaller towards the center; in the mold with EMS, the rotary flow is generated, and the flow pattern are upper recirculation zone, rotary zone and down recirculation zone, the location of hot area is moved up compared with the condition without EMS; in the considered parameters range, electromagnetic force and velocity of molten steel increase with the rise of current intensity and frequency.

scholarly journals Analytical Solutions for Navier-Stokes Equations in the Cylindrical Coordinates

2012 ◽  
Vol 2 ◽  
pp. 16-23 ◽  
Author(s):  
V. Adanhounme ◽  
A. Adomou ◽  
F.P. Codo
Keyword(s):  
Temperature Field ◽  
Fluid Flow ◽  
Incompressible Fluid ◽  
Heat Transport ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Cylindrical Coordinates ◽  
Navier Stokes Equations ◽  
Vorticity Vector

We consider the problem of convective heat transport in the incompressible fluid flow and the motion of the fluid in the cylinder which is described by the Navier-Stokes equations with the heat equation.The exact solutions of the Navier-Stokes equations, the temperature field and the vorticity vector are obtained.

Flow Patterns and Electrokinetic Mixing Performance in Heterogeneous Microchannels

2011 ◽  
Author(s):  
Jafar Jamaati ◽  
Hamid Niazmand ◽  
Metin Renksizbulut
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Concentration Field ◽  
Velocity Slip ◽  
Experimental Investigations ◽  
Mixing Efficiency ◽  
Surface Charges ◽  
Complex Flow ◽  
Single Vortex ◽  
Mixing Performance

Due to the recent advances in microfabrication techniques, it is possible to produce microchannels with positive, negative, or even neutral surface charges. According to several numerical and experimental investigations, such a combination of charge patterns on the microchannel walls results in complex flow fields with circulation zones that are highly desirable for fluid mixing requirements as in lab-on-a-chip devices. In this paper, the mixing efficiency associated with electro-osmotic flows in heterogeneous microchannels is investigated. The Navier-Stokes equations are solved for the flow field along with species transport equations to obtain the concentration field. The effects of the Electric Double Layer (EDL) on the flow field are considered using the Helmholtz-Smoluchowski model in which the EDL effects on the fluid adjacent to the walls are replaced by velocity slip at walls. Different configurations and profiles for the wall charges can be applied to the microchannel walls. In the present study, heterogeneous patterns consisting of different patches with constant zeta-potentials are considered. The flow pattern of a single patch consists of a single vortex attached to the channel wall, which significantly increases the mixing performance. It is expected that a combination of several patches would increase the mixing performance considerably. Therefore, the effects of the size, number, and locations of multiple patches on the mixing performance are investigated in detail. The results for a single patch indicate that the mixing efficiency increases with the size of the patch and its proximity to the microchannel inlet. It is expected that with a suitable combination of patches, an optimized configuration can be found in which the mixing efficiency is maximized and the length of the mixing section is minimized. The results can be applied to the design of micro-mixers to minimize their size while achieving the desired mixing requirements.

One demonstration of the minimum entropy theorem ruling the fluid flow field.

2021 ◽  
Author(s):  
Takashi Hotta
Keyword(s):  
Fluid Flow ◽  
Flow Field ◽  
Viscous Fluid ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stationary Condition ◽  
Minimum Entropy ◽  
External Energy ◽  
Navier Stokes Equations ◽  
Viscous Fluid Flow

Abstract The minimum entropy theorem of the several fields is well known, but there is no clear review that it shows the possibility of minimum entropy theorem mainly rules the general viscous fluid flow field. In this article, I define appropriately total external energy function and is resolved by variational method, and shows that stationary condition always satisfies the continuity and general Navier-Stokes equations. So on that condition, the minimum entropy theorem could decide directly the general viscous fluid flow field.

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