Simulation of electro-magnetic effects with ANSYS CFX

The coupling of computational fluid dynamics (CFD), i.e. the simulation of mass, momemtum and energy transport in fluids and solids, with other physical effects is becoming more important. Among fluid-structure interaction, the coupling to electro-magnetic effects opens a wide area of applications to CFD programs. While CFD is based on conservation equations, especially continuity and Navier-Stokes equations, electro-magnetics can be described by Maxwells equations together with material relations, e.g. permeability and permittivity.

Coupling of both areas can be done externally, i.e. by data transfer between separated programs specialized for CFD, e.g. ANSYS CFX, and electro-magnetics, e.g. ANSYS EMAG; or it can be done internally, i.e. all equations are solved in one solver. The main advantages of the latter approach are the strong internal coupling and the ease of use (single program, single mesh, single setup, no coupling interface). Since a direct implementation of Maxwells equations into a CFD solver is difficult and often needless complex, assumptions and simplifications lead to three separate areas of application of coupled CFD and electro-magnetics:

Ferro-Hydrodynamics (FHD) : magnetic dipoles are accelerated by Kelvin force in magnetic fields; electric effects are neglected; examples are ferrofluids for ink jet printers or separation of magnetic cells

Electro-Hydrodynamics (EHD) : charged particles (electric monopols or dipoles) are accelerated by Coulomb force in electric fields; magnetic effects are neglected; typical examples are electrophoresis, electroosmosis, fuel cells, electrolysis, electrostatic coating

Magneto-Hydrodynamics (MHD) : electric conducting fluids or solids in electric and/or magnetic fields are accelerated by Lorentz force and heated by resistive heating; free electric charges or magnetic dipoles are neglected; examples are arc welding, plasma cutting, circuit breakers, heating, retarding and stirring of casts

Ferro-Hydrodynamics FHD deals with magnetic dipoles that are accelerated and rotated in inhomogeneous magnetic fields by Kelvin force. The dipoles can be implemented as discrete particles or as dipole density distribution. The calculation of the magnetic field takes into account materials susceptibility.

tDjH

+=

rrr

curl

0div =Br

t

BE

=

rr

curl

eD =r

div0)div( =+

ut

r

Kr

+

=+

ii

i

x

puu

tu )div()(

Basic CFD equations Maxwells equations

Left hand side: Magnetic potential (color) and magnetic field H (vectors) of channel in external magnetic induction field with paramagnetic steel cylinder inside. Right hand side: Particle tracks of magnetic dipoles.

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Electro-Hydrodynamics EHD deals with free electric charges that are accelerated in electric fields by the Coulomb force. The charges can be implemented as discrete particles via the Lagrangian description or charge density distribution via an Eulerian description. In aqueous solutions of ions, acceleration by Coulomb force is often replaced by ion mobilities that relate ion drift velocity to the local electric field. Electric field is calculated by a Poisson equation.

Magneto-Hydrodynamics

In MHD, free electric charges and free magnetic dipoles are neglected. The fluids and solids can be described by their electric conductivity (often strongly temperature dependent) and relative permeability. Electric current is generated by an applied external voltage and by fluid motion in the magnetic field (Ohms law). The current leads to resistive heating and generates a magnetic field; current and magnetic field cause a Lorentz force onto the fluid.

Left hand side: Charged particles in electric field between cylinder and channel walls with gravity. Right hand side: Electrophoresis (Isotachophoresis) for separation of acids in aqueous solution.

Left hand side: Electro-magnetic stirring of an acid, caused by an external magnetic field and an applied voltage between the electrodes (blue); vertical velocity by colors and a typical streamline. Right hand side: Electric arc between wire tip and workpiece in Gas Metal Arc Welding with temperatures up to 17,000 K (color at right hand side; left hand side shows electron number densities and equipotential lines of electric potential).

negative charge

positive charge

zero charge

Initial concentrations

after 300 min

Terminator: lactic acid

Leader: Chlor

Sample: malic, citric, tartaric, maleic acid