Magnetohydrodynamics in

Steel-Casting

Hunter SceatsPh70

November 20, 2012

or

The Electromagnetic Teaspoon, and How to Use It

Outline

● The Importance of Steel

● Steel Properties

● The Steel-Casting Process

● Magnetohydrodynamics

● Magnetic Stirring

● Magnetic Damping

● High-Frequency Fields

The Importance of Steel:Architecture

● Skyscrapers

● Suspension Bridges

● Reinforcing bar

The Importance of Steel:Transportation

● Railroads

● Automobiles

● Ships

● Planes?

The Importance of Steel:Tools

● Construction

● Cutlery

● Paperclips

The Properties of Steel:Strength

● Young's Modulus● Force per area versus percent elongation● “Stiff” versus “loose” spring

The Properties of Steel:Hardness

● Brinell Hardness● Ability of material to resist deformation● Squeeze sphere into sample with given force● Measure depression in material

The Properties of Steel:Toughness

● Ability to absorb energy without breaking● Strength● Continuous deformation● Malleability and ductility

The Properties of Steel:Customizable!

● Methods:● Alloying

● Carbon, chromium, vanadium, molybdenum, tungsten, etc.● Controlled heating and cooling

● Quenching● Annealing

● Properties● Hardness● Corrosion resistance● Workability

The Properties of Steel:Workable!

● Forging● Hot and cold● Bending, hammering, rolling, etc.

● Machining● Precision

● Pressing● Stamping, embossing, etc.

● Casting● Initial ingots, or final products

The Production of Steel:Ore to Iron to Steel

● Iron ore● Iron oxide, plus phosphorus, sulfur, etc.

● Pig Iron● Blast furnace● Reduced by means of coke → high

carbon content● Steel

● Oxidation of impurities● Increases flexibility, resilience,

workability

The Production of Steel:Casting

● Gradual cooling of molten metal● Ingot, slab

● Continuous casting vs batch process● Saves heating● Steady-state operation● No transport

Problems in Steel Casting:Porosity

● Oxidation process requires introduction of hot gases

● Trapped gas must be released from molten metal before cooling

● Requires effective mixing

Problems in Steel Casting:Grain Structure

● Desire fine-grained steel● Microscopic structure of

separate crystals, with boundaries

● Crystal-crystal boundaries inhibit movement and growth of dislocations

● Make material stronger and more tougher on the macroscale

● More boundaries → more inhibition → tougher

Potential Problems in Steel Casting:Impurities

● Slag● Layer of oxidized impurities on top of molten steel● If remain in metal, can reduce material properties ● If crystallize separately, can lead to fatigue crack

and catastrophic failure● Must keep separate from steel

Magnetohydrodynamics:History

● Isolated experiments by Faraday● Astrophysical interest in 1930s● Geophysicists studying movement of molten metal

core in 1940s● Plasma physicists concerned with thermonuclear

fusion from 1950s

The Physics Behind MHD:Lorentz Force and Induction

● Lorentz Force● Charged particles experience force in magnetic field● Manifested as “J x B” term in MHD

● Induction● Relative motion of fluid and field lines induces

currents● Produces secondary magnetic field● Fluid ↔ Field interaction

Aside:Intuition vs Mathematics

● “Nothing can be more fatal to progress than a too confident reliance on mathematical symbols; for the student is only too apt to take the easier course, and consider the formula and not the fact as physical reality.” -Kelvin

● Mathematics is hard, often only soluble numerically● ...but intuition is easy, and valuable, too!

The Intuition Behind MHD:The Damping of Relative Motion

● Thought experiment● Conducting loop in

magnetic field● Changing flux

→voltage

→ current

→ secondary field

MHD in Molten Metals:Low Magnetic Reynolds Number

● Analogous to Reynolds Number in ordinary hydrodynamics● Describes relative importance of viscous to inertial

forces● Magnetic Reynolds number depends on conductivity,

permeability, length scale, velocity● Much lower for metals than for plasmas● Magnetic field influences flow to a large degree, but

reverse is not true

Stirring: Motivation

● Ice Cream● Beat out trapped gases● Homogeneous mixture● Fine-grained

● Axial symmetry of crystals● Snowflakes vs hoarfrost● Uniform behavior for strains from

different directions● Allows for higher casting temperatures

and rates

Ekman Pumping: “Tea-cup” Spin-Down

● Rotating fluid and stationary boundary● Centrifugal force creates pressure gradient

● Lower near axis● Within boundary layer, swirl is reduced by viscosity

● → Imbalance of pressure gradient and centrifugal forces● Radial inflow → conservation of mass → drifts out of boundary layer in secondary flow

Magnetic Stirring● Rotating magnetic field

● Induces currents → delayed motion of metal● Essentially an induction motor with a liquid metal

rotor● Ekman flows keep metal homogeneous

Turbulence, Slag, and Impurities

● In certain parameter regimes, flow can become unpredictable and non-uniform● Creation of vortices, disruption of surface, etc.

● Steel-Casting● Non-uniformity → bad● Disruption of slag – steel interface can induce

slag particles into molten metal

A Solution: Magnetic Damping

● Impose “strapping” field in axial direction● Appeals to magnetofluid's opposition to relative

field-fluid motion● Can damping turbulent vortices or jets

● Resulting from injection of molten metal into mold

● Essentially results in conversion of kinetic energy into heat via Ohmic heating

High-Frequency Fields:Heating

● High-quality steel

→ Requires fewer impurities

→ Alternative method of heating metal● Induction furnace

● Alternating solenoidal field

● Induces current in boundary layer

● Ohmic heating

High-Frequency Fields:Electromagnetic Valves

● Alternating solenoidal field

● Induces opposing currents in conductor

● Repels conductor● Can be used to control

flow rate as a sort of valve

● Bernoulli's Equation in MHD?

Conclusion

● Electromagnetic fields enable a degree of control over steel casting which is unable to be obtained through mechanical means

● MHD describes the interaction between conducting fluid and EM fields

● Intuition is relatively easy, even it mathematics is difficult or even not analytically soluble

References● Howard , David and Jamie Angus. “Acoustics and Pschoacoustics: Introduction to Sound.”

http://www.eetimes.com/General/PrintView/4015859

● “A Teacher's Guide to Teaching Material Properties.” http://www-materials.eng.cam.ac.uk/mpsite/physics/str-tough_article/default.html

● “Development of a Process to Continuously Melt, Refine and Cast High Quality Steel” http://web.mst.edu/~kpeaslee/research/ContCast.html

● Ashby, Michael and David Jones. Engineering Materials 1: An Introduction to Their Properties & Applications. 2nd Edition. Oxford: Butterworth-Heinemann, 1996.

● Hardin, Richard and Christoph Beckermann. “Effect of Porosity on the Stiffness of Cast Steel.”

● “Steel for many purposes.” http://resources.schoolscience.co.uk/corus/16plus/steelch1pg5.html

● Bellan, Paul. Fundamentals of Plasma Physics. Cambridge: Cambridge University Press, 2006.

● Davidson, P.A. An Introduction to Magnetohydrodynamics. Cambridge: Cambridge University Press, 2001.

● The Way Things Work: An Illustrated Encyclopedia of Technology. New York: Simon and Schuster, 1967.

● Clark, Donald S. Engineering Materials & Processes. Pasadena: California Institute of Technology, 1931.

Questions?