# The importance of secondary flow in the rotary electromagnetic stirring of steel during continuous casting

DOI: 10.1007/BF00412016

- Cite this article as:
- Davidson, P.A. & Boysan, F. Applied Scientific Research (1987) 44: 241. doi:10.1007/BF00412016

## Abstract

This paper considers some aspects of the flow generated in a circular strand by a rotary electromagnetic stirrer. A review is given of one-dimensional models of stirring in which the axial variation in the stirring force is ignored. In these models the magnetic body force is balanced by shear, all the inertial forces being zero (except for the centripetal acceleration).

In practice, the magnetic torque occurs only over a relatively short length of the strand. The effect of this axial dependence in driving force is an axial variation in swirl, which in turn drives a secondary poloidal flow. Dimensional analysis shows that the poloidal motion is as strong as the primary swirl flow.

The principle force balance in the forced region is now between the magnetic body force and inertial. The secondary flow sweeps the angular momentum out of the forced region, so that the forced vortex penetrates some distance from the magnetic stirrer. The length of the recirculating eddy is controlled by wall shear. This acts, predominantly in the unforced region, to diffuse and dissipate the angular momentum and energy created by the body force.

### Notation

**B**magnetic field strength

**E**electric field

**ê**unit vector

*F*_{θ}force

*f*(*z/R*)dimensionless variation of force with depth

**J**current density

*k*turbulence kinetic energy

*k′*wall roughness

*L*axial length scale in unforced region

*p*pressure

*R*radius

- Re
Reynolds number

*r*radial coordinate

**T**torque

*t*time

**u**velocity

- \(\bar V\)
characteristic velocity \(B\omega R\sqrt {(\sigma /\rho \omega )}\)

*V*_{*}shear velocity

**v**fluctuating velocity

*z*axial coordinate

- Γ
angular momentum

*u*_{θ}*r**δ*boundary layer thickness

- ε
viscous dissipation rate

*θ*angular coordinate

*ν*viscosity

*ν*_{t}eddy viscosity

*ρ*density

*σ*conductivity

*τ*_{ij}shear stress

- Ω
angular velocity

**ω**vorticity

*ω*frequency

### Subscripts

*R*wall

*r*radial

*θ*azimuthal

*z*axial

- O
core

*p*poloidal