tundish cfd

Prepared by:- Manas V. More. (133374006)

CFD modelling of liquid metal flow in tundish and validation with an

experimental model

Guide:- Prof. Sandip Kumar Saha

Prof. Rajneesh Bhardwaj

7/5/2014 1IIT Bombay

Contents

Tundish Fundamentals

Why CFD in tundish metallurgy?

Mathematical modelling

Previous work results and discussions

2IIT Bombay7/5/2014

Tundish Fundamentals

3IIT Bombay7/5/2014

Tundish Parameters

4IIT Bombay7/5/2014

Tundish geometry

Capacity

Refractory

Flow modifiers

Metering devices

Tundish slag Source: “Tundish metallurgy and clean steel”, Department of material science and engineering, IIT-Kanpur, 21-22 September 2012.

Physio-Chemical Phenomena

5IIT Bombay7/5/2014

Ladle changeover and grade intermixing

Temperature drop and heat loss

Re-oxidation, inclusion generation

Slag emulsification

Slag vortexing

Inclusion removal

Strand freezing

Why CFD in tundish metallurgy?

6IIT Bombay7/5/2014

Design of tundish

Optimization of fluid flow

Turbulence or velocity distribution

Residence time

Inclusion floatation and removal

Appropriate location of flow control device

Mathematical modelling

7IIT Bombay7/5/2014

Boundary conditions

Turbulence model K-ξ

Phase I (Melt) Model

Phase II (Slag)Model

Model outputsFlow distribution,Temperature distribution, Velocity distribution,turbulence field etc

Two phase, unsteady three dimensional flow

Incompressible Newtonian fluid

Isothermal

8IIT Bombay7/5/2014

Thermal energy transport in multiphase tundish:-

1. Liquid or primary phase thermal energy

conservation equation

=

2. Gas or secondary phase energy conservation

=

= Gas compressibility effect, = HTC/unit Vol.

hc= Heat transfer coefficient, αg = Hydrodynamic model

9IIT Bombay7/5/2014

Fluid flow mathematical modelling:-

Continuity and RANS equations

ρ = Liquid density, (kg.m−3)

ui = Velocity component in xi direction, (m.s−1)

μeff = Effective viscosity, (kg.m−1.s−1)

μeff = μo+ μt; μo = Laminar viscosity & μt = Turbulence viscosity.

β = Thermal expansion coefficient of the molten steel, (K−1)

The κ-ε model gives the turbulent viscosity as-

Cμ= 0.09, κ = Turbulent kinetic energy (m2.s−2),

ε = Turbulent energy dissipation rate, (m2.s−3)

10IIT Bombay7/5/2014

Fluid flow mathematical modelling:-

Turbulent K.E

Dissipation rate

=1.0, ε =1.3, =1.44, =1.92.

h = Enthalpy in (J.kg−1) Prt = 0.85, CP = Specific heat (J.kg−1.K−1) Ko = Laminar thermal conductivity

keff = Effective thermal conductivity (Wm−1K−1)

11IIT Bombay7/5/2014

Transport and removal of inclusions:-

Langrangian particle tracking method-

= Inclusion location at any time, (m)

The inclusion velocity equation can be derived from the force balance:

Total force acting on the inclusion F : FD + FG

mp = Particle mass,

ap = Particle acceleration rate,

u = Known liquid velocity, (m/s)

ρ = Inclusion and liquid densities, (kg.m−3)

Source: “Tundish metallurgy and clean steel”, Department of material science and engineering, IIT-Kanpur, 21-22 September 2012.

12IIT Bombay7/5/2014

Transport and removal of inclusions:-

CD = Drag coefficient as a function of inclusion Reynolds number

Turbulent fluctuation on the motion of inclusions are modeled using κ-ε flow field by

adding a random velocity fluctuation at each step.

Non-Stochastic model: Time averaged fluid flow velocity

Stochastic model:

u = Instantaneous fluid velocity, (m/s)

= Random velocity fluctuation, m/s.

13IIT Bombay7/5/2014

Volume of fluid method:-

Free surface or interface tracking method.

Phase Fraction whose values define the two phases creating the interface.

Uses Eulerian approach - Interface movement is calculated on a fixed grid.

Phase fraction:

Advection equation:

Source :International Journal of

Heat and Mass Transfer 49 (2006) 740–754

14IIT Bombay7/5/2014

Volume of fluid method:-

Interface reconstruction- Maintains accurate interface shape in two-phase

cells.

Reconstruction done using Optimization Techniques : e.g. Least squares Volume-of fluid Interface Reconstruction algorithm (LVIRA).

Continuous iterations calculating interface normal and distance for a given volume fraction in two-phase cell.

Source :International Journal of Heat and Mass Transfer 49 (2006) 740–754

15IIT Bombay7/5/2014

Boundary conditions:-

Geometrical parameter

Molten metal properties

Process parameters

Source :Lifeng Zhang,” Fluid flow, heat transfer and inclusion motion in molten steel continuous casting tundishes”, Fifth International Conference on CFD, Australia 13-15 December 2006

Previous work results and discussions

16IIT Bombay7/5/2014

Fluid flow: Isothermal & Non-isothermal Simulation

Source :Lifeng Zhang,” Fluid flow, heat transfer and inclusion motion in molten steel continuous casting tundishes”, Fifth International Conference on CFD, Australia 13-15 December 2006

Previous work results and discussions

17IIT Bombay7/5/2014

Temperature distribution at longitudinal center face

Temperature distribution on walls and bottom of tundish

Source :Lifeng Zhang,” Fluid flow, heat transfer and inclusion motion in molten steel continuous casting tundishes”, Fifth International Conference on CFD, Australia 13-15 December 2006

Previous work results and discussions

18IIT Bombay7/5/2014

Inclusion motion

Effect of random walk on

trajectory of inclusion

with different size.

Minimum and maximum

time required for

inclusion to travel to

outlet and top surface of

tundish

19IIT Bombay7/5/2014

THANK YOU