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 1 IIT Bombay
Dec 27, 2015
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
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Tundish Fundamentals
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Tundish Parameters
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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
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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?
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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
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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
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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
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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)
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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)
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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.
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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.
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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
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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
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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
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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
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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
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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
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