Finite Element Method - Application using Fastflo
Turbulent flow in a tundish
A tundish is a large box-shaped vat, with minimum
dimension of about 2 m, which is used to hold molten steel for final
processing prior to continuous casting. It is very important that the
steel does not freeze. The Australian steel firm BHP has therefore
undertaken experimental and numerical investigations of residence times
for different parts of the steel flow. Some experiments have been
performed in water with dye tracing.
A typical Reynolds number for the steady flow based on nozzle diameter
is 170,000, so the flow is certainly turbulent.
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Mean velocity vectors |
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5% dye isosurface at time 7.44 s |
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5% dye isosurface at time 20.53 s |
Download QuickTime
animation (21.9MB)
Computations
Due to symmetry, only half of the tundish is required
to be meshed. This mesh contains 7,210 bricks with a total of 33,389
nodes. The total number of degrees of freedom for velocity components,
pressure, k and e is about 175,000. The
top horizontal plane is a fixed free surface in which fluid can move
freely.
Fastflo's operator splitting k-e
turbulence module was used for solving this problem. On solid walls,
no-slip was imposed for velocity, and the von Driest wall function was
used for turbulent viscosity in the viscous sub-layer. The preconditioned
conjugate gradient method was used for the symmetric problems, and GMRES
for the transport equations. The Crank-Nicolson method was used for the
dye transport equation.
Typically, about 50 to 80 variable time steps were used to reach steady
state, taking about 20 hours CPU time on a 133 MHz DECstation. The dye
motion was computed with much smaller time steps, and it took several
hundred time steps to reach a peak concentration at the outlet. However
the solution procedure was fast because the incomplete ILU factorisations
for the GMRES preconditioning were saved and re-used.
Results
As seen from the velocity vectors shown above, the
impinging jet spreads radially outwards at the floor underneath the inlet
nozzle, but converges radially towards the inlet nozzle near the top.
Outside the recirculation region, the flow everywhere is towards the
outlet; no reverse flow (towards the inlet) is observed in our numerical
results.
The 5% dye concentration isosurfaces at 7.44 and 20.53
seconds are also shown above. These were displayed using a separate
program. An animation of the results has been made, and examined in detail
for signs of stalling or recirculation.
Table 1 compares predicted minimum residence time with BHP's water
model experiment at the two flow rates. While the agreement is good in
general, the calculations predicted slightly longer residence time,
perhaps indicating an under-prediction of turbulence intensity or
diffusivity by the k-e model. Also shown
in the table are the value of peak concentration at the outlet Cmax
and the time it took to reach the peak value Tmax.
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Flowrate 1/min
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MRT Exp't
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MRT Num
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Cmax
|
Tmax
|
|
654
|
47 s
|
51 s
|
0.01220
|
368 s
|
|
523
|
56 s
|
59 s
|
0.00929
|
454 s
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Table 1: Dye injection minimum residence times (MRT).
Reference
X.-L. Luo, Modelling 3D turbulent flow in a
continuous casting tundish using Fastflo, Proc 12th
Australasian Fluid Mechanics Conference (University of Sydney, 1995), 581
- 584.
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