Modeling of Two-Phase Flow in RH Vacuum Degassing Vessel
With the Effect of Rotating Magnetic field
Baokuan Li
Northeastern University, China
z
Fumitaka Tsukihashi
y
x
o
The University of Tokyo, Japan
Research motivation
Vacuum
Pump
To promote the removal of
non- metallic inclusions of
molten steel.
θ
To increase the flow rate of
molten steel in RH vacuum
degassing vessel.
r
Air
z
water
y
o
x
To prolong the life of RH
equipment.
Research ideas
Vacuum
Pump
θ
r
Air
z
water
y
o
x
To concentrate the argon gas
bubbles and inclusions in central
zone of up-leg of RH vessel by
using the centripetal force, which
is produced as the result of
density difference between gas
bubbles or inclusions and molten
steel in the swirling flow.
Therefore, collisions and
coalescences increase.
Swirling flow is produced by the
application of rotating magnetic
field.
Water model experiments examine the research ideas
Manometer
Impeller
Gas distributor
Rotameter
Nozzle distribution
RH degassing vessel
Ultrasonic flowmeter
(a)
(b)
(c)
(d)
Effect of impeller input power on gas bubbles distribution,
Q=0.5 m3/h. (a) 0, (b) 20 W, (c) 25 W and (d) 35 W
9
8
7
6
Circulation flow rate, 10-5 m3/s
10
6.944×10-5m3/s
11.111×10-5m3/s
16.667×10-5m3/s
40
35
30
25
20
15
10
5
0
Input power, W
Effect of plane blade impeller on circulation flow rate of RH vessel
Mathematical model
• To develop a mathematical model for the
two-phase turbulent flow in the RH vessel
with the rotating magnetic field in the upleg.
• To analyze the gas bubbles driven
circulation flow characteristics in RH
degassing vessel with the swirling flow.
Formulation
  ( V )  0
V ( V )  e 2V  p  F  g
Spitzer et al. [1]
v
1
Fr   B02 (   ) 2  2 m r 3
8
r
v
1
F  B02 (   )r
2
r
Fx  Fr cos   F sin 
F y  Fr sin   F cos 
k   turbulence model
 = g  (1   ) Liq
(u  u in  u slip )


 





 (v  v in  v slip )
 ( w  wslip )

( e
)  ( e
)  ( e
)
x
y
z x
x
y
y
z
z
Penetrating velocity and slip velocity
Horizontal penetrating velocity:
uin  v in 
Up-leg
1 2
y
nA
Qg : total argon gas flow rate,
n :nozzle number
A : cross nozzle inlet area
Nozzle
z
Qg
Gas jet zone
α : gas volume fraction (at inlet α0)
x

Centripetal force and horizontal slip velocity
caused by rotating magnetic field
Fr  r ( L   g )
2
R 2 2 r
Vr  2( L   g )
9
u slip  Vr cos , v slip  Vr sin 
Vertical slip velocity
wslip  exp( a0 ) exp( a1 ln d g ) exp[ a2 (ln d g )2 ]
Boundary conditions and solution method
Blackage technique
Flow field
 1, for fluid
 1, for fluid
Volume factor f V  
, Area factor f A  
0, for solid
0, for solid

0
n
Near wall: The wall law function is used to calculate e , k , and 
Free surface and symmetrical sections:Vin  0,
Gas volume fraction
Inlet:  in is calculated by Thermodynamic equation of gas
Other sections:

0
n
Vacuum
Pump
θ
r
Air
z
water
y
o
x
Schematic of physical model of
RH degassing vessel with the
rotating magnetic field.
(d)
(c)
(b)
(a)
(a)
(b)
(c)
(d)
Calculated flow velocities at horizontal sections of RH
degassing vessels, (a) up-leg, (b) bottom of vacuum chamber,
(c) middle of vacuum chamber, and (d) surface of vacuum
chamber.
0.7
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.4
0.4
0.4
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0
0
0
0.1
0.2
0.3
(a)
0.4
0.5
0
0
0.1
0.2
0.3
0.4
0.5
(b)
Computed gas volume fraction at main sections of RH
degassing vessels, (a) no swirling flow (b) with swirling flow.
0.8
0.5
Vertical velocity, m/s
Gas volume fraction
0.7
0.4
0.3
0.2
0.1
No swirling flow
With swirling flow
-0.04
0
0.6
0.5
0.4
0.3
No swirling flow
With swirling flow
0.2
0.1
0.04
-0.04
Diameter of up-leg, m
Gas volume distribution
of RH degassing vessel
0
0.04
Diameter of up-leg, m
Velocity distribution of
RH degassing vessel
CONCLUSIONS
Water model experiments verified that the gas bubbles may
be moved toward the central zone of up-leg of RH vessel in
the swirling flow.
The numerical results showed that a swirling flow may be
produced and extended into the vacuum chamber in case
that rotating magnetic field is applied in up-leg. The
maximum of gas volume fraction moves toward the center
zone of the up-leg.
The larger circulation flow rate can be obtained in RH
degassing vessel with the effect of swirling flow.
Thank you!