GIFA-Forum – 16.6.2015
Minimizing Air Entrainment in High Pressure Die Casting
Shot Sleeves
Using flow analysis software to optimize piston velocity
M. Barkhudarov, Flow Science, Inc., USA
R. Pirovano, XC Engineering, Italy
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GIFA-Forum – 16.6.2015
XC Engineering & Flow Science
XC ENGINEERING
FLOW SCIENCE
•Italian society born in 2002
•
Founded in 1980, by Dr. Tony Hirt who
developed the Volume of Fluid (VOF) method
for free-surface tracking at the Los Alamos
National Laboratory
•
Commercial software FLOW-3D first released
in 1985
•
Develops and sells FLOW-3D, a highly-accurate
computational fluid dynamics (CFD) software,
with FLOW-3D Cast as an intuitive interface
specifically for casting simulations
•
Offers high performance computing with
parallel processing capabilities
•Located in Cantù, Italy
•Field of activity: virtual simulations and optimization
with FLOW-3D®, FLOW-3D® CAST, Flownex IOSO
Technology
•Provides consultancies, trainings and technical
support, as well as the reselling of the softwares
Minimizing Air Entrainment in HPDC Shot Sleeves
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Introduction
A challenge in HPDC is to achieve optimal
conditions in the shot sleeve, controlling the
speed of the plunger to:
• Avoid unnecessary entrainment of air in the
metal
• Minimize heat losses in the sleeve
Two different solutions to find the best piston
velocity profile during the slow shot phase:
• A general analytical 2D solution for the flow
of metal in a shot sleeve
• A numerical parametric optimization, in a
fully 3D, viscous and turbulent environment
Minimizing Air Entrainment in HPDC Shot Sleeves
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First solution:
ANALYTICAL METHOD
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Analytical model
•
•
General solution for the plunger speed as a function of time and of the maximum
admitted surface slope
Approximations:
•
The cylindrical shot sleeve is approximated with a channel of rectangular cross-section
filled initially with liquid metal to the depth h0 (justified for initial fill fractions in the range
of 40-60% [Lopez et al, 2003])
•
Shallow water approximation [Lopes et al, 2000] (vertical direction is neglected, h<H)
•
The flow is modeled in two dimensions
•
Viscous forces are omitted
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Analytical model
•
Location, metal speed and depth in a wave that separates from the surface of the plunger at
time t=tp are given by [Lopes et al, 2000]:
3


x(t )  X (t p )   c 0  X ' (t p )   (t  t p )
2


u ( x, t )  X ' (t p )
1
1

h( x, t )   gh0  X ' (t p ) 
g
2

2
c 0  gh0
•
•
The metal speed u, and depth h
•
In each wave are constant
•
They depend only on the time of the wave separation from the plunger, tp
•
They both increase with the speed of the plunger X’
First conclusion: to maintain a monotonic slope of the metal surface in the direction away
from the plunger, the latter must not decelerate
X ' ' (t )  0
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Analytical model – Controlling the waves
•
Once a wave detaches from the plunger it travels at a constant speed given by:
u  c  X ' (t p )  gh  gh0 
3
X ' (t p )
2
•
If the plunger accelerates, each successive wave will move faster: steepening of
the surface slope and potentially overturning
•
Analysis of the evolution of the surface slope between two waves generated at
the plunger at close instances, t2>t1, linearized with respect to Dt=t2-t1:
1


 c0  X ' (t1 )   X ' ' (t1 )
dh
h h
1
2


tan(  )  
 1 2  
dx
x1  x2 g c  1 X ' (t )  3 X ' ' (t )  (t  t )
0
1
1
1
2
2
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Analytical model – Controlling the waves
1


 c0  X ' (t1 )   X ' ' (t1 )
1
2


tan(  )  
g c  1 X ' (t )  3 X ' ' (t )  (t  t )
0
1
1
1
2
2
•
•
•
If X’’(t1)=0 (costant speed) the slope of the free surface is horizontal
If X’’(t1)>0, the slope increases with time
When the denominator reaches zero, the slope becomes vertical
Initial surface slope for a wave
detaching from the plunger:
Setting a maximum slope in a wave (when
it reaches the end of the shot sleeve):
 min  t  t1
 max  x  L  t L  t1 
tan(  min ) 
X ' ' (t1 )
g
L  X (t1 )
3
c0  X ' (t1 )
2
1
3

 

 c0  X ' (t1 )    c0  X ' (t1 )   tan(  max )
2
2

 

X '' max (t1 ) 
1 
1
3


  c0  X ' (t1 )  c0  X ' (t1 )   tan(  max )  L  X (t1 ) 
g 
2
2


In this range:
•the slope will not exceed the angle defined by αmax at any time, preventing
wave overturning and the entrainment of air in the metal
•the slope is directed away from the plunger, helping to direct the air into the
runner system
0  X ' ' (t )  X '' max (t )
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Analytical model – Results
•
The equation is numerically integrated with
respect to t1 using the initial values of the
plunger location and speed at t=0: X(0)=0
and X’(0)=0, to obtain the solutions for X(t)
and X’(t)
•
The integration was done for a shot cylinder
of length L=0.7 m and height of H=0.1 m
and the initial fill fraction of 40%, i.e.,
h0=0.04 m
•
An additional constraint of the plunger
velocity can be added not to exceed the
critical velocity at which the metal surface
reaches the ceiling of the channel at h=H
[Garber, 1982]: it can be derived from the
solution for the metal depth h(t,x) [Tszeng
and Chu, 1994]:

X cr'  2 gH  gh0

Solutions of the equations for the plunger position (a),
acceleration (b), velocity (c) and velocity as a function of
distance along the length of the shot channel (d), at
different maximum surface slopes max: 1 – 90°, 2 – 60°, 3
– 45°, 4 – 30°, 5 – 15° and 6 – 5°. The horizontal dashed
lines on plots c and d represent the critical plunger velocity
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Analytical model – Validation
Realistic conditions are used:
• Viscous flow and circular channel cross-section
• L=0.7m, D=0.1m, h0=0.04m (as before)
• Velocity of the plunger function of time, from the solution for max=5°
• Heat transfer and solidification are not included (negligible)
Several aspects match the analytical solution:
• The slope of the wave largely stays within the 5° limit
• The circular shape does not affect much the free surface in the
transverse direction
• The metal touches the top of the channel at t=1.37s (th. 1.35s)
• The velocity of the plunger at that time is 0.725 m/s (th. 0.73m/s)
• The first wave arrives at x=L at t=1.15s (th. 1.12s)
Differences in the two solutions:
• A viscous boundary layer develops at the bottom of the shot sleeve
• The flow near the free surface moves faster than the metal below it,
resulting in a sort of a surge wave (larger than 5°)
• There is a reflection of the wave around 1.3 sec, and as a result air
may be entrained in the last stages of the process
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Second solution:
NUMERICAL OPTIMIZATION
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Numerical optimization
To overcome the limits of the analytical theory, it’s
possible to perform a numerical optimization in order
to find the best piston velocity curve in a fully 3D and
realistical environment
Coupling between IOSO and FLOW-3D
•
FLOW-3D is one of the best software for this
kind of analysis, because of its capabilities to
track fastly and accurately the free surface of the
fluid, to evaluate the amount of air entrained and
to manage moving objects coupled with the fluid
•
IOSO is an optimization software able to interact
with several software packages in order to run
simulations, obtain data and find the optimal
configuration in the lowest number of iterations,
managing several parameters and objectives.
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Numerical optimization - Optimization parameters
The parameters are based on a standard Buhler
machines:
•
•
Up to 20 points (for 1° and 2° phase) of
“velocity” vs “run length” can be setup
A linear interpolation is adopted betweeen
one point and another one.
2
1.6
1.2
Usually, for 1° phase, 5-6 points are used
0.8
10 design parameters: 6 velocities + 4 run lengths
0.4
To fix an upper limit for the velocity and to prevent
from “reversed” initial run lengths (ex.: 3° length
< 2° length) the design variables are defined as
ratios of some quantity:
•
velocity = ratio * velMax (0.0<ratio<1.0)
•
run length = ratio * remaining length
(0.0<ratio<1.0)
0
0
50
100
150
200
Minimizing Air Entrainment in HPDC Shot Sleeves
250
300
350
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400
450
500
GIFA-Forum – 16.6.2015
Numerical optimization - Optimization results
2 Objectives:

find the fastest first phase (minimize simulation time),

but not so fast to entrain air and bubbles (minimize “air entrainment”)
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GIFA-Forum – 16.6.2015
Numerical optimization - Optimization results
2 Objectives:

find the fastest first phase (minimize simulation time),

but not so fast to entrain air and bubbles (minimize “air entrainment”)
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Numerical optimization - Optimization results
(air entrained minimized)
Velocity magnitude
Entrained air
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Numerical optimization - Optimization results
(air entrained minimized)
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GIFA-Forum – 16.6.2015
Numerical optimization - Results compared to theory
Similarities:
Minimizing Air Entrainment in HPDC Shot Sleeves
1.
The initial
acceleration of the
plunger from t=0 to
about t=0.6 are
similar
2.
The leveling off of
acceleration
happens almost at
the same time.
3.
The constant
critical velocity in
theory and the part
where it stays
constant until the
end, after metal
reaches the ceiling
is somewhat
arbitrary
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GIFA-Forum – 16.6.2015
Conclusions and future developments
•
The analytical method calculates a good acceleration curve, that conservatively
minimize in most of the cases the amount of air entrained (this method is
actually implemented as a simple calculator in FLOW-3D)
•
With a numerical optimization it’s possible to determine a more accurate curve,
that optimize more than one objective simultaneously
•
This kind of technology can be extended to different analysis:
•
Switching time to the second phase
•
Optimization of the geometry of the feeding and gating system in order to obtain a
uniform filling
•
Waves generated by the filling of the cylinder
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GIFA-Forum – 16.6.2015
Thank you for your attention
M. Barkhudarov, R. Pirovano
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