1. 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

2. XC Engineering & Flow Science
Italian society born in 2002
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
FLOW SCIENCE
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

3. 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
end of first phase

4. First solution:
Analytical Method

5. 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

6. 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]:
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

7. Analytical model – Controlling the waves
Once a wave detaches from the plunger it travels at a constant speed given by:
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:

8. Analytical model – Controlling the waves
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):
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

9. 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]:
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

10. 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 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

11. Numerical optimization
Second solution:
Numerical optimization

12. 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.

13. 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.
Usually, for 1° phase, 5-6 points are used
10 design parameters: 6 velocities + 4 run lengths
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)

14. 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”)

15. 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”)

16. Numerical optimization - Optimization results (air entrained minimized)
Velocity magnitude
Entrained air

17. Numerical optimization - Optimization results (air entrained minimized)

18. Numerical optimization - Results compared to theory
Similarities:
The initial acceleration of the plunger from t=0 to about t=0.6 are similar
The leveling off of acceleration happens almost at the same time.
The constant critical velocity in theory and the part where it stays constant until the end, after metal reaches the ceiling is somewhat arbitrary

19. 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

20. Thank you for your attention
M. Barkhudarov, R. Pirovano