Analysis of Aluminium Filling in Cylindrical Pipe under High Pressure by Experiment and Mathematical Modelling

Introduction

Die casting is the process of forcing molten metal under high pressure in metal casting. It is one of the oldest manufacturing processes and widely used [1]. It is an effective method for mass-producing metallic parts and structures with complex shapes and geometries. It is widely utilized in industries such as the automotive sector, where productivity is a crucial factor in the choice of manufacturing process for large-scale production. It is suitable for large- scale production of components with low per-part costs [2].

The process of die casting involves injecting molten metal into a reusable steel mold (the die) using high pressure. A metal is heated in a furnace until it reaches a liquid state, after which it is forced into a mold [3]. The demand for aluminum die casting continues to grow thus making it crucial to understand the process in order to make informed manufacturing decisions. There has been extensive research into modeling the die casting process, examining how different factors impact it.

Paul, et al. [4] employed the Lagrangian method and the smooth particle hydrodynamics (SPH) interpolation kernel to perform a computational modeling of thin-walled high- pressure die casting. The numerical modeling was validated using a water analogue experiment, and the results showed good agreement between the simulation and experiment. In another study Fu, et al. [5], the filling process of semi-solid state alloy A356 was modeled using two non-Newtonian constitutive equations and the CFD software PROCAST. The results revealed that the semi-solid metal alloy has a unique die filling behavior compared to liquid filling.

Some other research that has been done include modeling of high pressure die casting using different techniques such as steady state approximation with the boundary element method [6] and Lagrangian method that uses an interpolation kernel of compact support known as smooth particle Hydrodynamics (SPH) [7].

The investigation on the effects of cooling channels on the casting steps and final properties of the products in standard and conformal cooling gravity die casting molds was done by Karani, et al. [8]. They compared the numerical analysis results with the experimental data and then were verified. They measured the pressure losses in cooling channels, the times for molds to reach the required temperature and the cycle times. The pressure losses in standard and conformal cooling channels were measured at 5250 Pa and 12100 Pa, respectively.

Kun, et al. [9] focused on enhancing the mechanical properties of high-pressure die casting (HPDC) aluminum alloy. Two sets of shot curves (baseline and optimized) were analyzed to assess their impact on the ultimate tensile strength (UTS) and elongation (El) distributions of as-cast ASTM tensile samples. They established a mathematical model to examine the behavior of melt flow, heat transfer, solidification, and defect formation (entrapped gas, oxides, porosities) during the HPDC process with the two shot curves. The results indicated that the optimized shot profile leads to a noticeable improvement in the UTS and El.

In another study Yazman, et al. [10], the impact of casting parameters such as temperature, molding pressure, and gate speed on the microstructure, mechanical properties, and machinability of the samples was investigated. The grain size of the conventional casting sample was found to be around 50 microns, while the grain size in other cold chamber die casting tests varied based on temperature, pressure, and gate speed. The tensile strength of samples produced with 1000 bar mold pressure was higher compared to other samples. The feed rate was found to have a greater impact on thrust force than cutting speed. The least tool wear was observed in the drilling of the As-cast sample, while the highest tool wear occurred when the sample was produced with a combination of low pressure and low gate speed. Three different types of chips were formed during the drilling tests, including fan, spiral cone, and long ribbon, depending on casting and cutting parameters. Additionally, uniform and transient burrs of varying sizes were observed.

In this study, we compare experimental results with the mathematical modelling results and experimental results of Aluminium filling in cylindrical pipe under high pressure

Methodology

Our mathematical model equation was derived by considering a considering a vertical cylindrical pipe made of aluminum titanate immersed in molten aluminum (alloy

226) as shown in Figure 1. The pipe is immersed to a depth of 50mm. The total length of the pipe is 570mm and positive pressure relative to the air on the surface is applied which causes the melt in the pipe to rise to some height h.

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Governing Equations

The mathematical model was derived by considering the total force acting on the liquid column (the kinetic energy and potential energy) and analyzing the causes of dissipation (friction due to the pipe wall and singular pressure loss at the entry) in the system. To get the total potential energy, the force acting in the liquid column is considered and integrated. Thus, the potential energy is given as:

$$ E _ {p} = \frac {1}{2} \rho g A h ^ {2} \tag {1} $$

The kinetic energy is given as:

$$ E _ {k} = \frac {1}{2} m v ^ {2} = \frac {1}{2} \rho A (h + H) \dot {h} ^ {2} \tag {2} $$ The total sum of energy in the column is obtained by summing up equations 1 and 2. The differentiated energy together with the 1st principle of thermodynamics gives the balance of energy equation. Energy lost due to dissipation is analyzed and incorporated into the sum of equations 1 and 2. The losses in the pipe are due to friction on account of the roughness of the wall and also due the singular pressure loss at the entrance or exit of the pipe if liquid rises or if liquid goes down respectively.

The energy loss due to friction can be written as:

$$ d E _ {w} = \frac {1}{2} k _ {w} \rho A \left(\frac {h}{H} + 1\right) \dot {h} ^ {2} | \dot {h} | \tag {3} $$ The singular pressure loss is given as:

$$ d E _ {E} = \frac {1}{2} k _ {E} \rho \dot {h} ^ {2} \left| \dot {h} \right| \tag {4} $$ Equations 5 and 6 are included in the sum of the potential and kinetic energy equation to obtain the total final equation:

( ) ( ) 2 ¨ 1 1 2 2 E w p t h h h H h gh k k h h H ρ   (5) $$ \left(\left(h + H\right) \dot {h} + \frac {\dot {h} ^ {2}}{2} + g h\right) + \frac {1}{2} \left(k _ {E} + k _ {w} \left(\frac {h}{H} + 1\right)\right) \dot {h} | \dot {h} | = $$ where h is the height to which the liquid rises, and H is the length of pipe submerged under the liquid surface, E k is the coefficient of pressure lost at the entry of the pipe and KW the major coeffiecient of pressure lost is given by $$ K _ {w} = \frac {\lambda H}{2 r} $$ . λ is the friction factor and it is calculated from Moody’s diagram for a pipe made of Aluminium titanate with relative pipe roughness of 2.5.

Experimental Set-Up

The experimental set-up (Figure 2) consists of a tank containing colored water. Two cylindrical pipes of the same pipe diameter but different entry diameters (Pipe 1: Diameter of entry/Diameter of rise pipe=40/40 and Pipe 2: Diameter of entry/Diameter of rise pipe=16/40) were immersed in a tank of colored water to the same depth. The initial height of the water in the tank is noted. A camera is attached to a laptop to record the experiment. Water is sucked to an initial height in Pipe 1 and then released. The same process is repeated for pipe 2. The initial height of water in the tank is noted.

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Analysis of the Experimental Data

From the recordings, it was possible to determine the height of the first oscillation of pipe 1 and the frequency of both the pipes for the different initial conditions which is presented in summary form in Table 1. From Table 1, it is seen that pipe 2 is damped faster than pipe 1.

To compare the oscillations of the two pipes, the data of the oscillations is presented in the form of a graph. From the graphs presented in Figure 3 (initial height inside the pipes is 25cm) and Figure 4 (initial height inside the pipes is 27cm), it is clear that pipe 1 has higher oscillations than pipe 2. This is due to the fact that pipe 2 has a higher singular pressure loss at the entry due to the small diameter at the entry as compared to pipe 1.

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Conclusion

Experiments were done in order to visualize the behavior

of a column of water falling in a vertical pipe. It is seen that

for pipe 1 which has the same diameter at the entry as the

pipe diameter, there is a high oscillation of 4.5cm to 7.55 cm

depending on the initial conditions whereas for pipe 2 whose

entry diameter is not the same as the pipe diameter, the

oscillations are indistinguishable. The mathematical model

with the same initial conditions gives some results which are

close to the experimental data when imposed

14 E K = and 60 E K =

for pipe 1 and pipe 2 respectively. Using

$$ K _ {E} = 0 $$

(pipe 1) and

$$ K _ {E} = 0. 5 $$

(pipe 2), the Mathematical model

results are much different from the experimental results.