Inputs into the Model

In order to simulate the casting process, ProCAST required initial conditions such as the temperature of the melt and mould, the percentage fill of the melt, the length of time for the simulation, the maximum time step and the material types. The inputted values were chosen to correlate with the casting experiments as described above.

Thermo-physical properties are also necessary for both the melt and the mould such as thermal conductivity, emissivity and latent heat of fusion. ProCAST has an inbuilt

0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (s) A ir -g a p ( m m ) Elastic Elastic-Plastic Visco-Elastic-Plastic

59

material property database to include information for an LM25 equivalent and H13 steel. These figures were verified against supplier’s data and determined to be representative.

Boundary conditions are also essential; this can either be between the mould and the environment or between any two interfaces. At these points IHTCs have to be applied and can be treated in three ways:

1. As a constant

2. As a proscribed IHTC dependent only on time (i.e. using the data in Figure 4-12)

3. By iteratively predicting the IHTC within the model based upon the size of the air-gap using the initial IHTC from Figure 4-12.

It was found that if the initial IHTC was kept constant, the mould temperature was over- estimated and the melt temperature under-estimated, also seen by Kron (Kron et al., 2004). The time dependant IHTC had to be applied identically across the entire ingot and mould interface. However, in practice the local size of the air-gap will vary, leading to a varying IHTC across different regions of the interface, as found by Arunkumar (Arunkumar et al., 2008). Therefore for the simulation results a gap- dependent IHTC was used with an initial value of 2569 W/m2K. Typical ProCAST run parameters can be found in Appendix C.

The model was run for the same duration as the casting experiment to include both the pouring and the solidification of the melt. Illustrated in Figure 4-18 are equivalent time steps between the ProCAST simulation and the casting experiment which shows a good agreement with filling time and the formation of pipe on the melt’s surface as it solidifies.

60

Note consistant temperatre colour chart throughout all images

a) t=5 – Before pour – note the simulation start pour time was offest by 6 seconds so it ran at the same time as the video.

61

b) t=7 seconds – Start of pour

c) t=10 seconds – The mould is half full and has reached the locations of the tungsten rod and internal thermocouple.

62

e) t=15 seconds – Pour complete

f) t=27 seconds – Formation of pipe begins on the surface of the melt

63

h) t=87 seconds – Last stages of pipe as minimal liquid is left on the surface of the melt

i) t=231 seconds – Pipe is fully formed and surface skin is 100% solid

Figure 4-18 – Time steps taken from ProCAST simulation (left) and the casting experiment (right) for LM25 casting.

Once the simulation was complete, nodes were selected to extract time-temperature histories. Identical positions of the thermocouples, both within the mould’s wall and the melt’s surface, were chosen and are illustrated in Figure 4-19. This allowed the direct comparison between the experimental data and the simulation predictions; these results are presented in Figure 4-20. The node at the interface was also chosen which allowed for the predicted air-gap to be exported; this is displayed in Figure 4-21.

64

Figure 4-19 – Illustration to show the locations of nodes selected in ProCAST for the extraction of predicted temperatures within the mould’s wall and melt concurring with experimental

65

Figure 4-20 – Graph to show the ProCAST temperature predictions (dashed lines) and the experimental measurements of the thermocouples 10 and 18 mm within the mould wall and the

melt thermocouples for the LM25 casting.

Figure 4-21 – Graph to show the ProCAST air-gap predictions (dashed lines) and the experimentally measured air-gap for the LM25 casting.

0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 100 200 300 400 500 600 700 800 Time (s) T e m p e ra tu re (  C) ProCAST Experiment 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.4 -0.2 0 0.2 0.4 0.6 Time (s) S ize o f a ir g a p ( m m )

Exp air-gap _{ProCAST air-gap}

Ingot displacement Mould displacement

Liquidus 616˚C Solidus 556˚C

66

As illustrated in Figure 4-20, the simulated and experimental melt temperatures are in close relationship, and the time taken for them to reach the solidus temperature is within 10 seconds.

In both the experimental and the model predictions, reaching the solidus temperature coincides with an increased rate in air-gap formation, which can be seen in Figure 4-20 and Figure 4-21 for temperature and displacement respectively. This increased rate in air-gap formation reflects the presence of the newly solidified skin of the casting, which begins to cool and contract whilst the mould is still gaining heat and expanding.

The rate of increase in air-gap begins to fall after 400 seconds which can be attributed to the peak temperature of the mould is reached. From here, and in agreement with the experimental results, the mould begins to cool and consequently contracts resulting in both the melt and the mould moving in the same direction. The rate of increase in the air-gap from this point onwards is equivalent to the experimental results; even though the magnitude of the predicted air-gap for the model is lower than the measured value. Some key differences between the predicted and experimental results are observed within Figure 4-20 and Figure 4-21 these are:

1. The melt’s super heat for the simulation is immediately lost, however for the experiment this occurs over the first few seconds. For the simulation a surface node was selected, and therefore representative of the true melts’ surface. However, for the experiment a thermocouple was positioned in the mould cavity as close as practical to the surface of the melt. After cooling the ingot was removed from the mould and sectioned to determine the location of the

67

thermocouple tip by a progressive grinding technique. The location of the thermocouple tip was found to be 1.5 mm form the melt’s surface (Figure 4-22).

Beginning of pig tail on the melts surface. Distance approximately 1.5 mm to centre of thermocouple. Location of the thermocouples tip. Thermocouple - 1 mm in diameter

Figure 4-22 – Photograph to show the location of thermocouple tip solidified within the LM25 casting.

2. Once steady state had been reached, approximately after 600 seconds, disagreement in the temperature difference between the melt and the mould is witnessed between experimental and simulated results. This was measured at 25˚C and predicted at 14˚C. This could also be attributed to the melt’s thermocouple measuring the temperature at a depth of 1.5 mm and not the melt’s surface.

3. The maximum predicted mould temperature for the simulation was lower and delayed by 150 seconds compared to the experimental results. Parameters within the simulation which have not been explored and may have an influence on this are the mould’s thermal conductivity and the initial IHTC. It is predicted that an increase in either/both of these would lead to a better fit between

68

simulated and experimental results. However the investigation for this is out of the scope of this work.

4. The final measured air-gap is slightly larger than the predicted counter-part. The simulated mould’s temperature not reaching the same maximum as the experiment may have contributed to this, as a lower amount of expansion occurs within the mould occurs.

As with the experimental results, the simulated IHTC was calculated using the temperature readings and the size of the air-gap; this is presented in Figure 4-23.

Figure 4-23 – Graph to show the comparison of the predicted interfacial heat transfer coefficient using ProCAST and the calculated values from the LM25 casting.

This section of work was presented at the Liquid Metals Technology conference in 2013 (Swan et al., 2013) 0 50 100 150 200 250 300 350 400 450 500 0 500 1000 1500 2000 2500 3000 Time (s) In te rf a c ia l H e a t T ra n s fe r c o e ff ic e n t ( W /m 2 K) EXP IHTC ProCAST IHTC

69