Development and analysis of continuous metal casting process and using FEM

The following projects builds on metal casting process in a given shape/pattern. For casting, solid metal is placed in a blast furnace and is impacted to very high temperatures for a long period of time. This prolong treatment with high temperature leads to metal transforming from a solid state to a molten state. To perform casting, a mold is created in sand/ground. All edges of soil are taken to be adiabatic.

For this project , a molten material is considered at the initial temperature of 900K. The desired pattern to be achieved by metal casting, which looks like number 5 on the dice is shown above (in gray). All of the 5 circles are extended into the ground for the length of 0.2 m through the ground and the molten material is poured in all the 5 circle together. Consider the case when the amount of metal poured is such that all 5 circles are just fully filled with it. To regulate the flow of heat in the ground, additional channels are created. The above figure shows that there are 4 air columns with h = 100W/m2K and these are always kept at 300K. Similar to these there are 4 water columns which further absorb heat from ground.

Dimensions –

The outer ground domain is a square of side W = 2m;

Radius of molten material circles R1 = 0.2m

Radius of air columns R2 = 0.1m

Center to center distance of middle molten circle to air columns W2 = 0.15+R1 m

Center to center distance of molten circles W3/cos(45) = 2*W2 m

Length of water column = 0.4m

Breadth of water column = 0.1m

Distance of leading edge of water column from center molten circle W4 = W2+R2+0.1 m

The final steady state temperature will be analyzed. Also, the results will be shown using Euler and Crank Nicolson, adaptive Crank Nicolson and Runga-Kutta techniques. All the thermal properties are temperature independent. The second part of the project deals with the center circle isolated from the entire geometry. The molten fluid is poured in the whole with a pressure gradient of 1Pa/m. The aim is to analyse the velocity profile throughout the length of pipe and to obtain the temperature distribution as we go deep in the ground at various depths.

The above left plot shows the initial temperature of the surface, all the five circles are initially set to 900 K and all water baths are at 274 K. The ground is at 300 K. The above right plot shows the steady state temperature distribution, across the surface. The maximum temperature has now dropped from 900 K to 890 K. The temperature behind and across the water baths are lower, because of the presence of air columns and due to low initial temperature. The temperature of the water bath has increased up to roughly 315K.

For the rest of the part, consider the middle mold isolated from rest of the geometry. The effects of gravity are ignored in this case and the molten material is poured at the pressure gradient of 1Pa/m.

Velocity profile and surface plot at pressure gradient of 1Pa/m

The above plot shows the expected parabolic velocity profile in the cylindrical tube flowing through the ground. Now, the temperature profile is analyzed at various depth in the ground. The total length of the column taken is 0.20 m and the temperature profile are developed at z = 0 m , z = 0.05m ; z = 0.1 m ; z = 0.15 m and z = 0.2 m;