Meshing the Nozzle

The study of the effect of the nozzle mesh was started by doing a simple simulation of a pipe with the nozzle inner diameter and a length that is sufficient for a fully developed profile to form. The mesh at the pipe wall was inflated for five cells. Figure 8.2 shows a plot of the velocity profile from the nozzle centre to the wall at the outlet for different grid sizes. It is therefore immediately clear that the velocity profile is far from flat, which explains why assuming the inlet boundary at the nozzle port significantly affects the results. However, it can also be seen that the profile obtained by the solution changes with the grid size, with changes becoming small below 2mm.

Figure 8.2 - Velocity profile at the nozzle outlet as for different mesh sizes

By looking at the development of the velocity profile from the inlet of the pipe, it was decided to simulate 400 mm of the nozzle as part of the tundish flow volume. However, it was observed that the profile was already nearly fully developed after 150mm. This corresponds to 300mm in the industrial tundish-ladle setup; therefore it is safe to assume that a fully developed velocity profile will develop from the ladle to the nozzle port in the tundish.

When comparing the RTD curves for the TID case using a mesh size of 10mm for the tundish and different mesh sizes for the nozzle, it can be seen in Figure 8.3 that changing the resolution of the grid in the nozzle has a negligible effect on the tracer response at the outlet. It can therefore be concluded that a uniform velocity profile should not be assumed at the nozzle port, but that highly accurate solutions of the profile are not necessary.

80 Figure 8.3 - Comparison of overall C-curves for the TID case for different mesh resolutions in the nozzle

Despite the similar overall c-curves, it was decided to use the 2mm mesh, instead of the 5mm mesh, in subsequent runs since the number of additional cells (approximately 70 000) is small compared to the overall number of cells used in the final adapted mesh. This will make the model more robust in case the effect of the difference in the port velocity profiles on the overall C-curves becomes significant for different configurations or for the gradient adapted mesh.

8.1.3. Gradient Adaptation

The next step in the grid study was to determine the value of the gradient function at which the cells should be adapted. Before the gradient adaptation, a boundary adaptation was done near the walls and the top surface. Through some experimentation a suitable criterion for boundary adaptation was determined: Cells within 1cm of the walls and with a gradient function larger than .

After obtaining a solution with the boundary adaptation, the mesh was then refined using the curvature boundary adaptation approach. The value of the adaptation function was changed to increase the final mesh size in increments of 800 000 cells. In Figure 8.4 the C- curves of the simulations are compared to those of the physical experiment. It can be seen that with increased gradient adaptation the peak shifts later and lower. This moves the curve closer to that of the physical experiment and eventually past it. It must therefore be noted that a good comparison between the physical experiment and numerical C-curves does not necessarily assure accurate results, as a simulation using 3.6 million cells matches the physical model C-curve much more closely than that of the more accurate solution using 4.8 million cells. In this case likely causes for this occurrence are the numerical assumptions of symmetry and dynamically steady flow and the choice of turbulence model. As more cells

81 are adapted, the C-curve approaches a limit as grid independence is reached. Consequently, it was decided that the solution no longer changes appreciably after 4.4 million cells and the gradient adaptation function value of was selected for the adaptation value for further simulations.

Figure 8.4 - Comparison of physical model and numerical simulation C-curves for different extentof gradient adaptation

Despite the peak of the numerical C-curve shifting slightly lower and later than that of the physical experiment, the slope of the tail data and the general shape is very similar. Another positive comparison comes from comparing the C-curves of the individual strands between the physical model and the numerical simulation using 4.4 million cells, as shown in Figure 8.5. It can be seen that the simulated C-curve for the outer strand is nearly identical when compared to the physical model result. Similar to the physical model, the peak for the inner strand is also predicted earlier and higher than for the outer strand and the two curves cross after the peek. Despite these differences between the inner and outer strands not being a large as for the physical results, the comparison is still very favourable and suggests that the numerical model is reasonably successful in predicting the real behaviour.

82 Figure 8.5 - Comparison of RTD curves for the individual strands of the physical experiment and numerical simulation