4.5 Results and Discussion
4.5.3 Temperature at the Impact Point
Comparison of the present numerical predictions with available experimental results for the impact point temperature is shown in Fig. 4.8. The overprediction of the experiment by the simulation is clearly due to the presence of the predicted air bubble in the region of the impact.
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t, ms 80
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T w, °C
experimental variable properties constant properties re-initialized numerical:
Figure 4.8: Comparison of the present numerical predictions (lines) with experimen-tal results for the temporal evolution of the impact point temperature for the case A from Pasandideh-Fard et al. [74] (symbols).
In order to further analyze the reasons for such an outcome a hypothetical case was computed using the same impact parameters by re-initializing the distri-bution of the phase fraction field. The simulation was stopped at the moment of impact and values of the phase fractionγ = 1 were prescribed in those cells occupied by the entrapped bubble. Afterwards the simulation was continued. The impact point temperature agrees very well with experiments in the latter case. However, a small bubble was subsequently entrapped at some distance from the symmetry axis even in this case, following exactly the same mechanism as described by Mehdi-Nejad et al. [58]. Therefore, this is only a hypothetical case used to examine the performance of the computational model and this result is not considered as rele-vant for the overall analysis of heat transfer. The reason for resolving the bubble in numerics could be explained by observations reported by Elmore et al. [22]. It was indicated that the drop shape at the instant of impact, being either more pro-late or obpro-late, influences the final outcome after the impact by either allowing or preventing an air bubble to be entrapped. Even in a single experiment with the same parameters, the bubble may appear in one run, but not in the second. In the present simulations, the drop is always initialized as perfectly spherical and although the afore-mentioned observations were made in the case of the drop impacts on a shallow pool, similar mechanisms could be responsible for air bubble entrapment in impacts on a solid target as well.
Similar computational results of the impact point temperature were recently obtained by Strotos et al. [109], where drop impact and heat transfer were com-puted for the same impact parameters as those used in Pasandideh-Fard et al. [74], but including phase change. The small bubble at the impact region was resolved in simulations in the receding phase, after the lamella collapses around the axis of symmetry. Traces of a small bubble are visible also in the results for the initial spreading phase upon the impact (c.f. Fig. 8 in Strotos et al. [109]), however this was not explicitly reported and therefore cannot be commented. The predicted mean drop temperatures were lower compared to those obtained in the present work (shown in Fig. 4.14), which is the consequence of taking the phase change due to evaporation into consideration. However, the computed impact point temperatures were still higher than in experiments from Pasandideh-Fard et al. [74], which seems to be contradictory. Strotos et al. [109] used three different estimations for the thermal conductivity in cells containing both fluids, namely the mass-averaged, the volume-averaged and the harmonic volume-averaged. The mass-averaged thermal conductivity showed the lowest disagreement with the experimental results, tending to indicate that this model should be the most accurate for the thermal conductiv-ity. However, the computed temperature at the impact point represents actually the temperature of the contact between the entrapped air bubble and the solid surface, as in the present study, and thus it should not approach the measured values, if the bubbles were not observed in the experiments. It can be shown that the reason for a better agreement obtained using the mass-averaged thermal conductivity lies in the fact that the mass-averaged thermal conductivity value contains much more contri-bution of the liquid fraction due to the much larger liquid density, even in the case of small liquid phase fraction values in cells containing the bubble. Therefore, the
common phase fraction-based weighting used in the present work for the evaluation of the physical properties is considered to be more physical, yielding more accurate results.
The predicted temporal evolutions of the impact point temperature are shown in Fig. 4.9 for all simulated cases. As expected, the impact point temperature exhibits higher values than the theoretically predicted ones, given in Table 4.2, the outcome representing the consequence of the air bubble entrapment. Furthermore, very similar behavior is observed in all cases except in the case F representing the impact onto a glass substrate, being characterized by two peaks followed by sudden temperature changes.
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t, ms 20
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T w , °C
case A case B case C case D case E case F
Figure 4.9: Computationally obtained temporal evolution of the impact point tem-peratures for the cases A-F.
The latter changes are to be explained with help of Fig. 4.10, where the lamella shape and the entrapped bubble are shown at several time instances, plotted as the γ = 0.5 contours. It can be seen that, after entrapment, the bubble starts to oscillate.
Although similar bubble oscillations were also encountered in other simulated cases, the amplitudes of the oscillations were much larger in this case. At the time instant t = 0.5 ms the bubble has a lower height compared to the previous time instant, leading to the temperature rise in the bubble and at the underlying solid surface, represented by the minimum at the temperature curve in Fig. 4.9 for the case F. At the time t = 2.85 ms the lamella becomes very thin and comparable to the bubble size. When the top surface of the lamella at a later time reaches the bubble, it breaks and the temperature adjusts accordingly showing the local decrease in that region due to a sudden heat release from the solid substrate. This explains the sudden temperature drop at t = 2.95 ms in Fig. 4.9. Afterwards, approximately at the time when the lamella starts to retract, the sides of the formed circumferential ring collapse, leaving only a tiny bubble entrapped. A clear physical mechanism for the oscillation of the bubble may not be recognized from these results. However, since this study is mainly devoted to the formulation and validation of the computational
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Figure 4.10: Free surface morphology variation illustrating the entrapped bubble oscillation and its consequent breakup in the case F.
model for combined simulations of free-surface flow and conjugate heat transfer, the hydrodynamics of the oscillating bubble is out of scope and is not further analyzed.