# Ultrasonic Deicing Efficiency Prediction and Validation for a Flat Deicing System
## 4 Results and Discussion
### Standard-Explicit Co-Simulation Analysis  
With the help of transient dynamic analysis by using standard-explicit co-simulation, the whole process of wave propagation and deicing can be revealed more clearly. Similarly, configuration 2 was studied in the process. The distribution of displacement for the aluminum plate and ice layer at different times was calculated and shown in Figure 16. After the PZT actuator was turned on 6 \(\upmu\)s,  
Figure 14: Variance of maximum shear stress along Y axis (**a**) and X axis (**b**).  
Figure 15: Average shear stress amplitude varies along the Z axis.  
waves were generated and started to spread around the actuator. After 12 \(\upmu\)s, waves reached and reflected from the left edge of the aluminum plate. Then, the reflected waves were superimposed with waves generated by the actuator and propagated toward the ice layer. Around 27 \(\upmu\)s later, waves reached the left edge of the ice layer. In the process, the waves continued spreading to the right edge of the aluminum plate and reflected from the edges around 180 \(\upmu\)s. Gradually, displacement started to concentrate on the ice layer after 429 \(\upmu\)s. Then, 498 \(\upmu\)s later, the left edge of ice layer started to peel off symmetrically along the neutral axis of the aluminum plate. Delamination developed towards the inside of the ice layer within 519 \(\upmu\)s. After that, delamination started at the bottom and top of the ice layer the ice layer about 546 \(\upmu\)s. Then, detachment developed towards the bottom and top of the ice layer after 555 \(\upmu\)s. After 564 \(\upmu\)s, detachment developed to the center and right edge of the ice layer. Finally, delamination finished at 570 \(\upmu\)s.  
To reveal the deicing process more clearly, an index for damage degree (SDEG) was utilized to elaborate the interface damage evolution process. Figure 17 shows the evolution process of SDEG for the cohesive layer. When SDEG was equal to 1, the area was detached and deleted. After the actuator was turned on 450 \(\upmu\)s, damage initiation occurred at the left, bottom, and top edge of the cohesive layer. After 498 \(\upmu\)s, the left edge of the cohesive layer started to damage and deleted. The ice layer started to detach from the aluminum plate. Then, damage developed along the wave propagation direction after 531 \(\upmu\)s. With the evolution of damage, the bottom and top of the ice layer was peeled off at 549 \(\upmu\)s. Then, the detached area continued to increase. The detachment developed to the center and right edge  
Figure 16: Displacement distribution for the aluminum plate and ice layer over time.  
of the ice layer around 564 \(\upmu\)s. Finally, the delamination finished within 570 \(\upmu\)s. The detachment area was around 88.2% of the icing area. Although the ice layer was not totally detached, the remaining area of the cohesive layer also showed varying degrees of damage, which meant that the ice layer was likely to be removed completely under a small external load.  
Based on results of dynamic analysis, the processes of wave propagation, reflection, and superposition can be better observed and understood. Besides, the entire peeling process of the ice layer can be studied and presented. From the results of the above simulation, it can be found that the detachment started at the edge of the ice layer, which coincided with the stress distribution analysis in Section 4.2. In the harmonic analysis for configuration 2, the detached area was 83.3%. In the above dynamic analysis, the detached area was 88.2%. It showed that good agreements between these two analyses were obtained.