# Ultrasonic Deicing Efficiency Prediction and Validation for a Flat Deicing System
## 4 Results and Discussion
### Experimental Verification  
The deicing results for configuration 2 are shown in Figure 18. Three deicing experiments under different frequencies were compared. When frequency was 190 kHz, there was no visible change observed. When frequency was 236 kHz, only some cracks but without any delamination were observed. When frequency was 213 kHz, the ice layer was cracked and partially detached from the aluminum plate. After the actuator was turned on 24 s, delamination started from the edge of the ice layer. The delamination area increased along the wave propagation direction with some cracks after 47 s. Then, the detached area continued to increase with more cracks generated. Finally, delamination finished within 71 s. The detached area could be estimated from the nephogram in an open source  
Figure 17: Cohesive layer damage evolution process.  
image processing software named ImageJ [35]. Firstly, the experimental results image was converted into grayscale images. The detached area can be identified by comparing the images before and after the experiment. Then, the color threshold was set according to the color of the detached area. Based on these, the detached area was calculated. In the ice layer nephogram, the detached area was in white. The percent of shear stress exceeded the adhesion stress at 83.3% and 88.2% in harmonic analysis and dynamic analysis while it was 76.4% in the experiment. The main error came from the difference in ice properties between the simulation and experiment.  
Simultaneously, the different performances at frequency 190 and 236 kHz were also corresponding with simulation results. The final results are shown in Table 4. Neither frequency, 190 nor frequency  
Figure 18: Deicing effects for different frequencies.  
236 kHz could detach the ice layer, since both shear stresses of them were smaller than the adhesion strength of the ice. The crack existed at frequency 236 kHz rather frequency 190 kHz due to shear stress \(\tau_{12}\) which contributed to ice cracking. Shear stress \(\tau_{12}\) was higher at frequency 236 than 190 kHz. Thus, the crack could observe at frequency 236 kHz rather than 190 kHz.  
Meanwhile, deicing experiments were also performed for the remaining six groups at their optimal frequency, respectively. The trend of detached areas after deicing experiments and total shear stress \(\tau_{\text{total}}\) for delamination from FE simulation results were compared. The trend of total shear stress \(\tau_{\text{total}}\) and the detached area are shown in Figure 19.  
The result of Figure 19 can prove the optimal frequency for configuration 2 was 213 kHz. From the results of Figure 19, it can be found that the trend of detached areas in experiments is consistent with total shear stress in FE simulations, which can verify the correctness of FE simulation results and feasible of the deicing method. Finally, deicing experiments for four different icing cases mentioned before were conducted. The deicing results for these four cases are shown in Figure 20. The trend of the detached area for these four cases is consistent with the trend of DEF predicted in the FE simulation.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency (kHz)** & **Experimental Results** & **Simulation Results** \\ \hline \multirow{2}{*}{190} & \multirow{2}{*}{Without visible change} & Maximum \(\tau_{\text{total}}\) = 0.23 MPa; \\  & & Maximum \(\tau_{12}\) = 0.11 MPa \\ \hline \multirow{2}{*}{213} & Ice delamination and & Maximum \(\tau_{13}\) = 4.3 MPa; \\  & cracking & Detached area is 83.3\%; \\  & & Maximum \(\tau_{12}\) = 3.0 MPa \\ \hline \multirow{2}{*}{236} & \multirow{2}{*}{Cracks only} & Maximum \(\tau_{\text{total}}\) = 0.16 MPa; \\  & & Maximum \(\tau_{12}\) = 0.28 MPa \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of experimental and simulation results for three different frequencies.  
Figure 19: The trend of total shear stress \(\tau_{\text{total}}\) and detached area.