## 3 Validation of Numerical Models
### Results and Discussions  
[PERSON] et al. [61] conducted wing electric-impulse de-icing experiments in an icing wind tunnel under actual icing conditions, obtaining the deflection curves of the doubler one center skin and de-icing results with impulse action time and comparing the simulation and experimental results for the subsequent verification of the numerical model of wing electric-impulse de-icing. In order to adjust the uniform pressure operating on the doubler region, numerical simulations were first performed in a without-ice environment. For the without-ice situation, an initial voltage is chosen. Figure 15a shows experimental and numerical simulation comparisons of the skin deflection curves at the center of doubler one when doubler one is pulsed once. The displacement cloud is shown in Figure 16. The maximum deflection distance of the experimental clean skin is 2.05 mm, while the maximum deflection distance of the simulated clean skin is 2.04 mm, both with a relative error of 0.5%. Next, the de-icing process is simulated using the established finite element model of wing icing. Under the wing ice-covering situation, one, two, and three pulses are applied to the doubler one, and the experimental and numerical simulations of the skin deflection curves at the center of the doubler one are compared in Figure 15b-d. The ice layer increases the structure's stiffness, reducing the skin deflection distance under impulse action. The comparison of experimental and numerical simulation results shows that the loads acting on the doubler are appropriate.  
Figure 14: Finite Element Modeling of Wing Icing.  
Figure 13: Schematic of the doubler’s position.  
Figure 16: Clouds of the center displacement of doubler one under the action of one impulse in the clean skin state.  
Figure 15: Skin deflection curve of the double one center: (**a**) one impulse in without-ice state, (**b**) one impulse in icing state, (**c**) two impulses in icing state, and (**d**) three impulses in icing state [51].  
Finally, based on the verified load amplitudes operating on the doubler's surface, two, four, and seven impulses were applied to the doubler one's surface, with a comparison of experimental and simulated de-icing outcomes given in Figure 17. The fourth impulse load amplitude is equal to the third impulse load amplitude in the ice-covered condition, and the fifth, sixth, and seventh impulse amplitudes are equal to the first impulse amplitude in the without ice state. The de-icing effect of the electric impulse is quantitatively described by the de-icing rate, which is defined as the ratio of the area of the ice-shedding region to the original total area. In the numerical simulation, this is equivalent to the ratio of the number of cohesive elements deleted between the ice-wing skin to the total number. A higher de-icing rate indicates better de-icing performance. Under two impulses, skin deformation is small. However, de-icing may be discovered at the ice edge downstream of the airfoil, with an experimental de-icing rate of 20% and a simulation de-icing rate of 25% compared to the initially iced-over area. The experimental skin was deformed with four impulses, and a substantial amount of ice was removed, leaving only 10% of the ice on the wing, resulting in a 64% simulated de-icing rate. The experiment with seven impulses resulted in additional de-icing, eventually leaving 5% of the ice on the wing and a simulated de-icing rate of 67%. Compared to [PERSON] et al.'s simulation work [51], the number of de-icing impulses in this study is consistent with the experiment, and the skin deflection curve and de-icing effect are more accurate.