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Aerospace 2020, 7, 123 13 of 15 the leading edge, and the effects of the heating area on icing and aerodynamic performance were investigated. The present simulation method using the modified extended Messinger model is more suitable for use in de-icing simulations for both rime and glaze ice conditions, because it reproduces the thin ice layer behind the heater due to the runback phenomenon. It is well known that the extended Messinger model is suitable for both rime and glaze icing conditions as compared with the original Messinger model. Therefore, our proposed modification of the extended Messinger model is important in predicting the effect of a heater on icing. The results obtained in this study reveal that the lift and drag depend on the heater area. In the case of the heating area of 4% of the chord length, the lift coefficient deteriorated, becoming smaller than that of the clean airfoil. However, increasing the heating area improved the lift coefficient by up to 4%. The large ice vanished owing to the heater, although a thin ice layer formed behind the heater. On the other hand, the drag decreased and converged to that in the case of the clean airfoil. The present study shows that the de-icing effect created by the heater can be simulated using the modified extended Messinger model. Although the computational target was the NACA 0012 airfoil in this study, the results suggest the possibility of using the heater for de-icing in other icing conditions and situations. Therefore, a more comprehensive study using a numerical method that is more robust against, for example, larger AoA cases and other airfoil shapes, will be pursed in future work. Author Contributions: Conceptualization, S.U., K.F., and M.Y.; methodology, S.U. and M.Y.; validation, S.U., K.F., and M.Y.; formal analysis, S.U.; investigation, S.U.; resources, S.U.; data curation, K.F., H.M., and N.F.; writing—original draft preparation, K.F.; writing—review and editing, S.U., K.F., H.M., N.F., and M.Y.; visualization, S.U. and K.F.; supervision, M.Y.; project administration, M.Y.; funding acquisition, M.Y. All authors have read and agreed to the published version of the manuscript. Funding: This research was partially supported by Japan Society for the Promotion of Science (KAKENHI grant number: 16H03918). Conflicts of Interest: The authors declare no conflict of interest. Abbreviations The following abbreviations are used in this manuscript: AoA Angle of attack BBO Basset–Boussinesq–Oseen EMM Extended Messinger model FAA Federal Aviation Administration LWC Liquid water content MEMM Modified extended Messinger model MVD Median volumetric diameter References 1. Alekseyenko, S.; Sinapius, M.; Schulz, M.; Prykhodko, O. Interaction of Supercooled Large Droplets with Aerodynamic Profile; Technical Report, SAE Technical Paper; SAE International: Warrendale, PA, USA, 2015. 2. Takahashi, T.; Fukudome, K.; Mamori, H.; Fukushima, N.; Yamamoto, M. Effect of Characteristic Phenomena and Temperature on Super-Cooled Large Droplet Icing on NACA0012 Airfoil and Axial Fan Blade. Aerospace 2020, 7, 92. [CrossRef] 3. Macarthur, C. Numerical simulation of airfoil ice accretion. In Proceedings of the 21st Aerospace Sciences Meeting, Reno, NV, USA, 10–13 January 1983; p. 112. 4. Bidwell, C.S.; Potapczuk, M.G. Users Manual for the NASA Lewis Three-Dimensional Ice Accretion Code (LEWICE 3D); Technical Report, NASA Technical Memorandum 105974; NASA: Washington, DC, USA, 1993. 5. Britton, R. Development of an analytical method to predict helicopter main rotorperformance in icing conditions. In Proceedings of the 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 6–9 January 1992; p. 418. 6. Hedde, T.; Guffond, D. ONERA three-dimensional icing model. AIAA J. 1995, 33, 1038–1045. [CrossRef]PDF Image | Anti-Icing Electric Heaters for Icing on the NACA 0012 Airfoil
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