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Aerospace 2020, 7, 123 6 of 15 2.5. Validation of Flow and Heating Simulation The numerical results are compared with experimental results to validate the simulation, as described below. First, the aerodynamic performance of clean airfoil (without icing and heating) is compared with the experimental results obtained by Sheldahl and Klimas [36] and Harris [37]. The present study simulated the aerodynamic performance of a NACA 0012 airfoil at Reynolds number Re = 2,800,000 and Mach number Ma = 0.17, where the Re is defined by the chord length and the uniform flow velocity and Ma is defined by the sonic and ambient air speeds. In addition, we simulated the flow with a 1.5 times finer grid system. Figure 3 shows the lift and drag coefficients (CL and CD, respectively), which are normalized by the dynamic pressure and chord length, with a different angle of attack (AoA) in comparison to those for Re = 2,000,000, Re = 3,000,000, and Re = 5,000,000. Sheldahl and Klimas [36] used a clean airfoil and Harris [37] used a clean airfoil with tripping wire. The present results for lift coefficients show reasonable agreement with experimental results from Harris [37] without grid dependency. For the drag coefficient, the Reynolds number dependency was weak for AoA ≤ 4◦. Because the numerical results obtained in this study are in reasonable agreement with the experimental values at an AoA ≤ 4◦, we focus on a case with a small AoA (0◦ ≤ AoA ≤ 4◦), as described below. Additionally, Figure 4 shows pressure coefficients Cp defined as Cp = p − p0 , (10) 0.5ρU2 where p is the static pressure on the airfoil, while p0 and U are the static pressure and uniform flow velocity, respectively, at the inlet. This clearly indicates the validity of the present numerical simulation for the flow field. In addition, the results obtained for the 1.5 times finer grid system in all directions were plotted. Cp and CL show no grid dependency. On the other hand, CD shows grid dependency and it seems to converge toward the experimental results. The y+ values for the first grid locations from the wall were distributed from 50 to 300 in the present simulation and from 30 to 70 for the finer-grid case. Therefore, the wall function model should be changed to converge more closely toward the experimental result. Present (Re = 2,800,000) Finer resolusion Sheldahl et al. (1981) Re = 2,000,000 Re = 5,000,000 Harris (1981) Re = 3,000,000 (Ma = 0.3) Black: CL Red: CD 1 0.8 0.6 0.4 0.2 0.04 0.03 0.02 0.01 5 AoA[ ] 10 0 Figure 3. Aerodynamic performance of the NACA 0012 airfoil. 0 0 CD CL rPDF Image | Anti-Icing Electric Heaters for Icing on the NACA 0012 Airfoil
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