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Aerospace 2020, 7, 123 3 of 15 are in good agreement with experimental results. Asaumi et al. [25] conducted an experimental study using a simple model to evaluate the anti-icing performance of NACA 0013 airfoil with a heater. They reported that the heater temperature threshold for achieving the anti-icing effect is 2–5 degrees Celsius. More recently, simulations of anti-icing by heating have been conducted using a commercial solver, not only for airfoils [26], but also for wing turbines [27,28]. As previously mentioned, many experimental and numerical simulation studies have been conducted on de- and anti-icing devices. The effectiveness of thermal heaters has been clarified, and the heater input has been optimized. However, optimization is required with regard to the heater area. In this study, a new model is proposed in order to predict the occurrence of icing with a heater. Two-dimensional icing simulations were conducted using the NACA 0012 airfoil to investigate the effect of the heating area on the aerodynamic performance. The extended Messinger model (EMM) was modified (MEMM) [29] to consider the heat transfer from the airfoil surface in order to simulate the ice growth. Through this study, the influence of the heating area on residual ice formation and on the drag and lift of the airfoil are elucidated. The numerical scheme is described and validated in Section 2. Section 3 presents the simulation of icing with a heater for NACA 0012. 2. Numerical Scheme and Validation The numerical simulation is based on the Euler–Lagrange method. The computation comprises four steps: (1) grid generation; (2) computation of the flow field; (3) computation of droplet trajectories; and, (4) thermodynamics computations. Each step is computed using in-house code and it is described below. 2.1. Grid generation The computational targets were NACA 0012 airfoil for the icing simulation and NACA 0013 airfoil for the validation. Figure 1 shows the computational domain system and grid. In this study, C-type grids and an overset grid system were employed. Interpolation between the main grid and sub-grid was performed using the Lagrangian interpolation method. These grids were generated based on Hermite polynomials [30]. A main grid of 221 × 71 points was used to simulate the entire flow field around the airfoil, and the sub-grid of 301 × 51 points had sufficiently high resolution to correctly obtain the ice shape around the leading edge and boundary layer on the airfoil. The total number of grid points was approximately 26,000. The convergence of the ice shape by the grid points had preliminarily been confirmed through our previous investigation [31]. Figure 1. Computational grid for NACA 0012. The left and right figures show the overall and enlarged view around the airfoil, respectively. The red and yellow grids show the sub- and main computational grids, respectively. 20 chord 20 chordPDF Image | Anti-Icing Electric Heaters for Icing on the NACA 0012 Airfoil
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