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found to be higher for the profiles with smaller thicknesses. The maximum lift coefficient of about 0.84 is found to be for NACA 4406, whereas for the largest thickness profile of NACA 4418 a lift coefficient of nearly 0.43 is obtained. The drag coefficient increases as the thickness of the airfoil increases. The trend of the lift and drag coefficients for the different aforementioned five profiles is similar to that shown in previous maximum camber deflection of the tested wings is 4.0% of the chord, and located at 40% of their chord. This preliminary test is performed at a =2°, h/C=0.1 and R,=2x10° with the incoming turbulent intensity of 0.10% and aims at selecting a profile with the highest value of the GEV efficiency.

Figure 4 found to be higher for the profiles with smaller thicknesses. The maximum lift coefficient of about 0.84 is found to be for NACA 4406, whereas for the largest thickness profile of NACA 4418 a lift coefficient of nearly 0.43 is obtained. The drag coefficient increases as the thickness of the airfoil increases. The trend of the lift and drag coefficients for the different aforementioned five profiles is similar to that shown in previous maximum camber deflection of the tested wings is 4.0% of the chord, and located at 40% of their chord. This preliminary test is performed at a =2°, h/C=0.1 and R,=2x10° with the incoming turbulent intensity of 0.10% and aims at selecting a profile with the highest value of the GEV efficiency.

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The realizable k-—é€ model has been extensively validated for a wide range of flows [21,23], including rotating homogeneous shear flows, free flows including axisymmetric and planar jets, mixing layers, channel and boundary layer flows, and separated flows. The Reynolds averaged Navier- Stokes equations and the transport equations for the turbulent kinetic energy and dissipation rate are solved by the SIMPLE algorithm with a second-order spatial discretization scheme that based on finite volume method. No-slip boundary conditions are imposed on the surface of the wing, whereas the symmetry condition is set for the far-field boundary. The uniform flow with a free-stream velocity U7, and low turbulent intensity are applied on the inflow boundary while the convective boundary condition is applied at the outflow boundary. The ground surface is considered as a moving wall boundary at the free- stream velocity.
The realizable k-—é€ model has been extensively validated for a wide range of flows [21,23], including rotating homogeneous shear flows, free flows including axisymmetric and planar jets, mixing layers, channel and boundary layer flows, and separated flows. The Reynolds averaged Navier- Stokes equations and the transport equations for the turbulent kinetic energy and dissipation rate are solved by the SIMPLE algorithm with a second-order spatial discretization scheme that based on finite volume method. No-slip boundary conditions are imposed on the surface of the wing, whereas the symmetry condition is set for the far-field boundary. The uniform flow with a free-stream velocity U7, and low turbulent intensity are applied on the inflow boundary while the convective boundary condition is applied at the outflow boundary. The ground surface is considered as a moving wall boundary at the free- stream velocity.
Table 1. Grid-dependency for 2-D NACA 4406 airfoil at a = 2' and h/C =0.1 The size of the computational domain is defined as -7C <x<10C and -h<y<7C for the streamwise and vertical directions, respectively, where C is the chord length of the wing. In case of the isolated wing, the domain size is increased to -7C < y<7C in the vertical direction. Fig. l(a) shows the physical model of the 2-D WIG problem, the size of the computational domain, and the coordinate system.
Table 1. Grid-dependency for 2-D NACA 4406 airfoil at a = 2' and h/C =0.1 The size of the computational domain is defined as -7C <x<10C and -h<y<7C for the streamwise and vertical directions, respectively, where C is the chord length of the wing. In case of the isolated wing, the domain size is increased to -7C < y<7C in the vertical direction. Fig. l(a) shows the physical model of the 2-D WIG problem, the size of the computational domain, and the coordinate system.
Table 2. Aerodynamic characteristics of 2-D NACA four digits airfoils in ground effect
Table 2. Aerodynamic characteristics of 2-D NACA four digits airfoils in ground effect
Fig. 2. Distributions of mean pressure coefficient on the surface of 2-D NACA 0006 and NACA 4406 airfoils for @ = 2° and h/C=0.1 The minimum vertical grid spacing on both the wing and the ground surface is chosen to be about 10~C at the same Reynolds number of 2x10°, similar to that of Moon et al. [7]. In order to capture accurately the separating shear layers on both the wing and the ground, the grids are distributed non- uniformly near these regions, especially in the gap and the wake regions. To consider the variation of ground clearance, dense resolutions are maintained near both the wing and the ground surface and also in the area under the wing. Fig. 1(b) shows the grid distribution near the wing corresponding to an angle of attack @=0° at a ground clearance ofh/C=0.1, and the ground surface. The number of the grid points used in the y direction is tuned up to maintain a dense resolution near the wing, moving wall and also in the gap spacing, which in turn reflects the variation of the gap ratio. The commercial CFD package namely FLUENT 6.2 is employed for all numerical calculations.
Fig. 2. Distributions of mean pressure coefficient on the surface of 2-D NACA 0006 and NACA 4406 airfoils for @ = 2° and h/C=0.1 The minimum vertical grid spacing on both the wing and the ground surface is chosen to be about 10~C at the same Reynolds number of 2x10°, similar to that of Moon et al. [7]. In order to capture accurately the separating shear layers on both the wing and the ground, the grids are distributed non- uniformly near these regions, especially in the gap and the wake regions. To consider the variation of ground clearance, dense resolutions are maintained near both the wing and the ground surface and also in the area under the wing. Fig. 1(b) shows the grid distribution near the wing corresponding to an angle of attack @=0° at a ground clearance ofh/C=0.1, and the ground surface. The number of the grid points used in the y direction is tuned up to maintain a dense resolution near the wing, moving wall and also in the gap spacing, which in turn reflects the variation of the gap ratio. The commercial CFD package namely FLUENT 6.2 is employed for all numerical calculations.
The present study started by testing numerically five different 2-D wings NACA 4406, NACA 4412, NACA 4412, NACA 4415 and NACA 4418 that shown in Fig. 3. The
The present study started by testing numerically five different 2-D wings NACA 4406, NACA 4412, NACA 4412, NACA 4415 and NACA 4418 that shown in Fig. 3. The
Fig. 6. Mean streamlines around the NACA 4406 airfoil for a=14 at (a) h/C =0.25,(b) h/C =0.5 and (c) h/C =1.25
Fig. 6. Mean streamlines around the NACA 4406 airfoil for a=14 at (a) h/C =0.25,(b) h/C =0.5 and (c) h/C =1.25
Fig. 7. Distribution of the mean pressure coefficient on the surface of the NACA 4406 airfoil for different ground clearances at (a)a =0°, (b) ~@=4°, (c) a@=8°, and (d) a =10°
Fig. 7. Distribution of the mean pressure coefficient on the surface of the NACA 4406 airfoil for different ground clearances at (a)a =0°, (b) ~@=4°, (c) a@=8°, and (d) a =10°
Fig. 8. Distribution of the mean pressure coefficient on the surface of the NACA 4406 airfoil for different ground clearances at (a)a@ =12°, (b) a =14°, (c) a= 20°, and (d) a = 30°
Fig. 8. Distribution of the mean pressure coefficient on the surface of the NACA 4406 airfoil for different ground clearances at (a)a@ =12°, (b) a =14°, (c) a= 20°, and (d) a = 30°
Fig. 9. Lift coefficient as a function of the ground clearance for different angles of attack in the range of (a) 0° <a@<10°, and (b) 12° <a <30°
Fig. 9. Lift coefficient as a function of the ground clearance for different angles of attack in the range of (a) 0° <a@<10°, and (b) 12° <a <30°
Fig. 10. Drag coefficient as a function of the ground clearance for different angles of attack in the range of (a) 0° <@ < 10°, and (b) 12° <a <30°
Fig. 10. Drag coefficient as a function of the ground clearance for different angles of attack in the range of (a) 0° <@ < 10°, and (b) 12° <a <30°
At a constant @ in the range 0°<@<6°, Cp Slightly increases with increasing h/C as shown in Fig. 10(a). For a = 8°,9°,and10°, Cp has a maximum at the lowest h/C of 0.1 and then it decreases by moving towards h/C = 0.25. For h/C =0.25, the values of Cp are almost the same for the cases of @ = 8°,9°,and10° as shown in Fig. 10(a). At constant h/C, Cp increases slightly as @ increases. In contrast to C;, in Fig. 9(a), the reduction rate of Cp with respect to h/C Fig. 11. Efficiency of the GEV as a function of the ground clearance for different angles of attack over the ranges of (a) 0° <a@<12°, and (b) 14° <a <30°
At a constant @ in the range 0°<@<6°, Cp Slightly increases with increasing h/C as shown in Fig. 10(a). For a = 8°,9°,and10°, Cp has a maximum at the lowest h/C of 0.1 and then it decreases by moving towards h/C = 0.25. For h/C =0.25, the values of Cp are almost the same for the cases of @ = 8°,9°,and10° as shown in Fig. 10(a). At constant h/C, Cp increases slightly as @ increases. In contrast to C;, in Fig. 9(a), the reduction rate of Cp with respect to h/C Fig. 11. Efficiency of the GEV as a function of the ground clearance for different angles of attack over the ranges of (a) 0° <a@<12°, and (b) 14° <a <30°
Fig. 13. (a) Lift coefficient, (b) drag coefficient and (c) lift-to- drag ratio as function of Reynolds number
Fig. 13. (a) Lift coefficient, (b) drag coefficient and (c) lift-to- drag ratio as function of Reynolds number
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