Numerical Investigation of Aerodynamic Characteristics of Supercritical RAE2822 Airfoil with Gurney Flap

G urney flap (GF) is well-known as one of the most attractive plain flaps because of the simple configuration and effectiveness in improving the lift of the airfoil. Many studies were conducted, but the effects of GF on the various airfoil types need to be further investigated. This study aimed to clarify the effect of GF in the case of the supercritical airfoil RAE2822. This research includes a steady, two-dimensional computational investigation carried out on the supercritical airfoil type RAE-2822 to analyze Gurney flap (GF) effects on the aerodynamic characteristics of this type of airfoil utilizing the Spalart-Allmaras turbulence model within the commercial software Fluent. The airfoil with the Gurney flap was analyzed for three different height values 1%c, 2%c, and 3%c, and five mounting angles (30°,45°,60°,75°, and 90°) with the axial chord for angles of attack (-1°,-2°,-3°,0°,1°,2°,3°). The calculations showed that when GF height is increased, the maximum suction pressure on the upper surface increases by 25.4%, 36.5%, and 68.83% when the height of the Gurney flap is 1%c, 2%c, and 3%c, respectively, compared with that on the airfoil without GF. The lift coefficient was also increased, and the shock waves moved downward by increasing GF height. As Gurney flap heights increase, the drag coefficient increases gradually for positive angles of attack but for negative angles of attack. The drag coefficient also decreases with increasing the GF heights. As long as the angle of the mounting is between 45 o and 90 o , the lift coefficient does not differ on a large scale. For mounting angles less than 45 o , the lift coefficient drops quite fast. As a result, reducing the Gurney flap’s lift enhancement and the drag coefficient increases gradually for positive angles of attack, but for negative angles, it can be noted that the drag coefficient decreases with increasing the mounting angles of GF. The calculated values of the lift and drag coefficients with an attack angle and pressure coefficient compared with the experimental values, and a good agreement was noticed.


INTRODUCTION
Utilizing high-lift devices to enhance the aerodynamic performance of the airfoils has been an active research area in applied aerodynamics. Flap, a type of high-lift device, is generally used to enhance the aerodynamic performance of the wing sections during flight. Among flap types, as shown in Fig. 1, GF is a micro tab that is affixed to the airfoil near the trailing edge on the pressure side. D. Gurney used it on the top trailing edge of the rear wing of the race vehicle he owned to provide additional rearend downforce with minimum aerodynamics disturbances (Jang, C. S. et al.,1998). Due to the sharp corner flap, two counter-rotating vortices are formed. The total circulation around the airfoil gets increased, which adds to the lift. For supercritical airfoils, the lift enhancement of the Gurney flap mainly comes from its ability to shift the shock on the upper surface downstream, further delaying the onset of stall. In the present work, a steady, two-dimensional computational investigation is carried out on the supercritical airfoil type RAE 2822 for the analysis of Gurney flap (GF) effects on the aerodynamic characteristics of this type of airfoil utilizing the Spalart-Allmaras turbulence model within the commercial software Ansys-Fluent 14.5. Additionally, the lift estimation, wake measurements, and numerical simulations are performed to clarify the low-speed aerodynamic characteristics of the SC airfoil with GF. They observed that when the height of the flap was increased, the lift and drag coefficients increased. Installing a GF with a height equal to 1% of the airfoil chord length significantly improved the low-speed aerodynamic performance.

GOVERNING EQUATIONS
The governing equations for computations of a two-dimensional steady turbulent compressible flow, in the absence of gravitational body force, external body force, and any volumetric heat sources, are (Dhruva Koti and Ayesha Khan M., 2018). The continuity equation: And the energy equation:

GEOMETRY & GRID GENERATION
The Ansys-Fluent 14.5 finite element program was used for analyzing the flow around the supercritical RAE2822 airfoil with GF. The airfoil with a chord length of 1m and the GF with a height of 3%c and itʼs mounting angle (Φ = 90 ∘ ). To create the geometry of an airfoil, the coordinates were taken from (http://airfoiltools.com/airfoil/naca4digit). A C-mesh domain was chosen for the flow analysis and generated a structured mesh called 'mapped face mesh'. The dimension of the arc radius is set at 10c, whereas the sides of the other two squares are set at 25c. The airfoil was discretized into 407600 elements with 409377 nodes. The computational domain is shown in Fig. 2, and the details of the mesh are shown in Table 1.

VALIDATION STUDY
In order to validate the computational results, pressure coefficient, lift and drag coefficients are compared with the results of experimental work, case 9 of (AGARD report, 1979), as shown in are set to be 0.729 and 2.79º, respectively, and Re = 6.5×10 6 . Good agreement is obtained between the experimental and the present computed results.

RESULTS AND DISCUSSION
The simulations were carried out for the far filed Mach number of 0.75, and the angle of attack varies between -3° to 3° with a 1-degree increment.

Pressure coefficient distribution
Pressure coefficient distribution at an AOA = 0 ∘ for various Gurney flap (GF) height levels has been illustrated in Fig.4. When GF height is 1%c, 2%c, and 3%c, the maximum suction pressure on the airfoil suction surface increased by 25.4%, 36.5%, and 68.83%, respectively, on airfoil without GF. Actually, the GF is a chord alteration: increased camber. In effect, it alters the airfoil Kutta condition. Also, it can be seen that the shock moves downstream with increasing the GF height. The shock delay resulting from the GF may be explained by the increased camber and combined with the rotating vortex at the trailing edge. Vorticities are clearly seen behind the flap Journal of Engineering Volume 28 June 2022 Number 6 6 on the trailing edge, as shown in Fig.5. It has been believed that a rotating vortex provides "pulling" force to the suction surface, which forces the flow to attach along the surface. Also, flow velocity increases as well by that force. For better illustration in this case, where the Mach number at far-field is 0.75, the Mach number contours are provided in Fig.6. Table 3 shows the effect of GF height on the location of the shock wave.

Lift coefficient
Lift coefficient variation with the AOA for GF height values of 0% (without GF), 1%c, 2%c, and 3%c is depicted in Fig.7. Generally, lift coefficient increases with increasing the GF height. The increase in lift coefficient because of changing the GF height from 0%c to 1%c is greater than the lift coefficient due to changing the height of the GF from 2%c to 3%c. According to the analyses, the angle of zero lift decreases while the height of the GF increases.
As shown in Fig.5, the GF causes the flow to turn downward beyond the flap, indicating the fact that the GF is generating the increase of the lift. This agrees with (Liebeck, R. H.1978) wind tunnel test.  Fig.8. depicts the variation of drag coefficient with angles of attack at different GF heights. With the increase in the GF height values, the drag coefficient is gradually increased, the maximum drag coefficient at maximum GF heights of 3% c for positive angles of attack, but for negative angles of attack, it can be noted that the drag coefficient decreases with increasing the GF height.

Pressure coefficient distribution
The computed pressure coefficient distribution on the airfoil surface with a GFʼs height of 3%c and AOA = 0° is shown in Fig.9. GF Mounting angle only affects the static pressure distribution near the trailing edge. Suction pressure decreases with decreasing the mounting angle, and the location of maximum suction pressure moves downstream with increasing the mounting angle. Flow near the trailing edge of the airfoil with GFʼs height of 3%c and different GFʼs mounting angles at an AOA of 0∘ is shown in Fig.10. The vortex near the suction surface does not form entirely when the GFʼs mounting angle drops, resulting in less suction and a decrease in lift.

Lift coefficient
values for GF mounting angles of Φ = 30 ∘ , 45 ∘ , 60 ∘ ,75°, 90 ∘ at AOA=0° have been depicted in Fig.11. In comparison to the airfoil without GF, the GF installation results in increasing by 60. 88%, 66.86%, 70.48%, 67.9%, and 72.35% in the case where the GF has been mounted at Φ = 30 ∘ , 45 ∘ , 60 ∘ , 75 ∘ , and 90 ∘ , respectively. When the mounting angle ranges from 45 ∘ and 90 ∘ , the lift coefficient does not vary on a large scale. For the values of Φ < 45 ∘ , drops quite fast, thus, increasing in lift enhancement of GF, as shown in table 4.  Fig.12, it can be seen that, with the increase of GF°s mounting angles, the drag coefficient increases gradually for positive angles of attack but for negative angles, the CD decreases with increasing the mounting angles of GF.

CONCLUSIONS
1. Lift enhancement is accomplished for higher GFʼs height values, however, at the expense of the increase in drag value. The lift increment rate decreases for larger heights, and the drag increases rapidly for >2%c. Increasing lift coefficient as a result of altering the height of GF from 0%c to 1%c is more when compared to the change that has been found from the alteration of the height of GF from 2%c to 3%c. 2. When the value of GFʼs height increases, the maximum suction pressure on the suction surface increases by 25.4%, 36.5%, and 68.83% when the GF height is 1%c, 2%c and 3%c, respectively compared with that on the airfoil without GF. 3. The angle for zero lift decreases while the length of the gurney flap increases.
4. The shock delay results from the GF and moves downstream with increasing GFʼs height. 5. As the height of GF increases, the drag coefficient increases gradually for positive AOA but for negative AOA, the CD decreases with increasing the height of GF. 6. The maximum value of suction moves downstream by increasing GF's mounting angle. 7. With the decrease in GFʼs mounting angle, the vortex near the suction surface of the airfoil isn't entirely formed. For Φ < 45 ∘ , the vortex almost disappears, leading to a decrease in the suction pressure, thereby a drastic reduction in the lift coefficient. 8. When the mounting angle ranges from 45 ∘ and 90 ∘ , the lift coefficient does not vary on a large scale. For the values of Φ < 45 ∘ , the value of reduced quite rapidly.