3.1. Analysis of CFD Calculation Results
Figure 8 shows the static pressure iso-contours on the leeward side of the VG. It can be seen that the low-pressure area on the leeward side of the VG appears at the middle position of the chord, and it is not generated at the leading edge of the tip. The main reason for this phenomenon is that the kinetic energy of the bottom fluid in the boundary layer is very weak because of the viscous wall. Instead of forming leading-edge separation vortices, concentrated vortices are induced when the fluid passes over the swept leading edge of the VG from the pressure surface. However, there are still low-pressure zones on the leeward side of the VG that are caused by the concentrated vortices on that side. With the increase in the height of the VG (
H) relative to the thickness of the boundary layer (
δ), the pressure value on the leeward side of the VG is lower. The result shows that the larger the height of the VG, the greater the fluid kinetic energy in the boundary layer; thus, the concentrated vortices generated by the VG will show a stronger trend, which leads to a lower pressure in the low-pressure zone on the leeward side of the VG.
Figure 9 shows the distribution of the static pressure coefficient on the leeward surface of the VG; in the figure,
S is the local height,
l is the bottom length of the VG. Firstly, the maximum amplitude of the low-pressure coefficients occurs at about
x = 0.4
l, and the strongest vortex intensity can be found at 0.4
l. With the increase in the flow distance, the strength of the vortex core decreases gradually, and the low-pressure amplitude of the static pressure coefficient on the leeward side of the VG also presents a decreasing trend. This result shows that when the VG is placed on the wall, concentrated vortices are generated at the upper end of the VG, and the intensity of the vortices reaches the maximum value near the position 0.4
l. This is because the vortex gradually dissipates and is deflected away from the VG. Secondly, at any chord position, the magnitude of the static pressure coefficient increases with the increase in VG height, and the magnitudes of the static pressure coefficients are close to each other when
H = 1.0
δ, 1.5
δ, and 2.0
δ. When the value of
H is 0.1
δ and 0.2
δ, the gentle pressure amplitude of the static pressure coefficient is lower, and when
H = 0.5
δ, the static pressure coefficient amplitude is in the middle position.
Figure 10 shows the distribution of static pressure coefficients at the center of the vortex core. It can be seen that the static pressure coefficient at the center of the vortex core first increases and then decreases in the direction of the flow and reaches the maximum at the position of 0.5
l. The higher the
H, the lower the static pressure at the center of the vortex core.
Figure 11 shows the vortex core area and vortex circulation varying with the flow direction in the range of the VG surface. The area of the vortex core is almost the same at different VG heights, but it is slightly different at the trailing edge of the VG surface. The area of the vortex core is approximately exponentially distributed as the flow direction distance increases. With the increase in VG height, the vortex circulation increases gradually, and the difference becomes progressively larger as the flow becomes closer to the trailing edge of the VG.
Figure 12 shows the variation in the vortex core area and vortex circulation with the flow direction distance downstream of the VG. The area of the vortex core downstream of the VG varies linearly with the distance of the flow direction, which is slightly different from that on the VG surface. The higher the VG height, the larger the area of the vortex core, and the vortex core area difference downstream of the VG is more pronounced. However, the variation in the core circulation in the downstream direction along the VG approximately exponentially dissipates, which is very different from that on the VG surface. It can be seen that the maximum position of the VG vorticity appears at the trailing edge of the VG.
Figure 13 shows the variation in the vortex core area and vortex circulation as VG height increases at its trailing edge. It is shown that the vortex core area is the largest when
H/
δ = 1.0. The area of the vortex core decreases slightly when
H/
δ > 1.0 and increases rapidly when
H/
δ < 1.0. Vortex circulation is proportional to VG height: with the increase in VG height, the vortex circulation increases gradually, but it does not possess a linear relationship with VG height as it increases. When
H/
δ < 1.0, the slope of vortex circulation increases when VG height is larger, but when
H/
δ > 1.0, the slope of vortex circulation increases as VG height decreases.
Figure 14a shows the velocity profiles in the boundary layer of the inflow, and
Figure 14b shows the average velocity of the fluid in the range of VG height. From
Figure 14a, when the VG is in boundary layers with different thicknesses and velocity profiles of the inflow, the kinetic energy of the fluid in the boundary layer becomes progressively lower within the VG height range as the height of the boundary layer increases. It can also be seen from
Figure 14b that with the increase in VG height, i.e., the decrease in the thickness of the boundary layer, the average velocity of the fluid in the VG height range becomes increasingly higher. The increase in average velocity is exponentially distributed with the height of the VG. When
H/
δ < 1, the slope of average velocity in the boundary layer increases as the height of the VG presents a larger trend; after
H/
δ > 1, the slope of average velocity in the boundary layer decreases with the increase in VG height.
Figure 15 shows the variation in the lift, drag coefficient, and lift–drag ratio of the VG. With the increase in
H/
δ, the lift coefficient of the VG increases gradually. When
H/
δ = 2.0, the maximum lift coefficient of the VG is about 0.65. The drag coefficient of the VG increases with the increase in
H/
δ, and the maximum drag coefficient is 0.25 when
H/
δ = 2.0. The lift of the VG comes from the vortex-induced lift, and the drag is primarily pressure drag, that is, the profile drag of the VG. The variation in the lift coefficient and drag coefficient with the increase in
H/
δ basically shows the same trend. The dynamic energy of the fluid in VG height, vortex circulation, lift coefficient, and drag coefficient are essentially consistent with the variation in
H/
δ. The result shows that the vortex strength and drag of VG vortices are closely related to the
H/
δ value, and the greater the height of the VG, the less obvious the change effect. The lift–drag ratio of the VG reaches the maximum at
H/
δ = 0.5. It would be advisable to have a vorticity with a certain intensity to control the flow, but the profile drag is not too large. However, whether the ratio of
H/
δ is optimal should be discussed in relation to the kinetic energy of the fluid in the boundary layer.
Figure 16 shows the axial velocity contours in different flow directions downstream of the VG. The kinetic energy of the fluid in the vortex core height is ineffective when the value of
H/
δ is small. The high-energy fluid outside the vortex core is contained in the bottom layer of the boundary layer from the rotation of concentrated vortices when VG is used for flow control. From the axial velocity contours, it can be seen that with the rotation of the vortex core, the fluid kinetic energy outside the vortex core decreases, while the fluid’s streamwise kinetic energy inside the vortex core increases.
Figure 17 shows the axial velocity distribution for the normal height at the vortex core position downstream of the VG. The horizontal line is placed at the center of the vortex core. With the increase in the flow distance, the area of the vortex core varies at different VG heights. The height of the vortex core marked in the figure is the height of the vortex core when
H = 1.0
δ.
Table 5 shows the relative increase in near-wall (y/
H < 1) momentum for different VGs. Firstly, it can be observed that the center height of the vortex core increases with the increase in the flow direction distance. Secondly, the velocity profiles in the boundary layer are basically distributed in an S-line along the center of the vortex core, and the increase in fluid kinetic energy inside the vortex core corresponds to the decrease in fluid kinetic energy outside. From
Table 5, comparing the kinetic energy of the bottom fluid of the boundary layer at different
H/
δ values, it can be seen that the kinetic energy for the bottom fluid of the boundary layer is the lowest when
H = 0.1
δ and 0.2
δ, and there is little difference between them. When
H = 0.5
δ, the value is intermediate; when
H = 1.0
δ, 1.5
δ, and 2.0
δ, the values are almost the same, and the curves basically coincide. This result shows that the kinetic energy of the fluid in the boundary layer remains largely unchanged with the increase in VG height. However, the profile drag increases with the increase in VG height, as shown in
Figure 15. For flow control, it is hoped that VG can generate concentrated vortices with sufficient intensity to increase the fluid kinetic energy in the boundary layer, and this will not increase the drag of the boundary layer by much. In terms of the increasing fluid kinetic energy in the boundary layer, the value of
H = 1.0
δ is the best choice.
3.2. Analysis of Experimental Results
The results of CFD calculation show that when the VG height is about 1.0δ, the fluid kinetic energy in the near-wall basically reaches the maximum, and as the VG height continues to increase, the kinetic energy remains virtually unchanged. The experimental design was guided by CFD calculation results. The thickness of the BL of the airfoil is different at different angles of attack. To quantify the relationship between VG height and BL thickness, the airfoil was computed using Xfoil; the thickness of the BL at the VG installation position is about 5.9 mm when the maximum lift coefficient angle of attack (8°) of the airfoil is reached. Considering the machining accuracy of VGs, three VGs were designed with different heights: 4 mm, 6 mm, and 8 mm. The ratio of VG height to BL thickness is 0.66δ, 1.0δ, and 1.33δ, respectively.
Figure 18 shows the lift coefficient, drag coefficient, and lift–drag ratio of the airfoil with and without the VG airfoils.
Table 5 shows the relative variation in
Cl,
Cd, and lift–drag ratio. Before the stall angle of attack (8°), the lift coefficients for the airfoil with VGs and without VGs (clean) are similar to each other in the linear section; after the 8° angle of attack, the lift coefficient of the airfoil without VGs remains basically unchanged, while the lift coefficient of the airfoil with VGs continues to increase. The stall angle of the clean airfoil is 8°, while that of the airfoil with VGs is 18°, so there is a 10° increase in the stall angle of the airfoil. When the angle of attack reaches 23°, the separation position of the clean airfoil is located upstream of 0.2
C (VG installation position), and the VGs cannot control the flow separation, so the lift coefficient of the airfoil with VGs is no different from that of the clean airfoil. The comparison of the differences among the three VG heights shows that the maximum lift coefficient of the airfoil with VGs increases by 42.8% compared with that of the clean airfoil when
H = 0.66
δ; when
H = 1.0
δ and 1.33
δ, the maximum lift coefficient increases by 48.7% and 48.6%, respectively. From the analysis of the maximum lift coefficient, it can be found that the VG flow control effect is the best when
H = 1.0
δ.
From
Figure 18b and
Table 6, it can be seen that the drag coefficient for
H = 1.33
δ is larger before the 8° angle of attack. However, beyond the 8° angle of attack, the drag coefficient of the clean airfoil increases rapidly. For this VG height, the drag coefficient of the airfoil with VGs is much smaller than that of the clean airfoil. With respect to the difference among the three VG heights, before the angle of attack of 18°, the drag coefficient of the airfoil with
H = 1.33
δ is the largest, while the drag coefficients for the other two VG Heights do not much differ. The drag coefficient of the airfoil with
H = 0.66
δ is 84.9% lower than that of the clean airfoil; when
H = 1.0
δ, the drag coefficient of the airfoil decreases by 83.2%; when
H = 1.33
δ, the drag coefficient of the airfoil decreases by 76.8%. So, among these three heights, the drag coefficient of the airfoil with
H = 0.66
δ is reduced the most because the VG height is lower, and the profile drag of the VGs is minimum.
For the lift–drag ratio of the airfoil, the maximum lift–drag ratio of the clean airfoil is the highest, while the maximum lift–drag ratio of the airfoil with VGs is decreased. Therefore, the VGs cannot increase the maximum lift–drag ratio of the airfoil, but raising the angle of attack produces the best lift–drag ratio for the airfoil. The lift–drag ratio of the airfoil with VGs is larger than that of the clean airfoil after the angle of attack of 10°. Compared with the maximum lift–drag ratio of the airfoil with and without VGs, the maximum lift–drag ratio of the airfoil with H = 0.66δ is 19.7% lower than that of the clean airfoil; the maximum lift–drag ratio of the airfoil with H = 1.0δ and 1.33δ is decreased by 19.3% and 51.2%, respectively. However, when the angle of attack is 18° (stall angle of the airfoil with VGs), the lift–drag ratio of the airfoil with H = 0.66δ increases by 880.3% compared with that of the clean airfoil; the lift–drag ratio increases by 821.8% when H = 1.0δ; and the lift–drag ratio increases by 564.8% when H = 1.33δ. So, in summary, if considering increases in the lift coefficient and the lift–drag ratio, H = 1.0δ has a good effect on controlling airfoil flow separation. If considering the optimal lift–drag ratio, H = 0.66δ can meet the requirements.
Figure 19 shows the static pressure coefficient (
Cp) distribution on the airfoil surface at different angles of attack. The pressure taps are located on the pressure side of the two VGs, so the
Cp curve will be prominently downward near the installation locations of the VGs. The
Cp curves of the airfoil with and without VGs are similar to each other at 0° and 5° angles of attack, and there are no differences among the three VG heights. A pressure plateau appears on the
Cp curve of the clean airfoil about 88
H away from the installation position of the VGs when the angle of attack is 10°. The reverse pressure gradient of the clean airfoil is about −0.77 kpa/m; with the action of the VGs, the pressure plateau on the
Cp curve for the airfoil with VGs disappears, and the
Cp curves do not differ among the three VGs heights. With the increase in the angle of attack, the separation position of the clean airfoil is closer to the installation position of the VGs, and this configuration is beneficial to the control flow separation by the VGs when the angle of attack is 15°, 18°, and 20°. However, with the increase in the angle of attack, the reverse pressure gradient for the clean airfoil becomes progressively larger. Therefore, with the increase in the angle of attack, the VGs cannot completely inhibit the flow separation, although they can postpone it.
The separation position of the airfoil is very close to the installation positions of the VGs, and the reverse pressure gradient is further increased where a large pressure plateau appears on the Cp curve for the airfoil with VGs when the angle of attack is 22°. In this scenario (22° angle of attack), the amplitude of the Cp curve is slightly lower at H = 1.33δ, and the position of the pressure plateau appears earlier than for the other two VG heights. When the angle of attack is 25°, because the flow separation of the clean airfoil has been occurring upstream of the VGs, the Cp curve of the airfoil with VGs coincides with that of the clean airfoil.
Figure 20 shows the distribution of the total pressure coefficient of the wake rake. It can be seen that the total pressure loss of the airfoil with VGs is higher than that of the clean airfoil at 0°, 5°, and 10° angles of attack. The total pressure loss for
H = 1.33
δ is higher than that for the other two VG heights at the 5° and 10° angles of attack. The total pressure loss of the airfoil with VGs is obviously smaller than that of the clean airfoil at 15° and 18° angles of attack; in this case, there is little difference among the three VG heights. The total pressure loss of the airfoil with VGs is still less than that of the clean airfoil at 20° and 22° angles of attack, for which the total pressure loss is the smallest when
H = 0.66
δ, and there is little difference between the other two VG heights. The total pressure coefficient curves of the airfoils with VGs coincide with that of the clean airfoil when the angle of attack is 25°.