3.2. Effect of the Injection Location
The injection slot size, suction slot size and suction surface translation are fixed to 0.65% chord, 1.33% chord and 1.43% chord, respectively. The suction location is fixed to the 80% chord-wise location from the leading edge and the
Cμ is fixed to 0.04. The injection location varies from a 1% chord-wise location to a 20% chord-wise location from the leading edge. Effects of six injection locations with the 1%, 5%, 9%, 13%, 17%, and 20% chord-wise locations, as illustrated in
Figure 4, on the performance of S809 CFJ airfoil are investigated.
Figure 5 presents aerodynamic coefficients comparisons of S809 CFJ airfoils with various injection locations. When the AoA is below 8.2°, the lift and drag coefficients of S809 CFJ airfoils with various injection locations are almost the same. As the injection slot is moved downstream, the power consumption coefficient decreased when the AoA is below 2.02° and increased when the AoA is between 2.02° and 8.2°. Thus, when the AoA is below 8.2°, the corrected lift-to-drag ratio of S809 CFJ airfoil increased as the injection slot is moved upstream. But at the large AoA, the more downstream the injection location, the better the lift characteristic of S809 CFJ airfoil, resulting in the better corrected lift-to-drag ratio of S809 CFJ airfoil. The lift curves of S809 CFJ airfoils with the 17% and 20% chord-wise injection locations almost coincide expect that the AoA is above 16.24°. The curvature of the suction surface of the S809 airfoil at the 1% chord-wise location is larger than those at other chord-wise locations. The adverse pressure gradient region of the suction surface is near 1% chord-wise location at high angle of attack. When the injection slot of S809 CFJ airfoil is located at 1% chord-wise location, more energies are needed to overcome the adverse pressure gradient. Meanwhile, the existence of the injection destroys the smoothness of the suction surface of the S809 airfoil, which will cause the separation point to move upstream and the separation region to become larger when stall occurs. The more upstream the injection, the greater the fluence on the smoothness of the suction surface. Therefore, when the S809 CFJ airfoil with the 1% chord-wise injection location stalls at the AoA of 8.2°, the jet momentum coefficient of 0.04 is not enough to overcome the large adverse pressure gradient and the drag is suddenly increased.
Table 3 presents the maximum lift coefficients and maximum lift-to-drag ratios of S809 CFJ airfoils with various injection locations. As the injection slot is moved downstream, the maximum lift coefficient is increased. The range of corrected lift-to-drag ratio increment of S809 CFJ airfoil with various injection locations is between 29.3% and 36.2% when compared with the baseline. When the injection slot is at the 1% chord-wise location, the maximum lift coefficient and maximum lift-to-drag ratio of S809 CFJ airfoil are 2.6% lower and 34.3% higher than that of the baseline, respectively. The S809 CFJ airfoil with the 9% chord-wise injection location has the optimum maximum corrected lift-to-drag ratio, which is 36.2% higher than that of the baseline. The S809 CFJ airfoil with the 20% chord-wise injection location has the optimum maximum lift coefficient, which is 76.5% higher than that of the baseline.
Figure 6 and
Figure 7 show the Mach number contours and streamlines of S809 CFJ airfoils with various injection locations when the AoAs are 8.2° and 16.24°, respectively. It can be seen that at 8.2° AoA, the flows of S809 CFJ airfoils with various injection locations are attached. The high local Mach number region of S809 CFJ airfoil is near the leading edge. Thus, the closer the injection location is to the leading edge, the easier it is for the mass flow to be injected into the main flow and the less the energy is consumed. This is why the S809 CFJ airfoil with the injection location near the leading edge has low power consumption coefficient and high corrected lift-to-drag ratio at the small AoA. At 16.24° AoA, the large flow separations appear on the suction surfaces of S809 CFJ airfoils with the 1%, 5%, and 9% chord-wise injection locations, but the flows of S809 CFJ airfoils with the 13%, 17%, and 20% chord-wise injection locations are attached. The separation region is large and the separation point is near the leading edge at 16.24° AoA. When the injection location is close to the leading edge, the injection location is too close to the adverse pressure gradient region and the jet energy of S809 CFJ airfoil with 0.04
Cμ is not enough to suppress the flow separation, and most of the jet energy is converted into heat. When the injection slot is moved downstream, the injection location is near the vortex core and it is easier to inject the jet energy into the main flow to suppress the large flow separation.
In order to more intuitively characterize the performance enhancement of the CFJ technology on the S809 airfoil, the surface pressure coefficient distributions comparisons and velocity profiles comparisons of the baseline and S809 CFJ airfoil are implemented, as shown in
Figure 8 and
Figure 9. It is obvious to find that CFJ technology can greatly increase the peak of negative pressure at the leading edge of the S809 airfoil, and the negative pressure region is expanded especially when the AoA is 16.24°. Therefore, the lift coefficient of the S809 airfoil can be significantly enhanced by the CFJ technology. In
Figure 9, the variable of x-axis is the dimensionless velocity near the suction surface of the airfoils, and the variable of y-axis is the distance from the suction surface given in the percent chord length. The velocity profiles of the baseline and S809 CFJ airfoil at the 50% and 70% chord-wise locations when the AoAs are 8.2° and 16.24 are taken perpendicular to suction surface of the airfoil. It can be seen that when AoA is 8.2°, no separation occurs in the boundary layers of the baseline and S809 CFJ airfoil, but the velocity profiles of S809 CFJ airfoil are fuller than those of the baseline. When AoA is 16.24°, large separations occur in the boundary layer of the baseline, while the flow in the boundary layer of the S809 CFJ airfoil is still attached because the jet energy is injected into the main flow.
The unsteady simulations for the baseline and S809 CFJ airfoil with 13% chord-wise injection location are implemented to explore the effects of CFJ technology on the vortex structures when AoA is 20.15°. The time histories of lift coefficient and drag coefficient of the baseline and S809 CFJ airfoil are given in
Figure 10 and
Figure 11, respectively. It can be found that the amplitudes of lift coefficient and drag coefficient of S809 CFJ airfoil are significantly smaller than those of the baseline. The lift coefficient amplitude of S809 CFJ airfoil is only 0.004 while that of the baseline is 0.0225. The drag coefficient amplitude of S809 CFJ airfoil is only 0.0016 while that of the baseline is 0.0076. Moreover, the vortex shedding frequency of S809 airfoil, which is 139 Hz, is larger than that of the baseline, which is 73 Hz.
Figure 12 shows the instantaneous Mach number contours and streamlines of the baseline and S809 CFJ airfoil within one time cycle. The separation region of S809 CFJ airfoil is obviously smaller than that of the baseline. Meanwhile, the secondary vortex of S809 CFJ airfoil near the trailing edge, induced by the primary vortex, is also smaller than that of the baseline.
3.3. Effect of the Jet Momentum Coefficient
The injection slot size, suction slot size, and suction surface translation are also fixed to 0.65% chord, 1.33% chord, and 1.43% chord, respectively. The suction location is also fixed to the 80% chord-wise location from the leading edge. The effects of five jet momentum coefficients, which are 0.02, 0.04, 0.06, 0.08, and 0.10 respectively, are studied. Two different injection locations, which are 9% chord-wise location and 1% chord-wise location from the leading edge, are selected because that the S809 CFJ airfoils with the two injection locations achieve the largest and second largest corrected lift-to-drag ratios when the Cμ is 0.04.
When the injection location is at 1% chord-wise location from the leading edge, the aerodynamic coefficients comparisons of S809 CFJ airfoils with various jet momentum coefficients are presented in
Figure 13. As shown in
Figure 13a,b, the lift and drag characteristics of S809 CFJ airfoil are enhanced with the increased
Cμ. When the
Cμ is 0.02, the lift coefficient of S809 CFJ airfoil is higher than that of the baseline only at the low AoA, and the S809 CFJ airfoil has the worse lift and drag characteristics at the high AoA. When the
Cμ is 0.04 and the AoA is below 8.2°, the lift coefficient of S809 CFJ airfoil is higher than that of the baseline. But when the AoA is higher than 8.2°, the lift coefficient of S809 CFJ airfoil remains almost the same as that of the baseline and the drag coefficient is worse than that of the baseline. While the
Cμ is greater than 0.06, the S809 CFJ airfoil has the higher lift coefficient than the baseline almost at each AoA. The maximum lift coefficients are improved by 9.0%, 44.7%, and 67.4% respectively when the
Cμ is 0.06, 0.08, and 0.10. As shown in
Figure 13c, the power consumption coefficient is first decreased and then increased with the increased AoA for each
Cμ. Moreover, as the
Cμ increases, the power consumption coefficient increases at the same small AoA, and the relative increment in the power consumption of S809 CFJ airfoil is larger than the relative increment in the lift coefficient. For example, at 2.05°AoA, the power consumption coefficient of S809 CFJ airfoil with 0.08
Cμ is 2.7 times higher than that with 0.04
Cμ, while the lift coefficient with 0.08
Cμ is only 13.2% higher than that with 0.04
Cμ. Thus, as shown in
Figure 13d, the greater the
Cμ, the lower the corrected lift-to-drag ratio at the low AoA. However, at the high AoA, the S809 CFJ airfoil with small
Cμ also has a large power consumption coefficient, but most of the energy is converted into heat and is dissipated, while the S809 CFJ airfoil with high
Cμ can effectively overcome the flow separation and has the higher lift coefficient. Thus, the greater the
Cμ, the greater the corrected lift-to-drag ratio at the high AoA. Because of the above reasons, the AoA at the maximum corrected lift-to-drag ratio increases with the increased
Cμ. The maximum corrected lift-to-drag ratios are improved by 10.4%, 34.3%, 33.4%, 22.5%, and 8.7% respectively when the
Cμ is 0.02, 0.04, 0.06, 0.08, and 0.10. When the
Cμ is 0.04 and 0.06, the S809 CFJ airfoil has the maximum corrected lift-to-drag ratios.
Although the S809 CFJ airfoil with a given
Cμ has the higher maximum corrected lift-to-drag ratio than the baseline, the S809 CFJ airfoil with small
Cμ has the lower corrected lift-to-drag ratio than the baseline at the high AoA and the S809 CFJ airfoil with high
Cμ has the lower corrected lift-to-drag ratio than the baseline at the low AoA. Thus, to ensure that the S809 CFJ airfoil has the higher corrected lift-to-drag ratio and lift coefficient than the baseline at all AoAs, a S809 CFJ strategy with the adaptive
Cμ is proposed. The small
Cμ is used at the low AoA, and the
Cμ gradually increases as the AoA rises. Therefore, based on the performance of S809 CFJ airfoil at different
Cμ, the
Cμs of S809 CFJ airfoil with the 1% chord-wise injection location at various AoAs are tabulated in
Table 4.
Figure 14 shows the lift coefficients and lift-to-drag ratios of S809 CFJ airfoil with different
Cμ at various AoAs. As shown in
Figure 14, the lift coefficient and the corrected lift-to-drag ratio of S809 CFJ airfoil with the adaptive
Cμ strategy are comprehensively improved when compared with the baseline, and the maximum lift coefficient and maximum lift-to-drag ratio are improved by 67.4% and 34.3%, respectively.
In order to further verify the above conclusions and CFJ strategy, the effect of
Cμ on the performance of S809 CFJ airfoil is studied when the injection location is at 9% chord-wise location from the leading edge.
Figure 15 shows aerodynamic coefficients comparisons of S809 CFJ airfoils with various jet momentum coefficients. Similarly, the lift and drag characteristics of S809 CFJ airfoil with the 9% chord-wise injection location are enhanced with the increased
Cμ. As the
Cμ increases, the power consumption coefficient increases at the same small AoA. Moreover, the greater the
Cμ, the lower the corrected lift-to-drag ratio at the low AoA and the larger the corrected lift-to-drag ratio at the high AoA. At the same time, there are some differences in the aerodynamic characteristics of S809 CFJ airfoil with the 9% chord-wise injection location and with the 1% chord-wise injection location. When the
Cμ is greater than 0.04, the S809 CFJ airfoil with the 9% chord-wise injection location has the higher lift coefficient than the S809 CFJ airfoil with the 1% chord-wise injection location. The maximum lift coefficient increment of S809 CFJ airfoil with the 9% chord-wise injection location using a given
Cμ is greater than that with the 1% chord-wise injection location. The maximum lift coefficients of S809 CFJ airfoil with the 9% chord-wise injection location are improved by 84.8%, 106.6%, and 119.7% respectively when compared with that of the baseline when the
Cμ is 0.06, 0.08, and 0.10. As the AoA increases, the power consumption coefficient of S809 CFJ airfoil with the 9% chord-wise injection location decreases lower than that with the 1% chord-wise injection location. Therefore, at the high AoA and high
Cμ, the S809 CFJ airfoil with the 9% chord-wise injection location consumes more energy, which shows that the maximum corrected lift-to-drag ratios of S809 CFJ airfoils with the 0.08 and 0.10
Cμ are 0.4% and 20.6% lower than that of the baseline. Thus, it is necessary to explore the effect of the injection location.
Figure 15d shows that the same CFJ strategy with the adaptive
Cμ can be used for the S809 CFJ airfoil with the 9% chord-wise injection location in order to achieve the higher corrected lift-to-drag ratio and lift coefficient. Based on the performance of S809 CFJ airfoil with the 9% chord-wise injection location, the
Cμs at various AoAs are tabulated in
Table 5.
Figure 16 presents the lift coefficients and lift-to-drag ratios of S809 CFJ airfoils with different
Cμs at various AoAs. As shown in
Figure 16, the lift coefficient and the corrected lift-to-drag ratio of S809 CFJ airfoil with the 9% chord-wise injection location using the adaptive
Cμ strategy are also comprehensively improved when compared with the baseline, and the maximum lift coefficient and maximum lift-to-drag ratio are improved by 119.7% and 36.2%, respectively.