Numerical Simulation and Flow Display of Bionic Alula on Rectangle Airfoils

Some birds have small wings (Alula) in the middle of their main wings. These small wings will tilt upward when the bird flies at a high attack angle to maintain a stable flying posture. This paper explores the lift effects of bionic Alula on rectangular airfoils with different aspect ratios through numerical simulation and flow display experiments. According to the numerical simulation, Alula can increase the rectangular airfoil lift coefficient by a maximum of 24% when the airfoil aspect ratio is 2. By comparing simulation results with flow display results, the low-pressure area generated by Alula and the merge of the Alula vortices with the airfoil tip vortices mainly contribute to the lift enhancement.


Introduction
Birds are important research objects in the development of the aviation field.Inspirations from birds have been widely applied in such fields as increasing lift, reducing drag, boundary layer control, and flow control [1].For example, by observing the wings of birds, human beings find that their appearance usually presents a certain curvature and all sections are streamlined, then design the airfoil.According to the flight stability of birds controlled by their tails, the flat tail of fixed-wing aircraft is designed.The shape of birds in flight inspired the large, slender fuselage of airplanes.The upturned feathers of birds' wing tips are the source of the winglet.The behavior of birds' folding their legs in flight is the inspiration for the landing gear [2,3].
Alula is a small structure observed between some kinds of bird's hand wing and arm wing.It is composed of a finger bone and 2 to 6 feathers.It is usually used when birds fly at low speed and high angle of attack, such as landing, and is a very important aerodynamic structure for those birds to improve their flight stability.Usually, when birds take off and land, due to the low flight speed, they increase the angle of attack to obtain higher lift force to balance the gravity.However, with the increase of the angle, the wings and body of birds, are followed by the risk of stalling, which poses a great threat to the safety of birds, and Alula usually works under such circumstances.
In recent years, studies on Alula have gradually formed three cognitions on the mechanism of Alula: A) Mesegure [4] believes that Alula is similar to aircraft slats in both effect and shape.Through experiments, Austin [5] verifies that the wings of birds with Alula have a large high-speed flow area.

Numerical Simulation Method
Digital models were designed to study the practical effect of Alula on the lift of rectangular airfoils.The chord length of the rectangular airfoil is 73.6mm.According to the aspect ratio (AR) range, which is 1 to 6, the corresponding span length is 73.6mm, 147.2mm, 220.8mm, 294.4mm, 368mm, and 441.6mm respectively.The Alula chord length is 8.8mm and the aspect ratio is 3.The airfoils and Alula are treated with four-sided arc chamfering.The thickness of the airfoils is 3mm and the thickness of the Alula is 2mm.The angle between the Alula and the airfoil is 25 degrees, which is a proper angle based on previous research.The above parameters are determined after considering the actual UAV's size and experimental facilities.
ICEM was used for generating the structured mesh, and ANSYS Fluent was used for calculation.The distance between the models and the far field is shown in Figure 3. Considering the complexity of the flow field near the Alula, node encryption was carried out for the grid near the Alula.

Experimental System
The experiments in this paper were carried out in the water tunnel of Lu Shijia Laboratory (Key Laboratory of Aeroacoustics, Ministry of Industry and Information Technology) at Beihang University.3D printing models were used to carry out the flow display experiments.Through 3D printing technology, dye pipes with a diameter of 1.2mm were arranged in rectangular airfoils with a thickness of 3mm.The dye outlets were arranged on the leading edge and tip of the airfoil.At y = ±30mm and y = ±15mm of the airfoil leading edge, four leading-edge dye outlets were arranged sympathetically, and at x = 4.5mm of both sides of the airfoil wingtip, two wingtip dye outlets were arranged.

Result and analysis
Lift coefficients of models with and without Alula at different aspect ratios were calculated, as shown in Figure 6.With the increase of aspect ratio, the effect of Alula on lift experienced a process of first increase and then decrease.When the aspect ratio is 1, Alula has almost no effect on the lift of the airfoil.At a high Angle of attack, Alula even has a negative effect on the lift.When the aspect ratio is 2, Alula has a significant lift improvement effect on the airfoil.The lift coefficient increased by 24%.When the aspect ratio increases to 3, the lifting effect is still relatively obvious (15%), but when compared to the AR2 model, the lifting enhancement has slightly decreased.When the aspect ratio is 4, the lift effect of Alula decreases further, and the lift coefficient lines of the models with and without Alula begin to converge.With the aspect ratio increasing to 5 and 6, the effect of Alula on the lift coefficient of the model becomes indistinguishable.

Figure 6. Lift coefficient of different models
Considering that, when calculating the lift coefficient of different aspect ratio models, the increased reference area S will weaken the area-unchanged Alula's contribution to lift force.Therefore, it is of certain significance to study the contribution of Alula to lift force.Figure 7 shows the lift force difference of the models with and without Alula, reflecting the absolute amount of lift contributed by Alula to the airfoil with different aspect ratios.From the perspective of lifting force, with the increase of aspect ratio, the contribution of Alula also becomes larger and then smaller.It is worth mentioning that when the aspect ratio increases from 1 to 2, the lift contribution of Alula is prominent, when the aspect ratio increases from 4 to 5, the lift contribution significantly decreases.However, when the aspect ratio is 2, 3, and 4, the maximum lift increment is achieved at different angles of attack, but the absolute value of the increment is almost the same.

Figure 7. Lift force difference between models with and without Alula
The reason for this result can be interpreted from the perspective of the development of the vortices system.As shown in Figure 8, when the aspect ratio is 2, the vortices system of the wing suction surface can generate obvious flow vorticity under the influence of Alula.This flow vorticity moves towards the wing tip area under the combined action of initial velocity and induced velocity, and then winds and merges with the wing tip vorticity.In the cases of the aspect ratio of 1 and 6 where the lift effect of Alula is not obvious, the generation and development process of the Alula vortices is missing.
By calculating surface pressure coefficients for different flow sections of the suction surface, as demonstrated in Figure 9, it can be found that the surface pressure drops significantly, and lift increases within the range of the Alula vortices.Meanwhile, it can be observed at the tip of the airfoil that the wingtip vortices move towards the wing root because of the merge of Alula vortices and wingtip vortices.The merged vortices create low-pressure areas near the wing tips which were significantly different from the surface pressure of the model without Alula, which is beneficial to the lift.Although under the control of Alula, there will be some area on the suction surface with higher pressure, the general effect of Alula to lift is positive.

Conclusion
Through numerical simulation and experiment study of Alula, the lift characteristic effects Alula can make on different aspect ratio rectangular airfoils are as follows: (1) Based on the numerical simulation, Alula located at the wing root can make contributions to the airfoil's lift when the airfoil aspect ratio is between 2 to 5. When the airfoil aspect ratio is 1 and 6, Alula has little effect on the lift coefficient.From the perspective of lift coefficient, the rectangular airfoil with an aspect ratio of 2 benefits most from the Alula.Under Alula's effect, the lift coefficient can increase by max 24%.From the perspective of lift force, rectangular airfoils with an aspect ratio of 2 to 4 benefit from Alula equally.