Investigation of lift enhancement through circulation control for distributed propulsion

To meet the design requirements for high lift airfoils, an optimization design platform was established using the SNOPT (Sparse Nonlinear Optimizer) method. Two airfoils were designed to achieve both low-speed takeoff/landing and high-speed cruise performance. A comparison between the self-designed airfoils and mature airfoils was carried out at different operating conditions, and the airfoil that met the target requirements was selected. Subsequently, an integrated design of ducted-fan/wing was conducted to study the effect of integrated constraints on the lift augmentation of the wing with the action of the propeller. The results showed that under the integrated layout, the ducted-fan significantly changed the flow velocity field from the front of the inlet and the tail jet, which to some extent changed the upper surface circulation of the wing. Compared with the pure wing, the maximum lift increase was up to 332 %.


Introduction
Circulation control technology, as an effective active flow control technology, has great potential facts in improving the aerodynamic performance and attitude control of aircraft.Compared to traditional highlift devices, circulation control technology has advantages of simple operation, light weight, and fewer moving parts, and has considerable advantages in environmental protection and economy.In the past nearly 30 years, extensive research has been conducted in the field of aviation on circulation control technology.
Studies on circulation control technology have been conducted relatively early, and a large number of research results have been formed.Jones and Englar [1] have studied and concluded that circulation control not only yields more efficient lift, but also generates effective control forces and moments.Jones [2] provided a summary of the application of numerical simulation and fluid mechanics calculations in circulation control.Englar [3] studied and implemented wing circulation control technology for highspeed civil aircraft, and conducted A-6/CCWSTOL demonstrator flight tests in 1979.Burnazzi [4] and Golden [5] mainly studied the circulation control flap structure and analyzed its aerodynamic characteristics.In addition, Boeing's YC-14 and YC-17 Globemaster III, Antonov An-72' Coaler', and McDonnell Douglas' YC-15 are typical examples of circulation control augmentation technology.NASA [6] has proposed six future new concept aircrafts in the 'Vehicle System' project that involve circulation control technology, including ultra-short take-off and landing, personal aviation, and supersonic aircraft projects that use circulation control wings.The remaining three projects have also considered using circulation control wings to achieve goals such as noise reduction and replacing rotors.
Zhang Panfeng [7] used a compact, low-power and high-reliability synthetic jet exciter to numerically simulate an airfoil at a specific angle of attack.Their research revealed that synthetic jets enhance airfoil circulation through affecting the position of the airfoil's trailing vortex and upper surface separation point, indicating that synthetic jets have higher efficiency than previous circulation control devices.In addition, the research on the dual-jet circulation control airfoils by He Yujuan and his collaborators [8], on stable-jet circulation control techniques by Zheng Wuji [9], and on pulsed-jet circulation control techniques by Lei Yuchang and his collaborators [10] have analyzed the circulation control law and aerodynamic characteristics under their respective conditions, and achieved relatively satisfactory results.Zhu Ziqiang [11] summarized the research progress of the circulation control technology and discussed how it could effectively postpone the location of the shock wave according to the results of wind tunnel experiments, thus increasing the stalling angle of attack.They also emphasized the importance of computational fluid dynamics (CFD) technology in the application of circulation control technology to aircraft design.Liu Xiaodong [12] summarized the inverse relationship between the effectiveness of circulating airflow control under wing configurations and nozzle height through adjustments of wing trailing edge shape and nozzle placement studies.The optimal ratio range of ejector pressure is between 1. 5 and 2. 0, with Ma = 0. 2 resulting in a higher control torque than mechanical rudder surfaces.The effect of different shapes on the effectiveness of circulating airflow control also varies significantly.
In this study, an optimal design platform using SNOPT methods was built to select a target airfoil and integrate it with a propeller.Under this integrated layout condition, a propeller was installed on the surface of the wing and used fan suction to change the flow rate and pressure distribution above the wing to achieve circulation control.By solving the Navier-Stokes equation and comparing the control situation of integrated configuration with the pure wing under the condition of fan pressure ratio of 1.15 and Ma=0.12/0.55.Two aspects of the thruster integration to achieve the control of the circulation are discussed, and the control law and aerodynamic characteristics of the integrated configuration are summarized.

Airfoil optimization design
To meet the design requirements of high lift airfoils, an optimization design platform is established based on the process framework shown in Figure 1.The SNOPT (Sparse Nonlinear Optimizer) method is used for optimization, where the optimization method uses SQP (sequential quadratic programming) sequential quadratic programming and quasi-Newton methods.The initial variable design is based on the SNOPT method, and the FFD (Free-Form Deformation) method is used to control the displacement of the points and control the geometric shape and surface mesh of the object surface.For the problem of surface mesh deformation caused by FFD geometric deformation, IDW (inverse distance weight interpolation) method is used to perform volumetric mesh deformation to ensure orthogonality of the viscous layer mesh.Perform CFD calculations based on the volumetric mesh generated in the previous steps, and return the calculated aerodynamic parameters and objective function values of the airfoil to the SNOPT optimization module.At the same time, the discrete companion module built-in the flow solver is used to obtain the grid sensitivity of flow field variables, which is then transferred to the dynamic grid companion solver module, thereby obtaining the sensitivity of the dynamic grid to the surface grid.Finally, the gradient of the objective function is obtained through the parameterized sensitivity module, which is then transferred to the SNOPT optimization module.The SNOPT optimization module determines whether an optimal result that meets the design goals is obtained by comparing the objective function value, the objective function gradient value, and multi-variable constraints.
Based on the SNOPT optimized airfoils shown in Figure 1, Two independently designed airfoils, namely DG-1 and DG-2, are compared with two mature foils USA-35B and MS-0317.Using Pointwise to perform structured grid and three-dimensional stretching of a two-dimensional airfoil in Figure 2, ignoring the spanwise flow characteristics of the airfoil, to simulate quasi-3D conditions.Figure 3 shows the schematic diagram of structured grid division for the airfoils, with a total grid size of approximately 400000.

An analysis of airfoil flow characteristics
2.1.1.Low-speed condition.Figure 4 shows the Mach number contour and streamline distribution of the airfoil at AOA = 0°, Ma=0.12.It can be seen that there is a significant high-speed region on the lower surface of the DG-1 airfoil, which leads to a decrease in lift.This is due to the concave shape of the leading edge of the DG-1, which creates an initial negative angle of attack.The flow field of the USA and DG-2 airfoils is better.Figure 5 shows the flow field and streamline distribution of the airfoil at different angles of attack.At high angles of attack, the airflow is subject to viscous effects on the airfoil surface, and a recirculation vortex forms near the wall due to boundary layer effects.As the angle of attack increases, this vortex may detach from the airfoil surface.The separation vortex at high angles of attack seriously affects the aerodynamic distribution of the aircraft, resulting in increased drag and reduced lift.From the flow field distribution of different airfoils at high angles of attack in Figure 6, the separation vortices of DG-1 and DG-2 are small, but the high-speed regions on the upper surface of DG-1 are less distributed.Therefore, considering the flow field distribution of the airfoil at low and high angles of attack with Ma=0.12, the DG-2 airfoil is relatively better.2.1.2.High-speed condition.Figure 7 shows the Mach number contour and streamline distribution of the airfoil at Ma=0.55 with AOA=0°.For DG-1 airfoil, a low-speed region appears near the leading edge of the lower surface, similar to the low-speed state.The rear section of the lower surface presents a high-Mach low-pressure distribution, which is unfavorable for lift generation.Although MS-0317 also shows a significant high-speed region on the lower surface, the upper surface velocity is higher, and the pressure difference between the upper and lower airfoil surfaces is greater, resulting in greater lift at low angles of attack.According to the analysis of the maximum lift-drag ratio curve of each airfoil, the cruise angle of the four airfoils in high-speed state is about 4°.Compared with the flow field distribution of the other three airfoils, the DG-1 airfoil has differences in velocity flow field distribution, mainly due to the acceleration of the airflow caused by the protrusion of the lower surface, which reduces the pressure difference between the upper and lower airfoil surfaces and results in reduced lift.

Aerodynamic performance analysis
The following analysis covers the variation in aerodynamic performance with angle of attack for the four airfoils in different conditions.Under low-speed take-off and landing conditions, the wings need to generate enough lift to meet the take-off and landing requirements.Figure 8 shows the aerodynamic performance curve of the original airfoil.By comparing the curve of lift coefficient versus angle of attack, it is concluded that, with the exception of the DG-1 airfoil, the other three airfoils have similar lift performance.However, in terms of drag coefficient, the DG-1 airfoil has the best performance with respect to the change in angle of attack, while the MS-0317 airfoil has the worst performance, while the other two airfoils have similar performance.Considering the lift-drag characteristics comprehensively, USA and DG-2 airfoils meet the requirements of integrated design for low-speed take-off and landing performance.Under high-speed cruise conditions, the airfoil lift coefficient changes with the angle of attack, following the Prandtl-Glauert law.In the low angle of attack range, the lift coefficient increases linearly with the increase of angle of attack, while at high angle of attack, stall occurs, leading to a non-linear decrease in the lift coefficient.Figure 9 shows the aerodynamic performance curves of four airfoils under high-speed cruising conditions.Through analysis, it can be preliminary determined that the stalling angle of attack of the four airfoils is approximately 8 degrees.Compared to mature airfoils, DG-2 airfoils perform better than DG-1 airfoils and resemble USA airfoils, particularly in terms of their liftto-drag characteristics under cruising conditions.It is worth noting that the DG-2 airfoil adopts a unique lower surface configuration, with a convex lower surface shape that helps air flow evenly across it, thus reducing drag.However, the acceleration of air flow in the lower surface caused by the shape of the airfoil's leading edge is also responsible for the small pressure difference between the upper and lower surfaces.When conducting aerodynamic design at high speeds, it is necessary to fully consider the effects of air compressibility, shock wave effects, and other nonlinear factors on the aerodynamic performance of airfoils to obtain more accurate results.At the same time, the lower surface configuration of the airfoil can also affect the wing's drag characteristics.It is necessary to consider the aerodynamic performance of the wing under different flight conditions in order to choose the optimal solution.

Airfoil deep optimization
Based on the comparison of the aerodynamic performance of the four airfoils under takeoff and cruise conditions, the self-designed DG-2 was selected for the subsequent integrated design work.However, it was found through comparison that there is a small recessed area on the lower surface of the DG-2 airfoil, which does not transition smoothly.Therefore, further local optimization of the lower surface of the DG-2 airfoil is required.Figure 10 shows two local optimizations for the DG-2 airfoil, defined as opt-1 and opt-2, where opt-1 is a major modification to the DG-2, and opt-2 is a minor modification to opt-1 in a localized manner.Based on the comparison of the aerodynamic performance of the original DG-2 airfoil and the optimized two airfoils in Figure 11, it can be seen that both the overall performance of the locally optimized airfoils opt-1 and opt-2 have been improved.

Circulation control Lift-enhancement
Circulation control is a method of flow control using the Coanda effect.In a narrow sense, circulation control is typically applied to airfoils with curved trailing edges.In a broad sense, circulation control augmentation can be achieved using various methods, including static pressure gas source methods and dynamic pressure gas source methods.The static pressure air source method involves extracting highpressure air from the aircraft's internal pressure system and injecting it onto the wing surface under control, altering the flow field structure and velocity distribution, thereby achieving lift augmentation.This method has the advantages of simplicity and reliability, but it requires the consumption of part of the aircraft engine power to provide pressure, which may affect the actual performance of the aircraft.Another method for increasing circulation is the dynamic pressure gas source method, which changes the dynamic pressure distribution of the airflow by injecting external energy into the system, thereby changing the flow field structure of the airfoil and achieving lift augmentation.Compared to static pressure gas source methods, dynamic pressure gas source methods allow for more flexible adjustment of airflow velocity and pressure, resulting in better results in some special situations.In this paper, an electric propeller is installed on the upper surface of the wing, and the velocity and pressure distribution of the air flow on the wing surface are changed through the suction of the ducted-fan to obtain better cyclic lift of the wing.

Definition of integrated layout
Integrating propellers and wings on the opt-2 airfoil.Figure 12 shows the opt-2 airfoil with integrated propellers, which is redefined as the DEPNF scheme.In the figure, OB is the chord of the airfoil, point A is the intersection of the propeller inlet exit section and the chord of the airfoil, and point C is the lower end point of the inlet exit section.The position and attitude of the thruster are precisely controlled through three parameters: chordwise position, height, and propulsion deflection angle.The specific definitions are as follows: chordwise position=OA/OB, height=AC/d, deflection angle= 90°-∠CAB d is the diameter of the intake outlet.
Based on the determination of the position and attitude of the propeller, the inlet and outlet area and shape design of the inlet and nozzle are completed, including the optimization design of design points such as the shape of the inlet lip, the shape of the flow pipe, the curvature of the nozzle's tail and the curvature of the nozzle's convergent section.Figure 13 shows three ducted-fan with wings formed a distributed propulsor.This section focuses on the integrated design of the propulsor and wing.The chordwise position of the propeller is 0.582, the height of the propeller is 0. 437, and the angle between the propeller axis and the horizontal plane is 8°.The inlet throat is 129mm high and 210mm wide, and the inlet outlet is equipped with a 50mm straight section.The outer diameter of the inlet outlet is 210mm and the inner diameter is 77.6mm.The nozzle inlet has an outer diameter of 21 mm and an inner diameter of 110mm.The nozzle has a 259mm equallength tube with a conical tail, which is 202mm long.The nozzle outlet area is 210mm×120mm.The aerodynamic chord length of the wing is 2. 050m, and the upper surface of the wing is equipped with ducted-fan.The width of a single duct is 0. 22m.Considering the influence of boundary conditions on both sides, a three-channel ducted-fan is used for calculation, and the symmetric boundary conditions on both sides are given.This integrated ducted-fan/wing configuration can generate large lift during takeoff and can induce a boundary layer on the body during cruise, which can improve the efficiency of cruise propulsion.

Numerical method
The numerical simulation is performed based on the finite volume method to discretize the Navier-Stokes equations, and solves the aerodynamic characteristics and three-dimensional flow field of a wing's circulation control augmentation scheme.When ignoring the effects of external heating and body forces, the conservation integral form of the three-dimensional compressible N-S equations in Cartesian coordinates is: is a conserved vector, and the transpose matrix contains density , velocity components in Cartesian coordinates, and the total energy per unit mass of gas; V  considers the boundary of the control volume; n is the outer normal vector of the boundary; and the vector F can be decomposed into a convective vector c F and a viscous vector v F .The spatial discretization uses a second- order central difference scheme, which approximates the values in the neighboring nodes layer by layer without sacrificing accuracy, improving computational stability and reliability.At the same time, to prevent numerical oscillations caused by "overshoots" or "over-inflation" near shock waves, a Minmod limiter is used.By comparing the slope values of adjacent nodes, if there is a large gradient change between adjacent nodes, the limiter can be used to improve and adjust the numerical solution.The viscous flux is solved using the Roe scheme. Figure 14 shows the integrated design scheme for the farfield and wall mesh, with approximately 8 million grid cells.The following four boundary conditions are mainly used in the calculation: far-field boundary, left and right section symmetric boundary, subsonic outlet boundary at the inlet exit, and given total temperature and pressure boundary at the nozzle entrance.The inlet and outlet boundary conditions are used to simulate the flow conditions with a fan, and the flow rate conditions are used to ensure that the flow rate inside the inlet and nozzle is consistent.This section mainly discusses the effect of propeller on lift force.Given a fan pressure ratio of 1. 15, Ma = 0. 12. Figure 15 shows the lift comparison curve between the DEPNF-1 and Opt-2 options, which shows that the lift increase for the DEPNF-1 option is significant.Table 1 provides the incremental lift for the DEPNF-1 option.Compared to the pure wing, the circulation control scheme has a significant lift increase effect, with a maximum increase of 332 % at a given angle of attack.Figure 16 shows the flow field analysis of the DEPNF-1 and the opt-2 airfoil under AOA-0° condition, revealing that the effect of fan suction on airflow acceleration on the upper surface of the airfoil is significant.At the same time, due to the thruster's certain deflection angle, the airflow ejected from the nozzle has a certain influence on the velocity distribution of the entire flow field.Figure 17 shows the circulation increase principle in the integrated design scheme.The integration design of the thruster changes the velocity field in two ways, and the effect areas are the A and B regions in the figure.On the one hand, the far field inflow flows on the upper surface of the blade and is accelerated by the fan into the interior of the propeller.On the other hand, air flow is compressed by the fan and accelerated by the nozzle to form a high-speed jet, which affects the flow field structure of the trailing edge of the wing.Through the combined effect of regions A and B, the fusion layout of the propeller changes the upper surface pressure field and velocity field, achieving the purpose of increasing circulation throughout the wing surface and enhancing wing lift.Considering the impact of fan speed on pressure ratio and flow rate, changing the fan pressure ratio further studies the effect of circulation augmentation under different flow rates.Figure 18 shows the variation curve of lift coefficient with angle of attack for the fan at different pressure ratios, compared to the opt-2 airfoil.At higher pressure ratios, the fan has a more pronounced suction effect on the airflow ahead, causing more airflow to enter the inlet and be accelerated and ejected by the engine, effectively increasing the airflow velocity field on the upper wing surface, affecting the circulation distribution of the wing and enhancing lift.Figure 19 shows the flow field distribution of the integrated design under different pressure ratios for the fan.It can be concluded that as the pressure ratio increases, the airflow speed increases significantly near the inlet, leading to stronger wing lift effects.

Conclusion
This article uses the SNOPT (Sparse Nonlinear OPTimizer) method to build an optimization design platform and designs a wing shape that takes into account both low-speed takeoff and landing and high-speed cruise performance.The self-designed wing shape is compared with mature wing shapes in terms of low-speed takeoff and landing and high-speed cruise performance, and a high-lift wing shape suitable for integrated design with the propeller is selected.At the same time, the wing shape is deeply optimized, and the self-designed DG-2 wing shape is ultimately chosen for integrated propeller/wing design.Through the analysis of the integrated circulation augmentation scheme design, the following main conclusions are obtained: (1) The integrated propeller/wing design scheme can significantly increase the lift of the wing.Compared with the pure wing, the circulation control augmentation scheme has a significant lift increase effect, and the maximum lift increment can reach 332% within a given angle of attack range.
(2) The integrated design of the propeller changes the velocity field in two ways.On the one hand, the far-field flow is accelerated by the fan and enters the propeller, significantly increasing the flow velocity in front of the propeller.On the other hand, the airflow is compressed by the fan and accelerated by the nozzle to form a high-speed jet, affecting the flow field structure at the trailing edge of the wing.
(3) The fan pressure ratio is a key parameter that significantly affects the lift augmentation effect of the wing.Within a certain range, the higher the fan pressure ratio, the more obvious the circulation augmentation effect.

Figure 12 .
Figure 12.The control of thruster position and attitude.

Figure 13 .
Figure 13.Integrated design of geometry model.

Figure 16 .
Figure 16.Mach contour flow field and local streamline distribution.

Figure 17 .
Figure 17.Schematic diagram of circulation increase principle.

Figure 18 .
Figure 18.The influence of different pressure ratios on lift coefficient.

Figure 19 .
Figure 19.Integrated flow field distribution under different fan pressure ratios.

Table 1 .
Comparison of lift increment at different AOA.