Aerodynamic optimization of a high-lift system with adaptive dropped hinge flap

Qing JI, Yufei ZHANG, Hixin CHEN, Junke YE

a School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

b 63870 PLA Troops, Huayin 714200, China

c Shanghai Aircraft Design and Research Institute, Shanghai 200236, China

KEYWORDS Adaptive dropped hinge flap;Aerodynamic design;High-Lift aerodynamics;Multidisciplinary optimization;Optimization of aircraft design

Abstract The Adaptive Dropped Hinge Flap(ADHF)is a novel trailing edge high-lift device characterized by the integration of downward deflection spoiler and simple hinge flap, with excellent aerodynamic and mechanism performance. In this paper, aerodynamic optimization design of an ADHF high-lift system is conducted considering the mechanism performance. Shape and settings of both takeoff and landing configurations are optimized and analyzed, with considering the kinematic constraints of ADHF mechanism, and the desired optimization results were obtained after optimization. Sensitivity analysis proves the robustness of the optimal design. Comparison shows that the ADHF design has better comprehensive performance of both mechanism and aerodynamics than the conventional Fowler flap and simple hinge flap design.

1. Introduction

The design of an efficient high-lift system is a challenging task in the aerospace industry. Modern civil aircrafts require complex multi-element high-lift systems to increase the lift coefficient to compensate for the low velocity during the takeoff and landing phases.1Takeoff and landing performances for civil airplanes are constrained by strict requirements, such as FAR(Federal Aviation Regulations) Part 25,2to meet the safety demands. It has also been evidenced that even minor improvements of high-lift systems’aerodynamic characteristics can produce significant gains in the aircraft’s overall weight and performance. An increase in the lift coefficient can reduce the approach attitude and shorten the landing gear;an increase in the takeoff lift-to-drag ratio(L/D)can increase the payload or range.3

High-lift system design in the early years was mainly targeted to improve aerodynamic performance. Based on the analysis of Smith,4a high-lift system that has more elements can generate a larger lift coefficient.Consequently,some complex high-lift configurations, e.g., triple-slotted or doubleslotted Fowler flap systems, were commonly adopted to increase the maximum lift coefficient in the 1960 s to 1990s.5However, the complex flap mechanism also results in heavy weight, high manufacturing cost, and low reliability. It was not surprising that the high-lift system accounts for approximately 10%of the manufacturing cost of typical jet transport,and an alteration from a triple-slotted flap to a double-slotted flap led to an approximately 1/3 flap cost reduction.6

In recent years, the attention of the high lift design has turned to reduce the complexity, weight, and maintenance costs while keeping an acceptable lift level, which gives a beneficial effect on the overall cost of the aircraft. Rudolph’s report6pointed out that the change from multi-slotted flaps to single-slotted flaps delivered the largest weight and cost reduction of the high-lift system and suggested the singleslotted flap as a recommendation for future development.Both Airbus and Boeing simplified their trailing edge configuration from multi-slotted flaps to a single-slotted flap in their latest airliner design.5

The high-lift system mechanism is used to support and deploy high-lift movables to the desired position at landing or takeoff phases. There are many different types of trailing edge flap mechanisms used on commercial aircraft,which were reviewed in detail by Rudolph7and van Dam.8Two types of commonly used flap mechanisms are simple hinge flap and fowler flap, as shown in Fig. 16.

The simple hinge mechanism was commonly adopted in McDonnell-Douglas series aircraft. As shown in Fig. 1(a), a simple hinge flap is characterized by a simple mechanism of a flap connected to a fixed hinge and pure rotational movement. It is mechanically simple and lightweight but has a very restricted rotation trajectory. To obtain more extension of the flap, the pivot point of the hinged flap has to be located far from the wing, which results in a large flap fairing and cruise drag penalty. Moreover, because of the kinematic constraint of the simple hinge mechanism, the optimal configurations of the landing and takeoff may not be realized at the same trajectory.

Fig. 1 Conventional trailing-edge high-lift devices on commercial aircraft (based on Ref. 6).

Fowler flaps are the dominant trailing-edge high-lift mechanism in civil aircraft. It is characterized by a nearly translational movement to extend the wing area in takeoff and a rotational movement to increase the wing camber in landing,which provides optimum aerodynamic efficiencies for both takeoff and landing.However,the mechanism is more complex than a simple hinge flap. Three types of mechanisms are commonly used on the Fowler flap: linkage system, track system,and hybrid system; however, all these types of systems tend to be heavy and costly, as well as with lower reliability and maintainability.

A particularly novel trailing edge device called the Adaptive Dropped Hinge Flap(ADHF)was first introduced on the Airbus A350XWB in 2013.9–10As shown in Fig.2,it is characterized by the integration of a downward deflection spoiler and a simple hinge flap. The ADHF is mechanically simpler than a conventional Fowler flap and requires fewer moving parts,resulting in a considerable weight reduction. The multifunctional spoiler allows regular operation as an airbrake during landing and is able to perform downward deflection to adjust the gap of the single slotted flap. It can significantly increase the flap efficiency without increasing the complexity or the structure weight of the high-lift system. Wang,11Gubsky,12Wang13–14and Liu15further studied the aerodynamic of the dropped spoiler, and pointed out the dropped spoiler will increase the lift coefficient in the linear section, but also decreases the stall Angle of attack.When the spoiler deflection Angle is large, it is easy to separate the upper surface of the spoiler first. Drooped spoilers coupled with a low-setting flap are also used for variable camber technology16, which can reduce the drag coefficient by up to two percent, resulting in considerable fuel economies.17

Fig. 2 Multifunctional ADHF of A350XWB.10

The high-lift mechanism not only has an important influence on the aerodynamic performance but also has a significant impact on the weight, cost, maintainability, and reliability of an airplane. With the increasing attention of the comprehensive performance in practical engineering applications, the design methodology of high-lift systems has evolved progressively from an aerodynamic-focused design to a multidisciplinary design in the last few decades.In 1996,Rudolph6–7developed weight and cost modules of different types of highlift devices based on statistical data and recommended a multidisciplinary design methodology that incorporates aerodynamic performance, weight, and cost for future aircraft development. van Dam18proposed an aeromechanical design methodology to evaluate the aerodynamic performance of a high-lift device considering the kinematic constraints of four different trailing edge flap mechanisms. Recently, more and more studies considered the additional kinematic constraints in aerodynamic optimization.19–22Franke23–25improved the aerodynamic performance and reduced the takeoff and landing distance while fulfilling the kinematic constraints, leading to a more realistic design. Pires et al.26–27developed a combined methodology to take the weight, structure, aerodynamic improvements, and cost into account at an early design stage to improve the design quality. Niu et al.28conducted a multipoint aerodynamic optimization of trailing-edge variablecamber by deflecting the flaps and spoiler synchronously,and effectively improved flight efficiency in a wide range of CLby reducing wave drag and form drag. Liu et al.29conducted an aerodynamics/mechanism coupling optimization to a new configuration of link/straight track mechanism coupling with downward deflection of spoiler. The present study constructs an aerodynamic optimization platform considering the mechanism performance to explore the potential of ADHF design.The multi-element airfoil shape,deflection setting, and mechanism parameters of the ADHF are optimized for the best comprehensive performance of both mechanism and aerodynamics. Several aerodynamic and kinematic constraints are included in the optimization. Parametric analysis is conducted for the optimum configuration to test the sensitivity of the ADHF design. A comparison study between the ADHF optimization and the conventional design of Fowler flaps and simple hinge flaps was conducted to test the advantages of the ADHF configuration.

2. Numerical method and validation

A Reynolds-Averaged Navier-Stokes (RANS) solver is used for Computational Fluid Dynamics (CFD) simulation. The Spalart-Allmaras (S-A) turbulence model is adopted for the Reynolds stress closure. The 30P30N multi-element airfoil is adopted as the validation case. It has plenty of experimental data from the Low Turbulence Pressure Tunnel (LTPT) at NASA Langley Research Center in a cooperative effort with McDonnell-Douglas Aerospace.30Three sets of grids of the 30P30N airfoil with different grid numbers are adopted to test the grid convergence.The grid information is listed in Table 1,in which Nxis the number of grid points along the circumference of the solid surface. The computational domain size is[-50c, 50c] in the x-direction and [-40c, 40c] in the ydirection to fulfill the requirement of the far-field boundary condition. c is the chord length of the retracted airfoil. The mesh is refined in close proximity to the slat and the flap, as well as the upper surface of the main element, to ensure that the wakes can be well captured. The grid spacing of the first grid layer normal to the wall is 5×10-6c to ensure Δy+<1.The medium grid is shown in Fig. 3. The flow conditions are Ma∞=0.2 and Re=5×106.

The lift curves of the computational results are compared with the experimental data, as shown in Fig.4.Both the medium and fine grids agree well with the experimental data,except that the stall angle is slightly later. The relative error of the maximum lift coefficient is less than 2.2%. Fig. 5 demonstrates that the Cpand Cfdistribution predicted at α=21°is in good agreement with the experimental data.This shows that the present computational method is reliable and the grid convergence is achieved. Consequently, the present CFD solver with the S-A turbulence model and the medium grid are adopted in the following study.

3. Optimization of ADHF airfoil

The design of the present ADHF airfoil is based on the retracted geometry of the 30P30N airfoil. The maximum thickness-to-chord ratio t/c of the airfoil is 0.106. The ADHF high-lift configuration is a simple three-element airfoil that consists of a slat, a main wing with a downward deflectable spoiler, and a single-slotted flap. The optimization of ADHF is to find the optimal shape,deflection setting,and mechanism parameters of an ADHF for the best comprehensive performance of both mechanism and aerodynamic.The aerodynamic and kinematic constraints are also included in the optimization. This approach is general and can also be extended to three-dimensional configurations. The present optimization is performed under both takeoff and landing conditions of freestream Mach number Ma∞= 0.2 and Reynolds number Re=9×106based on the retracted chord length.

3.1. Parametrization and optimization settings

3.1.1. Aerodynamic and kinematic constraints

To obtain a realistic design, the optimization process must handle the aerodynamic constraints and the kinematic constraints of the ADHF mechanism. The following constraints are considered in the optimization:

(1) The chord lengths of the slat and flap are limited by the front spar and rear spar of the wing to ensure the stiffness and fuel tank capacity, as shown in Fig. 6. For a conventional commercial transport aircraft,the position of the wing front spar is between 0.15c-0.20c,and the position of the wing rear spar is between 0.65c -0.75c.12–13For the ADHF, the trailing edge high-lift device of the Airbus A350XWB is realized by a small flap chord of 0.19c,which is smaller than a conventional high-lift system. It is beneficial for wing stiffness and weight reduction.In this study,the wing front spar position is located at x=0.145c, and the wing rear spar is located at x=0.75c.The chord of the flap is a variable to be optimized between 0.15c -0.25c.

Table 1 Grid information of 30P30N airfoil.

Fig. 3 Medium grid of 30P30N multielement airfoil.

(2) The spoiler of ADHF is downward deflectable following the flap. Due to the kinematic constrains of the mechanism,the spoiler is connected to a fixed hinge and moved in a pure rotational trajectory, and should not interfere with the flap.The geometry interference check is automatized in the optimization process.The spoiler chord and the flap chord together determine the clean overlap of the flap, which will also be further determined by optimization design.

(3) Mechanism depth of flap is also an important constraint, because the mechanism depth determines the flap fairing size and weight, and also fairing drag. For commercial transport aircraft, the typical fairing depth of the Fowler flap is 0.09c-0.16c.26The ADHF design of A350XWB and B787 further reduces the fairing size and achieves excellent mechanism performance. In this paper, the hinge depth Yhof ADHF is constrained to be less than 0.075c, and also be taken as the optimization objective for the optimization design. In addition,the ADHF mechanism also brings strong kinematic constraints to the design of the high-lift device,both the slat and the flap moves along the circular trajectories around the hinge points.The slat and flap positions of the takeoff and landing configurations have to be compatible in the same circular trajectories.

(4) To avoid a sudden drop in the lift coefficient in the linear section, which often occurs due to flow separation occurring on the flap designs at large deflection (≥30°)at lower angle of attack,31the lift coefficient CLat α=4° of the landing configuration is constrained to be larger than 2.7 as aerodynamic constraint.

Fig. 4 Variation of experimental and computational CL with α.

Fig. 5 Variation of experimental and computational Cp and Cf at α=21°.

3.1.2. Design parameters

The shape of both the slat and flap and the settings at both takeoff and landing are used as design parameters. Twentysix design variables are defined in the optimization process,as shown in Fig. 7 and listed in Table 2:

(1) Slat shape parameters: the shape of the slat is cut from the baseline clean airfoil by a cubic spline curve. The curve forms both the leading edge of the main element and the cove shape of the slat. The shape of the slat is controlled by 5 control points and has 6 variables. As shown in Fig. 7(a), Ps0and Ps4control the chord of the slat. Ps1is the leading-edge point of the mainelement.Ps2and Ps3control the shape of the nose shape of the main element.

Fig. 6 General constrains on high-lift design.

(2) Flap shape parameters: the geometry of the flap is controlled by 6 control points, including 10 variables. As shown in Fig.7(b),Pf5controls the chord of the spoiler.Pf1determines the chord of the flap. Pf3dominates the maximum thickness and maximum thickness position of the flap. Pf2controls the leading edge shape of the flap.Pf4is used to adjust the shape of flap upper surface.

(3) Takeoff and landing settings: including gaps s, overlaps d, and deflection angles δ of the slat, flap, and spoiler.Because the deflection trajectories of the takeoff and the landing are the same,the takeoff and landing parameters are dependent.In this paper,the hinge locations of the slat and flap are determined by the landing configuration.Once the gaps,overlaps,and deflection angles of the slat or flap of the landing configuration are provided,the hinge locations can be computed by rigid body rotation,as shown in Fig.7.Then,the takeoff configuration can be generated only by the deflection angles of the slat,flap,and spoiler.Consequently,the design parameters of the landing configuration have 7 variables,and the takeoff configuration has 3 variables, as listed in Table 2.

3.1.3. Optimization objectives

The present optimization aims to increase the aerodynamic performance of both takeoff and landing conditions and the mechanism performance of the high-lift device. Tri-objective optimizations with several engineering constraints are adopted in the current study to cover the following design requirements:

(1) The first objective is to increase the maximum lift coefficient CL,maxin the landing configuration since the increase in CL,maxcan increase the maximum landing weight and decrease the approach speed and landing range.32

(2) The second objective is to improve the lift-to-drag ratio L/D under the takeoff condition(CL=2.5).Because the takeoff climb gradient is dependent on the lift-to-drag ratio, increasing L/D at a given lift coefficient can improve the climb performance during the second segment climb, which is a key component in measuring the total range of an aircraft.

(3) The third objective is the hinge depth Yh, which represents the distance of the flap hinge to the wing. In this study, the hinge depth Yhis chosen as the key indicator for the mechanism performance of ADHF, because a lower hinge depth Yhleads to a smaller support structure and a lighter mechanism weight, a lower manufacturing cost, a smaller and lighter flap fairing, and also lower fairing drag. The hinge depth Yhis computed based on the settings of the flap. It is worth noting that the hinge depth of the slat is not optimized in this study because the slat is usually driven by an internal gear rack, and no external faring of the mechanism is required.

Fig. 7 Sketch of design parameters.

3.2. Optimization modules

3.2.1. Geometry generation and grid automation

An in-house-developed high-lift geometry generator is used to generate new configurations. The geometry generator takes design parameters as input and generates high-lift geometry quickly and robustly. The geometry constraints, such as the trajectory constraint of the landing and takeoff and the gapand overlap feasibility, are implemented in the geometry generator.

Table 2 Range of design parameters.

The computational grid is automatically generated using a grid deformation script. The baseline grid is a multiblock structured grid based on the medium grid of the 30P30N three-element airfoil. The grid deformation script contains a sequence of operations to readapt the baseline block topology around the new configuration. By carefully designing the grid topology and grid deformation operations,the deformed mesh preserves a good grid quality even at the upper or lower limits of the design variables.

3.2.2. Optimization algorithm

Because there are multiple optimization variables and multiple optimization objectives, and the optimization can be highly nonlinear and difficult to converge. Genetic-type algorithms are often used in high-lift design to achieve a globally optimized solution in either two-dimensional33or threedimensional problems.34

An in-house developed hybrid surrogate-aided differential evolution optimization algorithm called HSADE35is chosen to find the global optimal solution in the current study. The parallel combination of differential evolution and the radial basis function response surface improves the elitist performance and guarantees population diversity at the same time.36The optimization efficiency and high robustness of the HSADE algorithm have been verified by our previous studies.28,37–39

3.2.3. Optimization process

The optimization flow chart is illustrated in Fig. 8. An initial set of design variables representing the configuration designed manually is provided to the optimizer.A vector of design variables represents each design candidate. Then, the vector is transferred to the geometry generation module. The landing configuration and takeoff configuration are optimized in a parallel process. The geometry generation module translates the design parameters into landing and takeoff configurations with respect to the kinematic law of the ADHF mechanism. The grid automation module separately generates the grid of landing and takeoff automatically.The CFD analysis module computes the flow fields and evaluates the aerodynamic performance of the configurations.Constant lift coefficient calculation of the takeoff configuration is performed by automatically iterating the angle of attack.Several discrete angles near the stall angle of attack are calculated and compared to determine the maximum lift coefficient of the landing configuration.The aerodynamic performances of landing and takeoff configurations and the hinge depth of the ADHF form the objective functions. If an optimal solution is not achieved, the function values of the objectives are fed back to the HASDE optimizer to generate new populations for the next design generation.The process is repeated until the Pareto front of the optimal solutions is converged.

Fig. 8 Flow chart of optimization procedure.

3.3. Optimization results

The optimization was performed on an Intel 32-core 2.4 GHz workstation. Thirty individuals are computed in each generation.It takes approximately 1 core hour to evaluate an individual. Sixty generations and 1800 individuals are computed for each optimization.

3.3.1. Selection of optimal solutions

The tri-objective optimization leads to a three-dimensional Pareto front. Three projections of the three-dimensional (3D)Pareto front are shown in Fig. 9 for better display. The gray dots represent the valid individuals generated in the optimization. The color dots present the individuals of the third objective from the 3D Pareto front of the optimization.As shown in Fig.9(a),the color of dots marks out the Yhvalue of the optimization. As shown in the figure, a sharp Pareto front or an‘‘L-shaped” Pareto front (refer to Refs. 26,16) is obtained in the L/D vs CL,maxplane, indicating that the two objectives are almost independent. It also indicates that the takeoff and landing settings have a more significant influence than the common parameters of the shape on the aerodynamic objectives.A unique optimal solution of the aerodynamic objectives could be obtained at the corner of the ‘‘L-shaped” Pareto front.

Fig. 9 Individual distributions of tri-objective optimization.

The smooth Pareto front in Fig.9(b)and 9(c)indicates that both the aerodynamic objectives of L/D and CL,maxare influenced by the mechanism objective of Yh. There is a trade-off between the mechanism size and the aerodynamic performance.

Three individuals on the Pareto front are chosen for comparison to decide the final optimal individual. The first one has the shortest Yhnamed as ‘‘Yhbest”. The second one is a trade-off of the three objectives named the ‘‘Trade-off”. The third one has the best aerodynamic performance named‘‘Aero best”.

The landing and takeoff geometries of the three designs,as well as the original multi-element airfoil, are shown in Fig. 10 and Fig. 11. The design parameters are also shown in Table 3 and Table 4.The landing configuration and the takeoff configuration share the same shape and hinge point. The leading edge shapes of the main element and flap of the 3 alternatives almost coincide and show a plump leading edge of both the main element and flap and a shorter spoiler and longer flap chord than the original configuration,which indicates the convergence of the shape parameters.

The candidate landing configurations have larger deflection angles of the flap and spoiler,and smaller Fowler motions than the original configuration. By comparing the three candidate designs,one can see that a larger CL,maxof the landing configuration, corresponding to a larger slat deflection angle and smaller spoiler and flap deflection angles. And a smaller flap deflection angle leads to a longer hinge depth Yh.

The candidate Takeoff configurations have larger deflection angles of the flap and spoiler,a smaller angle and nearly sealed slat, and smaller Fowler motions than the original configuration. By contrast, the three takeoff configurations are quite similar.This demonstrates that a larger L/D of the takeoff configuration corresponds to a smaller slat deflection angle and bigger Fowler motions. The nearly sealed slat leadings to better L/D performance and reduces the slat noise,9–10the larger Fowler motion leads to longer hinge depth Yh.

To further assess the performance at different angles of attack, the lift curves and lift-to-drag curves of the three designs are computed and shown in Fig. 12.

The‘‘Aero best”configuration has the largest CL,maxin the landing configuration, but the lift curve is lower in the linear section. The ‘‘Aero best” has the best L/D when the takeoff CLis above 2.2.

The‘‘Yhbest”configuration has the highest CLin the linear section, but it falls suddenly below α=3°. The streamline at α=2° is shown in the cyan frame in Fig. 12(a). The flow detached at the upper surface of the flap.

Compared with the ‘‘Yhbest” and ‘‘Trade-off” configurations,the‘‘Trade-off”configuration has a moderate maximum lift coefficient CL,max,and lift-to-drag ratio L/D.It also has the largest stall angle of attack (α=24°). Therefore, the ‘‘Tradeoff” configuration is selected as the optimal individual of this optimization. In the following study, this configuration is denoted as the ‘‘ADHF opt” for convenience.

3.3.2. Performance and flow analysis of landing configuration

Compared with the original configuration, the performance improvement of the‘‘ADHF opt”is the result of the combined action of the optimized shape and settings.To separately study the contributions of the shape and the settings, a new landing configuration is generated by the original airfoil shape,and the settings of the selected optimal configuration ‘‘ADHF opt”.This configuration is denoted as the ‘‘opt setting” in this section. The lift curves of the original airfoil, the ‘‘ADHF opt”configuration, and the ‘‘opt setting” configuration are shown in Fig. 13.

(1) Contribution of settings.

By comparing three CLcurves, it can be seen that the settings have the most important influence on the landing configuration. The lift coefficient of the ‘‘opt setting” improves considerably by approximately 0.6 at a low angle of attack,which is beneficial for reducing the landing gear length.3With the increase in the angle of attack, the slope of the lift curve decreases. The stall lift coefficient of the ‘‘opt setting” is slightly lower than that of the ‘‘original” configuration.

The pressure coefficients Cpof the three landing configurations at α=4°are shown in Fig.14.The larger flap deflection angle of the optimized solution tends to increase the loading on the main element and the slat by enhancing the upwash of the upstream element.

The drooped spoiler increases the loading on the main element by increasing the aft camber of the main element and increases the loading on the slat by enhanced upwash. It also reduces the leading-edge suction peak on the large deflected flap by the downwash, thus reducing the pressure gradient and delaying separation, increasing the lift coefficient.

As the angle of attack increases,the load on the main wing increases rapidly, which increases the downwash to the flap and results in the decrease of the local angle of attack of the flap. The drooped spoiler further reduced the local angle of attack of the flap,which reduces the adverse pressure gradient and delays the trends of flap separation. The reduced loading on the flap also weakens the upwash to the main wing in turn,resulting in the decrease of lift coefficient increment and the decrease in the lift curve slope, as shown in Fig. 13.

Fig. 10 Sketches of alternative landing configurations.

Fig. 11 Sketches of alternative takeoff configurations.

Table 3 Parameters of alternative landing configurations.

Table 4 Parameters of alternative takeoff configurations.

(2) Contribution of shapes.

The difference between the‘‘ADHF opt”and the‘‘Opt setting” comes from the different nose shapes of the two configurations. This shows that the optimized shape is also beneficial for the improvement of the lift coefficient. The stall lift coefficient of the optimized configuration is higher than that of the ‘‘original” configuration.

However, the nose shape has a limited influence, mainly affecting the leading edge suction peak, as shown in Fig. 14.The larger curvature shape just behind the slat and flap slot accelerates the slot jet flow and increases the leading-edge suction peak of the main element and the flap,as shown in Figs.15 and 16.When the attack angle increases,the jet flow speeds up,and the leading-edge suction peak increases simultaneously.

Fig.12 Aerodynamic performance of alternative configurations.Consequently,the difference in CLcurves of the‘‘ADHF opt”and ‘‘opt setting” is also increasing, as shown in Fig. 13.

3.3.3. Performance and flow analysis of takeoff configuration

The takeoff configuration and the L/D curves of the‘‘original,‘‘the‘‘ADHF opt”and the‘‘opt setting”are shown in Fig.17.

(1) Contribution of settings

The improvement between the ‘‘original” and the ‘‘opt setting” comes from the different settings of the two configurations. The larger flap of the ‘‘opt setting” increases the aft camber of the high-lift system, and the spoiler deflection increases the downwash to the flap, delaying the trends of trailing-edge separation,40–41which reduces the angle of attack for the takeoff angle of attack from 10.3° to 5.1°. This is beneficial for the reduction of the drag coefficient and the improvement of the L/D.

(2) Contribution of shapes

Fig. 13 Landing configuration and lift curves comparison.

The difference between the ‘‘ADHF opt” and the ‘‘opt setting” comes from the different nose shapes and the different trajectories of the two configurations. Fig. 17(a) shows that the ‘‘ADHF opt” configuration has an almost sealed slat gap in the takeoff configurations. The trajectory of the slat gap and deflection angle is shown in Fig. 18. The gap size of the‘‘original”and‘‘opt setting”configurations increases homogeneously as the slat angle increases, while ‘‘ADHF opt” maintains an almost sealed slat gap when the slat angle is less than 10° but increases rapidly as the slat angle continues to increase. This results in enough gap for landing but a sealed slat gap for takeoff. Fig. 19 illustrates the Cpcontour of the‘‘ADHF opt” and the ‘‘opt setting” configurations at α=4°.The greater suction at the leading edge of the ‘‘ADHF opt”slat, and larger pressure in the sealed slat cove improves the CLand reduces the pressure drag, and the sealed slat also reduces the friction drag caused by jet flow, as shown in Fig. 20. Consequently, it improves the L/D of the ‘‘ADHF opt”configuration by 11.87%than that of the‘‘original”configuration. Moreover, the non-slotted slat at takeoff also benefits the slat noise reduction of modern civil aircraft.42

3.3.4. Sensitivity study

Fig. 14 Cp landing configuration comparison.

Fig. 15 Slot flow of ‘‘ADHF opt” landing configuration(α=24°).

A practical design should have both good performance and robustness. It is worth studying the influence of each parameter on the performance of the optimized design.When an optimum design is obtained, the shape and the mechanism of the high-lift system would not change. The hinge depth and the trajectory of the slat and flap would not change either. However, the gaps, overlaps, and deflection angles of the slat and flap might be slightly changed during flight because of elastic deformation. The disturbance of these parameters may interfere with aerodynamic performance. Therefore, the aerodynamic performance under the disturbance of slat and flap settings is analyzed in this section. Because of the kinematic constraints of the ADHF mechanism, the changes in the gap and overlap are correlated with the deflection angle of the slat and flap.

(1) Landing configuration

The optimal slat deflection angle for the landing configuration is 25.99°. The landing performance of 21 different slat deflection angles from 24.00°to 28.00°are assessed and shown in Fig. 21. The baseline value is marked out in the figure. The CLat α=4° decreases gently as the slat angle increases. The optimal configuration has the maximum landing CLat α=25.99°, and the CLdecreases slightly near the baseline value.The lift coefficient drops rapidly when the slat deflection angle is too large or too small. The streamlines of the critical deflection angles are also shown in the figure. When the slat angle is larger than 27.2°,the increased slat deflection weakens the jet flow, which leads to massive flow separation above the spoiler,as marked by the blue frame in Fig.21.If the slat angle continues to increase,the flow separation expands to the main wing and destroys the circulation of the airfoil. By contrast, if the slat angle is smaller than 24.6°, the decrease in the slat angle increases the suction peak on the leading edge, which leads to the presence of the separation bubble on the slat, as marked by the red frame in Fig. 21. The formation and shedding of the separation bubble leads to the instability of the flow.

For the flap and spoiler deflections, the optimal values are δf=40.63°and δsp=12.56°.441 configurations of δfranging from 38.6° to 42.6° and δspranging from 10.6° to 14.6° are assessed and shown in Fig.22.For α=24°,CLincreases when the flap deflection increases and the spoiler deflection decreases. Interestingly, CLremains the same value when the flap and spoiler deflections increase or decrease simultaneously.When α=4°,there is a sudden drop in CLwhen the flap deflection increases and the spoiler deflection decreases.

Fig. 16 Slot flow of ‘‘Opt setting” landing configuration(α=24°).

Changing the deflection angles of the flap and spoiler also changes the gap and overlap of the flap.To further investigate the effect of the design parameters, the result of Fig. 22 is redrawn against the changing gap and overlap, as shown in Fig.23.This reveals that the gap is the most important parameter on the lift coefficient CL. When the flap deflection increases and the spoiler deflection decreases simultaneously,the flap gap size increases. The increased gap leads to an increasing CLat 24° but a sudden drop in CLat 4°. Because the increasing flap deflection and the decreasing spoiler deflection increase the suction peak of the flap, the wider flap gap increases the mass flow in the gap and enhances the upwash of the main wing, resulting in a higher CLat 24°. However,a high suction peak on the flap at 4°increases the adverse pressure gradient and tends to flow separation. When the gap size is smaller than 0.0125c, CLincreases gently as the gap size increases. When the gap size exceeds the size of 0.0125c, the CLfalls suddenly because of flap separation, as shown in Fig.23(b).The optimal configuration is at the edge of the flap separation, which proves the convergence of the optimization.For an ADHF high-lift system, the gap size of the flap can be easily controlled by the flexible spoiler. Reducing the gap size improves the robustness at a low angle of attack.However,the maximum lift coefficient of the landing configuration decreases as the penalty increases.

(2) Takeoff configuration

Fig. 17 Takeoff configuration and lift curve comparison.

Fig. 18 Trajectory of slat gap and deflection angle.

The slot of the flap is determined by both the flap and the drooped spoiler. Therefore, the flap deflection and the spoiler deflection are assessed simultaneously. The coupling effects of the two parameters are also studied. The optimal values of the flap deflection angle and the spoiler deflection angle are δf=29.42°and δsp=7.75°.441 configurations of δfranging from 27.4° to 31.4° and δspranging from 5.8° to 9.8° are computed and shown in Fig. 24. This shows that the CLand the L/D of the takeoff configuration are sensitive to the flap angle. The increase in flap deflection leads to an increase in CLbut a decrease in L/D. The spoiler deflection seems optimum in the baseline configuration.Both CLand L/D decrease as the spoiler deflection deviates from the baseline value.

Fig. 19 Cp contour map of ‘‘ADHF opt” and ‘‘Opt setting”(α=4°).

Fig. 20 Cf of ‘‘ADHF opt” and ‘‘Opt setting” (α=4°).

Fig. 21 Landing configurations with different δs.

The contours in Fig.24 also demonstrate a strong coupling effect between the two parameters acting on the CLand L/D.This coupling effect decreases the lift coefficient CLif the flap deflection decreases and the spoiler deflection increases simultaneously.This is expected since this movement closes the flap gap, reducing the flux of jet flow and reducing the suction on the flap’s upper side. In contrast, the coupling effect decreases the L/D when the flap deflection increases and the spoiler deflection decreases simultaneously. The opposite tendency indicates that a compromise has to be made between the lift coefficient CLand the lift-to-drag ratio L/D.

3.4. Comparison with conventional designs

Two more optimizations of the conventional configuration of the Fowler flap and simple hinge flap are carried out to evaluate the efficiency of the ADHF high-lift device.Both optimizations follow a conventional optimization process, as shown in Fig. 25. A landing configuration optimization of maximizing CL,maxruns first to obtain the best shape and settings. Then,a takeoff configuration optimization runs to maximize the L/D, which has the same shape and kinematic constraint provided by the landing optimization.Both conventional configurations of the Fowler flap and simple hinge flap have the same chord length of the slat and flap and have no spoiler deflection.

Two optimal configurations of the Fowler flap and simple hinge flap are obtained from the conventional optimization process. Both configurations are compared with the optimal design of the ADHF optimization. The geometries of three designs are shown in Fig. 26, and the parameters are shown in Table 5 and Table 6.

The simple hinge flap has the same landing configuration as the Fowler flap configuration because of the same objectives and the same optimization process. The conventional design has an almost coincidentally plump shape as the ADHF design to obtain a higher lift. The landing configuration of the conventional design has a smaller flap angle and a larger Fowler motion than the ADHF design.

For the Fowler flap, the takeoff configuration is optimized separately from the landing configuration. Both the best landing and takeoff configurations have large Fowler motions but a rather different flap deflection angles. A mechanism of at least 2 degrees of freedom is needed to reach the different flap locations. The most commonly used Fowler flap mechanisms are linkage systems, track systems, and hybrid systems.6

Fig. 22 Landing configurations with different δsp and δf.

Fig. 23 Landing performance with respect to sf and df.

Fig. 24 Takeoff configurations with different δsp and δf.

Fig. 25 Flow chart of conventional optimization process.

For the simple hinge flap, the flap is connected to a fixed hinge and moved in a pure rotational trajectory.When the best landing configuration is obtained, the hinge point and the trajectory of the flap are determined.The takeoff configuration is a result of the intermediate configuration.The desired optimal configurations in landing and takeoff cannot be met at the same time.The simple hinge flap is mechanically simple,lightweight, and reliable; however, the hinge point of the flap is quite far from the wing, resulting in a large flap fairing and cruise drag penalty.By contrast, the ADHF has a relatively short extension motion. The downwash of the drooped spoiler ensures that the flap deflects to a larger angle without flow separation.This helps to reduce the hinge bar length Yhby 50.6% compared with the simple hinge system. The size and weight of the trailing edge mechanisms can be reduced considerably to reduce the fairing size and the fairing drag, which makes the ADHF an efficient design.

Table 5 Parameters of 3 types of high-lift designs at landing configurations.

Table 6 Parameters of 3 types of high-lift designs at takeoff configurations.

3.4.1. Comparison of aerodynamic performance

The aerodynamic performance of three designs is compared in Fig. 27.

Fig. 26 Geometries of the 3 types of high-lift designs.

Fig. 27 Aerodynamic performance of 3-type high-lift design.

Table 7 Estimated weights of trailing-edge high-lift mechanisms (lb/ft2 of stowed flap area).

For landing configuration,the drooped spoiler and the larger flap deflection angle increase the overall camber of the ADHF, resulting in an increment of approximately 0.5 for the landing CLat small angles of attack. The CL,maxof the ADHF landing configuration is slightly decreased by 2.4%,but it still maintains a higher CLbefore 20.5°. The lift coefficient increment at the linear section results in a reduction in the approach attitude. This might lead to a shortening of the landing gear due to lower ground clearance requirements and thus saving weight.

For takeoff configuration, because of the kinematic constraint of the trailing edge mechanism, the L/D of the simple hinge is approximately 2.6%lower than that of the Fowler flap for a given takeoff CLof 2.5. The L/D of ADHF is considerably increased by 10.3%, and the takeoff angle of attack is reduced from 7.7° to 4.1°, compared with that of the Fowler flap design. The increase in takeoff L/D leads to an increase in the payload or an increase in range. The reduction of the takeoff angle of attack is also conducive to reducing the demand of the plane’s taildownangle and improving the comfort of passengers during takeoff.

3.4.2. Comparison of mechanism performance

The weight of different trailing edge mechanisms is estimated by empirical equations based on statistical data.Pepper et al.43divided the weight of a high-lift mechanism into 3 parts: supports & linkages, actuation systems, and fairings, and proposed a fairly accurate prediction method of the weights of the trailing edge high-lift mechanisms. In this paper, the trailing edge weights are evaluated based on Pepper’s method.43The weights estimation of the 4 different types of trailing edge high-lift mechanisms for a representative single slotted flap is presented in Table 7. The support and fairing weight of the ADHF is estimated as half of the simple hinge flap. A reference airplane with a maximum gross weight of 113400 kg(250000 lb) is used for evaluation. For a trailing-edge flap stowed area of 30.67 m2(330 ft2), the evaluated weights are estimated in Table 8.

Table 8 Estimated weights for trailing-edge high-lift mechanisms of 113400 kg (250000 lb) gross weight airplane.

It shows that the hooked track and link/track systems for the conventional Fowler mechanisms are quite heavy.The simple hinge mechanism is 36.8%lighter than the link/track mechanism due to its simplicity. The ADHF is even lighter because of its shorter hinge. The weight of the ADHF trailing-edge mechanism is reduced by 315.9 kg compared to that of the link/track mechanism.Since the reduction of structural weight cycles into the airplane takeoff gross weight with a sensitivity factor of 1.5 to 2.5,6the 315.9 kg weight reduction could make the airplane 473.9 kg to 789.8 kg lighter at the same payload or would allow a significant increase in the payload or fuel. This weight estimation demonstrates that the ADHF has an outstanding mechanism performance.

4. Conclusions

In this paper, an aerodynamic optimization of ADHF considering the mechanism performance is conducted based on the retracted clean airfoil of the 30P30N airfoil.The optimal takeoff and landing configurations with good comprehensive performance of mechanism and aerodynamics are obtained through optimization.

(1) The optimization demonstrates the downward deflection of the spoiler,and the optimized settings lead to lift coefficient increments of approximately 0.6 over most of the lift curve.The larger curvature shape behind the slat and flap slots accelerates the slot jet flow and increases the leading-edge suction peak of the main element and the flap.The sealed slat of the ADHF takeoff configuration improves the takeoff L/D by 11.87%.

(2) A parametric analysis was conducted to test the sensitivity of the ADHF design. This reveals that the gap is the most important parameter on the landing lift coefficient CL. The performance of the landing configuration is robust when keeping a flap gap size smaller than 0.0125c. The robustness of the takeoff configuration is also validated.

(3) Comparisons between the ADHF optimization and the conventional designs of Fowler flaps and simple hinge flaps shows that the ADHF design has excellent aerodynamic performance of 10.3% higher in takeoff L/D and approximately 0.5 higher in landing CLover most of the lift curve than that of the Fowler flap design, With mechanism of 50.6% shorter and 34.2% lighter than that of simple hinge flap design. Demonstrating that the ADHF design has outstanding comprehensive performance.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11872230, 91852108, 91952302,92052203),and the Aeronautical Science Foundation of China(No. 2020Z006058002).