Aerodynamic optimization and mechanism design of flexible variable camber trailing-edge flap

Weishung LU,Yun TIAN,Peiqing LIU

aSchool of Aeronautic Science and Engineering,Beihang University,Beijing 100083,China

bNational Laboratory for Aeronautics and Astronautics,Beihang University,Beijing 100083,China

Aerodynamic optimization and mechanism design of flexible variable camber trailing-edge flap

Weishuang LUa,Yun TIANb,*,Peiqing LIUa

aSchool of Aeronautic Science and Engineering,Beihang University,Beijing 100083,China

bNational Laboratory for Aeronautics and Astronautics,Beihang University,Beijing 100083,China

*Corresponding author.

E-mail address:aircraft@buaa.edu.cn(Y.TIAN).

Peer review under responsibility of Editorial Committee of CJA.

Production and hosting by Elsevier

http://dx.doi.org/10.1016/j.cja.2017.03.003

1000-9361©2017 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Trailing-edge flap is traditionally used to improve the takeoff and landing aerodynamic performance of aircraft.In order to improve flight efficiency during takeoff,cruise and landing states,the flexible variable camber trailing-edge flap is introduced,capable of changing its shape smoothly from 50% flap chord to the rear of the flap.Using a numerical simulation method for the case of the GA(W)-2 airfoil,the multi-objective optimization of the overlap,gap,deflection angle,and bending angle of the flap under takeoff and landing con figurations is studied.The optimization results show that under takeoff con figuration,the variable camber trailing-edge flap can increase lift coefficient by about 8%and lift-to-drag ratio by about 7%compared with the traditional flap at a takeoff angle of 8°.Under landing con figuration,the flap can improve the lift coefficient at a stall angle of attack about 1.3%.Under cruise state,the flap helps to improve the lift-todrag ratio over a wide range of lift coefficients,and the maximum increment is about 30%.Finally,a corrugated structure–eccentric beam combination bending mechanism is introduced in this paper to bend the flap by rotating the eccentric beam.

©2017 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Aerodynamic optimization;

GA(W)-2 airfoil;

Mechanism design;

Trailing-edge flap;

Variable camber

1.Introduction

Aircraft wing design generally takes the efficiency of the cruise flight and the high-lift performance at takeoff and landing into consideration.In the actual flight,the flight condition is ever-changing,but the shape of the wing is almost unchanged.In order to improve the efficiency of the mission profile of the flight,a mission-adaptive wing would be ideal.At present,one feasible method for improving mission efficiency is to install a flexible variable camber trailing-edge flap on the wing.Such a device,combined with the large aircraft high-lift device concept and structure-deformation technology,has great application prospects in aircraft wing design.

Trailing-edge high-lift devices have been widely used on many kinds of aircraft previously.The structure-deformation technology has also been regarded as promising in the field of aircraft design.Traditional high-lift devices have a precedent of using the concept of deformation,which is mainly applied to the rear of wing,in order to improve the performance of takeoff and landing.Among such devices,the‘Smart High-Lift Devices for Next Generation Wings(SADE)”cooperative research project among Airbus,the German Aerospace Center(DLR),and 11 other European institutions,is most representative of studies taking place outside of China.Smart leading edge(SLE)and smart single slotted flap(SSSF)are studied respectively in the project,and stress analyses of flexible variable camber mechanisms and skins are carried out,but there are less aerodynamic data available for these two kinds of flexible variable camber device.1–8Aeroelastic analyses have been carried out by Li et al.9using the SADE concept.The ‘Variable Camber Continuous Trailing Edge Flap(VCCTEF)”10–13project launched by NASA is another representative study related to deformation technology and aircraft high-lift devices.Preliminary results show that the VCCTEF can increase the lift-to-drag ratio by about 4.85%.Analyses of the mechanism behind VCCTEF and the rigidity and aeroelasticity of the material have been carried out by Eric Ting and Sonia Lebofsky respectively.14–18

In addition,Yokozeki et al.19,20designed the variable camber morphing airfoil using corrugated structure to change the trailing-edge camber of a wing.Similarly,the variable-camber compliant wing is being studied by Joo et al.21,22

In China,Yin23and Chen et al.24have carried out similar research,mainly focusing on the aerodynamic performance of the trailing edge of variable camber airfoils.

Based on the existing research concerning high-lift devices and structure-deformation technology,the optimization of flap position parameters and the bending angle of the flexible variable camber flap of the GA(W)-2 airfoil at takeoff and landing is studied in this paper.The aerodynamic characteristics of the variable camber flap in cruise configuration are investigated.Finally,a corrugated structure and eccentric beam combination bending mechanism is designed in this paper,capable of bending the flap by rotating the eccentric beam.

2.Model design

In this paper,the GA(W)-2 airfoil is selected as an analytical model;this is an advanced airfoil for general aviation with a maximum thickness of about 13%of its chordc.25

The baseline configuration of the takeoff and landing configuration25is shown in Fig.1,and δfis the deflection angle of the flap,xpis the translation amount in the horizontal direction andzpis the translation amount in the vertical direction,which are refer to Ref.25.In this paper,the geometry of the variable camber trailing-edge flap is shown in Fig.2.The trailing edge of the flap bends f l exibly starting at 50%.Here,δangleis the bending angle of the flap,cflapis its chord length,andO/Lis the overlap between the main wing and the flap;gap refers to the width of seam,and δ is the deflection angle of the flap.

In order to find the appropriate bending angle and flap position parameters(overlap,gap,and δ),the takeoff and landing configurations are optimized separately in the iSIGHT optimization platform,as shown in Fig.3.The optimization objective26,27of the takeoff configuration is the lift coefficientsCL8,and the lift-to-drag ratio,CL8/CD8,is at an attack angle of 8°.The optimization objectives of the landing configuration are the lift coefficientsCL8andCL12at attack angles of 8°and 12°,respectively.As shown in Fig.428, α is the attack angle,CLis lift coefficients and CL0is lift coefficients at attack angle of 0°.For most of the general aircraft,8°is the normal attack angle for aircraft takeoff and landing,and 12°is near the stall angle of attack.The multi-island genetic algorithm is selected for optimization,and the optimization variables and objectives are shown in Table 1.

A certain type of general aviation aircraft is chosen to verify the 2D results,and the main parameters of this aircraft are shown in Fig.5 and listed in Table 2.The GA(W)-2 airfoil is selected as the wing cross-section and maintains equal proportions upon stretching into three dimensions.Here,the flap chord accounted for 25%of the local wing chord and the flap was stretched to 70%of the span.

Table 1 Optimization parameters and objectives.

The geometric parameters of the wing are defined in Table 3.The design points of this aircraft are shown in Table 3.

3.CFD verification

In this paper,the structure grid is used,and the computational fluid dynamics software Fluent is applied as the solver.Inorder to verify the reliability of the numerical simulation,the 30P30N airfoil is selected to verify the calculation.The grid topology of the numerical simulation is shown in Fig.6,and the first-layer grid height of the wall is 1×10-5times the reference chord length.

Table 2 Geometric parameters of selected general aviation aircraft.

On the basis of experimental data,the Mach number is set to 0.2 and the Reynolds numberReis 9×106.The model is placed at angles of attack in the range of 0°–24°.The pressure is one atmosphere,and the reference chord length is 1.9.

The FLUENT solution is set to an implicit algorithm,namely the coupled solver.The S-A model is used for turbulence,which deals with the problem of air flow with a wall boundary.29,30The momentum and turbulent kinetic energy in the equation are two-order upwind schemes.Fig.7 shows a comparison of the lift coefficientsCLobtained in numerical simulation with wind tunnel test results.31At an attack angle below 19°,the total lift coefficients of the airfoil increases with the angle of attack,agreeing well with experimental results.The aerodynamic forces of the leading-edge slat wing and main body and trailing-edge flap are also in good agreement with experiment.When the angle of attack is greater than 19°,the calculated lift coefficients of the leading-edge slat wing is larger,making the calculated lift coefficients of the multi-airfoil become relatively larger,and the stall angle of attack is around 23°,which represents an increase of about 2°compared with the experimental data.

Fig.831shows a comparison of the pressure coefficients distribution,Cp,obtained by numerical simulation and by wind tunnel test results when the angle of attack is 8°.The pressure-coefficients distributions of the main body,flap,and slat are in good agreement.

In order to further verify the reliability of the numerical simulation,the velocity profiles of the cross-section of the airfoil measured along the direction of a straight line at four representative positions (x=0.45c,x=0.89c,x=1.03c,x=1.11c)are compared,as shown in Fig.931when the angle of attack is 8°.Here,ordinate refers to the distance along the vertical direction from the surface of the airfoil(n/c)and abscissa refers to the ratio between measured and farfield velocities(V/V∞).The wakes of the main body obtained by both experiment and numerical simulation can be seen from Fig.9 and are found to be in good agreement.Numerical simulation of the speed loss of the wake of the slat clearly exceedsits experimental value.When the angle of attack is 8°,the boundary layer of the main section(x=0.45c)is plump and uniform,whereas that of the flap section is not,which is consistent with the pressure-coefficients curves.The flap section(x=0.89c,x=1.03c,x=1.11c)shows an inverse-pressure gradient trend in the flap.The wake of the main body appears to experience a slight separation at the flap,with variable thickness and wake velocity reduction with the growth of chord length.Overall,the results of the numerical simulation are in good agreement with experiment.

Table 3 Design point parameters of selected general aviation aircraft.

In summary,the results of numerical simulation are credible.

4.Results

4.1.Results under takeoff configuration

4.1.1.2D results

The Pareto optimal solutions of the takeoff configuration are shown in Fig.10.According to the optimization objective,the lift coefficients and lift-to-drag ratio of the optimized configuration are better than those of the baseline configuration.Three typical results(A,B,and C)on the Pareto Frontier are selected for further analysis.The geometries of the different takeoff configurations are shown in Fig.11,and the geometric parameters of the selected takeoff configurations are shown in Table 4.In order to simplify the legend,‘base”is used instead of ‘baseline” in the figure below.

The aerodynamic performances of selected takeoff configurations is shown in Fig.12,and the lift coefficients and the maximum lift-to-drag ratio of the three optimized takeoff configurations are greater than the baseline configuration before the stall angle.

In the lift coefficients linear section,the lift coefficients of configurations A and B are larger than that of the baseline configuration,and the increment of lift coefficients is about 0.2.The stall angles of attack of configurations A and B are decreased by 1°compared with the baseline takeoff configuration.Configuration C basically maintains the original stall angle of attack,and the lift coefficients is 0.1 higher than that of the baseline configuration.

Compared with the baseline configuration,the lift-to-drag ratios of the three optimized configurations have been slightly increased.The maximum lift-to-drag ratio of configurations A and C is at 8°,whereas that of configuration B is at 4°.At an angle of 8°,the drag coefficients is obviously increased,leading to a decrease of the lift-to-drag ratio.When the angle of attack increases,the drag coefficients is sharply increased to be near the stall angle of attack(13°),and the lift-to-drag ratio is decreased.

The pitching momentsCmof the three optimized takeoff configurations are higher than that of the baseline configuration.Here,the pitching moment of configuration B is the largest.

The pressure distributions of different takeoff configurations at 8°are shown in Fig.13.It can be seen that the suction peaks of the front of main body and the flap of the optimized takeoff configurations are higher than that of the baseline configuration.Because of the change of the camber and seam parameters of the flap,the effective camber of the airfoil is changed,leading to a significant increase in the negativepressure value of the flap upper surface,especially for configurations B and C.The negative-pressure value of the upper surface and the positive-pressure value of lower surface of the main body are higher than those under the baseline configuration.The local picture of the streamlines and velocity magnitudes of different takeoff configurations at 14°are shown in Fig.14.It can be seen that the main body and flap maintain an attached flow well without flow separation,except at the cavity between them.Here,the flow velocity of configuration A is significantly higher than those of the other three configurations,leading to an increase in negative-pressure value of the upper surface and the positive-pressure value of the lower surface,so that the lift coefficients of configuration A is higher than the others at α =14°.

It can be seen that the effective camber of configuration A is greater.The lift coefficients and lift-to-drag ratio before the stall angle are improved because of the small increase of the effective camber.And the pitching moment of configuration A is modest.Therefore,configuration A is chosen as the optimal takeoff configuration.

4.1.2.3D results

The locations of the spanwise stations are shown in Fig.15.By stretching the wing sections given by configuration A and the baseline configuration into three dimensions while maintaining equal proportions,the wing and fuselage are determined.Because the twist angle is set to-5°,the geometrical shapesof different spanwise positions are shown in Fig.16.The half models and surface meshes are shown in Fig.17.

Table 4 Geometrical parameters of different takeoff con figurations.

The 3D results of the optimal and baseline takeoff configurations are shown in Fig.18.In the 3D case,the growth trend of the aerodynamic performance is similar to that of the 2D results.Because of the presence of the incidence angle of the wing and the washing effect of the fuselage,the wing and fuselage stall angle of attack is smaller by about 4°in the 3D case.

The pressure coefficients distributions of various takeoff configurations are shown in Fig.19.The negative pressure values of the main upper surface decrease gradually from root to tip,and the pressure distribution of the flap remains basically unchanged.Compared with the baseline configuration,the suction peak,the upper-surface negative-pressure value,and lower-surface positive-pressure value of the main body and flap are larger,as was the case for the 2D calculation results;this is especially true in case of the suction peak at the wing tip of the optimized takeoff configuration.

There are slight differences between the baseline configuration and the optimized takeoff configurations in terms of streamlines and pressure,as shown in Fig.20.Only in the individual position,the upper-surface pressure of the optimized configuration is slightly lower.

4.2.Results under landing configuration

4.2.1.2D results

The Pareto optimal solutions of the landing configurations are shown in Fig.21.According to the optimization objective for the landing configuration,three better landing configurations A,B,and C are selected from the optimization result.A comparative analysis of the aerodynamic characteristics of the three optimized landing configurations and the baseline landing configuration is studied.The geometries of the landing configuration are shown in Fig.22,and the geometric parameters of the different takeoff configurations are shown in Table 5.

The aerodynamic performances of different landing configurations is shown in Fig.23.It can be seen that the lift coefficient of configuration C in the linear section is larger than the others by 0.15,but the stall characteristics of configuration C are clearly inferior to the others in terms of the stall angle of attack.

When the angle of attack is less than 8°,the drag coefficients of configuration A is slightly less than that of the baseline landing configuration.Therefore,the advantages of configuration A in terms of the lift-to-drag ratio are obvious,and this configuration,having the maximum lift-to-drag ratio,maintains this advantage up to the stall angle.However,the lift-to-drag ratios of configurations B and C are lower than that of the baseline configuration.When the angle of attack is about 12°,these liftto-drag ratios decrease sharply.

The pitching moments of the three optimized landing configurations are higher than that of the baseline configuration.Here,the

growth of the pitching moment of configuration A is lower.

The pressure distributions of different landing configurations at α =8°are shown in Fig.24.It can be seen that the suction peak,negative-pressure value of the upper surface,and positive-pressure value of the lower surface of the main bodies of configurations A and C are higher than those of the baseline configuration.The negative-pressure values of the flap fronts of configurations A and C are lower than that of the baseline configuration.

The local streamlines and velocity contours for different landing configurations at α =12°are shown in Fig.25.It can be seen that the upper surface of configuration C produces serious flow separation.Moreover,the flow velocities of other two optimized landing configurations increase slightly compared with the flow velocity of the baseline configuration.

It can be seen that the effective camber of configuration A is slightly increased.The small increase in the effective camber not only improves both the separation at the trailing edge of the flap at a small angle of attack and the lift coefficients and lift-to-drag ratio below the stall angle but also maintains the stall angle of attack of the baseline landing configuration.Therefore,configuration A is chosen as optimal for landing conditions.

4.2.2.3D results

By stretching the wing sections given by configuration A and the baseline configuration into three dimensions while maintaining equal proportions,the wing and fuselage are determined Thegeometricalshapesofthecross-sectionsat different spanwise positions are shown in Fig.26.The half models and surface mesh are shown in Fig.27.

The 3D calculation results for the optimal and baseline landing configurations are shown in Fig.28,and they appear similar to the results for the takeoff configuration.In the 3D case,the optimized configurations still retain their advantages in terms of lift coefficients and lift-to-drag ratio.The 3D stall angle of attack is smaller by about 3°,and the lift coefficients of the 3D wing is significantly smaller than that of the 2D airfoil.The lift-to-drag ratio is decreased and the pitching moment is reduced.

It can be seen from Fig.29 that the negative-pressure peak decreases gradually from root to tip,and the negative-pressure value on the flap’s upper surface gradually increases.For an optimized landing configuration,the pressure distribution on the main body is similar to that of the baseline configuration,but the negative pressure on the flap value is decreased at the middle of the wing,thereby reducing the inverse-pressure gradient on the flap’s upper surface and delaying the flow separation(Fig.30).

From the picture of the pressure contours and streamlines at each individual position at α=7°(Fig.30),it can be seen that the upper-surface pressure of the optimized configuration is slightly lower.Flow separation appears at the flap.For the baseline configuration,the flow separation position is at the front of the flap,and for optimized configurations this separation appears at the rear of flap.

Table 5 Geometric parameters of different landing configurations.

4.3.Results under cruise configuration

4.3.1.2D results

Under cruise configuration,the different conditions for the bending angle of the flexible variable-camber flap are calculated separately using the method of computational fluid dynamics.The values of the bending angle are 0°,6°,10°,-6°,and 10°,and the geometries of the cruise configurations with different bending angles are shown in Fig.31.

The effects of the variable-camber trailing-edge flap upon the aerodynamic force in the cruise configuration are shown in Fig.32,and as the lift coefficients and drag coefficients increase,the stall angle decreases with the increase of flap camber.Below the stall angle,the lift coefficients undergoes a clear increase when bending angle is greater than 0°,and the greater the value of δangleis,the larger the increment of the lift coefficient will be.But this increment is close to 0 when the attack angle is near the stall angle of attack,and even afterward,the lift coefficients presents negative growth.At the same time,the increase of the flap camber leads to flow separation in advance,reducing the stall angle of attack by 2°when the bending angle is 10°.The pitching moment increases along with the effective airfoil camber.

From the lift-to-drag ratio curve,the increase of effective airfoil camber reduces the angle of attack corresponding to the maximum lift-to-drag ratio.When the bending angle is greater than 6°,the increase of the camber is conducive to enhancing the maximum lift-to-drag ratio,but doing so will be harmful.From Fig.32(c),which show the envelope of the lift-to-drag ratio,it can be seen that this ratio can be improved with the lift coefficients ranging from 0 to 2 by changing the flap bending angle during the cruise.

The effect of the variable camber trailing-edge flap upon the pressure coefficients distribution in the cruise configuration at 8°is shown in Fig.33.It can be seen that negative-pressure value of the upper surface and the positive-pressure value of the lower surface are higher for the optimized configurations than those for the baseline configuration when the bending angle is greater than 0°,leading to an increased inversepressure gradient between the upper and lower surfaces.Moreover,there is no sudden pressure change at the bending position.Compared with the traditional flap and aileron,a flexible variable camber flap reduces the loss of lift at the deflection position.

4.3.2.3D results

Using the GA(W)-2 airfoil as a wing section and stretching it into three dimensions whilst maintaining the same proportions,the wing and fuselage are determined.The incidence angle is set to 3.2°and the twist angle is set to-5°.The geometrical shapes at different spanwise positions are shown in Fig.34.The half model and surface meshes are shown in Fig.35.

The 3D calculation results for the cruise configuration are shown in Fig.36,and appear to be similar to those for the takeoff and landing configurations.The 3D stall angle of attack is smaller by about 3°than the 2D case,and the lift coefficients of the 3D wing is significantly smaller than that of the 2D airfoil.The lift-to-drag ratio is also decreased.

It can be seen from Fig.37 that negative-pressure value on upper-wing surface decreases gradually from root to tip.As with the 2D calculation results,the larger the bending angle is,the larger the negative-pressure value on upper surface and the positive-pressure value on lower surface are;this is especially true at the wing tip because of spanwise flow.

The pictures of the pressure contours and streamlines,as shown in Fig.38,indicate that larger bending angles correspond to lower upper-surface pressure values on the wing.The flow separation is most serious when the bending angle is 10°.

5.Mechanism design

Throughout the above analysis of the effect of a flexible variable camber flap upon airfoil aerodynamic performance and the optimization results,the bending angle was not assumed to be too large.At the same time,stress and strain analyses of skin materials in the literature4have indicated that skin is prone to wrinkling with bending angles beyond 8°.Therefore,in the design of the bending mechanism,the bending angle is set from-8°to 8°.

In the design of the bending mechanism for the flexible variable-camber trailing-edge flap,as shown in Fig.39,a corrugated structure is used as the stringer in the skin(Fig.39(b))and an eccentric beam is used as the deformation mechanism from the 50%flap chord to the rear of the flap(Fig.39(c)).Here,the corrugated structure is not in the stress state,and the flap is not distorted.

The corrugated structure is strongly deformable along the chordwise direction but strongly resistant to deformation along the spanwise direction.This mechanism can decrease the drive force required for the realization of flap deformation.It can also better maintain the flap shape along the spanwise direction and decrease the number of eccentric beams,thereby decreasing its necessary weight.

In order to realize the flexible deformation of the flap,it is necessary to use the deflection curve of the skin material.The deflection is the centroid of the cross-section along the vertical axis,and the direction of the line displacement refers to the bending deformation.The axis of the beam will be changed into a plane curve in the longitudinal plane of the beam,which is known as the beam’s deflection curve.31This curve is shown in Fig.40.32Thelis the length of curve in the horizontal direction andyis the deformation in the vertical direction,which can be seen from the Ref.32.The functional expression of deflection curve, ν（x）,is usually expressed up to third order,as in Eq.(1):

The constantsAandBare related to the material properties and stress conditions whereasCandDare arbitrary.

The eccentric beam parameters are shown in Fig.41.This design guarantees that the curve of flap shape does not manifest second-order discontinuous points over the whole deformation process,and also ensures a smooth transition in the pressure distribution under flap deformation.The eccentric beam is rotated 90°upward and downward,which respectively raises and presses the trailing edge of the flap to realize variable camber from 50%of the flap chord,as shown in Fig.42.

The use of the bending mechanism combining a corrugated structure and eccentric beam can achieve the requirements of variable camber from 50%of the flap chord,and the maximum bending angle is 8°.Fig.43 shows the geometric shapes of the flap bent 8°upward and downward.

6.Conclusions

In this paper,the optimization of the takeoff and landing configurations of the GA(W)-2 airfoil with a 25%cflexible variable camber trailing-edge flap was carried out.This trailing edge flap can smoothly change its shape from 50%of its chord to its rear.The optimization variables included the overlap,gap,deflection angle of the flap,and bending angle.Under the takeoff configuration,the optimization objective was to maximize the lift coefficients,CL8,and the lift-to-drag ratio,CL8/CD8,at a takeoff angle of 8°.Under the landing configuration,the optimization objective was to maximize the lift coefficientsCL8at an attack angle of 8°and the lift coefficientsCL12at an attack angle of 12°.The influence of the bending angle upon the aerodynamic performance in the cruise state has been analyzed.A bending mechanism has been designed according to the deformation characteristics of the flexible variable camber trailing-edge flap.

(1)For the optimized takeoff configuration,the effective camber of the airfoil was increased slightly,which improved the lift coefficients at the takeoff angle(8°)by 8%and the lift-to-drag ratio by 7%,although the stall angle of attack decreased by 1°.

(2)For the optimized landing configuration,the deflection angle of the flap was decreased.The flexible variable camber trailing-edge flap not only made up for the deficiency of flap deflection but also improved the lift coefficients at the stall angle by 1.5%while maintaining the original stall characteristics.

(3)For the cruise configuration,the flexible variable camber trailing-edge flap not only improved the lift characteristics by 0.4 at a cruise angle of 3°in the 2D case but also improved the lift-to-drag ratio in the lift-coefficients range from 0 to 2.Here,the maximum lift-to-drag ratio was increased by 1.2%.

(4)The corrugated structure was used as the stringer in the skin,and the eccentric beam was used as the deformation mechanism.The bending mechanism satisfied the requirements of deformation from-8°to 8°.

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28 March 2016;revised 27 October 2016;accepted 14 December 2016 Available online 20 April 2017