Transient Flow Analysis and Static Bench Measurements for an Active Trailing-Edge Flap Umberto Visconti 1 and WonJong Eun 2 Seoul National University, Seoul, Korea, 151-742 JungPyo Kang 3 Republic of Korea Navy, Korea JaeHoon Lim 4 Samsung Engineering, Offshore and Subsea Technology Research, Korea JiSoo Sim 5 Seoul National University, Seoul, Korea, 151-742 and SangJoon Shin 6 Seoul National University, Seoul, Korea, 151-742
The paper discusses the analyses implemented for the design improvement of the SNUF (Seoul National University Flap), a small-scaled flap-driving mechanism aimed at reducing vibratory loads in a helicopter rotor. Predictions of the hinge moment, both in steady and transient flow, were obtained through CFD (Computational Fluid Dynamics) calculations. When compared with results originating from theoretical formulation, it showed good correlation. Furthermore, the displacement occurring in the piezo-ceramic stack according to different frequencies was measured thanks to a further capable highvoltage amplifier able to span through the actuating frequency range, namely 0-65 Hz. Future proceedings aimed at verifying the effect of centrifugal loads in the SNUF, such as pulling test and contact analysis, are also illustrated.
Nomenclature h,H δ c cf Ch Cl Clα Cload f Ipeak αeff r R1,R2 Ω ρ
1 2 3 4 5 6
= = = = = = = = = = = = = = =
hinge moment per unit span, total hinge moment flap deflection angle blade chord flap chord hinge moment coefficient lift coefficient lift curve slope load capacitance frequency peak current effective angle of attack radius inboard radius, outboard radius rotation speed density
Graduate Student, School of Mechanical and Aerospace Engineering,
[email protected] Graduate Student, School of Mechanical and Aerospace Engineering,
[email protected] Republic of Korea Navy,
[email protected] Samsung Engineering, Offshore and Subsea Technology Research,
[email protected]. Graduate Student, School of Mechanical and Aerospace Engineering,
[email protected] Professor, School of Mechanical and Aerospace Engineering,
[email protected], AIAA Senior Member 1 American Institute of Aeronautics and Astronautics
ΔV
= voltage
I. Introduction
R
OTARY-wing aircrafts have always encountered more issues than fixed-wing aircrafts due to the complex dynamics and the absence of a symmetry plane. Among the numerous challenges, we investigate, in this paper, the vibratory loads mostly induced by the interaction between the rotor and the air flow and then transmitted through the shaft to the rotorcraft fuselage. The different solutions proposed to counteract this phenomenon can be divided into two main categories: passive and active methods. The former include devices such as swashplate and pitch link which dissipate and transmit the least amount of vibratory loads to the vehicle. Whereas this functioning logic is straightforward and the results achieved are satisfying, the increase in drag produced by the bulkiness of the above solutions plays a major disadvantage in their exploitation.1 Active methods, on the other hand, face the problem at its origin, that is the flow over the blade, which is smoothened by trailing edge flaps or other movable surface which are actuated through an automated closed loop and require lower electrical input. Among these solutions, ACF (Active Controlled trailing-edge Flap) is so far one of the most successful solutions; a number of different researches have already been conducted, both on small and full scale, and the results obtained proved to be satisfactory. Walz and Chopra2 conceived a bimorph flap actuation system to be placed within the fixed frame which would deflect and thus move the flap it is connected to. Although no rotating test was conducted, the mechanism in use shows great versatility and, what is more, room for improvement once design is perfected. Konstanzer, et al.3 instead applied the active trailing edge flap to a full scale rotor and measured the reduction in vibration caused by 4/rev hub loads and obtained a 90% decrease of the original disturbance. SNUF blade was developed according to this principle and a first version4 was designed based on the use of APA 200M actuators driving a trailing-edge flap. Despite the different layouts tempted, the desired flap deflection could not be obtained and this led to the choice of a more powerful actuator able to achieve the requirements.5 This paper focuses on the estimation through CFD analysis of the hinge moment acting on the flap and the consequent ability of the selected actuator to drive the movable surface in contrast with the flow generated pressure distribution. The airfoil chosen and deployed for analysis is NACA 0015, 0.135 m long equipped with a detached flap whose hinge is located at 0.11442 m chordwise. All the results obtained refer to the small-scaled model actually in use whose length flapwise is 0.3 m. In addition, a pulling test was conducted to verify the flap behavior in an environment which would simulate the centrifugal load occurring in a whirl tower. Also, a contact analysis was implemented through NASTRAN so as to validate the structural strength of the link mechanism components when the SNUF blade operates in a rotating frame.
II. Theoretical background A. Hinge moment estimation A momentous aspect in the ATF design is the prediction of the action of the hinge moment on the flap and a comparison of this with the capability of the actuator to overcome aerodynamic forces. The formula by Walz and Chopra2 was not applicable directly here as it was designed for a three-dimensional model, instead, a simpler prediction based on the two-dimensional model and the absence of any loss was used as a comparative measure with CFD results. Section hinge moment is defined as
= h
1 r (Ωr ) 2 c 2f Ch 2
(1)
If integrated spanwise, it results in R2 R2 1 1 1 2 2 H= hdr = r (Ωc f ) 2 Ch ( R23 − R13 ) ∫R1 ∫R1 2 (Ωr ) c f Ch dr = 2 3
(2)
Whereas all the data appearing in Eq. (2) originate from geometric features of the flap or from environmental conditions, the hinge moment coefficient has to be defined accordingly. As the lift coefficient and the flap deflection angles are the only variables affecting the hinge moment coefficient, the latter can be defined as a linear combination of the formers.
2 American Institute of Aeronautics and Astronautics
Therefore:
Ch = Cl
∂Ch ∂Ch ∂Ch ∂Ch +δ = Clα α eff +δ ∂Cl ∂Cδ ∂Cl ∂Cδ
(3)
The variation of hinge moment coefficient with respect of the lift coefficient and the deflection angle can be extracted, as a function of ratio between airfoil chord and flap chord, as in Abbot and Doenhoff6.
cf ∂Ch = −0.01018 − 0.5494 ∂Cl c cf ∂Ch = −0.8469 + 0.9833 ∂δ c
2
3
cf cf cf + 1.028 − 0.9934 + 0.2770 c c c 2
3
4
cf cf cf − 0.07663 + 0.2567 − 0.3205 c c c
4
(4)
The outcome is a positive trend due to the increasing pressure on the lower side of the flap, thus contributing to an enlargement of the value of the hinge moment coefficient. In order to properly estimate the hinge moment affecting the SNUF airfoil, a new design was selected for the CFD (Computational Fluid Dynamics) analysis. As a matter of fact, the prediction deriving from the previous mono-block airfoil would give a rough estimate of the pressure distribution over the latter as there was no neat separation between the front and the flap. On the other hand, the improved design in Fig. 1 displays a detachment between the main block and the flap itself leading to more precise calculations and reliable results7. Slotted flaps, as they are called when a gap exists between the main portion and the deflected flap, increase the effectiveness of the airfoil thanks to an increase of the camber and the chord. In spite of the relevant gain in aerodynamic performance, the complex geometry of the layout does not allow a reliable prediction of pressure loads and aerodynamic coefficients which are either retrieved experimentally or through CFD simulations. The first step, as proceeded in the previous design8, consisted of a static analysis where the flap was deflected by an angle, of precisely 10 degrees, which exceeds the expected range to obtain a safe estimate of the maximum occurring hinge moment and compare it with the capability of the chosen piezo-actuator.
Figure 1. Detail of the meshing near the trailing-edge flap Successively, transient analysis was also implemented. The selected methodology consists of a dynamic mesh encompassing the motion of the flap actuated according to a sinusoidal movement and the consequent deformation of the fluid elements surrounding the flap. As is customary in transient analysis a triangular unstructured mesh was chosen over hexahedral due to the capability of the former to modify its layout in a smoother way and without noticeably varying the overall quality. According to ANSYS requirements9 a few layers of prismatic mesh had to be added both along the physical walls of the airfoil and along the external boundaries of the domain; this procedure is driven by the inability of the mesh to deform when in contact with walls and by the likeliness of negative volume being created at the inlet and outlet boundaries. The number of layers chosen amounts to four, built according to an exponential trend; a further expansion of the prismatic zone would have completely filled the gap between the flap and the main block, leading to numerical inaccuracies. In order to implement the transient state analysis, an appropriate movement has to be imposed to the airfoil, such request is accomplished in ANSYS FLUENT thanks to a C function which denotes the flap deflection in terms of frequency and amplitude. The specifications of the considered device include oscillations up to 65 Hz and a deflection range of ± 4°. Aiming at optimizing the rate between calculation time and accuracy of the solution, a generally coarse mesh was implemented, taking care, though, of the regions where instability is more 3 American Institute of Aeronautics and Astronautics
likely to surge such as the gap between the airfoil and the flap, in such areas a greater refinement was introduced so as to consider any anomaly which may raise due to wall discontinuity.
B. Flap mechanisms analyses The displacement of the flap also has to be verified directly as issues may rise due to imperfections in the link mechanism or an improper use of the piezoelectric actuator. As a consequence, measurements will be conducted with the aid of a laser sensor able to register the position of the flap as it moves when the whole ATF device is actuated. An extensive frequency range of measurements is made available thanks to the newly acquired CEDRAT amplifier LA75C; in fact, the maximum input frequency is calculated as
f =
I peak
p Cload ∆V
(5)
The previously used TREK amplifier PZD-2000 had a maximum current of 0.2 A. Thus, considering a peakto-peak voltage of 100 V and being the capacitance of the APA 1000L actuator to be 40 μF, the maximal frequency resulted to be 15.9 Hz. Instead, new CEDRAT amplifier is characterized by a continuous maximum current of 2.4 A which, not changing the actuator and the voltage range, results in 191.0 Hz as the maximal actuation frequency. As a consequence, the presently acquired amplifier allows to operate in the whole frequency range required. Also, piezoelectric actuators are characterized by hysteretic behavior, as shown in Fig. 2, which depends on the Weiss domains present within the material10; as a consequence, this property will be investigated and results retrieved.
Figure 2. Piezoelectric hysteretic behavior11 The high velocity considered for the CFD analysis will also induce a large centrifugal force on the flap and all the other components. While a study over the actuator was already implemented,5 a static load analysis had yet to be conducted. As a matter of fact, given that the ultimate goal of the SNUF blade is its actuation in a whirl tower, design also has to consider the influence of the centrifugal force on the whole device. As also highlighted by Mainz12, the flap deflection range will witness a decrease when in a rotating environment and this may affect the effectiveness of the ATF whose displacement may not ample enough to properly dampen the vibratory load. As a result, a specifically manufactured test bed was exploited to verify the influence of the centrifugal load, in this case simulated through a set of weights clamped to the flap.
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Figure 3. Previous actuators layout In the previous researches,4 flap deflection proved to be smaller than the minimum requirements also in the case where no external loads were applied. The link mechanism proved to be one of possible reasons due to the complex layout and unwanted shear among the different components. As a consequence, given that centrifugal force will also be responsible for the rub which occurs between the contact guide and the push rod, as it was the case in the layout shown in Fig. 3, an additional verification is implemented. This consists of a contact analysis through NASTRAN which will be able to forecast the amount of stress occurring and the chances of ruptures, especially in points highlighted in Fig. 4, or excessive wearing when the rotor reaches full speed. actuator
flap guide
Figure 4. Stress critical points in the present version of the actuation mechanism C. Multibody dynamic analysis The fluid dynamics analysis is not sufficient to confirm that the whole mechanism would work properly instead, aerodynamic loads have to be coupled with structural properties and the layout of the whole mechanism to verify no major displacements or distortions would occur in the rotating environment. DYMORE is an opensource finite element analysis tool for non-linear elastic multibody systems developed by Prof. O. Bachau at Georgia Institute of Technology. The elements available in the program include, among the others, beams, rigid bodies and a variety of joints and constraints: the joints exploited in the analysis include revolute joints in the push rod mechanism and a prismatic joint which simulates the contraction and dilation of the piezostack actuator. The blade instead, is composed of four different beams: the first and last section will host the fiberglass roving which runs in the front part, chord-wise, of the blade, the second and third block will instead encompass the titanium block designed to hold the actuator.
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link mechanism
blade flap Figure 5. Present DYMORE model The model represented in Fig. 5 will also include the oscillation of flap driven by an external force imposed in the proximity of the prismatic joint. The function which is imposed to the flap mechanism is related with the actual movement of the actuator and the input voltage provided to it. Whereas previously no connection was taken into account between the input voltage and block force-stroke relationship which characterizes the actuator, a new revision showed instead a more detailed connection among the quantities, as it can be inferred from Fig. 6. Variation in the supplied voltage directly affects the actuator performances according to the formula
F x V + = Fmax xmax Vmax
(6)
where F is block force, x is the stroke and V is the input voltage.
Figure 6. Block force, input voltage, stroke relationship
Also, a kinematic equation is formulated in order to describe the flap motion during its actuation.
M = −kϑ F= −
k ϑ L2
= x L2 (ϑ0 − ϑ )
(7) (8) (9)
where M and F are respectively the moment and force applied at the flap hinge, ϑ is the angular displacement, L2 is the moment arm and k the torsional spring stiffness. Being all the parameters defined, the final formulation which connects input voltage, block force and stroke results from the combination of Eqs. (6) and (9).
k LV L V= −Vmax + 2 ϑ + 2 max ϑ0 xmax L2 Fmax xmax 6 American Institute of Aeronautics and Astronautics
(10)
III. Numerical and experimental results
A. Hinge moment estimation First, ideal fluid formulation was exploited using flap deflection angle and airfoil angle of attack as parameters. The retrieved results in Fig. 7 show a clear increasing trend in hinge moment value as the angle of attack grows due to the pressure on the lower side of the flap which is then forced to rotate counter-clockwise. What is more, a negative deflection of the flap (i.e. counter-clockwise) will instead create a hinge moment forcing the flap to rotate downwards. All the results extracted were considered for a 0.3 m long flap spanwise.
Figure 7.
Hinge moment as a function of angle of attack for different flap deflection angles
On the other hand, results originating from ANSYS FLUENT static simulation, as shown in Fig. 8, do not highlight a definite trend; although the variation range width is similar there is the lack of a constant rise in hinge moment values. As a matter of fact, CFD analysis, along with the pressure magnitude, also consider the shift of the high pressure area which results in a shorter moment arm and thus, in a smaller hinge moment. A comparison between the methods shows that ANSYS FLUENT results are higher than ideal fluid prediction and are therefore chosen in light of a more conservative approach.
Figure 8.
Hinge moment comparison for 10°flap deflection angle
The angle of attack was varied and the relevant hinge moment extracted from ANSYS FLUENT as the moment concerning the flap wall zone. Transient analysis was performed for three chosen frequencies: 2 Hz, 20 Hz and 65 Hz, and for each value the airfoil angle of attack was varied from 0 to 9 degrees. The retrieved results are shown in Figs. 9, 10, and 11. 7 American Institute of Aeronautics and Astronautics
.
Figure 9. Hinge moment coefficient at 2 Hz flap actuation
Figure 10. Hinge moment coefficient at 20 Hz flap actuation
Figure 11. Hinge moment coefficient at 65 Hz flap actuation 8 American Institute of Aeronautics and Astronautics
In a comparison between the hinge moment coefficient in the steady case and the transient analysis, we obviously observe higher values in the former case due to the deflection of the flap which obstacles the fluid free flow and results in an increased pressure load over the lower surface. As far as the transient state is considered, there is no clear connection between the hinge moment coefficient values and the angle of attack growth, at least in the range examined. Nonetheless, given that the range of oscillation for all the frequencies remains constant, we can conclude that no major energy losses occur during flap actuation despite the viscosity of the fluid
Figure 12. Maximum aerodynamic hinge moment (predicted) In the light of the hinge moment acting on the flap during the transient analysis, in Fig. 12 we extracted the highest value occurring in the computation and, as we can see, the indefinite trend obtained in the steady results appears here as well. These instabilities are mostly due to the presence of the slot between the main block and the flap which contributes to turbulent phenomena affecting numerical quality. What is more, in Fig. 13 the deflection angle was evaluated in terms of the available moment arm length was evaluated and showed that when aerodynamic conditions are applied, despite the hinge moment acting over the flap which moves at 20 Hz, the minimum requirement of 4°flap deflection is still achievable.
Figure 13. Flap deflection as a function of the moment arm length (predicted)
B. Displacement measurements As the target to be achieved is ±4° flap oscillation, the displacement of the latter was measured through a laser displacement sensor both in the steady and transient state where a sinusoidal wave, whose frequency reached 80 Hz, was used as input. Fig. 14 shows that the initial measured offset of the angle was 10° and decreased to -6° once a steady static voltage was applied. 9 American Institute of Aeronautics and Astronautics
Figure 14. Deflection angle measurement with static input Furthermore, when the flap was driven by a sinusoidal signal its displacement spanned from -5° to +13°, much wider than the expected range, as visible in Fig. 15.
Figure 15. Deflection angle measurement with 1 Hz sinusoidal input When the actuation frequency exceeded 45 Hz, the flap deflection reached an overly uplifted position and remained almost constant, thus preventing the whole expected measurement scope. The mentioned problem, however, is not related with the newly acquired amplifier, which allowed to reach the actuation goal of 65 Hz (2/rev) but instead with the flap mechanism. In order to retrieve the possible origin of the issue, Fig. 16 shows how the displacement of the actuator only was investigated. It resulted that, within the frequency range applied a peak value of 0.77 mm appears when 50 Hz sinusoidal wave was imposed.
Measurement point Figure 16. Actuator only displacement measurement 10 American Institute of Aeronautics and Astronautics
At the same time hysteresis of the piezo-ceramic stack was investigated as it is a typical property of the material which can be observed in a deflection angle-voltage curve. The behavior is displayed with 65 Hz input frequency given that it represents the highest value possibly applied in the flap actuation. In Fig. 17, this measurement is compared with the results obtained by using the previous amplifier which, due to its inefficiency, despite higher voltage would not allow frequencies greater than 11 Hz. On the contrary, the newly acquired Cedrat amplifier permits the achievement of the present target frequency only when a smaller amplitude of voltage is applied.
Figure 17. Deflection-voltage curve (measurement)
C. Static Bench Experiment including the Effect of Centrifugal Loads Given that the SNUF blade will be tested in a whirl tower, the ATF withstanding centrifugal force is a major requirement in designing the components; whereas structural analysis on the single actuator has already been conducted, the whole set is yet to be tested. In the previous proceedings, centrifugal load was considered in the case of 21.08 rad/s rotation speed and 1.125 m radius and the maximum strain resulted to be only 33.5 % of the allowable microstrain, predicted to be 800. The current simulation of centrifugal force will be implemented through a pulling test which aims at recreating the stress distribution the flap would encounter in a rotating environment. As the rotating test may decrease the oscillation of the flap due to the friction between the latter and the static section of the blade and due to the difficulty of measuring the rubbing, the static bench experiment will be able to predict how much the centrifugal force will affect the flap displacement. The test bed shown in Fig. 18 is equipped with a case specifically designed to accommodate a Halleffect sensor which supplements laser sensor in displacement measurement.
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Flap
Actuator
Figure 18.
Picture of the present static bench fixture
The experiment consists of screwing the test bed to a base in a vertical layout and successively hang weights to the flap through punched holes, as represented in Fig. 19. A system of pulleys is also added, two of which are fixed so as to avoid lateral displacements in the weight due to flap oscillations.
actuator flap
pulleys
weights
Figure 19. Representation of the pulling test setting Due to the flap weight of 20 g, the load exerted on the surface will reach the ultimate goal of 40 kg in a gradual way. As expected, Fig. 20 shows that already in the first stages of the experiment, a decrease in the angular displacement could be witnessed.
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Figure 20. Flap deflection under dead loads The detail in Fig. 21 shows how, compared to the initial maximum deflection of 11.5 degrees, when 10 kg were applied as a dead load, the resultant deflection diminished to 10.9 degrees.
Figure 21. Flap deflection under dead loads [detail] In spite of the visible decrease in deflection range, its limited amount raises hopes for a positive outcome once the expected final load will be applied. Also, the actuator will be subject to a specific pulling test as its mass, 190 g, plays a momentous role among the loads applied in the rotating test. At first, the push rod will be clamped in correspondence of the guide and the load exerted through different weights; once the first stage proves to be successful, the ultimate load, 400 kg, will be applied thanks to the use of an Instron machine, a device able to simulate high values of tension. In addition to that, in order to reduce the overall weight, the actuator case, first designed to be made out of steel, will be manufactured with a much lighter composite material. D. Static structural analysis due to centrifugal loads The rotating conditions encountered during the whirl test will not only contribute to a reduction of the effectiveness of the device but also have a strong influence over the stress and the wearing within the link mechanism. As a consequence, a contact analysis was implemented through NASTRAN so as to predict the likely values which may rise due to the centrifugal loads over the blade skin and the actuation part. When the von Mises stress distribution was observed, the contact surface between the guide and the push rod, visible in Fig. 22, resulted to be the area with the highest stress which resulted being 91.01% of the allowable values.
(a)
(b)
(c)
Figure 22. Existing stress/allowable stress ratio on the guide respectively for (a) aluminum, (b) steel, (c) steel with safety factor. 13 American Institute of Aeronautics and Astronautics
Figure 23. Representation of the blade skin and the incorporated flap-driving system The analysis focusing on the blade skin, displayed in Fig. 23, was conducted over all the seven plies which constitute the final shape and the region where the highest stress, up to 71 % of the allowable value, was observed coincides with bracket clamping zone. This specific area depicted in Fig. 24, which works as a connection between the blade and the flap, is subject to the loads of both surfaces and therefore the likelier to encounter damage.
Figure 24. Existing stress/allowable stress ratio over the blade skin plies The analyses conducted so far still have room for improvement both in the computer-based aspect and in the practical side. Multibody dynamic analysis with DYMORE will be equipped with additional details to better resemble the real situation; these consist of the built-in twist angle and an added lifting line along the flap while the pulling test will be conducted up to its ultimate value of 40 kg. As far as actuator is concerned, an Instron machine will be exploited in order to apply the expected load of 400 kg to the device so as to simulate the centrifugal force which would act in a rotating environment. Nonetheless, before implementing such test, a reduced amount of weights will be applied solely in a selected location between the guide and push rod.
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IV. Conclusion In this paper, the ATF blade device denominated as SNUF aiming at reducing vibrations in helicopter flight was employed. Calculations of the hinge moment performed through CFD software were adopted as values were higher than theory prediction and thus suggested a more conservative approach. Given that the transient analysis was performed with the expected deflection range, spanning between +4 and -4 degrees, the outcomes were able to give a more realistic view of the to-be-implemented aerodynamic test and the expectable hinge moment which will top up to 1.6 N-m. What is more, displacement of the flap was measured to verify the target goal of ±4° and resulted to, not only fully fulfill the requirements but also reach definitely greater values. As a matter of fact, in the static case the deflection reached an overall value of 16 degrees of displacement whereas the 1 Hz actuation frequency made the flap displace within a 18 degree range. Pulling test will be applied up to the pre-determined value and a similar experiment will be conducted over the actuator in order to verify satisfying flap displacement in rotating conditions as well as spanwise strength of the whole device.
Acknowledgments This work was supported by by the Advanced Research Center Program (NRF-2013R1A5A1073861) through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) contracted through the Advanced Space Propulsion Research Center at Seoul National University.
References 1
Besebel, M., Schoell, E., and Polz, G., “Aerodynamic and Aeroacoustic Layout of ATR (Advanced Technology Rotor)”, 55th AHS Annual Forum, Montreal, Canada, May 1999. 2 Walz, C., Chopra, I., “Design and Testing of a Helicopter Rotor Model with Smart Trailing Edge Flaps”, 35th Structures, Structural Dynamics and Materials Conference, Adaptive Structures Forum, April 1994. 3 Konstanzer, P., Enenki, B., Aubourg, P., and Cranga, P., “Recent Advances in Eurocopter’s Passive and Active Vibration Control”, 64th American Helicopter Society Annual Forum, Montreal, Canada, May 2008. 4 Natarajan, B., “Structural Analysis and Actuation Tests of an Active Trailing-edge Flap (ATF) Blade for Helicopter Vibration Control 2013”, Seoul National University, Master’s Thesis, School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, February 2013. 5 Kang, J.P., ‘Design Improvements of the Smart Active Trailing-edge Flap (ATF) for Rotating Test”, Seoul National University, Master’s Thesis, School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, February 2015. 6 Abbot, I. H., and Von Doenhoff, A. E., Theory of Wing Sections, Dover Publications, Inc., New York, 1959. 7 Li, L., Padthe, A.K., Friedmann, P.P., Quon, E., Smith, M.J., ”Unsteady Aerodynamics of an Airfoil/Flap Combination on a Helicopter Rotor Using Computational Fluid Dynamics and Approximate Methods”, 65th American Helicopter Society Annual Forum, Grapevine, Texas, May 2009. 8 Kang, J. P., Eun, W.J., Lim, J.H., Visconti, U., Shin, S.J., ”Design Improvements of the Smart Active Trailing-edge Flap (ATF) for Rotating Test”, AIAA Science and Technology Forum and Exposition (SciTech 2015), Kissemee, Florida, 2015. 9 Anonymous, ANSYS FLUENT, Software Package, Ver. 15.0 10 Ru, C., Liguo, C., Shao, B., Rong, W., Sun, L., ”A hysteresis compensation method of piezoelectric actuator: Model, identification and control”, Control Engineering Practice, September, 2009 . 11 Anonymous, “Piezo Motion for Precision Positioning Introduction”, pi-usa.us 12 Mainz, H., van der Wall, B., Leconte, P., Ternoy, F., Mercier des Rochettes, H., “ABC Rotor Blades: Design, Manifacturing and Testing”, 31th European Rotorcraft Forum, Florence, September 2005
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