Aerodynamic loads and coupled calcu- calcu-lations

In the following section mainly those results of the CFD computations will be discussed, that were used to generate the design loads and check the steady and unsteady behavior of the model i.e. the coupled calculations. Especially the spanwise distributed coefficients are good indicators for the change of the load distribu-tion. Furthermore, surface plots of the pressure difference between the upper and lower surface were used to illustrate the local loads. For this purpose, the results were interpolated with a barycentric approach to a structured grid, equal on upper and lower side, to facilitate the analy-sis and the computation of sectional values.

Steady results

The typical vortex at round leading edges [11] is a thickness caused vortex (Fig. 7) which is strongly affected by an interaction with the boundary layer. During the design process, stat-ic and coupled dynamstat-ic simulations were

per-formed using the Navier - Stokes solver TAU [12] and a modal representation of the FE-models [6], [13]. For the final design loads, the wind tunnel walls were included. For the basic studies and the initial sizing, the geometry with-out wind tunnel walls was used. In the following this will be called reference geometry.

Fig. 7 Pressure distribution with beginning vortex de-velopment,  15 deg, upper side

The steady behavior is mainly influenced by the heavily changing load and moment distribu-tions. With increasing , the main vortex moves inboard and detaches from the surface. At the outer part of the wing, the slope of the normal force is already decreasing, whereas at the inner part it is still positive (Fig. 8). This results in a more triangular distribution. The force main-tains almost constant at the outer part where the vortex has detached from the leading edge.

Fig. 8 Normal force coefficient distribution, 14-20 deg, Mach 0.5, Re 2.65 Mil, reference geo.

The moment distribution (Fig. 9) is also af-fected by the inboard moving vortex extending from the leading edge of the inner part over the trailing edge of the outer part (Fig. 7). Hereby, the moment distribution, especially at the outer part, changes significantly. For lower , the slope of the distributed moment is positive which then turns into negative. The effect of the decreasing lift at the leading edge is augmented by the increased suction at the trailing edge.

Fig. 9 Moment coeff. (at 50% chord) distribution,  14-20 deg, Ma 0.5, Re 2.65 Mil, reference geo.

Combining both effects, the center of pres-sure xcp moves further to the trailing edge (Fig.

10). On the one hand, this amplifies the strong washout effect (Fig. 11) caused by the high sweep angle. On the other hand, it will shift the vortex outboard again as the local  is reduced.

Under coupled dynamic conditions this could cause very non- linear behavior.

Fig. 10 Center of pressure over local chord l,  14-20 deg, Ma 0.5, Re 2.65 Mil, reference geo.

Main vortex tip vortex

Y

Development of an unsteady wind tunnel experiment for vortex dominated flow at a Lambda – wing

CEAS 2013 The International Conference of the European Aerospace Societies

Fig. 11: Steady deformation only of the wing /m

Further computations at the Mach number 0.5, but a higher Reynolds number, showed that the effect on the center of pressure is reduced by an increase of the suction peak at the leading edge. This postpones the detachment of the vor-tex and minimizes the effect of the suction of the vortex at the rear part of the outer wing on the spanwise distributed values. But the local effects still exist in the same manner. These computations were already performed including the wind tunnel walls and the peniche. The cor-rect flow conditions were adapted iteratively by a variation of the mass flow and checked at a monitoring point. The dynamic pressure was the same as for the computations at Mach 0.7 to ob-tain similar deformations.

Fig. 12 Normal force and moment coefficient distrib.,

 12-18 deg, Ma 0.7, Re 2.65 Mil, model geo.

With increasing transonic effects the vortex development changes. Shocks trigger the vortex to detach from the surface and change the direc-tion due to the smaller velocity perpendicular to the shock front. Furthermore, the vortex - shock interaction shifts the development of the vortex to smaller angles of attack, compared to the

sub-sonic cases (Fig. 3). This results in a decreasing normal force slope and hereby aerodynamic load (Fig. 12). Beyond an  of 16° at the Mach number 0.7, the strong vortex lift is reduced and the lift slope becomes negative.

This effect is very sensitive and strongly af-fected by the position of the shock. Depending e.g. on the turbulence model that can easily vary by some percent of the chord length already for the flow without vortices at a smaller . To ex-clude the uncertainty of the computations re-garding the extent of the transonic behavior and at which  the vortex moves inboard, all loads for the sizing process were scaled to a maxi-mum lift force as reached for the subsonic cases, which was described before. This maximum global normal force Fz,max is:

)

The steady coupled calculations generally showed a good and fast convergence behavior.

So, no steady stability problem exists. From the polar plots and the pressure distributions, it was determined that the relevant cases for the stabil-ity examinations are at the angles of attack of 14.5° and 16.5°. The first one is slightly before the development and detachment of the vortex and the second one is thereafter.

Unsteady calculations

The coupled unsteady calculations, that will be discussed, consisted of the following combina-tions:

Unsteady aerodynamic calculations can be started based on the jig- shape or on the flight - shape of the coupled computations with steady aerodynamics. This yields for steady or oscillat-ing angle of attack. To increase the convergence speed, coupled unsteady simulations usually are started based on coupled steady results. Theoret-ically:

If the aerodynamic loads have a damping char-acter, calculations starting from the jig - or the flight - shape should yield the same results after some time. If the calculations with constant  and unsteady aerodynamics do not converge or

result in a limit cycle oscillation, a dynamic sta-bility problem exists.

Vice versa, the non-equilibrium state of the jig - shape can be used to trigger and/or check if dy-namic stability problems can occur. Further-more, the modes mainly responsible for the stat-ic deformation are inherently excited by this.

This was especially important due to the high impact on the lower eigenfrequencies and the difficulties in modeling the stiffness of the mounting of the model. The tests also included pitch amplitudes of 1°, starting from jig- and flight – shape, to examine the non-linear aero-dynamic behavior and produce higher inertial effects. Amplitudes of 0.2° with frequencies from 5 - 30 Hz were used to study the general unsteady behavior of the vortex system.

The wavy characteristics of the lift and mo-ment coefficient of the first 3 periods in Fig. 13 and Fig. 14 are caused by the strong influence of the small bending motion. This was excited by starting the computation based on the jig - shape. Consequently, even small dynamic de-formations can have a huge effect on the global results. This yields for both, numeric and exper-imental tests. Vice versa, the aerodynamic re-sponse can be significantly different for coupled than for uncoupled computations if special modes are triggered. Additionally, it can be no-ticed that the bending mode is damped over time.

Fig. 13: CL, CMy over phase angle of motion, Ma 0.5,

 = 14.5 ± 1deg, 20Hz, Period 1 – 6

A restart was done after the 3^rd period, based on the flight - shape geometry. Even though the rotational motion is about 10 times higher than

the bending motion, a significant discrepancy exists between the case with an active bending motion and where the deformations are small and mainly with the frequency of the excitation.

Fig. 14: CL, CMy over , Ma 0.5,  14.5 ± 1deg, 20Hz

The frequency variations at a mean  of 14.5°, where the vortex development begins, show that the influence of the high sweep angle and hereby the strong plunge - like movement of the outer part of the wing affects the vortex at the tip differently than the main one (Fig. 15).

The normal force slope of the “quasi-steady”

load becomes negative. Hence, at the outer part it decreases in phase with the angle of attack but increases in phase with the plunge velocity.

Fig. 15: 1st harmonic freq. response to  14.5 ± 0.2deg, 25Hz, of normal force and moment, Ma 0.5

A phase shift exists (Fig. 16) between the main vortex and the tip vortex developing at the outer triangle of the wing (Fig. 7). Additionally, it is fed by a narrow co-rotating vortex along the leading edge. A phase angle  of -180° of the transfer function, representing the harmonic part

Development of an unsteady wind tunnel experiment for vortex dominated flow at a Lambda – wing

CEAS 2013 The International Conference of the European Aerospace Societies of dcp/d, means increasing suction with . So,

the main vortex is in phase with the angle of at-tack. This means that both vortices could induce vibrations similar to a seesaw. However, the ei-genfrequencies, that can be excited hereby, are much higher. In the simulations, this system of vortices seemed to be stable and the behavior was not changing significantly after the second or third simulated period of motion.

Fig. 16: 1st harmonic frequency response to pitching motion, 25Hz, of pressure,  14.5 ± 0.2deg, Ma 0.5

The coupled dynamic simulations showed a damping of the structural vibration after an ini-tial excitation, arising from the start, based on the jig-shape geometry. In Fig. 17, the heave and twist deformation of the first three periods is plotted over the wing span. This is the same case as shown in Fig. 13 and Fig. 14.

Fig. 17: spanwise heave and twist over time, Ma 0.5 ,  14.5 ± 1deg, 20 Hz period 1-3

In the last step it had to be ensured that the dominant part of the deformation is caused by the pitch excitation. It can be analyzed by a Fast Fourier Transformations (FFT) (Fig. 18) and if deemed necessary, again over time, of the spanwise heave and twist distribution. This is essential for the quasi - steady simplification of design loads as a superposition of aerodynamic

loads and the rotational acceleration. The FFTs of the spanwise force and moment coefficients give an indication how the deformation affects the aerodynamic loads or vice versa - similar to Fig. 18. For these stability tests it was decided not to display the forces as generalized forces as the actual value is lost. For the future analysis of the aerodynamic data, the comparison with the wind tunnel data and sensitivity tests this repre-sentation will be more appropriate.

Fig. 18: FFT of heave and twist, along the wing span,

 14.5 ± 0.2deg, 20 Hz, Ma 0.5

As the deformations were small, their behav-ior damped and the dominant part with the fre-quency of the pitch excitation, the superposition was a fair simplification for the design loads.

Conclusion

For the design of the experiment and the wind tunnel model, the following criteria were important:

A good optical access to the measurement section should be achieved by the new wind tunnel walls. Wall interference effects had to be reduced.

The model had to be designed for high loads with small deformations. Important load cases had to be selected based on the analysis of CFD calculations and scaled as design loads.

Shocks triggered the vortex to develop at small-er angles of attack for transonic than for subson-ic cases. Steady and unsteady coupled fluid/

structure computations were performed for the

stability analysis of the model. They were com-pared to the superposition of the inertial and steady aerodynamic loads used for the design and sizing.

Especially the CFD computations including the wind tunnel walls and in a later phase also the deformation of the model were important to find a concept for a new test rig, wind tunnel walls and plan the experiment. The comparison to the reference geometry without the wind tun-nel was used to verify influences. The scaling of the loads reduced the uncertainties of the sensi-tivity to transonic effects and ensured that the global normal force can be used as a safe moni-toring parameter.

In the future, computations will be compared to the results of the experiments. The signals of the piezoelectric balance as well as the unsteady pressure and acceleration sensors can be used therefor. Additionally, the optical measurements deliver surface and flow field information (PIV, iPSP and optical deformation measurement sys-tem). Hereby, an increased understanding of the vortex development at round leading edges is achieved. Furthermore, the current simulation capabilities can be evaluated. The hereby gained experiences will be used for the design and analysis of real scale configurations.

References

[1] Livne E., “Future of Airplane Aeroelasticity”, Journal of aircraft, Vol. 40, No. 6, Nov. – Dec.

2003, pp. 1066-1092

[2] Hartwich P. M., Dobbs S. K., Arslan A. E. and Kim S. C., “Navier–Stokes Computations of Limit-Cycle Oscillations for a B-1 like Configuration”, Journal of Aircraft, Vol. 38, No.

2, 2001, pp. 239–247

[3] Gursul I., Gordnier R., Visbal M., “Unsteady aerodynamics of nonslender delta wings”, Progress in Aerospace Sciences 41, 2005, pp.

515–557

[4] Hummel D., Loeser T., “Low speed wind tunnel experiments on a delta wing oscillating in pitch”, 21st Congress of the International Council of the Aeronautical Sciences, 98-3.9.3. 21. ICAS Congress, Melbourne, 1998

[5] Voss G., Cumnuantip S., Neumann J., “A Steady Aeroelastic Analysis of an Unmanned Combat Aircraft”, Vehicle Conceptual Design, 29th AIAA Applied Aerodynamics Conference,

[6] Khrabrov A., Greenwell D., “Chapter 9 - TSAGI 70° AND 65° DELTA WINGS TEST CASES”, NATO RTO-TR-AVT-080

[7] Vicroy D. D., Loeser T. D., Schütte A.,

“SACCON Forced Oscillation Tests at DNW-NWB and NASA Langley 14x22-foot Tunnel”, AIAA Paper 2010-4394, 2010

[8] Gand F., Deck S., Brunet V. and Sagaut P.,

„Flow dynamics past a simplified wing body junction“, Physics of Fluids, Vol. 22, 115111, 2010

[9] Wiggen S., Voß G., ”Computations of the vortex development for a steady and unsteady Lambda-wing wind tunnel experiment”, accepted for DGLR Jahrestagung in Stuttgart, 2013

[10] Klimmek T., „Parameterization of topology and geometry for the multidisciplinary optimization of wing structures“, in Proceedings European Air and Space Conference, Manchester, 2009.

[11] Konrath R., Roosenboom E., Schröder A., Pallek D. and Otter D., “Static and Dynamic SACCON PIV Tests - Part II: Aft Flow Field”, AIAA Paper 2010-4396, June 2010

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[13] Neumann J., “PyCSM – Python Computational Fluid Dynamics and Computational Structure Mechanics Coupling System”, Software Documentation and Technical Report, Institute of Aeroelasticity, Goettingen, November, 2010

CEAS 2013 The International Conference of the European Aerospace Societies Abstract

Ornithopter is an aircraft that moves its wings to fly like a bird. A flight model of an ornithopter is constructed and analyzed its flight characteristics experimentally in the present study. Size of the model for the experimental demonstration is wingspan 3.3m and, length 1.4m. The present flight model is constructed to enable the following three movements in the main wing: 1) flapping motion to move the wing into the vertical direction, 2) feathering motion to change the angle of attack in the flapping motion, and 3) lead-lag motion to move the wing into the horizontal direction.The flapping mechanism is implemented in the model employed with the ornithopter concept and feathering and lead-lag motions are realized in order to let the model produce both lift and thrust. Results of the experiment show sufficient lift to suspend the body with about 4kg and thrust with controllability.

1 Introduction

A model of the ornithopter has flown but not completely by Prof. Delawrier at the Institute of Aeronautics Study of University of Toronto in

2006 employed with jet engine as an auxiliary propulsion device.[1]

Aerodynamics of the ornithopter is studied by many researchers [2]-[12] and the importance of the three kinds of motion is understood in order to produce lift and thrust by the wing. These three kinds of motion includes, 1) flapping motion to move the wing into the vertical direction, 2) feathering motion to change the angle of attack in the flapping motion, and 3) lead-lag motion to move the wing into the horizontal direction. Wing motion is also studied rather than bird including insects, butterfly, mosquito, cicada, and some mechanisms are reported in their performance in order to simulate the motion of small air vehicles.

A model of bird flight is constructed by Nakazato and the model has flown successfully in 2007 [13]. The model has its wing span 3.3m with an engine 31,000rpm to flapping the wing and flew in average flight velocity 6m/s and ascending velocity 1m/s. The model is able to realize three movement, flapping, feathering, and lead-lag motion, and furthermore the flapping motion is synchronized to change its frequency increasing in the upward motion and decreasing in the downward motion, in other words, asymmetric flapping motion. The change of frequency in the flapping motion is a key idea

Experimental Analysis on Dynamic Characteristics of an Ornithopter

Mitsuhiro Kamii¹⁾, Hironori A. Fujii¹⁾ and Ichiro Nakane¹⁾

1) Kanagawa Institute of Technology, Japan

Keywords: Ornithopter, dynamic behavior, flapping, feathering, lead-lag

to increase the efficiency in producing lift and thrust also increasing the performance of maneuverability in the flight of ornithopter and is designed in the model of Nakazato.

A flapping-of-wings wings machine differs in the flight method from the conventional airplane definitely. Therefore, there are merits and demerits in a flapping-of-wings wings machine. In this experiment, an experimental model is constructed and its flight characteristic is studied experimentally and improved in its design to obtain better flight performance.

Fig.1 Flight of Cygnus 2 Wing section and definition

2.1 Model

The dimensions of the model in the present study are as follows:

Wing area: S = 1.0 [m²], Span: b = 3.3 [m], Mean aerodynamic cord: =0.30, Mass of the main wing: M = 2.6 [kg].