Drag Minimisation Using Adaptive Aeroelastic Structures
Vijaya Hodigere-Siddaramaiah * Jonathan E. Cooper†, Gareth A Vio‡ and G. Dimitriadis§
School of Mechanical, Aerospace and Civil Engineering, University of Manchester,
PO Box 88, Manchester, M60 1QD, UK.
This paper describes the latest developments in a research program investigating the development of “adaptive internal structures” to enable adaptive aeroelastic control of aerospace structures. Through controlled changes of the second moment of area, orientation or position of the spars, it is possible to control the bending and torsional stiffness characteristics of aircraft wings or tail surfaces. The aeroelastic behaviour can then be controlled as desired. A number of different adaptive internal structure concepts (rotating, moving and split spars) are compared here using a simple rectangular wing structure in order to determine which are the most effective for achieving minimum drag at different points in a representative flight envelope. A genetic algorithm approach is employed to determine the optimal spar orientation for rotating spars concept. It is shown that it is feasible to adjust the structure and trim characteristics of such wing structures in order to achieve minimum drag at all conditions.
I. Introduction There is a growing interest in the development of adaptive aeroelastic structures to allow aeroelastic deflections
to be used in a beneficial manner1,2. They are a subset of Morphing Structures, but rather than attempting to change the wing plan-form, the stiffness of the structure is adjusted to influence the aerodynamic performance. Such an approach will lead to more efficient aircraft designs. For example, the wing twist could be adjusted throughout the entire flight in order to maintain a shape giving optimal lift-drag ratio for maximum range, and also as a means of roll and loads control. Other concepts are being developed to change the wing leading and trailing edge shape in order to adjust the lift coefficient, and also to change the wing planform shape. In recent years, a number of research programs, for example the Active Aeroelastic Wing3 and the Morphing Programme4, have started to develop active aeroelastic concepts. In Europe, the 3AS (Active Aeroelastic Aircraft Structures) research programme5,11 developed and demonstrated various active aeroelastic concepts on a number of large wind tunnel models.
Part of the 3AS research program, and continuing work at the University of Manchester6,7, was devoted towards investigating the use of changes in the internal aerospace structure in order to control the static aeroelastic behaviour. Such an approach is desirable and arguably advantageous compared to other possible concepts. For instance, the use of leading and trailing control surfaces to control wing twist can lead to increased drag and poor observability characteristics. The use of smart materials (e.g. piezo and shape memory alloys) has received considerable attention in recent years, but still suffers from limits in the amount of force that can be achieved currently in relation to that required to twist or bend a wing.
The key idea exploited in the Adaptive Internal Structures approach is to make use of the aerodynamic forces acting upon the wing to provide the moment to twist the wing. By changing the position of the shear centre of the wing, the bending moment, and hence the amount of twist, will also change. A far smaller amount of energy is required to adjust the structure compared to that required to twist the wing and keep it in that shape. Such an approach is very attractive for active aeroelastic wing concepts and leads the way for the adaptive structural control of aerodynamic performance as well as roll and loads control. * Research Student † Professor, AFAIAA. ‡ Research Assistant, MAIAA § Lecturer, MAIAA
American Institute of Aeronautics and Astronautics
1
48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<br> 15th23 - 26 April 2007, Honolulu, Hawaii
Prototype experimental studies6,7 have demonstrated that it is possible to change the wing shear centre position, and the bending and torsional stiffness, by using spars that can move in a chord-wise sense, or can rotate. Other work8-10 has focused upon the rotating the spars but with roll control as the goal. However, having demonstrated that such adaptive devices can be made to work, there is a need to be able to decide the most effective way of implementing adaptive aeroelastic structures. Obviously it is infeasible to move the massive internal structures of large commercial aircraft, e.g. A380, close to the wing root, however, the wing structure is much smaller towards the wing tip and this region of the wing also has a much greater effect upon the aerodynamics.
This paper describes some of current work that is being performed to use optimization methods to determine the most beneficial stiffness distributions that could be utilized using adaptive internal structures. Some sample results are shown on a simple rectangular wing structure. A range of different concepts are compared in order to assess which is the most suitable for drag reduction.
II. Adaptive Aeroelastic Structures The key idea exploited in the Adaptive Internal Structures approach is to make use of the aerodynamic forces
acting upon the wing to provide the moment to twist the wing. Consider the schematic of the wing shown in figure 1, with the lift acting at the aerodynamic centre on the quarter chord. By changing the position of the shear centre of the wing, the bending moment, and hence the amount of twist, will also change. A far smaller amount of energy is required to adjust the structure compared to that required to twist the wing and keep it in that shape. Such an approach is very attractive for active aeroelastic wing concepts.
American Institute of Aeronautics and Astronautics
2
Research at the University of Manchester has investigated the use of a number of different adaptive aeroelastic concepts including the use of rotating spars and spars that can move in a chord-wise manner. Figure 2 shows the underlying spar/rib structure for prototype wind tunnels that were designed, manufactured and tested successfully to demonstrate both concepts.
A further concept that is currently being considered is the so-called “split spars” approach shown conceptually in Figure 3, whereby the top and bottom halves of a spar can be moved away from the centroidal axis. Simple comparison with the rotating spar concept shows that there can be a much greater gain in the change of second moment of area using the split spars concept as the distance of the components from the centroidal axis has greatest effect. However, there are complications that result in the design, manufacture and implementation of such a device, the load must be carried through the connections at the ends of the spars. A number of different implementations are under consideration presently at Manchester.
Figure 3. Spilt Spar Concept
III. Aerodynamic Performance Requirements Aircraft are designed currently to meet a maximum lift/drag ratio at some single point mid-way through the
cruise condition, as shown in figure 4. Consequently, the aircraft is off-optimum throughout the flight due to its changing fuel load and distribution. Further points that need to be considered are that often flight control considerations enforce a flight path at a non-optimal height and speed; new environmental considerations to flight traffic control (e.g. to reduce the occurrence of con-trails) are likely to enforce further constrictions on the flight path of future civil aircraft.
The use of adaptive aeroelastic structures concepts enables the bending and twisting properties to change along the wing, which in turn can be used to control the lift and drag at any particular flight and fuel loading condition. Although the lift and drag are primarily functions of the local angle of incidence (and hence twist) along the wing, due to the coupling between the bending and torsion modes of a swept wing it is not possible to simply consider torsion in isolation of bending, and vice versa.
For any given time in the flight path and altitude, the amount of lift that is required will be the same and consequently the problem of maximising the CL/CD ratio reduces to minimising the drag whilst keeping the same lift. This approach is complicated somewhat if fuel distribution is also considered, and consequently the amount of lift required reduces throughout the flight with diminishing fuel load. Some aircraft employ fuel management systems that redistribute the fuel throughout flight to ensure that aeroelastic constraints are met, and this would once again complicate the optimum employment of adaptive aeroelastic structures.
High IxxLow Ixx
American Institute of Aeronautics and Astronautics
3
Figure 4. Flight Envelope Showing Possible Flight Points and Single Current Design Point
IV. Example Adaptive Aeroelastic Wing Structure Consider the finite element model of the prototype wind tunnel model shown in figure 5. The effect of rotating
the spars can be simulated by simply varying the second moment of area properties of the spars and it is also straightforward to move the spars in a chord-wise manner. The implementation of the split spar concept is a little more complicated, however, a single beam can be simply used with its properties changed to take the varying distance between both parts of the spar into account. As we are only considering the problem in a static aeroelastic sense, there is no need to worry about modelling the system as the changes in internal structure are made. However, dynamic effects such as flutter must always be considered as a constraint as well.
As each of the spars in the wind tunnel model was able to rotate between 0 and 90 degrees, this could lead to a large number of possible configurations, depending upon the increment between the different rotation angles that was considered. In the case covered here, it was also assumed that the spars were divided in four separate sections, between each set of ribs, which could independently assume any rotation angle. Lift, Drag and pitching moment coefficients were determined at a single flight condition for all structural configurations considered and are shown in figures 6, 7 and 8. Obviously care must be taken for all of the different configurations that aeroelastic instabilities such as flutter and divergence do not occur, however, this will not be considered further here. The calculations were performed using the ZAERO software package. The drag calculations used the induced drag as the aerodynamic calculations are based upon a higher order panel method. For this initial study it was considered that this approximation and not using higher fidelity CFD aerodynamics was acceptable, particularly as only low speeds were considered and also it kept the calculation times to a much more manageable level. It is envisaged that higher fidelity CFD methods will be introduced once the optimization methodology has been established, but even then it is likely that the simpler panel method approach will still be made use of to some extent, possibly to provide initial starting estimates.
It can be seen that even with a relatively low number of possible spar orientations (only 0/30/60/90 degrees are considered in this example for 6 of the structural elements) there is an extremely wide range of different lift and drag coefficients that need to be considered along with constraints such as the divergence speed. Therefore, it is prohibitive to consider the problem of determining the internal spar orientation that results in either maximum lift / drag ratio, or minimum drag for a range of different speeds and altitudes without using some form of optimisation technique. Note also that these figures only relate to a single flight speed and altitude, and similar plots can be drawn for each case.
American Institute of Aeronautics and Astronautics
4
Figure 5. Typical Finite Element Model of Wind Tunnel Prototype for Rotating Spars Concept
Figure 8. CM vs. CD for Different Structural Configurations at a single flight condition
American Institute of Aeronautics and Astronautics
6
V. Optimisation Strategy Random search algorithms have been used in this work as they are particularly adept at searching through the
design space in an efficient manner. Other factors in favour of the use of a directed Random Search method are that the design space is relatively smooth, and that by setting up a macro to link the algorithm with the aeroelastic computation package, it was possible to get the estimates for each structural configuration in relatively few iterations. Convergence to the best structural stiffness layout was achieved by only considering a small subset of the total possible cases. Other points also considered were the inclusion of different altitudes and flight speeds as well as different fuel loads and distributions.
In this work a conventional Genetic Algorithm was employed to search for the most suitable stiffness distribution at some particular flight condition taking the aircraft trim into account in order to determine the minimum drag whilst maintaining some reference lift. Figure 9 shows the approach that has been taken. At some given flight condition and spar orientation / position / distance, an inner loop determines the required trim angle through a simple iterative scheme based on finding the lift and then estimating the change of trim angle needed to find it. Then the Genetic Algorithm loop determines what the spar orientation is that gives the minimum drag.
Trim Angle Determination
Loop GA Loop Define spar parameters
Drag Calculation
Figure 9. Optimisation Approach
Genetic Algorithms are based upon Darwinian theory of natural selection, with the characteristics of the best
solutions being used to “breed” new solutions, and have been shown to give good optimization results over a wide range of different cases. A “gene” is defined that contains a set of binary elements and can represent each possible case. In this case the orientation of the specified spars, and the corresponding values of lift coefficient, drag coefficient, divergence speed, flutter speed can be estimated. It is possible to define a cost function based upon minimizing the drag, however, this approach is complicated by needing to maintain some constant amount of lift. The flutter and divergence speeds (and structural parameters such as maximum stress need to be included for a full optimisation) can also be used to impart constraints on the optimization. Experience has shown that using a penalty function approach is more effective rather than simply ignoring those solutions that exceed the constraints. Note that although a binary representation for each gene was used, it is possible to employ a genetic algorithm based upon a real number representation.
A “pool” of genes is defined randomly and the cost function determined for each one. Pairs of genes are then selected based upon a random selection biased towards the best genes (but also ensuring that the selection is not totally dominated by a single gene). The “cross-over” approach was then used to produce the next pair of genes, with a certain amount of “translation” and “mutation” being employed as well in order to ensure that there is an adequate amount of new possible solutions included in the optimization. Occasionally “new-blood” terms are included into the optimization. In this work, terms were introduced that were furthest away from previous solutions.
American Institute of Aeronautics and Astronautics
7
Rather than just simply continuing with the above traditional approach, every so often a “meta-model” is created that is a simplified model based upon the solutions that have been considered previously. A simple polynomial model fitting the relationship between the spar orientations and the lift and drag coefficients was used, although a more complex approach, employing for instance radial basis functions, can be used, particularly if the design space is not smooth.
VI. Results Static aeroelastic analysis was performed at various speeds at a trim angle of 5 degree. Figures 10-13 show the
drag coefficient (CD), the lift coefficient (CL), the lift to drag ratio (CL/CD) and the tip angle for the rotating, moving and split spars concepts. Here the aeroelastic behaviours of the wing at 100m/s and a trim angle of 5o are compared. For the rotating spar concept there are 9 cases based on the combination between three different angles, namely 0o, 45o and 90o. For the moving spar concept there are 25 cases based on a combination of distances between front and rear spar. The front spar is allowed to move 60mm and its most forward position is located 30mm aft of the leading edge. The rear spar can move by 60mm and its most forward location is 102.5mm aft of the leading edge. For the split spar concept the spar sections are allowed to move between 12.5% and 80% of the width of the spar, where the 0% case corresponds to the spars been locked together.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20 25 30
Cases for Different Concepts
Drag
Coe
ffici
ent,C
d
Rotating Spars
Moving Spars
Split Spars
Figure 10. Variation of Drag Coefficients for Three Different Concepts at V=100m/s and Trim Angle 5o
American Institute of Aeronautics and Astronautics
8
0
1
2
3
4
5
6
7
0 5 10 15 20 25 30
Cases for Different Concepts
Lift
Coef
ficie
nt,C
l
Rotating Spars
Moving Spars
Split Spars
Figure 11. Variation of Lift Coefficients for Three Different Concepts at V=100m/s and Trim Angle 5o
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Cases for Different Concept
Cl/C
d Rotating Spars
Moving Spars
Split Spars
Figure 12. Variation of Lift to Drag Coefficients for Three Different Concepts at V=100m/s and Trim Angle 5o
American Institute of Aeronautics and Astronautics
9
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30
Cases for different Concept
Tip
Angl
e in
Deg
Rotating Spars
Moving Spars
Split Spars
Figure 13. Variation of Tip Angle for Three Different Concepts at V=100m/s and Trim Angle 5o
Figures 10-13 show that there are variations in lift and drag depending on the case under analysis. The moving
and split spars yield fairly constant values of lift and drag, while the rotating spar concept shows the largest variations in both these quantities. The results presented in these figures seem to suggest that the only concept yielding any improvement in lift to drag ratio is the split spar concept. Both the rotating and moving spar concepts actually tend to decrease the lift to drag ratio, the former one by quite a margin. Nevertheless, the rotating spar concept can be quite useful in cases where additional lift is required irrespective of any collateral increase in drag. The moving spar concept has no apparent relative merits compared to the other two concepts.
The tip twist angle results of figure 13 are a measure of the mechanical effort required to achieve the corresponding changes in configuration. Large tip angles require higher amounts of mechanical effort in the actuation of the spars and vice versa, due to the deformations that may affect the operation of the chosen mechanisms. The split spar concept results in consistently lower tip angle deformations.
In order to optimise the drag for the rotating spar concept, the 45-45 degree case was taken as reference. The lift for this reference condition was calculated at 180.6N at sea level conditions, an air speed of 100 m/s and a trim angle of 5o. The optimisation process was performed at four different altitudes, namely 0, 10k, 20k and 30k feet and three different airspeeds, ie 60, 80 and 100 m/s. For each altitude and speed case, all nine angle combinations from the rotating spar concept are analysed. In figures 14 to 16 the drag results are displayed, while in figures 17 to 19 the required trim angle to main the constant lift are displayed.
The drag results of figures 14 to 16 show that overall the best angle configuration is the 0o -90o combination. At low altitudes for the 60m/s and 100m/s airspeeds, though, the lowest drag is obtained from the 0o-0o and 90o-45o combinations. This is an important result because it shows that, even though only one angle combination is required for most of the flight envelope, notable exceptions do exist. Therefore, the maintenance of minimum drag at all flight conditions can only be achieved through the use of flexible internal structures.
The trim angle results of figures 17 to 19 show that the optimum rotation angle configuration is associated with higher but realistic trim angles. The lowest necessary trim angles are required by the 90o-90o angle combination.
American Institute of Aeronautics and Astronautics
10
15
16
17
18
19
20
21
22
23
24
0 3048 6096 9144
Altitude in m
Drag
in N
V=100m/s-R00-00
-R00-45
-R00-90
-R45-00
-R45-45
-R45-90
-R90-00
-R90-45
-R9-090
Figure 14. Relation Between the Drag and Altitude at Speed 100 m/s
15
17
19
21
23
25
27
29
0 3048 6096 9144
Altitude in m
Dra
g in
N
V=80m/s-R00-00
-R00-45
-R00-90
-R45-00
-R4-545
-R45-90
-R90-00
-R90-45
-R90-90
Figure 15. Relation Between the Drag and Altitude at Speed 80 m/s
American Institute of Aeronautics and Astronautics
11
Figure 16. Relation Between the Drag and Altitude at Speed 60 m/s
0
5
10
15
20
25
30
35
40
0 3048 6096 9144
Altitude in m
Dra
g in
N
V=60m/s-R00-00
-R00-45
-R00-90
-R45-00
-R45-45
-R45-90
-R90-00
-R90-45
-R90-90
0
1
2
3
4
5
6
7
0 3048 6096 9144
Altitude in m
Trim
Ang
le in
Deg
V=100m/s-R00-00
-R00-45
-R00-90
-R45-00
-R45-45
-R45-90
-R90-00
-R90-45
-R90-90
American Institute of Aeronautics and Astronautics
12
Figure 17. Relation Between Altitude and Required Trim Angle for Constant Lift at 100 m/s
1
2
3
4
5
6
7
8
9
0 3048 6096 9144
Altitude in m
Trim
Ang
le in
Deg
V=80m/s-R00-00
-R00-45
-R00-90
-R45-00
-R45-45
-R45-90
-R90-00
-R90-45
-R90-90
Figure 18. Relation Between Altitude and Required Trim Angle for Constant Lift at 80 m/s
6
7
8
9
10
11
12
0 3048 6096 9144
Altitude in m
Trim
Ang
le in
Deg
V=60m/s-R00-00
-R00-45
-R00-90
-R45-00
-R45-45
-R45-90
-R90-00
-R90-45
-R90-90
Figure 19. Relation Between Altitude and Required Trim Angle for Constant Lift at 60 m/s
American Institute of Aeronautics and Astronautics
13
VII. CONCLUSIONS AND FUTURE WORK An initial investigation has been made into the use of optimisation methods to determine the optimum
orientation of the rotating spars adaptive aeroelastic structures concept. It has been shown that it is possible to achieve minimum drag whilst maintaining the same lift for different speeds and altitudes.
Further work is continuing to increase the scope of the optimization through the introduction of the fuel condition and an increase in the number of spars and ribs whose stiffness can be adjusted. The application to swept wings will then be investigated, along with the inclusion of higher fidelity aerodynamics.
Optimization results will also be obtained for other adaptive spar concepts, such as the moving and split spar configurations presented in this paper. These results will help- in determining which of the tested spar concepts is the most effective and efficient and whether the aerodynamic gains outweigh the extra weight and power penalties to use such an approach on full-scale aircraft.
VIII. REFERENCES
1Pendleton, E., ‘Back to the Future - How Active Aeroelastic Wings are a Return to Aviation’s Beginnings and a Small Step to Future Bird-like Wings’, RTO-SMP Panel Meeting. 2001. 2Flick. P., & Love. M., ‘The Impact of Active Aeroelastic Wing Technology on Conceptual Aircraft Design’. AVT Panel. Ottawa. 1999. 3E. Pendleton. E, Bessette D., Field P., Miller G. & Griffen K., ‘ The Active Aeroelastic Wing Flight Research Program’ 39th SDM Conf 1998. 4Wlezien R.W., Horner G.C., McGowan A.R., Padula S.L., Scott M.A., Silcox R.J. & Simpson J.O. , “The Aircraft Morphing Program” SPIE Smart structures and Materials Meet 1998. pp 176-187 5Kusmina, S et al. „Review and Outlook for Active and Passive Aeroelastic Design Concepts for Future Aircraft“ ICAS 2002. 6M. Amprikidis & J.E. Cooper, “Experimental Validation of Wing Twist Control using Adaptive Internal Structures” AIAA SDM Conference 2004 7J.E. Cooper “Adaptive Aeroelastic Structures” Chapter in Adaptive Structures – Engineering Applications John Wiley 2007. 8J. Florance et al “Variable Stiffness Spar Wind Tunnel Model Development and Testing” AIAA 2004-1588 9J Heeg et al “Experimental Results from the Active Aeroelastic Wing Wind Tunnel Test Program ” AIAA 2005-2234 10P C Chen et al “Variable Stiffness Spar Approach for Aircraft Manouevre Enhancement using ASTROS” J.Aircraft v37 n5 pp865 – 871. 11J Schweiger & A Suleman “The European Research Project – Active Aeroelastic Aircraft Structures” CEAS Int Forum on Aeroelasticity and Structural Dynamics 2003.
American Institute of Aeronautics and Astronautics
