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Effects of Different Thickness Variation Strategies on Dynamic Stall in an Oscillating Airfoil

Hossein R. Hamdani*, Rizwan Riaz†, Humayun Qureshi ‡, K. Parvez§, M. Ali** and S. Sheikh †† College of Aeronautical Engineering, National University of Science and Technology, Pakistan

An active flow control technique has been a challenge for aeronautical engineers since the beginning of flight. One of the more modern ideas is that of adaptive airfoils where the airfoil itself changes shape in response to flow conditions. In this research a code was modified to incorporate the airfoil deformation. Earlier the code had been validated for the oscillating NACA 0012 airfoil without deformation. The study was focused on the incorporation of thickness variation strategy to control the onset of dynamic stall. The results show appreciable reduction in stall effects including the delayed separation, reduced drag and improved negative moment separation.

Nomenclature

oα = mean angle of oscillation

1α = maximum amplitude of oscillation ω = angular velocity; corresponding to reduced frequency k = reduced frequency c = characteristic length, chord (m) t = time M = Mach number Re = Reynolds number CL = lift coefficient CD = drag coefficient CM = pitching moment coefficient

I. Introduction DAPTIVE airfoils and wings have the promise to revolutionize aeronautics and bring the artificial flying machines ever so closer to the efficiency achieved by nature. Adaptive wing technology returned to aircraft design through incremental steps. These were primarily in the form of gross adjustments to wing orientation,

such as the invention of variable pitch in propellers (circa 1924) or variable sweep wings1. The aim was to improve performance in as many flight regimes as possible. Additional attempts at altering wing efficiency included momentum transfer devices such as blowing or suction slots or wings that polymorphed with telescoping or folding tips. Though each of these concepts showed some success in improving airfoil efficiency, only the basic lift devices (flaps, slats, spoilers) have seen widespread application. Only recently have the aeronautical engineers been able to start thinking of the airfoils (and wings) as active surfaces, i.e. structures that can physically deform in the presence of stimuli.

Dynamic stall is a phenomenon that affects airfoils, wings and rotors in unsteady flows and occurs due to changes in the inflow conditions and/or the angle of attack. In some cases, such as helicopter rotors, dynamic stall is

* Associate Professor, Department of Aerospace Engineering, CAE NUST. † Graduate Student, Department of Aerospace Engineering, CAE NUST. ‡ Graduate Student, Department of Aerospace Engineering, CAE NUST. § Associate Professor, Department of Aerospace Engineering, CAE NUST. ** Graduate Student, Department of Aerospace Engineering, CAE NUST. †† Associate Professor, Department of Aerospace Engineering, CAE NUST.

A

3rd AIAA Flow Control Conference5 - 8 June 2006, San Francisco, California

AIAA 2006-3691

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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intrinsic to the state of operation while in wind turbines it is the result of atmospheric turbulence, wind shears, earth boundary layer, etc2. In general, the parameters affecting the dynamic behavior of an airfoil under periodic variations of inflow conditions are: amplitude of the oscillation, mean angle of attack, reduced frequency, Reynolds and Mach numbers, airfoil shape (thickness, leading edge radius, etc.), surface roughness, and free stream turbulence3. In the case of an oscillating airfoil, once the dynamic stall occurs, it may lead to an abrupt fluctuation of aerodynamic forces and impose excessive loads on structures. It is, therefore regarded as a crucial factor that limits the ability of an aircraft or a helicopter to perform high agility maneuvers. The prevention, delay, or control of dynamic stall has been the subject of many recent studies. Recently, much work has been done in technologies utilizing suction/blowing on the upper surface, leading edge flaps and slats, and dynamic deformation of the airfoils (or part thereof). Some of these techniques focus on preventing the stall vortex from forming while others aim at preventing the vortex from being shed.

The development of a workable scheme to eliminate or reduce these effects is, therefore, of great importance to aeronautical engineers. The use of an adaptive strategy allows the wing to vary its geometric parameters in flight during encounters with changing flow conditions such as wind speed or direction. Several issues need to be investigated for the development of an adaptive wing system, including selection of initial and perturbed airfoil shapes, unsteady aerodynamic analysis of an adaptive airfoil, and control systems for real-time shape control of an adaptive wing system.

II. Recent Advances In the experimental work of Carr and McAlister, the installation of a slat in front of an airfoil which is then

oscillated has been demonstrated to suppress the dynamic stall vortex (DSV) in wind tunnel tests 4. Two recent studies have looked at the thickness variation/shape deformation concept as means of dynamic stall control. In the work by Lee et al5, the airfoil was transformed from a NACA 0012 to NACA 0016 as it oscillated between 5 and 25 degrees α and analyzed different schedules for this thickness variation. After analyzing various schedules for both the s trokes of the oscillation, the research team came to the conclusion that for higher maximum lift coefficient, lift stall delay and moment stall delay, thickness variation rate should take a large value in early stage of up and down stroke. But for small maximum negative pitching moment, it should take a small value in early stage of each phase. Thus, there exists a trade-off relation between the stall delay and the pitching moments. This implies that a proper compromise should be made when applying any thickness variation strategy.

In the study by Geissler and Trenker6, the effects of a localized deformation at the leading edge were considered vis -à-vis the dynamic stall characteristics of the airfoil. It is based on the premise that the local curvature along the airfoil leading edge plays a key role with respect to the development of the dynamic stall vortex. The dynamically deforming leading edge (DDLE) concept7 results in a local flattening of the airfoil leading edge. In their work, Geissler and Trenker were able to demonstrate a significant improvement in the dynamic behavior of the oscillating airfoil.

The few examples cited above are by no means an exhaustive list of the techniques that have been, or are being applied to the problem of dynamic stall control. Various other methods of energizing the boundary layer, preventing the leading edge vortex formation, preventing or delaying vortex shedding, minimizing dynamic stall effects, etc are being studied.

The work by Lee et a l was, in fact, the seed that germinated into the thickness variation idea studied in the present project. The impact of the leading edge curvature, as so effectively demonstrated by the work of Geissler and Trenker, on the DSV formation and shedding became the foundation of the thickness variation strategies employed in the current study. Present study focuses on a NACA-0012 airfoil oscillating between 5 and 25 degrees angles of attack. During the analysis phase, different deformation schemes were attempted and their results studied vis -à-vis their effectiveness in suppressing or minimizing the DSV effects. The resultant deformation strategy was then further analyzed to understand the mechanism at work.

III. Numerical Method The governing equations are the two-dimensional, comp ressible, Reynolds averaged Navier-Stokes equations.

The equations are expressed in strong conservation form. They are well documented in the literature8 and will not be repeated here. The perfect gas law, Sutherland`s viscosity formula, a constant Prandtl number and an algebraic eddy viscosity model for turbulence are used with the governing equations.

The governing equations are solved using the implicit, approximate factorization algorithm of Beam and Warming9. The scheme is formulated using three-point-backward implicit time differencing and second-order finite

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difference approximation for all spatial derivatives. Constant coefficient fourth-order explicit and second-order implicit spectral dampings are added to damp high frequency oscillations and enhance stability behavior8.

The Baldwin-Lomax two layer eddy viscosity model10 was chosen in the present flow simulations. This two-layer eddy viscosity model has been used successfully in calculating separated flow in oscillating airfoils 11, 12 and has been validated by Rizzetta and Visbal 13 for airfoil dynamic stall. Ref. 14 studied the validity of the Baldwin–Lomax turbulence model for the airfoil static and dynamic stalls. It was shown that for steady flow, the Baldwin-Lomax model produced an inordinate amount of leading edge suction at highα , thereby delaying stall to an angle of attack greater than observed physically. In the present work with flow control applied, the flow is practically attached; therefore, it is proper to use the Baldwin -Lomax model.

At the inflow boundary, the velocity components and temperature are specified as freestream conditions while the pressure is extrapolated from the interior. At the outflow boundary, the pressure is set equal to the free-stream static pressure and the velocity and temperature are extrapolated from the interior. Along the grid cut-line, periodic boundary conditions were enforced. On the airfoil surface, adiabatic, impermeable wall and no-slip boundary conditions were applied, and the pressure on the boundary is obtained through the normal component of the momentum equation.

An additional consideration in terms of boundary conditions was the dynamic nature of the airfoil surface itself. The movement of the physical surface during the deformation phase had to be catered for in the boundary conditions. To achieve this, the velocity components ‘u’ and ‘v’ at the surface were defined as functions of the thickness variation in a time step, i.e. the velocity at any given surface point would be the distance that point had moved in one time step:

1n ni i

ix x

uτ

+ −=

∆ and

1n ni i

iy y

vτ

+ −=

∆ (1)

The surface would then impart this velocity to the fluid owing to the no slip condition at the boundary. The two-dimensional grid is generated by using a special Poisson solver based on the method of Thomas15 with modifications incorporated by Liu et al 16. The solver uses a multi-regional approach to determine the source term, resulting in a better control of grid line distribution. The grid topology used in this work is an O-grid, with the grid cut line extending from the airfoil nose to the outer boundary. A close-up of the grid near the airfoil is shown in Figure 1.

x/c

y/c

0 0.5 1

-0.4

-0.2

0

0.2

0.4

Figure 1: Close-up View of Grid around Airfoil

As mentioned before, the original code was designed for a rigid airfoil and had no provision for a deforming airfoil. To account for the shape variation study carried in the current project, there was a requirement to modify the original code to allow updating of grid and flow data at each time step during the deformation phase of the oscillation. Facing a similar situation, Chyu, Davis and Chang17 suggested interpolation between two extreme values as the solution. For reasonably small changes in airfoil shapes, interpolation can be used to calculate the intermediate grid positions, thus saving valuable computational time. In this project, it was decided that the grid generation code would be used to develop meshes for only the extreme shapes i.e. the two end points of the adaptive process, while grids for the intermediate shapes would be created using a linear interpolation method, much similar to the one used by Geissler and Trenker 6. Thus, the grid generation would be completed before the solver actually starts and all grid data required during the solution of the Navier-Stokes equations would be provided by an algebraic interpolation module which would use the two terminal grid files as input. The solver would, as a result, be able to run nearly unhindered through the complete adaptive process.

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IV. Code Validation The code used in the current study has been developed and validated for a variety of cases over a period of many

years 18, 19. The first experimental case used for validation was a study by McCroskey et al 20 which involved a NACA-0012 airfoil oscillating between 5 and 25 degree angles of attack with k = 0.151. While the second case validated against was at k =0.25 21. The results of the validation are depicted on the plots for the lift, drag and moment coefficients shown in Figure 2 for Case 1 and Figure 3 for Case 2. As the graphs show, there is very good qualitative consensus between the experimental and numerical results. However, quantitatively there are some differences, especially in the higher angles of attack and during the down-stroke motion of the airfoil; both regions of motion where the flow is separated. This is attributed to the use of the Baldwin-Loma x turbulence model. Fortunately, since the research being carried out in this project is primarily of a qualitative nature, the code can be used with reasonable confidence.

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NUMERICALEXPERIMENTAL

Figure 2: Code Validation - Case 1 Figure 3: Code Validation - Case 2

V. Grid Independence Three grid sizes were tested in the current research, and their results compared with the experimental data. The

three grid choices were:

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ANGLE OF ATTACK

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0 5 10 15 200

0.2

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1

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0 5 10 15 20-0.35

-0 .3

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-0.05

0

0.05

Table 1: Grid Sizes Tested for Grid Independence

The criterion for comparison was chosen to be the force curves (as with the validation). Figure 4 shows the effect of the grid size on the accuracy of results. After testing only three grids, it was felt that using the fine grid of 196 x 120 points would be reasonable as increasing the grid size any further would increase computational time and complexity without any significant accuracy gains. Outer Boundary is placed at 10 chord lengths and first body line is 0.0001 chord lengths away from the airfoil surface.

ANG LE O F ATTAC K

CL

5 10 1 5 2 0 2 50

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2 96 x 1 20 G rid1 96 x 8 0 Gri dE xp erim e ntal

3 96 x 1 50 G rid

Figure 4: Grid Independence Check

A. Dynamic Stall without Flow Control The baseline case for the oscillation of NACA -0012 airfoil was at M8 = 0.283, Re = 3.45 x 106 and

2c

kUω

∞

= = 0.1 (2)

The motion was specified as follows:

1 sin( )o tα α α ω= + (3)

where, oα = 10o and 1α = 10o

A look at the force and moment plots (Figure 5) for this case shows the fully developed dynamic stall at the end of the upstroke. This is followed by a subsequent recovery leading to a minor secondary stall, after which the flow stabilizes and returns to static lift values during the second half of the downstroke. The negative pitching moment is also very evident and forms the centre of motivation for most of the work being done on dynamic stall control studies.

Figure 5: CL, CD and CM vs. α for NACA-0012

Grid Type Body Points Body Lines Total Points Coarse 196 80 15680

Fine 296 120 35520 Finest 396 150 59400

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VI. Application of Control Strategy The actual implementation and analysis of the different flow control strategies are now discussed. The final

setup for the study was set at M8 = 0.283, Re = 3.45 x 106 and k = 0.1. The motion specified was same as defined by Equation 3 with same values for oα , 1α , M and Re.

An initial condition of uniform flow conditions was taken as the starting point. The oscillations were given until the force and moment data for two oscillations coincided with each other. Three thickness variation strategies are explored in this study: full airfoil thickness change; upper surface thickness change; and localized thickness variation. The three strategies are explained below: B. Full Airfoil Deformation (Strategy A)

Designated Strategy A, this was the simplest case, where the whole airfoil underwent a thickness change. In this strategy, the base airfoil (NACA -0012) would be allowed to deform gradually to a thicker airfoil (For example NACA-0016) as it moved in the upstroke of the oscillation. This is very similar to the work done by Lee et al6. The deformation would be reversed during the downstroke, bringing the airfoil back to its original shape at the completion of one cycle of oscillation. Figure 6 shows the deformation strategy by superimposing the initial and final shapes that the airfoil would take.

Figure 6: Strategy A - Full airfoil deformation

C. Upper Surface Deformation (Strategy B) Designated Strategy B, this strategy is a variation of the model described above i.e. only the upper surface of the

airfoil went through the thickness change. In other words, the resulting airfoil would be a hybrid of two airfoils, e.g. NACA-0012 and 0016 such that the airfoil could be considered to be 0012 on the pressure side and 0016 on the suction side. The choice regarding the upper surface was made for the obvious reasons that the dynamic stall phenomenon is connected primarily to the flow over the upper surface, with very little input of the happenings on the lower surface of the airfoil. Figure 7 depicts this variation scheme:

Figure 7: Strategy B - Upper surface deformation

D. Local Deformation (Strategy C) Strategy C is the most complex deformation planned and analyzed. In the local deformation concept, a bump (or

a dimple) can be placed anywhere on the upper surface of the airfoil. The size of the deformation, i.e. the height and width, can be varied to allow different deformation positions and amplitudes to be studied. Therefore, during the oscillation, a local deformation can be generated by specifying the starting and ending chord positions and the thickness variation required. The airfoil would start as the basic airfoil and start to deform gradually as it went through the upstroke reaching the fully deformed state at the end of the upstroke. The deformation would then disappear as gradually during the downstroke. In the current study the deformation studied was a 30% increase in thickness between 0 and 30% chord length. To allow for smooth transitions, the local deformation, or bump, is created using a ‘sine’ function allowing for smoother blending. Figure 8 depicts examples of such a deformation:

Base Airfoil

Deformed Airfoil

Base Airfoil

Deformed Airfoil

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Figure 8: Strategy C - Localized deformation

E. Strategy Comparison In the first stage (Figures 9 & 10), all the strategies are compared for their force and moment characteristics. A

look at Figure 9 immediately throws two curves into the limelight: the red and the blue, corresponding to the Hybrid airfoil (strategy B) and the 0012 – 0016 (strategy A) respectively. In fact, the dynamic stall is completely eliminated in the hybrid airfoil (strategy B). On the merit of its lift curve alone, this hybrid airfoil becomes the favorite of the study.

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0016 /0012 HYBR IDNAC A 0012 -0016NAC A-0012

Leading Edge Bump

Figure 9: Lift curve comparison of different thickness variation strategies

A look at the drag and moment comparisons (Figure 10) also favors the same two strategies. However, in these

plots, the difference is not as marked as noticed in the lift curve.

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0 5 10 15 200

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0012/0016 HYBRIDNACA 0012-0016NACA 0012

Leading Edge Bump

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-0.05

0

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0012/0016 HYBRIDNACA 0012-0016NACA 0012

Leading Edge Bump

Figure 10: Drag and moment comparison of different deformation strategies

Now that the choice has been made, a look at the 0012/0016 hybrid airfoil (Strategy B) warrants a closer look. Figures 11 and 12 present the upstroke and downstroke flow pictures of the 0012/0016 hybrid airfoil (Strategy B)

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respectively. The immediate impact of the upstroke plots is the absence of the large separated regions and the DSV from the picture. The flow is able to round the corner presented by the leading edge, thus preventing the separation bubble to form and velocity vectors clearly shows that the hybrid airfoil has a fuller boundary layer and the flow is attached.

AOA=10 deg AOA=10 deg

AOA=17 deg AOA=17 deg

AOA=19 deg AOA=19 deg

AOA=20 deg AOA=20 deg

Figure 11: Flow picture for Strategy B during Upstroke

During the downstroke, the flow re -adjusts to the downward moving airfoil surface without separation and the flow remains attached; thus the absence of spikes in the force and moment curves. In fact, except for minor separation near the trailing edge, the downstroke flow pictures do not present any evidence of flow separation at all due to the oscillation. A closer look at the vector plots also shows a fuller boundary layer profile; the flow conditions are similar to the ones seen at the end of the upstroke (Figure 11 above).

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AOA=19 deg AOA=19 deg

AOA=18 deg AOA=18 deg

AOA=17 deg AOA=17 deg

Figure 12: Flow picture for Strategy B during Downstroke

At this point, a closer look at the flow around the first 25% of the airfoil would be enlightening, especially if placed side-by-side with the baseline case. Figure 13 presents a comparison of velocity vectors at 18o angle of attack during the upstroke:

AOA=18 deg

NACA 0012

AOA=18 deg

HYBRID

Figure 13: Comparison of Flow at the Leading Edge

The base airfoil has a large reverse-flow due to the inability of the flow to follow the sharper contour of the

leading edge. On the other hand, the hybrid airfoil shows no signs of flow reversal implying that the flow is energized and attached. A comparative look at the vorticity contours for the base case and Strategy B is warranted at this point in order to further clarify the performance imp rovement being delivered by the hybrid airfoil. This comparison is shown in Figure 14 below:

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X

Y

0 0.5 1

-0.2

0

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NACA 0012

AOA=10 deg

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X

Y

0 0.5 1

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0

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0.4 AOA=19.5 deg

Figure 14: Vorticity comparison between the basic and hybrid airfoils

The vorticity contours paint a very descriptive picture of the difference in the flow characteristics of the two

airfoils as they go through the end of the upstroke. While the basic airfoil shows the classic dynamic stall vortex being formed and shed at the end of the upstroke, the hybrid airfoil manages to keep the vorticity closer to the

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surface, thus energizing the boundary layer enough to keep the dynamic stall at bay. The result is a smooth transition through the end of the stroke and an even better performance during the downstroke owing to the better start it gets.

The level of success of the hybrid airfoil is such that one is forced to question the veracity of the results. Strategy B was re-tested for grid independence and no difference with a super fine mesh was observed. The performance of the two airfoils (NACA 0012 & the hybrid) will be studied under steady state conditions at high α (18o) to put their static behaviors in perspective. The angle of attack is chosen because it is above the steady state stall angle for the NACA 0012 airfoil. The comparison shown in Figure 15 immediately throws the contrast into focus when the highly separated flow over the NACA 0012 airfoil is placed alongside the smoothly attached flow over the hybrid airfoil. Given that the hybrid airfoil is cambered, it makes sense that the flow remains attached to a higher a, thus providing a better CLmax and α CLmax. This basic difference between the NACA 0012 and the cambered hybrid airfoil is the basic reason behind the success of strategy B in eliminating the dynamic stall. In very simple words, the recipe for flow separation is already present in the NACA 0012 airfoil before it reaches the end of the upstroke, while the flow around the hybrid airfoil remains similar in both steady and dynamic states. Therefore, even though the dynamic effects allow the NACA 0012 airfoil to delay stall till the end of the upstroke, the large separation makes the stall inevitable. On the other hand, the dynamic effects of the oscillating hybrid airfoil only augment its already stable flow and allow it to complete the cycle without suffering the ill effects of dynamic stall.

NACA 0012

AOA=18 deg

HYBRID

AOA=18 deg Figure 15: Steady State Comparison at α = 18o

Non-adaptive airfoil to be studied is the hybrid airfoil of Strategy B (0016/0012 hybrid). The reason for this analysis is to compare the results of the adaptive strategy with the normal dynamic behavior of the final shape in strategy B i.e. airfoil shape at the end of upstroke. The comparison is carried out by overlaying the lift plots and displaying the flow pictures at the same stages of the oscillation as those presented earlier for strategy B (Figures 16 and 17).

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Hybrid Airfoil (Non-adaptive)

Strategy B ( Adaptive)

NACA-0012

Figure 16: Lift Curve Performance of Hybrid Airfoil

The lift curve comparison underlines the fact that the cambered hybrid airfoil performs better at all stages of the oscillation. Thus, the gradual changing of the symmetric base airfoil to this cambered shape during the upstroke in strategy B resulted in flow conditions almost as good. A comparison between the flow pictures of the hybrid airfoil and those of strategy B also highlights the similarities.

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AOA=17 deg AOA=17 deg

AOA=18 deg AOA=18 deg

AOA=19 deg AOA=19 deg

AOA=20 degAOA=20 deg

Figure 17: Hybrid Airfoil during Upstroke

Now the camber of the hybrid airfoil is varied and the difference this makes to the flow around the original

airfoil is observed. It is a variation of strategy B in which two new hybrid airfoil are compared with the original hybrid of strategy B. The new hybrid airfoils are created by replacing the top half of the 0012 airfoil with 0014 and 0018 airfoils. Thus the first (designated H1) is thinner than the 0016/0012 hybrid (H2), while the other (H3) is thicker than the original. This will form a spectrum of gradual camber change from the symmetric 0012 allowing a look at the flow effects caused by this gradual increase in camber.

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Hybrid 3: 0018/0012

Hybrid 1: 0014/0012

NACA-0012

Hybrid 2: 0016/0012

Figure 18: Lift Comparison of 3 Hybrid Airfoils

The force and moment comparisons between the three hybrid airfoils (Figure 18 and 19) show that increasing camber (or upper surface thickness) performs better during the up and down strokes i.e. the loop becomes thinner. In fact, the 0014/0012 hybrid actually goes through the stages of dynamic stall though it is much tamer than the base airfoil.

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Hybrid 2: 0016/0012

Hybrid 1: 0014/0012

NACA 0012

Hybrid 3: 0018/0012

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NACA 0012

Hybrid 2: 0016/0012

Hybrid 1: 0014/0012

Hybrid 3: 0018/0012

Figure 19: Drag and Moment Comparison of 3 Hybrid Airfoils

Figures 18 and 19 would seem to indicate that a camber increase somewhere beyond the 0014/0012 combination takes the wind out of the dynamic stall.

VII. Strategy Refinement Once a deformation strategy was chosen, it was time to refine it; to find variations that may promise an even

better improvement. In the process of this refinement it was decided that a two-pronged approach would be taken to address both the extent of the deformation and its duration during the oscillation cycle. Thus, in one analysis, different hybrid-deformations were compared while in the other, a single hybrid airfoil was studied as different deformation durations were applied i.e. the starting and stopping angles of attack of the deformation were varied. Both these concepts are described in the subsequent paragraphs. A. Physical Parameter Variation

Since the original hybrid airfoil had already shed some light on the advantage of having a small curvature on the bottom half of the airfoil while having a thicker upper half, it was decided that three hybrid variations would be tried.

The nomenclature used throughout this study for the hybrid airfoils reflects the formula ‘lower/upper’ in describing the combination. Thus, a 0012/0016 hybrid has the lower portion of the NACA-0012 and the upper half of the NACA-0016. The results are shown in Figure 20.

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0 010/001 6 H YBRID0 012/001 6 H YBRIDN ACA-00 12

0 010/001 2 H YBRID

Figure 20: Lift Curve Comparison for Variations in Hybrid Combinations

At first glance, we can see two distinct features, the two thicker hybrids (0012/0016 & 0010/0016) managed to avoid the dynamic stall condition altogether with improved lift performance during the downstroke. However, even in these results, the thinner lower half provides better performance, owing, as suggested earlier, to the reduced obstruction to the flow going around the leading edge of the airfoil at high angle of attack.

The 0010/0012 hybrid shows a significantly higher CLmax and better lift performance during the downstroke than the base airfoil. Although, the dynamic stall could not be prevented, the flow conditions were still improved by the thinning of the bottom, thus reducing the curvature of the lower portion of the leading edge.

The two thicker hybrids show similar results in the drag and moment arenas (Figure 21), with the 0010/0016 taking a slight edge over the other. However, the 0010/0012 hybrid has to pay the penalty for the higher CLmax in the form of higher negative moment and drag spikes at the end of the upstroke.

Angle of Attack

CD

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0010/0016 HYBRID0012/0016 HYBRIDNACA 0012

0010/0012 HYBRID

Angle of Attack

CM

0 5 10 15 20-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0010/0016 HYBR ID0012/0016 HYBR IDNACA 0012

0010/0012 HYBR ID

Figure 21: Drag and Moment Comparison for Variations in Hybrid Combinations

B. Strategy SCHEDULING Study

In the study of the effects of the point of start of the deformation, it was decided to compare three cases for the same basic hybrid airfoil (the 0012/0016 hybrid). These three cases would be as follows: 1. Schedule 1 - Continuous Deformation

On the one extreme it was decided that the airfoil would start deforming to the hybrid shape as soon as the oscillation started and would complete the shape change as the airfoil reached the highest angle of attack. Similarly, the return to original shape would start as soon as the downstroke started with the airfoil returning to its original shape at the lowest angle of attack. Graphically, the deformation process can be depicted as follows:

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Angle of Attack

Def

orm

atio

n

0 5 10 15 20

0

1

1

Figure 22: Schedule 1 - Continuous deformation

2. Schedule 2 - Mid-Point Deformation In the case already taken as the standard during the early parts of this project, the airfoil would start its

deformation from the mid point of the oscillation. Thus, if the airfoil is oscillating between zero and twenty degrees, the deformation would start at ten degrees. This would mean a slightly faster upward movement of the surface during the deformation stage which may, or may not, be helpful. In any case, this method makes practical sense in that it is not necessary to deform the airfoil in the lower angles of attack where even the original shape can cope well with the flow conditions.

Angle of Attack

Def

orm

atio

n

0 5 10 15 20

0

1

1

Figure 23: Schedule 2 - Mid-point deformation

3. Schedule 3 - Short Duration Deformation On the second extreme, the deformation was designed to start very close to the end of the upstroke. The idea

was to see if the deformation would still be helpful if it started at about the same time as the dynamic stall vortex appears. Also, the much faster normal velocity induced by the surface motion may become a factor in energizing the boundary layer. In this study, the airfoil was slated to start the deformation at fifteen degrees, just five degrees short of the end of the upstroke.

Angle of Attack

De

form

atio

n

0 5 10 15 20

0

1

1

Figure 24: Schedule 3 - End of stroke deformation

One thing that the deformation plots make clear is the difference in the slopes of the deformation processes i.e. the deformation rates. One of the consequences of the faster deformation rate could be that the adapting surface would induce a small normal velocity into the boundary layer. The effects of this disturbance could be beneficial if the dominant result is the energizing of the boundary layer, or detrimental if the main effect is the disruption of the boundary layer.

The resultant lift curves are placed below (Figure 25). It would appear that the sooner the shape change starts, the better it is as far as the CLmax is concerned. However, all three cases exhibit the same dynamic stall free flow conditions. The result does seem logical since a gradual change in the shape would allow the flow more time to adjust to the change in curvature. A look at the top portion of the graph (15 degree onwards) shows the detrimental effects of the abrupt change in shape as the lift curve slope suddenly drops. On the other hand the gradual change allows even the thicker airfoil to maintain the high lift capability of the thinner 0012 airfoil.

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Angle of Attack

CL

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

From 0 to 20 degNACA 0012

From 15 to 20 deg

From 10 to 20 deg

Figure 25: Lift Curve Comparison of Different Deformation Schedules

Following are the drag and moment plots for the same analysis:

Angle of Attack

CD

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

From 10 to 20 degFrom 0 to 20 degNACA 0012

From 15 to 20 deg

Angle of Attack

CM

0 5 10 15 20-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

From 10 to 20 degFrom 0 to 20 degNACA 0012

From 15 to 20 deg

Figure 26: Drag and Moment Comparison of Different Deformation Schedules

It is seen that Schedule 1 performs better than the other schemes and provides better drag and moment penalties for operating in the given regimes.

VIII. Optimum Thickness Variation Strategy On a practical note, however, designing and building an airfoil that deforms in its entirety may not be feasible, or

at least practical. In contrast, a deformation involving only the upper surface could be more realistic, where a flexible skin can be added to a rigid basic shape to allow the top surface to be inflated to thicker contours. In any case, as the aerodynamic force plots show the difference in deforming the lower surface or not are minor compared to the improvement gained overall by even the simple upper-surface-deformation case. Given the immense importance of reducing the negative moment in oscillating blades (such as helicopter rotors), the simplest deformation involving the upper surface thickening is considered the best choice.

IX. Stall Control in Highly Separated Flows The same scheme would be applied to an airfoil undergoing oscillation between 5 and 25 degrees while the

remaining flow conditions remain the same. The idea was to observe the effects of strategy B in flow conditions far more adverse than those studied earlier.

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Angle of Attack

CL

5 10 15 20 250.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

StrategyB

N ACA -0012

Figure 27: Lift curve comparison for high angle of attack oscillation

The first difference that jumps out is that unlike the cases at lower angles of attack, both airfoils exhibit dynamic stall behavior. However, the lift curve exhibited by the hybrid airfoil indicates that unlike the base airfoil which experiences dynamic stall before it reaches the end of the upstroke, and then suffers a subsequent secondary stall at the end of the upstroke, the hybrid airfoil delays the dynamic stall to the end of the upstroke. Additionally, strategy B provides a better lift performance during the downstroke. This difference seems to be a result of the amount of flow separation suffered by both airfoils during the upstroke. Obviously, flow around the base airfoil is far more disturbed during the latter half of the upstroke, which ultimately results in the shedding of the DSV 3-4 degrees before the upstroke is completed. The immediate recovery from the stall is again thwarted by the end of the upward motion, resulting in a secondary stall. On the other hand, flow around the hybrid airfoil is separated only in the last couple of degrees of the upstroke which causes the dynamic stall at the top of the loop. However, due to the better conditions, the hybrid airfoil is able to recover quickly at the start of the downstroke and thus gives a better lift curve during the downstroke. The drag and moment plots for these cases are as follows:

ANGLE OF ATTACK

CD

5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

STRATEGY B

NACA 0012

ANGLE OF ATTACK

CM

5 10 15 20 25-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

STR ATEGY B

NACA 0012

28: Drag and moment comparison for high angle of attack oscillation

Once again, like the lift curve, the hybrid scheme does not produce results as spectacular as in the lower angles of attack. However, the improvement is there and it is marked. Both the drag and moment coefficients exhibit a reduction of about 10% at the moment of stall, as compared to the original airfoil. But the main effect is that the spikes have been delayed and restricted in a very small range at the top of the upstroke. Similarly, the recovery from the dynamic stall is much faster than the other strategies, resulting in a far quicker return to somewhat normal flow.

X. Conclusion Reduction, if not outright elimination, of the effects of dynamic stall was the focus of this study which centered

around flow control techniques based on the concept of thickness variation of a 2-D airfoil undergoing oscillatory motion. As a result of the analysis carried out in the previous sections of the study, the optimum thickness variation strategy was finalized to be the case in which the original airfoil is continuously deforming during the oscillation

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such that as the angle of attack increases, the upper surface grows thicker and the lower surface gets thinner. The purpose of this deformation is not to give the airfoil camber, as such, but to create a leading edge which is favorable to the flow at the higher angles of attack. Additionally, the upper surface is required to thicken to keep the flow attached after it has rounded the bend of the leading edge.

References 1 Jacob, J. D. “On The Fluid Dynamics Of Adaptive Airfoils”, Proceedings of 1998 ASME International

Mechanical Engineering Congress and Exposition, November 15-20, 1998, Anaheim, CA, USA. 2 Filippone, A. “Dynamic Stall”, http://aerodyn.org, 2001. 3 Carr, L. W. and McCroskey, W. J. “A Review of Recent Advances in Computational and Experimental

Analysis of Dynamic Stall”, 1992. 4 Carr, L. W. and McAlister, K. W. “The Effect of a Leading Edge Slat on the Dynamic Stall of an Oscillating

Airfoil”, AIAA Paper 83-2533, AIAA/AHS Aircraft Design, Systems and Operations Meeting, Ft. Worth, TX, October 17-19, 1983.

5 Joo, W., Yee, K. and Lee, D. “Numerical Investigation on Dynamic Stall Control via Airfoil Thickness Variation”, AIAA Journal of Aircraft, Vol 39, No2.

6 Geissler, W. and Trenker, M. “Numerical Investigation of Dynamic Stall Control by a Nose-Drooping Device”, AHS Aerodynamics, Acoustics, and Test and Evaluation Technical Specialist Meeting, San Francisco, CA, Jan 23-25, 2002.

7 Chandrasekhara,M.S., Wilder,M.C., Carr,L.W., ”Control of Flow Separation Using Adaptive Airfoils”, AIAA-Paper No.97-0655.

8 Steger, J. L. “Implicit finite-difference simulation of flow about arbitrary two-dimensional geometries”, AIAA Journal, 16, 679-696, 1978.

9 Beam, R. M. and Warming, R. F. “An Implicit factored scheme for the compressible Navier-Stokes equations”, AIAA Journal, 16, 393-402, 1978.

10 Baldwin, B. and Lomax, H., “Thin-layer Approximation and Algebraic model for separated Turbulent flows”, AIAA paper 78-257, 1978.

11 Sun, M. and Sheikh, S. R. “Dynamic Stall Suppression on an Oscillating Airfoil by Steady and Unsteady Tangential Blowing”, Aerospace Science and Technology, 1999, No. 6.

12 Tuncer, I. H., Wu, J. C. and Wang, C. M. “Theoretical and Numerical Studies of Oscillating Airfoils”, AIAA J. 28 (1990) 1615-1624.

13 Rizzetta, D. P. and Visbal, M. R. “Comparative Study of Two Turbulence Models for Airfoil Static and Dynamic Stall”, AIAA J. 31 (1993) 784-786.

14 Rizzeta, D. D. and Visbal, M. R., “Comp arative Study of two Turbulence models for Airfoil Static and Dynamic stall”, AIAA Journal, Vol. 31, 1993, pp. 784-786.

15 Thomas, P. D. “Composite three-dimensional grids generated by elliptic systems”, AIAA Journal, 20, 1195-1202, 1982.

16 Liu, J. C., Sun, M. and Wu, L. Y. “Navier-Stokes analysis of circulation control airfoil” , Acta Mechanica Sinica, 11, 137-143, 1995.

17 Chyu, W. J., Davis, S. S. and Chang, K. S. “Calculation of Unsteady Transonic Flow over an Airfoil”, AIAA 12th Fluid and Plasma Dynamics Conference, Williamsburg, Va, 23-25 July, 1979.

18 Sheikh, S. R. “A Study on the Mechanism and Control of Dynamic Stall on an Airfoil”, PhD Dissertation at Beijing University of Aeronautics and Astronautics, February, 1998.

19 Hamdani, H. R. “A Study Of The Mechanisms Of High-Lift Generation By Airfoil And Wing At Small Reynolds Number”, PhD Dissertation at Beijing University of Aeronautics and Astronautics, March, 2000

20 McCroskey, W. J., McAlister, K. W., Carr, L. W., and Pucci, S. L. “An Experimental Study on Dynamic Stall on Advanced Airfoil Section”, NASA TM 84245, Vol. 1-3, 1982.

21 McCroskey, W. J., Carr, L. W., and McAlister, K. W. “Dynamic Stall Experiments on Oscillating Airfoils”, AIAA Journal 14, 1976.