Aerodynamic Modelling of the Fish Bone Active ... - Michael I Friswell

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panel method, XFOIL, against OpenFOAM, a high-fidelity computational fluid ..... A meshing tool was written in MATLAB to interface with OpenFOAM's own ...
Aerodynamic Modelling of the Fish Bone Active Camber Morphing Concept Benjamin K. S. Woods1 James H. S. Fincham2 Michael I. Friswell3 Swansea University, Swansea, UK ABSTRACT

INTRODUCTION

This paper presents a comparison of two different aerodynamic analysis methods for active camber morphing airfoils. Morphing camber airfoil concepts have for a long time been popular subjects of study. Both lower fidelity panel methods and higher fidelity computational fluid dynamics software have been extensively employed in previous work, but little direct comparison exists between the two. To this end, this paper compares a low-fidelity panel method, XFOIL, against OpenFOAM, a high-fidelity computational fluid dynamics code. A series of 2D analyses encompassing a range of morphing camber shapes and operating conditions are analyzed. The impact of changing angle of attack, start location of morphing, amount of morphing and Reynolds number on the predictions is shown. The codes compare well over a wide range of configurations, although higher angles of attack and larger camber changes lead to increased disparity.

Changing the amount of camber, or curvature, present in an airfoil is a powerful means of controlling the forces and moments that it generates under fluid flow. Furthermore, the control authority provided is significant even if only a modest portion of the airfoil chord has the ability to change camber. This is the case with trailing edge flaps, which create camber change through rotation of a discrete portion of the chord, typically the last 20-30%, relative to the rest of the airfoil. The simplicity and efficacy of these devices has led to their near ubiquitous use as the control effectors of fixed wing aircraft1 and as high lift devises for takeoff and landing.2 They have also been used for some time in a wide range of applications across a broad spectrum of fluid control applications, including helicopter rotors,3 ship rudders,4 submarines,5 and hydrofoil boats6 amongst others. Trailing edge flaps are not without drawbacks however. Chief among these is a significant increase in drag when they are used. Due to the sharp, discrete manner in which they change the airfoil‟s camber, sudden changes in pressure and flow separation are typical, resulting in large increases in drag over the baseline airfoil, particularly at large lift coefficients.2 Many researchers and inventors have sought to address this shortcoming by using “morphing” structures to create a smooth and continuous change in camber along the chord. Even as early as 1920 engineers were attempting to design structures which, through various combinations of mechanism motion and material compliance, could significantly change their camber.7 Recently this has become an intensely active area of research, with over 60 different concepts being proposed in the last two decades alone. A thorough overview of the work done is given in the review paper by Barbarino et al.,8 and several other review papers discuss it as well.9-11 Over the last two decades, compliance based approaches have become more common than mechanisms, presumably due to concerns about the weight penalty and maintenance/reliability issues associated with the large number of moving parts typical of the mechanism based concepts. Table 1 shows several examples of morphing camber concepts, in which can be

NOMENCLATURE c cd cl cmac Cp t V∞ wte x (xl, yl) (xu, yu) xs y y+ yc yt α θ

chord drag coefficient lift coefficient pitching moment coefficient coefficient of pressure non-dimensional airfoil thickness freestream velocity non-dimensional trailing edge deflection non-dimensional chordwise coordinate lower surface coordinates upper surface coordinates chordwise start location of morphing non-dimensional thicknesswise ordinate dimensionless wall distance airfoil camber distribution airfoil thickness distribution angle of attack local angle of camber line

Presented at the RAeS Applied Aerodynamics Conference, 22/7/2014, Bristol, UK 1

Senior Research Officer, College of Engineering Research Officer, College of Engineering 3 Professor, College of Engineering 2

seen a general progression over time towards simpler, compliance based designs. The detailed design of morphing active camber airfoil concepts is often a difficult, multi-disciplinary problem. This is due to the complexity and non-traditional nature of the structural geometries employed and the presence of significant fluid driven deformations, particularly in the case of concepts relying on compliance. This makes it imperative that any design effort include coupled fluidstructure interaction (FSI) analysis methods to find static equilibrium points between structural and aerodynamic forces. FSI requires accurate aerodynamic analysis tools to predict the aerodynamic forces and moments acting on the structure at each iteration as an equilibrium solution is found. While there are a number of different tools available for predicting the aerodynamic performance of an arbitrary airfoil shape, it is useful to classify them in terms of their level of “fidelity”. A high fidelity aerodynamic analysis is one which a large number of parameters are considered, within a scheme which is designed to capture as much of the flow physics as possible. These methods typically involve the solution of very large matrices of equations and are usually solved numerically. Computational fluid dynamics (CFD) is considered the benchmark for high-fidelity simulation of fluid flows, although since CFD is a general method with a number of different implementations and components, there is also a wide range of fidelity associated with it, particularly with respect to how boundary layers and fluid vorticity are modeled. In contrast, low-fidelity methods are typically simpler and less complete. They often make bigger assumptions about the fluid flow to simplify the governing equations. There are some methods which are purely analytical, often based on potential flow theory, and others which combine analytical elements with empirical corrections. Panel methods are an example of a lower fidelity aerodynamic analysis tool, as they assume inviscid flow and use potential flow theory to calculate the pressure distribution around an object. Again though, it is possible to increase or decrease the fidelity of a panel method through inclusion or exclusion of different aspects of the flow physics. The terms “high-fidelity” and “low-fidelity” are therefore not precise descriptors, by instead general labels which are useful for categorizing analysis methodologies in a wide range of fields, with the understanding that the specifics of a given analysis method and the context in which it is used are the final determiners of the quality and usefulness of the method. Within the context of morphing airfoil research it is important to choose the appropriate level of fidelity for a given task. High-fidelity methods are often more accurate and able to capture higher order flow physics, but their higher computational cost can make them too slow to use for a large number of solutions, for instance within a geometry optimization.

Table 1. Examples of mechanism and compliance based active camber concepts

(Parker, 1920)7

(Antoni, 1932)12

(Bryant and Stewart, 1963)13

Boeing (Zapel, 1978)14

DLR Belt Rib (Campanile and Anders, 2004)15

DARPA Smart Wing (Bartley-Cho et.al., 2004)16

(Daynes, Weaver, and Potter, 2010)17

Flexsys, (Hetrick, Kota, and Ervin, 2013)18

Low-fidelity methods, on the other hand, while much cheaper, can often not be relied upon to provide the level of accuracy required for more detailed design efforts, particularly where viscous or three-dimensional flow effects are important. While it can perhaps be generally said that low-fidelity tools are cheaper but less accurate, it is more informative to consider a specific case, and to explore in detail the differences.To accomplish this, we will consider a specific active camber mechanism which has been extensively studied and which therefore behaves in a manner which is well understood. We will then generalize the shape of this active camber concept such that it can be considered representative a generic active camber morphing airfoil. Two specific analysis tools, one a panel method and one CFD, will then be used to study the aerodynamics of these shapes and the results will then be compared. We begin by introducing the morphing concept.

Wind tunnel testing of the prototype seen in Fig 2 found that the FishBAC provided improved aerodynamic efficiency when compared to traditional trailing edge flaps, with increases in lift-to-drag ratio of 25% being realized at equivalent lift conditions.20 An increase in lift coefficient of ∆Cl = 0.72 between unmorphed and morphed was measured at a freestream velocity of = 20 m/s and an angle of attack of α = 0°. The large achievable deflections and continuous compliant architecture make this concept universally applicable to fixed wing applications ranging in scale from small UAVs to commercial airliners, and to rotary wing applications including wind turbines, helicopters, tilt-rotors, and tidal stream turbines.

THE FISH BONE ACTIVE CAMBER CONCEPT The Fish Bone Active Camber (FishBAC) morphing airfoil provides an alternative design architecture to both traditional discrete flaps and the other morphing camber designs in the literature. Introduced by Woods and Friswell,19 this design employs a biologically inspired compliant structure to create large, continuous changes in airfoil camber and section aerodynamic properties. The structure consists of a thin chordwise bending beam spine with stringers branching off to connect it to a pre-tensioned Elastomeric Matrix Composite (EMC) skin surface. Unlike many previous designs, all of the structural deformation occurs through compliance, with no mechanisms, linkages, or sliding skins. Additionally, both core and skin are designed to exhibit near-zero Poisson‟s ratio in the spanwise direction. Pre-tensioning the skin in the chordwise direction significantly increases the out-of-plane stiffness and eliminates lower surface skin buckling when morphing. Smooth, continuous bending deflections are driven by a high stiffness, antagonistic tendon system. Actuators mounted in the D-spar drive a tendon spooling pulley through a nonbackdrivable mechanism (such as a low lead angle worm and worm gear). A schematic overview of the FishBAC concept is shown in Fig 1. Since the tendon system is nonbackdrivable, no actuation energy is required to hold the deflected position of the structure, reducing control action and power requirements. Furthermore, the automatic locking action of the non-backdrivable mechanism allows the stiffness of the tendons to contribute significantly to the chordwise bending stiffness of the trailing edge under aerodynamic load, without increasing the amount of energy required to deflect the structure.

Fig 1. Fish Bone Active Camber concept

Fig 2. FishBAC wind tunnel test model showing deflected shape20 A significant amount of the research done to date on the FishBAC concept has focused on the development of an FSI analysis code to allow for predictions of the deformed shape and aerodynamic performance of the FishBAC under combined aerodynamic and actuator loading.21 To date this work has used XFOIL to provide the pressure distributions acting on the structure to be feed into the structural solver, and to determine the resulting performance of the converged shape. While the XFOIL code has proved useful and fast running in this work, the underlying validity of this method for airfoils with large amounts of camber at varying locations along the chord was unknown. It is for this reason that the general family of shapes achievable by the FishBAC are used in this aerodynamic analysis method comparison. If XFOIL can be shown to provide similar accuracy to a high-fidelity CFD code then its use for initial design optimization, by these authors and others exploring active camber morphing, will be well justified. COMPARISON OF ANALYSIS METHODS This section details the methodology of a generalized comparison of aerodynamic analysis methods for active camber applications, and the range of geometries and operating points studied will be defined. This study is intended to cover a wide range of potential camber morphing concepts and implementations including the FishBAC concept, and seeks to establish the general range over which the low-fidelity XFOIL panel method may be deemed sufficiently accurate relative to the higher-fidelity, but more computationally expensive OpenFOAM CFD method. Both methods predict the distribution of pressure coefficient over the airfoil surface, which is integrated to

produce lift and moment coefficients. Drag coefficient predictions including viscous effects are also available from each, as are different levels of information about the boundary layer and flow separation. These are the metrics most useful to morphing aircraft designers and will serve as the basis for our comparison. Active Camber Airfoil Geometry Definition The intention of this study is to compare the panel method and the CFD for the specific problem of the FishBAC, but in a manner which may more generally useful for a range of different morphing concepts. To this end the geometry definition has been generalized, with the specifics of the internal geometry of the FishBAC neglected. A generalized parameter driven methodology is used instead, driven by a polynomial shape function overlaid onto a NACA 4-series airfoil.

in a manner which allows for direct control of the amount of trailing edge deflection: { (

)

(

(2)

)

with the value of wte determining the maximum deflection of the camber line at the trailing edge. Note that the camber line is defined in a piecewise fashion due to the “rigid” portion of the airfoil at the leading edge. The thickness distribution, yt, is then overlaid on the camber deflection, yc, at right angles to the camber line to define the points for the upper (xu,yu) and lower (xl,yl) surfaces, according to: (3) (4) (5) (6) Where θ is the local slope of the camber line, found from: ( )

Fig 3. Morphing camber geometry definition The basic definition of the active camber geometry can be seen in Fig 3. The baseline airfoil is the NACA 0012, which a common choice in previous research due to its wellknown behavior, moderate thickness (which is useful when installing mechanisms and actuators), and applicability to a wide range of applications.8 In this study the baseline airfoil is morphed by adding camber to specified regions of the chord. As can be seen in Fig 3, a portion of the leading edge remains fixed, or non-morphing. The start of the morph is given by the parameter xs and is one of the primary variables of interest in this study. The airfoil shape is built up by overlaying the thickness distribution for the NACA 0012 airfoil onto a parametrically defined camber line. As in the standard definition of NACA airfoils, the thickness is added perpendicular to the local camber line. The NACA four series thickness distribution, yt(x), is defined analytically according to:22 [ ( )

( )

√ ( ) ]

(1)

where x is the non-dimensional chord, t is the nondimensional airfoil thickness (t = 0.12 for a NACA 0012), and the resulting thickness distribution is also nondimensional. The camber line for the morphing portion of the airfoil is defined from a third order polynomial shape function. A third order polynomial is well suited to the FishBAC concept,21,23 but is also likely to be generally useful for describing the shape of any morphing camber concept which relies on compliance or bending of internal structural members. In this study, the shape function is parameterized

(

)

(7)

This simple parameterization of a generalized active camber morphing airfoil shape allows for a wide variety of different configurations to be made quickly and efficiently. A range of different active camber shapes were created by varying the start location of the morph and the amount of deflection at the trailing edge. Furthermore, each airfoil shape was run over a range of angles of attack, α, and at two different Reynolds numbers. The configurations tested are outlined in Table 2 and the different geometries are shown in Fig 4. Table 2. Analysis parameters Parameter baseline airfoil chord, c morphing start, xs max. deflection, wte angle of attack, α Reynolds # freestream velocity,V∞

Value NACA 0012 300 [0.25, 0.5, 0.75] [0, 0.05, 0.1] [0 ─ 14] [6.75e5, 1.35e6] [34, 68]

Units n/a mm n/a n/a deg n/a m/s

Note that since the chord is fixed, defining the Reynolds number automatically determines the freestream velocity. The velocity was not varied separately; the relevant values are shown here for reference. The step size used for the angle of attack sweeps differed between the analysis methods, as will be discussed further below.

density a priori is difficult and would likely require multiple mesh-dependency studies to be performed. This might negate any time saving gained in the first place.

(a)

(b) Fig 5. Typical mesh for CFD analysis – close up of airfoil region, xs = 0.25, wte = 0.1

(c) Fig 4. Geometries studied, a) xs = 0.25, b) xs = 0.5, c) xs = 0.75 OpenFOAM Computational Fluid Dynamics Analysis OpenFOAM, a set of open source fluid simulation and numerical solution tools, is used to produce the CFD results in this study. A meshing tool was written in MATLAB to interface with OpenFOAM's own blockMesh tool to rapidly generate structured multiblock hexahedral meshes. Although these structured meshes tend to contain more cells than comparable unstructured meshes, they allow for good control of the cells within the boundary layer so that the first cell height, total boundary layer thickness, and growth rate can be carefully controlled. Additionally, meshing can be automated easily, with a selected mesh being produced within a few seconds. In this work, a low Reynolds number mesh is used, where the first cell height is located at a dimensionless wall distance of y+ = 1. An example mesh can be seen in Fig 5. A C-shaped flow field was used, which extended in a circular arc 30 chord lengths vertically and upstream, with a rectangular extension covering 60 chord lengths downstream. Each mesh contained 120,000 hexahedral shells. Computational cost in CFD methods is highly dependent upon the number of cells used. The 120k cell meshes used in this paper are far finer than required to compute most of the flows examined. However, a high density of cells is required for high angle of attack flows in order to capture regions where separation develops. In this study, the mesh density was chosen for these high α cases, and then used for all angles of attack. Computation time could be dramatically reduced by using coarser meshes for the cases where no separation is expected, but selection of an appropriate mesh

Since steady state solutions are sought, the simpleFoam solver within OpenFOAM is used which utilises the SIMPLE algorithm to solve the incompressible Reynolds Averaged Navier-Stokes (RANS) equations. Spatial gradients are approximated with 2nd order linear schemes, limited by the Sweby flux limiter for stability.24 In these RANS simulations, closure is provided by Menter's k-ω SST turbulence model, as this two-equation model is known for its stability and accuracy. Automatic wall treatment is utilized in OpenFOAM which blends the known analytical solutions for ω in the viscous sub-layer with those in the log-law region based upon the distance of the first cell to the surface. The formulation of Menter's SST, in addition to this blending of ω based upon distance to the wall, allows the turbulence model to work for both low ) meshes y+ = 1 and high Reynolds number ( without the need to change its formulation or boundary conditions. A simple zero-gradient condition for k provides an accurate boundary regardless of the mesh used.25 Freestream turbulence conditions are based upon estimates for turbulence intensity, taken to be 1%, and length-scale, taken to be the chord length. The standard formulation of Menter's SST has been modified in OpenFOAM to incorporate some of the modifications by Hellsten,26 but does not include a transition model. This means that turbulent boundary layers are produced from the leading edge of the airfoil regardless of Reynolds number. For the OpenFOAM analysis, the angle of attack was incremented by two degrees over the chosen range: α = [0:2:14]°. XFOIL Panel Method Code The aerodynamic performance of the 2D cambered airfoils was also estimated using the XFOIL panel method code. XFOIL is based on an analytical high-order panel method which uses a linear-vorticity stream function method to solve for the flow field which produces streamlines along the boundaries of the airfoil.27 As linear-vorticity theory

assumes inviscid flow, it alone cannot predict viscous drag effects. To improve prediction accuracy, XFOIL therefore also includes a viscous boundary layer component to calculate skin friction drag and flow separation, offering a more complete drag prediction than purely inviscid codes. A two-equation lagged dissipation integral boundary layer formulation with an en transition model is used to describe the wake and boundary layer.27 XFOIL is intended to be used in situations with small to moderate boundary layer thickness and for angles of attack up to and just beyond stall. The extremes of the chosen range of geometries and angles of attack will likely create large amounts of separation and will take the airfoils past stall, such that these stated limitations can be tested. The code requires as inputs the aerodynamic conditions, [Mach number, M#, angle of attack, α, and Reynolds number, Re] and the non-dimensionalized airfoil skin coordinates. Due to the lack of a flow field mesh, XFOIL requires less pre-processing than OpenFOAM. Just the coordinates of the airfoil surface are sufficient to fully define the analysis geometry. In order to speed convergence, the built in panel refinement command is used on the geometry to concentrate the panels in the areas of highest surface curvature. As mentioned above, the OpenFOAM solver uses a fully turbulent boundary layer. XFOIL on the other hand includes a transition model to model the transition from laminar to turbulent. In order to provide the most meaningful comparison between the two codes, the flow in the XFOIL analysis has been forced to trip from laminar to turbulent at a point very close to the leading edge. For the XFOIL analysis, the angle of attack was incremented by a quarter of a degree over the chosen range: α = [0:0.25:14]°. Computational Cost There is a significant difference in the computational cost of these two methods. This is typical when comparing a lower fidelity method to a higher one, and it is important to have an understanding of the differences. Each OpenFOAM runs require two separate steps; meshing and solving. The structured mesher developed here is able to mesh a given geometry in roughly 5 seconds on a single CPU core. For the CFD solutions parallel processing was implemented, using ten Xeon X5650 2.67 GHz cores. Table 3 shows a number statistics for the run times.

Reynolds numbers simulated (Re = 1.35e6) took on average more than twice as long, in part due to a small number of the cases which took significantly longer to converge. Taking the two steps together, the average time for a single OpenFOAM solution was 915 seconds. In contrast, each point in the XFOIL analysis was able to run in an average of 0.17 seconds. This difference is even more significant given that the XFOIL was not parallelized, being run on a single Intel i7 CPU clocked at 3.0 GHz. For use in design work, particularly in optimization algorithms which will often consider a large number of analysis points, it is important to manage the computational cost of the aerodynamic analysis to keep overall solution times reasonable. It is therefore desirable to be able use low-fidelity codes for the bulk of such work, with perhaps high-fidelity analysis serving as a design check at the end of, or at various points during, a design iteration. It is important when considering the results and discussion below to consider the relative cost of the two methods. RESULTS AND DISCUSSION This section will compare the two analysis codes through consideration of the predicted pressure coefficient distributions, the calculated aerodynamic coefficients and the impact of the various design variables. Pressure Coefficient Distributions The distribution of pressure coefficient, CP, over the surface of the airfoil leads to the generation of lift, pitching moment, and the inviscid portions of the drag. It is therefore important to be able to predict pressure coefficient accurately. Consider first the pressure distribution of the baseline NACA 0012 airfoil at a high angle of attack, as seen in Fig 7. Note the high level of agreement between the two methods. XFOIL does predict higher Cp‟s on the upper surface for the range of non-dimensional chord (0.007 < x < 0.03), and there is a small degree of difference towards the trailing edge, but generally the agreement is very good. As this is a well behaved symmetric airfoil, one would expect good agreement.

Table 3. OpenFOAM solution time statistics Parameter Re = 6.75e5 Min time (s) 246.4 Max time (s) 2646.3 Mean time (s) 524.6 Median time (s) 352.9 Standard deviation 521.3

Re = 1.35e6 235.3 2776.0 1294.9 631.7 985.3

For the entire data set run here (both Reynolds numbers), the average run time was 910 seconds. However, this single number does not tell the full story, as the higher of the two

Fig 6. Pressure coefficient distribution, NACA 0012, α = 14º, Re = 6.75e5

If we now investigate the more challenging case of a cambered airfoil with the morphing portion starting at 25% chord (xs = 0.25), 10% trailing edge deflection (wte = 0.1) at an angle of attack of 8 degree, then we can start to see the impact of camber on the pressure coefficient distribution. In Fig 7 it can be seen that the shape of the Cp plot has changed from that in Fig 6. Lower pressures (indicated by larger magnitude negative Cp‟s) are developed over more of the chord on the upper surface, and there is a distinct inflection at a non-dimensional chord of x = 0.75, which is the location of the beginning of the added camber. The XFOIL and OpenFOAM are still in very good agreement though, with a slight disparity right after the leading edge suction peak, in the same location as was seen in Fig 6.

8, the disparities between the methods are indeed larger than in the other cases, with a large difference in the magnitude of the pressure peak on the upper surface of the leading edge. Interestingly though, the overall shape of the Cp plot is still quite similar, with the general behavior being fairly well captured. Aerodynamic Coefficients We will now consider the effect of integrating the Cp distributions and fully incorporating the viscous effects by considering a number of polar plots of the various aerodynamic coefficients. In Fig 9 we see the predictions for the lift coefficient, cl, versus angle of attack for Re = 6.75e5 and xs = 0.25. All three amounts of camber are plotted together. In this and all the plots that follow, the solid lines are the XFOIL results and the circles are the OpenFOAM results. Here we see that the two methods are in close agreement for most of the angles of attack and trailing edge deflections tested. XFOIL is predicting earlier stall however, particularly for the 10% deflection case (wte = 0.1) where stall appears to be occurring 2-3 degrees before the CFD result. The predicted stall behavior is fairly mild however, so the agreement is still fairly good even after stall. Note that the XFOIL results for wte = 0.1 do not cover the full alpha range due to a lack of convergence in the code. The unconverged results are omitted in all of the plots which follow as well.

Fig 7. Pressure coefficient distribution, xs = 0.25, wte = 0, α = 8º, Re = 6.75e5

Fig 9. Lift predictions for xs = 0.25 and Re = 6.75e5, solid lines are XFOIL, circles are OpenFOAM

Fig 8. Pressure coefficient distribution, xs = 0.75, wte = 0.1, α = 14º, Re = 6.75e5 Moving to the more extreme end of the configurations tested, we now consider the cambered airfoil starting at 75% chord (xs = 0.75) with 10% trailing edge deflection (wte = 0.1) at an angle of attack of 14 degrees. This particular airfoil has the most extreme change in camber tested, and is at the highest angle of attack tested. It is here that we would perhaps expect to see the greatest difference in predictions, given the very different methodologies used to handle the boundary layers and flow separation. As can be seen in Fig

The drag coefficient, cd, predictions for the Re = 6.75e5, xs = 0.25 cases are shown in Fig 10. Here we see very good agreement for the uncambered airfoil (wte = 0), but increasing levels of difference as the trailing edge deflection is increased. XFOIL is consistently predicting higher drag in these cases. While at the extreme end of the alpha range the differences are quite large, over the range of angles typically used in most aerospace applications, roughly (0 < α < 8), the agreement is actually quite good. The rapid increase in drag beyond this in the XFOIL results can be linked to the earlier prediction of stall seen in Fig 9. The flow at this point has separated and the large wake disturbance created leads to larger drag predictions.

Fig 10. Drag predictions for xs = 0.25 and Re = 6.75e5

Fig 12. Lift predictions for xs = 0.5 and Re = 6.75e5

Next we consider the pitching moments about the quarter chord, cmac, which are shown in Fig 11. While these predictions are again in generally good agreement, there is noticeably more difference between the methods over the primary range of interest (0 < α < 8) than there was for lift and drag. Again, the differing predictions of the onset of stall lead to divergence in the predictions for the wte = 0.1 airfoil at high angles of attack.

In Fig 13 can be seen the drag predictions for xs = 0.5 and Re = 6.75e5. The agreement is again very good for angles of attack up to 8°, after which XFOIL predicts higher drag.

Fig 13. Drag predictions for xs = 0.5 and Re = 6.75e5

Fig 11. Moment predictions for xs = 0.25 and Re = 6.75e5 These same three polars will now be shown for the 50% chord morphing camber cases, xs = 0.50, at the same Reynolds number, Re = 6.75e5. Fig 12 shows the lift polar, where again the solid lines are the XFOIL results and the circles the OpenFOAM predictions. Interestingly, for the wte = 0.05 case XFOIL was only able to converge for angles up to 11.25°, whereas it was able to solve to 13º for the larger deflection wte = 0.1 case. This may be due to particulars of the geometry, but generally speaking convergence of XFOIL at such large angles of attack cannot be guaranteed. As was the case with xs = 0.25, stall is predicted earlier in XFOIL, leading to divergence at higher angles of attack.

Fig 14. Moment predictions for xs = 0.5 and Re = 6.75e5 In Fig 14 can be seen the moment coefficient predictions versus angle of attack. In comparison to Fig 11 we see that significantly higher levels of pitching moment are predicted with the xs = 0.5 airfoils than was seen for xs = 0.25. Considering that the differences in lift produced by the different starting locations is significantly less (as seen by

comparing Fig 9 to Fig 12), the large increase in moment would logically be attributable to the rearward movement of the camber. This generates larger magnitude pressure coefficients further back on the airfoil, leading to larger pitch down moments. Again the agreement between the methods is good.

in Fig 4c, the change in camber for these cases is actually quite severe. It is not surprising then that there can be seen here more difference in the two methods. For both the lift and drag there are larger differences over the full range of angles of attack than what was seen in the previous results, although the divergence due to earlier stall with XFOIL looks very similar. Despite this increasing disparity as the camber moves rearwards, the overall agreement between the models is still quite good over the entire range tested. Effect of Start Location of Morphing We can further consider the impact of the start location of the morph by setting the trailing edge deflection to 5% and varying xs, as is done in Fig 18 and Fig 19. The lift predictions in Fig 18 show a moderate increase in lift at a given angle of attack with increasing xs. It can also be seen that XFOIL generally predicts higher lift coefficients and, as noted before, earlier stall than OpenFOAM.

Fig 15. Lift predictions for xs = 0.75 and Re = 6.75e5

Fig 18. Lift predictions for wte = 0.05 and Re = 6.75e5

Fig 16. Drag predictions for xs = 0.75 and Re = 6.75e5

Fig 19. Drag predictions for wte = 0.05 and Re = 6.75e5

Fig 17. Moment predictions for xs = 0.75 and Re = 6.75e5 We now consider the most rearward camber that was simulated. Fig 15 – 16 show the lift, drag and moment predictions for the xs = 0.75 and Re = 6.75e5 cases. As seen

Interestingly, the effect of xs on drag is less pronounced. While both analysis methods predict an increase in drag at a given angle attack as xs increases, the amount of change is quite small. Taken together, the lift and drag results in Fig 18 and Fig 19 provide an interesting insight for the morphing aircraft designer. It can be seen that for the range of lift coefficients

achieved here, pushing the start of the morphing section back towards the trailing edge can increase lift production with little drag penalty. Larger values of xs are also useful from a structural standpoint, as less of the baseline structure has to be modified leading to likely improvements to the global strength and stiffness of the wing/blade, and potentially reducing any weight penalties associated with the morphing device. Of course any such decision must be made in the context of a full system level analysis, but this result from an aerodynamic point of view is interesting and perhaps unexpected. This can be further seen in Fig 20 where the lift versus drag results are shown. Only the XFOIL results are plotted as overlaying the OpenFOAM results makes for a very cluttered plot in the initial steep region of the figure. Here it is clear that the xs = 0.75 airfoil is outperforming the others above lift coefficients of Cl ~ 1.1. Below this, the performance is so similar as to be nearly indistinguishable.

Fig 21. Lift results, xs = 0.5, solid lines and circles: Re = 6.75e5, dashed lines and diamonds: Re = 1.35e6

Fig 22. Drag results, xs = 0.5, solid lines and circles: Re = 6.75e5, dashed lines and diamonds: Re = 1.35e6 Fig 20. Lift versus drag results, wte = 0.05 and Re = 6.75e5, XFOIL only Effect of Reynolds Number Here we consider the effect of Reynolds number on the predictions of these two codes. This is done in an abbreviated fashion by considering Fig 21 and Fig 22. Here the solid lines are the XFOIL results and the circles the OpenFOAM results for Re = 6.75e5 wheras the dashed lines are the XFOIL results and the diamonds the OpenFOAM results for Re = 1.35e6. The trends with respect to Reynolds number are the same for both codes: increasing the Reynolds number leads to increased lift and decreased drag across the entire range of angles of attack. The agreement between the two analysis methods does not seem to change significantly for the two Reynolds numbers, although the CFD does predict slightly larger differences in lift due to Reynolds number at lower angles of attack than the XFOIL.

Note on Flow Filed Visualization One advantage of the high-fidelity code is the ability to fully visualize the flow field around the airfoil. This allows for a more detailed understanding of the flow physics, particularly with respect to viscous effects such as boundary layers and flow separation. While XFOIL does also calculate the boundary layer (using a viscous analysis tool coupled to the inviscid panel method), it does not include viscosity effects in the full flow field solution, and does not include the powerful flow visualization tools available with CFD methods. The CFD results are therefore useful for considering again the observation made above with respect to the potential advantages of moving the morphing section towards the trailing edge. It was noted in Fig 20 that the xs = 0.75 airfoil had lower drag at high lift coefficients than the xs = 0.25 airfoil. Fig 23 and Fig 24 show OpenFOAM flow field velocity plots for these two geometries at α = 14º.

trailing edge displacement. A wide range of angles of attack were studied, in addition to two different Reynolds numbers corresponding to two different freestream velocities. Generally, the two tools were found to have quite good agreement across the range of configurations tested, and the following detailed conclusions can be drawn:  With an average run time of 915 seconds for a single solution in OpenFOAM versus 0.17 seconds for XFOIL, the CFD code was significantly more computationally expensive.  Agreement between the codes is very good with all of the geometries studied for angles of attack up to roughly 8º.  The differences between the methods grow at larger angles of attack, but are still reasonably small at the upper extents of the range tested.  XFOIL predicts higher levels of lift and drag at a given angle of attack for all of the configurations tested.  XFOIL predicts stall at angles of attack 2-3° lower than OpenFOAM.  The start location of the morph is found to impact performance; morphing closer to the trailing edge is found to reduce drag over a wide range of lift coefficients.  Changing Reynolds number has a similar effect on both codes, with higher lift and lower drag predicted at Re = 1.35e6 than at Re 6.75e5.

Fig 23. OpenFOAM flow field predictions, xs = 0.25, wte = 0.1, α = 14º, Re = 6.75e5

Fig 24. OpenFOAM flow field predictions, xs = 0.75, wte = 0.1, α = 14º, Re = 6.75e5 The velocity contours are useful for highlighting the location of the boundary layers. In both cases we see that the high angle of attack leads to similar regions of separated flow and a similar sized wake trailing the airfoil. The predicted coefficients for xs = 0.25 are cl = 1.64 and cd = 0.103, and for xs = 0.75 cl = 1.951 and cd = 0.099. These results therefore provide insight into the similar drag performance of these two airfoils in this operating condition. From the perspective of lift generation, it can be seen that the delayed camber of the xs = 0.75 airfoil leads to a thinner boundary layer for more of the upper surface of the airfoil, leading to higher surface velocities and lower surface pressure, and therefore more lift generation. The larger suction peak seen on the front of the xs = 0.75 airfoil is another likely source of increased lift. Taken together, the increased lift generation of the xs = 0.75 airfoil with its similar drag performance leads to its improved performance over the xs = 0.25 airfoil, as seen in Fig 20. CONCLUSIONS This paper has presented a comparison of two different aerodynamic analysis tools for use in the analysis of active camber morphing airfoils. XFOIL, a low-fidelity panel method and OpenFOAM a high-fidelity computational fluid dynamics code were used to predict the performance of a range of generalized active camber morphing airfoil shapes. The airfoil geometries studied included a range of starting locations for the morphing with different levels of morphed

Overall, the low-fidelity XFOIL panel method has been shown to provide very similar aerodynamic performance predictions to the high-fidelity OpenFOAM computational fluid dynamics code over a wide range of geometries and operating conditions relevant to active camber morphing airfoils, but at greatly reduced computational cost. ACKNOWLEDGEMENTS The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. [247045]. REFERENCES 1

Abzug, M.J., and Larrabee, E.E. 2002. Airplane Stability and Control, Second Edition; A History of the Technologies That Made Aviation Possible, Cambridge University Press, Cambridge, UK, pg. 3. 2 Raymer, D. 2006. Aircraft Design: A Conceptual Approach, 4th Edition, American Institute of Aeronautics and Astronautics, Reston, VA. 3 Kaman, C.H. 1948. “Aircraft of Rotary Wing Type,” U.S. Patent No. 2,455,866, filed August 19, 1946, issued December 7. 4 Overgaard. O., and Livingston, J. 1926. “Recent Development of the Ship Rudder with Particular Reference to the „Flettner Rudder‟,” Trans. Soc. Naval Arch. And Marine Eng., 34:205.

5

Burcher, R., and Rydill, L. 1995. Concepts in Submarine Design, Cambridge University Press, Cambridge, England. 6 Shinners, S. 1998. Modern Control System Theory and Design, John Wiley & Sons, Inc., New York, NY, pp. 22-23. 7 Parker, H.F. 1920, “Variable Camber Rib for Aeroplane Wings,” US Patent 1,341,758, filed July 17, 1919, issued June 1, 1920. 8 Barbarino, S., Bilgen, O., Ajaj, R.M., Friswell, M.I., Inman, D.J. 2011. “A Review of Morphing Aircraft,” Journal of Intelligent Material Systems and Structures, June, 22(9):823-877. 9 Giurgiutiu, V. 2000. “Recent Advances in Smart-Material Rotor Control Actuation,” Proceedings of the AIAA/ASME/ASCE/AHS/ASC 41st Structures, Structural Dynamics and Materials Conference, AIAA-2000-1709, Atlanta, GA, April 3-6. 10 Chopra, I. 2002. “Review of State of Art of Smart Structures and Integrated Systems,” AIAA Journal, 40:2145- 2187. 11 Weisshaar, T.A. 2013. “Morphing Aircraft Systems: Historical Perspectives and Future Challenges,” AIAA Journal of Aircraft, 50(2), March-April. 12 Antoni, U. 1932 “Construction of Flexible Aeroplane Wings Having a Variable Profile,” US Patent No. 1,886,362, filed August 24, 1931, issued November 8, 1932. 13 Bryant, G.D., and Stewart, A.W. 1963. “Variable Camber Airfoil,” US Patent No. 3,109,613, filed Nov. 28, 1960, issued Nov. 5, 1963. 14 Zapel, E.J. 1978. “Variable Camber Trailing Edge for Airfoil,” US Patent No. 4,131,253, filed July 21, 1977, issued Dec. 26, 1978. 15 Campanile, L.F. and Sachau, D. 2000. “The Belt-Rib Concept: A Structural Approach to Variable Camber,” Journal of Intelligent Material Systems and Structures, 11(3). 16 Bartley-Cho, J.D., Wang, D.P., Martin, C.A., Kudva, J.N., and West M.N. 2004. “Development Of High-Rate, Adaptive Trailing Edge Control Surface For The Smart Wing Phase 2 Wind Tunnel Model,” Journal of Intelligent Material Systems and Structures, 15: 279– 291. 17 Daynes, S., Weaver, P., and Potter, K. 2010. “Device Which Is Subject To Fluid Flow,” US Patent Application No. US 2010/0213320, filed Feb. 17, 2010. 18 Hetrick, J.A., Kota, S., and Ervin, G.F. 2013. “Compliant Structure Design of Varying Surface Contours,” US Patent No. 8,418,966, filed Apr. 27, 2007, issued Apr. 16, 2013. 19 Woods, B.K.S., and Friswell, M. I. 2012. “Preliminary Investigation of a Fishbone Active Camber Concept,” Proceedings of the ASME 2012 Conf. on Smart Materials, Adaptive Structures and Intelligent Systems, Sept 19-21, Stone Mountain, GA. 20 Woods, B.K.S., Bilgen, O., and Friswell, M.,I. 2014. “Wind Tunnel Testing of the Fishbone Active Camber Morphing Concept,” Journal of Intelligent Material Systems and Structures, Published online before print, Feb. 5. DOI: 10.1177/1045389X14521700 21 Woods, B.K.S., and Friswell, M.I. 2013a. “Fluid-Structure Interaction Analysis of the Fish Bone Active Camber Mechanism,” Proceedings of the 54th AIAA Structures, Structural Dynamics, and Materials Conference, Boston, MA, April 8-11.

22

Moran, J. An Introduction to Theoretical and Computational Aerodynamics, Dover, New York, 1984. 23 Woods, B.K.S. and Friswell, M.I., “Structural Characterization of the Fish Bone Active Camber Morphing Airfoil,” AIAA SciTech Conference, January 13-17, 2014, National Harbor, MD. 24 Sweby, P.K., “High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws” SIAM Journal on Numerical Analysis, October 1984, 21, (5), pp. 995-1011. 25 Menter, F., Ferreira, F.C., Esch, T., and Konno, B., “The SST Turbulence Model with Improved Wall Treatment for Heat Transfer Predictions in Gas Turbines,” Proceedings of the International Gas Turbine Congress, 2003, Tokyo. 26 Hellsten, A., “Some Improvements in Menter's k-ω SST Turbulence Model,” Proceedings of the 29th AIAA Fluid Dynamics Conference, June 15 – 18, 1997, Albuquerque, NM, AIAA-98-2554 27 Drela, M. 1989. “XFOIL: An Analysis and Design System of Low Reynolds Number Airfoils,” Low Reynolds Number Aerodynamics - Lecture Notes in Engineering, Springer-Verlag, 54:1-12.