Aerodynamic Response of Stationary and Flapping wings in Oscillatory Low Reynolds Number Flows. Russell Prater *, Yongsheng Lian

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1 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 09-2 January 202, Nashville, Tennessee AIAA Aerodynamic Response of Stationary and Flapping wings in Oscillatory Low Reynolds Number Flows Russell Prater *, Yongsheng Lian University of Louisville, Louisville, KY, In this paper, the flight characteristics of stationary and flapping wings in low Reynolds number flows with gusting conditions are examined numerically. The aerodynamic forces are calculated by solving the incompressible Navier-Stokes equations on overlapping grids using the pressure-poisson method. The impact of a gust modeled as a uniform flow with a sinusoidal velocity component on the cycle averaged lift force and the lift variation over a gust cycle are examined. Comparisons are made between stationary wings and flapping wings to assess if either mode offers an advantage in reducing the force variations or increasing the force generation over the other mode. Different tandem wing configurations are assessed and compared to a single wing in isolation. The spacing between the two wings in a tandem configuration is also considered. Our study found that compared to a stationary wing, the flapping wing can effectively alleviate the lift variation due to wind gust. However, a flapping wing in isolation exhibits less of an increase in lift force at the higher gust s compared to a stationary wing. For tandem wing configuration the addition of a stationary wing behind a flapping wing can not only reduce the gust effect but increase the lift generation. Nomenclature c = Chord length C L = Coefficient of lift f = Frequency of freestream oscillation, Hz h = Plunge height k = Reduced frequency = πfc/u ave L = Lift L 0 = Lift from a non-oscillating freestream velocity p = Pressure Re = Reynolds Number St = Strouhal Number t = time, seconds T = Oscillation period U = Freestream velocity α = Angle of attack (AoA) ρ = Density σ = Viscous Stresses μ = Viscosity θ = Pitch Angle φ = Phase Angle Subscripts amp = The of a parameter ave = The average of a parameter flap = A parameter describing the pitch-plunge motion gust = A parameter describing the gust * Ph.D Snt, Mechanical Engineering department Assistant Professor, Mechanical Engineering department, Senior AIAA Member Copyright 202 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

2 Non-Dimensional Wind Shear I. Introduction There is a growing interest in developing Micro Air Vehicles (MAVs) for both civil and military applications. Anderson identified many of these applications including, but not limited to, indoor and outdoor proximal reconnaissance, urban and military environmental assessment, airborne telecommunication relays in countries that lack infrastructure, geophysical surveying, and search and rescue missions. Anderson identified as key characteristic of MAVs as being sufficiently small to be able to fly inside buildings, caves, etc., operable in all types of weather, including harsh gusts, able to be highly maneuverable in confined spaces and capable of performing long cruise segments. Additionally, for the specific case of a flapping hovering MAV, Anderson identified as two of the key challenges for the vehicles the environmental concerns (the large number of obstacles in the operation area) as well as the gusty and sheared winds that will be encountered. These two challenges are related to each other in that the specific makeup of the environment as well as the placement of obstacles tends to directly affect the nature of the wind flow. Recent research 2,3 has enabled the engineering requirements of MAVs to be mapped into two broad categories: range/endurance and maneuverability/gust tolerance, both will be investigated in this paper. In this paper we study the impact of gusts on lift generation which has a direct impact on the endurance of the vehicle and we also investigate the impact of gust on lift variation measured by the peak to peak lift force generation. There have been a large number of studies that have sought to quantify the expected variations in wind profiles both in urban and non-urban environments. These studies describe the wind shear gradients through the use of the non-dimensional parameters describing the terrain 4. The accuracy of these predications are variable, Högström 5 found that under idealized conditions the accuracy in predicating the long term averaged momentum transfer above the roughness sublayer (RSL) may be adequate but the instantaneous predications are inaccurate more than 80% of the time. Below the RSL the accuracy is much worse because the individual local roughness elements (terrain features, buildings, vegetation, etc.) will directly impact a measurement whereas above the RSL a homogenous horizontal roughness derived from the bulk roughness of the area can assumed making it much easier to map the area. This distinction is significant for MAV applications because the region of MAV operation will include the roughness sublayer. Raupach et al. 6 in a study of different urban and suburban areas showed that the roughness sublayer extends hundreds of meters above the ground. In an experimental study carried out by Vogel and Pendergrass 7, measurements of the wind shear were taken within the roughness sublayer at various altis in Washington D.C. The measurements were averaged over a 2.5 hour period for a year long period and were compared with a proposed predication by Garratt 8. Figure shows the comparison between the predication and the measurements taken Experimental Data Theoretical Predicition Alti Over Chareceristic Length Figure : Non-Dimensional wind shear versus measurement height over RSL height from Vogel and Pendergrass 7. As can be seen the predicted trend significantly deviates from the measurements. In addition to the deviation from the predication there was a large range of recorded values at the altis the measurements were taken. This illustrates one of the challenges in studying MAVs operating in gusty conditions, the impracticality of accurately predicting the exact nature of a gust even under ideal conditions. The time instantaneous nature of the environment is purely chaotic. Studies by Graybeal 9 have shown a correlation among wind gust factors such as the peak gust factor, peak five minute gust factor and the peak mile gust factor and the mean daily wind speed. However conditions that would be needed to predict these gust factors in advance are not currently understood in detail. 2

3 In urban environments the specific layout of the surrounding area directly impacts the nature of the wind gusts. In wind tunnel tests carried out by Carpenter and Locke 0 it was shown that terrain factors such as the size of, the spacing between, the general smoothness of, and the number of non-homogenous terrain elements all play a role in the gust. Experimental measurements by Dutt showed that the influence of building geometry and spacing on the fication of wind speeds. He noted that the alleyways between buildings had significant channeling effects that lead to large increases in the local wind velocity. Kastner-Klein et al. 2 and Vachon et al. 3 have experimentally shown that turbulence created by traffic is a significant source of disturbance when compared to the mean wind flow. This turbulence is attributed to both the increases in the thermal energy from the traffic and the kinetic energy imparted by the traffic motion. These studies all illustrate one of the main challenges in MAV flight control, i.e., it is difficult to accurately model the wind profiles. The wind profiles are dependent on the immediate surroundings which differ greatly from area to area. The chaotic behavior of the local incoming wind and the behavior of moving objects within the immediate area further complicates the problem. The success of an active control strategy to reduce variation in the lift force generation highly depends on the accuracy of the wind profile. Lissaman 4, and Patel and Kroo 5 have used active controls to extract energy from gusts in real UAV flights and have shown a large swath of results: most trials provided positive results but some decreased the flight efficiency. A previous study by Lian and Shyy 6 showed that introducing a sinusoidal oscillation to the flow velocity around an airfoil can trip flow that would be laminar into turbulence. Additionally they showed that the response of a flexible wing in oscillatory flow is similar to that of a rigid airfoil. In another paper Lian and Shyy 7 showed that a flapping wing can alleviate the force variations due to gust. Yang 8 has shown that the structural response of an MAV has relatively little impact on the loads or motion of an MAV in oscillatory flow. Kerstens et al 9 studied the effects of gusting on a semi-circular wing. Their studies looked at the phase between the lift variation and the oscillating freestream, noting that the phase was dependent on both the angle of attack (AoA) and the dimensionless frequency (k). They proposed a gust suppression active control strategy that uses pulsed blowing jets to modify the flow around an airfoil. They showed that the strategy can reduce the variation in the force generation but add higher frequency oscillations from the control mechanism. Gobulev et al. 20,2 performed analysis on the interactions between wind gusts and airfoil flight response wherein the wind gusts are represented by a Taylor-like vortex. They showed correlations between the strength and size of the vortex and the fluctuation in the lift generation. They found large force fluctuations occur at the high angles of attack. Additionally they studied the impact of wind gust on a flapping airfoil and observed that the flapping motion can decrease the response in the lift force. Prater and Lian 25 studied the response of a stationary airfoil in gusty environment. They found that predictions for the lift variation and for the increase in lift generation in oscillating flow tended to under predict the numerical results. This amount it under predicted increased with larger angles of attach and higher gust frequencies. In this paper we extend the wind gust study from stationary airfoils to flapping wings. The impact of a wind gust on the aerodynamic performance of flapping wings with the focus on the lift variation will be studied numerically. Comparison will be made with a stationary wing to illustrate the benefits of flapping wings in gust resistance. The rest of the paper is structured as follows: we first introduce the numerical methods; then we present the computational setup; this is followed by the introduction of relevant parameters. In the numerical result section we first study single flapping wing and then wings in tandem configuration. II. Numerical Method The numerical simulation is carried out at a mean Reynolds number of 500, which is the lower range of Reynolds number for MAVs. At this Reynolds number, flow is laminar and its behavior can be described by the incompressible Navier-Stokes equations and the continuity equation () where ρ is the density, is the velocity vector, p is the pressure, is the viscous stresses and is equal to, µ is the viscosity. The incompressible Navier-Stokes equations are solved with the pressure-poisson (2) 3

4 method 22. The equations are discretized in space with second-order accurate central differences. The second-order Crank-Nicolson scheme is used for time integration. The PETSc package is used to solve the system of equations. III. Computational setup. In this study a flat plate with a 5% thickness and rounded leading and trailing edges is used. The computational setup follows the work of Broering and Lian 24 and is shown in Figure 2. A hyperbolic mapping scheme is used to create an O-type grid around the flat plate. The grid is stretched to cluster grid points near the flat plate surface to resolve the boundary layer around the plate. A Cartesian grid overlapping the O-grid is added in the wake region to better capture the wake flow structure behind the flat plate as well as to maintain the vortex cohesiveness as it moves downstream between the two flatplates. The background grid uses a uniform Cartesian grid. A Dirichlet boundary condition is applied at the inlet (left side) and zero pressure gradient boundary condition is applied at the outlet (right side). A slip boundary condition is applied at the top and bottom surfaces. Grid sensitivity analysis has been performed by Broering and Lian 24 and this study uses the same grid. Slip Wall Uniform Background Grid Slip Wall Uniform Background Grid Inflow Flatplate Body Fitted Grid Outflow Inflow Flatplate Body Fitted Grid Flatplate Body Fitted Grid Outflow Cartesian Grid Cartesian Grid Slip Wall Slip Wall a) Single Flat Plate Configuration b) Double Flat Plate Configuration Figure 2: a) Single and b) Double Flat Plate(s) Grid Configurations. IV. Simulation Parameters In this paper we study a single frequency gust with harmonic variation (3) where U ave is the mean freestream velocity, U amp is the of freestream oscillation, and f gust is the frequency of the gust. The single frequency pitching and plunging motion are mathematically expressed as follows: (4) (5) where θ and h are the pitch and plunge respectively and f flap is the frequency of the flapping maneuver and is the phase angle. These studies were performed at a chord based average Reynolds number of 500. For the flapping kinematics a reduced flapping frequency ( of 0.2 is used, the pitch is 0 and the average angle of attack ( for both the stationary and the flapping case is 6. To vary the Strouhal number only the plunge is varied, all other parameters remain consistent with the other flapping case. The ratio between the flapping and wind gust reduced frequencies is 30: and the gust (U amp ) is between 0 and 0.3. The ratio between the flapping and gust frequencies is representative of the real world characteristics for hummingbirds or insects where they can flap at a much higher frequency than the natural occurring gusts. Prater and Lian 25 have shown that at low gust frequencies the response of a flat plate to wind gust can be accurately predicted by Theodorsen s flat plate theory 26. The theory assumes an infinitely thin flatplate in inviscid flow that remains fully attached and satisfies the Kutta condition at the trailing edge. Greenberg 27 extended Theodorsen s theory to incorporate a sinusoidal variation in the mean flow velocity. It has been shown that Greenberg s theory is able to 4

5 30% tud e 20% tud e 0% tud e reasonably predict the variation in the resulting normalized lift. normalized response is Greenberg s theoretical predication for the 6 here F and G are constant parameters from Theodorsen 26 which are a function of the reduced frequency k. For the reporting of the data all forces are normalized by the force of the same case in a non-oscillatory flow. For flapping wing cases the forces are averaged over a flapping cycle. V. Single Wing Results In Table we compare the performance of a single flapping wing and a stationary wing. Three gust oscillation s are tested. In each case the flapping wing can significantly reduce the lift variation by more than 60%. Between the two tested Strouhal numbers, the higher Strouhal number case can reduce the variation more than the low number case. Case Normalized % Decrease From Peak to Peak Stationary Stationary Flatplate Predicted by Eq Flapping Flatplate St % Flapping Flatplate St % Stationary Flatplate Predicted by Eq Flapping Flatplate St % Flapping Flatplate St % Stationary Flatplate Predicted by Eq Flapping Flatplate St % Flapping Flatplate St % Table : Single Wing Result Summary Figure 3 shows the normalized force histories at the three different gust levels. The alleviation in the force variation is evident in all three cases..5.2 Flapping St 0.3 Flapping St 0.2 Stationary Period(T, Based on Cycle) Period(T, Based on Cycle) a)0 % b) 20 % 0.5 Flapping St 0.3 Flapping St 0.2 Stationary 5

6 Flapping St 0.3 Flapping St 0.2 Stationary Period(T, Based on Cycle) c) 30% Figure 3: Comparison of Lift Force over a Single Cycle at with a a) 0% b) 20% and c) 30%. One interesting aspect from Figure 3 is the lift force for the 0.3 Strouhal number case does not follow the freestream gust variation. There is a lag of about 270 between the velocity and force generation. From Eq. 6 we can see that for a stationary wing the lift generation increases as a function of the square of the gust. Table 2 compares the gust cycle averaged lift between stationary and flapping wings. All cases show an increase in the lift generation as the gust increases except the flapping wing case at St of 0.3. The change in the lift is greater for stationary wings than for flapping wings. In all cases, however, the gust changes the lift by less than 6%. It is also noted that under same gust conditions the flapping wing generates higher lift than the stationary wing with the lower Strouhal flapping case generating the most lift. Stationary Wing: Comparison to No Flapping Wing St 0.2: Comparison to No Flapping Wing St 0.3: Comparison to No Flapping Wing St 0.3: Comparison to Stationary Wing Flapping Wing St 0.2: Comparison to Stationary Wing No 0% 20% 30% % 02.04% 04.65% % 0.2% 02.9% % 98.03% 95.9% 08.87% 08.3% 04.58% 99.79% 2.58% 2.27% 20.59% 9.57% Table 2: Comparison of Single Wing Lift Generation in s VI. Tandem Wing Results Nagai et al. 28 have shown through experimental studies proper adjustment of the relative motion of the fore and hindwings can provide benefits in flight stability. In this section we investigate whether/how wings in tandem configuration can alleviate the gust effect by reducing the lift variation. The distance between the fore and hind wings will be considered because early work by Broering and Lian 24 has shown that the spacing between the tandem wings has an impact on the force generation. Three tandem configurations are selected. The first one consists of two stationary wings, the second one consists of one flapping fore wing and a stationary hind wing, and the third consists of a stationary forewing and a flapping hind wing. A. Two Stationary Tandem Wings The two wings are separated by a single chord length. The force variations under three gust conditions are summarized in Table 3. Case Normalized % of Single Wing % of Combined 6

7 30% 20% 0% Peak to Peak Variation Force Forewing Hindwing Combined Forewing Hindwing Combined Forewing Hindwing Combined Table 3: Comparison of the Force Results for only Tandem Stationary Wings Seperated by a Full Chord. It is seen that for this tandem configuration, each individual wing has similar force variation as a single wing in isolation. It is also noted the force variation for the combined wings is similar to the single wing in isolation despite the unequal contribution to the total force by the fore and hind wing. Figure 4 shows the normalized lift force the forewing, hindwing, combined wings, and the single wing in isolation. They are normalized by their corresponding non-gust cycle averaged lift. As can be seen the addition of a gust affects two stationary wings in tandem the same way as the gust affects the single wing in isolation Period(T, Based on Cycle) Stationary Tandem Fore Wing Stationary Tandem Hind Wing Stationary Tandem Both Wings Stationary Single Wings Period(T, Based on Cycle) Stationary Tandem Fore Wing Stationary Tandem Hind Wing Stationary Tandem Both Wings Stationary Single Wings a)0 % b) 20 % Period(T, Based on Cycle) Stationary Tandem Fore Wing Stationary Tandem Hind Wing Stationary Tandem Both Wings Stationary Single Wings c) 30% Figure 4: Comparison of Lift Force over a Single Cycle at with a a) 0% b) 20% and c) 30%. Table 4 shows a comparison of the gust cycle averaged lift at the various gust intensities. Similar to the single wing case, increases in the wind gust slightly increases the lift generation of both the fore and hind wings. Compared to single wing in isolation the fore wing has a slight decrease in the lift while the hind wing sees a 7

8 nearly 60% decrease. When combined, the two tandem wings have a slightly higher lift under a gusting condition than under constant velocity condition. No 0% 20% 30% Forewing: Comparison to No % % 04.6% Forewing: Comparison to Single Wing in isolation 98.8% 98.4% 97.94% 97.7% Hindwing: Comparison to No % 02.6% 04.89% Hindwing: Comparison to Single Wing in isolation 43.46% 43.50% 43.5% 43.56% Combined: Comparison to No % 0.92% 04.39% Combined: Comparison to Single Wings in isolation 72% 72% 70.73% 74% Single Wing: Comparison to No % 02.% 04.7% Table 4: Comparison of Averaged Wing Lift Generation in s Also tested is a tandem wing configuration in which the two wings are half chord away from each other. The conclusions are similar to those drawn from the configuration in which the wings are one chord from each other. One change, however, is that in the new configuration the hind wing contribute about 28% of the total force instead of 3% in the previous case. Figure 5 shows the normalized force histories for the fore and hindwing as well as the combined force and includes the single stationary wing and the tandem wings at a full chord for comparison Period(T, Based on Cycle) Stationary Tandem Fore Wing Stationary Tandem Hind Wing Stationary Tandem Both Wings Half Chord Stationary Tandem Both Wings Full Chord Stationary Single Wings Period(T, Based on Cycle) Stationary Tandem Fore Wing Stationary Tandem Hind Wing Stationary Tandem Both Wings Half Chord Stationary Tandem Both Wings Full Chord Stationary Single Wings a)0 % b) 20 % 8

9 30% 20% 0% Period(T, Based on Cycle) Stationary Tandem Fore Wing Stationary Tandem Hind Wing Stationary Tandem Both Wings Half Chord Stationary Tandem Both Wings Full Chord Stationary Single Wings c) 30% Figure 5: Comparison of Lift Force over a Single Cycle at with a a) 0% b) 20% and c) 30%. Again, similar to the full chord separation case, both forewing and hingwing produce higher lift under gust condition than under non-gust condition. In this configuration the lift generation capability of the hind wing is reduced to 36% of the single wing in isolation compared to 43% in the configuration where wings are one chord away from each other. B. Flapping Forewing and Stationary Hindwing In this tandem configuration the fore wing is flapping and the hind wing is stationary. Table 5 has the summary of the force variation over one gust period when two wings are separated by a full chord. In this case and the next cases the flapping hind/forewing is compared to a flapping wing in isolation and the stationary hind/forewing is compared to a stationary wing in isolation. Case Normalized % of Single Wing % of Combined Peak to Peak Variation Force Forewing Hindwing Combined Forewing % Hindwing % Combined Forewing % Hindwing % Combined Table 5: Comparison of the Force Results for a Flapping Forewing and Stationary Hindwing at a Full Chord. There are a few interesting aspects in the table. First, the forewing contributes a larger percentage of the total force than the hindwing, but the percentage attributed to the forewing is lower than that in the two stationary tandem wing configuration. Second, the forewing flapping has a much higher variation than a single wing flapping in isolation, indicating that the stationary hind wing affects the force generation of the flapping fore wing. Third, though both wings have a large variation in the force as a whole the variation in the force is small. The small variation of the combined force can be explained by Figure 6 which shows the force histories for the forewing, hindwing and combined force over a single wind gust. It is clear when the forewing reaches the force peak, the hind wing is near its force trough and vice visa. From the figure the different timing of the peaks can be seen to limit the variation in the combined force which is beneficial. Additionally it can be seen that the hindwing s peak becomes less sharp and more elongated as the gust intensities increase. 9

10 Period(T, Based on Cycle) Flapping Fore Wing Full Chord Seperation Stationary Hind Wing Full Chord Seperation Combined Wings Full Chord Period(T, Based on Cycle) Flapping Fore Wing Full Chord Seperation Stationary Hind Wing Full Chord Seperation Combined Wings Full Chord a)0 % b) 20 % Period(T, Based on Cycle) Flapping Fore Wing Full Chord Seperation Stationary Hind Wing Full Chord Seperation Combined Wings Full Chord c) 30% Figure 6: Comparison of Lift Force over a Single Cycle at with a a) 0% b) 20% and c) 30%. Table 6 shows the average lift generation. For this configuration both wings show a much higher lift generation than a similar wing in isolation. This observation is consistent with Zhang and Lu 29 who found that interactions between the fore and hindwing can increase the lift in the forewing. In this configuration the gust has less impact on the forewing (with change of less than 2%) than on the hind wing (with more than 0% change). No 0% 20% 30% Forewing: Comparison to No % 00.20% 00.93% Forewing: Comparison to Single Wing 34.34% 34.23% 37.32% 4.37% Hindwing: Comparison to No % 07.40% 0.45% Hindwing: Comparison to Single Wing in isolation 2.57% 3.73% 8.48% 8.82% Combined: Comparison to No % 03.33% 05.07% Combined: Comparison to Single Wings in isolation 23.92% 24.38% 28.% 30.08% Table 6: Comparison of Averaged Wing Lift Generation in s at a Full Chord Table 7 summarizes the results when the two wings are one half chord away apart. Compared to the full chord configuration case, the half chord configuration shows a greater variation in the combined force. 0

11 30% 20% 0% Case Normalized Peak to Peak % of Single Wing Variation % of One Chord Variation Forewing Hindwing Combined Forewing Hindwing Combined Forewing Hindwing Combined Table 7: Comparison of the Force Results for a Flapping Forewing and Stationary Hindwing Separated by one Half Chord. Figure 7 shows the force histories over the gust cycle which, in comparison to Figure 6 doesn t have the counteracting variation Period(T, Based on Cycle) Flapping Fore Wing Half Chord Seperation Stationary Hind Wing half Chord Seperation Combined Wings half Chord Seperation Period(T, Based on Cycle) Flapping Fore Wing Half Chord Seperation Stationary Hind Wing half Chord Seperation Combined Wings half Chord Seperation a)0 % b) 20 % Period(T, Based on Cycle) Flapping Fore Wing Half Chord Seperation Stationary Hind Wing half Chord Seperation Combined Wings half Chord Seperation c) 30% Figure 7: Comparison of Lift Force over a Single Cycle at with a a) 0% b) 20% and c) 30%. Table 8 shows the averaged force generation for this case, in general there is a larger force generated compared to the single wing in isolation; the forewing generally creates larger lift than at a full cord separation and the hindwing generates less. The offsetting change means that there is a minimal variation in the combined force generation when compared with the full chord separation case.

12 30% 20% 0% No 0% 20% 30% Forewing: Comparison to No % 02.70% 06.35% Forewing: Comparison to Single Wing 36.97% 38.52% 43.50% 5.87% Forewing: Comparison to One Chord 0.95% 03.20% 04.50% 07.43% Hindwing: Comparison to No -- 3% 05.4% 2.37% Hindwing: Comparison to Single Wing in isolation 99.26% 00.42% 02.54% 06.60% Hindwing: Comparison to One Chord 88.8% 88.30% 86.55% 89.72% Combined: Comparison to No % 03.78% 08.75% Combined: Comparison to Single Wings in isolation 8.92% 20.2% 23.48% 29.2% Combined: Comparison to One Chord 95.96% 96.65% 96.38% 99.33% Table 8: Comparison of Averaged Wing Lift Generation in s at a Half Chord C. Stationary Forewing and Flapping Hindwing The third configuration looked at has a forewing that is stationary while the hind wing is flapping. Table 9 summarizes the computed results for this configuration when there is a full chord separation. For this configuration, as in the first configuration where both wings are stationary, the forewing contributes about 75% of the total force. It is also noted that this configuration is less effective in alleviating the gust variation. Large variations are recorded in all three gust s tested. Case Normalized % of Single Wing % of Combined Peak to Peak Variation Force Forewing Hindwing Combined Forewing Hindwing Combined Forewing Hindwing Combined Table 9: Comparison of the Force Results for a Stationary Forewing and Flapping Hindwing at a Full Chord Separation. Figure 8 shows the force history over the gust cycle. As can be seen there is a phase difference between the forewing and hindwing. As the gust intensifies the hindwing s force history becomes less sinusoidal and the ability of the hind wing to generate lift over the entire cycle is detrimentally impacted. 2

13 Period(T, Based on Cycle) Stationary Fore Wing Full Chord Seperation Flapping Hind Wing Full Chord Seperation Combined Wings Full Chord Seperation Period(T, Based on Cycle) Stationary Fore Wing Full Chord Seperation Flapping Hind Wing Full Chord Seperation Combined Wings Full Chord Seperation a)0 % b) 20 % Period(T, Based on Cycle) Stationary Fore Wing Full Chord Seperation Flapping Hind Wing Full Chord Seperation Combined Wings Full Chord Seperation c) 30% Figure 8: Comparison of Lift Force over a Single Cycle at with a a) 0% b) 20% and c) 30%. Table 0 shows the cycle averaged lift generation. For this configuration there is a general degradation of performance as the gust intensity increases, and an overall loss of lift production compared to a single wing configuration. We also tested the performance when distance between the two wings is reduced by half. We found that the change in the lift variation compared to the one chord case is fairly small (less than 2%). No 0% 20% 30% Forewing: Comparison to No % 00.0% 99.60% Forewing: Comparison to Single Wing 05.75% 05.5% 03.74% 06% Hindwing: Comparison to No % 83.20% 65.66% Hindwing: Comparison to Single Wing in isolation 37.57% 36.03% 3.89% 65.66% Combined: Comparison to No % 95.39% 90.4% Combined: Comparison to Single Wings in isolation 70.22% 69.4% 67.0% 63.23% Table 0: Comparison of Averaged Wing Lift Generation in s at a Full Chord This configuration shows more variation at the higher gusts than the full separation with most of the variation increases arising from the hindwing which suggests that the decrease in the separation fies the 3

14 detrimental interaction between the wings. Figure 9 shows the force histories over an entire gust cycle. As the gust increases the hindwing s lift generating capability decreases, at the highest gust s there are even some flapping cycles where it produces negative lift Period(T, Based on Cycle) Stationary Fore Wing Half Chord Seperation Flapping Hind Wing Half Chord Seperation Combined Wings Half Chord Seperation Period(T, Based on Cycle) Stationary Fore Wing Half Chord Seperation Flapping Hind Wing Half Chord Seperation Combined Wings Half Chord Seperation a)0 % b) 20 % Period(T, Based on Cycle) Stationary Fore Wing Half Chord Seperation Flapping Hind Wing Half Chord Seperation Combined Wings Half Chord Seperation c) 30% Figure 9: Comparison of Lift Force over a Single Cycle at with a a) 0% b) 20% and c) 30%. The effects of this on the average lift generation can be seen in Table. The half chord configuration without gust produces more lift than the full chord configuration; however the addition and escalation of gust intensities are especially detrimental to the lift generation, with the extreme of the hindwing producing 45% of the lift over the 30% gust cycle compared to no gust. Forewing: Comparison to No Forewing: Comparison to Single Wing Forewing: Comparison to One Chord Hindwing: Comparison to No Hindwing: Comparison to Single Wing in isolation Hindwing: Comparison to One Chord No 0% 20% 30% % 96.75% 92.29% 09.44% 07.9% 00.02% 96.53% 03.49% 02.27% 00.02% 95.89% % 7.6% 44.37% 44.44% 40.77% 32.46% 20.56%.828%.38% 0% 79.93% 4

15 Normalized peak to Peak Lift Variation % of Lift with No Combined: Comparison to No % 89.04% 77.60% Combined: Comparison to Single Wings in isolation 75.56% 73.03% 67.32% 58.58% Combined: Comparison to One Chord 07.6% 05.2% 00.45% 92.65% Table : Comparison of Averaged Wing Lift Generation in s at a Half Chord VII. Conclusions The different configurations can play a remarkably profound role in both the variation and lift generation in response to flow at varying gust s. In general adding a flapping wing will reduce the peak to peak lift variation (Figure 0) with a single wing in isolation best accomplishing this. Adding a flapping wing behind a stationary flatplate offers minimal reductions compared to just a stationary flatplate. Additionally the different cases offering varying increases in the lift generation with some cases showing reductions in the lift generation with increasing gust intensities and some showing increases. If a tandem wing configuration was used the location of the wings and whether the fore or hindwing was flapping plays a great role in the percentage reduction/increase. From the cases studied the tandem wing case with a forewing flapping and stationary hindwing was the best at minimizing the variation of the forces encountered while maximizing the lift generated in increasing gusts Ampli Ampli Figure 0: Summary of Different Cases 5

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