University of Central Florida University of Central Florida STARS STARS Electronic Theses and Dissertations, 2020- 2021 The Effect of Dynamic Span Wise Bending on the Forces of a The Effect of Dynamic Span Wise Bending on the Forces of a Pitching Flat Plate Pitching Flat Plate Manoj Prabakar Sargunaraj University of Central Florida Part of the Acoustics, Dynamics, and Controls Commons Find similar works at: https://stars.library.ucf.edu/etd2020 University of Central Florida Libraries http://library.ucf.edu This Masters Thesis (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations, 2020- by an authorized administrator of STARS. For more information, please contact [email protected]. STARS Citation STARS Citation Sargunaraj, Manoj Prabakar, "The Effect of Dynamic Span Wise Bending on the Forces of a Pitching Flat Plate" (2021). Electronic Theses and Dissertations, 2020-. 758. https://stars.library.ucf.edu/etd2020/758
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University of Central Florida University of Central Florida
STARS STARS
Electronic Theses and Dissertations, 2020-
2021
The Effect of Dynamic Span Wise Bending on the Forces of a The Effect of Dynamic Span Wise Bending on the Forces of a
Pitching Flat Plate Pitching Flat Plate
Manoj Prabakar Sargunaraj University of Central Florida
Part of the Acoustics, Dynamics, and Controls Commons
Find similar works at: https://stars.library.ucf.edu/etd2020
University of Central Florida Libraries http://library.ucf.edu
This Masters Thesis (Open Access) is brought to you for free and open access by STARS. It has been accepted for
inclusion in Electronic Theses and Dissertations, 2020- by an authorized administrator of STARS. For more
STARS Citation STARS Citation Sargunaraj, Manoj Prabakar, "The Effect of Dynamic Span Wise Bending on the Forces of a Pitching Flat Plate" (2021). Electronic Theses and Dissertations, 2020-. 758. https://stars.library.ucf.edu/etd2020/758
The Lift force ( ð¿ð¿ððððð ð ðð) in a pure bending wing consists of two terms, the first term is the
inertial term and the second term is the induced angle of attack, and the second term lift due
to the induced angle attack modified by the based on the Theodorsen function C (k) = F+iG
defined in terms of Hankel functions HV (2) = Jv â iYv where Jv and Yv are Bessel first and
second kind functions respectively, and expressed as
ð¶ð¶(ðð) â¶= ð»ð»1
(2)(ðð)ð»ð»1
(2)(ðð) + ððð»ð»0(2)(ðð)
and k â¶= ð¹ð¹fc/U is the reduced frequency.
Similarly, the lift force (ð³ð³ðððððððððð) in a pure pitching wing consists of an inertial term
proportional to the angular acceleration (ᅵᅵð¶) involving the product ððᅵᅵð¶ expressed as the
âMagnusâ term equivalent to the second Fourier harmonic for quasi-steady theory(Stevens
and Babinsky, 2017). And the second term includes circulatory lift due to the change of angle
of attack and rate of change of angle of attack modified by the Theodorsen deficiency
function C (k).
33
CHAPTER 4 RESULTS AND DISCUSSION
4.1 An Unsteady pitching flat plates,
This section the results of the pitching thin flat plate net lift and aerodynamic force history at
the Re= 11882 and 0.131 < K < 0.3925. The flat plate is rotated at the different reduced
frequencies from the angle of attack 0 deg to AOA (30,45,60,90deg) ends at 0 deg. Lift and
drag forces are measured in the force senor are projections of the flat plate wing-normal force
in the respective directions.
Figure 19 Effect of angle of attack on a Lift and Drag force of a pitching wing.
In all the cases the total cycle time (t* = 2) of the pitching wing was kept constant. So, the pitch
rate increases or decreases according to the maximum angle of attack achieved in total cycle
time. The effect of the angle of attack along with the reduced pitch rate is immediately visible
in Figure 18. At a lower reduced pitch rate, K = 0.131 with the maximum AOA of 30o, the
increase in a lift is slow compared to a rapid rise in lift the higher angle of attack cases of 90
deg at K = 0.3925. At a higher reduced pitch rate, K = 0.3925 with the maximum AOA of 90o,
one can observe a decrease in a lift after the rapid rise in lift force earlier compared to a lower
reduced pitch rate, lift curve is increasing monotonically with the increase in the angle of attack
34
(AOA) until it reaches peak lift angle of attack. It is observed from Figure 18 peak lift saturates
early in the case of higher K = 0.1927 around â 15o. But in the case of lower reduced pitch
rate K = 0.1308, the peak lift saturates at higher AOA around â 20o. The decrease in
aerodynamics force is qualitative evidence of detachment of leading-edge vortices from the flat
plate. It is evident from the comparable lift and drags force trends in the results at each
respective reduced pitch rate. It suggests that dominant aerodynamics force is exerted in a plate
in normal directions. Similar trends are observed at different velocities and reduced pitch rates.
It is apparent from the results that, the lift and drag forces do not follow the same while rating
forward and reverse. It is clear evidence of the existing pitching rate-dependent hysteresis as
shown in Figure 18. With the higher reduced pitch rate, the difference in lift and drag force
values in the forward and reverse directions is small compared to the large difference in the
higher reduced pitch rate.
4.2 Force Measurements
Initially, the effect of dynamic bending on a pitching flat plate, moving at a constant velocity
of 0.1 m/s, is quantified using dynamic force measurements. The tests have been performed
for sinusoidal pitch-up to three different maximum geometric AoAs (αmax) of 30°, 45°, and 60°,
followed by an immediate pitch-down motion to 0o (0°- αmax - 0o) during the forward motion.
For the pitch-bent case, the flat plate was dynamically bent along with the pitching motion
simultaneously without any phase difference (Figure 17). The measured lift and drag
coefficient curves for the pitch-only and pitch-bent configurations are presented in Figure 19.
It is observed that with increasing pitch rate, the lift coefficient increases during the upstroke
(0°-30°, 0°-45°, 0°-60°). This is expected due to a higher rate of change of momentum which
has also been reported by Grunnland et al. (2012). The rapid increase in the lift coefficient is
35
accompanied by a steep drop in the downstroke part of the motion. It is to be noted that the
upstroke motion is completed at t* = 1, and the downstroke starts soon after that. Similar lift
augmentation was not observed during the downstroke part (30°-0°). We will show later that
the origin of this rapid increase in lift coefficient in both the pitch-only and pitch-bend case is
non-circulatory in nature.
During the pitch-bend case, the lift coefficient values were observed to reduce during the
upstroke part of the motion, while they increased during the downstroke part, compared to the
pitch-only case. This difference is negligible in the lowest pitch rate case (0-30-0). However,
the difference becomes prominent with the increasing pitch rate. This observation alludes to
the excellent force manipulation capabilities of morphing during an unsteady maneuver. We
Figure 20 Comparison of lift force and drag force of the pure pitching case (black) compared against a pitch-bend case (grey). Green shading shows where the pitching wing force is higher than the pitch-bent case, while yellow shows when the pitch-bent case is more than the pitch case.
36
surmise that by varying the bending ratio or flexion ratio and the amplitude of bending, it is
possible to reduce the lift excursions to a further extent. Our present morphing mechanism
did not permit us to try higher flexion amplitudes, but a higher bending amplitude (or flexion
angle) during the upstroke will result in a more decrease in the lift peak.
4.3 PIV Measurements
In this section, vorticity fields are calculated from the velocity fields measured by PIV. The
vorticity dynamics of the pitching and translation are majorly influenced by the pitch rate
(Kp)(Granlund, Ol and Bernal, 2013; Onoue and Breuer, 2016; Chen, Kolomenskiy and Liu,
2017; Eldredge and Jones, 2018). Similar dependency is observed in the current PIV
Experiments as shown in Figure 23, during convection time, t* = 0.00â1.50 s. From top to
bottom, the rows represent three different instants in the pitching cycle: t* = 0.5, 1, and 1.5
respectively. At the initial stage of pitching
At t* = 0.5, the initial stage of pitching, the emergence of the Trailing Edge Vortex (TEV)
(blue) is caused by the initial acceleration of the wing. At this stage between the time t* = 0-1
s, the emergence of the Leading-Edge Vortex (LEV)rapidly grows near the leading edge with
the increase in α. The LEV (red contours) is attached to the leading edge of the wing until the
pitch-up wing increase in α ceases. In the meantime, the TEV is convected away downstream
from the Trailing edge and further new vortices are produced. After the pitch-up motion at t*
= 1 s, circulation addition through the shear layer to LEV is stopped. At t* = 1â2 s the pitch
down motion of the wing starts. As the flow evolves the reattachment point of the flow field
moves downstream and the LEV separates and convects downstream. Around t*= 1.5 s LEV
pinch off from the upper surface of the wing as the vortex convects downstream. The secondary
vortex formation with the opposite sign to the LEV is seen between the LEV and the plate.
37
This flow field remained the same for all the cases discussed. Similar observations are made in
the previous investigations at high pitch rates.(Ol and Bernal, 2009; Baik et al., 2012; Buchner
et al., 2012). The changes in the vortex structure are expected between the pitch and pitch-bend
case. Meanwhile, the vortex size and position comparison pitch-bend case closely follow the
pure pitching case, including the Tailing edge vortex formation at t* = 0.5 s.
Figure 21. Snapshots results of the spanwise vorticity fields related to several reduced
pitch rate fâ at Re = 12000 The solid black rectangle denotes the flat plate cross section
(a) fâ = 0.4112, f = 0.5 Hz, αmax = 30 o (b) fâ = 0.6119, f = 0.5 Hz αmax = 45 o (c) fâ = 0.8225,
f = 0.5 Hz αmax= 60 o The vorticity is scaled by c/Uâ, clockwise (red) and negative,
anticlockwise (blue)
To demonstrate this effect, the normalized pressure field is shown in Figure 21 for pure pitching
and pitch-bend motion airfoils at different time intervals. Current non-intrusive PIV-based
pressure analysis is the same method shown in Dabiri et al.(Dabiri et al., 2014) was used to
38
observe the pressure loads on the wing. The pressure field derived from the velocity data
captured important flow features near the wing. In particular, the field shows a low-pressure
region in the place of LEV and a high-pressure region where the fluid is accelerating from the
wing. The pressure field at the various span location from the tip to the mid-span shows the
variation in the pressure values. And the upward displacement of the Pitch-bend wing shows
a minimal effect on the wing pressure loading compared to the pressure loading of the pitching
wing.
Figure 22 comparison of the pressure distribution fâ = 0.8225 at Re = 12000 The solid
black rectangle denotes the flat plate cross-section (a) 50% span, αmax= 60 o (b) 70%
span, αmax= 60 o (c) 86% span, αmax= 60 o .
39
4.4 Total Circulation Temporal Evolution
Figure 23 Historical development of the Total circulation for various motion profiles.
40
To determine the strength of the vortex above the wing, the spanwise circulation of the wing is
calculated for various pitch and pitch-bend kinematics. The experiments are conducted over
the various pitch rates in the range of 0.4112 < Kp < 0.8225, amplitudes αmax = 30,45,60 deg
at Re = 12000. In this section, several total circulation histories are compared for the pitch and
pitch-bend cases as shown in Figure 22. The method used here to calculate to find the total
circulation is adapted from literature(Carr, Devoria and Ringuette, 2015). In this method, the
total circulation is determined by constraining the flow field data within the rectangle region
aligned above the chord of the wing. The vorticity field data below the wing and ahead of the
wing is not used due to the shadow formed by the laser sheet. The rectangle domain uses all
positive vorticity in a region near the leading edge and any positive vorticity near the plate.
The circulation due to the Trailing edge is neglected since it would contribute to the incorrect
total circulation measurements(Carr, Devoria and Ringuette, 2015).
Total circulation values below and ahead of the plate are not captured due to a laser shadow
and the camera lines-of-sight being blocked by the plate. Here t*= 0 is a time instant where the
plate starts the pitching from idle at α = 0. It is observed for all the cases discussed here; the
total circulation of the wing increases monotonically with the increase in the angle of attack
until the LEV separates from the plate. Subsequently, the circulation decreases as the LEV
convects downstream during the pitch down motion. The effect of reduced pitch rate with the
increase in amplitude is seen in the circulation values. The circulation trend is expected since
the feeding shear layer velocity/tip velocity of the wing increases with the increase in pitch
rate. The main objective of this study is to address the effect of bending on the pitching wing
circulation growth. But manipulation of the tip velocity introduced by the bending motion on
the vortex development is not observed in all the cases. This highlights that introduced
manipulation on the pitching wing total circulation growth of the wing is insignificant.
41
Figure 24 (Color online) (aâc) Snapshots results of the spanwise vorticity fields related
to several reduced pitch rate fâ = 0.8225 at Re = 12000 The solid black rectangle denotes
the flat plate cross-section (a) 50% span, αmax= 60o (b) 70% span, αmax= 60 o (c) 86%
span, αmax= 60 o. The vorticity is scaled by c/Uâ, clockwise (red) and negative,
anticlockwise (blue)
4.5 Discussion And Outlook
The performance results of the dynamic bending on the pitching wing have been discussed
42
until now. In this section, an effort has been made to understand the load alleviation observed
due to the morphing wing. In the experimentally measured unsteady aerodynamic force results
shown clearly show the difference in loads acting on the wing. It is well known that the total
aerodynamics force acting on the wing is a combination of circulatory and Non-circulatory
effects. To test the significance of the non-circulatory force due to the bending wing on the
force results. Lift due to bending wing contribution from a pitching wing isolated to a single
parameter to understand the performance of the morphing wing as calculated as âð¿ð¿ððððð ð ðð =
ð¿ð¿ððð ð ð¡ð¡ððâ â ð¿ð¿ððð ð ð¡ð¡ððââððððð ð ðð. The difference is shown as the shades as the isolated Lift force due to
the bending wing (âð¿ð¿ððððð ð ðð) compared with the Noncirculatory force of the bending wing
(ð¿ð¿ððððð ð ððâðððð) obtained by the analytical model. An analytical model based on the Theodorsen
theory is used to calculate non-circulatory forces. This model has shown an ability to estimate
the non-circulatory forces even in separated flow such as surge and stall regions
recently(Corkery, Babinsky and Graham, 2019)(Bull et al., 2020). It was observed that the
force from the model compares well with the experimentally measured lift forces. It is noted
that the non-circulatory forces contributed to the positive lift in the first part of the pitching
wing (0-1 sec) and it gives a positive lift in the next part (1-2 sec) of the pitching wing. It is
understood that discrepancy between the model non-circulatory values and the experimental
results. But the model considers only non-circulatory effects to show the isolated effects. In the
previous section, it is seen that the sensitivity of the circulatory effects on the morphing wing
in terms of the circulation values around the wing and the vortex structure is less or nil. Also,
the effectiveness of the 2D model predicting the experimental values is less compared to the
3D model(Liu and Sun, 2018).
43
Figure 25 Time history of non-circulatory mass forces
From the above results, it is evident that the non-circulatory forces are the major contributors
to the performance of the morphing wing similar to the aerodynamic force production
mechanisms of a flapping wing(Liu and Sun, 2018; Guvernyuk et al., 2020; Liu, Du and Sun,
44
2020). The effects of non-circulatory forces could not be eliminated while finding the total
aerodynamics forces of the morphing wing.
45
CHAPTER 5 CONCLUSION
In this study, the force production mechanisms around pitching and the bending wing are
experimentally investigated for pitch up and pitch down motion kinematics over a range of
maximum angle of attack and reduced frequency. Based on the research study concluding
remarks are mentioned below.
⢠It is found that pitch-bent wing results in less lift force during the pitch-up motion
and higher lift forces in the pitch-down motion.
⢠PIV experiments are conducted to explore the observed force difference with the
morphing wing compared to the non-morphing wing. The PIV results indicate that
there are very few changes in flow field topology. Further vortex circulation
analyses are conducted to observe the difference between morphing and non-
morphing wing. It is observed that the total circulation growth of the morphing
wing is like the non-morphing wing.
⢠Finally, an analytical model based on the Theodorsen theory is used to calculate
non-circulatory forces. It is found that non-circulatory forces play a greater role in
the load alleviation in a morphing wing. It should be noted that while finding a
force acting on a morphing wing; It is important not to neglect the added Mass
Contribution.
46
APPENDIX: INSTURUMENTATIONS
47
Figure 26 Model instrumentation
A proximity sensor is used to detect and control the motion of the wing.
Arduino Uno micro controller is used for triggering the remaining instruments i.e., Pitching
motor, PCO camera, Servo motor for the bending motion, ATI mini 40 force sensor.
48
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