ADDITIONAL FIGURES
C.5 Interaction with heaving plate gusts
Figures C.14-C.16 display the drag, lift, and moment coefficients from the airfoil- gust interactions due to the heaving plate withS= 0.1, at different angles of attack.
Time has been shifted such that the estimated gust impact is att = 0. Experiments were performed at three angles of attack forS =0.1, but only one forS =0.25. The envelopes of these forces are shown in Figures C.17 - C.19.
FigureC.1:PlotsofthesimulatedvariationinCL(t)forα=0°,normalizedbythemagnitudeofthesteadythinairfoiltheorypeakCL. Thecyanlineisthequasi-steadythinairfoiltheory,redisthewakelesspanelmethod,blueisWagnerthinairfoiltheory,greenisthe extendedTchieu-Leonardmodel,andblackistheunsteadypanelmethod.Thenumbersineachframeare(Γv/(Uc),yv/c)
FigureC.2:PlotsofthesimulatedvariationinCL(t)forα=5°,normalizedbythemagnitudeofthesteadythinairfoiltheorypeakCL. Thecyanlineisthequasi-steadythinairfoiltheory,redisthewakelesspanelmethod,blueisWagnerthinairfoiltheory,greenisthe extendedTchieu-Leonardmodel,andblackistheunsteadypanelmethod.Thenumbersineachframeare(Γv/(Uc),yv/c)
FigureC.3:PlotsofthesimulatedvariationinCL(t)forα=10°,normalizedbythemagnitudeofthesteadythinairfoiltheorypeak CL.Thecyanlineisthequasi-steadythinairfoiltheory,redisthewakelesspanelmethod,blueisWagnerthinairfoiltheory,greenisthe extendedTchieu-Leonardmodel,andblackistheunsteadypanelmethod.Thenumbersineachframeare(Γv/(Uc),yv/c)
(a)Flowaroundtheplatesat0.1tcbefore thechangeindirection.Platesaremoving upward.
(b)Flowaroundtheplatesat0.25tcafter thechangeindirection.Thewakesare rollingup.
(c)Flowaroundtheplatesat1.0tcafter thechangeindirection.Thevorticesare movingdownstream. FigureC.4:ThissequenceoffiguresshowstheevolutionoftheflowaroundtheplatewhenRecandSarevaried.
Figure C.5: Paths of vortices from the pitching airfoil: the x-axis is time, and y-axis is the x-position of the identified strongest vortex at that timestep. The columns are, from left to right,S=-5°, -10°, -13°. The first five rows are individual repetitions of the experiment. The bottom row is from the average PIV field of those experiments.
Figure C.6: Paths of vortices from the pitching airfoil: the x-axis is time, and y-axis is the y-position of the identified strongest vortex at that timestep. The columns are, from left to right,S=-5°, -10°, -13°. The first five rows are individual repetitions of the experiment. The bottom row is from the average PIV field of those experiments.
Figure C.7: Average and standard deviations of forces on the airfoil: with an unperturbed freestream, or with the presence of the gust-generating plate or airfoil.
Figure C.8: Estimated drag coefficient due to gusts from the pitching airfoil interact- ing with the airfoil. Each frame contains force traces from a single release position and initial direction, but different airfoil angles of attack.
-10 0 10 20 0
0.5 1
C L
(α
2, yupstream): (-13, 1 ca )
-10 0 10 20
0 0.5 1
C L
(α
2, yupstream): (13, 1 ca )
-10 0 10 20
0 0.5 1
C L
(α
2, yupstream): (-13, 0.5 ca )
-10 0 10 20
0 0.5 1
C L
(α
2, yupstream): (13, 0.5 ca )
-10 0 10 20
0 0.5 1
C L
(α
2, yupstream): (-13, 0 ca )
-10 0 10 20
0 0.5 1
C L
(α
2, yupstream): (13, 0 ca )
-10 0 10 20
0 0.5 1
C L
(α
2, yupstream): (-13, -0.5 ca )
-10 0 10 20
0 0.5 1
C L
(α
2, yupstream): (13, -0.5 ca )
-10 0 10 20
0 0.5 1
C L
(α
2, yupstream): (-13, -1 ca )
-10 0 10 20
0 0.5 1
C L
(α
2, yupstream): (13, -1 ca )
α=0o α=5o α=10o
τa τ
a
Figure C.9: Lift coefficient due to gusts from the pitching airfoil interacting with the airfoil. The dashed lines correspond to the simulations, and dotted lines denote the semi-analytic estimate. Each frame contains force traces from a single release position and initial direction, but different airfoil angles of attack.
Figure C.10: Moment coefficient due to gusts from the pitching airfoil interacting with the airfoil. Each frame contains force traces from a single release position and initial direction, but different airfoil angles of attack.
−20 0 20 40 0
0.02 0.04 gCD,est
(α
2, yupstream): (−13, 1 ca )
−20 0 20 40
0 0.02 0.04 gCD,est
(α
2, yupstream): (13, 1 ca )
−20 0 20 40
0 0.02 0.04 gCD,est
(α
2, yupstream): (−13, 0.5 ca )
−20 0 20 40
0 0.02 0.04 gCD,est
(α
2, yupstream): (13, 0.5 ca )
−20 0 20 40
0 0.02 0.04 gCD,est
(α
2, yupstream): (−13, 0 ca )
−20 0 20 40
0 0.02 0.04 gCD,est
(α
2, yupstream): (13, 0 ca )
−20 0 20 40
0 0.02 0.04 gCD,est
(α
2, yupstream): (−13, −0.5 ca )
−20 0 20 40
0 0.02 0.04 gCD,est
(α
2, yupstream): (13, −0.5 ca )
−20 0 20 40
0 0.02 0.04 gCD,est
(α
2, yupstream): (−13, −1 ca )
−20 0 20 40
0 0.02 0.04 gCD,est
(α
2, yupstream): (13, −1 ca )
α=0o α=5o α=10o τa
τ
a
Figure C.11: Average envelope of the drag coefficient due to gusts from the pitching airfoil interacting with the airfoil. Each frame contains traces from a single release position and initial direction, but different airfoil angles of attack.
−20 0 20 40 0
fCL 0.2
(α
2, yupstream): (−13, 1 ca )
−20 0 20 40
0
fCL0.2
(α
2, yupstream): (13, 1 ca )
−20 0 20 40
0
fCL 0.2
(α
2, yupstream): (−13, 0.5 ca )
−20 0 20 40
0
fCL0.2
(α
2, yupstream): (13, 0.5 ca )
−20 0 20 40
0
fCL 0.2
(α
2, yupstream): (−13, 0 ca )
−20 0 20 40
0
fCL0.2
(α
2, yupstream): (13, 0 ca )
−20 0 20 40
0
fCL 0.2
(α
2, yupstream): (−13, −0.5 ca )
−20 0 20 40
0
fCL0.2
(α
2, yupstream): (13, −0.5 ca )
−20 0 20 40
0
fCL 0.2
(α
2, yupstream): (−13, −1 ca )
−20 0 20 40
0
fCL0.2
(α
2, yupstream): (13, −1 ca )
α=0o α=5o α=10o τa
τa
Figure C.12: Average envelope of the lift coefficient due to gusts from the pitching airfoil interacting with the airfoil. Each frame contains traces from a single release position and initial direction, but different airfoil angles of attack.
−20 0 20 40 0
5 gCM
(α 2, y
upstream): (−13, 1 c a )
−20 0 20 40
0 5 gCM
(α 2, y
upstream): (13, 1 c a )
−20 0 20 40
0 5 gCM
(α 2, y
upstream): (−13, 0.5 c a )
−20 0 20 40
0 5 gCM
(α 2, y
upstream): (13, 0.5 c a )
−20 0 20 40
0 5 gCM
(α 2, y
upstream): (−13, 0 c a )
−20 0 20 40
0 5 gCM
(α 2, y
upstream): (13, 0 c a )
−20 0 20 40
0 5 gCM
(α 2, y
upstream): (−13, −0.5 c a )
−20 0 20 40
0 5 gCM
(α 2, y
upstream): (13, −0.5 c a )
−20 0 20 40
0 5 gCM
(α 2, y
upstream): (−13, −1 c a )
−20 0 20 40
0 5 gCM
(α 2, y
upstream): (13, −1 c a )
α=0o α=5o α=10o
Figure C.13: Average envelope of the moment coefficient due to gusts from the pitching airfoil interacting with the airfoil. Each frame contains traces from a single release position and initial direction, but different airfoil angles of attack.
−100 −5 0 5 10 0.05
0.1 C D,est
negative initial motion to y peak = 1c
a
−100 −5 0 5 10
0.05 0.1 CD,est
positive initial motion to y peak = 1c
a
−100 −5 0 5 10
0.05 0.1 C D,est
negative initial motion to y
peak = 0.5c a
−100 −5 0 5 10
0.05 0.1 CD,est
positive initial motion to y
peak = 0.5c a
−100 −5 0 5 10
0.05 0.1 C D,est
negative initial motion to y peak = 0c
a
−100 −5 0 5 10
0.05 0.1 CD,est
positive initial motion to y peak = 0c
a
−100 −5 0 5 10
0.05 0.1 C D,est
negative initial motion to y
peak = −0.5c a
−100 −5 0 5 10
0.05 0.1 CD,est
positive initial motion to y
peak = −0.5c a
−100 −5 0 5 10
0.05 0.1 C D,est
negative initial motion to y
peak = −1c a
−100 −5 0 5 10
0.05 0.1 CD,est
positive initial motion to y peak = −1c
a
Figure C.14: Estimated drag coefficient due to gusts from the heaving plate interact- ing with the airfoil. Each frame contains force traces from a single release position and initial direction, but different airfoil angles of attack.
-10 -5 0 5 10 0
0.5 1
C L
positive initial motion to y
peak = 1c a
-10 -5 0 5 10
0 0.5 1
C L
positive initial motion to y
peak = 0.5c a
-10 -5 0 5 10
0 0.5 1
C L
negative initial motion to y
peak = 0c a
-10 -5 0 5 10
0 0.5 1
C L
positive initial motion to y
peak = 0c a
-10 -5 0 5 10
0 0.5 1
C L
negative initial motion to y
peak = -0.5c a
-10 -5 0 5 10
0 0.5 1
C L
positive initial motion to y
peak = -0.5c a
-10 -5 0 5 10
0 0.5 1
C L
negative initial motion to y
peak = -1c a
-10 -5 0 5 10
0 0.5 1
C L
positive initial motion to y
peak = -1c a
α=0o, S=0.1 α=5o, S=0.1 α=5o, S=0.25 α=10o, S=0.1
-10 -5 0 5 10
0 0.5 1
C L
negative initial motion to y
peak = 1c a
-10 -5 0 5 10
0 0.5 1
C L
negative initial motion to y
peak = 0.5c a
Figure C.15: Lift coefficient due to gusts from the heaving plate interacting with the airfoil. The dashed lines correspond to the simulations, and dotted lines denote the semi-analytic estimate. Each frame contains force traces from a single release position and initial direction, but different airfoil angles of attack.
Figure C.16: Moment coefficient due to gusts from the heaving plate interacting with the airfoil. Each frame contains force traces from a single release position and initial direction, but different airfoil angles of attack.
Figure C.17: Average envelope of the drag coefficient due to gusts from the heaving plate interacting with the airfoil. Each frame contains traces from a single release position and initial direction, but different airfoil angles of attack.
Figure C.18: Average envelope of the lift coefficient due to gusts from the heaving plate interacting with the airfoil. Each frame contains traces from a single release position and initial direction, but different airfoil angles of attack.