The aerodynamics of finite-span inclined flat plates in ground effect is experimentally investigated at a chord-based Reynolds number of 50 000 for aspect ratios of 1 and 2. The minimum ground height is varied between 0.1 and 1.0 chord lengths, and lift and drag forces are measured using a force balance for angles of attack between −90° and 90°. Planar, two- and three-component particle image velocimetry is used to perform streamwise and cross-plane measurements at the midspan and one chord length downstream of the trailing edge, respectively. Ground effect is significant at ground clearances below 0.5 chord lengths, most notably near the stall angle, where it leads to significant changes to flow development. At sufficiently low free flight pre-stall angles, the increase in edge velocity at low gap ratios caused greater suction, generating higher lift with a minimal increase in drag for both orientations. Closer to the free flight stall angle, a decrease in aerodynamic loading is observed for negative orientations due to earlier onset of stall with a decreasing gap ratio. The exception was the higher aspect ratio plate at negative orientations, where the loading was largely invariant to changes in gap ratio for all angles tested. At positive orientations, the increase in average static pressure along the pressure surface in ground proximity led to an overall increase in loading prior to deep-stall conditions for both aspect ratios. The ground effect was minimal at post-stall angles of attack. The results may be used to guide the design of photovoltaic supports at relevant latitudes.

1.
A.
Jafari
,
F.
Ghanadi
,
M.
Arjomandi
,
M. J.
Emes
, and
B. S.
Cazzolato
, “
Correlating turbulence intensity and length scale with the unsteady lift force on flat plates in an atmospheric boundary layer flow
,”
J. Wind Eng. Ind. Aerodyn.
189
,
218
(
2019
).
2.
D.
Li
,
Y.
Wu
,
A.
Da Ronch
, and
J.
Xiang
, “
Energy harvesting by means of flow-induced vibrations on aerospace vehicles
,”
Prog. Aerosp. Sci.
86
,
28
(
2016
).
3.
F. M.
Fang
,
W. D.
Hsieh
,
S. W.
Jong
, and
J. J.
She
, “
Unsteady turbulent flow past solid fence
,”
J. Hydraul. Eng.
123
,
560
(
1997
).
4.
K. V.
Rozhdestvensky
, “
Wing-in-ground effect vehicles
,”
Prog. Aerosp. Sci.
42
,
211
(
2006
).
5.
R.
Bleischwitz
,
R.
de Kat
, and
B.
Ganapathisubramani
, “
Aeromechanics of membrane and rigid wings in and out of ground-effect at moderate Reynolds numbers
,”
J. Fluids Struct.
62
,
318
(
2016
).
6.
R.
Fu
,
D.
Feldman
, and
R.
Margolis
, “
U. S. Solar photovoltaic system cost benchmark: Q1 2018
,”
Technical Report No. NREL/TP-6A20-72399
(
National Renewable Energy Laboratory
,
Golden, CO
,
2018
).
7.
A.
Fage
and
F. C.
Johansen
, “
On the flow of air behind an inclined flat plate of infinite span
,”
Proc. R. Soc. A
116
,
170
(
1927
).
8.
C. W.
Knisely
, “
Strouhal numbers of rectangular cylinders at incidence: A review and new data
,”
J. Fluids Struct.
4
,
371
(
1990
).
9.
C.
Norberg
, “
Flow around rectangular cylinders: Pressure forces and wake frequencies
,”
J. Wind Eng. Ind. Aerodyn.
49
,
187
(
1993
).
10.
J. M.
Chen
and
Y. C.
Fang
, “
Strouhal numbers of inclined flat plates
,”
J. Wind Eng. Ind. Aerodyn.
61
,
99
(
1996
).
11.
W. W.
Yeung
and
G. V.
Parkinson
, “
On the steady separated flow around an inclined flat plate
,”
J. Fluid Mech.
333
,
403
(
1997
).
12.
Z. G.
Yang
,
W.
Yang
, and
Q.
Jia
, “
Ground viscous effect on 2D flow of wing in ground proximity
,”
Eng. Appl. Comput. Fluid Mech.
4
,
521
(
2010
).
13.
K.
Taira
and
T.
Colonius
, “
Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers
,”
J. Fluid Mech.
623
,
187
(
2009
).
14.
A.
Pfahl
and
H.
Uhlemann
, “
Wind loads on heliostats and photovoltaic trackers at various Reynolds numbers
,”
J. Wind Eng. Ind. Aerodyn.
99
,
964
(
2011
).
15.
J. D.
Eldredge
and
A. R.
Jones
, “
Leading-edge vortices: Mechanics and modeling
,”
Annu. Rev. Fluid Mech.
51
,
75
(
2019
).
16.
T. J.
Mueller
, “
Aerodynamic measurements at low Reynolds numbers for fixed wind micro-air vehicles
,”
Technical Report No. ADP010760
(
Notre Dame University in Department of Aerospace and Mechanical Engineering
,
2000
).
17.
A.
Gharakhani Siraki
and
P.
Pillay
, “
Study of optimum tilt angles for solar panels in different latitudes for urban applications
,”
Sol. Energy
86
,
1920
(
2012
).
18.
J. S.
Yu
,
M. J.
Emes
,
F.
Ghanadi
,
M.
Arjomandi
, and
R.
Kelso
, “
Experimental investigation of peak wind loads on tandem operating heliostats within an atmospheric boundary layer
,”
Sol. Energy
183
,
248
(
2019
).
19.
A. C.
Devoria
and
K.
Mohseni
, “
On the mechanism of high-incidence lift generation for steadily translating low-aspect-ratio wings
,”
J. Fluid Mech.
813
,
110
(
2017
).
20.
X.
Ortiz
,
D.
Rival
, and
D.
Wood
, “
Forces and moments on flat plates of small aspect ratio with application to PV wind loads and small wind turbine blades
,”
Energies
8
,
2438
(
2015
).
21.
J.
Peterka
and
R.
Derickson
, “
Wind load design methods for ground-based heliostats and parabolic dish collectors
,”
Technical Report No. SAND-92-7009
(
Sandia National Laboratories (SNL)
,
Albuquerque, NM, and Livermore, CA
,
1992
).
22.
Z.
Li
,
C.
Lan
,
L.
Jia
, and
Y.
Ma
, “
Ground effects on separated laminar flows past an inclined flat plate
,”
Theor. Comput. Fluid Dyn.
31
,
127
(
2017
).
23.
I. H.
Liu
and
A.
Oztekin
, “
Three-dimensional transient flows past plates translating near a wall
,”
Ocean Eng.
159
,
9
(
2018
).
24.
K.
Fukuda
,
R.
Balachandar
, and
R. M.
Barron
, “
Analysis of the ground effect on development of flow structures around an inclined solar panel
,”
Environ. Fluid Mech.
20
,
1463
(
2020
).
25.
R.
Bleischwitz
,
R.
de Kat
, and
B.
Ganapathisubramani
, “
Near-wake characteristics of rigid and membrane wings in ground effect
,”
J. Fluids Struct.
80
,
199
(
2018
).
26.
G. P.
Reina
and
G.
De Stefano
, “
Computational evaluation of wind loads on sun-tracking ground-mounted photovoltaic panel arrays
,”
J. Wind Eng. Ind. Aerodyn.
170
,
283
(
2017
).
27.
L.
Dong
,
K. S.
Choi
, and
X.
Mao
, “
Interplay of the leading-edge vortex and the tip vortex of a low-aspect-ratio thin wing
,”
Exp. Fluids
61
,
200
(
2020
).
28.
M.
Shademan
and
A.
Naghib-Lahouti
, “
Effects of aspect ratio and inclination angle on aerodynamic loads of a flat plate
,”
Adv. Aerodyn.
2
,
14
(
2020
).
29.
P.
Gutierrez-Castillo
,
J.
Aguilar-Cabello
,
S.
Alcalde-Morales
,
L.
Parras
, and
C.
del Pino
, “
On the lift curve slope for rectangular flat plate wings at moderate Reynolds number
,”
J. Wind Eng. Ind. Aerodyn.
208
,
104459
(
2021
).
30.
T.
Linehan
and
K.
Mohseni
, “
Leading-edge flow reattachment and the lateral static stability of low-aspect-ratio rectangular wings
,”
Phys. Rev. Fluids
2
,
113901
(
2017
).
31.
M. J.
Emes
,
A.
Jafari
,
F.
Ghanadi
, and
M.
Arjomandi
, “
Hinge and overturning moments due to unsteady heliostat pressure distributions in a turbulent atmospheric boundary layer
,”
Sol. Energy
193
,
604
(
2019
).
32.
H.
Merarda
,
M.
Aksas
, and
T.
Andrianne
, “
Shape effects on aerodynamic loading of heliostats
,”
Mech. Ind.
21
,
614
(
2020
).
33.
S. O.
Fadlallah
,
T. N.
Anderson
, and
R. J.
Nates
, “
Flow behaviour and aerodynamic loading on a stand-alone heliostat: Wind incidence effect
,”
Arabian J. Sci. Eng.
46
,
7303
(
2021
).
34.
M.
Shademan
,
R.
Barron
,
R.
Balachandar
, and
H.
Hangan
, “
Numerical simulation of wind loading on ground-mounted solar panels at different flow configurations
,”
Can. J. Civ. Eng.
41
,
728
(
2014
).
35.
R.
Bleischwitz
,
R.
de Kat
, and
B.
Ganapathisubramani
, “
On the fluid-structure interaction of flexible membrane wings for MAVs in and out of ground-effect
,”
J. Fluids Struct.
70
,
214
(
2017
).
36.
A.
Lu
and
T.
Lee
, “
Effect of ground boundary condition on near-field wingtip vortex flow and lift-induced drag
,”
J. Fluids Eng. Trans. ASME
143
,
031301
(
2021
).
37.
M. R.
Ahmed
, “
Aerodynamics of a cambered airfoil in ground effect
,”
Int. J. Fluid Mech. Res.
32
,
157
(
2005
).
38.
K.
Cooper
, “
Bluff-body blockage corrections in closed- and open-test-section wind tunnels
,”
Report No. AGARD AG-336
(
NTIS
,
Springfield, VA
,
1998
).
39.
A. K.
Yadav
and
S. S.
Chandel
, “
Tilt angle optimization to maximize incident solar radiation: A review
,”
Renewable Sustainable Energy Rev.
23
,
503
(
2013
).
40.
Y.
Wang
,
J.
Curran
,
G. D.
Padfield
, and
I.
Owen
, “
AirDyn: An instrumented model-scale helicopter for measuring unsteady aerodynamic loading in airwakes
,”
Meas. Sci. Technol.
22
,
045901
(
2011
).
41.
M. S.
Seif
and
M. T.
Dakhrabadi
, “
A practical method for aerodynamic investigation of WIG
,”
Aircr. Eng. Aerosp. Technol.
88
,
73
(
2016
).
42.
C.
Wieselsberger
, “
Wing resistance near the ground
,”
Technical Report No. NACA-TM-77
(
National Advisory Committee for Aeronautics Collection
,
1922
).
43.
C.
Lei
,
L.
Cheng
, and
K.
Kavanagh
, “
Re-examination of the effect of a plane boundary on force and vortex shedding of a circular cylinder
,”
J. Wind Eng. Ind. Aerodyn.
80
,
263
(
1999
).
44.
R. J.
Martinuzzi
,
S. C.
Bailey
, and
G. A.
Kopp
, “
Influence of wall proximity on vortex shedding from a square cylinder
,”
Exp. Fluids
34
,
585
(
2003
).
45.
B. W.
Van Oudheusden
, “
PIV-based pressure measurement
,”
Meas. Sci. Technol.
24
,
032001
(
2013
).
46.
P.
Zhang
,
S. D.
Peterson
, and
M.
Porfiri
, “
Combined particle image velocimetry/digital image correlation for load estimation
,”
Exp. Therm. Fluid Sci.
100
,
207
(
2019
).
47.
J. W.
Van der Kindere
,
A.
Laskari
,
B.
Ganapathisubramani
, and
R.
de Kat
, “
Pressure from 2D snapshot PIV
,”
Exp. Fluids
60
,
32
(
2019
).
48.
J.
McClure
and
S.
Yarusevych
, “
Optimization of planar PIV-based pressure estimates in laminar and turbulent wakes
,”
Exp. Fluids
58
,
62
(
2017
).
49.
T.
Jardin
,
A.
Farcy
, and
L.
David
, “
Three-dimensional effects in hovering flapping flight
,”
J. Fluid Mech.
702
,
102
(
2012
).
50.
J.
Jeong
and
F.
Hussain
, “
On the identification of a vortex
,”
J. Fluid Mech.
285
,
69
(
1995
).
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