The Leishman–Beddoes dynamic stall model is a popular model that has been widely applied in both helicopter and wind turbine aerodynamics. This model has been specially refined and tuned for helicopter applications, where the Mach number is usually above 0.3. However, experimental results and analyses at the University of Glasgow have suggested that the original Leishman–Beddoes model reconstructs the unsteady airloads at low Mach numbers less well than at higher Mach numbers. This is particularly so for stall onset and the return from the fully stalled state. In this paper, a modified dynamic stall model that adapts the Leishman–Beddoes dynamic stall model for lower Mach numbers is proposed. The main modifications include a new stall-onset indication, a new return modeling from stalled state, a revised chordwise force, and dynamic vortex modeling. The comparisons to the Glasgow University dynamic stall database showed that the modified model is capable of giving improved reconstructions of unsteady aerofoil data in low Mach numbers.

1.
McAlister
,
K. W.
,
Carr
,
L. W.
, and
McCroskey
,
W. J.
, 1978, “
Dynamic Stall Experiments on the NACA 0012 Airfoil
,” NASA Technical Paper 1100.
2.
McCroskey
,
W. J.
, 1976, “
Dynamic Stall Experiments on Oscillating Airfoils
,”
AIAA J.
0001-1452,
14
, pp.
57
63
.
3.
McCroskey
,
W. J.
,
McAlister
,
J. W.
,
Carr
,
L. W.
,
Pucci
,
S. L.
,
Lambert
,
O.
, and
Indergrand
,
R. F.
, 1981, “
Dynamic Stall on Advanced Airfoil Sections
,”
J. Am. Helicopter Soc.
0002-8711,
26
, pp.
40
50
.
4.
Wilby
,
P. G.
, 1980, “
The Aerodynamic Characteristics of Some New RAE Blade Sections, and Their Potential Influence on Rotor Performance
,”
Vertica
0360-5450,
4
, pp.
121
133
.
5.
Wilby
,
P. G.
, 2001, “
The Development of Rotor Airfoil Testing in the UK
,”
J. Am. Helicopter Soc.
0002-8711,
46
, pp.
210
220
.
6.
Lee
,
T.
, and
Gerontakos
,
P.
, 2004, “
Investigation of Flow Over an Oscillating Airfoil
,”
J. Fluid Mech.
0022-1120,
512
, pp.
313
341
.
7.
Ekaterinaris
,
J. A.
, and
Platzer
,
M. F.
, 1997, “
Computational Prediction of Airfoil Dynamic Stall
,”
Prog. Aerosp. Sci.
0376-0421,
33
, pp.
759
846
.
8.
Guilmineau
,
E.
, and
Queutey
,
P.
, 1999, “
Numerical Study of Dynamic Stall on Several Airfoil Sections
,”
AIAA J.
0001-1452,
37
, pp.
128
130
.
9.
Geissler
,
W.
,
Dietz
,
G.
, and
Mai
,
H.
, 2005, “
Dynamic Stall on a Supercritical Airfoil
,”
Aerosp. Sci. Technol.
1270-9638,
9
, pp.
390
399
.
10.
Spentzos
,
A.
,
Barakos
,
G. N.
,
Badcock
,
K. J.
,
Richards
,
B. E.
,
Wernert
,
P.
,
Schreck
,
S.
, and
Raffel
,
M.
, 2005, “
Investigation of Three-Dimensional Dynamic Stall Using Computational Fluid Dynamics
,”
AIAA J.
0001-1452,
43
, pp.
1023
1033
.
11.
Tan
,
C. M.
, and
Carr
,
L. W.
, 1996, “
The AFDD International Dynamic Stall Workshop on Correction of Dynamic Stall Models With 3-D Dynamic Stall Data
,” NASA Technical Memorandum 110375, also USAATCOM Technical Report 96-A-009.
12.
Petot
,
D.
,
Arnaud
,
G.
,
Stevens
,
J.
,
Dieterich
,
O.
,
van der Wall
,
B. G.
,
Young
,
C.
, and
Szechenyi
,
E.
, 1999, “
Stall Effects and Blade Torsion—An Evaluation of Predictive Tools
,”
J. Am. Helicopter Soc.
0002-8711,
44
, pp.
320
331
.
13.
McCroskey
,
W. J.
, 1982, “
Unsteady Airfoils
,”
Annu. Rev. Fluid Mech.
0066-4189,
14
, pp.
285
311
.
14.
Carr
,
L. W.
, 1988, “
Progress in Analysis and Prediction of Dynamic Stall
,”
J. Aircr.
0021-8669,
25
, pp.
6
17
.
15.
Carr
,
L. W.
, and
Chandrasekhara
,
M. S.
, 1996, “
Compressibility Effects on Dynamic Stall
,”
Prog. Aerosp. Sci.
0376-0421,
32
, pp.
523
573
.
16.
Leishman
,
J. G.
, 2000,
Principle of Helicopter Aerodynamics
, 1st ed.,
Cambridge University Press
,
Cambridge
.
17.
Beddoes
,
T. S.
, 1976, “
A Synthesis of Unsteady Aerodynamic Effects Including Stall Hysteresis
,”
Vertica
0360-5450,
1
, pp.
113
123
.
18.
Beddoes
,
T. S.
, 1978, “
Onset of Leading Edge Separation Effects Under Dynamic Conditions and Low Mach Number
,”
Presented at the 34th Annual National Forum of the American Helicopter Society
,
Washington, DC
, May.
19.
Beddoes
,
T. S.
, 1983, “
Representation of Airfoil Behaviour
,”
Vertica
0360-5450,
7
, pp.
183
197
.
20.
Beddoes
,
T. S.
, 1984, “
Practical Computational of Unsteady Lift
,”
Vertica
0360-5450,
8
, pp.
55
71
.
21.
Leishman
,
J. G.
, 1987, “
Practical Modelling of Unsteady Airfoil Behaviour in Nominally Attached Two-Dimensional Compressible Flow
,” UM-AERO-87–6, Department of Aerospace Engineering, University of Maryland.
22.
Leishman
,
J. G.
, 1987, “
A Semi-Empirical Model for Dynamic Stall
,” UM-AERO-87–24, Department of Aerospace Engineering, University of Maryland.
23.
Leishman
,
J. G.
, and
Beddoes
,
T. S.
, 1989, “
A Semi-Empirical Model for Dynamic Stall
,”
J. Am. Helicopter Soc.
0002-8711,
34
, pp.
3
17
.
24.
Beddoes
,
T. S.
, 1993, “
A Third Generation Model for Unsteady Aerodynamics and Dynamic Stall
,” Westland Helicopter Limited, RP-908.
25.
Sheng
,
W.
,
Galbraith
,
R. A. McD.
, and
Coton
,
F. N.
, 2006, “
A New Stall-Onset Criterion for Low Speed Dynamic-Stall
,”
ASME J. Sol. Energy Eng.
0199-6231,
128
, pp.
461
471
.
26.
Gutpa
,
S.
, and
Leishman
,
J. G.
, 2006, “
Dynamic Stall Modelling of the S809 Aerofoil and Comparison With Experiments
,”
Wind Energy
1095-4244,
9
, pp.
521
547
.
27.
Sheng
,
W.
,
Galbraith
,
R. A. McD.
, and
Coton
,
F. N.
, 2007, “
A Modified Dynamic Stall Model for Low Mach Numbers
,”
Presented at the 45th AIAA Aerospace Sciences and Meeting Exhibit
, Reno, NV, Jan. Paper No. AIAA-2007–0626.
28.
Niven
,
A. J.
, and
Galbraith
,
R. A. McD.
, 1997, “
Modelling Dynamic Stall Vortex Inception at Low Mach Numbers
,”
Aeronaut. J.
0001-9240,
101
, pp.
67
76
.
29.
Sheng
,
W.
, and
Galbraith
,
R. A. McD.
,
Coton
,
F. N.
, 2007, “
Improved Dynamic Stall Onset Criterion for Low Mach Numbers
,”
J. Aircr.
0021-8669,
44
(
3
), pp.
1049
1052
.
30.
Niven
,
A. J.
,
Galbraith
,
R. A. McD.
, and
Herring
,
D. G. F.
, 1989, “
Analysis of Reattachment During Ramp Down Tests
,”
Vertica
0360-5450,
13
, pp.
187
196
.
31.
Green
,
R. B.
, and
Galbraith
,
R. A. McD.
, 1994, “
Phenomena Observed during Aerofoil Ramp-down Motions from the Fully Separated State
,”
Aeronaut. J.
0001-9240,
98
, pp.
349
356
.
32.
Green
,
R. B.
, and
Galbraith
,
R. A. McD.
, 1995, “
Dynamic Recovery to Fully Attached Aerofoil Flow from Deep Stall
,”
AIAA J.
0001-1452,
33
, pp.
1433
1440
.
33.
Sheng
,
W.
,
Galbraith
,
R. A. McD.
, and
Coton
,
F. N.
, 2007, “
On the Return From Aerofoil Stall During Ramp-Down Pitching Motions
,”
J. Aircr.
0021-8669
44
(
6
), pp.
1856
1864
(also
Presented at the 45th AIAA Aerospace Sciences and Meeting Exhibition
, Reno, NV, Jan. 2007, Paper No. AIAA-2007–1075.
34.
Galbraith
,
R. A. McD.
,
Gracey
,
M. W.
, and
Leitch
,
E.
, 1992, “
Summary of Pressure Data for Thirteen Aerofoils on the University of Glasgow Aerofoil Database
,” G. U. Aero Report 9221, June.
35.
Sheng
,
W.
,
Galbraith
,
R. A. McD.
,
Coton
,
F. N.
, and
Gilmour
,
R.
, 2006, “
The Collected Data for Tests on an S809 Aerofoil, Volume I: Pressure Data From Static, Ramp and Triangular Wave Tests
,” G. U. Aero Report 0606, University of Glasgow.
36.
Sheng
,
W.
,
Galbraith
,
R. A. McD.
,
Coton
,
F. N.
, and
Gilmour
,
R.
, 2006, “
The Collected Data for Tests on an S809 Aerofoil, Volume II: Pressure Data From Static and Oscillatory Tests
,” G. U. Aero Report 0607, University of Glasgow.
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