1
Experimental Modeling of Compressible Dynamic Stall in Unsteady Flow through
Interpolation of Phase-Matched Conditions in Steady Flow
Shawn C. Naigle
Graduate Student
Matthew W. Frankhouser
Graduate Research
Associate
Kevin A. Williams
Undergraduate
Student
James W. Gregory
Associate Professor
Jeffrey P. Bons
Professor
Aerospace Research Center
The Ohio State University
Columbus, Ohio, United States
ABSTRACT
This experimental study compares the features of dynamic stall between a steady compressible freestream and an unsteady
compressible freestream on an oscillating SSC-A09 airfoil. Instantaneous non-dimensional parameters (Mach (M), Reynolds
number (Re), and reduced frequency (k)) were phase matched between steady and unsteady freestream conditions to isolate
the effects of unsteady characteristics on dynamic stall. This investigation was conducted at mean Mach and Reynolds
numbers of M
0
=0.4 and Re
0
=3.0 million, respectively, and at two reduced frequencies, k
0
=0.05 and 0.025. The steady
freestream Mach was set at fixed values ranging between M
0
=0.32 and M
0
=0.46, while the unsteady freestream Mach number
was modulated at M=0.4+0.07cos(ωt) and phase locked with α=9°−13°cos(ωt). This paper explores the feasibility of
simulating unsteady freestream dynamic stall physics using data acquired with a steady freestream.
NOTATION
AR Aspect ratio
b Airfoil span
c Airfoil chord
C
L
Lift coefficient
C
M
Moment coefficient
C
P
Pressure coefficient,
2
1
2
P P U
f Physical frequency
k Reduced frequency, 2 c U
M Mach number
P Pressure
Re Reynolds number
T Temperature
U Velocity
x Chordwise position
α Angle of attack
Phase angle
Δ Phase difference between M and α
ω Angular frequency, 2 f
Subscripts
0 Mean value
∞ Freestream value
Δ Amplitude change
Presented at the AHS Technical Meeting on Aeromechanics
Design for Vertical Lift, San Francisco, California, January
20-22, 2016. Copyright © 2016 by the American Helicopter
Society International, Inc. All rights reserved.
INTRODUCTION
As rotorcraft engage in forward flight, the effective
freestream velocity experienced by the advancing blade is
greater than that of the retreating blade. A cyclic feathering
pattern which matches maximum angle of attack with
minimum relative velocity and minimum angle of attack
corresponding to maximum relative velocity maintains
constant lift around the rotor azimuth. However, during high
speed or maneuvering flight, the retreating blade eventually
exceeds a critical angle of attack and a dynamic stall
sequence occurs. The resultant complex aerodynamic
phenomenon is accompanied by high lift coefficients and
strong negative pitching moments, which lead to aeroelastic
instabilities, increased vibration, and stress on rotor pitch
links that severely limiting rotorcraft performance.
Dynamic stall has been the subject of study for over four
decades. Early studies were focused on understanding the
basic phenomena and are thoroughly documented by
McCroskey et al. (Ref. 1) and Carr (Ref. 2), including the
effects of compressibility examined by Chandrasekhara et
al. (Ref. 3). Since dynamic stall on rotorcraft occurs during
the retreating blade motion at advance ratios approaching
0.3-0.4, the relative flow velocity “seen” by the retreating
airfoil also varies during the dynamic stall event. This time-
varying relative velocity has a direct influence on the
severity of the local pressure gradient. Several researchers
have investigated the combination of airfoil pitching and
relative velocity oscillations including Furman et al., (Ref.
4), Favier et al., (Ref. 5), and Hird et al. (Ref. 6) and
concluded that a strong coupling exists between the two
modes of oscillation and their relative time scales.
Accurate modeling of rotorcraft dynamic stall is necessary
for understanding rotorcraft dynamics and improving upon