N A S A C O N T R A C T O R
R E P O R T
N A S A CR-2322
ANALYSIS OF STALL FLUTTER
OF A HELICOPTER ROTOR BLADE
by Peter Crimi
AVCO SYSTEMS DIVISION
Wilmington, Mass. 01887
for Langley Research Center
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. NOVEMBER 1973
1. Report No.
4. Title and Subtitle
ANALYSIS OF STALL FLUTTER OF A HELICOPTER
I 2. Government Accession No.
3. Recipient's Catalog No.
5. Report Date
6. Performing Organization Code
Peter C r i m i
9. Performing Organization Name and Address
AVCO Systems Division
Wil mington, Massachusetts 01887
8. Performing Organization Report No.
10. Work Unit No.
11. Contract or Grant No.
13. Type o f Report and Period Covered
2. Sponforing Agency Name a?d Address
National Aeronautics and Space Administration
Washington, D.C. 20546
7. Key Words (Suggested by Author(s))
He1 icopt er rotor, Ae roe1 a st icity ,
Dynamic stall, Torsional stability
14. Sponsoring Agency Code
18. Distribution Statement
Unclassified - Unlimited
5. Supplementary Notes
The contract research effort which has lead to the results in this report was
financially supported by USAAMRDL (Langley Directorate).
This is a final report.
A study of rotor blade aeroelastic stability was carried out, using an analytic
model of a two-dimensional airfoil undergoing dynamic stall and an elastomechanical
representation including flapping, flapwise bending and torsional degrees of freedom.
Results for a hovering rotor demonstrated that the models used are capable of
reproducing both classical and stall flutter.
occurrence of stall flutter in hover was found to be determined from coupling between
torsion and flapping. Instabilities analogous to both classical and stall flutter were
found to occur in forward flight. However, the large stall-related torsional
oscillations which commonly limit aircraft forward speed appear to be the response
to rapid changes in aerodynamic moment which accompany stall and unstall, rather
than the result of an aeroelastic instability. The severity of stall-related instabilities
and response was found to depend to some extent on linear stability.
linear stability lessens the susceptibility to stall flutter and reduces the magnitude
of the torsional response to stall and unstall.
The minimum rotor speed for the
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ANALYSIS OF STALL FLUTTER
OF A KELICOPTER ROTOR BLADE
By Peter C r i m i
Avco Systems Division
A study of rotor blade aeroelastic s t a b i l i t y was
carried out, using an analytic model of a two-dimensional
a i r f o i l undergoing dynamic s t a l l and an elastomechanical
representation including flapping, flapwise bending and
torsional degrees of freedom. Results f o r a hovering rotor
demonstrated that the models used are capable of reproducing
both classical and stall flutter. The minimum rotor speed
for the occurrence of stall f l u t t e r i n hover was found t o
be determined from coupling between torsion and flapping.
I n s t a b i l i t i e s analogous t o both classical and stall f l u t t e r
were found t o occur i n forward flight. However, the large
stall-related torsional oscillations which commonly l i m i t
a i r c r a f t forward speed appear t o be the response t o rapid
changes i n aerodynamic moment which accompany stall and
unstall, rather than the result of an aeroelastic instabil-
i t y . The severity of stall-related instabilities and re-
sponse was found t o depend t o some extent on linear stabil-
i t y . Increasing linear s t a b i l i t y lessens the susceptibility
t o stall f l u t t e r and reduces the magnitude of the torsional
response t o stall and unstall.
Aeroelastic s t a b i l i t y of a helicopter rotor blade is
a multifaceted problem because of the extreme variations of
the aerodynamic environment within the flight envelope of
the aircraft. In hovering f l i g h t , a blade can undergo
classical binary f l u t t e r (Ref. 1) or stall f l u t t e r (Ref, 2 ) .
In forward flight, the linear Instability experienced by
systems with periodically varying parameters can occur
( R e f , 3). While these types of instability are not normally
encountered with blades of current design, due t o the rela-
tively low disc loading and weak coupling of translational
and rotational degrees of freedom, they are certainly not
precluded from new designs, particularly those intended t o
extend present performance capabilities.
concern, however, i n both design and operation, is the
occurrence of large-amplitude torsional oscillations and
excessive control-linkage loads associated with blade stall
on the retreating side of the rotor disc at high forward
speed o r gross weight, effectively limiting aircraft per-
formance. This problem has prompted a number of recent
studies of dynamic s t a l l and the effects of stall on blade
dynamics (Refs. 4-8).
O f immediate
While stall has been identified as a causal element of
the problem, the nonlinearity of the s t a l l process, coupled
with the unsteady aerodynamic environment, has precluded an
analysis t o the depth required t o gain a thorough under-
standing of the mechanisms invol.ved.
not been clear whether the blade undergoes a true aero-
elastic instability, a simple forced response, or some
hybrid phenomenon which takes on the character of one o r
the other extreme, depending on flight conditions and blade
In particular, it has
S t a l l f l u t t e r for axial flight is amenable t o analysis
by empirical methods similar t o those developed for analyz-
ing s t a l l f l u t t e r i n cascades (Ref. 9 ) . The f l u t t e r
mechanism f o r that case has been identified as deriving
from the extraction of energy from the free stream by the
periodic variation of the aerodynamic moment.
methods applied t o the forward-flight problem (Refs. 10
and 11) have been inconclusive, however, the primary d i f f i -
culty possibly being i n applying empirical methods without
a clear definition of the underlying mechanism of the problem.
A method was recently developed for analyzing dynamic
stall of an a i r f o i l undergoing arbitrary pitching and
plunging motions which provides an ideal tool for analyzing
the stall problem i n forward flight. The method, which is
described i n detail i n R e f , 7, employs models for each of
the basic flow elements contributing t o the unsteady stall
of a two-dimensional a i r f o i l . Calculations of the loading
during transient and sinusoidal pitching motions are i n
good qualitative agreement with measured loads.
overshoot, o r l i f t i n excess of the maximum static value,
as well as unstable moment variation, are in clear evidence
i n the computed results.
This study was directed t o analyzing the aeroelastic
stability of a helicopter rotor, particularly a s it relates
t o s t a l l , using the method of R e f . 7 t o compute aerodynamic
loading. The representation of the elastomechanical system
includes flapping and flapwise bending degrees of freedom
as well as torsion.
t o perform the calculations is given i n Appendix A .
A l i s t i n g of the computer program used