The effect of the unsteady aerodynamic loading of oscillating airfoils in the low-reduced frequency regime on the work per cycle curves is investigated. The theoretical analysis is based on a perturbation analysis of the linearized Navier–Stokes equations for real modes at low-reduced frequency. It was discovered that a new parameter, the unsteady loading, plays an essential role in the trends of the phase and modulus of the unsteady pressure caused by the airfoil oscillation. Here, the theory is extended in order to quantify this new parameter. It is shown that this parameter depends solely on the steady flow-field on the airfoil surface and the vibration mode-shape. As a consequence, the effect of changing the design operating conditions or the vibration mode onto the work-per-cycle curves (and therefore in the stability) can be easily predicted and, what is more important, quantified without conducting additional flutter analysis. The relevance of the parameter has been numerically confirmed in the Part II of the paper.

References

References
1.
Corral
,
R.
,
Gallardo
,
J. M.
, and
Vasco
,
C.
,
2007
, “
Aeroelastic Stability of Welded-in-Pair Low Pressure Turbine Rotor Blades: A Comparative Study Using Linear Methods
,”
ASME J. Turbomach.
,
129
(
1
), pp.
72
83
.
2.
Corral
,
R.
,
Gallardo
,
J. M.
, and
Martel
,
C.
,
2009
, “
A Conceptual Flutter Analysis of a Packet of Vanes Using a Mass-Spring Model
,”
ASME J. Turbomach.
,
131
(
2
), p.
021016
.
3.
Waite
,
J.
, and
Kielb
,
R.
,
2015
, “
Physical Understanding and Sensitivities of Low Pressure Turbine Flutter
,”
ASME J. Eng. Gas Turbines Power
,
137
(
1
), p.
012502
.
4.
Corral
,
R.
, and
Vega
,
A.
,
2016
, “
The Low Reduced Frequency Limit of Vibrating Airfoils—Part I: Theoretical Analysis
,”
ASME J. Turbomach.
,
138
(
2
), p.
021004
.
5.
Vega
,
A.
, and
Corral
,
R.
,
2016
, “
The Low Reduced Frequency Limit of Vibrating Airfoils—Part II: Numerical Experiments
,”
ASME J. Turbomach.
,
138
(
2
), p.
021005
.
6.
Corral
,
R.
, and
Vega
,
A.
,
2016
, “
Physics of Vibrating Turbine Airfoils at Low Reduced Frequency
,”
AIAA J. Propul. Power
,
32
(
2
), pp.
325
336
.
7.
Barbarossa
,
F.
,
Parry
,
A. B.
,
Gallardo
,
J. M.
, and
Mare
,
L.
,
2016
, “
An Aerodynamic Parameter for Low-Pressure Turbine Flutter
,”
ASME J. Turbomach.
,
138
(
5
), p.
051001
.
8.
Barbarossa
,
F.
,
Parry
,
A. B.
,
Green
,
J. S.
, and
di Mare
,
L.
,
2016
, “
An Aerodynamic Parameter for Low Pressure Turbine, Flutter
,”
ASME J. Turbomach.
,
138
(
5
), p. 051001.
9.
Li
,
H.
, and
He
,
L.
,
2008
, “
Blade Aerodynamic Damping Variation With Rotor-Stator Gap: A Computational Study Using Single-Passage Approach
,”
ASME J. Turbomach.
,
127
(
3
), pp.
573
579
.
10.
Vahdati
,
M.
,
Smith
,
N.
, and
Zhao
,
F.
,
2015
, “
Influence of Intake on Fan Blade Flutter
,”
ASME J. Turbomach.
,
137
(
8
), p.
081002
.
11.
Vega
,
A.
, and
Corral
,
R.
,
2016
, “
The Low Reduced Frequency Limit of Vibrating Airfoils. Part IIIB: Numerical Quantification and Influence of Unsteady Loading
,”
ASME
Paper No. GT2016-57288.
12.
Lemmerman
,
L.
, and
Sonnad
,
V.
,
1979
, “
Three-Dimensional Viscous-Inviscid Coupling Using Surface Transpiration
,”
J. Aircr.
,
16
(
6
), pp.
353
358
.
13.
Wolff
,
J.
, and
Fleeter
,
S.
,
1994
, “
Unsteady Inviscid-Viscous Analysis of Oscillating Aerodynamics
,”
AIAA
Paper No. 2797.
14.
Vahdati
,
M.
,
Simpson
,
G.
, and
Imregun
,
M.
,
2011
, “
Mechanisms for Wide-Chord Fan Blade Flutter
,”
ASME J. Turbomach.
,
133
(
4
), p.
041029
.
15.
Bölcs
,
A.
, and
Fransson
,
T. H.
,
1986
, “
Aeroelasticity in Turbomachines: Comparison of Theoretical and Experimental Cascade Results
,” Laboratoire de Thermique Appliquee et de Turbomachines, EPFL, Lausanne, Switzerland, Report No. 13.
16.
Fransson
,
T. H.
, and
Verdon
,
J. M.
,
1992
, “
Updated Report on Standard Configurations for Unsteady Flow
,” KTH, Stockholm, Sweden.
17.
Corral
,
R.
,
Escribano
,
A.
,
Gisbert
,
F.
,
Serrano
,
A.
, and
Vasco
,
C.
,
2003
, “
Validation of a Linear Multigrid Accelerated Unstructured Navier–Stokes Solver for the Computation of Turbine Blades on Hybrid Grids
,”
AIAA
Paper No. 2003-3326.
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