Research Papers

Quantification of the Influence of Unsteady Aerodynamic Loading on the Damping Characteristics of Airfoils Oscillating at Low-Reduced Frequency—Part I: Theoretical Support

[+] Author and Article Information
Roque Corral

Advanced Engineering Direction,
Industria de TurboPropulsores S.A.,
Madrid 28108, Spain;
Associate Professor
Department of Fluid Dynamics and
Aerospace Propulsion School of
Aeronautics and Space,
Madrid 28040, Spain
e-mail: roque.corral@itp.es

Almudena Vega

School of Aeronautics and Space,
Universidad Politécnica de Madrid,
Madrid 28040, Spain
e-mail: almudena.vega@upm.es

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received June 28, 2016; final manuscript received September 11, 2016; published online December 1, 2016. Assoc. Editor: Li He.

J. Turbomach 139(3), 031009 (Dec 01, 2016) (8 pages) Paper No: TURBO-16-1135; doi: 10.1115/1.4034976 History: Received June 28, 2016; Revised September 11, 2016

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.

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Fig. 1

Position of the airfoil in an arbitrary time instant

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Fig. 2

Nondimensional damping as a function of the IBPA for the LPT case vibrating in flap (M = 0.74, k = 0.1) for a viscous and an inviscid case

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Fig. 3

Distribution of the normal gradient of the velocity along an LPT airfoil computed using three different approaches

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Fig. 4

Unsteady loading parameter distribution

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Fig. 5

Isentropic Mach number distributions along the airfoil chord for the LPT and the NACA65 cases

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Fig. 6

Unsteady loading parameter distribution for the NACA65 airfoil. (a) M1 = 0.7 and (b) M1 = 0.8.

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Fig. 7

(a) Nondimensional influence coefficient modulus and (b) phase as a function of the reduced frequency for the flat plate case vibrating in flap (filled symbols) and torsion around the i.e. (open symbols)

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Fig. 8

Nondimensional damping as a function of the IBPA for an asymmetric cascade of flat plates vibrating in flap mode (filled symbols) and torsion about the plate midpoint (open symbols) (M=0.45,θ=45deg, s/c=0.5, k = 0.03)

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Fig. 9

Real (a) and imaginary (b) components of the unsteady pressure for an asymmetric cascade of flat plates vibrating in torsion about the l.e. (Min=0.45,θ=45 deg, s/c=0.5,k=0.1)




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