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Research Papers

A Physically Consistent Reduced Order Model for Plasma Aeroelastic Control on Compressor Blades

[+] Author and Article Information
Valentina Motta

Department of Aeronautics and Astronautics,
Technische Universität Berlin,
Berlin 10587, Germany
e-mail: valentina.motta@tu-berlin.de

Leonie Malzacher

Department of Aeronautics and Astronautics,
Technische Universität Berlin,
Berlin 10587, Germany
e-mail: leonie.malzacher@tu-berlin.de

Victor Bicalho Civinelli de Almeida

Department of Aeronautics and Astronautics,
Technische Universität Berlin,
Berlin 10587, Germany
e-mail: Victor.Bicalho@ilr.tu-berlin.de

Tien Dat Phan

Department of Machine Design,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: t.phan@tu-berlin.de

Robert Liebich

Department of Machine Design,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: Robert.Liebich@tu-berlin.de

Dieter Peitsch

Department of Aeronautics and Astronautics,
Technische Universität Berlin,
Berlin 10587, Germany
e-mail: dieter.peitsch@tu-berlin.de

Giuseppe Quaranta

Department of Aerospace Science and
Technology,
Politecnico di Milano,
Milan 20156, Italy
e-mail: giuseppe.quaranta@polimi.it

1Corresponding author.

Manuscript received March 3, 2019; final manuscript received April 13, 2019; published online May 3, 2019. Assoc. Editor: Harald Schoenenborn.

J. Eng. Gas Turbines Power 141(9), 091001 (May 03, 2019) (13 pages) Paper No: GTP-19-1090; doi: 10.1115/1.4043545 History: Received March 03, 2019; Revised April 13, 2019

Plasma actuators may be successfully employed as virtual control surfaces, located at the trailing edge (TE) of blades, both on the pressure and on the suction side, to control the aeroelastic response of a compressor cascade. Actuators generate an induced flow against the direction of the freestream. As a result, actuating on the pressure side yields an increase in lift and nose down pitching moment, whereas the opposite is obtained by operating on the suction side. A properly phased alternate pressure/suction side actuation allows to reduce vibration and to delay the flutter onset. This paper presents the development of a linear frequency domain reduced order model (ROM) for lift and pitching moment of the plasma-equipped cascade. Specifically, an equivalent thin airfoil model is used as a physically consistent basis for the model. Modifications in the geometry of the thin airfoil are generated to account for the effective chord and camber changes induced by the plasma actuators, as well as for the effects of the neighboring blades. The model reproduces and predicts correctly the mean and the unsteady loads, along with the aerodynamic damping on the plasma equipped cascade. The relationship between the parameters of the ROM with the flow physics is highlighted.

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Figures

Grahic Jump Location
Fig. 1

Schematic of a dielectric barrier discharge plasma actuator

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Fig. 2

Schematic of the computational geometry for the compressor cascade, corresponding to the experimental rig of Ref. [20]

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Fig. 3

Sketch of the blade section with the plasma actuators

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Fig. 4

Steady force coefficients versus the angle of attack for the clean central blade, together with the pressure or suction side actuated counterpart; PS: pressure side; SS: suction side; Re ∼ 3 × 105; plasma body force: 300 mN/m, both on PS and SS: (a) lift coefficient, (b) drag coefficient, and (c) quarter-chord moment coefficient

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Fig. 5

Sketch of PS and SS actuation triggering with respect to the blade motion α(t) and of its time derivative α˙(t)

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Fig. 6

Top: TE detail of velocity magnitude, normalized by thefreestream velocity, over the oscillation cycle; plasma actuation on. Middle: time history of lift and moment coefficient oscillations without and with actuation. Bottom: aerodynamic damping versus IBPA with and without plasma. Re ∼ 1.9 × 105; IBPA = −51.43 deg.; α=2+sin (2πf t+4×IBPAπ/180) deg; f = 19.17 Hz, T = 1/f; PS body force: 225 mN/m; and SS body force: 450 mN/m.

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Fig. 7

Sketch of the blade section with plasma actuators, together with the equivalent thin-line geometry

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Fig. 8

Top: parameters of the equivalent geometry. Bottom: force coefficients obtained with the fitting over the CFD data versus the plasma body force. Re ∼ 3 × 105; α = 0 deg; plasma body force: 300 mN/m, both on PS and SS: (a) deflection amplitude of PEF, (b) deflection amplitude of ETT, (c) lift coefficient, and (d) midchord moment coefficient.

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Fig. 9

Parameters of the ROM equivalent geometry; off design conditions; k = 0.2299; Re ∼ 1.6 × 105; PS plasma body force: 225 mN/m; SS body force: 450 mN/m: (a) deflection amplitude of PEF, (b) deflection amplitude of ETT, (c) phase angle of ETT, and (d) length of ETT

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Fig. 10

Nondimensional vorticity field for the central blade of the cascade with alternate PS/SS actuation, together with the equivalent geometry computed with the ROM; off design conditions; k = 0.2299; Re ∼ 1.6 × 105; oscillation amplitude: 1 deg.; PS plasma body force: 225 mN/m; and SS body force: 450 mN/m

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Fig. 11

Hysteresis curves of lift and moment coefficient for the central blade of the cascade with alternate PS/SS actuation, together with the counterpart of the ROM; off design conditions; Re ∼ 1.9 × 105; PS plasma body force: 225 mN/m; and SS body force: 450 mN/m

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Fig. 12

Hysteresis curves of lift and moment coefficient for the central blade of the cascade with alternate PS/SS actuation. Interpolation of the ROM parameters at IBPA = 112.5 deg and CFD simulations performed a posteriori; off design conditions; Re ∼ 1.9 × 105; PS plasma body force: 225 mN/m; and SS body force: 450 mN/m.

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Fig. 13

Parameters of the ROM equivalent geometry; design conditions; k = 0.0720; Re ∼ 3 × 105; PS plasma body force: 225 mN/m; SS body force: 450 mN/m: (a) deflection amplitude of PEF, (b) deflection amplitude of ETT, (c) phase angle of ETT, and (d) length of ETT

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Fig. 14

Nondimensional vorticity field for the central blade of the cascade with alternate PS/SS actuation, together with the equivalent geometry computed with the ROM; design conditions; k = 0.0720; Re ∼ 3 × 105; oscillation amplitude: 1 deg.; PS plasma body force: 225 mN/m; and SS body force: 450 mN/m

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Fig. 15

Hysteresis curves of lift and moment coefficient for the central blade of the cascade with alternate PS/SS actuation, together with the counterpart of the ROM; design conditions; k = 0.0720; Re ∼ 3 × 105; PS plasma body force: 225 mN/m; and SS body force: 450 mN/m: (a) lift coefficient, (b) midchord moment coefficient, (c) lift coefficient, and (d) midchord moment coefficient

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