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TECHNICAL PAPERS: Gas Turbines: Turbomachinery and Structures and Dynamics

Evaluation of Acoustic Flutter Suppression for Cascade in Transonic Flow

[+] Author and Article Information
P.-J. Lu, S.-K. Chen

Institute of Aeronautics and Astronautics, National Cheng Kung University Tainan, Taiwan R.O.C.

J. Eng. Gas Turbines Power 124(1), 209-219 (Nov 01, 2000) (11 pages) doi:10.1115/1.1365933 History: Received February 01, 1998; Revised November 01, 2000
Copyright © 2002 by ASME
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References

Figures

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Steady-state pressure and Mach number distributions on a NACA0006 airfoil (M=0.85, α=0)
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Transient response for acoustically suppressed flutter at M=0.85,αm=0.0 deg,pe=1.10p, σ=180 deg, G=1.0, μ=192.0, ah=−0.24,ωhα=1.0,V*=1.2VF*,rα=0.4735,Xα=0.076,Gα=0.5, ϕ=0, XC=0.95; (a) plunging mode and (b) pitching mode (–:open-loop no-control solution, and –: closed-loop acoustical-control solution)
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Damping rate versus phase angle using close-loop feedback control on NACA0006 cascade (M=0.85,αm=0 deg,pe=1.10p, σ=180 deg, G=1.0, μ=192.0, ah=−0.24,ωhα=1.0,V*=1.2VF*,rα=0.4735,Xα=0.076,Gα=0.5, and XC=0.95)
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Grid system of P&W TS33 Cascade (120×40 cells per passage)
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Mach number contours of P&W TS33 Case A (M=0.9848,Ω−∞=68.54 deg,G=0.736, Θ=60.59 deg, and pe=1.3408p)
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Mach number contours of P&W TS33 Case B (M=0.782,Ω−∞=68.54 deg,G=0.736, Θ=60.59 deg, and pe=1.1646p)
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Unsteady (a) lift and (b) pitching moment variations induced by acoustic excitation on P&W TS33 Case A cascade (M=0.9848,Ω−∞=68.54 deg,G=0.736, Θ=60.59 deg, σ=0 deg, pe=1.3408p,Q(t)=Qo sin ωt,Qo=5.E-3, and ω=0.64458)
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Unsteady (a) lift and (b) pitching moment variations induced by acoustic excitation on P&W TS33 Case B cascade (M=0.782,Ω−∞=68.54 deg,G=0.736, Θ=60.59 deg, σ=0 deg, pe=1.1646p,Q(t)=Qo sin ωt,Qo=5.0E-3, and ω=0.62497)
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Unsteady shock motion induced by acoustic excitation on P&W TS33 Case A cascade (M=0.9848,Ω−∞=68.54 deg,G=0.736, Θ=60.59 deg, σ=0 deg, pe=1.3408p,Q(t)=Qo sin ωt,Qo=5.0E-3, and ω=0.64458)
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Unsteady shock motion induced by acoustic excitation on P&W TS33 Case B cascade (M=0.782,Ω−∞=68.54 deg,G=0.736, Θ=60.59 deg, σ=0 deg, pe=1.1646p,Q(t)=Qo sin ωt,Qo=5.0E-3, and ω=0.62497)
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Work per cycle versus interblade phase angle for a torsional vibrating cascade of P&W TS33 Case A (M=0.9848,α=αmo sin ωt,αm=0.1388,αo=0.005 rad, and ω=0.64458)
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Work per cycle versus interblade phase angle for a torsional vibrating cascade of P&W TS33 Case B (M=0.782,α=αmo sin ωt,αm=0.1388,αo=0.005 rad, and ω=0.62497)
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Effect of control gain phase on the work per cycle for a torsional vibrating cascade of P&W Case A under actively controlled acoustic excitations (M=0.9848, σ=60 deg, α=αmo sin ωt,αm=0.1388,αo=0.005 rad, ω=0.64458, XC=0.95,Q(t)=Gα[α(ωt+nσ+ϕ)−αm], and Gα=0.5)
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Effect of control gain phase on the work per cycle for a torsional vibrating cascade of P&W Case B under actively controlled acoustic excitations (M=0.782, σ=60 deg, α=αmo sin ωt,αm=0.1388,αo=0.005 rad, ω=0.62497, XC=0.95,Q(t)=Gα[α(ωt+nσ+ϕ)−αm], and Gα=0.5)
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Schematic of typical section model with acoustic excitation
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A schematic illustrating the different time intervals characterizing the wave interaction phenomenon
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Pressure histories induced by impulsive excitations on a NACA64A006 airfoil. (M=0.5, α=0, Qo=5.0E-3,Δt=0.5,XC=0.75,XP=0.25; –: symmetric forcing, and ○: asymmetric forcing).
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Lift coefficient and circulation histories induced by asymmetric impulsive excitation on a NACA64A006 airfoil (M=0.5, α=0, Qo=5.0E-3,Δt=0.5, and XC=0.75)
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Steady-state pressure and Mach number distributions on a NACA0006 cascade (M=0.85, α=0, pe=1.10p,G=1.0, and σ=0 deg)
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Acoustically induced unsteady (a) life and (b) pitching moment coefficient histories on a NACA0006 cascade (M=0.85, α=0, pe=1.10p,G=1.0,Q=Qo sin ωt,Qo=5.0E-3, and ω=0.4)
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Acoustically induced unsteady (a) lift and (b) pitching moment coefficient histories on a NACA0006 airfoil (M=0.85, α=0, Q=Qo sin ωt,Qo=5.0E-3, and ω=0.4)
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Acoustic energy supply histories of an acoustically suppressed flutter motion (NACA0006 cascade, M=0.85,αm=0.0 deg,pe=1.10p, σ=180 deg, G=1.0, μ=192.0, ah=−0.24,ωhα=1.0,V*=1.1VF*,rα=0.4735,Xα=0.076,Gα=0.5, ϕ=0, and XC=0.95)
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Two-dimensional transonic cascade configuration

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