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TECHNICAL PAPERS

Thermoacoustic Stability of Quasi-One-Dimensional Flows—Part II: Application to Basic Flows

[+] Author and Article Information
Dilip Prasad, Jinzhang Feng

Aerodynamics Division, Pratt & Whitney Aircraft Engines, East Hartford, CT 06108

J. Turbomach 126(4), 645-653 (Dec 29, 2004) (9 pages) doi:10.1115/1.1791289 History: Received October 01, 2003; Revised March 01, 2004; Online December 29, 2004
Copyright © 2004 by ASME
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References

Figures

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(a) Mach number ([[dashed_line]] ), normalized area [A/A(l),- - -] and normalized pressure [p̄/p̄(l), — ⋅ — ⋅] distributions for diffusing subsonic flow. (b) Magnitude and (c) phase of the first three pressure modes p̃n(x):n=1 (— ⋅ — ⋅), n=2 ([[dashed_line]] ) and n=3 (– ).
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Spectra for subsonic diffuser flow with Min=0.5 and “open” inlet condition: results are shown for Mex=0.1 with “open” exit condition (□), Mex=0.1 with ζex=1+i (▵) and Mex=0.3 with “open” exit condition (○)
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(a) Mach number ([[dashed_line]] ), normalized area [A/A(l),] and normalized pressure [p̄/p̄(l), — ⋅ —⋅] distributions for accelerating subsonic flow. (b) Magnitude and (c) phase of the first three pressure modes p̃n(x):n=1 (— ⋅ — ⋅), n=2 ([[dashed_line]] ) and n=3 (– ).
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Spectra for subsonic nozzle flow with Min=0.5,Mex=0.9 and “open” inlet condition: results are shown for the “open” exit condition (□) and for ζex=−1+i (▵)
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(a) Mach number ([[dashed_line]] ), normalized area [A/A(0),- - -] and normalized pressure [p̄/p̄(0),[[dot_dash_line]] ] distributions for small length-scale transonic flow. (b) Magnitude and (c) phase of p̃1(x) and p̃3(x) determined using the exact (– ) and compact-nozzle ([[dashed_line]] ) boundary conditions.
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Spectrum for transonic flow through the nozzle of Fig. 5(a). Eigenvalues determined using the exact (□) and compact-nozzle (▵) boundary conditions are shown.
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(a) Mach number ([[dashed_line]] ), normalized area [A/A(0),] and normalized pressure [p̄/p̄(l), — ⋅ — ⋅] distributions for large length-scale transonic flow. (b) Magnitude and (c) phase of p̃1 and p̃3 as determined using the exact (– ) and compact-nozzle ([[dashed_line]]) boundary conditions.
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Spectrum for transonic flow through the nozzle of Fig. 7(a). Eigenvalues determined using the exact (□) and compact-nozzle (▵) boundary conditions are shown
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(a) Transonic diffuser flow, showing the normalized area [A/A(0),– ] distribution and Mach number variations for a shock located at x/l=0.2 ([[dashed_line]] ) and at x/l=0.4 (— ⋅ — ⋅). (b) Magnitude and (c) phase of p̃3 (– ), ũ3 ([[dashed_line]] ) and s̃3 (— ⋅ — ⋅).
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Spectrum for the transonic diffuser flow of Fig. 9(a) with a shock located at x/l=0.2 (○) and x/l=0.4 (□)
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(a) Normalized static temperature distribution for a ducted flame with concentrated (– ) and distributed heat ([[dashed_line]] ) release and δT̄/T̄t,in=3. (b) Magnitude and (c) phase of the corresponding first and second pressure modes. Also shown in (b) is the magnitude of the first entropic mode, s̃1 (— ⋅ — ⋅) for the distributed heat release.
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Spectra for the ducted flame model for β=10 (open symbols) and β=100 (filled symbols) with xc=0.3 in Eq. (14). Results are shown over a range of flame temperature ratios for the n=1 (– ), n=2 ([[dashed_line]] ) and n=3 (— ⋅ — ⋅) modes. The symbols represent eigenvalues obtained with δT̄/T̄t,in set to 1.0 (□), 2.0 (▿), 3.0 (○) and 4.0 (▵).

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