Abstract
We study shock wave structures (SWS), consisting of shock waves and expansion waves between them, that occur in supersonic flow past nonuniform fan cascades when the velocity component normal to their front (“axial” component) is subsonic. The cascade nonuniformity is due to the scatter in the setting angles of identical blades, either sharp or blunt. A result of the uniformity is the generation of combined noise, whose frequencies are much smaller than the fundamental frequency of the uniform cascade, and slower nonlinear SWS attenuation. The accurate and fast “simple wave method” and “nonlinear acoustics approximation”, together with numerical algorithms for integrating Euler equations on overlapping grids (in calculating flow past blunt edges) and on SWS-adapted grids, are applied to determine the “guiding” action of nonuniform cascades and to describe the SWS evolution. The application of the Fourier analysis gives the sound field spectrum. The use of blades with rectilinear initial regions of the “backs” for reducing supersonic fan blade noise is efficient only at small (less than 0.25°) scatter in the setting angles. The shock wave structures attenuate more rapidly ahead of nonuniform cascades composed of blunt blades than ahead of those with sharp blades. For uniform cascades the blade bluntness effect is not large.
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References
G.I. Taganov, “Peculiar Properties of Flows in Supersonic Axial Compressors,” Tr. TsAGI (1951).
G.L. Grozdovskii, A.A. Nikol’skii, G.I. Svishchev, and G.I. Taganov, Supersonic Gas Flows within Perforated Boundaries [in Russian], Mashinostroenie, Moscow (1967).
G.Yu. Stepanov, Hydrodynamics of Turbomachinery Cascades [in Russian], Fizmatgiz, Moscow (1962).
O.K. Lawaczek, “Calculation of the Flow Properties Up- and Downstream of and within a Supersonic Turbine Cascade,” ASME Paper No. GT-47 (1972).
H.J. Lichtfuss and H. Starken, “Supersonic Cascade Flow,” in: Progr. Aerospace Sci. Vol. 15, Pergamon Press, Oxford (1974), p. 37.
R.E. York and H.S. Woodrad, “Supersonic Compressor Cascades. An Analysis of the Entrance Region Flow Field Containing Detached Shock Waves,” Trans. ASME. Ser. A. J. Eng. Power 98, 247 (1976).
A.B. Bogod, A.N. Kraiko, and E.Ya. Chernyak, “Flow of a Supersonic Ideal Gas over a Planar Cascade in the Case of a Subsonic Normal Component in Regimes with Attached Shocks,” Fluid Dynamics 14(4), 559 (1979).
A.N. Kraiko, V.A. Shironosov, and E.Ya. Shironosova, “Steady-State Ideal-Gas Flow past a Plane Cascade,” Zh. Prikl. Mekh. Tekhn. Fiz. No. 6, 35 (1984).
C.L. Morfey and M.J. Fisher, “Shock-Wave Radiation from a Supersonic Ducted Rotor,” Aeronaut. J. 74(715), 579 (1970).
M.R. Fink, “Shock Wave Behavior in Transonic Compressor Noise Generation,” ASME Paper No. GT-7 (1971).
I.A. Brailko, A.N. Kraiko, K.S. Pyankov, and N.N. Tillyaeva, “Aerodynamic and Acoustic Characteristics of a Supersonic Fan Cascade with a Subsonic Axial Component of the Flow Velocity,” Aeromekh. Gaz. Din. No. 4, 9 (2003).
A.W. Goldstein, “Supersonic Fan Blading,” US Patent No. 3820918, 06/28/1974. Priority 01/21/1972.
A.N. Kraiko, D.E. Pudovikov, and N.N. Tillyaeva, “Minimum-Drag Cascade Design for Supersonic Flow with Subsonic Normal Velocity Component,” Fluid Dynamics 30(1), 112 (1995).
V.G. Aleksandrov, A.N. Kraiko, S.Yu. Krasheninnikov, et al., “Blading of the Rotor of an Axial Compressor (Fan) of a Turbojet Engine,” Russian Federation Patent No. 2213272, 09/27/2003. Priority 04/02/2002.
L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Pergamon Press, Oxford (1987).
G.B. Whitham, Linear and Nonlinear Waves, Wiley, New York (1974).
A.N. Kraiko, Textbook on TheoreticalGasdynamics [in Russian], Moscow Physical and Technical Institute (2007).
S.K. Godunov, A.V. Zabrodin, M.Ya. Ivanov, A.N. Kraiko, and G.P. Prokopov, Numerical Solution of Multidimensional Gasdynamics Problems, [in Russian], Nauka, Moscow (1976).
V.P. Kolgan, “Applying the Principle of Minimum Values of Derivatives to the Construction of Finite-Difference Schemes for Calculating Discontinuous Solutions in Gasdynamics,” Uch. Zap. TsAGI 3(6), 68 (1972).
N.I. Tillyaeva, “Generalization of the Modified Godunov Scheme to Arbitrary Irregular Grids,” Uch. Zap. TsAGI 17(2), 18 (1986). See also: A.N. Kraiko et al. (eds.) Gasdynamics. Selected Works. Vol. 2 [in Russian], Fizmatlit, Moscow (2005), p. 201.
D. Hawkins, “Multiple Tone Generation by Transonic Compressors,” J. Sound Vibr. 17, 241 (1971).
M. Kurosaka, “A Note on Multiple Pure Tone Noise,” J. Sound Vibr. 19, 453 (1971).
I.B. Shim, J.W. Kim, and D.J. Lee, “Numerical Study of N-Wave Propagation Using Optimized Compact Finite Difference Schemes,” AIAA J. 41, 316 (2003).
G.G. Chernyi, Gas Dynamics [in Russian], Nauka, Moscow (1988).
A.N. Kraiko and A.A. Osipov, “Damping of a Periodic Sequence of Weak Shock Waves in Channels with ’sound-Absorbing’ Walls,” Fluid Dynamics 11(4), 571, (1976).
N.A. Petersson, “An Algorithm for Assembling Overlapping Grid Systems,” SIAM J. Sci. Comput. 20, 1995 (1999).
R. Löhner, D. Sharov, H. Luo, and R. Ramamurti, “Overlapping Unstructured Grids,” AIAA Paper No. 0439 (2001).
N.I. Efremov, A.N. Kraiko, K.S. P’yankov, N.I. Tillyaeva, and Ye.A. Yakovlev, “Mathematical Simulation of Shock-Wave Structures ahead of Fan Plane Cascades and Wheels,” in: V.A. Skibin et al. (eds.), Turbomachines: Aeroelasticity, Aeroacoustics and Unsteady Aerodynamics, Torus Press, Moscow (2006), p. 281.
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Original Russian Text © N.L. Efremov, A.N. Kraiko, K.S. Pyankov, N.I. Tillyaeva, E.A. Yakovlev, 2010, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2010, Vol. 45, No. 2, pp. 135–152.
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Efremov, N.L., Kraiko, A.N., Pyankov, K.S. et al. Shock wave structures ahead of nonuniform fan cascades. Fluid Dyn 45, 289–304 (2010). https://doi.org/10.1134/S0015462810020146
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DOI: https://doi.org/10.1134/S0015462810020146