Skip to main content
SpringerLink
Log in

Linear and nonlinear approaches and digital signal processing in aeroacoustics

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The linear and nonlinear approaches to the calculation of small acoustic disturbance propagation and evolution in nonuniform flows are compared. In the conventional linear approach it is the linearized equations of time-dependent, ideal (inviscid and non-heat-conducting) or viscous gas flow that are integrated. In the nonlinear approach the original nonlinear equations governing the same time-dependent flow (Euler equations for an ideal gas) are integrated; these are the same equations that, together with time relaxation procedure, are used in the linear approach for calculating the stationary background. It is shown that the application of digital signal processing, widely used in acoustic experiments, makes it possible to isolate the harmonic acoustic waves from the results of integration of the nonlinear equations, though their intensity is smaller than that of the noise due to computational errors, including inadequate attainment of the stationary background.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H.H. Hubbard (ed.), Aeroacoustics of Flight Vehicles. Theory and Practice. Vol. 1. Noise Sources, Acoust. Soc. Amer. (1995).

  2. H.H. Hubbard (ed.), Aeroacoustics of Flight Vehicles. Theory and Practice. Vol. 2. Noise Control, Acoust. Soc. Amer. (1995).

  3. V. Aleksandrov and A. Osipov, “Two-Dimensional Numerical Simulation of Rotor-Stator Interaction and Acoustic Wave Generation,” in: V.A. Skibin et al. (eds.) Turbomachines: Aeroelasticity, Aeroacoustics, and Unsteady Aerodynamics, Torus Press, Moscow (2006), p. 295.

    Google Scholar 

  4. D.J. Maglieri and K.J. Plotkin, “Sonic Boom,” in: H.H. Hubbard (ed.), Aeroacoustics of Flight Vehicles. Theory and Practice. Vol. 1. Noise Sources, Acoust. Soc. Amer. (1995), p. 519.

  5. Collection of Studies on the Sonic Boom, Tr. TsAGI, No. 1489 (1973).

  6. Yu.L. Zhilin, L.G. Ivanteeva, and S.L. Chernyshev, “Bodies of Revolution of Minimum Sonic Boom,” Uch. Zap. TsAGI 37(3), 36 (2006).

    Google Scholar 

  7. V.V. Kovalenko and S.L. Chernyshev, “On Sonic Boom Reduction,” Uch. Zap. TsAGI 37(3), 53 (2006).

    Google Scholar 

  8. I.A. Brailko, A.N. Kraiko, K.S. Pyankov, and N.I. Tillyaeva, “Aerodynamic and Acoustic Characteristics of a Supersonic Fan Cascade with a Subsonic Axial Flow Velocity Component,” Aeromekh. Gaz. Din. No. 4, 9 (2003).

  9. C. Bread, “A Frequency-Domain Solver for the Non-Linear Propagation and Radiation of Fan Noise,” in: K.C. Hall et al. (eds.), Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, Springer, Dordrecht (2006), p. 275.

    Chapter  Google Scholar 

  10. N.L. Efremov, A.N. Kraiko, K.S. Pyankov, N.I. Tillyaeva, and E.A. Yakovlev, “Mathematical Simulation of Shock-Wave Structures Arising 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.

    Google Scholar 

  11. A.A. Osipov, “Propagation of Three-Dimensional Acoustic Perturbations in Channels of Variable Cross-Sectional Area at Frequencies near the Cutoff Frequency,” Fluid Dynamics 15(6), 912 (1980).

    Article  Google Scholar 

  12. A.A. Osipov, “Short-Wave Approximation for Sound Propagation in Potential Gas Flows in Channels,” Akust. Zh. 31, 83 (1985).

    ADS  Google Scholar 

  13. W. Eversman, “Theoretical Models for Duct Acoustic Propagation and Radiation,” in: H.H. Hubbard (ed.), Aeroacoustics of Flight Vehicles. Theory and Practice. Vol. 2. Noise Control, Acoust. Soc. Amer., New York (1995), p. 101.

    Google Scholar 

  14. M.P. Levin, A.A. Osipov, and I.A. Shirkovskii, “Using the Finite Element Method for Calculating Two-Dimensional Acoustic Fields Radiated by an Open End of a Channel,” Akust. Zh. 28, 250 (1982).

    ADS  Google Scholar 

  15. A.A. Osipov and I.A. Shirkovskii, “Using the Finite ElementMethod for Calculating Acoustic Fields Radiated in Nonuniform Gas Flows,” Zh. Vychisl. Mat. Mat. Fiz. 28, 362 (1988).

    MathSciNet  Google Scholar 

  16. I. Men’shov and Y. Nakamura, “An Accurate Method for Computing Propagation of Sound Waves in Non-Uniform Moving Fluid,” in: N. Satofuka (ed.) Computational Fluid Dynamics 2000, Springer, Berlin (2001), p. 549.

    Google Scholar 

  17. I. Men’shov and Y. Nakamura, “Numerical Simulation of Acoustic Waves Propagation in a Perfectly Expanded Jet Flow,” Comput. Fluid Dynamics 11(2), 178 (2002).

    Google Scholar 

  18. C. Bread, “Optimum Attenuation of Fan Tone Noise Radiation,” in: 42nd AIAA Aerospace Sciences Meeting and Exhibit. Reno, Nevada, USA, 2004. AIAA Paper No. 523 (2004).

  19. N. Nyukhtikov and A. Rossikhin, “Numerical Method for Calculating Three-Dimensional Fan Tonal Noise Due to Rotor-Stator Interaction,” in: V.A. Skibin et al. (eds.) Turbomachines: Aeroelasticity, Aeroacoustics, and Unsteady Aerodynamics, Torus Press, Moscow (2006), p. 268.

    Google Scholar 

  20. S.K. Godunov, A.V. Zabrodin, M.Ya. Ivanov, A.N. Kraiko, and G.P. Prokopov, Numerical Solution of Multidimensional Gasdynamic Problems [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  21. V.P. Kolgan, “Application of the Principle of Minimum Derivative Values to the Construction of Difference Schemes for Calculating Discontinuous Solutions in Gasdynamics,” Uch. Zap. TsAGI 3(6), 68 (1972).

    Google Scholar 

  22. N.I. Tillyaeva, “Generalization of the Modified Godunov Scheme to Arbitrary Irregular Grids,” Uch. Zap. TsAGI 17(2), 18 (1986).

    Google Scholar 

  23. A.N. Ganzhelo, A.N. Kraiko, V.E. Makarov, and N.I. Tillyaeva, “Increasing the Accuracy of the Solution of Gasdynamic Problems,” in: Topical Problems of Aeromechanics [in Russian], Mashinostroenie, Moscow (1987), p. 87.

  24. A.V. Rodionov, “Monotonic, Second-Order Scheme for Calculating Nonequilibrium Flows Using the Shock-Fitting Technique,” Zh. Vychisl. Mat. Mat. Fiz. 27, 585 (1987).

    MathSciNet  Google Scholar 

  25. L.R. Rabiner and B. Gold, Theory and Application of Digital Signal Processing, Prentice Hall, New Jersey (1975).

    Google Scholar 

  26. R.W. Hamming, Digital Filters, Dover Publ., New York (1998).

    Google Scholar 

Download references

Authors
  1. A. N. Kraiko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. M. Mel’nikova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. S. Pyankov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.N. Kraiko, O.M. Mel’nikova, K.S. Pyankov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2009, Vol. 44, No. 6, pp. 11–20.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kraiko, A.N., Mel’nikova, O.M. & Pyankov, K.S. Linear and nonlinear approaches and digital signal processing in aeroacoustics. Fluid Dyn 44, 804–812 (2009). https://doi.org/10.1134/S0015462809060027

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462809060027

Keywords

Search

Navigation