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Sound radiation in turbulent channel flows

By Zhiwei Hu, Christopher L. Morfey and Neil D. Sandham


Lighthill’s acoustic analogy is formulated for turbulent channel flow with pressure as the acoustic variable, and integrated over the channel width to produce a two-dimensional inhomogeneous wave equation. The equivalent sources consist of a dipole distribution related to the sum of the viscous shear stresses on the two walls, together with monopole and quadrupole distributions related to the unsteady turbulent dissipation and Reynolds stresses respectively. Using a rigid-boundary Green function, an expression is found for the power spectrum of the far-field pressure radiated per unit channel area. Direct numerical simulations (DNS) of turbulent plane Poiseuille and Couette flow have been performed in large computational domains in order to obtain good resolution of the low-wavenumber source behaviour. Analysis of the DNS databases for all sound radiation sources shows that their wavenumber–frequency spectra have non-zero limits at low wavenumber. The sound power per unit channel area radiated by the dipole distribution is proportional to Mach number squared, while the monopole and quadrupole contributions are proportional to the fourth power of Mach number. Below a particular Mach number determined by the frequency and radiation direction, the dipole radiation due to the wall shear stress dominates the far field. The quadrupole takes over at Mach numbers above about 0.1, while the monopole is always the smallest term. The resultant acoustic field at any point in the channel consists of a statistically diffuse assembly of plane waves, with spectrum limited by damping to a value that is independent of Mach number in the low-M limit

Topics: TL, QC
Year: 2003
OAI identifier:
Provided by: e-Prints Soton

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  5. (2002). Aeroacoustics of wall-bounded turbulent flows. doi
  6. (1960). Aerodynamic noise and the plane boundary. doi
  7. (1984). Aerodynamic sound generation by turbulent boundary layer flows along solid and compliant walls.
  8. (1985). Aerodynamic sound generation caused by viscous processes. doi
  9. (1968). Aerodynamic sound generation in a pipe. doi
  10. (1973). Ampli of aerodynamic noise by convected flow inhomogeneities. doi
  11. (1967). Berechnung aerodynamisch erzeugter Schallfelder mittels der Methode der `Matched Asymptotic Expansions'.
  12. C h a s e ,D .M .1991 Fluctuations in wall-shear stress and pressure at low streamwise wavenumbers in turbulent boundary-layer flow. doi
  13. (1993). Damping and reflection coecient measurements for an open pipe at low Mach and low Helmholtz numbers. doi
  14. (1995). Direct computation of the sound from a compressible co-rotating vortex pair. doi
  15. (1998). Direct simulation of turbulence using massively parallel computers. doi
  16. (2001). Influence of low Mach number shear flow on acoustic propagation in ducts. doi
  17. (1984). Influence of viscosity on aerodynamic sound emission in free space. doi
  18. (2001). Large-domain simulations of plane Couette and Poiseuille flow.
  19. (1958). Non-linear interactions in a viscous heat-conducting compressible gas. doi
  20. (1993). Numerical study of turbulent plane Couette flow at low Reynolds number. doi
  21. (1952). On sound generated aerodynamically: I. General theory. doi
  22. (1954). On sound generated aerodynamically: II. Turbulence as a source of sound. doi
  23. (1999). On the Mach- and Reynolds-number dependence of the flat-plate turbulent boundary layer wall-pressure spectrum. doi
  24. (1988). Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. doi
  25. (1968). Shallow water wave generation by unsteady flow. doi
  26. (1969). Sound generation by turbulence and surfaces in arbitrary motion. doi
  27. (1976). Sound radiation due to unsteady dissipation in turbulent flows. doi
  28. (1996). Sound radiation during local laminar breakdown in a low-Mach-number boundary layer. doi
  29. (1995). The damping of sound by wall turbulent shear layers. doi
  30. (1986). Theoretical Acoustics 2nd edn. Princeton University Press.302
  31. (1975). Thermodynamics of single-phase one-dimensional fluid flow. doi
  32. (1980). Treatment of incompressibility and boundary layer conditions in 3D numerical spectral simulations of plane channel flows. doi
  33. (1993). Turbulence in plane Couette flow. doi
  34. (1987). Turbulence statistics in fully developed channel flow at low Reynolds number. doi
  35. (1996). Very large structure in plane turbulent Couette flow. doi
  36. (1978). Waves in Fluids. doi

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