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Numerical study of the dynamics and sound generation of a turbulent vortex ring


Ran, Hongyu (2005) Numerical study of the dynamics and sound generation of a turbulent vortex ring. Dissertation (Ph.D.), California Institute of Technology.


In the present study, Direct Numerical Simulations (DNS) of the fully compressible, three-dimensional Navier-Stokes equations are used to generate an axisymmetric vortex ring to which three-dimensional stochastic disturbances are added. The radiated acoustic field is computed directly in the near field, and by solving the wave equation in a spherical coordinate system in the far field.

At high Reynolds number, a vortex ring will undergo an instability to azimuthal waves. The instability produces higher azimuthal modes and induces nonlinear interaction between the modes, and will cause the vortex ring to break down and transition to turbulence. The early stages of the simulation agree well with the linear instability theory. Nonlinear stage of instability, transition, formation of axial flow and streamwise vorticity are analyzed and compared with experimental results. After turbulent transition, the evolution of statistical quantities becomes independent of viscosity and the initial geometry, and the flow become self-similar. The temporal evolution of quantities including total circulation, axial velocity profile, vortex ring displacement and vorticity profile agrees well with the self-similarity law. Turbulent energy spectrum, Reynolds stresses and turbulence production are also presented.

The unsteady vorticity field generates acoustic waves with higher azimuthal modes, each mode with a distinctive spectrum and directivity. The ensemble averaged peak frequency, bandwidth, and the sound pressure level agrees qualitatively with reported experimental results. The directivity of each azimuthal mode is compared with predictions of vortex sound theory. The sound generation consists of three stages. The first is a deterministic stage when linear instability waves emerge and grow and generate relatively weak sound. The second stage is nonlinear interaction and vortex breakdown; at this stage the sound pressure level reaches a peak value. The third stage is the turbulent asymptotic decay of the acoustic field. Based on the self-similar decay of the turbulent near field, the self-similar decay of the sound field is investigated. Connection between the acoustic field and the vortex ring oscillations is also studied with vortex sound theory. Finally, we note some similarities between the sound radiated by a train of de-correlated vortex rings and turbulent jet noise. The sound pressure level, spectrum, and directivity of the train of vortex rings is similar to the sound field from a jet with similar Reynolds number and Mach number.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:acoustic field; azimuthal mode; compressible; directivity; DNS; ensemble average; instability; jet noise; nonlinear instability; Reynolds stress; self-similar; sound generation; spectrum; spherical harmonics; SPL; transition; turbulence; vortex ring; vortex sound; wave equation
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Colonius, Timothy E.
Thesis Committee:
  • Colonius, Timothy E. (chair)
  • Leonard, Anthony
  • Hunt, Melany L.
  • Gharib, Morteza
Defense Date:2 June 2004
Author Email:hongy (AT)
Record Number:CaltechETD:etd-06082004-151101
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2513
Deposited By: Imported from ETD-db
Deposited On:09 Jun 2004
Last Modified:26 Dec 2012 02:52

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