The acoustic field radiated by a turbulent vortex ring is studied. Direct Numerical Simulations (DNS) of the fully compressible, three-dimensional Navier-Stokes equations are used to generate an axisymmetric vortex ring to which 3D stochastic disturbances are added. The disturbances cause instability and turbulent transition of the vortex ring. Detailed information about temporal evolution of sound pressure level, spectrum and directivity associated with modes of oscillation and their turbulent breakdown are investigated. The peak frequency agrees well with experiments, and the modal directivities agree well with predictions of vortex sound theory. Based on the self-similar decay of the turbulent near field, the self-similar decay of the sound field is investigated. We also explore the connections with jet noise by modeling the jet as a de-correlated train of vortex rings.
GoldsteinM.LeibS., “The role of instability waves in predicting jet noise,”J. Fluid Mech., Vol. 525, 2005, pp. 37–72.
3.
GoldsteinM.LeibS., “The aeroacoustics of slowly diverging supersonic jets,”J. Fluid Mech., Vol. 600, 2008, pp. 291–337.
4.
KarabasovS.AfsarM.HynesT.DowlingA.“Using Large Eddy Simulation with an Acoustic Analogy Approach for Jet Noise Modelling,”, AIAA Paper 2008-2985, 2008.
5.
GlezerA., “The formation of vortex rings,”Phys. Fluids, Vol. 31, 1988, pp. 3532–3541.
6.
WidnallS.SullivanJ., “On the stability of vortex rings,”Proc. R. Soc. London Ser. A, Vol. 332, 1973, pp. 335–353.
7.
MaxworthyT., “Some experimental studies of vortex rings,”J. Fluid Mech., Vol. 81, 1977, pp. 465–495.
8.
WidnallS.TsaiC., “The instability of the thin vortex rings of constant vorticity,”Phil. Trans. R. Soc. London A, Vol. 287, 1977, pp. 273–305.
9.
SaffmanP., “The number of waves on unstable vortex rings,”J. Fluid Mech., Vol. 84, 1978, pp. 625–639.
10.
ShariffK.VerziccoR.OrlandiP., “A numerical study of the three-dimensional vortex ring instabilities: Viscous corrections and early nonlinear stage,”J. Fluid Mech., Vol. 279, 1994, pp. 351–375.
11.
KnioO.GhoniemA., “Numerical Study of a Three-Dimensional Vortex Method,”J. Comp. Physics, Vol. 86, 1990, pp. 75–106.
12.
GlezerA.ColesD., “An experimental study of a turbulent vortex ring,”J. Fluid Mech., Vol. 211, 1990, pp. 243–283.
13.
WeigandA.GharibM., “On the decay of a turbulent vortex ring,”Phys. Fluids, Vol. 6, No. 12, 1994, pp. 3806–3808.
14.
AuerbachD., “Stirring properties of vortex rings,”Phys. Fluids, Vol. 3, No. 5, 1990, pp. 1351–1355.
15.
ZaitsevM.KopievV.MuninA.PotokinA., “Sound radiation by a turbulent vortex ring,”Sov. Phys. Dolk., Vol. 35, 1990, pp. 488–489.
16.
ZaitsevM.KopievV.KotovaA., “Representation of the Sound Field of a Turbulent Vortex Ring as a Superposition of Quadrupoles,”Acoustical Physics, Vol. 47, No. 6, 2001, pp. 793–801.
17.
MöhringW., “On vortex sound at low Mach number,”J. Fluid Mech., Vol. 85, 1978, pp. 685–691.
18.
ShariffK.LeonardA.FerzigerJ.“Dynamics of a class of vortex rings,”, NASA TM 102257, NASA, 1989.
19.
TangS.KoN., “Sound sources in the interactions of two inviscid two-dimensional vortex pairs,”J. Fluid Mech., Vol. 419, 2000, pp. 117–201.
20.
TangS.KoN., “Basic sound generation mechanisms in inviscid vortex interactions at low Mach number,”J. Sound Vib., Vol. 262, No. 1, 2003, pp. 87–115.
21.
KopievV.ChernyshevS., “Vortex ring eigen-oscillations as a source of sound,”J. Fluid Mech., Vol. 341, 1997, pp. 19–57.
22.
LeleS. K., “Compact finite difference schemes with spectral-like resolution,”J. Comp. Physics, Vol. 103, No. 1, 1992, pp. 16–42.
23.
FreundJ., “Proposed Inflow/Outflow Boundary Condition for Direct Computation of Aerodynamic Sound,”AIAA J., Vol. 35, No. 4, 1997, pp. 740–742.
24.
MohseniK.ColoniusT., “Numerical treatment of polar coordinate singularities,”J. Comp. Phys, Vol. 157, 2000, pp. 787–795.
25.
MohseniK.RanH.ColoniusT., “Numerical experiments on vortex ring formation,”J. Fluid Mech., Vol. 430, 2001, pp. 267–282.
26.
RanH.“Numerical Study of the Dynamics and Sound Generation of a Turbulent Vortex Ring,”, Ph.d thesis, California Institute of Technology, 2004.
27.
SaffmanP., Vortex Dynamics, Cambridge University Press, 1992.
28.
BridgesJ.HussainF., “Direct evaluation of aeroacoustic theory in a jet,”J. Fluid Mech., Vol. 240, 1992, pp. 469–501.
29.
StrombergJ.McLaughlinD.TrouttT., “Flow field and acoustic properties of a Mach number 0.9 jet at a low Reynolds number,”J. Sound Vib., Vol. 72, 1980, pp. 159–176.
30.
LushP., “Measurement of subsonic jet noise and comparison with theory,”J. Fluid Mech., Vol. 46, No. 3, 1971, pp. 477–500.
31.
FreundJ., “Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9,”J. Fluid Mech., Vol. 438, 2001, pp. 277–305.
