Use of Stochastic Turbulence Models in Jet Acoustics

Document Type : Research Article


Corresponding Author, Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran. Center of Excellence in Computational Aerospace Engineering (AeroExcel) (e-mail:


There are many approaches to determine the sound propagated from turbulent flows.  In hybrid methods, the turbulent noise source field is computed or modeled separately from the far-field calculations.  To have an initial and quick estimation of the sound propagation, less computationally intensive methods can be developed using stochastic models of the turbulent fluctuations.   In this paper, turbulent mean flow of a two dimensional, compressible, cold-jet at Mach 0.56 is computed using RANS with 2 equation k-ε RNG model.  The above mean-flow quantities are then used in a stochastic model to generate the details of the turbulent velocity fluctuations.  This method is based on the use of classical Langevin equation to model the details of fluctuating flow field superimposed on the averaged computed quantities.   The resulting sound field due to the generated unsteady flow is then evaluated using Lighthill's acoustic analogy.   Our results are validated by comparing the directivity and the overall sound pressure level (OASPL) magnitudes with the available experimental data.  Numerical results show reasonable agreement with the experiments, both in maximum directivity and the magnitude of the OASPL.


[1]     S. Caro, “Review CEAS-ASC highlights 2006”, Journal of Sound and Vibration, vol. 304, pp.421–449, 2007.
[2]     M. J. Lighthill, “On sound generated aerodynamically: I. General theory”. Proc. R.Soc. London Ser.A, vol. 211, pp.564–587, 1952.
[3]     J.B. Freund, “Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9”, Journal of Fluid Mechanics, vol. 438, pp.277–305, 2001.
[4]     C. Bailly, P. Lafon, and S. Candel, “Subsonic and supersonic jet noise predictions from statistical source models”, AIAA journal, Vol. 35, pp.1688–1696, 1997.
[5]     T.F. Balsa, P.R. Gliebe, “Aerodynamics and noise of coaxial jets”, AIAA Journal, vol. 15, pp.1550–1558, 1977.
[6]     R. Mani, T.F. Balsa, P.R. Gliebe, “High-velocityjet noise source location and reduction”, Federal Aviation Administration Report, FAA-RD-76-II, 1978
[7]     A. Khavaran, “Computation of supersonic jet mixing noise for an axisymmetric convergent-divergent nozzle”, Journal of Aircraft, vol.31, pp.603–612, 1993
[8]     A. Khavaran, “Role of anisotropyin turbulent mixing noise”, AIAA Journal, vol.37, pp.832–841, 1999.
[9]     W. Bechara, C. Bailly, and P. Lafon, “Stochastic approach to noise modeling for free turbulent flows”, AIAA Journal, vol. 32, pp.455-463, 1994.
[10]  C. Bailly and D. Juve, “A stochastic approach to compute subsonic noise using linearized Euler's equations”, AIAA paper 99-1872, 1999.
[11]  A. Ahmadzadegan and M. Tadjfar, “Combination of Lighthill acoustic analogy and stochastic turbulence modeling for far-field acoustic prediction”, 16th Australasian Fluid Mechanics Conference, pp.163-166, 2007.
[12]  A. Ahmadzadegan and M. Tadjfar, “On the prediction of acoustics jet noise using stochastic turbulence modeling”, 15th Annual Conference of the CFD Society of Canada, 2007.
[13]  D. Thomson, “Criteria for the selection of stochastic models of particle trajectories in turbulent flow”, Journal of Fluid Mechanics, vol.180, pp. 529-556, 1987.
[14]  B.G. Zijnen, Van der Hagge, “Measurements of the Velocity Distribution In a Plane Turbulent Jet of Air”, Applied Sci. Res., A7, pp.256-276, 1958.
[15]  D. Choudhury, “Introduction to the Renormalization Group Method and Turbulence Modeling”, Fluent Inc. Technical Memorandum TM-107, 1993.
[16]  V. Yakhot and S.A. Orszag, “Renormalization group analysis of turbulence: I. Basic theory”, J. Sci. Comp., vol.1, pp.1-51, 1986.
[17]  H. Chunhong and G. Ahmadi, “Particle deposition in a nearly developed turbulent duct flow with electrophoreses”, J. Aerosol Sci, vol.30, pp.739-758, 1999..
[18]  G.E.P. Box and M.E. Muller, “A note on the generation of random normal deviates”, Annals Math. Stat., vol.29, pp.610-611, 1958.
[19]   B.J. Boersma, “Numerical simulation of the noise generated by a low Mach number, low Reynolds number jet”, Fluid Dynamics Research, vol.35, pp.42-447, 2004.
[20]  S. K. Lele, “Compact finite difference schemes with spectral-like resolution”, J. Comp. Phys. Vol.103, pp.16–42, 1992.
[21]  A. Hirschberg and S.W. Rienstra, An Introduction to Aeroacoustics, Eindhoven University of Technology (2004)
[22]  P. A. Lush, “Measurements of Subsonic Jet Noise and Comparison with Theory”, Journal of Fluid Mech., vol.46, pp.477-500, 1971.
[23]  P. A. Warrendale, “Gas Turbine Exhaust Noise Prediction, Society of Automotive Engineers”, ARP 876C, 1985.
[24]  G. M. Lilley, “On the noise from jets”, Technical Report CP-131, AGARD, 1974.