Journal of Scientific Computing

, Volume 21, Issue 3, pp 283–319 | Cite as

Application of Compact Schemes to Large Eddy Simulation of Turbulent Jets

  • Ali Uzun
  • Gregory A. Blaisdell
  • Anastasios S. Lyrintzis


We present 3-D large eddy simulation (LES) results for a turbulent Mach 0.9 isothermal round jet at a Reynolds number of 100,000 (based on jet nozzle exit conditions and nozzle diameter). Our LES code is part of a Computational Aeroacoustics (CAA) methodology that couples surface integral acoustics techniques such as Kirchhoff's method and the Ffowcs Williams– Hawkings method with LES for the far field noise estimation of turbulent jets. The LES code employs high-order accurate compact differencing together with implicit spatial filtering and state-of-the-art non-reflecting boundary conditions. A localized dynamic Smagorinsky subgrid-scale (SGS) model is used for representing the effects of the unresolved scales on the resolved scales. A computational grid consisting of 12 million points was used in the present simulation. Mean flow results obtained in our simulation are found to be in very good agreement with the available experimental data of jets at similar flow conditions. Furthermore, the near field data provided by the LES is coupled with the Ffowcs Williams–Hawkings method to compute the far field noise. Far field aeroacoustics results are also presented and comparisons are made with experimental measurements of jets at similar flow conditions. The aeroacoustics results are encouraging and suggest further investigation of the effects of inflow conditions on the jet acoustic field.

Large Eddy simulation Turbulent jets Jet noise Dynamic smagorinsky subgrid-scale model Compact finite difference schemes Implicit spatial filtering 


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  1. 1.
    Arakeri, V. H., Krothapalli, A., Siddavaram, V., Alkislar, M. B., and Lourenco, L. (2002). Turbulence suppression in the noise producing region of a Mach 0.9 jet, AIAA, Paper No. 2002–2523.Google Scholar
  2. 2.
    Bodony, D. J., and Lele, S. K. (2002). Influence of inlet conditions on the radiated noise of high speed turbulent jets. International workshop on "LES for Acoustics", DLR G¨ ottingen, Germany.Google Scholar
  3. 3.
    Boersma, B. J., and Lele, S. K. (1999). Large eddy simulation of a Mach 0.9 turbulent jet. AIAA, Paper No. 99–1874.Google Scholar
  4. 4.
    Bogey, C., Bailly, C., and Juv´e, D. (2000). Computation of the sound radiated by a 3-D jet using large eddy simulation, AIAA, Paper No. 2000–2009.Google Scholar
  5. 5.
    Bogey, C., and Bailly, C. (2002a). Three-dimensional non-reflective boundary conditions for acoustic simulations: far field formulation and validation test cases. Acta Acustica 88(4), 463–471.Google Scholar
  6. 6.
    Bogey, C., and Bailly, C. (2002b). A family of low dispersive and low dissipative explicit schemes for computing aerodynamic noise, AIAA, Paper No. 2002–2509.Google Scholar
  7. 7.
    Bogey, C., and Bailly, C. (2002c). Direct computation of the sound radiated by a high-Reynolds-number, subsonic round jet. CEAS Workshop From CFD to CAA.Google Scholar
  8. 8.
    Bogey, C., Bailly, C., and Juv´e, D. (2003a). Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible LES. Theor. Comput. Fluid Dyn. 16(4), 273–297.Google Scholar
  9. 9.
    Bogey, C., and Bailly, C. (2003b). LES of a high Reynolds, high subsonic jet: effects of the inflow conditions on flow and noise, AIAA, Paper No. 2003–3170.Google Scholar
  10. 10.
    Bogey, C., and Bailly, C. (2003c). LES of a high Reynolds, high subsonic jet: effects of the subgrid modellings on flow and noise, AIAA, Paper No. 2003–3557.Google Scholar
  11. 11.
    Boluriaan, S., Morris, P. J., Long, L. N., and Scheidegger, T. (2001). High speed jet noise simulations for noncircular nozzles. AIAA, Paper No. 2001–2272.Google Scholar
  12. 12.
    Choi, D., Barber, T. J., Chiappetta, L. M., and Nishimura, M. (1999). Large eddy simulation of high-Reynolds number jet flows, AIAA, Paper No. 99–0230.Google Scholar
  13. 13.
    Colonius, T., Lele, S. K., and Moin, P. (1993). Boundary conditions for direct computation of aerodynamic sound generation. AIAA, J. 31(9), 1574–1582.Google Scholar
  14. 14.
    Constantinescu, G. S., and Lele, S. K. (2001). Large eddy simulation of a near sonic turbulent jet and its radiated noise, AIAA, Paper No. 2001–0376.Google Scholar
  15. 15.
    Crighton, D. G., Dowling, A. P., Ffowcs Williams, J. E., Heckl, M., and Leppington, F. G. (1992). Modern Methods in Analytical Acoustics: Lecture Notes, Springer-Verlag, London.Google Scholar
  16. 16.
    Ffowcs Williams, J. E., and Hawkings, D. L. (1969). Sound generation by turbulence and surfaces in arbitrary motion. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 264(1151), 321–342.Google Scholar
  17. 17.
    Freund, J. B., Lele, S. K., and Moin, P. (2000). Direct numerical simulation of a Mach 1.92 turbulent jet and its sound field. AIAA, J. 38(11), 2023–2031.Google Scholar
  18. 18.
    Freund, J. B. (2001). Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9. J. Fluid Mech. 438, 277–305.Google Scholar
  19. 19.
    Gamet, L., and Estivalezes, J. L. (1998). Application of large-eddy simulations and Kirchhoff method to jet noise prediction. AIAA, J. 36(12), 2170–2178.Google Scholar
  20. 20.
    Germano, M., Piomelli, U., Moin, P., and Cabot, W. (1991). A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A, 3(7), 1760–1765.Google Scholar
  21. 21.
    Hunter, C. A., and Thomas, R. H. (2003). Development of a jet noise prediction method for installed jet configurations, AIAA, Paper No. 2003–3169.Google Scholar
  22. 22.
    Hussein, H. J., Capp, S. C., and George, W. K. (1994). Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet. J. Fluid Mech. 258, 31–75.Google Scholar
  23. 23.
    Khavaran, A. (1999). Role of anisotropy in turbulent mixing noise. AIAA, J. 37(7), 832–841.Google Scholar
  24. 24.
    Kirchhoff, G. R. (1883). —Zur theorie der lichtstrahlen. Annalen der Physik und Chemie 18, 663–695.Google Scholar
  25. 25.
    Koch, L. D., Bridges, J., and Khavaran, A. (2002). Flow field comparisons from three Navier-Stokes solvers for an axisymmetric separate flow jet. AIAA, Paper No. 2002–0672.Google Scholar
  26. 26.
    Koutsavdis, E. K. (2000). On the development of a jet noise prediction methodology. Ph.D. Thesis, School of Aeronautics and Astronautics, Purdue University.Google Scholar
  27. 27.
    Koutsavdis, E. K., Blaisdell, G. A., and Lyrintzis, A. S. (2000). Compact schemes with spatial filtering in computational aeroacoustics. AIAA J. 38(4), 713–715.Google Scholar
  28. 28.
    Lau, J. C., Morris, P. J., and Fisher, M. J. (1979). Measurements in subsonic and supersonic free jets using a laser velocimeter. J. Fluid Mech. 93(1), 1–27.Google Scholar
  29. 29.
    Lele, S. K. (1992). Compact finite difference schemes with spectral-like resolution. J. Comp. Phys. 103(1), 16–42.Google Scholar
  30. 30.
    Lew, P., Uzun, A., Blaisdell, G. A., and Lyrintzis, A. S. (2004). Effects of inflow forcing on jet noise using large eddy simulation, AIAA, Paper No. 2004–0516.Google Scholar
  31. 31.
    Lighthill, M. J. (1952). On sound generated aerodynamically: I. General theory. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 211(1107), 564–587.Google Scholar
  32. 32.
    Lush, P. A. (1971). Measurements of subsonic jet noise and comparison with theory. J. Fluid Mech. 46(3), 477–500.Google Scholar
  33. 33.
    Lyrintzis, A. S., and Mankbadi, R. R. (1996). Prediction of the far-field jet noise using Kirchhoff's formulation. AIAA, J. 1(2), 1–4.Google Scholar
  34. 34.
    Lyrintzis, A. S., and Uzun, A. (2001). Integral techniques for aeroacoustics calculations. AIAA, Paper No. 2001–2253.Google Scholar
  35. 35.
    Lyrintzis, A. S. (2003). Surface integral methods in computational aeroacoustics-From the (CFD) near-field to the (acoustic) far-field. Int. J. Aeroacoustics 2(2), 95–128.Google Scholar
  36. 36.
    Mankbadi, R. R., Hayder, M. E., and Povinelli, L. A. (1994). Structure of supersonic jet flow and its radiated sound. AIAA, J. 32(5), 897–906.Google Scholar
  37. 37.
    Moin, P., Squires, K., Cabot, W., and Lee, S. (1991). A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A, 3(11), 2746–2757.Google Scholar
  38. 38.
    Mollo-Christensen, E. Kolpin, M. A., and Martucelli, J. R. (1964). Experiments on jet flows and jet noise far-field spectra and directivity patterns. J. Fluid Mech. 18, 285–301.Google Scholar
  39. 39.
    Morris, P. J., Wang, Q., Long, L. N., and Lockhard, D. P. (1997). Numerical predictions of high speed jet noise, AIAA, Paper No. 97–1598.Google Scholar
  40. 40.
    Morris, P. J., Long, L. N., Bangalore, A., and Wang, Q. (1997). A parallel three-dimensional computational aeroacoustics method using nonlinear disturbance equations. J. Comp. Phys. 133, 56–74.Google Scholar
  41. 41.
    Morris, P. J., Long, L. N., Scheidegger, T. E., Wang, Q., and Pilon, A. R. (1998). High speed jet noise simulations, AIAA, Paper No. 98–2290.Google Scholar
  42. 42.
    Morris, P. J., Long, L. N., and Scheidegger, T. E. (1999). Parallel computations of high speed jet noise. AIAA, Paper No. 99–1873.Google Scholar
  43. 43.
    Morris, P. J., Scheidegger, T. E., and Long, L. N. (2000). Jet noise simulations for circular nozzles. AIAA, Paper No. 2000–2080.Google Scholar
  44. 44.
    Panchapakesan, N. R., and Lumley, J. L. (1993). Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jets. J. Fluid Mech. 246, 197–223.Google Scholar
  45. 45.
    Raman, G., Rice, E. J., and Reshotko, E. (1994). Mode spectra of natural disturbances in a circular jet and the effect of acoustic forcing. Exp. Fluids 17, 415–426.Google Scholar
  46. 46.
    Rizzetta, D. P., Visbal, M. R., and Blaisdell, G. A. (2003). A time-implicit high-order compact differencing and filtering scheme for large eddy simulation. Int. J. Numer. Methods Fluids 42, 665–693.Google Scholar
  47. 47.
    Self, R. H., and Bassetti, A. (2003). A RANS based jet noise prediction scheme, AIAA, Paper No. 2003–3325.Google Scholar
  48. 48.
    Smagorinsky, J. S. (1963). General circulation experiments with the primitive equations. Mon. Weather Rev. 91(3), 99–165.Google Scholar
  49. 49.
    Society of Automotive Engineers. (1985). SAE ARP 876C: Gas Turbine Jet Exhaust Noise Prediction.Google Scholar
  50. 50.
    Stromberg, J. L., McLaughlin, D. K., and Troutt, T. R. (1980). Flow field and acoustic properties of a Mach number 0.9 jet at a low Reynolds number. J. Sound Vibr. 72(2), 159–176.Google Scholar
  51. 51.
    Tam, C. K. W., and Dong, Z. (1996). Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow. J. Computational Acoust. 4(2), 175–201.Google Scholar
  52. 52.
    Uzun, A., Blaisdell, G. A., and Lyrintzis, A. S. (2002). Recent progress towards a large eddy simulation code for jet aeroacoustics. AIAA, Paper No. 2002–2598.Google Scholar
  53. 53.
    Uzun, A., Blaisdell, G. A., and Lyrintzis, A. S. (2003). Sensitivity to the Smagorinsky constant in turbulent jet simulations. AIAA, J. 41(10), 2077–2079.Google Scholar
  54. 54.
    Visbal, M. R., and Gaitonde, D. V. (2001). Very high-order spatially implicit schemes for computational acoustics on curvilinear meshes. J. Computational Acoust. 9(4), 1259–1286.Google Scholar
  55. 55.
    Wygnanski, I., and Fiedler, H. (1969). Some measurements in the self-preserving jet. J. Fluid Mech. 38(3), 577–612.Google Scholar
  56. 56.
    Yoshizawa, A. (1986). Statistical theory for compressible turbulent shear flows, with application to subgrid modeling. Phys. Fluids 29(7), 2152–2164.Google Scholar
  57. 57.
    Zaman, K. B. M. Q. (1998). Asymptotic spreading rate of initially compressible jets-experiment and analysis. Phys. Fluids 10(10), 2652–2660.Google Scholar
  58. 58.
    Zhao, W., Frankel, S. H., and Mongeau, L. (2001) Large eddy simulations of sound radiation from subsonic turbulent jets. AIAA, J. 39(8), 1469–1477.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • Ali Uzun
    • 1
  • Gregory A. Blaisdell
    • 2
  • Anastasios S. Lyrintzis
    • 2
  1. 1.School of Computational Science and Information TechnologyFlorida State UniversityUSA
  2. 2.School of Aeronautics and AstronauticsPurdue UniversityUSA

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