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Investigation of high frequency noise generation in the near-nozzle region of a jet using large eddy simulation

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Abstract

This paper reports on the simulation of the near-nozzle region of an isothermal Mach 0.6 jet at a Reynolds number of 100,000 exhausting from a round nozzle geometry. The flow inside the nozzle and the free jet outside the nozzle are computed simultaneously by a high-order accurate, multi-block, large eddy simulation (LES) code with overset grid capability. The total number of grid points at which the governing equations are solved is about 50 million. The main emphasis of the simulation is to capture the high frequency noise generation that takes place in the shear layers of the jet within the first few diameters downstream of the nozzle exit. Although we have attempted to generate fully turbulent boundary layers inside the nozzle by means of a special turbulent inflow generation procedure, an analysis of the simulation results supports the fact that the state of the nozzle exit boundary layer should be characterized as transitional rather than fully turbulent. This is believed to be most likely due to imperfections in the inflow generation method. Details of the computational methodology are presented together with an analysis of the simulation results. A comparison of the far field noise spectrum in the sideline direction with experimental data at similar flow conditions is also carried out. Additional noise generation due to vortex pairing in the region immediately downstream of the nozzle exit is also observed. In a second simulation, the effect of the nozzle exit boundary layer thickness on the vortex pairing Strouhal frequency (based on nozzle diameter) and its harmonics is demonstrated. The limitations and deficiencies of the present study are identified and discussed. We hope that the lessons learned in this study will help guide future research activities towards resolving the pending issues identified in this work.

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Abbreviations

c :

sound speed

D :

spatial derivative

D j :

jet nozzle diameter

e t :

total energy, ρ (u 2 +  v 2 +  w 2)/2 +  p/(γ − 1)

f :

arbitrary variable; frequency

F, G, H :

inviscid flux vectors in Navier–Stokes equations

F v , G v , H v :

viscous flux vectors in Navier–Stokes equations

i, j , k :

grid point indices

J :

metric Jacobian

L :

integral length scale

N :

number of grid points along given spatial direction

p :

static pressure

Q :

vector of conservative flow variables

Q :

Q/J

Re D :

jet nozzle Reynolds number, ρ j U j D j /μ j

Re θ :

momentum thickness Reynolds number, ρ j U j δθ/μ j

\({\mathcal R}_{rr}\) :

two-point velocity correlation in radial direction

\({\mathcal R}_{\theta \theta}\) :

two-point velocity correlation in azimuthal direction

\({\mathcal R}_{xx}\) :

two-point velocity correlation in streamwise direction

Sr D :

Strouhal number, f D j /U j

t :

time

U :

mean streamwise velocity

u τ :

friction velocity, \(\sqrt{{\tau}_{\rm wall}/\rho_{\rm wall}}\)

u, v, w :

Cartesian velocity components in x, y, and z directions

x, y, z :

Cartesian coordinates

α f :

filtering parameter

δexit :

boundary layer thickness at nozzle exit

δinlet :

boundary layer thickness at nozzle inlet

δrecycle :

boundary layer thickness at recycle station

δθ :

momentum thickness of boundary layer

Δ r :

wall normal or radial grid spacing

Δθ :

azimuthal grid spacing

Δ x :

streamwise grid spacing

Δt :

time increment

Δξ:

uniform grid spacing along ξ direction in the computational domain

\(\epsilon_I\) :

artificial dissipation parameter in implicit time stepping

γ:

ratio of specific heats of air, 1.4

μ:

molecular viscosity

ν:

kinematic viscosity (μ/ρ)

ρ:

fluid density

σ ijk :

spectral radius of inviscid flux Jacobian at grid point (i,j,k)

τ:

wall shear stress; time scale

ξ, η, ζ:

generalized curvilinear coordinates

〈 〉:

time averaging operator

i :

value at grid point i

∞:

ambient value

j :

value at nozzle exit centerline

r :

radial direction

rms:

root mean squared

x :

streamwise direction

θ:

azimuthal direction; value based on momentum thickness

wall:

value on nozzle wall

B :

backward operator in prefactored optimized compact scheme

F :

forward operator in prefactored optimized compact scheme

n :

time level

\(\overline{(\;)}\) :

spatially filtered quantity

p :

sub-iteration level

 + :

value given in wall units

′:

perturbation from mean value

\(\tilde{(\;)}\) :

Favre-filtered quantity

References

  1. http://www.ncsa.uiuc.edu/UserInfo/Resources/Hardware/XeonCluster

  2. http://www.psc.edu/machines/cray/xt3/

  3. Andersson N., Eriksson L.E., Davidson L. (2005) Investigation of an isothermal Mach 0.75 jet and its radiated sound using large-eddy simulation and Kirchhoff surface integration. Int. J. Heat Fluid Flow 26, 393–410

    Article  Google Scholar 

  4. Andersson N., Eriksson L.E., Davidson L. (2005) Large-eddy simulation of subsonic turbulent jets and their radiated sound. AIAA J. 43(9): 1899–1912

    ADS  Google Scholar 

  5. Andersson, N., Eriksson, L.E., Davidson, L.: LES prediction of flow and acoustic field of a coaxial jet. AIAA Paper 2005-2884 (2005)

  6. Ashcroft G., Zhang X. (2003) Optimized prefactored compact schemes. J. Comput. Phys. 190(2): 459–457

    Article  MATH  ADS  Google Scholar 

  7. Barré, S., Bogey, C., Bailly, C.: Computation of the noise radiated by jets with laminar/turbulent nozzle-exit conditions. AIAA Paper 2006-2443 (2006)

  8. Beam R.M., Warming R.F. (1978) An implicit factored scheme for the compressible Navier–Stokes equations. AIAA J. 16(4):393–402

    MATH  ADS  Google Scholar 

  9. Benek, J.A., Steger, J.L., Dougherty, F.C., Buning, P.G.: Chimera: A grid-embedding technique. Arnold Engineering Development Center Report AEDC-TR-85-64, Arnold Air Force Station, TN, USA (1986)

  10. Biancherin, A., Lupoglazoff, N., Rahier, G., Vuillot, F.: Comprehensive 3d unsteady simulations of subsonic and supersonic hot jet flow-fields: Part 2: Acoustic analysis. AIAA Paper 2002-2600 (2002)

  11. Birch, S.F.: A review of axisymmetric jet flow data for noise applications. AIAA Paper 2006-2602 (2006)

  12. Bodony, D.J., Lele, S.K.: Review of the current status of jet noise predictions using large eddy simulation (invited). AIAA Paper 2006-0468 (2006)

  13. Bridges J.E., Hussain A.K.M.F. (1987) Roles of initial condition and vortex pairing in jet noise. J. Sound Vibrat. 117(2): 289–311

    Article  ADS  Google Scholar 

  14. Choi H., Moin P. (1994) Effects of the computational time step on numerical solutions of turbulent flow. J. Comput. Phys. 113(1): 1–4

    Article  MATH  ADS  Google Scholar 

  15. Constantinescu G.S., Lele S.K. (2002) A highly accurate technique for the treatment of flow equations at the polar axis in cylindrical coordinates using series expansions. J. Comput. Phys. 183, 165–186

    Article  MATH  ADS  Google Scholar 

  16. DeBonis, J.R.: A large-eddy simulation of a high Reynolds number Mach 0.9 jet. AIAA Paper 2004-3025 (2004)

  17. DeBonis J.R., Scott J.N. (2002) Large-eddy simulation of a turbulent compressible round jet. AIAA J. 40(7): 1346–1354

    ADS  Google Scholar 

  18. Dong T.Z. (1997) On boundary conditions for acoustic computations in non-uniform mean flows. J. Comput. Acoust. 5(3): 297–315

    Article  Google Scholar 

  19. Drubka R.E. (1981) Instabilities in the near field of turbulent jets and their dependence on initial conditions and Reynolds number. PhD Thesis. Illinois Institute of Technology, Chicago

    Google Scholar 

  20. Ekaterinaris J.A. (1999) Implicit, high-resolution, compact schemes for gas dynamics and aeroacoustics. J. Comput. Phys. 156(2): 272–299

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. Freund J.B., Lele S.K., Moin P. (1996) Calculation of the radiated sound field using an open Kirchhoff surface. AIAA J. 34(5):909–916

    MATH  ADS  Google Scholar 

  22. Gaitonde D.V., Visbal M.R. (2000) Padé-type higher-order boundary filters for the Navier–Stokes equations. AIAA J. 38(11):2103–2112

    ADS  Google Scholar 

  23. Henshaw, W.: Ogen: An overlapping grid generator for overture. http://www.llnl.gov/casc/Overture

  24. Hussain A.K.M.F., Zaman K.B.M.Q. (1985) An experimental study of organized motions in the turbulent plane mixing layer. J. Fluid Mech. 159, 85–104

    Article  ADS  Google Scholar 

  25. Kim J.W., Lee D.J. (2000) Generalized characteristic boundary conditions for computational aeroacoustics. AIAA J. 38(11):2040–2049

    ADS  Google Scholar 

  26. Kim J.W., Lee D.J. (2004) Generalized characteristic boundary conditions for computational aeroacoustics, part 2. AIAA J. 42(1): 47–55

    ADS  Google Scholar 

  27. Lele S.K. (1992) Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103(1): 16–42

    Article  MATH  MathSciNet  ADS  Google Scholar 

  28. Lund T.S., Wu X., Squires K.D. (1998) Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140(2): 233–258

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. Lupoglazoff, N., Biancherin, A., Vuillot, F., Rahier, G.: Comprehensive 3d unsteady simulations of subsonic and supersonic hot jet flow-fields: Part 1: Aerodynamic analysis. AIAA Paper 2002–2599 (2002)

  30. Lyrintzis A.S. (2003) Surface integral methods in computational aeroacoustics—from the (cfd) near-field to the (acoustic) far-field. Int. J. Aeroacoust. 2(2): 95–128

    Article  Google Scholar 

  31. Mohseni K., Colonius T. (2000) Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157(2): 787–795

    Article  MATH  ADS  MathSciNet  Google Scholar 

  32. Narayanan S., Barber T.J., Polak D.R. (2002) High subsonic jet experiments: Turbulence and noise generation studies. AIAA J. 40(3): 430–437

    ADS  Google Scholar 

  33. Paliath, U., Morris, P.J.: Prediction of noise from jets with different nozzle geometries. AIAA Paper 2004-3026 (2004)

  34. Paliath, U., Morris, P.J.: Prediction of jet noise from circular beveled nozzles. AIAA Paper 2005-3096 (2005)

  35. Piomelli U., Balaras E. (2002) Wall-layer models for large-eddy simulations. Ann. Rev. Fluid Mech. 34, 349–374

    Article  ADS  MathSciNet  Google Scholar 

  36. Pulliam T.H. (1986) Artificial dissipation models for the Euler equations. AIAA J. 24(12): 1931–1940

    MATH  ADS  Google Scholar 

  37. Rai M.M., Moin P. (1993) Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer. J. Comput. Phys. 109(2): 169–192

    Article  MATH  ADS  Google Scholar 

  38. Rizzetta D.P., Visbal M.R., Blaisdell G.A. (2003) A time-implicit high-order compact differencing and filtering scheme for large-eddy simulation. Int. J. Numer. Methods Fluids 42(6): 665–693

    Article  MATH  ADS  Google Scholar 

  39. Sagaut P., Garnier E., Tromeur E., Larchevêque L., Labourasse E. (2004) Turbulent inflow conditions for large-eddy simulation of compressible wall-bounded flows. AIAA J. 42(3): 469–477

    ADS  Google Scholar 

  40. Schlichting, H.: Boundary-layer theory, 6th edn, chap. 14, pp 689–690. McGraw-Hill Book Company, New York (1968)

  41. Sherer S.E., Scott J.N. (2005) High-order compact finite-difference methods on general overset grids. J. Comput. Phys. 210(2): 459–496

    Article  MATH  ADS  Google Scholar 

  42. Spalart P.R. (1988) Direct simulation of a turbulent boundary layer up to Re θ =  1410. J. Fluid Mech. 187, 61–98

    Article  MATH  ADS  Google Scholar 

  43. Spalding D.B. (1961) A single formula for the law of the wall. J. Appl. Mech. 28, 455–457

    MATH  Google Scholar 

  44. Townsend A.A. (1976) The structure of turbulent shear flow. Cambridge University Press, Great Britain

    MATH  Google Scholar 

  45. Uzun, A.: 3-d large eddy simulation for jet aeroacoustics. PhD Thesis, School of Aeronautics and Astronautics, Purdue University, West Lafayette (2003)

  46. Uzun A., Blaisdell G.A., Lyrintzis A.S. (2004) Application of compact schemes to large eddy simulation of turbulent jets. J. Sci. Comput. 21(3): 283–319

    Article  MATH  MathSciNet  Google Scholar 

  47. Uzun A., Hussaini M.Y., Streett C.L. (2006) Large-eddy simulation of a wing tip vortex on overset grids. AIAA J. 44(6): 1229–1242

    ADS  Google Scholar 

  48. Uzun A., Lyrintzis A.S., Blaisdell G.A. (2004) Coupling of integral acoustics methods with LES for jet noise prediction. Int. J. Aeroacoust. 3(4): 297–346

    Article  Google Scholar 

  49. Visbal M.R., Gaitonde D.V. (2001) Very high-order spatially implicit schemes for computational acoustics on curvilinear meshes. J. Comput. Acoust.9(4): 1259–1286

    MathSciNet  Google Scholar 

  50. Visbal, M.R., Morgan, P.E., Rizzetta, D.P.: An implicit LES approach based on high-order compact differencing and filtering schemes (invited). AIAA Paper 2003-4098 (2003)

  51. Visbal M.R., Rizzetta D.P. (2002) Large-eddy simulation on curvilinear grids using compact differencing and filtering schemes. J. Fluids Eng. 124(4): 836–847

    Article  Google Scholar 

  52. Viswanathan K. (2004) Aeroacoustics of hot jets. J. Fluid Mech. 516, 39–82

    Article  MATH  ADS  Google Scholar 

  53. Viswanathan K., Clark L.T. (2004) Effect of nozzle internal contour on jet aeroacoustics. Int. J. Aeroacoust. 3(2): 103–135

    Article  Google Scholar 

  54. Viswanathan, K., Shur, M.L., Spalart, P.R., Strelets, M.K.: Computation of the flow and noise of round and beveled nozzles. AIAA Paper 2006–2445 (2006)

  55. Wu, X., Tristanto, I.H., Page, G.J., McGuirk, J.J.: Influence of nozzle modelling in LES of turbulent free jets. AIAA Paper 2005-2883 (2005)

  56. Zaman K.B.M.Q. (1984) Effect of initial condition on subsonic jet noise. AIAA J. 23(9): 1370–1373

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. School of Computational Science, Florida State University, Tallahassee, FL, 32306-4120, USA

    Ali Uzun & M. Yousuff Hussaini

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  1. Ali Uzun
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  2. M. Yousuff Hussaini
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Correspondence to M. Yousuff Hussaini.

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Communicated by T. Colonius.

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Uzun, A., Hussaini, M.Y. Investigation of high frequency noise generation in the near-nozzle region of a jet using large eddy simulation. Theor. Comput. Fluid Dyn. 21, 291–321 (2007). https://doi.org/10.1007/s00162-007-0048-z

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