Computation of Shock Induced Noise in Imperfectly Expanded Supersonic Jets

Abstract

Screech noise exists in imperfectly expanded jets. When the exit pressure of imperfectly expanded jet does not match its backpressure, expansion or compression waves appear out of the nozzle and generate shock cell patterns. Screech is generated by the interaction of shock cells and instability waves. Although many studies have been conducted to model screech noise, it still is not yet a well-understood phenomenon.

In the present computational study, the results help better understand screech generation mechanisms and they are compared with the latest available experiments. First, axisymmetric models are constructed for underexpanded jets of 25.4 mm diameter and Mach numbers of 1.19 and 1.43. Then, three dimensional (3D) models are computed for jets with Mach numbers of 1.43 and 1.80. The mathematical model consists of full Navier-Stokes equations in cylindrical coordinates, and large-eddy-simulation turbulence modeling. For spatial discretizations, a fifth-order, weighted essentially non-oscillatory scheme is used, as it is deemed the most suitable method for capturing shocks. Time discretization is a third-order total-variation-diminishing scheme. This methodology does not require artificial viscosity or “tuning up” of parameters.

The experimental results predict that the solution is in axisymmetric mode for Mach 1.19 and in helical mode for 1.43. The experimental screech frequencies of 8.4 kHz for Mach 1.19 and 5.4 kHz for Mach 1.43 are verified with the present axisymmetric results. Computed shock cell structure is in agreement with experiments and other published computations in all cases. As in the experiments, the present screech waves emerge from the second and third shock cells. The screech wavelength is roughly estimated as 1.5 D, which is close to other published computational studies. Axisymmetric results for Mach number 1.43 could predict general flow quantities, like shock cell pattern and screech frequency prediction. Therefore, three-dimensional helical effects are investigated by creating a simulation of planes with varying azimuthal angles. This has been useful to detect shock generation locations. In Mach 1.80 case, a barrel shock structure is observed just as in the experimental studies. In conclusion, this study is deemed as a good verification of experimental results.

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References

Adams

, and Shariff

, (1996), “A High-Resolution Hybrid Compact-ENO Scheme for Shock-Turbulence Interaction Problems,” Journal of Computational Physics, Vol. 127, pp 27–51.

Atkins

H. L.

, (1991), “High-Order ENO Methods for the Unsteady Compressible Navier-Stokes Equations,” AIAA Paper 91–1557.

Cai

, and Shu

C. W.

, (1993), “Uniform High-order Spectral Methods for One- and Two-dimensional Euler Equations,” Journal of Computational Physics, Vol. 104, pp. 427–443.

Cain

A. B.

, (1993), “Computation of Supersonic Jet Screech”, Computational Aero- and Hydro- Acoustics, Mankbadi

R.R.

Lyrintzis

A.S.

Baysal

Povinelli

L.A.

Hussaini

M.Y.

(Editors), ASME FED Vol. 147, pp. 123–129.

Casper

, and Atkins

, (1993), “A Finite Volume Highorder ENO Scheme for Two Dimensional Hyperbolic Systems,” Journal of Computational Physics, Vol. 106, pp. 62–76.

EPAPS Document No. EPHFLE611017912, http://www.aip.org/pubservs/epaps.html

Erlebacher

Hussaini

, and Shu

C. W.

, (1997), “Interaction of a Shock with a Longitudinal Vortex,” Journal of Fluid Mechanics, Vol. 337, pp. 129–153.

Gribben

B. J.

Badcock

K. J.

, and Richards

B. E.

, (2000), “Numerical Study of Shock Reflection in an Underexpanded Jet,” AIAA Journal, Vol. 38, No. 2, pp. 275–283

Harten

Engquist

Osher

, and Chakravarthy

, (1987), “Uniformly high order essentially nonoscillatory schemes, III,” Journal of Computational Physics, Vol. 71, pp. 231–303.

10.

Imamoglu

, and Balakumar

, (2002), “Computation of Shock Induced Noise in Imperfectly Expanded Supersonic Jets,” AIAA 2002–2527, 8th AIAA/CEAS Aeroacoustics Conference, Breckenridge, CO, June 2002.

11.

Imamoglu

, and Balakumar

, (2003), “Three Dimensional Computation of Shock Induced Noise in Imperfectly Expanded Supersonic Jets,” AIAA paper 2003–3249, 9th AIAA/CEAS Aeroacoustics Conference, Hilton Head, SC, May 2003.

12.

Ladeinde

O'Brien

Cai

, and Liu

, (1995), “Advection by Polytropic Compressible Turbulence,” Physics of Fluids, Vol. 7, pp. 2848–2857.

13.

Liu

X. D.

Osher

, and Chan

, (1994) “Weighted Essentially Nonoscillatory Schemes,” Journal of Computational Physics, Vol. 115, pp. 200–212.

14.

Loh

C. Y.

Himansu

Wang

X. Y.

, and Jorgenson

P. C. E.

, (2001), “Computation of an Underexpanded 3-D Rectangular Jet by the CE/SE Method”, AIAA paper 2001–0986.

15.

Manning

and Lele

S.K.

, (1998),. “Numerical Simulations of Shock-Vortex Interactions in Supersonic Jet Screech”, AIAA-Paper 98–0282.

16.

Norum

T. D.

, and Seiner

J. M.

, (1980), “Location and Propagation of Shock Associated Noise from Supersonic Jets,” AIAA paper 80–0983.

17.

Panda

, (1999), “An Experimental Investigation of Screech Noise Generation,” Journal of Fluid Mechanics, vol. 378, pp 71–96.

18.

Panda

, and Seasholtz

R. G.

, (1999), “Measurement of Shock Structure and Shock-Vortex Interaction in Underexpanded Jets Using Rayleigh Scattering,” Physics of Fluids, vol. 11, No. 12, pp. 3761–3777.

19.

Powell

(1953 a), “On the Noise Emanating from a Two-Dimensional Jet Above the Critical Pressure,” Aeronautical Quarterly, Vol. IV, pp 103122.

20.

Powell

(1953 b), “On the Mechanism of Choked Jet Noise,” Proceedings of the Physical Society (London), Vol. 66, pp 1039–1056.

21.

Raman

, and Rice

E. J.

(1994), “Instability Modes Excited by Natural Screech Tones in a Supersonic Rectangular Jet,” Physics of Fluids, 6, pp. 3999–4008.

22.

Shen

, and Tam

C.K.W.

, (1998), “Numerical Simulation of the Generation of Axisymmetric Mode Jet Screech Tones”, AIAA Journal, Vol. 36, No. 10, pp. 1801–1807.

23.

Shu

C. W.

Zang

T. A.

Erlebacher

Whitaker

, and Osher

, (1992), “High Order ENO Schemes Applied to Two- and Three-dimensional Compressible Flow,” Applied Numerical Mathematics, Vol. 9, pp. 45–71.

24.

Shu

C. W.

, (1997), “Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws,” ICASE Report No. 97–65, NASA Langley Research Center, Hampton, VA.

25.

Tam

C.K.W.

Shen

, and Raman

(1997), “Screech Tones of Supersonic Jets from Bevelled Rectangular Nozzles,” AIAA Journal, Vol. 35, No. 7, pp. 1119–1125.

26.

Walsteijn

, (1994) “Robust Numerical Methods for 2D Turbulence,” Journal of Computational Physics, Vol. 114, pp. 129–145.