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Coherent structure and sound production in the helical mode of a screeching axisymmetric jet

Published online by Cambridge University Press:  08 May 2014

Daniel Edgington-Mitchell*
Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
Kilian Oberleithner
Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
Damon R. Honnery
Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
Julio Soria
Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia Department of Aeronautical Engineering, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
Email address for correspondence:


The structure of a screeching axisymmetric jet in the helical C mode at a nozzle pressure ratio of 3.4 issuing from a convergent nozzle is studied using high-resolution particle image velocimetry. Proper orthogonal decomposition (POD) is used to extract the dominant coherent structures within the jet. The first two modes produced by the POD are used to reconstruct a phase-averaged data sequence. A triple decomposition into mean, coherent and random velocity components is performed. The embedded shock structures within the jet are shown to strongly modulate the coherent axial stresses within the shear layer and to weakly modulate the random axial stresses. Analysis of the third and fourth moments of the velocity probability density function is used as an indicator of possible regions of shock–vortex interaction and thus screech tone generation. Peaks of kurtosis (flatness) occur at the second, third and fourth shock–boundary intersection points, with the radial position shifting towards the centreline with increasing downstream distance. Analysis of the coherent component of vorticity shows that the largest fluctuations in coherent vorticity occur at the high-speed side of the shear layer in an area extending from the second to the fourth shock cell. With reference to prior literature, the argument is made that it is this increased magnitude of coherent vorticity fluctuation that is the primary factor in the determination of which shock cells act as dominant screech sources.

© 2014 Cambridge University Press 

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Agui, J. & Jimenez, J. 1974 On the performance of particle tracking. J. Fluid Mech. 185, 447468.CrossRefGoogle Scholar
Alkislar, M., Krothapalli, A. & Lourenco, L. 2003 Structure of a screeching rectangular jet: a stereoscopic particle image velocimetry study. J. Fluid Mech. 489, 121154.CrossRefGoogle Scholar
Alvi, F. S., Lou, H., Shih, C. & Kumar, R. 2008 Experimental study of physical mechanisms in the control of supersonic impinging jets using microjets. J. Fluid Mech. 613, 5583.CrossRefGoogle Scholar
Andre, B., Castelain, T. & Bailly, C. 2011 Experimental study of flight effects on screech in underexpanded jets. Phys. Fluids 23, 665673.CrossRefGoogle Scholar
Andre, B., Castelain, T. & Bailly, C. 2013 Broadband shock-associated noise in screeching and non-screeching underexpanded supersonic jets. AIAA J. 51, 126102.CrossRefGoogle Scholar
Batchelor, G. & Townsend, A. 1949 The nature of turbulent motion at large wavenumbers. Proc. R. Soc. Lond. A 199, 238255.Google Scholar
Berland, J., Bogey, C. & Bailly, C. 2007 Numerical study of screech generation in a planar supersonic jet. Phys. Fluids 19, 075105.CrossRefGoogle Scholar
Bogey, C., Marsden, O. & Bailly, C. 2012 Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of $10^{5}$ . J. Fluid Mech. 701, 352385.CrossRefGoogle Scholar
Davies, M. & Oldfield, D. 1962 Tones from a choked axisymmetric jet. Acustica 12, 257277.Google Scholar
Elsinga, G. E., van Oudheusden, B. W. & Scarano, F. 2005 Evaluation of aero-optical distortion effects in PIV. Exp. Fluids 39, 246256.CrossRefGoogle Scholar
Gao, J. & Li, X. 2010 A multi-mode screech frequency prediction formula for circular supersonic jets. J. Acoust. Soc. Am. 127, 12511257.CrossRefGoogle ScholarPubMed
Henderson, B., Bridges, J. & Wernet, M. 2005 An experimental study of the oscillatory flow structure of tone-producing supersonic impinging jets. J. Fluid Mech. 542, 115137.CrossRefGoogle Scholar
Herpin, S., Wong, C., Stanislas, M. & Soria, J. 2008 Stereoscopic PIV measurements of a turbulent boundary layer with a large spatial dynamic range. Exp. Fluids 45 (4), 745763.CrossRefGoogle Scholar
Huang, N., Shen, Z. & Long, S. 1999 A new view of nonlinear water waves: the Hilbert spectrum. Annu. Rev. Fluid Mech. 31, 417457.CrossRefGoogle Scholar
Hussain, A. & Reynolds, W. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41, 241258.CrossRefGoogle Scholar
Imamoglu, B., Baysal, O. & Balakumar, P. 2007 Computation of shock induced noise in imperfectly expanded supersonic jets. Aeroacoustics 6, 127146.CrossRefGoogle Scholar
Kennedy, D. & Corrsin, S. 1961 Spectral flatness factor and ‘intermittency’ in turbulence and in nonlinear noise. J. Fluid Mech. 10, 366370.CrossRefGoogle Scholar
Konstantinidis, E., Balabani, S. & Yianneskis, M. 2005 Conditional averaging of PIV plane wake data using a cross-correlation approach. Exp. Fluids 39, 3847.CrossRefGoogle Scholar
Kostas, J., Soria, J. & Chong, M. 2005 A comparison between snapshot POD analysis of PIV velocity and vorticity data. Exp. Fluids 38 (2), 146160.CrossRefGoogle Scholar
Manning, T.1999 A numerical investigation of sound generation in supersonic jet screech. PhD thesis, Stanford University.CrossRefGoogle Scholar
Manning, T. & Lele, S.2000 A numerical investigation of sound generation in supersonic jet screech. In 21st AIAA Aeroacoustics Conference.CrossRefGoogle Scholar
Melling, A. 1997 Tracer particles and seeding for particle image velocimetry. Meas. Sci. Technol. 8, 14061416.CrossRefGoogle Scholar
Mitchell, D.2013 Coherent structure and shock–vortex interaction in the screeching supersonic jet. PhD thesis, Monash University.Google Scholar
Mitchell, D., Honnery, D. & Soria, J. 2011 Particle relaxation and its influence on the particle image velocimetry cross-correlation function. Exp. Fluids 51, 933974.CrossRefGoogle Scholar
Mitchell, D., Honnery, D. & Soria, J. 2012 The visualization of the acoustic feedback loop in impinging underexpanded supersonic jet flows using ultra-high frame rate schlieren. J. Vis. 15, 333341.CrossRefGoogle Scholar
Mitchell, D., Honnery, D. & Soria, J. 2013 Near field structure of underexpanded elliptic jets. Exp. Fluids 54 (7), 113.CrossRefGoogle Scholar
Oberleithner, K., Sieber, M., Nayeri, C., Paschereit, C., Petz, C., Hege, H.-C., Noack, B. & Wygnanski, I. 2011 Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction. J. Fluid Mech. 679, 373414.CrossRefGoogle Scholar
Panda, J. 1998 Shock oscillation in underexpanded screeching jets. J. Fluid Mech. 363, 173198.CrossRefGoogle Scholar
Panda, J. & Seasholtz, R. 1999 Measurement of shock structure and shock–vortex interaction in underexpanded jets using Rayleigh scattering. Phys. Fluids 11 (12), 37613777.CrossRefGoogle Scholar
Powell, A. 1953 On the mechanism of choked jet noise. Proc. Phys. Soc. Lond. 66, 10391056.CrossRefGoogle Scholar
Ragni, D., Schrijer, F., van Oudheusden, B. & Scarano, F. 2011 Particle tracer response across shocks measured by PIV. Exp. Fluids 50, 5364.CrossRefGoogle Scholar
Raman, G. 1997 Cessation of screech in underexpanded jets. J. Fluid Mech. 336, 6990.CrossRefGoogle Scholar
Raman, G. 1999 Supersonic jet screech: half-century from Powell to the present. J. Sound Vib. 225, 543571.CrossRefGoogle Scholar
Raman, G. & Rice, E. 1994 Instability modes excited by natural screech tones in a supersonic rectangular jet. Phys. Fluids 6, 39994008.CrossRefGoogle Scholar
Sadr, R. & Klewicki, J. 2003 An experimental investigation of the near-field flow development in coaxial jets. Phys. Fluids 15, 12331246.CrossRefGoogle Scholar
Samimy, M., Kim, J., Kastner, J., Adamovich, I. & Utkin, Y. 2007 Active control of high-speed and high-Reynolds-number jets using plasma actuators. J. Fluid Mech. 578, 305330.CrossRefGoogle Scholar
Sirovich, L. 1987 Proper orthogonal decomopsition applied to turbulent flow in a square duct. Q. Appl. Maths 45, 561671.CrossRefGoogle Scholar
Soria, J. 1996 An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp. Therm. Fluid Sci. 12, 221233.CrossRefGoogle Scholar
Soria, J. 2006 Particle image velocimetry – application to turbulence studies. In Turbulence and Coherent Structures in Fluids, Plasmas and Nonlinear Media, pp. 319330. World Scientific.Google Scholar
Suzuki, T. & Lele, S. 2003 Shock leakage through an unsteady vortex-laden mixing layer: application to jet screech. J. Fluid Mech. 490, 139167.CrossRefGoogle Scholar
Tam, C. 1995 Supersonic jet noise. Annu. Rev. Fluid Mech. 27, 1743.CrossRefGoogle Scholar
Tedeschi, G., Gouin, H. & Elena, M. 1999 Motion of tracer particles in supersonic flows. Exp. Fluids 26, 288296.CrossRefGoogle Scholar
Umeda, Y. & Ishii, R. 2001 On the sound sourves of screech tones radiated from choked circular jets. J. Acoust. Soc. Am. 110, 17451858.CrossRefGoogle Scholar
Umeda, Y. & Ishii, R. 2002a Existence of Mach cones and helical vortical structures around the underexpanded circular jet in the helical oscillation mode. J. Acoust. Soc. Am. 112, 99107.CrossRefGoogle ScholarPubMed
Umeda, Y. & Ishii, R. 2002b Sound sources of screech tone radiated from circular supersonic jet oscillating in the helical mode. Aeroacoustics 1, 355384.CrossRefGoogle Scholar
Westley, R. & Wooley, J. 1968 Flow and sound visualization of an axisymmetric choked jet (10 in schlieren), (16 mm, silent film, running time 8.5 min). Natl Res. Counc. Can., Natl Aeronaut. Establishment 13.Google Scholar
Willert, C., Mitchell, D. & Soria, J. 2012 An assessment of high-power light-emitting diodes for high frame rate schlieren imaging. Exp. Fluids 53, 413421.CrossRefGoogle Scholar