zbMATH — the first resource for mathematics

Nonparallel and nonlinear stability of supersonic jet flow. (English) Zbl 0978.76030
From the summary: Linear and nonlinear evolution of disturbances in an axisymmetric, supersonic, low Reynolds number jet is studied using parabolized stability equations. We consider both axisymmetric and helical modes, and nonparallel effect is found to increase the disturbance growth rate, although there is a very little effect on the wavenumber. Nonlinear interaction of helical modes, which are dominant instability modes of the jet, results in disturbance saturation, spectrum filling and large mean flow distortions. Similar to that for the supersonic boundary layer flow, interaction of helical modes induces streamwise vortices which cause significant mean flow distortion and growth of other harmonics. The computed evolution of disturbances is in reasonably good agreement with experimental data.

76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76E30 Nonlinear effects in hydrodynamic stability
76M20 Finite difference methods applied to problems in fluid mechanics
Full Text: DOI
[1] Chang, C.-L.; Malik, M.R., Oblique-mode breakdown and secondary instability in supersonic boundary layers, J. fluid mech, 273, 323-359, (1994) · Zbl 0814.76040
[2] Morrison, G.L.; McLaughlin, D.K., Instability process in low Reynolds number supersonic jets, Aiaa j, 18, 7, 793-800, (1980)
[3] Tam CKW. Jet noise generated by large-scale coherent motion. In: Aeroacoustics of flight vehicles: theory and practice, vol. 1: Noise sources. NASA RP-1258, WRDC TR-90-3052, 1991
[4] Crow, S.C.; Champagne, F.H., Orderly structure in jet turbulence, J. fluid mech, 48, 3, 547-591, (1971)
[5] Brown, G.L.; Roshko, A., On density effects and large structure in turbulent mixing layers, J. fluid mech, 64, 4, 775-816, (1974) · Zbl 1416.76061
[6] Lepicovsky J, Ahuja KK, Brown WH, Burrin RH. Coherent large-scale structures in high Reynolds number supersonic jets. NASA CR-3952, 1985
[7] Tam, C.K.W., Directional acoustic radiation from a supersonic jet generated by shear layer instability, J. fluid mech, 46, 757-768, (1971) · Zbl 0226.76032
[8] Tam, C.K.W., On the noise of a nearly ideally expanded supersonic jet, J. fluid mech, 51, 69-95, (1972) · Zbl 0227.76099
[9] McLaughlin, D.K.; Morrison, G.L.; Troutt, T.R., Experiments on the instability waves in a supersonic jet and their acoustic radiation, J. fluid mech, 69, 73-95, (1975)
[10] Morris PJ, Tam CKW. Near and far field noise for large-scale instabilities of axisymmetric jets. AIAA 77-1351, 1977
[11] Morrison, G.L.; McLaughlin, D.K., The noise generated by instabilities in low Reynolds number supersonic jets, J. sound and vibration, 65, 2, 177-191, (1979)
[12] Troutt, T.R.; McLaughlin, D.K., Experiments on the flow and acoustic properties of a moderate-Reynolds-number supersonic jet, J. fluid meeh, 116, 123-156, (1982)
[13] Tam, C.K.W.; Burton, D.E., Sound generated by instability waves of supersonic flows. part 1. two-dimensional mixing layers, J. fluid mech, 138, 249-271, (1984) · Zbl 0543.76108
[14] Tam CKW, Chen P, Seiner JM. Relationship between instability waves and noise of high-speed jets. AIAA 91-0492, 1991
[15] Seiner JM, Bhat TRS, Ponton MK. Mach wave emission from a high temperature supersonic jet. AIAA 93-0734, 1993
[16] Plaschko, P., Helical instabilities of slowly divergent jets, J. fluid mech, 92, 2, 209-215, (1979) · Zbl 0398.76040
[17] Tam, C.K.W.; Morris, P.J., The radiation of sound by the instability waves of a compressible plane turbulent shear layer, J. fluid mech, 98, 349-381, (1980) · Zbl 0437.76053
[18] Tam, C.K.W.; Burton, D.E., Sound generated by instability waves of supersonic flows. part 2. axisymmetric jets, J. fluid mech, 138, 273-295, (1984) · Zbl 0543.76109
[19] Tam, C.K.W.; Chen, P., Turbulent mixing noise from supersonic jets, Aiaa j, 32, 9, 1774-1780, (1994) · Zbl 0825.76286
[20] Zaman KBMQ. Streamwise vorticity generation and mixing enhancement in free jets by ‘delta-tabs’. AIAA Paper 93-3253, 1993
[21] King CJ, Krothapalli A, Strykowski PJ. Streamwise vorticity generation in supersonic jets with minimal thrust loss. AIAA 94-0661, 1994
[22] Grosch, C.E.; Seiner, J.M.; Hussaini, M.Y.; Jackson, T.L., Numerical simulation of mixing enhancement in hot supersonic jet, Phys. fluids, 9, 4, 1125-1143, (1997)
[23] Viswanathan, K.; Sankar, L.N., Toward the direct calculation of noise: fluid/acoustic coupled approach, Aiaa j, 33, 12, 2271-2279, (1995) · Zbl 0849.76056
[24] Bangalore A, Morris PJ, Long LN. A parallel three-dimensional computational aeroacoustics methods using non-linear disturbance equations. AlAA 96-1728, 1996
[25] Spall, R.E.; Malik, M.R., Goertler vortices in supersonic and hypersonic boundary layers, Phys. fluids A, 1, 11, 1822-1835, (1989) · Zbl 0684.76070
[26] Herbert Th. Boundary-layer transition—analysis and prediction revisited. AIAA 91-0737, 1991
[27] Bertolotti, F.P.; Herbert, Th.; Spalart, P.R., Linear and nonlinear stability of the Blasius boundary layer, J. fluid mech, 242, 441-474, (1992) · Zbl 0754.76029
[28] Chang C-L, Malik MR, Erlebacher G, Hussaini MY. Compressible stability of growing boundary layers using parabolized stability equations. AIAA 91-1636, 1991
[29] Crighton, D.B.; Gaster, G., Stability of slowly diverging jet flow, J. fluid mech, 77, 397-413, (1975) · Zbl 0338.76021
[30] Li, F.; Malik, M.R., On the nature of PSE approximation, Theoretical and computational fluid dynamics, 8, 253-273, (1996) · Zbl 0947.76022
[31] Li, F.; Malik, M.R., Spectral analysis of parabolized stability equations, Computers and fluids, 26, 1, 279-297, (1997) · Zbl 0886.76029
[32] Anderson, D.A.; Tannehill, J.C.; Pletcher, R.H., Computational fluid mechanics and heat transfer, (1984), Hemisphere New York · Zbl 0569.76001
[33] Batchelor, G.K.; Gill, A.E., Analysis of the stability of axisymmetric jets, J. fluid mech, 14, 34, (1962) · Zbl 0118.21102
[34] Khorrami, M.R.; Malik, M.R.; Ash, R.L., Application of spectral collocation techniques to the stability of swirling flows, J. comput. phys, 81, 206, (1989) · Zbl 0662.76057
[35] Thompson, K.W., Time dependent boundary conditions for hyperbolic systems, J. comput. phys, 68, 1-24, (1987) · Zbl 0619.76089
[36] Tam, C.K.W.; Hu, F.Q., On the three-families of instability waves of high speed jets, J. fluid mech, 201, 447, (1989) · Zbl 0672.76054
[37] Stromberg JL, McLaughlin DK, Troutt TR. Flowfield and acoustic properties of a Mach number 0.9 jet at a low Reynolds number. AIAA 79-0593, 1979
[38] McLaughlin, D.K.; Morrison, G.L.; Troutt, T.R., Reynolds number dependence in supersonic jet noise, Aiaa j, 15, 526-532, (1977)
[39] Morris, P.J., Stability of a two-dimensional jet, Aiaa j, 19, 7, 857, (1981) · Zbl 0476.76035
[40] Goldstein, M.E.; Choi, S.-W., Nonlinear evolution of interacting oblique waves in two dimensional shear layers, J. fluid mech, 207, 97-120, (1989) · Zbl 0681.76053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.