Supersonic Jets

  • Mrinal KaushikEmail author


The control of high-speed jets has turned into an interesting research area due to its extensive variety of uses starting from household applications to space technology. Among these, the passive control technique has turned into a conspicuous research field because of its undeniable preference. The different passive controls for increasing aerodynamic mixing and aeroacoustic advantages have been discussed in this chapter. Additionally, the computational studies on jets performed by a few researchers in the past are likewise inspected at length.


  1. Abramovich GN (1963) The Theory of Turbulent Jets. MIT Press, CambridgeGoogle Scholar
  2. Agui JC, Hesselink L (1988) Flow visualization and numerical analysis of a co-flowing jet: a three-dimensional approach. J Fluid Mech 191:19–45CrossRefGoogle Scholar
  3. Ahuja AA (1973) Correlation and prediction of jet noise. J Sound Vib 29(2):155–168CrossRefGoogle Scholar
  4. Alkislar MB, Krothapalli A, Lourenco LM (2003) Structure of a screeching rectangular jet: a stereoscopic particle image velocimetry study. J Fluid Mech 489:121–154zbMATHCrossRefGoogle Scholar
  5. Ball CG, Fellouah H, Pollard A (2012) The flow field in turbulent round free jets. Prog Aerosp Sci 50:1–26CrossRefGoogle Scholar
  6. Bandyopadhyay PR, Watson RD (1988) Structure of rough-wall turbulent boundary layers. Phys Fluids 31(7):1877–1883CrossRefGoogle Scholar
  7. Batchelor GK, Gill AE (1962) Analysis of the stability of axisymmetric jets. J Fluid Mech 14:529–551MathSciNetzbMATHCrossRefGoogle Scholar
  8. Beavers GS, Wilson TA (1970) Vortex growth in jets. J Fluid Mech 44:97–112CrossRefGoogle Scholar
  9. Berg JR, Ormiston SJ, Soliman HM (2006) Prediction of the flow structure in a turbulent rectangular free jet. Int Commun Heat Mass Transf 33:552–563CrossRefGoogle Scholar
  10. Birky P, Page GJ (2001) Numerical predictions of turbulent under expanded sonic jets using a pressure-based methodology. Proc Inst Mech Eng, Part G: J Aerosp Eng 215:165–173Google Scholar
  11. Boussinesq JV (1897) Théorie de l’écoulement tourbillonnant et tumultueux des liquides dans les lits rectilignes a grande section. Gauthier-Villars et fils. (in French)Google Scholar
  12. Bradshaw P, Ferris O, Johnson RF (1964) Turbulence in noise producing region of a circular jet. J Fluid Mech 19:591–624zbMATHCrossRefGoogle Scholar
  13. Browand FK, Weidman PD (1976) Large scales in the developing mixing layers. J Fluid Mech 76:127–144CrossRefGoogle Scholar
  14. Brown GL, Roshko A (1974) On density effects and large structure in turbulent mixing layers. J Fluid Mech 64(4):775–816CrossRefGoogle Scholar
  15. Cai J, Tsai HM, Liu F (2010) Numerical simulation of vortical ows in the near eld of jets from notched circular nozzles. Comput & Fluids 39:539–552Google Scholar
  16. Chauvet N, Deck S, Jacquin L (2007) Numerical study of mixing enhancement in supersonic round jets. AIAA J 45(7):1675–1687Google Scholar
  17. Chue SH (1975) Pressure probes for uid measurement. Prog Aerosp Sci 16(2):147–223Google Scholar
  18. Chung TJ (1996) Applied Continuum Mechanics. Cambridge University Press, London, UKzbMATHGoogle Scholar
  19. Crighton D (1973) Instability of an elliptic jet. J Fluid Mech 59:665–672zbMATHCrossRefGoogle Scholar
  20. Crighton DG (1975) Basic principles of aerodynamic noise generation. Prog Aerosp Sci 16:31–96CrossRefGoogle Scholar
  21. Crow SC, Champagne FH (1971) Orderly structure in jet turbulence. J Fluid Mech 48(3):547–591CrossRefGoogle Scholar
  22. Curle N (1955) The influence of solid boundaries on aerodynamic sound. Proc R Soc Lond Ser A: Math Phys Sci 231:505–514MathSciNetzbMATHCrossRefGoogle Scholar
  23. Davies MG, Oldfield DE (1962) Tones from a choked axisymmetric jet. I. Cell structure, eddy velocity and source locations, Acustica. 12:257–267zbMATHGoogle Scholar
  24. Domaradzki JA, Holm DD (2001) Navier–Stokes-alpha model: LES equations with nonlinear dispersion. Modern simulation strategies for turbulent flow. ERCOFTAC Bulletin 48:2. Edwards PublishingGoogle Scholar
  25. Durbin PA (1996) On the k-\(\varepsilon \) stagnation point anomaly. J Heat Fluid Flow 17:89–90Google Scholar
  26. Elliott GS, Samimy M, Arnette SA (1992) Study of compressible mixing layers using filtered rayleigh scattering based visualizations. AIAA J 30(10):2567–2569CrossRefGoogle Scholar
  27. Elliott GS, Samimy M, Arnette SA (1993) The evolution of large scale structure in compressible mixing layers. In: 9th symposium on turbulent shear flows, Kyoto, JapanGoogle Scholar
  28. Faivre V, Poinsot T (2004) Experimental and numerical investigations of jet active control for combustion applications. J Turbul 5(1):025Google Scholar
  29. Ffowcs Williams JE (1969) Hydrodynamic noise. Ann Rev Fluid Mech 1:197–222CrossRefGoogle Scholar
  30. Ffowcs Williams JE (1977) Aeroacoustics. Ann Rev Fluid Mech 9:447–468zbMATHCrossRefGoogle Scholar
  31. Ffowcs Williams JE, Hall LH (1970) Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane. J Fluid Mech 40(4):657–670zbMATHCrossRefGoogle Scholar
  32. Franken PA, Westervelt PJ, Dyer I (1958) Jet noise reduction by induced flow. J Acoust Soc Am 30(8):761–764CrossRefGoogle Scholar
  33. Freund JB, Moin P (1998) Mixing enhancement in jet exhaust using fluidic actuators: direct numerical simulations. Proc ASME Fluids Eng Div Summer Meet. Washington DC, USA. FEDSM98–5235Google Scholar
  34. Georgiadis NJ, DeBonis JR (2007) Navier-Stokes analysis methods for turbulent jet flows with application to aircraft exhaust nozzles. Prog Aerosp Sci 42:377–418CrossRefGoogle Scholar
  35. Gohil TB, Saha AK, Muralidhar K (2012) Numerical study of instability mechanisms in a circular jet at low reynolds numbers. Comput & Fluids 64: 1–18MathSciNetzbMATHCrossRefGoogle Scholar
  36. Goldstein ME (1984) Aeroacoustics of turbulent shear flows. Ann Rev Fluid Mech 16:263–285zbMATHCrossRefGoogle Scholar
  37. Grant AJ (1974) A numerical model of instability in axisymmetric jets. J Fluid Mech 66(4):707–724zbMATHCrossRefGoogle Scholar
  38. Gutmark EJ, Schadow KC, Bicker CJ (1990) Near acoustic field and shock structure of rectangular supersonic jets. AIAA J 28(7):1163–1170CrossRefGoogle Scholar
  39. Harper BM, Fisher MJ (1974) The noise from shock waves in supersonic jets. AGARD-CP-131. 11, pp. 1–13Google Scholar
  40. Hattori H, Nagano Y (2004) Direct numerical simulation of turbulent heat transfer in plane impinging jet. Int J Heat Fluid Flow 25:749–758CrossRefGoogle Scholar
  41. Hawkings DL (1977) A generalized analysis of the vibration of circular rings. J Sound Vib 54(l): 67–74CrossRefGoogle Scholar
  42. Heinz S (2003) A model for the reduction of the turbulent energy redistribution by compressibility. Phys Fluids 5(11):3580–3583zbMATHCrossRefGoogle Scholar
  43. Hilgers A (2000) Control and optimization of turbulent jet mixing. Center for Turbulence Research, Annual Research Briefs, pp 47–54Google Scholar
  44. Ho CM, Gutmark EJ (1987) Vortex induction and mass entrainment in a small-aspect ratio elliptic jet. J Fluid Mech 179:383–405CrossRefGoogle Scholar
  45. Hussain AKMF (1986) Coherent structures and turbulence. J Fluid Mech 173:303–356CrossRefGoogle Scholar
  46. Kaushik M, Thakur PS, Rathakrishnan E (2006) Studies on the effect of notches on circular sonic jet mixing. J Propuls Power 22:211–214CrossRefGoogle Scholar
  47. Kaushik M, Rakesh K, Humrutha G (2015) Review of computational fluid dynamics studies on jets. Am J Fluid Dyn 5(3A):1–11Google Scholar
  48. Kosovic B (1997) Subgrid-scale modelling for the large-eddy simulation of high-Reynolds-number boundary layers. J Fluid Mech 336:151–182zbMATHCrossRefGoogle Scholar
  49. Krothapalli A, Bagano D, Karamcheti K (1981) On the mixing of a rectangular jet. J Fluid Mech 107:201–220CrossRefGoogle Scholar
  50. Krothapalli A, Hsia Y, Bagano D, Karamcheti K (1986) The role of screech tones on mixing of an underexpanded jet. J Sound Vib 106:119–143CrossRefGoogle Scholar
  51. Krothapalli A, McDaniel J, Bagano D (1990) Effect of slotting on the noise of an axisymmetric supersonic jet. AIAA J 28(12):2136–2138CrossRefGoogle Scholar
  52. Lardeau S, Lamballais E, Bonnet JP (2002) Direct numerical simulation of a jet controlled by uid injection. J Turbul 3(2)CrossRefGoogle Scholar
  53. Leray J (1934) On the motion of a viscous liquid filling space. Acta Mathematica 63:193–248MathSciNetzbMATHCrossRefGoogle Scholar
  54. Liepmann D, Gharib M (1992) The role of streamwise vorticity in the near-field entrainment of round jets. J Fluid Mech 245:643–668CrossRefGoogle Scholar
  55. Lighthill MM (1952) On sound generated aerodynamically:i. general theory. Proc R Soc Lond Ser A: Math Phys Sci 211:564–581MathSciNetzbMATHCrossRefGoogle Scholar
  56. Lighthill MM (1954) On sound generated aerodynamically: turbulence as a source of sound. Proc R Soc Lond Ser A: Math Phys Sci 222:1–32MathSciNetzbMATHCrossRefGoogle Scholar
  57. Lighthill MM (1963) Jet noise. AIAA J 1(7):1507–1517zbMATHCrossRefGoogle Scholar
  58. Lin JC, Selby GV, Howard FG (1991) Exploratory study of vortex-generating devices for turbulent flow separation control. AIAA Paper 910042Google Scholar
  59. Liu Y, Tucker PG, Kerr RM (2008) Linear and nonlinear model large-eddy simulations of a plane jet. Comput & Fluids 37: 439–449zbMATHCrossRefGoogle Scholar
  60. Lodato G, Domingo P, Vervisch L (2008) Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows. J Comput Phy 227:5105–5143MathSciNetzbMATHCrossRefGoogle Scholar
  61. Lush PA (1971) Measurements of subsonic jet noise and comparison with theory. J Fluid Mech 46(3):477–500CrossRefGoogle Scholar
  62. Lyubimov DA (2008) Development and applications of the efficient hybrid RANS/ILES approach for the calculation of complex turbulent jets. High Temp 46(2):243–253CrossRefGoogle Scholar
  63. Maidi M, Lesieur M (2005) Large eddy simulations of spatially growing subsonic and supersonic turbulent round jets. J Turbul 6(38):1–20MathSciNetCrossRefGoogle Scholar
  64. Maidi M, Lesieur M, Metais O (2006) Vortex control in large-eddy simulations of compressible round jets. J Turbul 7(49):1–22MathSciNetzbMATHCrossRefGoogle Scholar
  65. Martin JE, Meiburg E (1991) Numerical investigation of three-dimensionally evolving jets subject to axisymmetric and azimuthal perturbations. J Fluid Mech 230:271–318zbMATHCrossRefGoogle Scholar
  66. Massey K, Ahuja K, Jones R, Tam CKW (1994) Screech tones of supersonic heated free jets. Proceedings of the 32nd Aerospace Sciences Meeting and Exhibit. Aerosp Sci Meet AIAA-1994-141Google Scholar
  67. Matsuda T, Umeda Y, Ishii R, Yasuda A (1987) Numerical and experimental studies on choked under expanded jets. AIAA-87–1378Google Scholar
  68. McLaughlin DK, Morrison GL, Troutt TR (1975) Experiments on the instability waves in a supersonic jet and their acoustic radiation. J Fluid Mech 69:73–95CrossRefGoogle Scholar
  69. Michalke A (1971) Instability of compressible circular free jet with consideration of the influence of the jet boundary layer thickness. NASA-TM-75190Google Scholar
  70. Michalke A (1984) Survey on jet instability theory. Prog Aerosp Sci 21:159–199CrossRefGoogle Scholar
  71. Miller RS, Madnia CK, Givi P (1995) Numerical simulation of non-circular jets. Comput & Fluids 24(1): l–25zbMATHCrossRefGoogle Scholar
  72. Morris PJ, Giridharan MG, Lilley GM (1990) On the turbulent mixing of compressible free shear layers. Proc R Soc Lond A 431:219–243zbMATHCrossRefGoogle Scholar
  73. Morrison GL, McLaughlin DK (1979) The noise generation by instabilities in low reynolds number supersonic jets. J Sound Vib 65:177–191CrossRefGoogle Scholar
  74. Mouldon F, Acharya S (2010) Direct Numerical Simulation of pulsed jets in cross- ow. Comput & Fluids 39: 1745–1773Google Scholar
  75. Nagel R, Papathansiou A (1983) An experimental study of supersonic jet shock-associated noise. Proceedings of the AIAA 8th Aeroacoustics Conference. Atlanta, USA. AIAA-1983-708Google Scholar
  76. Norum TD (1983) Screech suppression in supersonic jets. AIAA J 21(2):235–240CrossRefGoogle Scholar
  77. Norum TD, Seiner JM (1982) Broadband shock noise from supersonic jets. AIAA J 20(1):68–73Google Scholar
  78. Pack DC (1950) A note on Prandtl’s formula for the wavelength of a supersonic gas jet. Q J Mech Appl Math 3:173–181MathSciNetzbMATHCrossRefGoogle Scholar
  79. Papamoschou D (1990) Communication paths in the compressible shear layers. AIAA Paper 90–0155Google Scholar
  80. Papamoschou D (1991) Structure of the compressible turbulent shear layers. AIAA J 29(5):680–681CrossRefGoogle Scholar
  81. Papamoschou D, Debiasi M (1999) Noise measurements in supersonic jets treated with the mach wave elimination method. AIAA J 37(2):154–160CrossRefGoogle Scholar
  82. Poinsot T, Lele S (1992) Boundary conditions for direct simulations of compressible viscous flows. J Comput Phys 101:104–129MathSciNetzbMATHCrossRefGoogle Scholar
  83. Pope SB (1978) An explanation of the turbulent Round-Jet/Plane-Jet anomaly. AIAA J 16(3):279–281CrossRefGoogle Scholar
  84. Pope SB (2000) Turbulent Flows. Cambridge University Press, New YorkzbMATHCrossRefGoogle Scholar
  85. Powell A (1953) On the mechanism of choked jet noise. Proc Phys Soc Lond 66:1039–1056CrossRefGoogle Scholar
  86. Powell A (1960) Aerodynamic noise and the plane boundary. J Acoust Soc Am 32(8):982–990MathSciNetCrossRefGoogle Scholar
  87. Prandtl L (1904) Beiträge zur Theorie der Dampfströmung durch Düsen. Z. Ver. Dtsch. Ing. 48(10):348–350 (in German)Google Scholar
  88. Prandtl L (1925) Bericht über Untersuchungen zur ausgebildeten Turbulenz. ZAMM. 5:136–139zbMATHGoogle Scholar
  89. Rajarathnam N (1976) Turbulent Jets. Elsevier Scientific Publishing Co., NetherlandsGoogle Scholar
  90. Raman G (1997) Screech tones from rectangular jets with spanwise oblique shock cell structures. J Fluid Mech 330:141–168CrossRefGoogle Scholar
  91. Rembold B, Adams NA, Kleiser L (2002) Direct numerical simulation of a transitional rectangular jet. Int J Heat Fluid Flow 23:547–553zbMATHCrossRefGoogle Scholar
  92. Reynolds O (1895) On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos Trans R Soc Lond 186(A): 123–164zbMATHCrossRefGoogle Scholar
  93. Ribner HS (1981) Perspective on jet noise. AIAA J 19(12):1513–1526zbMATHCrossRefGoogle Scholar
  94. Sandham ND, Reynolds WC (1990) Compressible mixing layer: linear theory and direct simulation. AIAA J 28:618–624CrossRefGoogle Scholar
  95. Sarkar S, Erlebacher G, Hussaini MY, Kreiss HO (1991) The analysis and modeling of dilatational terms in compressible turbulence. J Fluid Mech 227:473–493zbMATHCrossRefGoogle Scholar
  96. Sarkar S, Lakshmanan B (1991) Application of a reynolds stress turbulence model to the compressible shear layer. AIAA J 29(5):743–749CrossRefGoogle Scholar
  97. Sarohia V, Massier PF (1978) Experimental results of large scale structures in jet flows and their relation to jet noise production. AIAA J 16(8):831–835CrossRefGoogle Scholar
  98. Schlichting H (1951) Boundary Layer Theory. McGraw-Hill Co., New York, USAzbMATHGoogle Scholar
  99. Seiner JM (1984) Advances in high speed jet aeroacoustics. AIAA Pap 84–2275Google Scholar
  100. Seiner JM, Krejsa EA (1989) Supersonic jet noise and the high speed civil transport. AIAA Pap 89–2358Google Scholar
  101. Seiner JM, Norum TD (1979) Experiments on shock associated noise of supersonic jets. AIAA Pap 79–1526Google Scholar
  102. Seiner JM, Norum TD (1980) Aerodynamics aspects of shock containing jet plumes. AIAA Pap 80–0965Google Scholar
  103. Seiner JM, Ponton MK, Jansen BJ, Lagen NT (1992) The effect of temperature on supersonic jet noise emission. AIAA Pap 92–02–046Google Scholar
  104. Seiner JM, Yu JC (1984) Acoustic near field properties associated with broadband shock noise. AIAA J 22:1207–1215CrossRefGoogle Scholar
  105. Pai S-I (1954) Fluid Dynamics of Jets, 1st edn. D Van Nostrand Company, TorrontozbMATHGoogle Scholar
  106. Smagorinsky J (1963) General circulation experiments with the primitive equation: I. The basic experiment. Mon Weather Rev 91:99–164Google Scholar
  107. Stanley SA, Sarkar S, Mellado JP (2002) A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation. J Fluid Mech 450:377–407Google Scholar
  108. Suto H, Matsubara K, Kobayashi M, Kaneko Y (2004) Large eddy simulation of flow and scalar transport in a round jet. Heat Transf-Asian Res 33(3):175–188CrossRefGoogle Scholar
  109. Tam CKW (1995) Supersonic jet noise. Ann Rev Fluid Mech 27:17–43CrossRefGoogle Scholar
  110. Tam CKW, Chen P (1979) A statistical model of turbulence in twodimensional mixing layers. J Fluid Mech 192:303–306zbMATHCrossRefGoogle Scholar
  111. Tam CKW, Jackson JA, Seiner JM (1985) A multiple scale model of the shock cell structure of imperfectly expanded sonic jets. J Fluid Mech 153:123–149zbMATHCrossRefGoogle Scholar
  112. Tam CKW, Seiner JM, Yu JC (1986) Proposed relationship between broadband shock associated noise and screech tones. J Sound Vib 110:309–321CrossRefGoogle Scholar
  113. Tam CKW, Tanna HK (1982) Shock associated noise of supersonic jets from convergent-divergent nozzles. J Sound Vib 81(3):337–358zbMATHCrossRefGoogle Scholar
  114. Tandra DS, Kaliazine A, Cormack DE, Tran HN (2006) Numerical simulation of supersonic jet flow using a modified k-\(\varepsilon \) model. Int J Comput Fluid Dyn 20(1):19–27Google Scholar
  115. Tanna HK (1977) An experimental study of jet noise part i: turbulent mixing noise. J Sound Vib 50(3):405–428CrossRefGoogle Scholar
  116. Terrier DA, Lu FK (2001) Numerical Study of Passive Control of an Over Expanded Nozzle for Fighter Aircraft. Proc 23rd Int Symp Shock Waves. Texas, USA. ISSW24-3090Google Scholar
  117. Thies AT, Tam CKW (1996) Computation of turbulent axi-symmetric and non-axisymmetric jet flows using the K-epsilon model. AIAA J 34(2):309–316zbMATHCrossRefGoogle Scholar
  118. Tsujimoto K, Koji Ao, Shakouchiand T, Ando T (2011) Numerical investigation on flow structures and mixing performances of vector-controlled free jet using DNS. J Fluid Sci Technol 6(4):401–411CrossRefGoogle Scholar
  119. Tsujimoto K, Shakouchi T, Sasazaki S, Ando T (2006) Direct numerical simulation of jet mixing control using combined jets. JSME Int J: Ser B. 49(4):966–973CrossRefGoogle Scholar
  120. von-Kármán T (1930) Mechanische Ähnlichkeit und Turbulenz [Mechanical similarity and turbulence]. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen Mathematisch-physikalische Klasse (in German)Google Scholar
  121. Wang PC, McGuirk JJ (2013) Large Eddy Simulation of supersonic jet plumes from rectangular convergent divergent nozzles. Int J Heat Fluid Flow 43:62–73Google Scholar
  122. Westly R, Woolley JH (1975) The near eld sound pressures of a choked jet when oscillating in the spinning mode. AIAA-75-479Google Scholar
  123. Winant CD, Browand FK (1974) Vortex pairing: The mechanism of turbulent mixing-layer growth at moderate reynolds numbers. J Fluid Mech 63(2):237–255CrossRefGoogle Scholar
  124. Yamamoto S, Ozeki O (1984) Conducted noise measurements of automotive electrical and electronic devices using arti cial network. Electronics and Communications in Japan (Part I: Communications). 67(8): 81–89Google Scholar
  125. Yoshizawa A (1993) Bridging between eddy-viscosity-type and secondorder turbulence models through a two-scale turbulence theory. Phys Rev 48(1):273–281CrossRefGoogle Scholar
  126. Zaman KBMQ, Hussain AKMF (1981) Turbulence suppression in free shear flows by controlled excitation. J Fluid Mech 103:133–159CrossRefGoogle Scholar
  127. Zeman O (1990) Dilatation dissipation: the concept and application in modeling compressible mixing layers. Phys Fluids 2(2):178–188CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringIndian Institute of Technology KharagpurKharagpurIndia

Personalised recommendations